A stochastic MILP energy planning model incorporating power market dynamics

Applied Energy 205 (2017) 1364–1383

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A stochastic MILP energy planning model incorporating power market dynamics

MARK

⁎

Nikolaos E. Koltsaklisa,b, , Konstantinos Nazosa a b

Public Power Corporation S.A. (PPC), Department of Energy Management and Trading, 10436 Athens, Greece Energy & Environmental Policy Laboratory, School of Economics, Business and International Studies, University of Piraeus, 18532 Piraeus, Greece

H I G H L I G H T S MILP model for the optimal energy planning of a power system. • Stochastic market dynamics (offers/bids) are incorporated in the proposed model. • Power Carlo method for capturing the uncertainty of some key parameters. • Monte supply cost composition per power producer and activity. • Analytical • Clean dark and spark spreads are calculated for each power unit.

A R T I C L E I N F O

A B S T R A C T

Keywords: Energy planning Monte Carlo Dynamic energy offers Electricity trade CO2 emissions

This paper presents an optimization-based methodological approach to address the problem of the optimal planning of a power system at an annual level in competitive and uncertain power markets. More specifically, a stochastic mixed integer linear programming model (MILP) has been developed, combining advanced optimization techniques with Monte Carlo method in order to deal with uncertainty issues. The main focus of the proposed framework is the dynamic formulation of the strategy followed by all market participants in volatile market conditions, as well as detailed economic assessment of the power system’s operation. The applicability of the proposed approach has been tested on a real case study of the interconnected Greek power system, quantifying in detail all the relevant technical and economic aspects of the system’s operation. The proposed work identifies in the form of probability distributions the optimal power generation mix, electricity trade at a regional level, carbon footprint, as well as detailed total supply cost composition, according to the assumed market structure. The paper demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies designed by market participants, as well as on the strategic long-term decisions to be made by investors and/or policy makers at a national and/or regional level, underscoring potential risks and providing appropriate price signals on critical energy projects under real market operating conditions.

1. Introduction World gross electricity production has been risen from 6287 TWh to 23,815 TWh between 1974 and 2014, reporting an average annual growth rate of 3.4% [1]. Until the last two decades of the twentieth century, state-owned, vertically-integrated utilities were owners and responsible for the operation and management of the whole electricity supply chain, involving the sectors of electricity generation, transmission, distribution, and retail. Nowadays, in general, electricity markets foster competition in the generation and retail sectors, while transmission and distribution remain a monopoly managed by relevant

⁎

system operators [2]. The liberalization of the electricity markets along with the rapid penetration of renewables into the power systems have increased the complexity of the power systems operation, highlighting the importance of the robust and secure determination of the optimal electricity mix. Clò et al. [3] investigated how the ownership status is associated with the environmental performance in the European power industry. Their findings suggest that public ownership goes in line with the market-based environmental quality improvement, placing also emphasis on the limited impact of the European Emissions Trading Scheme. Puka and Szulecki [4] provided a discussion about the political and economic-related issues that influence possible investments and

Corresponding author at: Public Power Corporation S.A. (PPC), Department of Energy Management and Trading, 10436 Athens, Greece. E-mail address: [email protected] (N.E. Koltsaklis).

http://dx.doi.org/10.1016/j.apenergy.2017.08.040 Received 25 May 2017; Received in revised form 22 July 2017; Accepted 9 August 2017 Available online 19 September 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos

Nomenclature

availability factor of step f ∈ F of the priced energy offer of each hydroelectric unit i ∈ I h (p.u.) HBLi,f ,m,t capacity quantity of the energy offer function steps f ∈ F of each unit i ∈ I h during month m ∈ M and time period t ∈ T (MW) HOFi,f ,m,t priced energy offer cost function steps f ∈ F of each unit i ∈ I h during month m ∈ M and time period t ∈ T (€/MWh) Heating _Valuei heating value of the fuel used in each unit i ∈ I th (GJ/t for lignite-fired units and GJ/m3 for natural gas-fired units) IMAVint ,m availability factor of each importing cross-border electricity interconnection int ∈ INT imp during month m ∈ M (p.u.) IMOFint ,f ,m,t priced energy offer cost function steps f ∈ F of each importing cross-border electricity interconnection int ∈ INT imp during month m ∈ M and time period t ∈ T (€/MWh) INLs,m,t power grid injection losses coefficient in subsystem s ∈ S during month m ∈ M and time period t ∈ T (p.u.) Int _Capint ,f ,m,t capacity quantity of the energy offer (load bid) function steps f ∈ F of each importing (exporting) crossborder electricity interconnection int ∈ INT imp (int ∈ INT exp ) during month m ∈ M and time period t ∈ T (MW) Int _Capint power capacity of each cross-border electricity interconnection int ∈ INT Mat _Costi maintenance cost of each unit i ∈ I th (€/MWh) Max maximum value of the minimum average variMin _Var _CostLig able costs of all considered lignite-fired units (€/MWh) Min Min _Var _CostLig minimum value of the minimum average variable costs of all considered lignite-fired units (€/MWh) Max Min _Var _CostTh maximum value of the minimum average variable costs of specific thermal units (€/MWh) Min minimum value of the minimum average variable Min _Var _CostTh costs of specific thermal units (€/MWh) Min _Var _Costi minimum average variable cost of each unit i ∈ I th (€/MWh) PMBDpm,f ,m,t priced load bid function steps f ∈ F of each pumped storage unit pm ∈ PM during month m ∈ M and time period t ∈ T (€/MWh) PUBLpm,f ,m,t capacity quantity of the load bid function steps f ∈ F of each pumped storage unit pm ∈ PM during month m ∈ M and time period t ∈ T (MW) Pi,fix non-priced part of the energy offer function of each unit m,t i ∈ I during month m ∈ M and time period t ∈ T (MW) Pimax technical maximum of each unit i ∈ I (MW) Pimin technical minimum of each unit i ∈ I (MW) Rm _Costi raw material cost of each unit i ∈ I th (€/MWh) THBLi,f ,m,t capacity quantity of the energy offer function steps f ∈ F of each unit i ∈ I th during month m ∈ M and time period t ∈ T (MW) THOFi,f ,m,t priced energy offer cost function steps f ∈ F of each unit i ∈ I th during month m ∈ M and time period t ∈ T (€/MWh) Var _Costi variable (associated with fuel) cost of each unit i ∈ I th (€/MWh)

HAFi,f

Indices and sets set of Monte Carlo samples set of all units (thermal + hydroelectric + renewables) set of thermal units (lignite-fired + natural gas-fired) set of hydroelectric units set of hydrothermal units (thermal + hydroelectric) set of lignite-fired units set of natural gas-fired units set of renewable units (wind + photovoltaics + biomass + small hydroelectric + high-efficiency combined heat and power units) f∈F set of the energy (load) offer (bids) function steps of each hydrothermal, pumped storage unit and cross-border electricity interconnection int ∈ INT imp set of importing cross-border electricity interconnections int ∈ INT exp set of exporting cross-border electricity interconnections pm ∈ PM set of pumped storage units int ∈ INT set of cross-border electricity interconnections m∈M set of months t∈T set of hourly time periods s∈S set of domestic power grid subsystems i ∈ IS set of units i ∈ I installed in subsystem s ∈ S int ∈ INT s set of cross-border electricity interconnections int interconnected with subsystem s ∈ S

mc ∈ MC i∈I i ∈ I th i ∈ Ih i ∈ I ht i ∈ I lg i ∈ I ng i ∈ I rn

Parameters

Border _priceint average electricity price (at the market point) of each cross-border electricity interconnection int ∈ INT CFMi,m capacity factor of each unit i ∈ I th during month m ∈ M (p.u.) annual capacity factor of each pumped storage unit CFpm pm ∈ PM (p.u.) CO2_Costi average annual CO2 emissions cost of each unit i ∈ I th (€/MWh) CO2_Emis _Factori CO2 emissions factor of each unit i ∈ I th (tonne CO2/MWh) CO2_Emis _pricei average annual CO2 emissions allowances price (€/tonne CO2) COEFi,f ,m,t cost coefficient of each unit i ∈ I ht in step f of the energy offer function during month m ∈ M and time period t ∈ T (€/MWh) COEFint ,f ,m,t cost coefficient of each cross-border electricity interconnection int ∈ INT in step f of the energy offer (load bid) function during month m ∈ M and time period t ∈ T (€/MWh) Demm,t total electricity demand during month m ∈ M and time period t ∈ T (MW) duration of each representative day of each month m ∈ M Durm (days) EXAVint ,m availability factor of each exporting cross-border electricity interconnection int ∈ INT exp during month m ∈ M (p.u.) EXBDint ,f ,m,t priced load bid function steps f ∈ F of each exporting cross-border electricity interconnection int ∈ INT exp during month m ∈ M and time period t ∈ T (€/MWh) thermal efficiency of each unit i ∈ I th (%) max F total number of the set of the energy offer (bids) function steps of each hydrothermal, pumped storage unit and cross-border electricity interconnection Fuel _Costi fuel cost of each unit i ∈ I th (€/t for lignite-fired units and €/m3 for natural gas-fired units)

Continuous variables

bpi,f ,m,t bimint ,f ,m,t

bex int ,f ,m,t

bppm,f ,m,t 1365

quantity of power capacity step f ∈ F of unit i ∈ I ht cleared during month m ∈ M and time period t ∈ T (MW) quantity of power capacity step f ∈ F of importing crossborder electricity interconnection int ∈ INT imp cleared during month m ∈ M and time period t ∈ T (MW) quantity of power capacity step f ∈ F f of exporting crossborder electricity interconnection int ∈ INT exp cleared during month m ∈ M and time period t ∈ T (MW) quantity of power capacity step f ∈ F of pumped storage

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos

COM

unit pm ∈ PM cleared during month m ∈ M and time period t ∈ T (MW)

DOM IND IPP MILP SUF TRN

Binary variables

x i,m,t

1, if power unit i ∈ I ht is operational during month m ∈ M and time period t ∈ T

Acronyms CHP

second group of the cross-border electricity interconnections dominant power company first group of the cross-border electricity interconnections independent power producers mixed integer linear programming sufficient domestic generating capacities transit countries

combined heat and power

[19] provided an analysis of price and quantity risk hedging and management strategies in power markets from the perspective of electricity retailers, underlining the importance of intraday portfolios over daily ones. In the same context, Conejo et al. [20] proposed a stochastic mixed integer linear programming model in order for an electricity producer to determine the optimal selection of forward contracts as a hedge against the volatility of the electricity spot prices. Finally, Meunier [21] implemented an analysis investigating the effects of riskaversion and risk-neutral strategies on the electricity technology mix, consisting of base-load units with fixed variable cost and peak-load plants with uncertain variable cost. With respect to the power systems’ future evolution and its impact on the resulting power mix, Pattupara and Kannan [22] made use of the Swiss TIMES electricity model in order to examine possible long-term pathways of the Swiss electricity systems under different CO2 emission scenarios. The authors stressed emphasis on the trade-off between coal and natural gas, as well as on the interaction between renewables and electricity trade when considering nuclear capacities phase-out. Similarly, Totschnig et al. [23] made use of a simulation model and examined, through scenarios in the Austrian and German systems, the impact of climate change and fuel price shocks on the power generation cost and capacities. Rodriguez et al. [24] proposed a methodological framework so as to evaluate the optimal design of a power system with significant penetration of renewables and stressed the interaction between backup, transmission and renewables’ capacities with the resulting levelized cost of energy, as well as Farnoosh et al. [25] presented a scenario-based analysis in order to examine the consequences of a transition from a fossil fuel dominant (i.e., oil) towards a lower carbon power generation mix in an oil exporting country (i.e., Saudi Arabia). In the same context, Ryu et al. [26] examined possible scenarios for the power generation mix of Korea and Mongolia, focusing on three different aspects, including carbon emissions reduction targets, energy security and electricity generating costs. Focusing on the renewables’ penetration impacts on the power systems, Cleary et al. [27] implemented a scenario-based analysis with the aim of capturing the effects of large scale wind installations in the power systems of the UK and Ireland, in terms of wholesale system marginal prices, electricity generation costs and CO2 emissions. Norvaiša and Galinis [28] discussed about the alternatives of the future evolution of the Lithuanian power system, underscoring the importance of electricity imports in terms of economic competitiveness, and that of the domestically installed capacities in terms of energy security. Sharifzadeh et al. [29] developed a mixed integer linear programming model so as to determine the optimal design and operation of a power grid with high renewables’ penetration through stochastic scenario generation. Also, Li and Trutnevyte [30] examined scenario pathways so as to evaluate the total investment cost requirements of the UK electricity sector by 2050, spotlighting the increased investments required in carbon mitigation cases. Moreover, Cucchiella et al. [31] applied a portfolio analysis to evaluate the economic performance of investments in a series of capacities of renewable energy technologies. Brand and Missaou [32] presented a methodological approach in order to assess, through

expansion of the transmission grid, including cross-border electricity interconnections. The literature is rich in works dealing with the problem of the optimal determination of the power mix in a given power system, involving or not the additional problems of generation and/or transmission expansion planning. Amrutha et al. [5] developed a linear programming model so as to identify the optimal annual generation mix of a given power system considering some renewables policy measures. A similar approach was also proposed by De Jonghe et al. [6], featuring the impacts of the operational constraints inclusion. Furthermore, Sithole et al. [7] provided an analysis in order to determine the optimal future power generation mix of the UK, satisfying also its environmental targets, while Vithayasrichareon and MacGill [8] provided an analysis for a power generation portfolio consisting of thermal technologies and high wind power penetration from the perspective of expected generation costs and CO2 emissions, taking also into account the uncertainty characterizing some key parameters. In addition, Nie et al. [9] proposed a stochastic risk management method to identify the optimal electricity mix under uncertainty, expressed in the form of probability distributions and interval values for the city of Beijing, while Costa et al. [10] proposed an optimization-based approach to deal with the problem of identifying the optimal electricity mix under uncertainties on model parameters. Kim and Kim [11] presented an optimization model to calculate the optimal fuel mix for the Korean power market, while Deane et al. [12] utilized the PLEXOS model, based on a mixed integer linear programming approach, to evaluate the annual optimal mix for the North-West region of Europe. The results underscore the importance of integrated modelling in the presence of national renewable energy policies, and the increasing role that electricity trading plays in the regional power demand satisfaction. Moreover, Bishop et al. [13] provided an optimization model to calculate the optimal annual electricity mix of the EU-25 countries, in comparison with the actual current one, as well as Yuan et al. [14] presented an optimization model to determine the power generation mix under specific emission targets. Focusing on the market participants’ side and their market behavior, Li et al. [15] presented a review of the approaches that have been developed for determining generation companies’ optimal bidding strategies for profits maximization and risk minimization, when participating in competitive electricity spot markets. Additionally, with the aim of examining the operational planning of a dominant power company, Vespucci et al. [16] proposed a mixed integer linear programming model for the market clearing of a power market from the perspective of a dominant power producer, whose aim is to guarantee a specific annual profit target. Their approach has been tested on the Italian power market. Focusing on the generation expansion planning of a dominant electricity company, Hesamzadeh and Amelin [17] presented a stochastic mixed integer linear programming model in order to determine the optimal investment planning decisions of a strategic power producer in liberalized electricity markets. Pang et al. [18] presented a methodological approach in order for the power producers to deal with their profits risk management, as well as Boroumand et al.

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supply options. The importance and the benefits of demand response on the optimal power generation mix of a system with intermittent renewable energy sources such as wind, has been highlighted by Jonghe et al. [48]. Empasizing on renewable energy policy issues, Amrutha et al. [49] made use of a mixed integer linear programming model to explore through several scenarios the effects of renewable energy targeted policies on the annual energy mix, while Dressler [50] discussed the effects that renewable energy support schemes can have on the behavior of conventional and renewable power producers, as well as on the competition level of the wholesale electricity markets. Finally, Lienert and Lochner [51] utilized a linear programming model focusing on the market interdependencies and interrelations of electricity and natural gas sectors, and their effects on the resulting power capacities and generation mixes of the EU-27 countries. This work proposes a systematic and analytical methodological approach to address the problem of determining the optimal annual energy mix of a given power system. Our work is based on a combination of approaches of our previous systematic contributions [52–55], providing now specific focus on the examination and quantification of the uncertainty of some key parameters, through the introduction of the Monte Carlo method, combined with the dynamic formulation and adaptation of the strategy applied by all the market participants in the market operation. The incorporation of stochasticity through the Monte Carlo method constitutes a robust and extensively used approach in order to examine and quantify the influence and the impact that various parameters have on the decision variables. A risk management optimization model related to the energy management activities has been developed, and its aim is to respond to the basic needs for exploring the daily energy scheduling strategy of the power producers. It can be also utilized for the monthly and annual (medium-term) forecasting requirements in order for the market participants to participate in the related interconnection auctions, and for their own portfolio management. The proposed optimization approach incorporates the capability of stochastic analysis of some crucial parameters through the Monte Carlo method, being capable of assessing the total cost and profits per activity and market participant, as well as of generating a distribution of potential profits and losses. The key decisions to be determined by the mathematical model include: (i) optimal yearly energy mix, (ii) electricity trade at a regional level, (iii) system’s zonal marginal price values, (iv) carbon footprint, and (v) detailed total supply cost composition according to the assumed market structure per market participant. The main contributions and the salient features of the proposed work include: (i) dynamic formulation of energy supply offers/load bids according to a specified strategy per market participant, (ii) detailed economic assessment of the total energy supply side cost, and (iii) quantification of the impacts of the uncertainty characterizing key parameters on the power system’s operational and financial aspects. The remainder of the paper is organized as follows: Section 2 presents the problem statement, while Section 3 provides the mathematical model’s formulation. Section 4 introduces the analysis of the employed case study, while Section 5 provides a critical discussion of the results obtained from the implementation of the proposed optimization approach. Finally, Section 6 underscores the main conclusions arising from the execution of this work.

possible scenarios, the future evolution of the power system of Tunisia, in terms of electricity generation costs, security supply, environmental impact and socio-economic criteria. In the same framework, Aryanpur and Shafiei [33] utilized the MESSAGE optimization model to evaluate through scenarios the optimal long-term pathways for the power system of Iran, analyzing also the influence of key parameters such as fuel prices, carbon tax and renewables subsidies, while Vidal-Amaro et al. [34] introduced a methodology to evaluate the optimal energy mix with high share of renewables in the Mexican power system for a future year. Correspondingly, Wierzbowski et al. [35] made use of a mixed integer linear programming model in order to determine the optimal roadmap of the coal-dominated Polish power system towards 2050. Mendes and Soares [36] proposed a methodology so as to quantify the impacts of the renewable energy penetration on the optimal annual power mix of the Iberian electricity market. Their findings show that wind power investment projects can exceed those in conventional technologies. Finally, Li et al. [37] proposed a methodological approach to determine the optimal future electricity mix of China under different environmental targets in terms of CO2 emissions. With the aim of investigating the regional electricity trading and its consequences, Abrell and Rausch [38] developed a multi-regional equilibrium model to examine the impacts of cross-border interconnections expansion and renewables’ penetration on the resulting CO2 emissions, as well as on the economic benefits of the electricity trade enhancement. In the same frame of reference, Shakouri et al. [39] provided a methodological optimization framework to explore the electricity cross-border trading potential between Iran and Turkey, taking additionally into consideration potential future generation and transmission expansion planning. In addition, Oseni and Pollitt [40] studied the conditions for promoting regional electricity trade in three regional developing country power pools in comparison with that of Northern Europe's Nord Pool, identifying the preconditions, the necessary institutional arrangements, as well as the appropriate timetabling for its successful implementation. Focusing on the economic benefits of electricity trade, Timilsina and Toman [41] applied a mixed integer optimization approach to quantify the potential net economic savings from the enhancement of electricity trade in South Asia, through investments in cross-border interconnection capacities. Finally, Brancucci Martínez-Anido et al. [42] made use of a mixed integer linear programming problem to calculate the impacts of the planned additional European cross-border transmission capacity investments (and possible requirements for more additions) on the annual dispatch cost, renewables curtailment, CO2 emissions, hydro storage utilization and on the unserved load. A series of works have attempted to deal with energy mix issues, drawing also attention to other aspects such as policy mechanisms, energy security issues and market interdependencies. More specifically, Qadrdan et al. [43] utilized a combined gas and electricity networks expansion planning optimization model, focusing on the effects of electricity demand side response on both the power and gas supply infrastructure. Their findings demonstrate significant cost savings for the power sector, as well as improvement of the natural gas-fired capacity factor. Herrero et al. [44] presented a methodological framework to investigate the influence of pricing mechanisms on the resulting power mix, consisting of thermal units and high penetration of renewable energy. Placing emphasis on energy security aspects, Hawker et al. [45] discussed the electricity security issue of the European Union, underscoring the conflicts between national self-sufficiency (national capacity mechanisms) and electricity competition and trade (single energy market), and proposed some possible compromising solutions and alternatives. Augutis et al. [46] presented a methodological framework to explore the impacts of different development scenarios of a reference energy system on its energy security, defined in terms of energy price increase and unsupplied energy due to stochastic disturbances. Hickey et al. [47] underscored the importance of diversity in the determination of a flexible and reliable portfolio of electricity

2. Problem statement This work addresses the problem of the optimal annual energy balance of a given power system under uncertainty (Monte Carlo simulation), with a specific focus on the financial issues of the power plants’ operation, and on the strategy followed by each market participant. The mathematical problem under consideration is formally defined in terms of the following items:

• The considered time period concerns a whole year (month and/or 1367

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•

•

•

•

•

border interconnection prices and availability, hydro and renewables availability, thermal units’ unavailability factor) the Monte Carlo method has been employed. The flowchart of the employed methodology is presented in Fig. 1. More specifically, in each Monte Carlo simulation mc ∈ MC , samples of each parameter considered as uncertain are created, according to the selected probability distribution for each parameter. Based on these created samples and the reference values of all the other parameters considered as deterministic, the energy offers/load bids of each power unit and interconnection (imports and exports) are dynamically calculated based on a systematic methodology to be analytically presented below. After the determination of all the market participants’ offers/bids strategy, the problem is iteratively solved for each Monte Carlo iteration, optimizing the objective function and satisfying a series of constraints. Finally, after the implementation of a desired number of Monte Carlo iterations (1000 in our case), the procedure has been successfully completed and a series of results are collected. As previously described, a novel characteristic of our proposed approach is that the energy offer (load bid) of each power unit/technology and market participant is dynamically determined in each Monte Carlo iteration, according to specific logical assumptions, satisfying simultaneously all the market requirements and the specific market rules. First of all, the minimum average variable cost of each thermal unit i ∈ I th is calculated according to the following:

day). In order to reduce the computational cost of the proposed approach – since it includes numerous Monte Carlo simulations – the examined annual time period is divided into a specific set of representative days per each month m ∈ M , each of which is further split into hourly time steps t ∈ T (24 h per representative day). The duration of each representative day of each month m ∈ M in days, is provided by the parameter Durm . The spatial characteristics of the examined power system are taken into consideration through the introduction of a set of domestic power grid subsystems s ∈ S . According to the electricity demand level during each month m ∈ M and time period t ∈ T , Demm,t , there is a specific assigned power grid injection losses coefficient in each subsystem s ∈ S , given by the parameter INLs,m,t . A set of power generating units i ∈ I is modelled, including conventional thermal units i ∈ I th , hydroelectric units i ∈ I h and renewable ones i ∈ I rn . Each power generating unit is installed in each subsystem i ∈ I S . The thermal units include lignite-fired i ∈ I lg and natural gas-fired units i ∈ I ng , while thermal and hydroelectric units are both referred to as hydrothermal ones i ∈ I ht . Each power generating unit is characterized by a technical minimum Pimin and maximum Pimax , in terms of operational capacity. Based on historical data, each thermal unit i ∈ I th is assigned with a maximum capacity factor during each month m ∈ M , CFMi,m . Pumped storage units pm ∈ PM are also included in the proposed approach. In the same way, each pumped storage unit pm ∈ PM is also assigned with a maximum annual capacity factor, CFpm . Cross-border electricity interconnections are introduced through the set int ∈ INT . These interconnectors are bi-directional having either imports int ∈ INT imp or exports direction int ∈ INT exp . Each crossborder power interconnector int ∈ INT is also interconnected with a specific domestic subsystem int ∈ INT s . Each cross-border electricity interconnection int ∈ INT is identified based on a specific available power capacity Int _Capint , which can be different according to the selected direction (imports or exports). As with the conventional thermal and the pumped storage units, specific maximum monthly availability factors are assigned to both importing IMAVint ,m and exporting EXAVint ,m cross-border electricity interconnections int ∈ INT . The available power capacity of each thermal unit i ∈ I th is split into a set of steps f ∈ F to represent in a realistic way the auction-based process of the electricity markets operation. Thus, the capacity quantity of the energy offer function steps f of each thermal unit i ∈ I th during month m and time period t is given by the parameter THBLi,f ,m,t (HBLi,f ,m,t for hydroelectric units i ∈ I h ), having also a corresponding specific priced energy offer cost function, THOFi,f ,m,t (HOFi,f ,m,t for hydroelectric units i ∈ I h ). With regard to the hydroelectric units i ∈ I h , they are also characterized by a given maximum availability factor per step for their priced energy offers, provided by the parameter HAFi,f . The same rule applies also to pumped storage units pm ∈ PM with the quantity-price pair given by PUBLpm,f ,m,t and PMBDpm,f ,m,t correspondingly, as well as for cross border electricity interconnections, either with an importing direction int ∈ INT imp (Int _Capint ,f ,m,t and IMOFint ,f ,m,t correspondingly), or with an exporting one int ∈ INT exp (Int _Capint ,f ,m,t and EXBDint ,f ,m,t correspondingly). The total number of the set of the energy offer (load bid) function steps of each hydrothermal, pumped storage unit and cross-border electricity interconnection amounts to F max . The energy offer of each hydrothermal unit i ∈ I ht is divided into two distinct parts, including a priced (described above) and a nonrn priced one Pi,fix are given priority m,t . Since the renewable units i ∈ I when entering the system, their energy offers are totally non-priced and given also by Pi,fix m,t .

Min _Var _Costi = CO2_Costi + Var _Costi + Rm _Costi + Mat _Costi ∈

∀i (1)

I th

where Min _Var _Costi accounts for the minimum variable cost of each unit i ∈ I th and equals the sum of the average annual CO2 emissions cost of each unit i ∈ I th , CO2_Costi , the variable (associated with fuel) cost of each unit i ∈ I th , Var _Costi , the raw material cost of each unit i ∈ I th , Rm _Costi , and the maintenance cost of each unit i ∈ I th , Mat _Costi . The average annual CO2 emissions cost of each unit i ∈ I th , CO2_Costi , is given by:

CO2_Costi = CO2_Emis _pricei ·CO2_Emis _Factori

∀ i ∈ I th

(2)

where CO2_Emis _pricei accounts for the average annual CO2 emissions allowances price and CO2_Emis _Factori represents the CO2 emissions factor of each unit i ∈ I th . The variable (associated with fuel) cost of each unit i ∈ I th , Var _Costi , is provided by:

Var _Costi =

⎛ Fuel _ Costi ⎞ ⎝ Heating _ Valuei ⎠ 0.27778

Efici

∀ i ∈ I th

(3)

where Fuel _Costi represents the fuel cost of each unit i ∈ I th (€/t for lignite-fired units and €/m3 for natural gas-fired units), Heating _Valuei the heating value of the fuel used in each unit i ∈ I th , and indicates the thermal efficiency of each unit i ∈ I th . The coefficient 0.27778 is used for the conversion from GJ to MWh. The corresponding offers for each power unit and market participant have to be equal to or greater than the corresponding minimum average variable cost (floor price) of each power generating unit, as imposed by the regulatory authority for energy. The assumed market participants include a dominant company (DOM), owning the majority of the power generating fleet, and some independent power producers (IPP), modelled as a single set. The dominant company has the control of the significant majority of the retail sector (90% in our case), and thus it comprises a net buyer in the wholesale market, while the independent power producers as a whole constitute net sellers. Not surprisingly, the dominant power company’s interest is to keep the system’s marginal price as low as possible, while the opposite strategy applied to the independent power producers. With regard to the reference strategy of the base-load lignite-fired units (owned totally by the dominant company) and the natural gas-

In order to capture the uncertainty characterizing a series of key model parameters (CO2 emission price, fuel prices, electricity cross1368

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Fig. 1. Methodology flowchart of the Monte Carlo-based approach and the dynamic energy offers/load bids formulation mechanism.

fired units owned by the dominant company, it is determined based on the following formula: Lignite-fired units

THOFi,f ,m,t = Min _Var _Costi + COEFi,f ,m,t THOFi,f ,m,t = THOFi,f − 1,m,t + COEFi,f ,m,t

∀i∈

I lg,f

= 1,m,t

THOFi,f ,m,t = THOFi,f − 1,m,t Min ⎛ Min _Var _CostLig −THOFi,f = 1,m,t −0.001 ⎞ +⎜ ⎟ F max −1 ⎝ ⎠ ∈ I ng,IPP ,f > 1,m,t

(4)

∀ i ∈ I lg ,f > 1,m,t

(5)

∀ i ∈ I ng,DOM ,f = 1,m,t (6)

THOFi,f ,m,t = THOFi,f − 1,m,t + COEFi,f ,m,t

∀ i ∈ I ng,DOM ,f > 1,m,t

(7)

I th,DOM

where COEFi,f ,m,t represents the cost coefficient of each unit i ∈ in step f of the energy offer function during month m and time period t . This cost coefficient represents the dominant company’s desired margin added to the minimum average variable cost of each lignite- and natural gas-fired unit in each capacity step. Regarding the reference strategy of the natural gas-fired units owned by the independent power producers, it is split into three cases. First of all, in each Monte Carlo simulation, the model calculates the minimum Min Max Min _Var _CostLig and the maximum value Min _Var _CostLig of the minimum average variable costs of all the considered lignite-fired units. Then it compares the minimum average variable cost of each selected natural gas-fired unit with these values and according to each condition, three possible strategies can be followed: Natural gas-fired units owned by the independent power producers Min ∀ i ∈ I ng,IPP Case A: If Min _Var _Costi ⩽ Min _Var _CostLig

THOFi,f ,m,t = Min _Var _Costi + ∈ I ng,IPP ,f = 1,m,t

Min Min _Var _CostLig −Min _Var _Costi

2

(9)

In Case A, where the minimum average variable cost of the selected natural gas-fired unit is lower than or equal to the minimum value of the minimum variable costs of all the considered lignite-fired units, the strategy followed indicates that the final step of the energy offer cost function of the selected natural gas-fired unit will be lower by 0.001 (or a very small value) than the minimum value of the minimum average variable costs of all the considered lignite-fired units. Min Min _Var _Costi > Min _Var _CostLig Case B: If & Max , ng IPP Min _Var _Costi < Min _Var _CostLig ∀i∈I

Natural gas-fired units owned by the dominant company

THOFi,f ,m,t = Min _Var _Costi + COEFi,f ,m,t

∀i

THOFi,f ,m,t = Min _Var _Costi +

Max Min _Var _CostLig −Min _Var _Costi

2

∈ I ng,IPP ,f = 1,m,t

∀i (10)

THOFi,f ,m,t = THOFi,f − 1,m,t Max ⎛ Min _Var _CostLig −THOFi,f = 1,m,t −0.001 ⎞ +⎜ ⎟ F max −1 ⎠ ⎝ ∈ I ng,IPP ,f > 1,m,t

∀i (11)

In Case B, where the minimum variable cost of the selected natural gasfired unit is between the minimum and the maximum values of the minimum average variable costs of all the considered lignite-fired units, the strategy followed indicates that the final step of the energy offer cost function of the selected natural gas-fired unit will be lower by 0.001 (or a very small value) than the maximum value of the minimum average variable costs of all the considered lignite-fired units.

∀i (8) 1369

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos Max Case C: If Min _Var _Costi ⩾ Min _Var _CostLig

THOFi,f ,m,t = Min _Var _Costi

∀i∈

I ng,IPP,f

THOFi,f ,m,t = THOFi,f − 1,m,t + COEFi,f ,m,t

∀ i ∈ I ng,IPP

= 1,m,t

of the energy offer cost function of the selected cross-border electricity interconnection will be lower by 0.001 (or a very small value) than the minimum value of the minimum average variable costs of all the considered specific thermal units.

(12)

∀ i ∈ I ng,IPP ,f > 1,m,t

(13)

EXBDint ,f ,m,t = Border _priceint

In Case C, where the minimum average variable cost of the selected natural gas-fired unit is higher than or equal to the maximum value of the minimum average variable costs of all the considered lignite-fired units, the strategy followed indicates that the first step of the energy offer cost function of the selected natural gas-fired unit will be equal to its minimum average variable cost, and the next steps follow an incremental increase according to the desired cost coefficient COEFi,f ,m,t . With regard to the cross-border electricity interconnections and the subsequent offers (bids) determination for imports (exports), they follow a similar procedure with that of the natural gas-fired units owned by the independent power producers. Initially, the cross-border electricity interconnections are divided into two groups:

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t −

IMOFint ,f ,m,t = Border _priceint

Max −Border _priceint −0.001 Min _Var _CostTh F max −1 ∈ INT IND,f > 1,m,t

+

IMOFint ,f ,m,t =

IMOFint ,f − 1,m,t +

2 ∈ INT IND,f = 2,m,t

EXBDint ,f ,m,t = Border _priceint

Min Border _priceint −Min _Var _CostTh −0.001 max F −1 ∈ INT IND,f > 1,m,t

∈ INT IND,f > 2,m,t

(21)

∀ int (22)

Regarding the corresponding electricity exports bids determination of Case B, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT IND will amount to its border price, while the bid price is going to proportionally decrease in the next steps, leading to the minimum value of the minimum variable costs of all the considered specific thermal units in the final step plus 0.001 (or a very small value), so as to keep its relevant economic competitiveness. Max ∀ int ∈ INT IND Case C: If Border _priceint ⩾ Min _Var _CostTh

∀ int

∀ int ∈ INT IND,f = 1,m,t

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t + COEFint ,f ,m,t

(23)

∀ int ∈ INT IND,f > 1,m,t (24)

(15)

F max −2

(20)

∀ int ∈ INT IND,f = 1,m,t

−

(14)

Min Min _Var _CostTh −IMOFint ,f = 2,m,t −0.001

∀ int

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t

In Case C, where the border price of the selected cross-border electricity interconnection int ∈ INT IND is higher than or equal to the maximum value of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the first step of the energy offer cost function of the selected cross-border electricity interconnection will be equal to its border price and the next steps follow an incremental increase according to the desired cost coefficient, COEFint ,f ,m,t .

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t +

(19)

n Case B, where the border price of the selected cross-border electricity interconnection int ∈ INT IND is between the minimum and the maximum values of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the final step of the energy offer cost function of the selected cross-border electricity interconnection will be lower by 0.001 (or a very small value) than the maximum value of the minimum average variable costs of all the considered specific thermal units.

IMOFint ,f ,m,t = Border _priceint Min Min _Var _CostTh

∀ int ∈ INT IND,f = 1,m,t

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t

To sum up, the IND group includes the SUF cross-border electricity interconnections that are interconnected with other SUF interconnections (SUF-SUF), as well as all the TRN cross-border electricity interconnections (TRN-TRN, TRN-SUF). On the other hand, the COM group incorporates the SUF cross-border electricity interconnections that are interconnected with TRN ones (SUF-TRN). For each Monte Carlo simulation and for both groups, the model Min calculates the minimum Min _Var _CostTh and the maximum value Max Min _Var _CostTh of the minimum average variable costs of all the considered specific thermal units (lignite-fired and the advanced natural gas combined cycle units owned by both the dominant company and the independent power producers). Then, for the first group (IND), it compares the border price of each selected cross-border electricity interconnection (Border _priceint ) with these values and according to each condition, three possible strategies can be followed: Electricity imports/exports from/to each cross-border interconnection Min ∀ int ∈ INT IND Case A: If Border _priceint ⩽ Min _Var _CostTh

∀ int ∈ INT IND,f = 1,m,t

∀ int ∈ INT IND,f > 1,m,t

Regarding the corresponding electricity exports bids determination of Case A, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection will amount to its border price, while the exports bid price is going to proportionally decrease in the next steps, leading to a zero value in the final step. Max Border _priceint < Min _Var _CostTh Case B: If & Min Border _priceint > Min _Var _CostTh ∀ int ∈ INT IND

connections that: i. have sufficient domestic generating capacities (SUF) being interconnected with other ones of the same type, i.e., sufficient domestic generating capacities. ii. their border price is highly influenced by other power exchanges (TRN), i.e., they mainly act as transit countries and they can be interconnected with borders either of the same (TRN) or of a different (SUF) type. The second group (COM) consists of cross-border electricity interconnections that have sufficient domestic generating capacities (SUF) and are interconnected with TRN borders. In the case of the specific SUF cross-border electricity interconnections, a diversified offers/bids strategy formulation methodology is followed.

IMOFint ,f ,m,t = 0

Border _priceint F max −1

(17)

(18)

• The first group (IND) consists of the cross-border electricity inter-

•

∀ int ∈ INT IND,f = 1,m,t

∀ int (16)

In Case A, where the border price of the selected cross-border electricity interconnection int ∈ INT IND is lower than or equal to the minimum value of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the final step

EXBDint ,f ,m,t = Border _priceint 1370

∀ int ∈ INT IND,f = 1,m,t

(25)

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t Max Border _priceint −Min _Var _CostTh −0.001 − F max −1 ∈ INT IND,f > 1,m,t

∀ int

+

IMOFint ,f ,m,t =

∀ int ∈ INT COM ,f = 1,m,t

Min IMOFint ,f − 1,m,t + Min _Var _CostTh

2 ∈ INT COM ,f = 2,m,t

F max −3−2

∀ int

∈ INT COM ,3 ⩽ f ⩽ F max −3,m,t

(26)

Regarding the corresponding electricity exports bids determination of Case C, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT IND will amount to its border price, while the bid price is going to proportionally decrease in the next steps, leading to the maximum value of the minimum average variable costs of all the considered specific thermal units in the final step plus 0.001 (or a very small value), so as to keep its relevant economic competitiveness. For the second group (COM), the model compares each cross-border electricity interconnection price (SUF and TRN) with minimum Max Min Min _Var _CostTh and/or the maximum value Min _Var _CostTh of the minimum average variable costs of all the considered specific thermal units (lignite-fired and the advanced natural gas combined cycle units owned by both the dominant company and the independent power producers) and according to each condition, four possible strategies can be followed: Min Border _priceint ⩽ Min _Var _CostTh Case A: If & Min Border _priceint′ ⩽ Min _Var _CostTh ∀ int ∈ INT COM ,int ′ ∈ INT TRN

IMOFint ,f ,m,t = 0

Min Min _Var _CostTh −IMOFint ,f = 2,m,t −0.001

Min IMOFint ,f ,m,t = Min _Var _CostTh + 0.001

∈

INT COM ,f

=

(34)

∀ int

F max −2,m,t

(35)

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t + ∈

Border _priceint′−IMOFint ,f = f max − 2,m,t −0.001

∀ int

2 INT COM ,int ′

∈

INT TRN ,F max −1

⩽f⩽

F max ,m,t

(36)

In Case B, where the border price of the selected cross-border electricity interconnection int ∈ INT COM is lower than or equal to the minimum value of the minimum average variable costs of all the considered specific thermal units, as well as the border price of the selected crossborder electricity interconnection int ′ ∈ INT TRN is higher than the minimum value of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the step (F max −3) of the energy offer cost function of the selected crossborder electricity interconnection int ∈ INT COM will be lower by 0.001 (or a very small value) than the minimum value of the minimum average variable costs of all the considered specific thermal units, while the final step of the energy offer cost function of the selected crossborder electricity interconnection int ∈ INT COM will be lower by 0.001 (or a very small value) than the border price of the selected cross-border electricity interconnection int ′ ∈ INT TRN .

(27)

∀ int (28)

EXBDint ,f ,m,t = Border _price int′

∀ int ∈ INT COM ,int ′ ∈ INT TRN ,f = 1,m,t (37)

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t +

Min Min _Var _CostTh −IMOFint ,f = 2,m,t −0.001 F max −2

∈ INT COM ,f > 2,m,t

EXBDint ,f ,m,t =

∀ int (29)

∀ int ∈ INT COM ,f = 1,m,t

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t +

Border _priceint F max −1

(30)

int ∈ INT COM ,int ′ ∈ INT TRN ,f > 1,m,t

(38)

IMOFint ,f ,m,t = Border _priceint + COEFint ,f ,m,t

∀ int ∈ INT COM ,f = 1,m,t (39)

∀ int

∈ INT COM ,f > 1,m,t

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t + COEFint ,f ,m,t

∀ int ∈

INT COM ,f

> 1,m,t (40)

(31)

In Case C, where the border price of the selected cross-border electricity interconnection int ∈ INT COM is higher than or equal to the maximum value of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the first step of the energy offer cost function of the selected cross-border electricity interconnection int ∈ INT COM will be equal to its border price plus a desired cost coefficient COEFint ,f ,m,t , and the next steps follow an incremental increase according to the desired cost coefficient COEFint ,f .

Regarding the corresponding electricity exports bids determination of Case A, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT COM will amount to its border price, while the exports bid price is going to proportionally decrease in the next steps, leading to a zero value in the final step. Min Case B: If & Border _priceint ⩽ Min _Var _CostTh Min Border _price int′ > Min _Var _CostTh ∀ int ∈ INT COM ,int ′ ∈ INT TRN

IMOFint ,f ,m,t = 0

∀

Regarding the corresponding electricity exports bids determination of Case B, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT COM will amount to the border price of the interconnection int ′ ∈ INT TRN , while the exports bid price is going to proportionally decrease in the next steps, leading to the minimum value of the minimum average variable costs of all the considered specific thermal units in the final step. Max ∀ int ∈ INT COM Case C: If Border _priceint ⩾ Min _Var _CostTh

In Case A, where the border prices of both selected cross-border electricity interconnections int ∈ INT COM ,int ′ ∈ INT TRN are higher than or equal to the minimum value of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the final step of the energy offer cost function of the selected crossborder electricity interconnection int ∈ INT COM will be lower by 0.001 (or a very small value) than the minimum value of the minimum average variable costs of all the considered specific thermal units.

EXBDint ,f ,m,t = Border _priceint

Min Border _priceint′−Min _Var _CostTh EXBDint ,f − 1,m,t − max F −1

∀ int ∈ INT COM ,f = 1,m,t

EXBDint ,f ,m,t = Border _priceint

(32)

∀ int ∈ INT COM ,f = 1,m,t

(41)

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t

IMOFint ,f ,m,t =

Min IMOFint ,f − 1,m,t + Min _Var _CostTh

2 ∈ INT COM ,f = 2,m,t

Max Border _priceint −Min _Var _CostTh −0.001 max F −1 ∈ INT COM ,f > 1,m,t

∀ int

+ (33) 1371

∀ int (42)

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos

alternative strategy followed indicates that all steps of the energy offer cost function of the selected cross-border interconnection int ∈ INT will be equal to the maximum allowable value, i.e. 300 €/MWh. Power exports: Minimum value (0 €/MWh) For electricity exports from each cross-border interconnection, the alternative strategy followed indicates that all steps of the load bid cost function of the selected cross-border interconnection int ∈ INT will be equal to the minimum allowable value, i.e. 0 €/MWh. The following relationships (49)–(55) define the capacity blocks per step for each type of power unit and interconnection including thermal units, cross-border electricity interconnections of both groups (COM and IND), importing and exporting, as well as the hydro capacity blocks for the relevant priced energy offers. Power capacity blocks for thermal units

Regarding the corresponding electricity exports bids determination of Case C, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT COM will amount to the border price of the interconnection int ∈ INT COM , while the exports bid price is going to proportionally decrease in the next steps, leading to the maximum value of the minimum average variable costs of all the considered specific thermal units plus 0.001 (or a very small value) in the final step. Max Border _priceint < Min _Var _CostTh Case D: If & Min Border _priceint > Min _Var _CostTh ∀ int ∈ INT COM

IMOFint ,f ,m,t = Border _priceint

∀ int ∈ INT COM ,f = 1,m,t

(43)

IMOFint ,f ,m,t = IMOFint ,f − 1,m,t Max −Border _priceint −0.001 Min _Var _CostTh F max −1 ∈ INT COM ,f > 1,m,t

+

∀ int

THBLi,f ,m,t = Pimin (44)

∀ int ∈ INT COM ,f = 1,m,t

Int _Capint ,f ,m,t = 40%·Int _Capint

THOFi,f ,m,t = THOFi,f − 1,m,t + 0.001

∀ i ∈ I lg ,f = 1,m,t ∀ i ∈ I lg ,f > 1,m,t

(50)

∀ int ∈ INT COM ,imp,f = 1,m,t

Int _Capint −Int _Capint ,f = 1,m,t ⎤ Int _Capint ,f ,m,t = ROUND ⎡ ⎢ ⎥ F max −1 ⎣ ⎦ ∈ INT COM ,imp,f > 1,m,t

(45)

(51)

∀ int (52)

Imports capacity blocks from interconnection group IND

Int _Capint ,f ,m,t = ROUND ⎡ ⎢ ⎣

∀ int

Int _Capint ⎤ ⎥ F max ⎦

∀ int ∈ INT IND,imp,f ,m,t

(53)

Exports capacity blocks from all interconnection groups (46)

Int _Capint ,f ,m,t = ROUND ⎡ ⎢ ⎣

Regarding the corresponding electricity exports bids determination of Case D, the strategy followed indicates that the first step of the load bid cost function of the selected cross-border electricity interconnection int ∈ INT COM will amount to the border price of the interconnection int ∈ INT COM , while the exports bid price is going to proportionally decrease in the next steps, leading to the minimum value of the minimum average variable costs of all the considered specific thermal units plus 0.001 (or a very small value) in the final step. The above described offers/bid per power generating unit and crossborder interconnection comprise the reference values, which are determined by the model process in each Monte Carlo simulation, according to the relative methodology. There is also the option for alternative offers, which can be selected from each market participant for some (or all of the) hours of each representative day. More specifically: Alternative offers Lignite-fired units

THOFi,f ,m,t = Min _Var _Costi + 0.001

∀ i ∈ I th,f > 1

Imports capacity blocks from interconnection group COM

EXBDint ,f ,m,t = EXBDint ,f − 1,m,t Min Border _priceint −Min _Var _CostTh −0.001 − max F −1 ∈ INT COM ,f > 1,m,t

(49)

P max −P min THBLi,f ,m,t = ROUND ⎡ i max i ⎤ ⎢ F −1 ⎥ ⎣ ⎦

In Case D, where the border price of the selected cross-border electricity interconnection int ∈ INT COM is between the minimum and the maximum values of the minimum average variable costs of all the considered specific thermal units, the strategy followed indicates that the final step of the energy offer cost function of the selected cross-border electricity interconnection will be lower by 0.001 (or a very small value) than the maximum value of the minimum average variable costs of all the considered specific thermal units.

EXBDint ,f ,m,t = Border _priceint

∀ i ∈ I th,f = 1

Int _Capint ⎤ ⎥ F max ⎦

∀ int ∈ INT exp,f ,m,t

(54)

Hydro capacity blocks (priced energy offers) max

fix

⎡ Pi −Pi,m,t ⎤ HBLi,f ,m,t = ROUND ⎢ F max ⎥ ⎣ ⎦

∀ i ∈ I h,f ,m,t (55)

3. Mathematical formulation 3.1. Objective function The mathematical model’s objective function to be optimized concerns the minimization of the total annual cost of the power system’s operation and it is analytically presented in (M1). More specifically, it includes:

• the total annual operational cost (including fuel cost, CO

(47) (48)

For lignite-fired units, the alternative strategy followed indicates that the first step of the energy offer cost function of the selected lignitefired unit will be equal to its minimum average variable cost plus 0.001 (or a very small value), and the next steps follow also an incremental increase of 0.001 (or a very small value) compared to the offer of the previous step. Natural gas-fired units: Cap value (300 €/MWh) For natural gas-fired units owned by the independent power producers, the alternative strategy followed indicates that all steps of the energy offer cost function of the selected natural gas-fired unit i ∈ I ng,IPP will be equal to the maximum allowable value, i.e. 300 €/MWh. Power imports: Cap value (300 €/MWh) For electricity imports from each cross-border interconnection, the

• • • 1372

2 emissions cost, raw material and maintenance cost) of the installed thermal power units (energy offers submitted by the power producers), including power grid injection losses (∑(i,s) ∈ I th,S ∑f ∑m ∑t (bpi,f ,m,t ·INLs,m,t ·THOFi,f ,m,t ·Durm) ), the total annual operational cost of the installed hydroelectric power units (energy offers submitted by the power producers), including power grid injection losses (∑(i,s) ∈ I h,S ∑f ∑m ∑t (bpi,f ,m,t ·INLs,m,t ·HOFi,f ,m,t ·Durm) ), the total energy supply cost of the cross-border electricity interconnections (electricity imports offers submitted by the power traders), including power grid injection losses (∑(int ,s ) ∈ INT imp,S ∑f ∑m ∑t (bimint ,f ,m,t ·INLs,m,t ·IMOFint ,f ,m,t ·Durm) ), the total energy withdrawal revenues of the cross-border electricity interconnections (electricity exports bids submitted by the power traders) (∑int ∈ INT exp ∑f ∑m ∑t (bex int ,f ,m,t ·EXBDint ,f ,m,t ·Durm) ), and

Applied Energy 205 (2017) 1364–1383

N.E. Koltsaklis, K. Nazos

• the total energy withdrawal revenues of the pumped storage units (load bids submitted by the load (∑pm ∑f ∑m ∑t (bppm,f ,m,t ·PMBDpm,f ,m,t ·Durm) ).

3.2.4. Pumping load capacity constraints

representatives),

bppm,f ,m,t ⩽ PUBLpm,f ,m,t

∑∑∑

(i,s ) ∈ I th,S

f

m

f

m

∑ ∑

f

f

pm

f

m

m

∑∑∑∑ m

t

f

m

(bimint ,f ,m,t ·INLs,m,t ·IMOFint ,f ,m,t ·Durm)−

t

(bex int ,f ,m,t ·EXBDint ,f ,m,t ·Durm)−

t

(bppm,f ,m,t ·PMBDpm,f ,m,t ·Durm) (M1)

t

3.2.5. Units’ operational limits

3.2. Model constraints

∑

3.2.1. Power demand balance

∑

+ ∑(i,s) ∈ I h,S ∑f (Pi,fix m,t · INLs,m,t )+ = Demm,t

bpi,f ,m,t ⩽ Pimax ·x i,m,t

∀ i ∈ I ht ,m,t

∑∑ f

∀ m,t

(M9)

m

Eq. (2) describe the power demand in each time period. More specifically, the priced power supply (including power injection losses) from the installed hydrothermal units ( ∑(i,s) ∈ I ht,S ∑f (bpi,f ,m,t ·INLs,m,t )) , plus the electricity imports (including power injection losses) ( ∑(int ,s) ∈ INT imp,s ∑f (bimint ,f ,m,t ·INLs,m,t )) , plus the non-priced power renewables ( ∑(i,s) ∈ I rn,S ∑f (Pi,fix m,t · INLs,m,t )) , minus the electricity exports

( ∑int ∈ INT exp ∑f bex int ,f ,m,t ) , must meet both power demand (Demm,t ) , and the priced pumping load ( ∑pm ∑f bppm,f ,m,t ) , in each time period. 3.2.2. Power capacity constraints

∀ i ∈ I h,f ,m,t

bpi,f ,m,t ·Durm ⩽ CFMi,m·Pimax ·Durm·24

∀ i ∈ I th,m

bpi,f ,m,t ·Durm ⩽

HAFi,f ·Pimax ·8760

∀ i ∈ I h,f

t

(M4)

Eqs. (3) and (4) define the power output limits per capacity step (block) of each thermal and hydroelectric unit correspondingly. More specifically, these constraints guarantee that the quantity of power capacity step f of unit i ∈ I th (i ∈ I h ) cleared during month m and time period t must not exceed the capacity quantity of the energy offer function steps f of each unit i ∈ I th (i ∈ I h ) during month m and time period t .

∑ ∑ bimint,f ,m,t ·Durm ⩽ IMAVint,m·Int _Capint ·Durm·24 f

∑ ∑ bex int,f ,m,t ·Durm ⩽ EXAVint,m·Int _Capint ·Durm·24 f

(M5)

bex int ,f ,m,t ⩽ Int _Capint ,f ,m,t

∀ int ∈ INT exp,f ,m,t

(M6)

∀ int ∈ INT imp,m

t

(M13)

3.2.3. Cross-border electricity interconnections capacity constraints

∀ int ∈ INT imp,f ,m,t

(M12)

3.2.6. Cross-border electricity interconnections operational limits Constraints (13) and (14) describe the maximum allowable electricity imports (exports) supply (consumption) of each cross-border electricity interconnections int ∈ INT during each month m , through the introduction of parameter IMAVint ,m (EXAVint ,m ), denoting the availability factor of each importing (exporting) cross-border electricity interconnection int ∈ INT imp (int ∈ INT exp ) during month m .

(M3)

bimint ,f ,m,t ⩽ Int _Capint ,f ,m,t

(M11)

Constraints (9) and (10) specify the power output limits (minimum and maximum correspondingly) of each hydrothermal unit i ∈ I ht , subject to the decision for the operation or not of the power unit i ∈ I ht during month m and time period t . Furthermore, constraints (11) describe the maximum allowable electricity generation of each thermal unit i ∈ I th during each month m , through the introduction of parameter CFMi,m , denoting the capacity factor of each thermal unit i ∈ I th during month m . Constraints (12) describe the maximum allowable priced electricity generation of each hydro unit i ∈ I h during each step f , through the introduction of parameter HAFi,f , denoting the availability factor (for priced energy offer) of each hydroelectric unit i ∈ I h during month m .

supply from both hydroelectric units ( ∑(i,s) ∈ I h,S ∑f (Pi,fix m,t · INLs,m,t )) and

∀ i ∈ I th,f ,m,t

(M10)

t

∑∑

(M2)

bpi,f ,m,t ⩽ HBLi,f ,m,t

∀ i ∈ I ht ,m,t

f

− ∑int ∈ INT exp ∑f bex int ,f ,m,t − ∑pm ∑f bppm,f ,m,t ∑(i,s) ∈ I rn,S ∑f (Pi,fix m,t · INLs,m,t )

bpi,f ,m,t ⩾ Pimin·x i,m,t

f

∑(i,s) ∈ I ht,S ∑f (bpi,f ,m,t ·INLs,m,t ) + ∑(int ,s ) ∈ INT imp,s ∑f (bimint ,f ,m,t ·INLs,m,t )

bpi,f ,m,t ⩽ THBLi,f ,m,t

∀ pm

t

(M8)

(bpi,f ,m,t ·INLs,m,t ·HOFi,f ,m,t ·Durm)+

∑∑∑

int ∈ INT exp

m

Eq. (7) define the power output limits per capacity step (block) of each pumping load. More specifically, these constraints guarantee that the quantity of power capacity step pm ∈ PM cleared during month m and time period t must not exceed the capacity quantity of the load bid function steps f of each pumped storage unit pm during month m and time period t . Moreover, constraints (8) describe the maximum annual allowable electricity withdrawal of each pumped storage unit pm ∈ PM , through the introduction of parameter CFpm , denoting the annual average capacity factor of each pumped storage unit pm .

t

∑∑∑

(int ,s ) ∈ INT imp,S

f

(bpi,f ,m,t ·INLs,m,t ·THOFi,f ,m,t ·Durm)+

t

∑ ∑∑∑ (i,s ) ∈ I h,S

(M7)

∑ ∑ ∑ bppm,f ,m,t ·Durm ⩽ CFpm· ∑ ∑ ∑ (PUBLpm,f ,m,t ·Durm)·24

Min Cost total

∑

∀ pm,f ,m,t

∀ int ∈ INT exp,m

t

(M14) The overall problem is formulated as an MILP problem, involving the cost minimization objective function (M1), and subject to the constraints (M2)–(M14).

Eqs. (5) and (6) define the power output limits per capacity step (block) of each power imports and exports interconnection correspondingly. More specifically, these constraints ensure that the quantity of the power capacity step f of the importing (exporting) cross-border electricity interconnection int ∈ INT imp (int ∈ INT exp ) cleared during month m and time period t must not exceed the capacity quantity of the energy offer (load bid) function steps f of each importing (exporting) crossborder electricity interconnection int ∈ INT imp (int ∈ INT exp ) during month m and time period t .

4. Case study description The interconnected Greek power system has been employed as an illustrative case study of the proposed mathematical model. The country has been divided into five zones, so as to realistically represent the spatial characteristics of the examined power system and to accurately calculate the power grid injection losses in each zone (Koltsaklis 1373

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the duration of each representative day per month (in days) and the relevant monthly electricity demand, while Fig. 2 depicts the electricity demand per representative day of each month of the interconnected Greek power system at an hourly level. Fig. 3 portrays the current structure with regard to the installed capacity per technology and the market representation of each market participant in the Greek power market. First of all, there are two main market participants, a dominant power company (DOM) and the independent power producers (IPP). The Greek power system consists of 14 lignite-fired units with a total installed capacity of around 4 GW, all of which are owned by the dominant power company. The generation portfolio of the dominant power company includes also around 3.1 GW of large hydroelectric units (the total installed capacity of those units), as well as around 2.2 GW of natural gas-fired power generating units. As far as the power generation fleet of the independent power producers (they are not all identical, but they are modelled as a common group) is concerned, it comprises 2.5 GW of natural gas-fired units, as well as 4.8 GW of renewable power units, of which 2 GW are wind turbines, 2.5 GW photovoltaics, 235 MW small hydroelectric units, 60 MW biomass-fired units, and 50 MW high-efficiency combined heat and power units (CHP). As previously described, the electricity generation from hydroelectric units is divided into two parts: (i) non-priced component, entering with priority into the system, and (ii) priced component, to be determined by the optimization process. Regarding the renewable electricity generation, the whole generation amount is non-priced and it is injected into the system with priority. Fig. 4 shows the hourly mandatory hydroelectric generation per representative day of each month, while Fig. 5 depicts the hourly mandatory renewable electricity generation per representative day of each month. Table 2 presents the main

Table 1 Duration of each representative day per month (days) and the relevant monthly electricity demand (GWh). Representative day per month

Duration (days)

GWh

January February March April May June July August September October November December

31 28 31 30 31 30 31 31 30 31 30 31

4505 4036 4173 3680 3818 4217 5029 4832 4025 3918 4169 4611

et al. 2014; Koltsaklis et al. 2015). With regard to its interconnection with other countries, the Greek power system is interconnected with the corresponding systems of Albania, FYROM, Bulgaria, Turkey and Italy. The interconnections with Albania and FYROM are modelled as a single one, since the power systems of those countries are not extensive and their power prices are highly influenced from the Hungarian power exchange (HUPX), acting mainly as transit countries in the electricity trading activities. The interconnections with Italy, Albania & FYROM, and Turkey belong to the first group of borders (IND), while the interconnection with Bulgaria belongs to the second group (COM). Twelve representative days, one per month, have been employed in order to effectively represent a whole year, capturing the renewable units’ seasonal contribution, as well as the electricity demand seasonal fluctuations in the most computationally efficient way. Table 1 presents

Fig. 2. Hourly electricity demand per representative day of each month of the interconnected Greek power system (MW).

9000 8000 7000

MW

6000 5000 4000 3000 2000 1000 0 1

Jan

2

3

Feb

4

5

Mar

6

7

Apr

8

9

May

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Jun

Jul

Aug

Sep

Oct

Dec

Fig. 3. Total installed capacity per technology and market participant in the Greek power market (MW).

4500 4000 3500 3000

MW

Nov

2500 2000 1500 1000 500 0

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Fig. 4. Hourly mandatory hydroelectric generation per representative day of each month (MW).

2250 2000 1750 1500

MW

1250 1000 750 500 250 0 1

Jan

2

3

Feb

4

5

6

Mar

7

8

Apr

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Fig. 5. Hourly mandatory renewable electricity generation per representative day of each month (MW).

2750 2500 2250 2000

MW

1750 1500 1250 1000 750 500 250 0 1

Jan

2

Feb

3

4

5

Mar

6

7

Apr

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

power system, i.e., domestic lignite and imported natural gas. Since lignite constitutes a domestic fuel, it is assumed that it is not characterized by significant uncertainty, and thus its price is considered as deterministic. On the other hand, imported natural gas is treated as an uncertain parameter and its annual average reference value equals 0.272 €/m3, while its minimum (maximum) value is assumed to be lower (higher) than 10% of the reference value. Fig. 6 depicts the cross-border annual average electricity prices (minimum, reference, maximum) per interconnection, while Fig. 7 shows the final annual average availability factors (minimum, reference, maximum) per renewable technology and large hydroelectric units. The reference values of the electricity cross-border interconnection availability are given in Table 2, while their minimum (maximum) values are assumed to be lower (higher) than 10% of their reference values. Finally, the unavailability factors of the thermal units are determined based on historical data, and they comprise an estimation of the potential operational limits of each thermal power unit.

techno-economic characteristics of the installed thermal units and the interconnections, including technical minimum and maximum, optimal efficiency, CO2 emission factor, as well as raw material and maintenance costs. Note also that lignite-fired units have been classified into six distinct categories and they are presented through the characteristics of a representative power unit of each category (A-F). Furthermore, the natural gas-fired units have been divided into new (advanced) and old (low efficiency) per market participant (dominant power company and independent power producers). The input parameters considered as uncertain in the employed case study of the Greek power system include:

• CO emission price, • fuel prices, • electricity cross-border interconnection prices and availability, • hydro and renewables availability, and • thermal units’ unavailability factor. 2

The probability distribution type that has been employed to capture the uncertainty of all the considered as uncertain parameters is the uniform. The specific characteristics of the uniform distribution required include the minimum and the maximum value. With regard to the CO2 emission price, its reference annual average value is assumed to be 6.2 €/tonne CO2, while its minimum (maximum) value is assumed to be lower (higher) than 10% of the reference value. With regard to the fuel prices, two fossil fuels are used in the Greek

5. Results and discussion This section provides the results and a detailed discussion of the Monte Carlo simulation (1000 iterations-samples) that have been considered. The problem has been solved to global optimality making use of the ILOG CPLEX 12.6.0.0 solver incorporated in the General Algebraic Modeling System (GAMS) tool [56]. An integrality gap of 1% has been achieved in all cases (1000 iterations-samples). 1375

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Table 2 Basic techno-economic data of the installed thermal units and the interconnections. Representative unit

Pmax

Pmin

Optimal efficiency (%)

CO2 emission factor (€/tn CO2)

Raw material cost (€/MWh)

Maintenance cost (€/MWh)

Lignite – A Lignite – B Lignite – C Lignite – D Lignite – E Lignite – F Natural gas – DOM – Old Natural gas – IPP – Old Natural gas – IPP – New Natural gas – DOM – New Imports from Bulgaria Imports from Albania & FYROM Imports from Italy Imports from Turkey Exports to Bulgaria Exports to Albania & FYROM Exports to Italy Exports to Turkey

283 275 255 256 273 289 476 49 390 417 400 600 500 134 400 600 500 216

155 151 154 195 150 151 130 10 220 182 – – – – – – – –

35 31 28 31 32 33 53 40 57 58 – – – – – – – –

1.49 1.52 1.81 1.55 1.53 1.23 0.42 0.53 0.37 0.37 – – – – – – – –

1.78 1.44 1.24 1.05 1.90 1.50 1.26 1.12 1.12 1.26 – – – – – – – –

0.76 0.62 0.53 0.45 0.81 0.64 0.54 0.48 0.48 0.54 – – – – – – – –

Fig. 6. Cross-border annual average electricity prices (minimum, reference, maximum) per interconnection (€/MWh).

50 45 40

€/MWh

35 30 25 20 15 10 5 0

Bulgaria Base Price Imports (€/MWh)

HUPX Base Price Imports (€/MWh)

Yearly Reference value

Italy Base Price Imports (€/MWh)

Yearly minimum value

Turkey Base Price Imports (€/MWh)

Yearly maximum value

50.0%

44.9%

42.8% 40.4%

45.0% 40.0%

38.3%

35.2%

35.0%

42.4%

40.7%

37.0%

33.5%

30.0% 25.0% 20.0% 15.0%

24.8% 15.3%

Fig. 7. Final annual average availability factors (minimum, reference, maximum) per renewable technology and large hydroelectric units (p.u.)

26.1%

23.6%

17.8%

14.5%

16.9%

16.0%

18.7%

10.0% 5.0% 0.0%

Reference Final Availability (p.u.)

Large Hydro

Wind

Minimum Final Availability (p.u.)

Photovoltaics

Small Hydro

Maximum Final Availability (p.u.)

Biomass

CHP

2–4 TWh 39%, between 4 and 6 TWh 26%, and finally in the range of 6–8 TWh amounts to almost 13%. There is also an almost negligible probability of being in the range of 8–10 TWh (0.1%). Significant variation is also reported in the lignite-fired power generation on the grounds that its probabilities to be in the ranges of 12–14 TWh and 16–18 TWh amount to 28% and 29% correspondingly, while the corresponding one to be between 14 and 16 TWh is equal to almost 34%. A probability of 9% is also recorded for being between 8 and 10 TWh. Natural gas-fired power generation coming from units owned by the independent power producers (IPP), is projected to be between 8 and

5.1. Power production mix The results indicate some variations regarding the power contribution from some electricity generation technologies, while others are characterized by a more stable production profile, as can be observed in Fig. 8, providing the probability distribution for the power generation allocation per technology type and power producer group. Natural gasfired power generation coming from units owned by the dominant company (DOM), is characterized by the highest uncertainty, since its probability to be in the range of 0–2 TWh equals 22%, in that of 1376

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100.00% 90.00% 80.00% 70.00%

0.10% 12.70%

7.40% 35.60% 29.30%

32.50%

33.90%

92.60% 100.00%

99.20%

94.10%

100.00% 64.60%

39.10% 62.80%

30.00%

Fig. 8. Probability distribution (%) of the annual power generation mix per technology type and power producer group (TWh).

99.20%

100.00%

50.00%

100.00% 28.20%

20.00% 10.00%

0.50%

0.80%

25.90%

60.00% 40.00%

0.80%

22.20%

0.00%

[0-2]

1.60% 8.60%

[2-4]

[4-6]

5.90%

[6-8]

[8-10]

[10-12]

[12-14]

2.40%

[14-16]

producers and third parties, contribute significantly to the electricity demand satisfaction, having a share of 18% of the total electricity supply. This percentage highlights the vital and increasing role that electricity trading plays in the context of the desired European energy union. Renewable energy sources including wind, photovoltaics, small hydroelectric, biomass and high-efficiency combined heat and power units, report a share of 18% of the total on average, while hydroelectric units are characterized by the lowest share on average (9% of the total). All in all, it can be concluded that the Greek power system is characterized by a diverse portfolio of energy sources contributing to the electricity demand satisfaction, since all sources are more or less in the range of 10–30% of the total on average. Fig. 10 depicts the monthly average values of the total production mix per technology type and power producer group. The seasonal characteristics of the hydroelectric power generation can be observed, as well as those of renewables. The more stable supply profile is that of net electricity imports which are not characterized by significant variations from month to month on average, reflecting also the economic competitiveness of that option and highlighting the pivotal role that power trading has on the current power systems. Lignite and natural gas-fired units follow more or less the fluctuations of the electricity demand regarding their production share.

10 TWh with a probability of 63%, and between 10 and 12 TWh with a respective one of 36%. One general conclusion is that fossil-fuelled power generation is highlighted by great uncertainty regarding the allocation of each technology and producer group, reflecting the competitiveness of each technology and the relevant sensitivity of their cost-driven operation. All the other sources of electricity contribution (hydroelectric and renewables) are characterized by relevant stability, while electricity trading, i.e., net electricity imports have a probability of 65% for being in the range of 8–10 TWh, and 33% in the range of 10–12 TWh. At this point, it should be emphasized that the results provided are highly dependent on the assumptions made and can alter to some extent under different data used. Fig. 9 depicts the annual average values of the total production mix per technology type and power producer group of the studied power system. Lignite-fired power generation constitutes the dominant technology in terms of annual average power generation with a percentage of 29% of the total contribution. Natural gas-fired electricity production (both from the dominant company and the independent power producers) approaches similar levels with lignite-fired power generation, reporting a percentage of 26% on average. The fact that natural gasfired power generation coming from independent power producers exceeds that of the dominant company is associated with technical parameters such as the thermal efficiencies of the specific power units, as well as with assumptions regarding the fuel cost of each group. Net electricity imports (imports minus exports) from neighboring countries, undertaken by the dominant company, the independent power

Renewables 18% Net Imports-IPP 6% Net ImportsDOM 12% Hydroelectric 9%

[16-18]

5.2. Total supply cost composition Table 3 presents the annual average, standard deviation, minimum and maximum values of the total supply cost composition, including the supply cost (fuel cost, CO2 emissions cost, raw material cost, maintenance cost) per technology type and power producer group, the electricity trading cost, i.e., imports cost and exports revenues per supplier, as well as the pumping revenues. It can be seen that fossilfueled power generation technologies, i.e., lignite-fired and natural gasfired units are characterized by the higher cost (and standard deviation) on average, amounting to almost 1.5 billion € on average at an annual level. Hydroelectric units and renewables account for around the half of the total fossil-fueled production cost (720 million €), while net imports supply cost amounts to almost 500 million €. The total supply cost for the annual operation of the system equals 2.6 billion €. Since the dominant company represents 90% of the total customers (consumption in the retail sector), its total supply cost amounts to 2.3 billion € (90% of the total). Focusing only and separately on the CO2 emissions cost (incorporated also as a component in the total cost of each power production technology), this equals 167 million € on average, or 6.4% of the total supply cost. Table 4 presents the annual average, standard deviation, minimum and maximum values of the total financial balance composition of the dominant power producer. All the production and trading costs per category are also depicted with percentage terms in Fig. 11. The total

Lignite 29%

Natural gasDOM 7% Natural gas-IPP 19%

Fig. 9. Annual average percentage values of the total production mix per technology type and power producer group (%).

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Fig. 10. Monthly average values of the total production mix per technology type and power producer group (GWh).

6000

5,029 5000

4000

4,505 727

GWh

324 3000

2000

1000

1,016

1,455 220 832

4,040 4,196 536 225 741 1,067

874

3,682 3,824

4,217

889

737

472 1,009

230

891

955

412

751

247 558

260 442

799

1,094

843

1,147 1,196

4,832 951 431 998

1,432 1,259

4,611 4,025 3,918 693 209

686 133

743

996

914 1,166

879

578

468

307

315

432

412

640

663

731

728

759

818

875

853

884

4,169 716 332 644

746 373 987

1,552 1,600

167

173

154

822

809

821

0 Jan Feb Mar Apr Net imports Hydroelectric Lignite

May Jun Jul Aug Sep Natural_gas_IPP Natural_gas_DOM

Oct Nov Dec Renewables Net load

additional charge imposed by the Regulatory Authority for Energy in Greece and equals 2 €/MWhel. Total trading cost (power purchases from the neighboring countries for imports, as well as power purchases from the internal market for exports) equal 368 million € on average (30% of the total operating and trading cost). As a consequence, the total production and trading cost for the dominant power company equals around 1.2 billion € on average. In addition to that, it has to pay an additional amount of 2.3 billion € for electricity purchased from the wholesale power market for the

cost for the operation of the power units amount to almost 900 million €, of which around 500 million € account for the lignite fuel cost (41% of the total operating and trading cost), followed by the variable cost (not including the CO2 emissions cost) of the natural gas-fired units (13% of the total operating and trading cost), the CO2 emissions cost for both lignite and natural gas-fired units (11% of the total operating and trading cost), the raw material and maintenance cost for the lignitefired units (3% of the total operating and trading cost), and finally the lignite tax cost (2% of the total operating and trading cost), which is an

Table 3 Annual average, standard deviation, minimum and maximum values of the total supply cost composition (million €). Type

Average

Standard deviation

Minimum

Maximum

Lignite-Dominant company Natural gas-Dominant company Natural gas-Independent power producers Hydroelectric-Dominant company Renewables-Independent power producers Imports-Dominant company Imports-Independent power producers Exports-Dominant company Exports-Independent power producers Pumping-Dominant company Total Supply Cost-Dominant company Total Supply Cost-Dominant company & Independent power producers Special natural gas consumption tax CO2 emissions cost

739 184 492 236 484 337 184 −21 −21 −2 2351 2612 0 167

103 89 37 10 15 25 15 −10 −10 0 63 70 0 14

513 17 377 215 447 275 143 0 0 −2 2222 2468 0 131

944 397 579 276 535 414 239 −40 −40 −2 2554 2838 0 203

Table 4 Annual average, standard deviation, minimum and maximum values of the total financial balance composition of the dominant power company (million €). Type

Average

Standard deviation

Minimum

Maximum

Lignite Tax Cost Lignite fuel cost Raw material & Maintenance costs (Lignite-fired units) Fuel cost & Raw material & Maintenance costs (Natural gas-fired units) CO2 emission cost Total power units' expenses Power imports purchases from northern interconnections Power imports purchases from Italy Internal power purchases for exports Power trading – Total expenses Special natural gas consumption tax Total supply cost Production revenues (Lignite, Natural Gas, Hydroelectric) Power exports revenues Power imports revenues Total revenues Net expenses

29 513 33 168 145 889 290 57 21 368 0 2351 −1158 −22 −184 −1364 2244

3 66 4 80 13 41 19 8 10 29 0 63 50 11 15 47 39

21 359 24 17 113 771 240 34 0 282 0 2222 −1334 −46 −239 −1545 2143

36 635 41 359 178 1054 345 81 40 455 0 2554 −1028 0 −143 −1243 2357

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Internal power purchases for exports 2%

Power imports purchases from Italy 5%

Lignite Tax Cost 2%

Fuel cost & Raw material & Maintenance costs (Natural gas-Įred units) 13%

Raw material & Maintenance costs (LigniteĮred units) 3%

Power imports purchases from northern interconnecƟons 23%

CO2 emission cost 11%

Fig. 11. Annual average percentage values of the total production and trading cost composition of the dominant power producer (%).

Lignite fuel cost 41%

average of the system’s marginal price. According to the results provided, the most probable ranges for the allocation of the system’s marginal price are those between 50–51, 51–52 and 49–50 €/MWh, recording probabilities of 32%, 20% and 19% on average correspondingly. The next most probable range is that of 52–53 €/MWh (with a probability of 15% on average), while the ranges between 48–49 and 54–55 €/MWh have probabilities of 3% and 2% on average, respectively. The total annual weighted average of the system’s marginal price equals 51.1 €/MWh, while its minimum and maximum values equal 48.3 €/MWh and 55.5 €/MWh correspondingly. As far as its standard deviation is concerned, it amounts to 1.37 €/MWh, or 2.7% of the average value, indicating that it comprises a robust projection.

satisfaction of its customers’ consumption (90% of the total). With regard to its revenues, they refer to its compensation from the wholesale power market for its electricity generation (amount of net electricity generated multiplied with the system’s marginal price), as well as to its revenues from the electricity trading. All the revenues per category are also depicted with percentage terms in Fig. 12. All these amount to 1.3 billion € in total on average, with production revenues to represent the highest share with 85% of the total and followed by imports revenues with 13%, and exports revenues with 2% of the total. As a result, the net position, i.e. the net expenses for the dominant power company at an annual level equal 2.2 billion € in total, which according to its pricing policy per customer group and profile, aims to more than cover (with a desired profit margin) from the retail market.

5.4. Environmental impact 5.3. System’s marginal price With regard to the environmental impact of the power system’s operation in terms of CO2 emissions, they amount to around 27 Mt at an

Fig. 13 portrays the probability distribution of the annual weighted

54-55 €/MWh 2.3%

Power imports revenues 13%

55-56 €/MWh 0.3%

48-49 €/MWh 3.0%

53-54 €/MWh 8.6%

Power exports revenues 2%

49-50 €/MWh 19.0% 52-53 €/MWh 15.0%

ProducƟon revenues (Lignite,Natural Gas, Hydroelectric) 85%

51-52 €/MWh 19.8%

Fig. 12. Annual average percentage values of the total production and trading revenues composition of the dominant power producer (%).

50-51 €/MWh 32.0%

Fig. 13. Probability distribution (%) of the annual weighted average of the system’s marginal price (€/MWh).

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30 25

Fig. 14. Annual average, standard deviation, minimum and maximum values of the total CO2 emissions per technology type and power producer group (Mt CO2).

26.9 22.1

20

Mt

15.9 15 10 5

3.6

2.6

1.4

0.7 0.2

3.2 4.1

2.8 0.1

0 Average

Standard deviaƟon

Minimum

Maximum

CO2 emissions from lignite-Įred units CO2 emissions from natural gas-Įred units of the dominant power producer CO2 emissions from IPP natural gas-Įred units

natural gas-fired units of the dominant power producer. Analyzing more the results for the consumption of these units, they share a probability of 48% to be between 254 and 654 mcm, while their probability to exceed that of 1 bcm equals 13.3%.

annual level on average, as depicted in Fig. 14, which presents the annual average, standard deviation, minimum and maximum values of the total CO2 emissions per technology type and power producer group. The significant majority of them come from the lignite-fired units (81.7% of the total), since their average emission rates are quite high, as presented in Table 2. The remaining part (18.3% of the total) is distributed among the natural gas-fired units owned by the dominant company (5.1%) and by the independent power producers (13.2%). The highest standard deviation (around 50% of the average value) is reported in the case of natural gas-fired units owned by the dominant company, highlighting their sensitivity and the trade-off with the lignite-fired units, which have also a noticeable standard deviation (12% of the average value). The results indicate that the more the lignite-fired power generation is, the less the corresponding natural gas-fired power production is and from that reduction, the largest decrease rate is recorded in the natural gas-fired units of the dominant power company.

5.6. Electricity trading Fig. 16 depicts the electricity trading, i.e., the electricity imports and exports among Greece and its neighboring countries, presenting the annual average values. As can be observed, Greece constitutes a net electricity importer in total and with each individual neighboring country. More specifically, it is determined to import 6.8 TWh on average at an annual level from its northern interconnections (Albania, FYROM, Bulgaria), while its exports to these countries correspond to 0.5 TWh. These countries, i.e., Albania, FYROM, Bulgaria, are characterized by significantly lower operating costs when compared to those of Greece. Regarding the electricity trading with Italy, the net position of Greece is translated into net electricity imports of 2.1 TWh. Finally, the power trade with Turkey is quite limited due to the small size of the electricity interconnector between the two countries, and Greece records net electricity imports of 0.7 TWh on average.

5.5. Fuel consumption As with CO2 emissions, similar results are also recorded for the fossil fuel consumption for the electricity production (see Fig. 15). Lignite fuel consumption amounts on average to 31.1 Mt, being in the range of 22.5 Mt (minimum value) and 37.8 Mt (maximum value). Total natural gas consumption equals 2.2 bcm on average and as in the case of CO2 emissions, the most significant standard deviation is reported for the

5.7. Economic competitiveness of each power generating group Table 5 presents the resulting annual average minimum variable

40

Fig. 15. Annual average, standard deviation, minimum and maximum values of the total lignite (Mt) and natural gas (mcm) consumption per power producer group.

2000 1800

35

1600 30 1400 1200

20

1000 800

15

600 10 400 5

200 0

0 Average

Standard deviaƟon

Lignite fuel consumpƟon (Mt)

Minimum

Maximum

Natural gas consumpƟon by DOM (mcm)

Natural gas consumpƟon by IPP (mcm)

1380

mcm

Mt

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Fig. 16. Electricity trading (imports and exports) between Greece and its neighboring countries (GWh).

unit group. Not surprisingly, the higher the clean dark spread, the higher the utilization factor and vice versa. Lignite-fired units with significant clean dark spreads (Lignite-C, Lignite-D and Lignite-F) report average annual utilization factors higher than 60%. The lignite unit group (Lignite-E) with close to zero clean dark spread are characterized by very low average annual utilization factors, i.e., 12.7%. Clean spark spreads are defined as “the average difference between the cost of gas and emissions, and the equivalent price of electricity. If the level of spark spreads is above 0, gas power plant operators are competitive in the observed period” [57]. Fig. 18 depicts the clean dark spreads and the utilization factor of each natural gas-fired unit group. Not surprisingly, the higher the clean spark spread, the higher the utilization factor and vice versa. Natural gas-fired units with noticeable clean spark spreads (Natural gas-IPP-New, Natural-gas-DOM-New) report average annual utilization factors between 38% and 46%. The natural gas unit groups (Natural gas-IPP-Old, Natural-gas-DOM-Old) with negative clean spark spreads are characterized by very low average annual utilization factors, i.e., 7.4% (Natural-gas-DOM-Old) or even zero utilization factor (Natural gas-IPP-Old).

cost per representative power unit, as derived from all the Monte Carlo samples, its standard deviation, as well as its relative standard deviation. Relative standard deviation is calculated by dividing the standard deviation with the average value. It comprises an indicator of high importance since the impact of absolute values is eliminated, making possible the comparison of different magnitudes. From Table 5, it is clear that the highest relative standard deviation is reported in natural gas-fired units, due to the combined effects of both the natural gas and CO2 emissions price uncertainty. Clean dark spreads are defined as “the average difference between the price of coal and carbon emission, and the equivalent price of electricity. If the level of dark spreads is above 0, coal power plant operators are competitive in the observed period” [57]. Fig. 17 depicts the clean dark spreads and the utilization factor of each lignite-fired Table 5 Annual average minimum variable cost (€/MWh) derived from all the Monte Carlo samples, standard deviation (€/MWh) and relative standard deviation (%) per representative power unit. Representative unit

Lignite – A Lignite – B Lignite – C Lignite – D Lignite – E Lignite – F Natural gas – DOM – Old Natural gas – IPP – Old Natural gas – IPP – New Natural gas – DOM – New

Standard deviation (€/MWh)

Relative standard deviation (%)

47.794 49.331 44.217 39.443 50.884 42.132 53.046

0.532 0.549 0.647 0.554 0.546 0.439 2.758

1.11% 1.11% 1.46% 1.40% 1.07% 1.04% 5.20%

66.337 46.385

3.479 2.406

5.24% 5.19%

49.207

2.554

5.19%

Average (€/MWh)

6. Concluding remarks This work presents a market-based, mixed integer linear programming (MILP) model for the optimal operational and financial annual planning of a given power system at a national and/or regional level. A key feature of the proposed approach is that it incorporates a dynamic determination of all the energy offers and load bids submitted to the market operator, according to an analytical methodological framework. In that context, the market participants are enabled to respond to the changing market conditions automatically and in the most effective way. The dynamic formulation of the market participant strategies along with the utilization of the Monte Carlo method for capturing the uncertainty of some key parameters, enables the market participants, 1381

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N.E. Koltsaklis, K. Nazos

14

60.8%

70%

64.4% 61.5%

Fig. 17. Clean dark spreads (€/MWh) and utilization factor (%) of each lignite-fired unit group.

60%

12

52.3% 11.7

€/MWh

10

50%

9.0

8

6

40%

6.9

31.6%

30%

20%

4

2

3.3

12.7% 1.8

10%

0.2

0%

0 Lignite - A

Lignite - B

Lignite - C

Clean Dark Spread (€/MWh)

10

Lignite - D

Lignite - E

Lignite - F

UƟlizaƟon factor (%)

50%

45.6%

45%

5

37.8%

4.7 €/MWh

0

1.9

-1.9

40% 35% 30%

-5

25%

-15.2

20%

-10 -15

Fig. 18. Clean spark spreads (€/MWh) and utilization factor (%) of each natural gas-fired unit group.

15%

7.4%

10% 5%

0.0% -20

0%

Natural gas-DOMOld

Natural gas-IPPOld

Clean Spark Spread (€/MWh)

Natural gas-IPPNew

Natural gas-DOMNew

UƟlizaƟon factor (%)

efficient and economic energy sources, and due to the fact that it constitutes one of the most effective strategies for a smoother and more efficient penetration of renewables into the energy systems. Finally, the introduction of the clean dark and spark spreads gives the opportunity to analytically examine the economic competitiveness of each power unit, indicating in a simple and coherent way the most competitive ones, the marginal ones, and those to be decommissioned. The proposed approach is generic and can be easily applied to the power systems of other (European) countries and/or regions. Interesting challenges that need to be addressed in future works include the development of a more detailed investment planning mathematical model, focusing on energy security issues, energy sources diversification, as well as on the optimal design of a power system with focus on minimizing the price shocks and the fluctuations entering the system from variable energy sources.

potential investors, and/or policy makers to implement risk management according to their specific requirements. The applicability of the proposed approach has been tested on a real case study of the Greek interconnected power system. The results provided highlight the resulting optimal power generation mix in the form of probability distributions, and reflect the relevant balance of the energy resources to be utilized in the Greek power system (lignite, natural gas, hydro, renewables, and electricity imports). Energy diversification boosts energy security and it could also be claimed that the higher the energy sources diversification, the more competitive an energy market becomes. The model provides also a detailed calculation of all the costs components of the total supply cost composition, indicating the fossil fuel cost dominance. The system’s marginal price is also characterized by some uncertainty, being the most crucial parameter for the economic profitability or not of the operational power units. Regarding the resulting environmental impact, the model’s findings underscore the significant carbon footprint that lignite-fired units have, underlining the needs for efficiency improvements (higher utilization of natural gas-fired units, retrofitting of the existing ones, or construction of new advanced technologies), enhancement of renewables in line with electricity storage development, and better coordination with neighboring systems with complementary energy mix (electricity trading). With regard to electricity trading, it is of utmost importance in the modern energy systems, since it plays a continuously increasing role in the electricity demand satisfaction, facilitating the access to more

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