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Optimal scheduling of interconnected power systems
Accepted Manuscript
Optimal Scheduling of Interconnected Power Systems Nikolaos E. Koltsaklis , Ioannis Gioulekas , Michael C. Georgiadis PII: DOI: Reference:
S0098-1354(18)30014-0 10.1016/j.compchemeng.2018.01.004 CACE 5993
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
31 May 2017 12 November 2017 8 January 2018
Please cite this article as: Nikolaos E. Koltsaklis , Ioannis Gioulekas , Michael C. Georgiadis , Optimal Scheduling of Interconnected Power Systems, Computers and Chemical Engineering (2018), doi: 10.1016/j.compchemeng.2018.01.004
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Highlights
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Optimal energy scheduling of interconnected power systems is addressed. MILP model considering technical, operational, economic and logical constraints. Assessment of the interconnection impacts on the system's operational scheduling. Significant price convergence is achieved in interconnected systems. Electricity trade affects the optimal power system's energy balance.
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Optimal Scheduling of Interconnected Power Systems Nikolaos E. Koltsaklisa,*, Ioannis Gioulekasa,† Michael C. Georgiadisa,*
Aristotle University of Thessaloniki, Department of Chemical Engineering, 54124 Thessaloniki, Greece
Abstract
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a
This paper presents an optimization-based approach to address the problem of the
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optimal daily energy scheduling of interconnected power systems in electricity markets. More specifically, a Mixed Integer Linear Programming model (MILP) has been developed to address the specific challenges of the underlying problem. The main focus of the proposed framework is to examine the importance and the impacts of electricity interconnections and cross-border electricity trade on the
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scheduling of power systems, both at a technical and economic level. The applicability of the proposed approach has been tested on an illustrative case study
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including five power systems which can be interconnected (with a certain interconnection structure) or not. The proposed model determines in a detailed and
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analytical way the optimal power generation mix, the electricity trade among the systems, the electricity flows (in case of interconnection options), the marginal price
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of each system, as well as it investigates through a sensitivity analysis the effects of the available interconnection capacity on the resulting power production mix. The
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work demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies followed by the market participants, as well as on the strategic long-term decisions to be implemented by investors and/or policy makers at a national and/or regional level, underlining
*
Corresponding authors. E-mail address: [email protected] (N. E. Koltsaklis), [email protected] (M. C. Georgiadis)
†
Current Address: Department of Chemical Engineering, University College London, UK 2
ACCEPTED MANUSCRIPT potential risks and providing appropriate price signals on critical energy infrastructure projects under real market operating conditions. Keywords: Energy scheduling; Electricity interconnections; Unit commitment; Electricity trade; Day-ahead market
1. Introduction
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The World gross electricity production has been increased from 6,287 TWh to 23,815 TWh between 1974 and 2014, reporting an average annual growth rate of 3.4% (IEA, 2016a). Power networks have been constructed for over a century. These types of networks lack the ability to support the transition to a low-carbon and decentralized energy system. A noticeable enhancement of long-distance transmission capacities
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as well as the extension of interconnections among energy systems is necessary in order to meet the environmental, economic and security objectives of the future energy systems. Affordable and large-scale interconnections are characterized by a series of advantages, including: (i) flexibility in balancing demand and supply
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mismatches and peak capacity savings, (ii) flexibility provision for the effective integration of variable renewable energy sources, and (ii) accessibility provision to
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remote energy sources (IEA, 2016b). Soroush and Chmielewski (2013) provided a process systems engineering-based overview of the whole power systems value
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chain, including power generation, storage and distribution. Nowadays, the increasing concern for the mitigation of the carbon impact has led to
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the growing utilization of renewable energy in the power sector (Zhang et al., 2013). The increasing penetration of renewable energy sources and their impacts on the
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power systems have been extensively addressed in the literature, especially in works dealing with the generation expansion planning problem (Koltsaklis et al., 2014a; Koltsaklis et al., 2015; Guo et al., 2017). The unit commitment problem is defined as the optimization problem which determines the operating schedule of a set of generating units at each time interval so as to satisfy a specific amount of electricity demand, considering a set of operational, technical, regulatory, economic and environmental constraints (Koltsaklis and Georgiadis, 2015). The unit commitment problem is a complex problem and is mainly formulated as a large scale, non-linear 3
ACCEPTED MANUSCRIPT mixed integer problem. The literature is rich in works dealing with the unit commitment problem from a variety of perspectives. Palmintier (2014) made use of the methodology of the unit clustering in the unit commitment problem in order to implement generation planning incorporating flexibility issues, while Palmintier and Webster (2011) presented the method of unit clustering for approximate unit commitment reporting significant gains in the execution time. The same authors
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concluded that the integration of unit commitment-based constraints into generation expansion planning models can alter the optimal generation mix results to a significant extent (Palmintier and Webster, 2014). A MILP approach for unit commitment-based mid-term (Koltsaklis et al., 2016) and long-term (Koltsaklis and Georgiadis, 2015) planning has been also developed, as well as on the design of
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energy networks based on combined heat and power units (Koltsaklis et al., 2014b). Abujarad et al. (2017) presented a review dealing with the impacts that significant penetration of renewables have on the development and usefulness of unit commitment models. Carrion and Arroyo (2006) developed a MILP formulation for
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the thermal unit commitment problem, while Niknam et al. (2009) proposed a similar approach based on benders decomposition method. Xiao et al. (2011)
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developed a two-stage stochastic programming formulation of the unit commitment problem with the aim to evaluate the spinning and non-spinning reserve levels of a
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power system along with the associated system costs under significant wind power penetration. Viana and Pedroso (2013) contributed to the same topic with a MILP-
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based formulation incorporating piecewise linear approximations of the quadratic fuel cost function, while Yang et al. (2017) presented an approach for the thermal
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unit commitment problem, as well as Marcovecchio et al. (2014) developed an optimization-based approach for the solution of same problem. Morales-España et al. (2013) developed also a formulation of the thermal unit commitment problem. Zheng et al. (2016) presented an approach for the solution of the unit commitment problem based on additional cuts to the branch and bound method as well as heuristic rounding technique. Lyzwa et al. (2015) developed three possible mathematical formulations for the determination of the optimal energy mix. Qin et al. (2005) presented a security-constrained unit commitment model with the aim of 4
ACCEPTED MANUSCRIPT achieving cost savings for the consumers. Lujano-Rojas et al. (2016) presented a methodology for the solution of the unit commitment problem from a probabilistic perspective on several parameters. Bigdeli and Karimpour (2014) presented a MILP formulation of the unit commitment model to minimize the total daily energy dispatch cost, while Frangioni et al. (2011) presented a sequential Langrangian-MILP approach for the solution of the hydrothermal unit commitment problem. Lima and
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Novais (2016) examined the impacts of symmetry in the unit commitment problems, while Zhang et al. (2016) proposed a unified unit commitment model formulation by modelling the generating units’ commitment status variables as binary, integer or continuous values.
The increasing wind penetration into the power systems raises flexibility issues due
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to the intermittent nature characterizing wind power contribution. Zhang et al. (2015) developed a MILP, risk-based unit commitment model considering wind power uncertainty through the incorporation of the loss of load risk, wind power curtailment and transmission congestion caused by wind power fluctuations.
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Delarue and D’haeseleer (2008) developed a MILP model for the solution of the unit commitment problem, examining also the impacts of limited forecasting of the
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electricity demand. Zugno and Conejo (2015) developed a mathematical approach for the co-optimization of energy dispatch and reserve capacity in a power market
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taking into consideration high penetration of stochastic renewable sources. Zhao and Wu (2014) proposed a MILP model in order to quantify the impact of demand
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response and wind generation on the locational marginal prices through a unit commitment model formulation. Bakirtzis and Biskas (2016) presented a MILP
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model for the stochastic power systems’ scheduling under significant renewables’ penetration, while Azizipanah-Abarghooee et al. (2016) presented a probabilistic unit commitment problem formulation incorporating demand response and significant wind penetration. Pezic and Cedrés (2013) proposed a MILP approach for the solution of the unit commitment problem for fully renewable energy systems, while Xie et al. (2011) presented a MILP formulation for the day-ahead wind-thermal unit commitment problem implemented by an independent power system operator. Parvania and Scaglione (2016) developed a MILP model for the day ahead wind5
ACCEPTED MANUSCRIPT thermal unit commitment problem evaluating expected energy not served and expected energy excess served due to unavailability of thermal units, as well as fluctuations of the wind power output. Mehamed et al. (2016) developed a unit commitment optimization model aiming to maximize the profits of an energy producer under uncertainty in market clearing prices and wind power contribution. The fact that the power and the natural gas systems are highly interlinked, since the
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natural gas-fired power units comprise the main back-up technology to deal with the fluctuations injected into the power grid by the variable wind power generation. As a consequence, the natural gas system operation is greatly affected by the intermittency and stochasticity characterizing the growing use of renewables into the power systems (Keyaerts et al., 2014). Cui et al. (2016) presented a bi-level
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programming optimization model for a coordinated operational scheduling of both an electricity network and a natural gas system taking into account demand response options. Correa-Posada and Sánchez-Martín (2015) developed a MILP model coupling the power and natural gas systems in short-term operation. Yazdani
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Damavandi et al. (2011) developed an MILP model so as to analyze the impacts of gas velocity and distances between gas areas in the unit commitment problem.
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Knudsen et al. (2014) presented a MILP model for the shale-gas scheduling for natural gas supply in power producers, with the aim of maximizing the profits of well
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operators.
The integration of national electricity markets into a single multi-area market is of
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utmost importance in the European Union agenda with the aim of achieving the optimal utilization of the interconnection transmission capacities. In that context,
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Chatzigiannis et al. (2016) proposed a mathematical model for the day ahead clearing process of the power markets at a European level. Dourbois and Biskas (2016) proposed a nodal-based security-constrained market clearing MILP mathematical model taking into account multi-period products. Greater resilience to climate change negative impacts is of utmost importance to the technical viability of the energy sector and its ability to affordably cover the increasing energy demands driven by global economic and population growth. Resilience of the energy sector refers to the “capacity of the energy system or its 6
ACCEPTED MANUSCRIPT components to cope with a hazardous event or trend, responding in ways that maintain their essential function, identity and structure while also maintaining the capacity for adaptation, learning and transformation” (IEA, 2015). Eskandarpour et al. (2016) presented a resilience-constrained unit commitment model formulation considering the simultaneous outage of multiple system components, while Wang et al. (2016) developed a risk adjustable MILP model for the solution of the unit
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commitment problem. Demand-response and electric vehicles concepts are also incorporated in unit commitment problem formulations. Zhou et al. (2017) presented a mathematical model for the clearing process of a wholesale electricity market incorporating also a demand response mechanism, while Safdarian et al. (2014) developed a MILP model
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for the incorporation of price-based demand response in the short-term operation of distribution companies whose objective is the maximization of the distribution companies’ expected profits. Huber et al. (2012) presented an MILP formulation of the unit commitment problem aiming at investigating the influences of large scale
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electric vehicles and photovoltaic power on the power system, while Koltsaklis and Georgiadis (2016) developed a MILP formulation to examine the influence of the
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electric vehicles’ penetration on the daily generation scheduling of a power system. Unit commitment concepts are also employed for the determination of optimal
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operational scheduling in microgrids. Alabedin et al. (2012) presented a MILP model for the optimal power generation scheduling in a microgrid consisting of a group of
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dispatchable and non-dispatchable generating units in both grid-connected and isolated modes. Kia et al. (2017) presented a stochastic MILP model for the optimal
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scheduling of combined heat and power units under electricity and thermal storage, while Nemati et al. (2015) developed a MILP model for the solution of the unit commitment and economic dispatch problem of microgrids consisting of controllable distributed generators and battery storage systems. Haddadian et al. (2015) presented a MILP-based unit commitment model for the optimal day-ahead scheduling in power systems involving thermal units, wind turbines and distributed storage.
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ACCEPTED MANUSCRIPT Examining the same problem from a power producer perspective, Laia et al. (2016) developed a MILP model for determining the optimal bidding strategy (selfscheduling problem) of thermal and wind power producers in a pool-based power market, while Shabanzadeh et al. (2015) presented a MILP model for the optimal daily and weekly self-scheduling of virtual power plants. Furthermore, Bakirtzis et al. (2007) presented an optimization model for determining the optimal offering
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strategies submitted by electricity produces in day ahead power auctions with stepwise energy supply offers. Pérez-Díaz et al. (2012) proposed an NLP unit commitment model for the optimal operational scheduling of a hydroelectric unit taking part in the day-ahead power market, whose objective is its revenues maximization. In addition to the above, Catalão et al. (2012) developed a MINLP
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model for the determination of the optimal operation of a hydro plant in a dayahead electricity market with the objective of maximizing its profits, while Simoglou et al. (2012) developed a MILP model for the optimal self-scheduling of a dominant electricity company, comprising of thermal and hydroelectric units in its portfolio, in
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both the generation and retail sectors of a power market. Finally, Lima et al. (2015) developed an optimization approach to determine the optimal self-scheduling,
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forward contracting, and pool involvement of a power producer whose portfolio includes hydrothermal and wind energy sources.
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This work presents a MILP-based, mathematical framework to cope with the unit commitment problem of a day-ahead electricity market (co-optimization of energy
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and reserve markets) in interconnected power systems based on a network flow formulation, taking into account both hydrothermal and renewable energy sources.
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This approach employs key features of our previous works (Koltsaklis et al., 2014; Koltsaklis and Georgiadis, 2015), while it is mainly focused on the scheduling (daily) operation of the studied power systems with emphasis on the systematic assessment of the impacts of (regional) potential interconnections on several key decisions including energy mix, market clearing price, and electricity transmission. The key contributions and the salient features of the proposed model is the simultaneous consideration of multiple distinct systems in an integrated approach, instead of focusing on an individual power system with potential interconnection 8
ACCEPTED MANUSCRIPT options. More specifically, the proposed framework includes: (i) incorporation of a optimization approach of the unit commitment problem (day-ahead energy and reserve markets) in the context of interconnected power systems, (ii) assessment of the interconnection impacts on the daily power mix and the market clearing price of each individual power system, and (iii) insights and indications for potential investments in each individual power system through the interconnection-based
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market clearing algorithm results (price-signals). As a consequence, with the proposed approach, the overall (regional) welfare is maximized and the utilization of the considered interconnections is optimally determined.
The remainder of the paper is organized as follows: the problem statement is presented in Section 2, while the model formulation is provided in Section 3. The
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details and data of the case study are given in Section 4, while Section 5 provides a detailed discussion of the results obtained. Finally, Section 6 draws up some concluding remarks arising from this work.
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2. Problem statement
This work addresses the problem of the optimal energy scheduling of a given power
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system in a day-ahead market, i.e., the unit commitment problem. It addresses the simultaneous optimization of both the energy and reserve markets. The problem
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under consideration is formally defined as follows: The time period under consideration concerns the day-ahead market and
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includes hourly time intervals
A set of power systems (
. ) is considered. Each system
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interconnected with other neighboring systems network structure
, according to their
.
A set of power generating units
is modeled, including thermal units
, hydroelectric units units
can be
(both referred to as hydrothermal
), as well as renewable energy sources
. Each power unit
belongs to a specific technology type, given by parameter
.
The majority of thermal units lack the ability to start-up or shut-down immediately after a relevant decision has been taken (Koltsaklis and 9
ACCEPTED MANUSCRIPT Georgiadis, 2015; Koltsaklis et al., 2016). As a consequence, there is a succession of several distinct operational phases for a specific thermal unit that has to be undertaken, each of which with its own duration and power output range according to the technology type of each unit and its individual characteristics (lifetime etc.). The possible operating phases of a hydrothermal power unit
include the synchronization, soak, dispatch,
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and desynchronization phases, when being online. There is a specific succession in the operational phases of each hydrothermal power unit. As soon as a start-up decision is taken for each hydrothermal unit
, the
unit enters the synchronization phase, characterized by a specific duration . The next phase of a unit’s operation is the soak one, which has also a , and during which the unit’s power output amounts to
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certain duration
a certain value given by the parameter
, which is a technical
characteristic of each unit. After the successful completion of the soak phase, the unit enters the dispatch phase, in which the unit’s power output can take
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any value between its technical minimum
, and maximum,
. The
corresponding values when the unit operates under Automatic Generation and
The power output changes of each unit in
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Control are
the dispatch phase during two consecutive time periods are subject to
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specific limits, i.e.,
which defines the ramp-up rate of each power unit
, while parameter
. In the case of unit’s operation under Automatic
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power unit
represents the ramp-down rate of each
Generation Control, the corresponding ramp rates are provided by the and
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parameters
, correspondingly. The last possible
operational phase of each unit
is that of the desynchronization
phase, which has a specific duration
. The minimum-up (operational)
time of each unit
is given by the parameter
, while the
corresponding minimum-down (non-operational) time of each unit
is
given by the parameter
is
provided by the parameter
. The start-up cost of each power unit
, while its shut-down cost by the parameter
. 10
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can provide specific types of power reserves to the
network. These include the primary (up and down), secondary (up and down), as well as tertiary, spinning and non-spinning reserves. More specifically, each power unit i.
is characterized by:
, denoting the maximum contribution of each power unit in primary reserve, , denoting the maximum contribution of each power unit in non-spinning tertiary reserve,
iii.
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ii.
, denoting the additional cost of each power unit time period
, when providing primary reserve,
, denoting the additional cost of each power unit time period
v.
in each
, when providing secondary reserve,
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iv.
in each
, denoting the additional cost of each power unit each time period
vi.
in
, when providing tertiary spinning reserve, and
, denoting the additional cost of each power unit
, when providing tertiary non-spinning reserve.
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each time period
in
Each power system is characterized by: , denoting the requirements of system
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i.
reserve at time period
,
, denoting the requirements of system
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ii.
reserve at time period
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iii.
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v.
, denoting the requirements of system
vi.
in secondary-up
,
, denoting the requirements of system
down reserve at time period
in secondary-
,
, denoting the requirements of system at time period
in primary-down
,
reserve at time period
iv.
in primary-up
in tertiary reserve
, and
, denoting the electricity demand of each power system time period
in
.
There is a specific nominal interconnection capacity between interconnected power systems
and
,
, given by the parameter 11
.
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is characterized by a certain availability in each time period
, provided by the
.
The power capacity of each thermal unit
is divided into a number of
blocks
,
, which represents the quantity of each power capacity
block
of the energy offer function of each power generating unit
.
of each power generating unit
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Each power capacity block has a certain marginal cost (energy offer function) , provided by the parameter
.
There are specific bounds for the total daily hydroelectric generation of each unit
, given by the parameters
and
, respectively.
In the beginning of the examined time period, each power unit
i.
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characterized by:
, denoting the power output of each power unit
is
at the
beginning of the time horizon under consideration, ii.
, denoting the number of operational hours of each power unit
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at the beginning of the time horizon under consideration, The objective is to minimize the total daily cost for the energy scheduling of the
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power system under consideration, including the variable operating cost of the power generation units along with their start-up and shut-down costs, as well as the
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reserves provision costs in order to fully meet the total electricity demand of the power system.
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3. Mathematical formulation
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3.1. Objective function The objective function consists of eight terms which determine the operating costs of all production units and systems. In particular, the first term expresses the variable cost that depends on the power output power of all the units during the examined period. The second term refers to the start-up cost of each power unit, provided the unit is selected to start-up. Similarly, the next term represents the shutdown cost of each power unit, if it is selected to shut-down. The next four terms
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⏞ ∑∑
⏞ ∑∑
(
(
)
)
(1)
⏞ ∑∑
⏞ ∑∑
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⏞ ∑∑
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⏞ ∑∑∑
3.2.1. Model constraints Synchronization phase constraints
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∑
Equations (2) specify the time periods during which the power unit
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operate in the synchronization phase. At the random time period power unit starts-up, the binary variable
will
in which the
equals 1, while the binary variable
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receives also the same value (1) for the time periods (hours) from to
,
and the unit has been synchronized to the power network. From the time period
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and then, the power unit enters the soak phase.
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Soak phase constraints
∑
Equations (3) specify the time periods during which the power unit operate in the soak phase. At the random time period starts-up, the binary variable
in which the power unit
equals 1, while the binary variable
13
will
receives
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to
, and the unit operates in the soak phase during that time period.
Equations (4) determine the power output of each unit
when it operates in the
soak phase. According to these equations, the continuous variable constant amount of
equals the
throughout this phase (in this phase the binary variable
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obtains the value of 1 according to Equations 3). As soon as the unit exits the soak phase and enters the dispatch phase, the unit’s power can vary between its technical minimum and maximum.
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Desynchronization phase constraints
∑
Equations (5) specify the time periods during which the power unit
will
operate in the desynchronization phase. If the unit is determined to shut-down in
to
will amount to 1, as well as the binary
will take the value of 1 for the times periods (hours) from
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variable
, the binary variable
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time period
. During that time period, the power unit will operate in the
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desynchronization phase.
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∑
Equations (6) determine the power output of each unit
when it operates in the
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desynchronization phase. These equations specify that the power output of the unit when it operates in this phase decreases at a rate equal to (
) for all steps of the
desynchronization phase up to zero. Therefore, the power output receives specific discrete values. Minimum up and down time constraints
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∑ Equations (7) guarantee that the power unit
will be online at time period
if its startup took place in any of the previous the unit starts-up in time period
time periods (hours). When
, then the binary variable
of 1, and the binary variable
takes the value
takes also the value of 1 for the next
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hours. In this way, the minimum operating time of each power unit guaranteed. ∑
is
that unit
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Equations (8) work in a similar way to Equations (7). This type of constraints ensure will be forced out of service at time period
down during any of the previous ( shuts-down at time period binary variable
, if it has been shut-
) time periods (hours). When the unit
, then the binary variable
is set to 1, and the
will necessarily get a zero value for the next (
) time
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periods (hours). In this way, the minimum down time constraint of each power unit
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is satisfied.
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Logical status of unit commitment
Equations (9) impose that at most one of the binary variables describing the various
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operating phases of a unit If power unit
will have a non-zero value at each time period
is offline in time period
, the binary variable
.
equals zero,
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so none of the other binary variables can get a non-zero value.
Equations (10) determine the transition of each power unit offline operating mode and vice versa. If a power unit , then shuts-down in time period
, and , then
from online to
starts-up in time period
. Similarly, if a power unit and
15
.
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to start-up and shut-
. If one of the two binary variables receives a
value of 1 in a time period
, then the other one will necessarily get the zero
value.
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Units’ power output constraints
Equations (12) states that each power generation unit
can operate under
Automatic Generation Control and provide the network with secondary (either upward or downward) reserve only when operating in the dispatch phase. In this operational phase, the binary variable
has a value of 1, and as a consequence
value of 1. In case the power unit
can obtain the
does not operate in the dispatch phase
), then from this type of equations follows that
.
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(
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the unit can provide secondary reserve, i.e., the binary variable
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Equations (13) and (14) define the maximum amount of primary reserve that the power unit
can provide to the network. The power unit
can provide
variable
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primary reserve only when it operates in the dispatch phase, i.e., when the binary is equal to 1. In this case the continuous variables
and
can
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take various values, subject to the maximum limit imposed by the parameter .
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which is a technical characteristic of each power unit
Equations (15) and (16) define the maximum amount of secondary reserve that the power unit
can provide to the network when it operates under Automatic
Generation Control, i.e., the binary variable the continuous variables
and
gets a value equal to 1. In this case,
can obtain different values, subject to the
maximum limit imposed by the parameters
16
and
, expressing the
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(in MW/min), while
the constant of 15 represents a time frame of 15 minutes.
Equations (17) define the maximum amount of tertiary reserve that the power unit can provide to the network. When the power unit dispatch phase, then the binary variable
is equal to 1, and the continuous
can obtain various values subject to a maximum limit imposed by the
parameter
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variable
operates in the
, which is a technical characteristic of each power unit
scalar 15 represents a time frame of 15 minutes.
can provide tertiary non-
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Constraints (18) ensure that a power generation unit
. The
spinning reserve to the network only when it is offline. In this case, the binary variable
takes a value of 0. As a consequence, the binary variable
obtain the value of 1. This enables the power unit
to provide tertiary non-
spinning reserve. Otherwise, i.e., when the power unit
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is able to
operates in one of the
synchronization, soak, dispatch, and desynchronization phases, the binary variable equals zero.
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receives a value of 1, and the binary variable
Equations (19) and (20) define the maximum and minimum amount of tertiary non-
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spinning reserve that the power unit equations (19), the power unit
can provide to the network. According to can provide an amount of reserve up to the , which is a technical characteristic
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maximum limit expressed by parameter
of each unit. Equally, equations (20) define the minimum amount of tertiary nonspinning reserve that the power unit
can provide (if it is selected for the
corresponding provision, expressed by the binary variable
(
)
17
) to the network.
ACCEPTED MANUSCRIPT Constraints (21) express in general terms the lower output limit of a power unit at time period
, when it is able to operate under Automatic Generation
Control. The decision variable
is taken into account only if the unit operates in
the dispatch phase and provides secondary reserve to the network. In all other cases the effect of this term is considered negligible. The right-hand side of inequality includes all possible values that power output can
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take. The first term refers to the time period during which a power unit operates in the synchronization phase. In this phase, the power unit
does not
produce power, resulting in the zero factor multiplied with the binary variable
.
The second term refers to the soak phase. The power output of each power unit , as has been set in equations (4). The third
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during this phase is equal to
term refers to the power offered by the plant in its desynchronization phase (
).
This amount of power varies according to the desynchronization time step of each unit and it is given by equations (6). The fourth and fifth term of the right hand side
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operates in the dispatch phase.
when it
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of the constraints (21) defines the power output of each power unit
(
)
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Similar to constraints (21), Constraints (22) define the upper limit of the power output of each power unit
at time period
, when it is capable of
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operating under Automatic Generation Control.
Equations (23) and (24) specify the upper and lower limit of the power output of a power unit
at time period
, when it is capable of operating under
Automatic Generation Control and simultaneously provides primary and secondary 18
ACCEPTED MANUSCRIPT downward reserves. The first three terms of the right hand side of constraints (23) and (24) refer to the synchronization, soak, and desynchronization phases. The output that each power unit
can offer at each of these phases is
predetermined, as has already been analyzed. In both constraints, the fourth term refers to the output of a power unit during which the binary variable
when it operates in the dispatch phase, has a non-zero value. . The binary variable
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Constraints (24) introduces the term
receives a non-zero value at the last hour of the time period before the power unit
shuts-down. During that specific period, the inequality takes the form and forces the unit to operate at that time at its
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technical minimum. The desynchronization phase, which is described by equations (5) and (6), is now possible. The above term is omitted for peak-load units which have the ability to change their output power from their technical maximum to zero over a few minutes.
M
Ramp-up and down limits of power units (
)
at time period
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Constraints (25) place limitations on the ramp-up rates of the output of each unit . It should be stressed that an output increase of each unit
PT
can occur when there is a change in the unit’s operating mode from offline to the synchronization phase, during the transition from the synchronization to the
CE
soak phase and during the dispatch phase. According to constraints (25), the difference in the value of the power output
AC
between two consecutive hours cannot be greater than a number equal to the product of
with 60. The parameter
symbolizes the unit's ramp-up rate
and it comprises a unit’s technical characteristic. Since the ramp rate is usually given in MW/min, the constant 60 is introduced, accounting for a 60-minute period. During the synchronization and soak phase, the output of each power unit
is
defined and knowledgeable (the unit does not produce power during the synchronization phase, while its output in the soak phase is predetermined and given 19
ACCEPTED MANUSCRIPT by equations 4). By inserting the N constant, which takes a very high value, the inequality is virtually inactive (25). In the synchronization phase, the binary variable inequality takes the form
takes the value 1 and the . It is also the same during
the soak phase. With the addition of the second term, the inequality does not limit the output increase occurring when the operating state of the each unit
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changes from the offline status to the synchronization phase, and from the synchronization to the soak phase. (
)
Correspondingly to constraints (25), constraints (26) place limitations on the rampat time period
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down rates of the output of each unit
. The output
decrease takes place during the desynchronization and dispatch phases. The first inequality term expresses again the maximum power difference between two consecutive hours, when the unit operates in the dispatch phase. This difference , where
accounts for the ramp-
M
cannot be greater than the product down rate of the unit.
ED
The second term is activated during the unit's desynchronization phase. The inequality then takes the form
is inserted to model the last operating time of each
before being shut down.
CE
power unit
PT
number). The binary variable
(where N is a very large
Power capacity limits
AC
∑
Each power unit
provides power to the network in the form of power blocks,
each of which has a different marginal cost. Equations (27) specify that the sum of the total power of these blocks should be equal to the total power output of each unit
for each time period
.
20
ACCEPTED MANUSCRIPT Equations (28) define the minimum and maximum values the continuous variable can take. The variable has a minimum value of zero (the unit does not provide power from that block), while its maximum bound is provided by the parameter . The units provide power starting from the block with the lowest electricity generating marginal cost.
∑
∑
∑
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Power demand balance
Equations (29) represents the energy balance of the problem. The first term is a sum referring to the total power output generated by all units at each time period
from the
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while the second sum refers to the total energy entering the system
,
all the other interconnected power systems. The third term is the demand of each system
at each time period
energy exporting from a system
to the other interconnected power systems.
M
∑
ED
∑
CE
PT
∑ ∑
, while the fourth term refers to the total
Constraints (30) and (31) refer to the coverage of the power network with primary (with upstream and downstream direction) reserve respectively. The sum of the
AC
contribution of all units of each system to primary reserve should be greater than or equal to the primary reserve system requirements. Correspondingly, constraints (32) and (33) are defined for covering each system requirements in secondary reserve. ∑
∑
21
ACCEPTED MANUSCRIPT Constraints (34) refer to the coverage of the network’s requirements for tertiary spinning and non-spinning reserves. An important element of the above equations is the fact that no separate requirements for each type of tertiary reserve are defined. Hydroelectric units’ constraints ∑
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The above constraints state that the total energy produced by each hydro unit at a daily level must be between a minimum and a maximum limit. )
(
)
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(
Constraints (36), (37) and (38) describe the operation of hydroelectric units and are proportional to the constraints (21), (22) and (24) for the thermal units. Hydroelectric units can enter almost immediately into the network without having to ). In addition,
M
go through the synchronization and soak phases (
their desynchronization phase lasts only for a very short period of time and for this
very short time (
ED
reason they have the ability to change their power output from any value to zero in a ). Finally, hydroelectric units are not able to contribute to a
PT
primary reserve and therefore the continuous variable
is not introduced into
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the constraint (38).
AC
The above constraint defines a limitation in energy transfer between interconnected systems. Therefore, there is a cap on the maximum electricity flow between interconnected systems.
Equation (40) specifies that the output power of each renewable unit is equal to the product of its nominal capacity availability of each renewable unit
with the parameter
, accounting for the
in each period of time
22
.
ACCEPTED MANUSCRIPT The overall problem is formulated as a Mixed-Integer Linear Programming problem (MILP), involving the cost minimization objective function (1) subject to constraints (2)–(40).
4. Case study The applicability of the proposed model is illustrated using a representative case
CR IP T
study, the main characteristics of which are presented below. More specifically, five power systems (s1-s5) have been considered, the detailed interconnection structure of which is provided in Table 1. It can be observed that the majority of them are interconnected among each other, with the exception of combinations s1-s4 and s3s5. For simplicity reasons, the transmission losses are assumed to be zero.
s1
M
200 400 500
s2
s3
s4
s5
200 250 150 300
400 250 250 -
150 250 250
500 300 250 -
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Interconnected systems s1 s2 s3 s4 s5
AN US
Table 1: Interconnection capacity and structure among the power systems (MW)
Figure 1 depicts the installed capacity per technology type in each power system.
PT
System 1 (s1) consists of seven units with a total installed capacity of 1900 MW, of which natural gas combined cycle (NGCC) units account for the largest part with an
CE
installed capacity of 850 MW, lignite-fired units follow with 650 MW, hydroelectric units have a capacity of 250 MW, and finally there is one natural gas-fired open-cycle
AC
gas turbine (NGGT) with a capacity of 150 MW. System 2 (s2) includes five units with a total installed capacity of 1800 MW, of which NGCC represent 850 MW of the total installed capacity, lignite-fired units amount to 650 MW, and renewable units’ capacity equals 300 MW. System 3 (s3) incorporates five units with a whole capacity of 1200 MW, four of which are hydroelectric with a total capacity of 750 MW, and one is NGCC unit with a capacity of 450 MW. Seven units are installed in System 4 (s4) amounting to 1750 MW, wherein lignite-fired units are the dominant technology with a total capacity of 1300 MW, followed by hydroelectric units with 250 MW and 23
ACCEPTED MANUSCRIPT renewables with 200 MW. Finally, System 5 (s5) constitutes the largest system among those examined, with a cumulative capacity of 2700 MW. 1200 MW of them are renewable units, while the remaining 1500 MW is allocated to NGCC units. 3000
2500
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MW
2000 1500
500 0
s1 Lignite-fired units
s2 NGCC units
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1000
s3
NGGT units
s4
Hydroelectric units
s5 Renewables
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Figure 1: Installed capacity per technology type in each power system (MW)
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7000
4000
CE
MW
5000
PT
6000
3000
AC
2000
1000
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s1
s2
s3
s4
s5
Figure 2: Hourly electricity demand of each power system (MWh)
24
ACCEPTED MANUSCRIPT
40% 35% 30%
(%)
25%
20%
10% 5% 0%
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15%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s4
s5
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s2
Figure 3: Renewables availability in each power system (%)
Figure 2 depicts a typical daily (24-h) profile for each of the examined power systems. System 5 is characterized by the highest demand, being equal to 34,053
M
MWh at a daily level, and followed by System 1 (28,738 MWh), System 4 (24,122 MWh), System 2 (22,703 MWh), and System 3 (11,350 MWh). The corresponding
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daily peaks for each system are 1744, 1453, 1235, 1162, and 581 MW respectively. In all cases, this peak is reported during the 22th hour of the day considered. Figure 3
PT
presents the availability factor of the renewables installed in each power system (s2, s4, and s5). Note that the type of renewables installed in each system is mainly wind
CE
turbines, having a daily average factor of around 24% in System 2, 29% in System 4, and 19% in System 5, reflecting the different meteorological conditions of each
AC
system.
As discussed in Sections 2 and 3, each hydroelectric unit is characterized by a minimum and a maximum non-priced electricity generation to be allocated to the system. Since it is non-priced, it is given priority when entering the system. Note that non-priced electricity generation means that this part of power generation is mandatory, does not have a price and is given total priority when entering the system. In practice, it reduces the net load (subtracting non-priced electricity generation from the total power load) to be satisfied by the remaining priced 25
ACCEPTED MANUSCRIPT electricity generation. The exact time allocation of that contribution is determined by the optimization process. Figure 4 highlights the minimum and maximum daily
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2000 1800 1600 1400 1200 1000 800 600 400 200 0
AN US
MWh
hydroelectric generation per unit installed in each power system.
Hydro - 1Hydro - 2Hydro - 3Hydro - 4Hydro - 5Hydro - 6Hydro - 7Hydro - 8 s1
s1
s3
s3
s3
Emin
Emax
s3
s4
s4
ED
33 32 31 30 29 28 27 26 25 24 23 22 21 20
PT
450 400 350 300 250 200 150 100 50 0
AC
CE
MW
system (MWh)
€/MW
M
Figure 4: Minimum and maximum daily hydroelectric generation per unit and power
Lignite-1 Lignite-2 Lignite-3 Lignite-4 Lignite-5 Lignite-6 Lignite-7 Lignite-8
s1 f1 (MW) f1 (€/MW)
s1
s2 f2 (MW) f2 (€/MW)
s2
s4 f3 (MW) f3 (€/MW)
s4
s4 f4 (MW) f4 (€/MW)
s4 f5 (MW) f5 (€/MW)
Figure 5: Quantity-price pair per block for each lignite-fired unit in each power system
26
ACCEPTED MANUSCRIPT The power capacity of each thermal unit is divided into capacity blocks (five in our case, f1-f5), from its technical minimum to its maximum, each of which is characterized by a specific marginal cost (energy supply function of each thermal unit). Figure 5 portrays the quantity-price pair per block for each lignite-fired unit in each power system wherein they are installed. The first block (f1) of each unit is its technical minimum in all cases. It can be observed that the lowest price in the first
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block (f1) of all units equals 24 €/MW (Lignite-8 unit, installed in s4), while the most expensive one in the last block (f5) amounts to 32 €/MW (Lignite-2 unit, installed in s1). In general, lignite-fired units are suitable for base-load operation and comprise the most economical power generation technology among the thermal units.
Figure 6 portrays the corresponding quantity-price pair per block for each NGCC unit
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in each power system wherein they are installed. The first block (f1) of each units is its technical minimum in all cases. It can be observed that the lowest price in the first block (f1) of all units equals 35.7 €/MW (NGCC-9 unit, installed in s5), while the most expensive one in the last block (f5) amounts to 55 €/MW (NGCC-2 unit, installed in
M
s1). In general, NGCC units are suitable for both base-load and intermediate load operation, and comprise the most environmentally friendly power generation
ED
technology among the thermal units. Since the natural gas does not comprise a domestic fuel in most of the power systems, its significant price deviation in the
PT
examined power systems reflects the different natural gas supply cost in each of the
AC
CE
examined power systems (country).
27
57 54 51 48 45 42 39 36 33 30
€/MW
500 450 400 350 300 250 200 150 100 50 0
CR IP T
MW
ACCEPTED MANUSCRIPT
NGCC-1 NGCC-2 NGCC-3 NGCC-4 NGCC-5 NGCC-6 NGCC-7 NGCC-8 NGCC-9 s1
s1
s2
s2
s3
s5
s5
s5
s5
f2 (MW)
f3 (MW)
f4 (MW)
f5 (MW)
f1 (€/MW)
f2 (€/MW)
f3 (€/MW)
f4 (€/MW)
f5 (€/MW)
AN US
f1 (MW)
Figure 6: Quantity-price pair per block for each natural gas combined cycle unit in each power system
Focusing on some specific technical characteristics per technology type, Figure 7
M
depicts some representative time-related technical characteristics per technology type, including minimum up and down times, as well as synchronization, soak, and
ED
desynchronization times. Lignite-fired have the advantage of low operating costs but they are characterized by particularly long start-up (synchronization, soak) and shut-
PT
down (desynchronization) times. Consequently, due to their high start-up costs, the frequent shut-downs and start-ups of the lignite-fired units are avoided, and
CE
therefore, they operate 24 hours a day with small deviations to cover the base load. This is the reason why they are characterized by noticeable minimum-up and down
AC
times.
The intermediate load (or load-following) power units are the NGCC units designed to cover the variable load of the grid. The processes for the start-up and the shutdown of these units are less time-consuming than those of lignite-fired units (lower minimum up and down times than the corresponding ones of lignite-fired units), so these units may be available shortly after their start-up (low synchronization, soak, and desynchronization times).
28
ACCEPTED MANUSCRIPT The peak-load units consist of NGGT and diesel units, the operating costs of which are particularly high, but they have very low start-up and shut-down times (zero synchronization, soak, and desynchronization times). For this reason, these units are typically used during few hours throughout the year, when peaks are observed in the load, and then they are typically out of order (very low minimum up and down times). Hydroelectric units are also included in this category.
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9 8 7
Hours
6 5 4
2 1 0 Minimum-up time Minimum-down time
Synchronization time
NGCC
NGGT
Soak time
Desynchronization time
Hydro
M
Lignite
AN US
3
Figure 7: Representative time-related technical characteristics per technology type
ED
(h)
Figure 8 presents representative ramp limits per type of operation (dispatch phase
PT
and operation under automatic generation control) and technology type. Hydroelectric units exhibit high ramp-up and down rates of their power output, as
CE
well as extremely short start-up and shut-down times (zero synchronization, soak, and desynchronization times). These two features make hydropower plants ideal for
AC
entering the system to meet the needs of the network during peak hours. The extremely low ramp rates of the lignite-fired units can be also observed in this Figure, reflecting the fact that this technology is ideal for base-load operation. Note also that these units cannot operate under automatic generation control (system for adjusting the power output of various generators at different power units, as a response to load variations and disturbances). On the other hand, NGCC units can be utilized as load following units (during sudden changes of electricity demand), since
29
ACCEPTED MANUSCRIPT they are characterized by noticeable ramp rates, in both dispatch phase and operation under automatic generation control. 120
80 60 40 20 0 Ramp-up rate
Lignite
NGCC
Ramp-down rate- Ramp-up rate-AGC AGC
NGGT
Hydro
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Ramp-down rate
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MW/min
100
Figure 8: Representative ramp limits per type of operation and technology type (MW/min)
M
5. Results and Discussion
This section provides the results and a detailed discussion of the model
ED
implementation for the illustrative case study that has been considered. The problem has been solved to global optimality making use of the ILOG CPLEX 12.6.0.0
PT
solver incorporated in the General Algebraic Modeling System (GAMS) tool (GAMS, 2017). The size of the model is 77,157 single equations, 59,390 single variables, and
CE
21,820 discrete variables. The solution time is approximately 20 CPU sec.
AC
5.1. Power generation composition Initially, the problem is solved taking into account the interconnections of the systems. The model determines the power output of each unit separately for each hour of the dispatch day. Figure 9 highlights the total power produced by each system throughout the dispatch day in the cases with (With INT) and without interconnections (Without INT) among each other, respectively. The results are provided per technology type.
30
ACCEPTED MANUSCRIPT
40000 35000 30000
MWh
25000 20000 15000
5000 0
CR IP T
10000
With Without With Without With Without With Without With Without INT INT INT INT INT INT INT INT INT INT s1
s2 Lignite
s2 NGCC
s3 NGGT
s3 s4 s4 Hydro RES
s5
s5
AN US
s1
Figure 9: Total energy produced by each technology type in each system throughout the dispatch day in the cases with (With INT) and without interconnections (Without INT) among each other (MWh)
M
From that figure and focusing on the case where the interconnections are incorporated (With INT), it seems that base-load (lignite-fired) units account for the
ED
largest share of the total electricity generation, while an equally large part of the total production emanates from load-following units (NGCC units). No electricity is
PT
generated by peak-load units (NGGT units), which is expected as peak-load units contribute generally a small amount of energy to the system at an annual level.
CE
Therefore, peak-load units with high operating costs are not selected to operate and the load is covered from the other available units.
AC
System 4 (s4) produces the largest proportion of the base-load generation, since 4 of its total 7 units are lignite-fired. Correspondingly, System 5 (s5) produces the largest proportion of load following units, since it is mainly composed of NGCC units. On the other hand, in the case where interconnections are not taken into account (Without INT), it seems that the biggest part of the total electricity production comes from load-following units and not from base-load units (lignite-fired). This is due to
31
ACCEPTED MANUSCRIPT the fact that since there is no option for energy flows among the systems, each system is based on its own units to meet its load demand. Regarding the power contribution from lignite-fired and NGCC units, it can be summarized that: Lignite-fired power generation decreases by 5% in s1, increases by 12% in s2,
alone to that of the interconnection.
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and rises by 29% in s4, when the systems move from the state of being stand-
NGCC power generation decreases by 93% in s1, increases by 37% in s2, reduces by 7% in s3, and falls by 9% in s5, when the systems move from the state of being stand-alone to that of the interconnection.
AN US
The amount of electricity generation coming from renewables and hydroelectric units is identical in both cases, on the grounds that they have zero operational cost and they are given priority when entering the power system.
From that figure, some general conclusions can be derived on the energy flow
M
between the examined systems, based on the following:
System 1 (s1): Reduction of total electricity production by 47.5%.
ED
System 2 (s2): Increase of the total electricity production by 22%. System 3 (s3): Reduction in total power generation by 4.3%.
PT
System 4 (s4): Increase of the total electricity production by 26%.
CE
System 5 (s5): Increase of the total electricity production by 8%. Not surprisingly, it can be expected from the results that systems 1 and 3 are going
AC
to import energy so as to cover their demand in the case with interconnections considered. 5.2. Energy flows among systems When solving the model, the continuous variable
receives non-zero values
only if there is an interconnection among the systems. This variable expresses the amount of energy transferred between the systems. Thus, from the solution of the model, Table 2 presents the energy flows among the systems in presence of interconnections. 32
ACCEPTED MANUSCRIPT Table 2: Total daily energy flows among the systems in presence of interconnections (MWh)
s5 584 2811 -
CR IP T
Systems that export energy (MWh)
Systems that import energy (MWh) System s1 s2 s3 s4 s1 s2 4475 263 s3 2881 s4 338 3108 s5 6132 -
In Table 2, there are dashes (-) in some cells, denoting that these power flows cannot be implemented. These prohibited interconnections concern logical constraints due to initial conditions that prohibit the flow of energy from a system to itself. In
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addition, prohibited interconnections arise due to the problem data (no interconnection between these systems). The non-zero values provide information about the exact amount of energy transferred between the systems. As can be observed in Table 2, it appears that System 1 (s1) imports the largest
M
amount of energy (13488 MWh), while systems 3 and 5 import approximately the same amount of energy, i.e., 3371 and 3395 MWh respectively. From the analysis
ED
made at section 5.1, it was concluded that systems 1 and 3 would definitely import energy. Although that conclusion was true, it can be also noticed that system 5
PT
imports energy, as well as a minimal (almost negligible) amount of energy is imported to system 2 (338 MWh). Although these two systems import energy, the
CE
energy they export to system 1 is greater, which converts them into net exporters and transit systems.
AC
Figure 10 highlights the hourly energy flows among the interconnected systems at a daily level. It can be seen that they are at relatively low levels during the first hours of the day where the electricity demand in each system is at low levels, while they approach and/or exceed the level of 1000 MWh after the 7 th hour of the examined day.
33
ACCEPTED MANUSCRIPT
0
200
AN US
CR IP T
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
400
From s2 To s1 From s4 To s2
600 MWh
From s2 To s3 From s4 To s3
800
From s2 To s5 From s4 To s5
1000
1200
From s3 To s1 From s5 To s1
M
Figure 10: Hourly energy flows among the interconnected systems (MWh)
ED
Figure 11 depicts the interconnection structure and the total daily electricity trade among the interconnected systems. As it can be observed, system s4 is interconnected with systems s3, s2, and s5, system s3 is interconnected with s1, s2,
PT
and s4, system s2 has interconnection with s1, s3, s4, and s5, as well as the system s5 with s1, s2, and s4. Finally, system s1 has interconnection with the systems s2, s3,
CE
and s5.
AC
Although there are some hourly differentiations, systems s2, s4, and s5 constitute net exporters in total, while systems s1 and s3 represent net importers. More specifically, system s1 reports a large production deficit, while system s3 has a more balanced mix and acts mainly as a transit system for electricity exports to the system s1. The main conclusions arising from the results presented in Table 2 are the following:
34
ACCEPTED MANUSCRIPT System s4 exports electrical energy to its neighboring systems s2, s3, and s5 which act (s4 -> s2, s4 -> s3, and s4 -> s5). Systems s2 and s5 export the amount of electricity they import from system s4, i.e. they act as transit systems (s4 -> s2 -> s1, s4 -> s5 -> s1), along with their production surplus, to system s1 (s2 -> s1, s5 -> s1). As a consequence, they are both transit systems and power exporters.
CR IP T
Due to transmission congestion during some hours of the studied period in the interconnection capacity between systems s2 and s1 (the interconnector reaches its maximum limit, from s2 to s1), system s2 exports some amount of electricity to the system s5, which is then transmitted again to the system s1 (s2 -> s5 -> s1). Note that the interconnection capacity between systems s5
AN US
and s1 is higher than the corresponding between the systems s2 and s1. As a consequence, system s5, apart from being a net exporter of its production surplus to the system s1 (s5 -> s1), acts as a transit system for the electricity transmission from both systems s4 (as analyzed above) and s2 to the system s1.
M
System s3 is characterized by a balanced mix, since it produces around 96%
ED
of its own demand. In order to meet its deficit, it imports electrical energy from systems s2 and s4. Since the amount of the imported electricity from system s4 exceed its requirements, it acts as a transit system for its
PT
transmission to the system s1. As a consequence, it acts as a net importer
CE
from the system s2 (s2 -> s3), and a transit system (s4 -> s3 -> s1). System s1 constitutes a net importer directly from system s5 (s5 -> s1), and indirectly
AC
from the system s4 through the three possible routes (s4 -> s2 -> s1, s4 -> s3 -> s1, and s4 -> s5 -> s1).
35
AN US
CR IP T
ACCEPTED MANUSCRIPT
Figure 11: Interconnection structure and total daily electricity trade among the interconnected systems (MWh) 5.3. System marginal price
M
Figure 12 shows that the system’s marginal price remains relatively stable throughout the day for systems 2-5 (s2, s3, s4, and s5). In particular, on average, the
ED
marginal price of system 4 is around 25 €/MWh, which is the lowest price compared to the other systems. The marginal prices of systems 2 and 5 are around 28 €/MWh
PT
and 37 €/MWh correspondingly (daily average). The marginal price of system 3 remains constant throughout the examined period at 47.7 €/MWh. These values are
CE
fully consistent with the data used, since the system's marginal price is based on the energy supply offer of each unit, which in this problem is expressed by the .
AC
parameter .
In contrast, the marginal price of system 1 reports significant variations during the day. Specifically, up to 8th hour of the day, the marginal price is set at around 30 €/MWh, while during the 9th hour of the day, the system’s marginal price rises to 52 €/MWh and remains relatively stable for the rest of the day.
36
ACCEPTED MANUSCRIPT
55
50
€/MWh
45 40
35 25
20
CR IP T
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s2
s3
s4
s5
AN US
s1
Figure 12: Hourly marginal price of each system in the case without interconnections (€/MWh) Figure 13 highlights the hourly marginal prices of each system in the case with interconnections. According to that figure, all systems have an approximately
M
constant marginal value up to the 7th hour of the day. Then, there is an increase up to the 9th hour of the day, being stabilized until the 16th hour of the day. During the
ED
time period between the 18th and the 20th hour of the day, a marginal price change is observed, while it is stabilized again until the 23th hour of the day. Finally, there is a
PT
fall in its value during the 24th hour of the day. The daily average values are 37.4 €/MWh for System 1, 35.6 €/MWh for System 2, 36.4 €/MWh for System 3, 35.4
AC
CE
€/MWh for System 4 and, 36.4 €/MWh for System 5.
37
ACCEPTED MANUSCRIPT
50
€/MWh
45
40 35 30
20
CR IP T
25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s1
s2
s3
s4
s5
AN US
Figure 13: Hourly marginal price of each system in the case with interconnections (€/MWh) The trends depicted in Figure 13 show great differences with respect to those of Figure 12. In Figure 13 where interconnections among the systems are incorporated, it can be observed that all systems have the same shape throughout the day. The
M
existence of interconnections between some systems may lead to a significant degree of convergence among the systems’ prices. As expected on the basis of
ED
economic theory, an increase of the marginal price is reported in the systems characterized by net electricity exports, since there is an increase in their total
PT
electricity production, utilizing more expensive power generation sources. On the other hand, systems characterized by net electricity imports show a fall in their
CE
respective marginal prices, on the grounds that they gain access in more economical power generation sources.
AC
In particular, in systems 1 and 3, which are characterized by net electricity imports, there is a decrease in the average values of their marginal prices of the order of 17% and 23%, respectively. In the opposite way, in systems 2 and 4, characterized by net electricity exports, there is an increase in the average values of their marginal prices of the order of 27% and 41%, respectively. The average values of the marginal prices of system 5 in both cases remain stable at 36 €/MWh, since this system has more than enough capacity to meet its own demand and export additional energy at uniform and highly competitive prices. 38
ACCEPTED MANUSCRIPT 5.4. Operational scheduling Figures 14 and 15 highlight the operational scheduling of power systems 1 and 4 in the cases with and without interconnections. Each box corresponds to a specific power unit (of a certain technology type) and hourly time period. There are five possible operational phases of a hydrothermal unit: 1. Operation in the synchronization phase (only for thermal units)
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2. Operation in the soak phase (only for thermal units)
3. Operation in the dispatch phase (both for thermal and hydroelectric units) 4. Operation in the desynchronization phase (only for thermal units)
5. The units have been shut-down, so they are offline (both for thermal and
AN US
hydroelectric units)
With interconnections
System 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite -1 Lignite -2
M
NGCC-1 NGCC-2
ED
NGGT Hydro-1 Hydro-2
Synchronization
Soak
Dispatch
PT
Without interconnections
System 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite -1
Desynchronization
CE
Lignite -2 NGCC-1 NGCC-2
Offline
AC
NGGT
Hydro-1 Hydro-2
Figure 14: Operational scheduling of power system 1 in cases with and without interconnections
39
ACCEPTED MANUSCRIPT
With interconnections System 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Synchronization
Lignite-5 Lignite-6 Lignite-7
Soak
Lignite-8 Hydro-7 Hydro-8
Dispatch
CR IP T
Without interconnections System 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite-5
Desynchronization
Lignite-6 Lignite-7 Lignite-8
Offline
Hydro-7
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Hydro-8
Figure 15: Operational scheduling of power system 4 in cases with and without interconnections The results presented in section 5.1 underscored that there will be a reduction in the total electricity production of system 1 by 47.5%, while there will be an increase in
M
the total electricity production of system 4 by 26%, when the systems move from the
ED
state of being stand-alone to that of the interconnection. With regard to system 1, this trend is clearly depicted in Figure 14 where the main
PT
finding is that the NGCC units do not operate in the case with the interconnections available, since the model determines that they are not enough cost-competitive in
CE
the presence of other available power generation sources. However, there was full utilization of them in the case without interconnections, in the absence of other
AC
available power generation sources. With reference to system 4, the expected increase of the total electricity production is justified by the more intense utilization of one more lignite-fired unit in the case with interconnections, which was shut-down in the case without interconnections, as depicted in Figure 15. This additional amount of electricity generation is going to be exported to other interconnected systems, which lack more economical sources of electricity generation. 5.5. Sensitivity analysis 40
ACCEPTED MANUSCRIPT This section presents a sensitivity analysis performed by varying the interconnection capacities between the interconnected systems each time. The analysis is within ± 50% of the reference values, with a ± 10% increment step each time. The results relate to the energy produced by each system presented per technology type. Table 3 provides the results of the analysis implemented for the interconnection capacity increase case.
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As can be seen in Table 3, it seems that with an increase in the maximum value of the interconnections capacities of the examined systems, no significant variations in the electricity produced by the units is observed. To sum up, regardless of how large the maximum allowable value of the electricity flow between the systems is, the
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results of the mathematical model are identical.
Table 4 presents the sensitivity analysis results for the interconnection capacity decrease case. From Table 4, it appears that for a reduction with a range of up to 40% in the interconnections capacities of the systems under consideration, no substantial difference is reported in the results. However, for a 50% reduction, it can
M
be noticed that there is an increase in the total power output of system 1, and a corresponding reduction in the system 2. As the value of the interconnection
ED
capacity decreases, for a reduction of more than 50%, the power output results tend
other.
PT
to approach those of the case in which the systems are not interconnected with each
CE
The differences are due to the fact that as the available capacity of the interconnection decreases, each system generates more energy at a domestic level to meet its load demand, regardless of the applied operating costs. Therefore, at low
AC
interconnection capacity rates, System 1 produces an additional amount of electricity from load following (NGCC) units rather than from base-load (lignite-fired) units.
Correspondingly, when the available capacity of the interconnection increases, a system with high operating costs is expected to reduce the total energy generated domestically, as there is the option for importing electricity from other systems at more affordable costs. 41
CR IP T
ACCEPTED MANUSCRIPT
Table 3: Sensitivity analysis results for the interconnection capacity increase case Lignite
NGCC
NGGT
Hydro
RES
20%
Lignite
NGCC
NGGT
Hydro
RES
s1
13185
935
-
770
-
s1
13185
935
-
770
-
s2
12460
13493
-
-
1734
s2
12460
13493
-
-
1734
s3
-
6240
-
4620
-
s3
-
6240
-
4620
-
s4
28092
-
-
900
1387
s4
28092
-
-
900
1387
s5
-
32167
-
-
4624
s5
-
32167
-
-
4624
30%
Lignite
NGCC
NGGT
Hydro
RES
40%
Lignite
NGCC
NGGT
Hydro
RES
s1
13177
935
-
770
-
s1
13120
935
-
770
-
s2
12475
13493
-
-
1734
s2
12679
13493
-
-
1734
s3
-
6240
-
4620
s4
28084
-
-
900
s5
-
32167
-
-
50%
Lignite
NGCC
NGGT
Hydro
s1
13120
935
-
770
s2
12679
13493
-
-
s3
-
6240
s4
27937
s5
-
-
6240
-
4620
-
s4
27937
-
-
900
1387
4624
s5
-
32167
-
-
4624
RES
Reference case
Lignite
NGCC
NGGT
Hydro
RES
-
s1
13185
935
-
770
-
1734
s2
12460
13493
-
-
1734
ED
M
s3
1387
4620
-
s3
-
6240
-
4620
-
-
900
1387
s4
28092
-
-
900
1387
32167
-
-
4624
s5
-
32167
-
-
4624
PT
-
-
CE AC
-
AN US
10%
42
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ACCEPTED MANUSCRIPT
Table 4: Sensitivity analysis results for the interconnection capacity decrease case Lignite
NGCC
NGGT
Hydro
RES
-20%
Lignite
NGCC
NGGT
Hydro
RES
s1
13185
935
-
770
-
s1
13185
935
-
770
-
s2
12460
13493
-
-
1734
s2
12460
13493
-
-
1734
s3
-
6240
-
4620
-
s3
-
6240
-
4620
-
s4
28092
-
-
900
1387
s4
28092
-
-
900
1387
s5
-
32167
-
-
4624
s5
-
32167
-
-
4624
-30%
Lignite
NGCC
NGGT
Hydro
RES
-40%
Lignite
NGCC
NGGT
Hydro
RES
s1
13190
935
-
770
-
s1
13233
675
431
770
-
s2
12481
13493
-
-
1734
s2
12710
13219
-
-
1734
s3
-
6240
-
4620
s4
28066
-
-
900
s5
-
32167
-
-
-50%
Lignite
NGCC
NGGT
Hydro
s1
13481
5618
-
770
s2
12866
6975
-
-
s3
-
7211
s4
28040
s5
-
-
6240
-
4620
-
s4
28061
-
-
900
1387
4624
s5
-
32003
-
-
4624
RES
Reference case
Lignite
NGCC
NGGT
Hydro
RES
-
s1
13185
935
-
770
-
1734
s2
12460
13493
-
-
1734
ED
M
s3
1387
4620
-
s3
-
6240
-
4620
-
-
900
1387
s4
28092
-
-
900
1387
32380
-
-
4624
s5
-
32167
-
-
4624
PT
-
-
CE AC
-
AN US
-10%
43
ACCEPTED MANUSCRIPT
6. Conclusions This work extends our previous contributions in the area of power generation expansion planning by proposing an integrated optimization framework for the optimal daily scheduling of interconnected power systems. In this problem which is also referred to as unit commitment problem in the literature, a set of power systems with their own power generating units of various technology types are
CR IP T
considered. Key model decisions include the production of energy by the various systems, the energy flow among them, their operational scheduling, as well as the resulting marginal price of each system.
A salient feature of the proposed framework is the detailed modelling of the
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different operational phases of the power generation units (synchronization, soak, dispatch, and desynchronization phase), power output limitations of the units, as well as ramp rates of the units. The objective is to optimally cover the electricity demand of all systems in a cost optimal way, while at the same time satisfying a
M
series of technical, economic and other logical constraints.
The applicability of the proposed framework has been tested using an illustrative
ED
case study. Emphasis is placed on considering potential interconnection options among the examined systems. Furthermore, a sensitivity analysis has been
PT
performed to investigate the impacts of the interconnection capacities on the resulting production mix.
CE
The results highlight that when the systems under consideration are not interconnected, each system meets its own electricity demand based on its locally
AC
installed units. On the other hand, if interconnection options are available, transmitting electricity from low-cost generation systems to systems with higher operating costs is the most economically attractive option. A more general conclusion that can be drawn is that cross-border electricity trade can reduce the overall cost of generating electricity to wider regions and unions, leading to price convergence of individual systems and enhancing their overall competitiveness. At the same time, it can also serve as price-signal to future investments in new power generation technologies to be installed in each system. 44
ACCEPTED MANUSCRIPT
Appendix Nomenclature Sets/Indices installed in each power system
Set including power systems
which are interconnected with
CR IP T
Set of power generating units
other power systems
according to a specific network
structure
Set of the distinct steps of each unit marginal cost function
AN US
Set of power generating units Set of considered power systems Set of hourly time periods
M
Subsets
Subset of hydroelectric units
ED
Subset of hydrothermal units
Subset of renewable energy units
Parameters
PT
Subset of thermal units
AC
CE
Availability of each renewable unit period
in each time
(%)
Nominal interconnection capacity between interconnected power systems
and
,
(MW)
Electricity demand of each power system period
in time
(MW)
Quantity of each power capacity block offer function of each power generating unit Marginal cost of each power capacity block
of the energy (MW) of the
energy offer function of each power generating unit
45
ACCEPTED MANUSCRIPT (€/MW) Maximum daily electricity generation from all hydroelectric units
(MWh)
Minimum daily electricity generation from all hydroelectric units
(MWh)
Shut-down cost of each power unit
(€)
Start-up cost of each power unit
(h)
CR IP T
Minimum down time of each power unit (€)
Minimum up time of each power unit
(h)
Additional cost of each power unit period
in each time
, when providing primary reserve (€/MW)
reserve (MW)
AN US
Maximum contribution of each power unit
Power output of each power unit
in primary
at the beginning of
the time horizon under consideration (MW)
M
Technical maximum of each power unit
, when
operating under automatic generation control (MW) (MW)
ED
Technical maximum of each power unit Technical minimum of each power unit
, when
PT
operating under automatic generation control (MW) Technical minimum of each power unit
AC
CE
Power output of each power unit
(MW) during soak phase
(MW) Ramp-down rate of each power unit
(MW/min)
Ramp-down rate of each power unit
, when operating
under automatic generation control (MW/min) Requirements of system time period
(MW)
Requirements of system time period
in primary-down reserve at
in primary-up reserve at
(MW)
Requirements of system
in secondary-down reserve 46
ACCEPTED MANUSCRIPT at time period
(MW)
Requirements of system time period
in secondary-up reserve at
(MW)
Requirements of system
in tertiary (spinning and
non-spinning) reserve at time period Ramp-up rate of each power unit
(MW) (MW/min) , when operating
CR IP T
Ramp-up rate of each power unit
under automatic generation control (MW/min) Additional cost of each power unit period
in each time
, when providing secondary reserve (€/MW)
Technology type of each power unit
(1, Lignite-fired
AN US
units, 2, Natural gas combined cycle units, 3, Natural gasfired open-cycle gas turbine units, 4, Hydroelectric units, 5, Renewables)
Additional cost of each power unit
, when providing tertiary spinning reserve
M
period
in each time
(€/MW)
ED
Maximum contribution of each power unit
in non-
spinning tertiary reserve (MW) Additional cost of each power unit
PT
period
in each time
, when providing tertiary non-spinning reserve
AC
CE
(€/MW) Number of operational hours of each power unit
at
the beginning of the time horizon under consideration (h) – positive number for units under operation and negative number for units being offline Desynchronization time of each power unit Soak time of each power unit
(h)
(h)
Synchronization time of each power unit
(h)
Continuous variables 47
ACCEPTED MANUSCRIPT Quantity of power capacity block of the energy offer function of each power unit cleared in time period
(MW)
Electricity flow between interconnected power systems and
,
in each time period
Total output of each power unit
(MW) in each time period
(MW) in each time period
,
CR IP T
Total output of each power unit
when operating in desynchronization phase (MW) Total output of each power unit
in each time period
when operating in soak phase (MW) Contribution of power unit (MW)
Contribution of power unit time period
in primary-up reserve in each
(MW)
Contribution of power unit
Contribution of power unit
ED
in each time period
in tertiary non-spinning reserve
(MW)
Contribution of power unit
PT
in secondary-up reserve in each
(MW)
Contribution of power unit
in tertiary spinning reserve in
(MW)
CE
each time period
in secondary-down reserve in
(MW)
M
each time period
time period
in primary-down reserve in each
AN US
time period
,
AC
Binary variables
1, if power unit
shuts-down in each time period
1, if power unit
starts-up in each time period
1, if power unit
is operational in each time period
1, if power unit
provides non-spinning tertiary reserve in
each time period 1, if power unit
operates under automatic generation control
in each time period 48
ACCEPTED MANUSCRIPT 1, if power unit
operates in desynchronization phase in each
time period 1, if power unit
operates in dispatch phase in each time
period operates in soak phase in each time period
1, if power unit
operates in synchronization phase in each
CR IP T
1, if power unit
time period
MILP:
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Acronyms Mixed integer linear programming
NGGC: Natural gas combined cycle
NGGT: Natural gas-fired open-cycle gas turbine Automatic Generation Control
ED
M
AGC:
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Optimal Scheduling of Interconnected Power Systems Nikolaos E. Koltsaklis , Ioannis Gioulekas , Michael C. Georgiadis PII: DOI: Reference:
S0098-1354(18)30014-0 10.1016/j.compchemeng.2018.01.004 CACE 5993
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
31 May 2017 12 November 2017 8 January 2018
Please cite this article as: Nikolaos E. Koltsaklis , Ioannis Gioulekas , Michael C. Georgiadis , Optimal Scheduling of Interconnected Power Systems, Computers and Chemical Engineering (2018), doi: 10.1016/j.compchemeng.2018.01.004
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Highlights
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Optimal energy scheduling of interconnected power systems is addressed. MILP model considering technical, operational, economic and logical constraints. Assessment of the interconnection impacts on the system's operational scheduling. Significant price convergence is achieved in interconnected systems. Electricity trade affects the optimal power system's energy balance.
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Optimal Scheduling of Interconnected Power Systems Nikolaos E. Koltsaklisa,*, Ioannis Gioulekasa,† Michael C. Georgiadisa,*
Aristotle University of Thessaloniki, Department of Chemical Engineering, 54124 Thessaloniki, Greece
Abstract
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a
This paper presents an optimization-based approach to address the problem of the
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optimal daily energy scheduling of interconnected power systems in electricity markets. More specifically, a Mixed Integer Linear Programming model (MILP) has been developed to address the specific challenges of the underlying problem. The main focus of the proposed framework is to examine the importance and the impacts of electricity interconnections and cross-border electricity trade on the
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scheduling of power systems, both at a technical and economic level. The applicability of the proposed approach has been tested on an illustrative case study
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including five power systems which can be interconnected (with a certain interconnection structure) or not. The proposed model determines in a detailed and
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analytical way the optimal power generation mix, the electricity trade among the systems, the electricity flows (in case of interconnection options), the marginal price
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of each system, as well as it investigates through a sensitivity analysis the effects of the available interconnection capacity on the resulting power production mix. The
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work demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies followed by the market participants, as well as on the strategic long-term decisions to be implemented by investors and/or policy makers at a national and/or regional level, underlining
*
Corresponding authors. E-mail address: [email protected] (N. E. Koltsaklis), [email protected] (M. C. Georgiadis)
†
Current Address: Department of Chemical Engineering, University College London, UK 2
ACCEPTED MANUSCRIPT potential risks and providing appropriate price signals on critical energy infrastructure projects under real market operating conditions. Keywords: Energy scheduling; Electricity interconnections; Unit commitment; Electricity trade; Day-ahead market
1. Introduction
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The World gross electricity production has been increased from 6,287 TWh to 23,815 TWh between 1974 and 2014, reporting an average annual growth rate of 3.4% (IEA, 2016a). Power networks have been constructed for over a century. These types of networks lack the ability to support the transition to a low-carbon and decentralized energy system. A noticeable enhancement of long-distance transmission capacities
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as well as the extension of interconnections among energy systems is necessary in order to meet the environmental, economic and security objectives of the future energy systems. Affordable and large-scale interconnections are characterized by a series of advantages, including: (i) flexibility in balancing demand and supply
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mismatches and peak capacity savings, (ii) flexibility provision for the effective integration of variable renewable energy sources, and (ii) accessibility provision to
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remote energy sources (IEA, 2016b). Soroush and Chmielewski (2013) provided a process systems engineering-based overview of the whole power systems value
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chain, including power generation, storage and distribution. Nowadays, the increasing concern for the mitigation of the carbon impact has led to
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the growing utilization of renewable energy in the power sector (Zhang et al., 2013). The increasing penetration of renewable energy sources and their impacts on the
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power systems have been extensively addressed in the literature, especially in works dealing with the generation expansion planning problem (Koltsaklis et al., 2014a; Koltsaklis et al., 2015; Guo et al., 2017). The unit commitment problem is defined as the optimization problem which determines the operating schedule of a set of generating units at each time interval so as to satisfy a specific amount of electricity demand, considering a set of operational, technical, regulatory, economic and environmental constraints (Koltsaklis and Georgiadis, 2015). The unit commitment problem is a complex problem and is mainly formulated as a large scale, non-linear 3
ACCEPTED MANUSCRIPT mixed integer problem. The literature is rich in works dealing with the unit commitment problem from a variety of perspectives. Palmintier (2014) made use of the methodology of the unit clustering in the unit commitment problem in order to implement generation planning incorporating flexibility issues, while Palmintier and Webster (2011) presented the method of unit clustering for approximate unit commitment reporting significant gains in the execution time. The same authors
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concluded that the integration of unit commitment-based constraints into generation expansion planning models can alter the optimal generation mix results to a significant extent (Palmintier and Webster, 2014). A MILP approach for unit commitment-based mid-term (Koltsaklis et al., 2016) and long-term (Koltsaklis and Georgiadis, 2015) planning has been also developed, as well as on the design of
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energy networks based on combined heat and power units (Koltsaklis et al., 2014b). Abujarad et al. (2017) presented a review dealing with the impacts that significant penetration of renewables have on the development and usefulness of unit commitment models. Carrion and Arroyo (2006) developed a MILP formulation for
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the thermal unit commitment problem, while Niknam et al. (2009) proposed a similar approach based on benders decomposition method. Xiao et al. (2011)
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developed a two-stage stochastic programming formulation of the unit commitment problem with the aim to evaluate the spinning and non-spinning reserve levels of a
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power system along with the associated system costs under significant wind power penetration. Viana and Pedroso (2013) contributed to the same topic with a MILP-
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based formulation incorporating piecewise linear approximations of the quadratic fuel cost function, while Yang et al. (2017) presented an approach for the thermal
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unit commitment problem, as well as Marcovecchio et al. (2014) developed an optimization-based approach for the solution of same problem. Morales-España et al. (2013) developed also a formulation of the thermal unit commitment problem. Zheng et al. (2016) presented an approach for the solution of the unit commitment problem based on additional cuts to the branch and bound method as well as heuristic rounding technique. Lyzwa et al. (2015) developed three possible mathematical formulations for the determination of the optimal energy mix. Qin et al. (2005) presented a security-constrained unit commitment model with the aim of 4
ACCEPTED MANUSCRIPT achieving cost savings for the consumers. Lujano-Rojas et al. (2016) presented a methodology for the solution of the unit commitment problem from a probabilistic perspective on several parameters. Bigdeli and Karimpour (2014) presented a MILP formulation of the unit commitment model to minimize the total daily energy dispatch cost, while Frangioni et al. (2011) presented a sequential Langrangian-MILP approach for the solution of the hydrothermal unit commitment problem. Lima and
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Novais (2016) examined the impacts of symmetry in the unit commitment problems, while Zhang et al. (2016) proposed a unified unit commitment model formulation by modelling the generating units’ commitment status variables as binary, integer or continuous values.
The increasing wind penetration into the power systems raises flexibility issues due
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to the intermittent nature characterizing wind power contribution. Zhang et al. (2015) developed a MILP, risk-based unit commitment model considering wind power uncertainty through the incorporation of the loss of load risk, wind power curtailment and transmission congestion caused by wind power fluctuations.
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Delarue and D’haeseleer (2008) developed a MILP model for the solution of the unit commitment problem, examining also the impacts of limited forecasting of the
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electricity demand. Zugno and Conejo (2015) developed a mathematical approach for the co-optimization of energy dispatch and reserve capacity in a power market
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taking into consideration high penetration of stochastic renewable sources. Zhao and Wu (2014) proposed a MILP model in order to quantify the impact of demand
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response and wind generation on the locational marginal prices through a unit commitment model formulation. Bakirtzis and Biskas (2016) presented a MILP
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model for the stochastic power systems’ scheduling under significant renewables’ penetration, while Azizipanah-Abarghooee et al. (2016) presented a probabilistic unit commitment problem formulation incorporating demand response and significant wind penetration. Pezic and Cedrés (2013) proposed a MILP approach for the solution of the unit commitment problem for fully renewable energy systems, while Xie et al. (2011) presented a MILP formulation for the day-ahead wind-thermal unit commitment problem implemented by an independent power system operator. Parvania and Scaglione (2016) developed a MILP model for the day ahead wind5
ACCEPTED MANUSCRIPT thermal unit commitment problem evaluating expected energy not served and expected energy excess served due to unavailability of thermal units, as well as fluctuations of the wind power output. Mehamed et al. (2016) developed a unit commitment optimization model aiming to maximize the profits of an energy producer under uncertainty in market clearing prices and wind power contribution. The fact that the power and the natural gas systems are highly interlinked, since the
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natural gas-fired power units comprise the main back-up technology to deal with the fluctuations injected into the power grid by the variable wind power generation. As a consequence, the natural gas system operation is greatly affected by the intermittency and stochasticity characterizing the growing use of renewables into the power systems (Keyaerts et al., 2014). Cui et al. (2016) presented a bi-level
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programming optimization model for a coordinated operational scheduling of both an electricity network and a natural gas system taking into account demand response options. Correa-Posada and Sánchez-Martín (2015) developed a MILP model coupling the power and natural gas systems in short-term operation. Yazdani
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Damavandi et al. (2011) developed an MILP model so as to analyze the impacts of gas velocity and distances between gas areas in the unit commitment problem.
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Knudsen et al. (2014) presented a MILP model for the shale-gas scheduling for natural gas supply in power producers, with the aim of maximizing the profits of well
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operators.
The integration of national electricity markets into a single multi-area market is of
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utmost importance in the European Union agenda with the aim of achieving the optimal utilization of the interconnection transmission capacities. In that context,
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Chatzigiannis et al. (2016) proposed a mathematical model for the day ahead clearing process of the power markets at a European level. Dourbois and Biskas (2016) proposed a nodal-based security-constrained market clearing MILP mathematical model taking into account multi-period products. Greater resilience to climate change negative impacts is of utmost importance to the technical viability of the energy sector and its ability to affordably cover the increasing energy demands driven by global economic and population growth. Resilience of the energy sector refers to the “capacity of the energy system or its 6
ACCEPTED MANUSCRIPT components to cope with a hazardous event or trend, responding in ways that maintain their essential function, identity and structure while also maintaining the capacity for adaptation, learning and transformation” (IEA, 2015). Eskandarpour et al. (2016) presented a resilience-constrained unit commitment model formulation considering the simultaneous outage of multiple system components, while Wang et al. (2016) developed a risk adjustable MILP model for the solution of the unit
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commitment problem. Demand-response and electric vehicles concepts are also incorporated in unit commitment problem formulations. Zhou et al. (2017) presented a mathematical model for the clearing process of a wholesale electricity market incorporating also a demand response mechanism, while Safdarian et al. (2014) developed a MILP model
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for the incorporation of price-based demand response in the short-term operation of distribution companies whose objective is the maximization of the distribution companies’ expected profits. Huber et al. (2012) presented an MILP formulation of the unit commitment problem aiming at investigating the influences of large scale
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electric vehicles and photovoltaic power on the power system, while Koltsaklis and Georgiadis (2016) developed a MILP formulation to examine the influence of the
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electric vehicles’ penetration on the daily generation scheduling of a power system. Unit commitment concepts are also employed for the determination of optimal
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operational scheduling in microgrids. Alabedin et al. (2012) presented a MILP model for the optimal power generation scheduling in a microgrid consisting of a group of
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dispatchable and non-dispatchable generating units in both grid-connected and isolated modes. Kia et al. (2017) presented a stochastic MILP model for the optimal
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scheduling of combined heat and power units under electricity and thermal storage, while Nemati et al. (2015) developed a MILP model for the solution of the unit commitment and economic dispatch problem of microgrids consisting of controllable distributed generators and battery storage systems. Haddadian et al. (2015) presented a MILP-based unit commitment model for the optimal day-ahead scheduling in power systems involving thermal units, wind turbines and distributed storage.
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ACCEPTED MANUSCRIPT Examining the same problem from a power producer perspective, Laia et al. (2016) developed a MILP model for determining the optimal bidding strategy (selfscheduling problem) of thermal and wind power producers in a pool-based power market, while Shabanzadeh et al. (2015) presented a MILP model for the optimal daily and weekly self-scheduling of virtual power plants. Furthermore, Bakirtzis et al. (2007) presented an optimization model for determining the optimal offering
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strategies submitted by electricity produces in day ahead power auctions with stepwise energy supply offers. Pérez-Díaz et al. (2012) proposed an NLP unit commitment model for the optimal operational scheduling of a hydroelectric unit taking part in the day-ahead power market, whose objective is its revenues maximization. In addition to the above, Catalão et al. (2012) developed a MINLP
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model for the determination of the optimal operation of a hydro plant in a dayahead electricity market with the objective of maximizing its profits, while Simoglou et al. (2012) developed a MILP model for the optimal self-scheduling of a dominant electricity company, comprising of thermal and hydroelectric units in its portfolio, in
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both the generation and retail sectors of a power market. Finally, Lima et al. (2015) developed an optimization approach to determine the optimal self-scheduling,
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forward contracting, and pool involvement of a power producer whose portfolio includes hydrothermal and wind energy sources.
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This work presents a MILP-based, mathematical framework to cope with the unit commitment problem of a day-ahead electricity market (co-optimization of energy
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and reserve markets) in interconnected power systems based on a network flow formulation, taking into account both hydrothermal and renewable energy sources.
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This approach employs key features of our previous works (Koltsaklis et al., 2014; Koltsaklis and Georgiadis, 2015), while it is mainly focused on the scheduling (daily) operation of the studied power systems with emphasis on the systematic assessment of the impacts of (regional) potential interconnections on several key decisions including energy mix, market clearing price, and electricity transmission. The key contributions and the salient features of the proposed model is the simultaneous consideration of multiple distinct systems in an integrated approach, instead of focusing on an individual power system with potential interconnection 8
ACCEPTED MANUSCRIPT options. More specifically, the proposed framework includes: (i) incorporation of a optimization approach of the unit commitment problem (day-ahead energy and reserve markets) in the context of interconnected power systems, (ii) assessment of the interconnection impacts on the daily power mix and the market clearing price of each individual power system, and (iii) insights and indications for potential investments in each individual power system through the interconnection-based
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market clearing algorithm results (price-signals). As a consequence, with the proposed approach, the overall (regional) welfare is maximized and the utilization of the considered interconnections is optimally determined.
The remainder of the paper is organized as follows: the problem statement is presented in Section 2, while the model formulation is provided in Section 3. The
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details and data of the case study are given in Section 4, while Section 5 provides a detailed discussion of the results obtained. Finally, Section 6 draws up some concluding remarks arising from this work.
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2. Problem statement
This work addresses the problem of the optimal energy scheduling of a given power
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system in a day-ahead market, i.e., the unit commitment problem. It addresses the simultaneous optimization of both the energy and reserve markets. The problem
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under consideration is formally defined as follows: The time period under consideration concerns the day-ahead market and
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includes hourly time intervals
A set of power systems (
. ) is considered. Each system
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interconnected with other neighboring systems network structure
, according to their
.
A set of power generating units
is modeled, including thermal units
, hydroelectric units units
can be
(both referred to as hydrothermal
), as well as renewable energy sources
. Each power unit
belongs to a specific technology type, given by parameter
.
The majority of thermal units lack the ability to start-up or shut-down immediately after a relevant decision has been taken (Koltsaklis and 9
ACCEPTED MANUSCRIPT Georgiadis, 2015; Koltsaklis et al., 2016). As a consequence, there is a succession of several distinct operational phases for a specific thermal unit that has to be undertaken, each of which with its own duration and power output range according to the technology type of each unit and its individual characteristics (lifetime etc.). The possible operating phases of a hydrothermal power unit
include the synchronization, soak, dispatch,
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and desynchronization phases, when being online. There is a specific succession in the operational phases of each hydrothermal power unit. As soon as a start-up decision is taken for each hydrothermal unit
, the
unit enters the synchronization phase, characterized by a specific duration . The next phase of a unit’s operation is the soak one, which has also a , and during which the unit’s power output amounts to
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certain duration
a certain value given by the parameter
, which is a technical
characteristic of each unit. After the successful completion of the soak phase, the unit enters the dispatch phase, in which the unit’s power output can take
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any value between its technical minimum
, and maximum,
. The
corresponding values when the unit operates under Automatic Generation and
The power output changes of each unit in
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Control are
the dispatch phase during two consecutive time periods are subject to
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specific limits, i.e.,
which defines the ramp-up rate of each power unit
, while parameter
. In the case of unit’s operation under Automatic
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power unit
represents the ramp-down rate of each
Generation Control, the corresponding ramp rates are provided by the and
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parameters
, correspondingly. The last possible
operational phase of each unit
is that of the desynchronization
phase, which has a specific duration
. The minimum-up (operational)
time of each unit
is given by the parameter
, while the
corresponding minimum-down (non-operational) time of each unit
is
given by the parameter
is
provided by the parameter
. The start-up cost of each power unit
, while its shut-down cost by the parameter
. 10
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can provide specific types of power reserves to the
network. These include the primary (up and down), secondary (up and down), as well as tertiary, spinning and non-spinning reserves. More specifically, each power unit i.
is characterized by:
, denoting the maximum contribution of each power unit in primary reserve, , denoting the maximum contribution of each power unit in non-spinning tertiary reserve,
iii.
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ii.
, denoting the additional cost of each power unit time period
, when providing primary reserve,
, denoting the additional cost of each power unit time period
v.
in each
, when providing secondary reserve,
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iv.
in each
, denoting the additional cost of each power unit each time period
vi.
in
, when providing tertiary spinning reserve, and
, denoting the additional cost of each power unit
, when providing tertiary non-spinning reserve.
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each time period
in
Each power system is characterized by: , denoting the requirements of system
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i.
reserve at time period
,
, denoting the requirements of system
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ii.
reserve at time period
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iii.
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v.
, denoting the requirements of system
vi.
in secondary-up
,
, denoting the requirements of system
down reserve at time period
in secondary-
,
, denoting the requirements of system at time period
in primary-down
,
reserve at time period
iv.
in primary-up
in tertiary reserve
, and
, denoting the electricity demand of each power system time period
in
.
There is a specific nominal interconnection capacity between interconnected power systems
and
,
, given by the parameter 11
.
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is characterized by a certain availability in each time period
, provided by the
.
The power capacity of each thermal unit
is divided into a number of
blocks
,
, which represents the quantity of each power capacity
block
of the energy offer function of each power generating unit
.
of each power generating unit
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Each power capacity block has a certain marginal cost (energy offer function) , provided by the parameter
.
There are specific bounds for the total daily hydroelectric generation of each unit
, given by the parameters
and
, respectively.
In the beginning of the examined time period, each power unit
i.
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characterized by:
, denoting the power output of each power unit
is
at the
beginning of the time horizon under consideration, ii.
, denoting the number of operational hours of each power unit
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at the beginning of the time horizon under consideration, The objective is to minimize the total daily cost for the energy scheduling of the
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power system under consideration, including the variable operating cost of the power generation units along with their start-up and shut-down costs, as well as the
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reserves provision costs in order to fully meet the total electricity demand of the power system.
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3. Mathematical formulation
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3.1. Objective function The objective function consists of eight terms which determine the operating costs of all production units and systems. In particular, the first term expresses the variable cost that depends on the power output power of all the units during the examined period. The second term refers to the start-up cost of each power unit, provided the unit is selected to start-up. Similarly, the next term represents the shutdown cost of each power unit, if it is selected to shut-down. The next four terms
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⏞ ∑∑
⏞ ∑∑
(
(
)
)
(1)
⏞ ∑∑
⏞ ∑∑
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⏞ ∑∑
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⏞ ∑∑∑
3.2.1. Model constraints Synchronization phase constraints
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∑
Equations (2) specify the time periods during which the power unit
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operate in the synchronization phase. At the random time period power unit starts-up, the binary variable
will
in which the
equals 1, while the binary variable
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receives also the same value (1) for the time periods (hours) from to
,
and the unit has been synchronized to the power network. From the time period
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and then, the power unit enters the soak phase.
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Soak phase constraints
∑
Equations (3) specify the time periods during which the power unit operate in the soak phase. At the random time period starts-up, the binary variable
in which the power unit
equals 1, while the binary variable
13
will
receives
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to
, and the unit operates in the soak phase during that time period.
Equations (4) determine the power output of each unit
when it operates in the
soak phase. According to these equations, the continuous variable constant amount of
equals the
throughout this phase (in this phase the binary variable
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obtains the value of 1 according to Equations 3). As soon as the unit exits the soak phase and enters the dispatch phase, the unit’s power can vary between its technical minimum and maximum.
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Desynchronization phase constraints
∑
Equations (5) specify the time periods during which the power unit
will
operate in the desynchronization phase. If the unit is determined to shut-down in
to
will amount to 1, as well as the binary
will take the value of 1 for the times periods (hours) from
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variable
, the binary variable
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time period
. During that time period, the power unit will operate in the
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desynchronization phase.
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∑
Equations (6) determine the power output of each unit
when it operates in the
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desynchronization phase. These equations specify that the power output of the unit when it operates in this phase decreases at a rate equal to (
) for all steps of the
desynchronization phase up to zero. Therefore, the power output receives specific discrete values. Minimum up and down time constraints
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∑ Equations (7) guarantee that the power unit
will be online at time period
if its startup took place in any of the previous the unit starts-up in time period
time periods (hours). When
, then the binary variable
of 1, and the binary variable
takes the value
takes also the value of 1 for the next
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hours. In this way, the minimum operating time of each power unit guaranteed. ∑
is
that unit
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Equations (8) work in a similar way to Equations (7). This type of constraints ensure will be forced out of service at time period
down during any of the previous ( shuts-down at time period binary variable
, if it has been shut-
) time periods (hours). When the unit
, then the binary variable
is set to 1, and the
will necessarily get a zero value for the next (
) time
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periods (hours). In this way, the minimum down time constraint of each power unit
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is satisfied.
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Logical status of unit commitment
Equations (9) impose that at most one of the binary variables describing the various
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operating phases of a unit If power unit
will have a non-zero value at each time period
is offline in time period
, the binary variable
.
equals zero,
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so none of the other binary variables can get a non-zero value.
Equations (10) determine the transition of each power unit offline operating mode and vice versa. If a power unit , then shuts-down in time period
, and , then
from online to
starts-up in time period
. Similarly, if a power unit and
15
.
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to start-up and shut-
. If one of the two binary variables receives a
value of 1 in a time period
, then the other one will necessarily get the zero
value.
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Units’ power output constraints
Equations (12) states that each power generation unit
can operate under
Automatic Generation Control and provide the network with secondary (either upward or downward) reserve only when operating in the dispatch phase. In this operational phase, the binary variable
has a value of 1, and as a consequence
value of 1. In case the power unit
can obtain the
does not operate in the dispatch phase
), then from this type of equations follows that
.
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(
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the unit can provide secondary reserve, i.e., the binary variable
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Equations (13) and (14) define the maximum amount of primary reserve that the power unit
can provide to the network. The power unit
can provide
variable
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primary reserve only when it operates in the dispatch phase, i.e., when the binary is equal to 1. In this case the continuous variables
and
can
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take various values, subject to the maximum limit imposed by the parameter .
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which is a technical characteristic of each power unit
Equations (15) and (16) define the maximum amount of secondary reserve that the power unit
can provide to the network when it operates under Automatic
Generation Control, i.e., the binary variable the continuous variables
and
gets a value equal to 1. In this case,
can obtain different values, subject to the
maximum limit imposed by the parameters
16
and
, expressing the
ACCEPTED MANUSCRIPT ramp-up and down rates, respectively, of each power unit
(in MW/min), while
the constant of 15 represents a time frame of 15 minutes.
Equations (17) define the maximum amount of tertiary reserve that the power unit can provide to the network. When the power unit dispatch phase, then the binary variable
is equal to 1, and the continuous
can obtain various values subject to a maximum limit imposed by the
parameter
CR IP T
variable
operates in the
, which is a technical characteristic of each power unit
scalar 15 represents a time frame of 15 minutes.
can provide tertiary non-
AN US
Constraints (18) ensure that a power generation unit
. The
spinning reserve to the network only when it is offline. In this case, the binary variable
takes a value of 0. As a consequence, the binary variable
obtain the value of 1. This enables the power unit
to provide tertiary non-
spinning reserve. Otherwise, i.e., when the power unit
M
is able to
operates in one of the
synchronization, soak, dispatch, and desynchronization phases, the binary variable equals zero.
PT
ED
receives a value of 1, and the binary variable
Equations (19) and (20) define the maximum and minimum amount of tertiary non-
CE
spinning reserve that the power unit equations (19), the power unit
can provide to the network. According to can provide an amount of reserve up to the , which is a technical characteristic
AC
maximum limit expressed by parameter
of each unit. Equally, equations (20) define the minimum amount of tertiary nonspinning reserve that the power unit
can provide (if it is selected for the
corresponding provision, expressed by the binary variable
(
)
17
) to the network.
ACCEPTED MANUSCRIPT Constraints (21) express in general terms the lower output limit of a power unit at time period
, when it is able to operate under Automatic Generation
Control. The decision variable
is taken into account only if the unit operates in
the dispatch phase and provides secondary reserve to the network. In all other cases the effect of this term is considered negligible. The right-hand side of inequality includes all possible values that power output can
CR IP T
take. The first term refers to the time period during which a power unit operates in the synchronization phase. In this phase, the power unit
does not
produce power, resulting in the zero factor multiplied with the binary variable
.
The second term refers to the soak phase. The power output of each power unit , as has been set in equations (4). The third
AN US
during this phase is equal to
term refers to the power offered by the plant in its desynchronization phase (
).
This amount of power varies according to the desynchronization time step of each unit and it is given by equations (6). The fourth and fifth term of the right hand side
ED
operates in the dispatch phase.
when it
M
of the constraints (21) defines the power output of each power unit
(
)
PT
Similar to constraints (21), Constraints (22) define the upper limit of the power output of each power unit
at time period
, when it is capable of
AC
CE
operating under Automatic Generation Control.
Equations (23) and (24) specify the upper and lower limit of the power output of a power unit
at time period
, when it is capable of operating under
Automatic Generation Control and simultaneously provides primary and secondary 18
ACCEPTED MANUSCRIPT downward reserves. The first three terms of the right hand side of constraints (23) and (24) refer to the synchronization, soak, and desynchronization phases. The output that each power unit
can offer at each of these phases is
predetermined, as has already been analyzed. In both constraints, the fourth term refers to the output of a power unit during which the binary variable
when it operates in the dispatch phase, has a non-zero value. . The binary variable
CR IP T
Constraints (24) introduces the term
receives a non-zero value at the last hour of the time period before the power unit
shuts-down. During that specific period, the inequality takes the form and forces the unit to operate at that time at its
AN US
technical minimum. The desynchronization phase, which is described by equations (5) and (6), is now possible. The above term is omitted for peak-load units which have the ability to change their output power from their technical maximum to zero over a few minutes.
M
Ramp-up and down limits of power units (
)
at time period
ED
Constraints (25) place limitations on the ramp-up rates of the output of each unit . It should be stressed that an output increase of each unit
PT
can occur when there is a change in the unit’s operating mode from offline to the synchronization phase, during the transition from the synchronization to the
CE
soak phase and during the dispatch phase. According to constraints (25), the difference in the value of the power output
AC
between two consecutive hours cannot be greater than a number equal to the product of
with 60. The parameter
symbolizes the unit's ramp-up rate
and it comprises a unit’s technical characteristic. Since the ramp rate is usually given in MW/min, the constant 60 is introduced, accounting for a 60-minute period. During the synchronization and soak phase, the output of each power unit
is
defined and knowledgeable (the unit does not produce power during the synchronization phase, while its output in the soak phase is predetermined and given 19
ACCEPTED MANUSCRIPT by equations 4). By inserting the N constant, which takes a very high value, the inequality is virtually inactive (25). In the synchronization phase, the binary variable inequality takes the form
takes the value 1 and the . It is also the same during
the soak phase. With the addition of the second term, the inequality does not limit the output increase occurring when the operating state of the each unit
CR IP T
changes from the offline status to the synchronization phase, and from the synchronization to the soak phase. (
)
Correspondingly to constraints (25), constraints (26) place limitations on the rampat time period
AN US
down rates of the output of each unit
. The output
decrease takes place during the desynchronization and dispatch phases. The first inequality term expresses again the maximum power difference between two consecutive hours, when the unit operates in the dispatch phase. This difference , where
accounts for the ramp-
M
cannot be greater than the product down rate of the unit.
ED
The second term is activated during the unit's desynchronization phase. The inequality then takes the form
is inserted to model the last operating time of each
before being shut down.
CE
power unit
PT
number). The binary variable
(where N is a very large
Power capacity limits
AC
∑
Each power unit
provides power to the network in the form of power blocks,
each of which has a different marginal cost. Equations (27) specify that the sum of the total power of these blocks should be equal to the total power output of each unit
for each time period
.
20
ACCEPTED MANUSCRIPT Equations (28) define the minimum and maximum values the continuous variable can take. The variable has a minimum value of zero (the unit does not provide power from that block), while its maximum bound is provided by the parameter . The units provide power starting from the block with the lowest electricity generating marginal cost.
∑
∑
∑
CR IP T
Power demand balance
Equations (29) represents the energy balance of the problem. The first term is a sum referring to the total power output generated by all units at each time period
from the
AN US
while the second sum refers to the total energy entering the system
,
all the other interconnected power systems. The third term is the demand of each system
at each time period
energy exporting from a system
to the other interconnected power systems.
M
∑
ED
∑
CE
PT
∑ ∑
, while the fourth term refers to the total
Constraints (30) and (31) refer to the coverage of the power network with primary (with upstream and downstream direction) reserve respectively. The sum of the
AC
contribution of all units of each system to primary reserve should be greater than or equal to the primary reserve system requirements. Correspondingly, constraints (32) and (33) are defined for covering each system requirements in secondary reserve. ∑
∑
21
ACCEPTED MANUSCRIPT Constraints (34) refer to the coverage of the network’s requirements for tertiary spinning and non-spinning reserves. An important element of the above equations is the fact that no separate requirements for each type of tertiary reserve are defined. Hydroelectric units’ constraints ∑
CR IP T
The above constraints state that the total energy produced by each hydro unit at a daily level must be between a minimum and a maximum limit. )
(
)
AN US
(
Constraints (36), (37) and (38) describe the operation of hydroelectric units and are proportional to the constraints (21), (22) and (24) for the thermal units. Hydroelectric units can enter almost immediately into the network without having to ). In addition,
M
go through the synchronization and soak phases (
their desynchronization phase lasts only for a very short period of time and for this
very short time (
ED
reason they have the ability to change their power output from any value to zero in a ). Finally, hydroelectric units are not able to contribute to a
PT
primary reserve and therefore the continuous variable
is not introduced into
CE
the constraint (38).
AC
The above constraint defines a limitation in energy transfer between interconnected systems. Therefore, there is a cap on the maximum electricity flow between interconnected systems.
Equation (40) specifies that the output power of each renewable unit is equal to the product of its nominal capacity availability of each renewable unit
with the parameter
, accounting for the
in each period of time
22
.
ACCEPTED MANUSCRIPT The overall problem is formulated as a Mixed-Integer Linear Programming problem (MILP), involving the cost minimization objective function (1) subject to constraints (2)–(40).
4. Case study The applicability of the proposed model is illustrated using a representative case
CR IP T
study, the main characteristics of which are presented below. More specifically, five power systems (s1-s5) have been considered, the detailed interconnection structure of which is provided in Table 1. It can be observed that the majority of them are interconnected among each other, with the exception of combinations s1-s4 and s3s5. For simplicity reasons, the transmission losses are assumed to be zero.
s1
M
200 400 500
s2
s3
s4
s5
200 250 150 300
400 250 250 -
150 250 250
500 300 250 -
ED
Interconnected systems s1 s2 s3 s4 s5
AN US
Table 1: Interconnection capacity and structure among the power systems (MW)
Figure 1 depicts the installed capacity per technology type in each power system.
PT
System 1 (s1) consists of seven units with a total installed capacity of 1900 MW, of which natural gas combined cycle (NGCC) units account for the largest part with an
CE
installed capacity of 850 MW, lignite-fired units follow with 650 MW, hydroelectric units have a capacity of 250 MW, and finally there is one natural gas-fired open-cycle
AC
gas turbine (NGGT) with a capacity of 150 MW. System 2 (s2) includes five units with a total installed capacity of 1800 MW, of which NGCC represent 850 MW of the total installed capacity, lignite-fired units amount to 650 MW, and renewable units’ capacity equals 300 MW. System 3 (s3) incorporates five units with a whole capacity of 1200 MW, four of which are hydroelectric with a total capacity of 750 MW, and one is NGCC unit with a capacity of 450 MW. Seven units are installed in System 4 (s4) amounting to 1750 MW, wherein lignite-fired units are the dominant technology with a total capacity of 1300 MW, followed by hydroelectric units with 250 MW and 23
ACCEPTED MANUSCRIPT renewables with 200 MW. Finally, System 5 (s5) constitutes the largest system among those examined, with a cumulative capacity of 2700 MW. 1200 MW of them are renewable units, while the remaining 1500 MW is allocated to NGCC units. 3000
2500
CR IP T
MW
2000 1500
500 0
s1 Lignite-fired units
s2 NGCC units
AN US
1000
s3
NGGT units
s4
Hydroelectric units
s5 Renewables
M
Figure 1: Installed capacity per technology type in each power system (MW)
ED
7000
4000
CE
MW
5000
PT
6000
3000
AC
2000
1000
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s1
s2
s3
s4
s5
Figure 2: Hourly electricity demand of each power system (MWh)
24
ACCEPTED MANUSCRIPT
40% 35% 30%
(%)
25%
20%
10% 5% 0%
CR IP T
15%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s4
s5
AN US
s2
Figure 3: Renewables availability in each power system (%)
Figure 2 depicts a typical daily (24-h) profile for each of the examined power systems. System 5 is characterized by the highest demand, being equal to 34,053
M
MWh at a daily level, and followed by System 1 (28,738 MWh), System 4 (24,122 MWh), System 2 (22,703 MWh), and System 3 (11,350 MWh). The corresponding
ED
daily peaks for each system are 1744, 1453, 1235, 1162, and 581 MW respectively. In all cases, this peak is reported during the 22th hour of the day considered. Figure 3
PT
presents the availability factor of the renewables installed in each power system (s2, s4, and s5). Note that the type of renewables installed in each system is mainly wind
CE
turbines, having a daily average factor of around 24% in System 2, 29% in System 4, and 19% in System 5, reflecting the different meteorological conditions of each
AC
system.
As discussed in Sections 2 and 3, each hydroelectric unit is characterized by a minimum and a maximum non-priced electricity generation to be allocated to the system. Since it is non-priced, it is given priority when entering the system. Note that non-priced electricity generation means that this part of power generation is mandatory, does not have a price and is given total priority when entering the system. In practice, it reduces the net load (subtracting non-priced electricity generation from the total power load) to be satisfied by the remaining priced 25
ACCEPTED MANUSCRIPT electricity generation. The exact time allocation of that contribution is determined by the optimization process. Figure 4 highlights the minimum and maximum daily
CR IP T
2000 1800 1600 1400 1200 1000 800 600 400 200 0
AN US
MWh
hydroelectric generation per unit installed in each power system.
Hydro - 1Hydro - 2Hydro - 3Hydro - 4Hydro - 5Hydro - 6Hydro - 7Hydro - 8 s1
s1
s3
s3
s3
Emin
Emax
s3
s4
s4
ED
33 32 31 30 29 28 27 26 25 24 23 22 21 20
PT
450 400 350 300 250 200 150 100 50 0
AC
CE
MW
system (MWh)
€/MW
M
Figure 4: Minimum and maximum daily hydroelectric generation per unit and power
Lignite-1 Lignite-2 Lignite-3 Lignite-4 Lignite-5 Lignite-6 Lignite-7 Lignite-8
s1 f1 (MW) f1 (€/MW)
s1
s2 f2 (MW) f2 (€/MW)
s2
s4 f3 (MW) f3 (€/MW)
s4
s4 f4 (MW) f4 (€/MW)
s4 f5 (MW) f5 (€/MW)
Figure 5: Quantity-price pair per block for each lignite-fired unit in each power system
26
ACCEPTED MANUSCRIPT The power capacity of each thermal unit is divided into capacity blocks (five in our case, f1-f5), from its technical minimum to its maximum, each of which is characterized by a specific marginal cost (energy supply function of each thermal unit). Figure 5 portrays the quantity-price pair per block for each lignite-fired unit in each power system wherein they are installed. The first block (f1) of each unit is its technical minimum in all cases. It can be observed that the lowest price in the first
CR IP T
block (f1) of all units equals 24 €/MW (Lignite-8 unit, installed in s4), while the most expensive one in the last block (f5) amounts to 32 €/MW (Lignite-2 unit, installed in s1). In general, lignite-fired units are suitable for base-load operation and comprise the most economical power generation technology among the thermal units.
Figure 6 portrays the corresponding quantity-price pair per block for each NGCC unit
AN US
in each power system wherein they are installed. The first block (f1) of each units is its technical minimum in all cases. It can be observed that the lowest price in the first block (f1) of all units equals 35.7 €/MW (NGCC-9 unit, installed in s5), while the most expensive one in the last block (f5) amounts to 55 €/MW (NGCC-2 unit, installed in
M
s1). In general, NGCC units are suitable for both base-load and intermediate load operation, and comprise the most environmentally friendly power generation
ED
technology among the thermal units. Since the natural gas does not comprise a domestic fuel in most of the power systems, its significant price deviation in the
PT
examined power systems reflects the different natural gas supply cost in each of the
AC
CE
examined power systems (country).
27
57 54 51 48 45 42 39 36 33 30
€/MW
500 450 400 350 300 250 200 150 100 50 0
CR IP T
MW
ACCEPTED MANUSCRIPT
NGCC-1 NGCC-2 NGCC-3 NGCC-4 NGCC-5 NGCC-6 NGCC-7 NGCC-8 NGCC-9 s1
s1
s2
s2
s3
s5
s5
s5
s5
f2 (MW)
f3 (MW)
f4 (MW)
f5 (MW)
f1 (€/MW)
f2 (€/MW)
f3 (€/MW)
f4 (€/MW)
f5 (€/MW)
AN US
f1 (MW)
Figure 6: Quantity-price pair per block for each natural gas combined cycle unit in each power system
Focusing on some specific technical characteristics per technology type, Figure 7
M
depicts some representative time-related technical characteristics per technology type, including minimum up and down times, as well as synchronization, soak, and
ED
desynchronization times. Lignite-fired have the advantage of low operating costs but they are characterized by particularly long start-up (synchronization, soak) and shut-
PT
down (desynchronization) times. Consequently, due to their high start-up costs, the frequent shut-downs and start-ups of the lignite-fired units are avoided, and
CE
therefore, they operate 24 hours a day with small deviations to cover the base load. This is the reason why they are characterized by noticeable minimum-up and down
AC
times.
The intermediate load (or load-following) power units are the NGCC units designed to cover the variable load of the grid. The processes for the start-up and the shutdown of these units are less time-consuming than those of lignite-fired units (lower minimum up and down times than the corresponding ones of lignite-fired units), so these units may be available shortly after their start-up (low synchronization, soak, and desynchronization times).
28
ACCEPTED MANUSCRIPT The peak-load units consist of NGGT and diesel units, the operating costs of which are particularly high, but they have very low start-up and shut-down times (zero synchronization, soak, and desynchronization times). For this reason, these units are typically used during few hours throughout the year, when peaks are observed in the load, and then they are typically out of order (very low minimum up and down times). Hydroelectric units are also included in this category.
CR IP T
9 8 7
Hours
6 5 4
2 1 0 Minimum-up time Minimum-down time
Synchronization time
NGCC
NGGT
Soak time
Desynchronization time
Hydro
M
Lignite
AN US
3
Figure 7: Representative time-related technical characteristics per technology type
ED
(h)
Figure 8 presents representative ramp limits per type of operation (dispatch phase
PT
and operation under automatic generation control) and technology type. Hydroelectric units exhibit high ramp-up and down rates of their power output, as
CE
well as extremely short start-up and shut-down times (zero synchronization, soak, and desynchronization times). These two features make hydropower plants ideal for
AC
entering the system to meet the needs of the network during peak hours. The extremely low ramp rates of the lignite-fired units can be also observed in this Figure, reflecting the fact that this technology is ideal for base-load operation. Note also that these units cannot operate under automatic generation control (system for adjusting the power output of various generators at different power units, as a response to load variations and disturbances). On the other hand, NGCC units can be utilized as load following units (during sudden changes of electricity demand), since
29
ACCEPTED MANUSCRIPT they are characterized by noticeable ramp rates, in both dispatch phase and operation under automatic generation control. 120
80 60 40 20 0 Ramp-up rate
Lignite
NGCC
Ramp-down rate- Ramp-up rate-AGC AGC
NGGT
Hydro
AN US
Ramp-down rate
CR IP T
MW/min
100
Figure 8: Representative ramp limits per type of operation and technology type (MW/min)
M
5. Results and Discussion
This section provides the results and a detailed discussion of the model
ED
implementation for the illustrative case study that has been considered. The problem has been solved to global optimality making use of the ILOG CPLEX 12.6.0.0
PT
solver incorporated in the General Algebraic Modeling System (GAMS) tool (GAMS, 2017). The size of the model is 77,157 single equations, 59,390 single variables, and
CE
21,820 discrete variables. The solution time is approximately 20 CPU sec.
AC
5.1. Power generation composition Initially, the problem is solved taking into account the interconnections of the systems. The model determines the power output of each unit separately for each hour of the dispatch day. Figure 9 highlights the total power produced by each system throughout the dispatch day in the cases with (With INT) and without interconnections (Without INT) among each other, respectively. The results are provided per technology type.
30
ACCEPTED MANUSCRIPT
40000 35000 30000
MWh
25000 20000 15000
5000 0
CR IP T
10000
With Without With Without With Without With Without With Without INT INT INT INT INT INT INT INT INT INT s1
s2 Lignite
s2 NGCC
s3 NGGT
s3 s4 s4 Hydro RES
s5
s5
AN US
s1
Figure 9: Total energy produced by each technology type in each system throughout the dispatch day in the cases with (With INT) and without interconnections (Without INT) among each other (MWh)
M
From that figure and focusing on the case where the interconnections are incorporated (With INT), it seems that base-load (lignite-fired) units account for the
ED
largest share of the total electricity generation, while an equally large part of the total production emanates from load-following units (NGCC units). No electricity is
PT
generated by peak-load units (NGGT units), which is expected as peak-load units contribute generally a small amount of energy to the system at an annual level.
CE
Therefore, peak-load units with high operating costs are not selected to operate and the load is covered from the other available units.
AC
System 4 (s4) produces the largest proportion of the base-load generation, since 4 of its total 7 units are lignite-fired. Correspondingly, System 5 (s5) produces the largest proportion of load following units, since it is mainly composed of NGCC units. On the other hand, in the case where interconnections are not taken into account (Without INT), it seems that the biggest part of the total electricity production comes from load-following units and not from base-load units (lignite-fired). This is due to
31
ACCEPTED MANUSCRIPT the fact that since there is no option for energy flows among the systems, each system is based on its own units to meet its load demand. Regarding the power contribution from lignite-fired and NGCC units, it can be summarized that: Lignite-fired power generation decreases by 5% in s1, increases by 12% in s2,
alone to that of the interconnection.
CR IP T
and rises by 29% in s4, when the systems move from the state of being stand-
NGCC power generation decreases by 93% in s1, increases by 37% in s2, reduces by 7% in s3, and falls by 9% in s5, when the systems move from the state of being stand-alone to that of the interconnection.
AN US
The amount of electricity generation coming from renewables and hydroelectric units is identical in both cases, on the grounds that they have zero operational cost and they are given priority when entering the power system.
From that figure, some general conclusions can be derived on the energy flow
M
between the examined systems, based on the following:
System 1 (s1): Reduction of total electricity production by 47.5%.
ED
System 2 (s2): Increase of the total electricity production by 22%. System 3 (s3): Reduction in total power generation by 4.3%.
PT
System 4 (s4): Increase of the total electricity production by 26%.
CE
System 5 (s5): Increase of the total electricity production by 8%. Not surprisingly, it can be expected from the results that systems 1 and 3 are going
AC
to import energy so as to cover their demand in the case with interconnections considered. 5.2. Energy flows among systems When solving the model, the continuous variable
receives non-zero values
only if there is an interconnection among the systems. This variable expresses the amount of energy transferred between the systems. Thus, from the solution of the model, Table 2 presents the energy flows among the systems in presence of interconnections. 32
ACCEPTED MANUSCRIPT Table 2: Total daily energy flows among the systems in presence of interconnections (MWh)
s5 584 2811 -
CR IP T
Systems that export energy (MWh)
Systems that import energy (MWh) System s1 s2 s3 s4 s1 s2 4475 263 s3 2881 s4 338 3108 s5 6132 -
In Table 2, there are dashes (-) in some cells, denoting that these power flows cannot be implemented. These prohibited interconnections concern logical constraints due to initial conditions that prohibit the flow of energy from a system to itself. In
AN US
addition, prohibited interconnections arise due to the problem data (no interconnection between these systems). The non-zero values provide information about the exact amount of energy transferred between the systems. As can be observed in Table 2, it appears that System 1 (s1) imports the largest
M
amount of energy (13488 MWh), while systems 3 and 5 import approximately the same amount of energy, i.e., 3371 and 3395 MWh respectively. From the analysis
ED
made at section 5.1, it was concluded that systems 1 and 3 would definitely import energy. Although that conclusion was true, it can be also noticed that system 5
PT
imports energy, as well as a minimal (almost negligible) amount of energy is imported to system 2 (338 MWh). Although these two systems import energy, the
CE
energy they export to system 1 is greater, which converts them into net exporters and transit systems.
AC
Figure 10 highlights the hourly energy flows among the interconnected systems at a daily level. It can be seen that they are at relatively low levels during the first hours of the day where the electricity demand in each system is at low levels, while they approach and/or exceed the level of 1000 MWh after the 7 th hour of the examined day.
33
ACCEPTED MANUSCRIPT
0
200
AN US
CR IP T
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
400
From s2 To s1 From s4 To s2
600 MWh
From s2 To s3 From s4 To s3
800
From s2 To s5 From s4 To s5
1000
1200
From s3 To s1 From s5 To s1
M
Figure 10: Hourly energy flows among the interconnected systems (MWh)
ED
Figure 11 depicts the interconnection structure and the total daily electricity trade among the interconnected systems. As it can be observed, system s4 is interconnected with systems s3, s2, and s5, system s3 is interconnected with s1, s2,
PT
and s4, system s2 has interconnection with s1, s3, s4, and s5, as well as the system s5 with s1, s2, and s4. Finally, system s1 has interconnection with the systems s2, s3,
CE
and s5.
AC
Although there are some hourly differentiations, systems s2, s4, and s5 constitute net exporters in total, while systems s1 and s3 represent net importers. More specifically, system s1 reports a large production deficit, while system s3 has a more balanced mix and acts mainly as a transit system for electricity exports to the system s1. The main conclusions arising from the results presented in Table 2 are the following:
34
ACCEPTED MANUSCRIPT System s4 exports electrical energy to its neighboring systems s2, s3, and s5 which act (s4 -> s2, s4 -> s3, and s4 -> s5). Systems s2 and s5 export the amount of electricity they import from system s4, i.e. they act as transit systems (s4 -> s2 -> s1, s4 -> s5 -> s1), along with their production surplus, to system s1 (s2 -> s1, s5 -> s1). As a consequence, they are both transit systems and power exporters.
CR IP T
Due to transmission congestion during some hours of the studied period in the interconnection capacity between systems s2 and s1 (the interconnector reaches its maximum limit, from s2 to s1), system s2 exports some amount of electricity to the system s5, which is then transmitted again to the system s1 (s2 -> s5 -> s1). Note that the interconnection capacity between systems s5
AN US
and s1 is higher than the corresponding between the systems s2 and s1. As a consequence, system s5, apart from being a net exporter of its production surplus to the system s1 (s5 -> s1), acts as a transit system for the electricity transmission from both systems s4 (as analyzed above) and s2 to the system s1.
M
System s3 is characterized by a balanced mix, since it produces around 96%
ED
of its own demand. In order to meet its deficit, it imports electrical energy from systems s2 and s4. Since the amount of the imported electricity from system s4 exceed its requirements, it acts as a transit system for its
PT
transmission to the system s1. As a consequence, it acts as a net importer
CE
from the system s2 (s2 -> s3), and a transit system (s4 -> s3 -> s1). System s1 constitutes a net importer directly from system s5 (s5 -> s1), and indirectly
AC
from the system s4 through the three possible routes (s4 -> s2 -> s1, s4 -> s3 -> s1, and s4 -> s5 -> s1).
35
AN US
CR IP T
ACCEPTED MANUSCRIPT
Figure 11: Interconnection structure and total daily electricity trade among the interconnected systems (MWh) 5.3. System marginal price
M
Figure 12 shows that the system’s marginal price remains relatively stable throughout the day for systems 2-5 (s2, s3, s4, and s5). In particular, on average, the
ED
marginal price of system 4 is around 25 €/MWh, which is the lowest price compared to the other systems. The marginal prices of systems 2 and 5 are around 28 €/MWh
PT
and 37 €/MWh correspondingly (daily average). The marginal price of system 3 remains constant throughout the examined period at 47.7 €/MWh. These values are
CE
fully consistent with the data used, since the system's marginal price is based on the energy supply offer of each unit, which in this problem is expressed by the .
AC
parameter .
In contrast, the marginal price of system 1 reports significant variations during the day. Specifically, up to 8th hour of the day, the marginal price is set at around 30 €/MWh, while during the 9th hour of the day, the system’s marginal price rises to 52 €/MWh and remains relatively stable for the rest of the day.
36
ACCEPTED MANUSCRIPT
55
50
€/MWh
45 40
35 25
20
CR IP T
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s2
s3
s4
s5
AN US
s1
Figure 12: Hourly marginal price of each system in the case without interconnections (€/MWh) Figure 13 highlights the hourly marginal prices of each system in the case with interconnections. According to that figure, all systems have an approximately
M
constant marginal value up to the 7th hour of the day. Then, there is an increase up to the 9th hour of the day, being stabilized until the 16th hour of the day. During the
ED
time period between the 18th and the 20th hour of the day, a marginal price change is observed, while it is stabilized again until the 23th hour of the day. Finally, there is a
PT
fall in its value during the 24th hour of the day. The daily average values are 37.4 €/MWh for System 1, 35.6 €/MWh for System 2, 36.4 €/MWh for System 3, 35.4
AC
CE
€/MWh for System 4 and, 36.4 €/MWh for System 5.
37
ACCEPTED MANUSCRIPT
50
€/MWh
45
40 35 30
20
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25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time period (h)
s1
s2
s3
s4
s5
AN US
Figure 13: Hourly marginal price of each system in the case with interconnections (€/MWh) The trends depicted in Figure 13 show great differences with respect to those of Figure 12. In Figure 13 where interconnections among the systems are incorporated, it can be observed that all systems have the same shape throughout the day. The
M
existence of interconnections between some systems may lead to a significant degree of convergence among the systems’ prices. As expected on the basis of
ED
economic theory, an increase of the marginal price is reported in the systems characterized by net electricity exports, since there is an increase in their total
PT
electricity production, utilizing more expensive power generation sources. On the other hand, systems characterized by net electricity imports show a fall in their
CE
respective marginal prices, on the grounds that they gain access in more economical power generation sources.
AC
In particular, in systems 1 and 3, which are characterized by net electricity imports, there is a decrease in the average values of their marginal prices of the order of 17% and 23%, respectively. In the opposite way, in systems 2 and 4, characterized by net electricity exports, there is an increase in the average values of their marginal prices of the order of 27% and 41%, respectively. The average values of the marginal prices of system 5 in both cases remain stable at 36 €/MWh, since this system has more than enough capacity to meet its own demand and export additional energy at uniform and highly competitive prices. 38
ACCEPTED MANUSCRIPT 5.4. Operational scheduling Figures 14 and 15 highlight the operational scheduling of power systems 1 and 4 in the cases with and without interconnections. Each box corresponds to a specific power unit (of a certain technology type) and hourly time period. There are five possible operational phases of a hydrothermal unit: 1. Operation in the synchronization phase (only for thermal units)
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2. Operation in the soak phase (only for thermal units)
3. Operation in the dispatch phase (both for thermal and hydroelectric units) 4. Operation in the desynchronization phase (only for thermal units)
5. The units have been shut-down, so they are offline (both for thermal and
AN US
hydroelectric units)
With interconnections
System 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite -1 Lignite -2
M
NGCC-1 NGCC-2
ED
NGGT Hydro-1 Hydro-2
Synchronization
Soak
Dispatch
PT
Without interconnections
System 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite -1
Desynchronization
CE
Lignite -2 NGCC-1 NGCC-2
Offline
AC
NGGT
Hydro-1 Hydro-2
Figure 14: Operational scheduling of power system 1 in cases with and without interconnections
39
ACCEPTED MANUSCRIPT
With interconnections System 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Synchronization
Lignite-5 Lignite-6 Lignite-7
Soak
Lignite-8 Hydro-7 Hydro-8
Dispatch
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Without interconnections System 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Lignite-5
Desynchronization
Lignite-6 Lignite-7 Lignite-8
Offline
Hydro-7
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Hydro-8
Figure 15: Operational scheduling of power system 4 in cases with and without interconnections The results presented in section 5.1 underscored that there will be a reduction in the total electricity production of system 1 by 47.5%, while there will be an increase in
M
the total electricity production of system 4 by 26%, when the systems move from the
ED
state of being stand-alone to that of the interconnection. With regard to system 1, this trend is clearly depicted in Figure 14 where the main
PT
finding is that the NGCC units do not operate in the case with the interconnections available, since the model determines that they are not enough cost-competitive in
CE
the presence of other available power generation sources. However, there was full utilization of them in the case without interconnections, in the absence of other
AC
available power generation sources. With reference to system 4, the expected increase of the total electricity production is justified by the more intense utilization of one more lignite-fired unit in the case with interconnections, which was shut-down in the case without interconnections, as depicted in Figure 15. This additional amount of electricity generation is going to be exported to other interconnected systems, which lack more economical sources of electricity generation. 5.5. Sensitivity analysis 40
ACCEPTED MANUSCRIPT This section presents a sensitivity analysis performed by varying the interconnection capacities between the interconnected systems each time. The analysis is within ± 50% of the reference values, with a ± 10% increment step each time. The results relate to the energy produced by each system presented per technology type. Table 3 provides the results of the analysis implemented for the interconnection capacity increase case.
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As can be seen in Table 3, it seems that with an increase in the maximum value of the interconnections capacities of the examined systems, no significant variations in the electricity produced by the units is observed. To sum up, regardless of how large the maximum allowable value of the electricity flow between the systems is, the
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results of the mathematical model are identical.
Table 4 presents the sensitivity analysis results for the interconnection capacity decrease case. From Table 4, it appears that for a reduction with a range of up to 40% in the interconnections capacities of the systems under consideration, no substantial difference is reported in the results. However, for a 50% reduction, it can
M
be noticed that there is an increase in the total power output of system 1, and a corresponding reduction in the system 2. As the value of the interconnection
ED
capacity decreases, for a reduction of more than 50%, the power output results tend
other.
PT
to approach those of the case in which the systems are not interconnected with each
CE
The differences are due to the fact that as the available capacity of the interconnection decreases, each system generates more energy at a domestic level to meet its load demand, regardless of the applied operating costs. Therefore, at low
AC
interconnection capacity rates, System 1 produces an additional amount of electricity from load following (NGCC) units rather than from base-load (lignite-fired) units.
Correspondingly, when the available capacity of the interconnection increases, a system with high operating costs is expected to reduce the total energy generated domestically, as there is the option for importing electricity from other systems at more affordable costs. 41
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ACCEPTED MANUSCRIPT
Table 3: Sensitivity analysis results for the interconnection capacity increase case Lignite
NGCC
NGGT
Hydro
RES
20%
Lignite
NGCC
NGGT
Hydro
RES
s1
13185
935
-
770
-
s1
13185
935
-
770
-
s2
12460
13493
-
-
1734
s2
12460
13493
-
-
1734
s3
-
6240
-
4620
-
s3
-
6240
-
4620
-
s4
28092
-
-
900
1387
s4
28092
-
-
900
1387
s5
-
32167
-
-
4624
s5
-
32167
-
-
4624
30%
Lignite
NGCC
NGGT
Hydro
RES
40%
Lignite
NGCC
NGGT
Hydro
RES
s1
13177
935
-
770
-
s1
13120
935
-
770
-
s2
12475
13493
-
-
1734
s2
12679
13493
-
-
1734
s3
-
6240
-
4620
s4
28084
-
-
900
s5
-
32167
-
-
50%
Lignite
NGCC
NGGT
Hydro
s1
13120
935
-
770
s2
12679
13493
-
-
s3
-
6240
s4
27937
s5
-
-
6240
-
4620
-
s4
27937
-
-
900
1387
4624
s5
-
32167
-
-
4624
RES
Reference case
Lignite
NGCC
NGGT
Hydro
RES
-
s1
13185
935
-
770
-
1734
s2
12460
13493
-
-
1734
ED
M
s3
1387
4620
-
s3
-
6240
-
4620
-
-
900
1387
s4
28092
-
-
900
1387
32167
-
-
4624
s5
-
32167
-
-
4624
PT
-
-
CE AC
-
AN US
10%
42
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ACCEPTED MANUSCRIPT
Table 4: Sensitivity analysis results for the interconnection capacity decrease case Lignite
NGCC
NGGT
Hydro
RES
-20%
Lignite
NGCC
NGGT
Hydro
RES
s1
13185
935
-
770
-
s1
13185
935
-
770
-
s2
12460
13493
-
-
1734
s2
12460
13493
-
-
1734
s3
-
6240
-
4620
-
s3
-
6240
-
4620
-
s4
28092
-
-
900
1387
s4
28092
-
-
900
1387
s5
-
32167
-
-
4624
s5
-
32167
-
-
4624
-30%
Lignite
NGCC
NGGT
Hydro
RES
-40%
Lignite
NGCC
NGGT
Hydro
RES
s1
13190
935
-
770
-
s1
13233
675
431
770
-
s2
12481
13493
-
-
1734
s2
12710
13219
-
-
1734
s3
-
6240
-
4620
s4
28066
-
-
900
s5
-
32167
-
-
-50%
Lignite
NGCC
NGGT
Hydro
s1
13481
5618
-
770
s2
12866
6975
-
-
s3
-
7211
s4
28040
s5
-
-
6240
-
4620
-
s4
28061
-
-
900
1387
4624
s5
-
32003
-
-
4624
RES
Reference case
Lignite
NGCC
NGGT
Hydro
RES
-
s1
13185
935
-
770
-
1734
s2
12460
13493
-
-
1734
ED
M
s3
1387
4620
-
s3
-
6240
-
4620
-
-
900
1387
s4
28092
-
-
900
1387
32380
-
-
4624
s5
-
32167
-
-
4624
PT
-
-
CE AC
-
AN US
-10%
43
ACCEPTED MANUSCRIPT
6. Conclusions This work extends our previous contributions in the area of power generation expansion planning by proposing an integrated optimization framework for the optimal daily scheduling of interconnected power systems. In this problem which is also referred to as unit commitment problem in the literature, a set of power systems with their own power generating units of various technology types are
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considered. Key model decisions include the production of energy by the various systems, the energy flow among them, their operational scheduling, as well as the resulting marginal price of each system.
A salient feature of the proposed framework is the detailed modelling of the
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different operational phases of the power generation units (synchronization, soak, dispatch, and desynchronization phase), power output limitations of the units, as well as ramp rates of the units. The objective is to optimally cover the electricity demand of all systems in a cost optimal way, while at the same time satisfying a
M
series of technical, economic and other logical constraints.
The applicability of the proposed framework has been tested using an illustrative
ED
case study. Emphasis is placed on considering potential interconnection options among the examined systems. Furthermore, a sensitivity analysis has been
PT
performed to investigate the impacts of the interconnection capacities on the resulting production mix.
CE
The results highlight that when the systems under consideration are not interconnected, each system meets its own electricity demand based on its locally
AC
installed units. On the other hand, if interconnection options are available, transmitting electricity from low-cost generation systems to systems with higher operating costs is the most economically attractive option. A more general conclusion that can be drawn is that cross-border electricity trade can reduce the overall cost of generating electricity to wider regions and unions, leading to price convergence of individual systems and enhancing their overall competitiveness. At the same time, it can also serve as price-signal to future investments in new power generation technologies to be installed in each system. 44
ACCEPTED MANUSCRIPT
Appendix Nomenclature Sets/Indices installed in each power system
Set including power systems
which are interconnected with
CR IP T
Set of power generating units
other power systems
according to a specific network
structure
Set of the distinct steps of each unit marginal cost function
AN US
Set of power generating units Set of considered power systems Set of hourly time periods
M
Subsets
Subset of hydroelectric units
ED
Subset of hydrothermal units
Subset of renewable energy units
Parameters
PT
Subset of thermal units
AC
CE
Availability of each renewable unit period
in each time
(%)
Nominal interconnection capacity between interconnected power systems
and
,
(MW)
Electricity demand of each power system period
in time
(MW)
Quantity of each power capacity block offer function of each power generating unit Marginal cost of each power capacity block
of the energy (MW) of the
energy offer function of each power generating unit
45
ACCEPTED MANUSCRIPT (€/MW) Maximum daily electricity generation from all hydroelectric units
(MWh)
Minimum daily electricity generation from all hydroelectric units
(MWh)
Shut-down cost of each power unit
(€)
Start-up cost of each power unit
(h)
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Minimum down time of each power unit (€)
Minimum up time of each power unit
(h)
Additional cost of each power unit period
in each time
, when providing primary reserve (€/MW)
reserve (MW)
AN US
Maximum contribution of each power unit
Power output of each power unit
in primary
at the beginning of
the time horizon under consideration (MW)
M
Technical maximum of each power unit
, when
operating under automatic generation control (MW) (MW)
ED
Technical maximum of each power unit Technical minimum of each power unit
, when
PT
operating under automatic generation control (MW) Technical minimum of each power unit
AC
CE
Power output of each power unit
(MW) during soak phase
(MW) Ramp-down rate of each power unit
(MW/min)
Ramp-down rate of each power unit
, when operating
under automatic generation control (MW/min) Requirements of system time period
(MW)
Requirements of system time period
in primary-down reserve at
in primary-up reserve at
(MW)
Requirements of system
in secondary-down reserve 46
ACCEPTED MANUSCRIPT at time period
(MW)
Requirements of system time period
in secondary-up reserve at
(MW)
Requirements of system
in tertiary (spinning and
non-spinning) reserve at time period Ramp-up rate of each power unit
(MW) (MW/min) , when operating
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Ramp-up rate of each power unit
under automatic generation control (MW/min) Additional cost of each power unit period
in each time
, when providing secondary reserve (€/MW)
Technology type of each power unit
(1, Lignite-fired
AN US
units, 2, Natural gas combined cycle units, 3, Natural gasfired open-cycle gas turbine units, 4, Hydroelectric units, 5, Renewables)
Additional cost of each power unit
, when providing tertiary spinning reserve
M
period
in each time
(€/MW)
ED
Maximum contribution of each power unit
in non-
spinning tertiary reserve (MW) Additional cost of each power unit
PT
period
in each time
, when providing tertiary non-spinning reserve
AC
CE
(€/MW) Number of operational hours of each power unit
at
the beginning of the time horizon under consideration (h) – positive number for units under operation and negative number for units being offline Desynchronization time of each power unit Soak time of each power unit
(h)
(h)
Synchronization time of each power unit
(h)
Continuous variables 47
ACCEPTED MANUSCRIPT Quantity of power capacity block of the energy offer function of each power unit cleared in time period
(MW)
Electricity flow between interconnected power systems and
,
in each time period
Total output of each power unit
(MW) in each time period
(MW) in each time period
,
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Total output of each power unit
when operating in desynchronization phase (MW) Total output of each power unit
in each time period
when operating in soak phase (MW) Contribution of power unit (MW)
Contribution of power unit time period
in primary-up reserve in each
(MW)
Contribution of power unit
Contribution of power unit
ED
in each time period
in tertiary non-spinning reserve
(MW)
Contribution of power unit
PT
in secondary-up reserve in each
(MW)
Contribution of power unit
in tertiary spinning reserve in
(MW)
CE
each time period
in secondary-down reserve in
(MW)
M
each time period
time period
in primary-down reserve in each
AN US
time period
,
AC
Binary variables
1, if power unit
shuts-down in each time period
1, if power unit
starts-up in each time period
1, if power unit
is operational in each time period
1, if power unit
provides non-spinning tertiary reserve in
each time period 1, if power unit
operates under automatic generation control
in each time period 48
ACCEPTED MANUSCRIPT 1, if power unit
operates in desynchronization phase in each
time period 1, if power unit
operates in dispatch phase in each time
period operates in soak phase in each time period
1, if power unit
operates in synchronization phase in each
CR IP T
1, if power unit
time period
MILP:
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Acronyms Mixed integer linear programming
NGGC: Natural gas combined cycle
NGGT: Natural gas-fired open-cycle gas turbine Automatic Generation Control
ED
M
AGC:
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