emission operational scheduling of a large scale virtual power plant

Energy 172 (2019) 630e646

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Day-ahead stochastic multi-objective economic/emission operational scheduling of a large scale virtual power plant Shahrzad Hadayeghparast, Alireza SoltaniNejad Farsangi, Heidarali Shayanfar* Center of Excellence for Power Systems Automation and Operation, School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 July 2018 Received in revised form 21 January 2019 Accepted 26 January 2019 Available online 28 January 2019

The reduction of global greenhouse gas emissions is one of the key steps towards sustainable development. The integration of Distributed Energy Resources (DERs) in power systems will help with emissions reduction. Virtual Power Plants (VPPs) can overcome barriers to participation of DERs in system operation. In this paper, a model is proposed for the energy management of a VPP including PhotoVoltaic (PV) modules, wind turbines, Electrical Energy Storage (EES) systems, Combined Heat and Power (CHP) units, and heat-only units. The multi-objective operational scheduling of DERs in the VPP focuses on maximizing the expected day-ahead profit of the VPP and minimizing the expected day-ahead emissions. The uncertainty of wind speed, solar radiation, market price, and electrical load is modeled using scenario based approach. Also, two-stage stochastic programming is implemented for modeling the VPP energy management. Three cases have been investigated for evaluating the proposed method: single-objective scheduling of VPP to maximize profit, single-objective scheduling of VPP to minimize emission and multi-objective economic/emission scheduling of VPP. The results indicate the appropriate economic and environmental performance of the proposed method, which provides the possibility of selecting a compromise solution for the VPP operator in accordance with environmental restrictions and economic constraints. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Virtual power plant (VPP) Energy management Renewable energy Emissions Distributed energy resource (DER) Electricity market

1. Introduction 1.1. VPP concept Controllable loads and DERs as demand-side resources have a lot of technical, economic and environmental benefits to the power system [1]. Due to the clean, flexible, and renewable characteristics of DERs, these resources have drawn widespread attention [2]. Nowadays, the installation of wind turbines, PV modules, and energy storage systems is increasing. The main reasons for the increase in installation and operation of renewable DERs in recent decades include high costs of energy generation, oil products dependency, and environmental issues [3]. DERs often have small capacities and are dispersedly connected to distribution network that causes their insignificant impact on the power system operation. However, the integration of these

* Corresponding author. E-mail addresses: [email protected] (S. Hadayeghparast), alireza_ [email protected] (A. SoltaniNejad Farsangi), [email protected], [email protected] (H. Shayanfar). https://doi.org/10.1016/j.energy.2019.01.143 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

resources can provide significant amount of energy for the operation of the system [1]. Despite the fact that deployment of DERs could significantly reduce the dependence of energy generation section of power system on conventional power plants, their integration in the power system still has problems, since DERs are ‘invisible’ to system operators due to their small capacities. In the case of an individual connection of a DER into power grid, it will face technical, regulatory, and commercial problems [2]. The renewable-based and intermittent part of distributed generation provokes important challenges in the power system operation: The number of generators increases, the size of generators decreases and more uncertainty arises in the power system operation [4]. Therefore, it is necessary to provide the possibility of DERs generation control as well as their participation in the electricity market [5]. The use of the VPP concept is an appropriate solution to overcome the mentioned obstacles. A VPP is a set of distributed generations, EESs, and loads that are aggregated together [5]. The aggregation of many demand-side resources into VPP is an appropriate option to ensure a viable operation [4]. Aggregation of DERs has been recognized as an effective solution to the problem of resource intermittency [6]. A VPP is an interface between DERs and

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Nomenclature

Sets s Set of scenarios, ranging from 1 to Ns t Set of time periods, ranging from 1 to 24 p Set of plants, ranging from 1 to Np Scenario-dependent parameters rem Energy market price at hour t and scenario s s;t ($/MWh) P el s;t;p vs;t sors;t

Total electric load power at hour t, scenario s and plant p (MW) Wind speed at hour t and scenario s (m/s)
 Solar radiation at hour t and scenario s kW m2

Input parameters ap ;bp ;cp ;dp ;ep ;fp Cost function coefficients of CHP unit at plant p sd C su p ; Cp

Startup and Shutdown cost of CHP unit at plant p, respectively($)

H ho max;p

Maximum thermal output power of the heat-only unit at plant p (MWth) ap ; bp ; gp Cost function coefficients of heat-only unit at plant p vcin ; vrated ; vcout Cut-in, rated, and cut-out wind speeds, respectively (m/s) Nominal power of wind turbine (MW) P wt rated N wt p

Number of wind turbines at plant p

Kv

Ambient temperature at hour t ð CÞ Nominal operating temperature of solar cell ð CÞ Solar cell temperature at hour t and scenario s ð CÞ Short circuit current of PV module (A) Open circuit voltage of PV module (V)
 Current temperature coefficient of PV module AC
 Voltage temperature coefficient of PV module VC

IMPP VMPP N pv p FF P st p;max;ch

Current at maximum power point of PV module (A) Voltage at maximum power point of PV module (V) Number of PV modules at plant p Fill factor of PV module Maximum charging power of EES system at plant p

P st p;max;dch

ATt NOT TCs;t Isc Voc Ki

rht

631

Heat price at hour t ($/MWth h)

NOX chp ; SO2 chp ; CO2 chp The NOX ; SO2 and CO2 emission rates of a
 kg CHP unit, respectively MWh NOX ho ; SO2 ho ; CO2 ho The NOX ; SO2 and CO2 emission rates of a
 kg heat-only unit, respectively MWth h NOX grid ; SO2 grid ; CO2 grid The average NOX ; SO2 and CO2 emission rates of all committed power plants in
 kg the main grid, respectively MWh

ps

Probability of scenario s

Binary variables X1;t;p ; X2;t;p Operation state of the CHP unit in the first/second convex section of FOR at hour t and plant p, respectively V chp t;p

Commitment status of the CHP unit at hour t and plant p

SU chp t;p ;

SDchp t;p

Startup and shutdown status of CHP unit at hour t

and plant p, respectively bst ; bst Binary variables of charging/discharging states at p;ch p;dch plant p, respectively Continues variables P chp t;p

Electrical output power of CHP unit at hour t and plant p (MW)

H chp t;p

Thermal output power of CHP unit at hour t and plant p (MWth)

C t;p

chp

Cost function of CHP unit at hour t and plant p ($/h)

H ho t;p

Thermal output power of heat-only unit at hour t and plant p (MWth)

C ho t;p

P pv s;t;p

Cost function of heat-only unit at hour t and plant p ($/h) Output power of wind turbines at hour t, scenario s and plant p (MW) Output power of PV modules at hour t, scenario s and

(MW) Maximum discharging power of EES system at plant

P st t;p;ch

plant p (MW) Charging power of EES system at hour t and plant p

P st t;p;dch

(MW) Discharging power of EES system at hour t and plant

Est p;min

p (MW) Maximum energy stored in EES system at plant p (MWh) Minimum energy stored in EES system at plant p

Est p;initial

(MWh) Initial level of energy in EES system at plant p (MWh)

C ens s;t;p

Final level of energy in EES system at plant p (MWh) Est p;final st hst ; h Charging/discharging efficiency of EES system at p;ch p;dch

P line s;t;p

Est p;max

ens Ps;t;p;max

plant p Max amount of involuntary curtailment power at

VOLL

hour t, scenario s and plant p (MW) Value of lost load ($/MWh)

P line p;max

Maximum crossed power of upstream line of plant p

rtret

(MW) Retail energy rate of VPP at hour t ($/MWh)

e

P wt s;t;p

p (MW) SOC st t;p

SoC of EES system at hour t and plant p (MWh)

P ens s;t;p

The amount of energy not served at hour t, scenario s and plant p (MW) Cost of energy that is not served at hour t, scenario s and plant p ($/h) Crossed power of upstream line of plant p at hour t and scenario s (MW)

P sel s;t;p

Served electric load power at hour t, scenario s and plant p (MW)

P grid s;t

The amount of power exchanged with the upstream network at hour t and scenario s (MW)

H tlt;p

Thermal load demand at hour t and plant p (MWth)

H sh t;p

Surplus heat power at hour t and plant p (MWth)

632

S. Hadayeghparast et al. / Energy 172 (2019) 630e646 chp

Et;p ; Eho t;p

Emissions by CHP unit and heat-only unit at hour t and plant p, respectively (kg/h)

system/market operator that improves visibility and handling of DERs for system/market operator. Given the VPP concept, DERs and conventional power plants become two alternatives for energy production and capacity; also DERs can increase profits by taking part in electricity market. In the presence of smart grids technology, VPPs can provide the possibility of participation in both energy and ancillary services markets for small generation unit owners [7]. Since VPPs include DERs, scheduling of these resources is an important issue [5]. The VPP is responsible for managing the load and scheduling of resources. It obtains energy from the DERs and contracts with consumers to supply their energy demand [8]. VPPs maximize the total profit, while ensuring that the energy produced by demand-side resources is used efficiently. 1.2. Literature review Many studies have already been carried out concerning the VPP energy management. The available literature on this field can be categorized from different perspectives such as integration of various types of DER technologies, implementation of demand response programs, uncertainty considerations, formulation type, solving method, multi-objective approach and emission. Literature in relation to the VPP energy management is classified in Table 1. In the studies presented in Table 1, VPP aggregates various kinds of DERs, including conventional generation units, renewable energy resources, stationary EES systems and electric vehicles. In Ref. [9], a stochastic model is proposed for optimal day-ahead scheduling of diverse DER technologies including PV modules, wind turbines, CHP systems, micro turbines, fuel cells and EES systems in a VPP which participates in both energy and spinning reserve markets. Due to the fact that the penetration of electric vehicles in the future power grid will be very high, an energy management model for VPPs is developed in Ref. [8], which investigates a real case study considering the penetration of plug-in hybrid vehicles. Pump-storage technology is seen as a tool that helps to the integration of more renewable energy sources. In Ref. [3], the optimum sizing of combined wind and pumpedstorage VPPs is studied taking into account the investor's perspective for the maximization of the return on the investment and system perspective for the maximization of renewable energy source penetration. A rescheduling strategy is applied in Ref. [10] to assess the ability of micro-CHP systems to reduce the imbalance errors caused by intermittent generation of PV installations in a VPP. In Ref. [11], Economic operation of a VPP consisting of solar and wind farms as renewable energy resource as well as hydrogen and thermal power system as dispatchable energy resource is investigated for participation in electricity market. Demand response is a change in normal electricity consumption patterns of consumers in response to electricity price or incentive payments [1]. An innovative mathematical model for including demand response schemes in VPP energy management is suggested in Ref. [12], so that it leads to more flexibility and increase in profit in both day-ahead market and balancing market. A simultaneous energy and reserve scheduling is proposed in Ref. [7], which implements an incentive-based three-level demand response program for improving the hourly profit of VPP. The energy management of a VPP is always faced with uncertainties, most notably in parameters such as load, electricity

grid

Es;t

Emissions by main grid generation system at hour t and scenario s (kg/h)

price, wind speed and solar radiation. In Ref. [13], probabilistic scenarios are used for modeling the uncertain parameters of dayahead market prices, PV and wind power outputs in optimal operation of a VPP, which participates in day-ahead and balancing energy markets. A weekly self-scheduling of a VPP is studied in Ref. [14] considering PV and wind power generation as well as electricity market prices as uncertain parameters. The optimization model proposed in the aforesaid study models the coordination of the day-ahead market bidding and long-term bilateral contracts. Short-term market operations of a VPP participating in day-ahead and balancing markets under uncertainties of generation of renewables, electricity price, load, and the losses allocation is proposed in Ref. [15] using a novel stochastic programming approach. Concerning the modeling of scheduling problem of DERs in VPPs, there are two kinds of formulation types namely stochastic and deterministic. Stochastic formulation takes into account uncertain parameters; however, deterministic modeling contains no degree of uncertainty [5]. A two-stage stochastic mixed-integer linear programming is implemented in Ref. [16] for modeling the VPP market offering problem. In the aforesaid study, the VPP is treated as a price-taker in the day-ahead market and as a deviator in the balancing market. A new algorithm is presented in Ref. [17] for optimizing thermal and electrical scheduling of a large scale VPP, while assuming all the input data to be deterministic. Also, some studies have considered multi-objective approach in VPP energy management. In Ref. [2], the optimal scheduling of VPP is based on maximization of profit and minimization of risk (quantified as expected energy not served) in order to obtain an optimal balance between economy and reliability. The optimization objectives in Ref. [3] are the increase in renewable energy source penetration and the maximization of the return on hybrid power station investment. Also, the two objectives of the VPP in Ref. [4] include self-supply, which means the maximization of supplying the demand with internal units, and benefit maximization by sale and purchase of energy in the market. Once the modeling of VPP energy management problem is done, then it is time to choose an appropriate solving method. There exist two types of solving methods: heuristic and mathematical optimization methods [5]. Mixed integer linear programming as a mathematical method is applied to solve the optimization problem in Ref. [18]. The aforesaid study presents a decision-making framework that allows commercial VPP to form an optimal coalition of DERs based on weekly bilateral contracting, futures-market involvement, and pool participation. On the other hand, genetic algorithms as heuristic methods are used for optimization in Ref. [3]. Although the emission from fossil fuel power plants is among the most important issues that should be considered with regard to environmental limitations, emission problem in relation to the VPP energy management is a topic that has not been considered so much [5]. Authors in Ref. [4] have discussed how the VPP strategy affects system emission. The concept of environmental VPP as a subcategory of commercial VPP is proposed in Ref. [6]. The developed methodology which is based on the EU Emissions Trading Scheme aims to control the emission from environmental VPP components. An energy management model for VPPs is developed in Ref. [8], which investigates how emission changes with the VPP formation in a network with high penetration of plug-in hybrid

✓ e e e ✓ e ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ e ✓ ✓ ✓ ✓ e e e e e e e e e e e e e e ✓ e e e e e e e e e e e e e e e e ✓ ✓ ✓ ✓ e e e e e e e e e e e e e ✓ [2] [3] [4] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] Current Paper

e e ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ e

Mathematical

Emissiona MO

MO: Multi-Objective WS: Wind Speed, SR: Solar Radiation, DER: Distributed Energy Resource, DG: Distributed Generation, EES: Electrical Energy Storage. a Considering emission as an objective function in the VPP energy management model.

e ✓ ✓ ✓ ✓ e ✓ e e ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ e ✓ ✓

e e e e e ✓ e e e e e e e e e e e

Stationary EES Renewable Energy Conventional Energy

e e e e ✓ e ✓ ✓ ✓ e ✓ ✓ ✓ e e ✓ ✓ e ✓ ✓ ✓ e ✓ e e e e e e e e ✓ e e

✓ e e e ✓ e ✓ e ✓ ✓ ✓ ✓ ✓ ✓ e ✓ ✓ ✓ e e e ✓ e ✓ e e ✓ e e ✓ e e e ✓

Deterministic Heuristic

Solving Method

e e e e ✓ e ✓ ✓ e ✓ ✓ ✓ ✓ ✓ e ✓ ✓

Uncertainty

Load

Formulation Type

Stochastic

Price

WS

SR

✓ e ✓ e ✓ e ✓ e e ✓ e e ✓ e e ✓ e

✓ e ✓ ✓ ✓ ✓ ✓ ✓ ✓ e ✓ ✓ ✓ ✓ ✓ e ✓

EES Demand Response

DER

1.3. Main contributions of this paper

Ref. No.

Table 1 Literature related to the VPP energy management.

633

vehicles. Despite the studies carried out in relation to emission, none of them have considered emission as an objective function which should be minimized.

DG

Movable Electric Vehicle

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Although a lot of research has been done in the field of the VPP energy management, they have not paid much attention to the emission and environmental issues. To the best of the author's knowledge, it is the first paper which studies the multi-objective energy management of VPP with the targets of maximization of profit and minimization of emission. Consequently, minimization of pollutants, which is an important criterion, is investigated in this paper. In this paper, a model is proposed to optimize the day-ahead scheduling of a VPP that includes power dispatching and unit commitment. The main contribution of this paper is multiobjective economic/emission operational scheduling of VPP. The Pareto-based approach is presented to solve the multi-objective problem, which focuses on maximizing the expected day-ahead VPP profit and minimizing the expected day-ahead emissions and has not yet been considered in the literature on VPPs. The most important features of this paper are:  Multi-objective consideration which focuses on maximizing the VPP net daily profit and minimizing daily emissions.  Using Pareto-based approach to solve the multi-objective problem.  Considering both electrical and thermal aspects in the VPP.  Taking into account the various technologies of DERs including wind turbines, PV modules, CHP units, EES systems and heatonly units.  Considering non-linear model for the technical constraints and cost function of a number of DERs.  Considering the actual location of DERs in the radial network, where grid constraints occur.  Modeling uncertainty of wind speed, solar radiation, market price, and electrical load.  Using two-stage stochastic programming for modeling the optimization problem.  Using Particle Swarm Optimization (PSO) and Multi-Objective PSO algorithms for single-objective and multi-objective optimizations, respectively. This paper is organized as follows: Section 2 describes the structure of the VPP, local network and the market framework. Section 3 presents the optimization procedure. The problem formulation is provided in Section 4. Section 5 explains the implementation of the proposed method. Section 6 presents the case study and simulation results. Finally, the conclusions are provided in Section 7. 2. The VPP 2.1. Topology of the VPP The local network containing VPP is a radial distribution network similar to the one presented in Ref. [17], as illustrated in Fig. 1. The exchanged power between VPP and the electricity market crosses through Line Np , which is connected to Point of Common Coupling (PCC) of VPP with upstream network. Each plant of VPP is individually connected to the distribution network [7]. Resources existing on the local network that are not part of the VPP can be modeled as independent resources with positive (DER) and

634

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Line 1

Line Np

PCC

Upstream Network

Substation Transformer Plant 1

Plant 2

Plant Np

Fig. 1. Local network of VPP.

negative (load) active powers. However, the presence of these independent resources in the local network has been ignored [9]. Therefore, all resources, including loads and DERs in the local network, are assumed to be controlled by VPP. Consequently, the power flow through each line can be controlled by VPP operator. It should be noted that only active power is considered in this paper. Reactive power consideration is left for our future work.

produced by CHP unit and heat-only unit exceed the thermal load,

2.2. Structure of each plant

2.3. Communication of VPP

Structure of each single plant is shown in Fig. 2. This structure is similar to the one investigated in Ref. [7], with the exception that the thermal storage and demand response resources have been ignored. Also, in order to improve the model proposed in Ref. [7], nonlinear mathematical model for DERs has been used instead of linear models. Each plant consists of an electrical section and a thermal section. Resources in the electrical section include electrical link of CHP unit, PV modules, wind turbines, and EES (electrochemical battery). These resources are used to supply electricity for VPP consumers in the local network or to inject energy to the upstream network based on transactions between the VPP and the energy market. The equivalent electric output power of each plant equals the total power of resources in the electrical section of the same plant. On the other hand, thermal load demand is locally supplied by resources available in the thermal section. These resources include thermal link of CHP unit and heat-only unit. If the total heat

As shown in Fig. 3, by implementing smart grid technologies, the VPP's operator can exchange information with electricity market, external entities, as well as loads and DERs in its territory in order to determine the optimal scheduling of resources and bidding strategy in electricity market [7]. Although companies or individuals can be owners of DERs, the operation of all resources is delegated to the VPP operator [17]. In this paper, the VPP operator manages all resources with the goals of maximizing profit and minimizing emission. The purchase and sale rates of electricity are both equal to the market clearing price.

then the thermal energy surplus Hsh is released into the atmosphere by using a heat exchanger. In this work, According to the definition proposed in Ref. [19], by considering the actual location of individual DERs in the network, DERs are aggregated into a large scale VPP.

3. The optimization problem The complete procedure of solving the non-linear optimization problem is shown in Fig. 4. The inputs for the optimization problem are:

Fig. 2. Structure of a single plant.

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

P’s VP itory r ter VPP

Fuel Price External entities Weather Data ...

DERs

635

Electricity market

Load

Two Way Data Flow Fig. 3. The VPP's framework.

Hourly average and standard deviation of uncertain parameters

Wind speed

Solar Market radiation price

Deterministic input parameter

Electric load

Thermal load

Scenario generation and reduction module Wind speed Solar radiation scenarios scenarios Output power computing module

Market prices scenarios

Electric loads scenarios

Output power Output power scenarios of wind scenarios of PV turbines modules

PSO/MOPSO optimization module

Technical constraints of distribution lines and DERs

Results presenting module Optimal bids/offers of VPP in energy market Daily optimal operation of DERs Fig. 4. Complete procedure of solving optimization problem.

 Hourly average and standard deviation of uncertain parameters of wind speed, solar radiation, market price, and electrical load.  Hourly values of thermal load demand as deterministic input parameters. The optimization is done with respect to the following constraints:  Operational constraints of DERs.  Thermal limit of distribution lines. The optimization algorithm calculates the following values as outputs with respect to the objective functions of maximizing the VPP net daily profit and minimizing daily emissions:  Optimal bids/offers of VPP in day-ahead market.  Day-ahead optimal operation of DERs.

4. The mathematical model 4.1. CHP unit The mathematical model of CHP units is taken from Ref. [20]. The electrical and thermal output power is assumed to be dependent on each other, thus forming a Feasible Operating Region (FOR). In this paper, the two first and second type CHP units are considered with convex and non-convex FORs, respectively. The FORs of CHP units are shown in Fig. 5. Relations (1)e(5) are used to model first type of CHP unit. Eq. (1) represents the area below the curve AB. Eqs. (2) and (3) express the area below the curves BC and CD, respectively. In these relations, M indicates a sufficient large number. In addition, if the binary variable V chp t;p is zero, the output power in Eqs. (2) and (3) will be zero. Eqs. (4) and (5) represent the maximum electrical and thermal

636

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

P (MW)

P (MW) A

A

B

chp P chp t;p  P p;E 

B

Sec I

Sec II

C

FOR

FOR

chp  P chp p;E  P p;F chp Hp;E



chp Hp;F

   chp Hchp   1  X1;t  M t;p  H p;E

G

D

(8) E

F C

D

chp P chp t;p  P p;D  H (MWth)

(a)

(b)

H (MWth)

chp chp P p;D  P p;E  chp HpD



chp Hp;E

   chp Hchp t;p  H p;D   1  X2;t  M (9)

Fig. 5. FOR for CHP units (a) first type, (b) second type. chp

chp

chp

chp P t;p

chp P t;p





chp P p;A

chp P p;B





chp P p;A chp H p;A

 

chp P p;B chp Hp;B



chp  P chp p;B  P p;C chp

chp

H p;B  Hp;C

chp Ht;p

chp Ht;p





chp Hp;A

chp Hp;B

chp

0  P t;p  P p;A  V t;p

output power constraints, respectively.





0

chp

(10)

chp

0  Ht;p  H p;C  V t;p

(11)

X1;t þ X2;t ¼ V chp t;p

(12)

  chp chp Ht;p  Hp;E  1  X1;t;p  M

(13)

  chp chp Ht;p  Hp;E   1  X2;t;p  M

(14)

(1)

  chp   1  V t;p  M (2)

The operational cost of a CHP unit C ope t;p is presented in Eq. (15).

P chp t;p



P chp p;C



chp chp P p;C  P p;D  chp

chp

H p;C  Hp;D

Hchp t;p



Hchp p;C



The cost of CHP unit is equal to the operational cost plus startup and shutdown costs as shown in Eq. (16). Also, startup and shutdown status of the CHP units is determined using Eqs. (17) and (18), respectively.

    1  V chp M t;p (3)

chp

chp

chp

0  P t;p  P p;A  V t;p

(4)

  2  chp chp ¼ ap  P chp C ope þ bp  P chp t;p P t;p ; H t;p t;p t;p þ cp þ dp 2    chp chp  Hchp þ ep  Hchp t;p t;p þ fp  P t;p  H t;p (15)

chp

chp

chp

0  Ht;p  Hp;B  V t;p

(5)

The features of the second type of CHP are presented by relations (6)e(14). Due to the non-convex FOR of the second type of CHP, it cannot be modeled with the proposed formulation for the first type of CHP with convex FOR. Therefore, in the formulation of the second type of CHP, two additional binary variables X1;t and X2;t have been used. Hence, the non-convex FOR is separated into two convex subsections I and II, as shown in Fig. 5. Eq. (6) represents the area under the curve BC. The area over the curve CD is represented by Eq. (7). The areas above the curves EF and DE are expressed in Eqs. (8) and (9), respectively. Eqs. (10) and (11) represent the maximum electrical and thermal output power constraints, respectively. In Eqs. (12)-(14), the binary variables X1;t and X1;t are used to specify the section where the operating point of CHP unit is located. Eq. (12) shows that when the CHP unit is ON, the operating section of this unit would be either I (X1;t ¼ 1; X2;t ¼ 0) or II (X1;t ¼ 0; X2;t ¼ 1).

chp

chp

P t;p  P p;B 

chp

chp

P t;p  P p;C 

chp chp P p;B  P p;C  chp H chp p;B  H p;C

chp  P chp p;C  P p;D chp H chp p;C  H p;D

chp

chp

chp

chp

Ht;p  Hp;B

Ht;p  Hp;C





0

(6)

0

(7)

chp

ope

chp

chp

sd C t;p ¼ C t;p þ C su p  SU t;p þ C p  SDt;p

(16)

  chp chp chp SU t;p ¼ V t;p  1  V t1;p

(17)

  chp chp chp SDt;p ¼ 1  V t;p  V t1;p

(18)

4.2. Heat-only unit Heat-only units are applied to supply thermal load. The operational constraint of heat-only units is expressed in Eq. (19). The production cost of heat-only unit is a quadratic and non-linear function of thermal output power as shown in Eq. (20) [21]. ho 0  Hho t;p  H max;p

(19)

  2    ho ho þ bp H ho C ho t;p H t;p ¼ ap  H t;p t;p þ gp

(20)

4.3. Wind turbine Wind turbine as a renewable distributed generation is modeled according to Ref. [22]. The available power from wind turbines in each plant is calculated using Eq. (21).

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

  wt P wt s;t;p vs;t ¼ N p

8 0 vs;t < vcin > > > > > !3 > > > vs;t  vcin > wt < P rated  vcin  vs;t < vrated vrated  vcin  > > > > wt c > > > P rated vrated  vs;t < vout > > : 0 vcout  vs;t (21)

637

network constraints, a load curtailment, which is known as Energy Not Served (ENS), is scheduled. As shown in Eq. (32), the amount of load curtailment, as a share of the electric load is bounded by a ens maximum value Ps;t;p;max [7]. The cost of load curtailment is calculated by Eq. (33), at a high price known as VOLL (Value of Lost Load). ens ens 0  Ps;t;p  Ps;t;p;max

(32)

  ens ens C ens s;t;p P s;t;p ¼ VOLL  P s;t;p

(33)

4.4. PV modules The ambient temperature of the site, the solar radiation, and the characteristics of the module itself are parameters that influence the output power of PV modules, as shown in Eqs. (22)-(26) [7].


TCs;t ¼ ATt þ sors;t 

NOT  20 0:8

 (22)

h  i Is;t ¼ sors;t  Isc þ Ki  TCs;t  25

(23)

Vs;t ¼ Voc  Kv  TCs;t

(24)

FF ¼

VMPP  IMPP Voc  Isc

 pv  P s;t;p sors;t

¼

pv Np

(25)  FF  Vs;t  Is;t

(26)

4.7. Thermal limit of power lines In this paper, the thermal limit of power lines is considered as a network constraint, which is presented in Eq. (34) [7]. In this paper, only the active power is considered and reactive power consideration is left for our future work. Therefore, it is assumed that system power factor is equal to unit.

   line  P s;t;p   P line p;max

(34)

4.8. Power balance Equations related to electrical and thermal power balance are expressed by Eqs. (35)-(39). The electrical power balance is given in Eq. (35). P eq s;t;p represents the equivalent electric output power of each plant. In Eq. (36), the served electrical load demand P sel s;t;p is equal to the load demand minus the ENS. The power flow through each line is calculated by Eq. (37). Eq. (38) represents the amount of

4.5. EES system The operational constraints of EES systems are expressed in Eqs. (27)-(31) [20]. The constraints imposed on charge and discharge power are given in Eq. (27). The State of Charge (SoC) of EES system is bounded by the minimum and maximum allowable level of energy as shown in Eq. (28). Initial and final SoC of EES system are determined in Eq. (29). Eq. (30) states that charging and discharging of EES system cannot occur simultaneously. The energy dynamic model of EES system is shown in Eq. (31). st st st st st 0  Pt;p;ch  Pp;max;ch  bst p;ch ; 0  Pt;p;dch  Pp;max;dch  bp;dch

(27) st st Est p;min  SOC t;p  Ep;max

(28)

st SOC st 0;p ¼ E p;initial ;

(29)

st SOC st 24;p ¼ E p;final

power exchanged with the upstream network. Also, P grid s;t is the same offered to day-ahead market; the power sold or purchased from the energy market is indicated with the positive and negative values of this variable, respectively. The thermal power balance is expressed by Eq. (39). eq

chp

pv

st sel P s;t;p ¼ P t;p þ P s;t;p þ P wt s;t;p þ P t;p  P s;t;p

(35)

el ens P sel s;t;p ¼ P s;t;p  P s;t;p

(36)

P line s;t;p ¼

p X

P s;t;i

eq

(37)

eq

(38)

i¼1

grid

P s;t ¼

Np X

P s;t;i

i¼1 dch bst p;ch þ bp;dch  1

st SOC st t;p ¼ SOC ðt1Þ;p þ

(30)

st hst p;ch  P t;p;ch 

P st t;p;dch hst p;dch

!

chp

sh Htlt;p ¼ H t;p þ Hho t;p  H t;p

(39)

(31)

4.6. ENS If it is not possible to fully supply the entire electric load demand, due to the insufficient production of VPP resources or

4.9. Objective function 4.9.1. Profit The expected day-ahead VPP profit is considered as the first objective function in this paper, as expressed in Eq. (40). Two-stage stochastic programming is used for implementing the first objective function. The variables in the first stage are scenario-

638

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

independent and include:  The cost of CHP units including operational, startup and shutdown costs.  The cost of heat-only units. On the other hand, the variables in the second stage are scenario-dependent and include:  The exchanged cash flow between VPP and electricity market.  Income from sales of electricity to end-consumers at retail rates.  The cost corresponding to not served electrical loads.

8 Np o Xn chp > > > C t;p þ C ho  > t;p > Ns 24 < X X 8 p¼1 Profit ¼ max ps  Np n < > > t¼1 > s¼1 > rem  P grid þ X rret > s;t t s;t :: p¼1

9 > > > > > =

9 o= > > > ens tl e h >  P sel s;t;p þ rt  H t;p  C s;t;p ; > ;

4.9.2. Emission Minimizing the expected day-ahead emission is the second objective function considered in the day-ahead VPP scheduling, as expressed in Eq. (41). Two-stage stochastic programming is used for modeling the second objective function. The first and second stage variables are scenario-independent and scenario-dependent, respectively. Scenario-independent variables are the emissions from the CHP units and heat-only units. Also, the only scenariodependent variable is emissions from the main grid generation system.

Emission ¼ min

Ns X

ps 

s¼1

8 9 Np n o> X > > > chp ho 24 < = X E þE t;p

> p¼1 t¼1 > :

grid þEs;t

t;p

> > ;

(41)

The total emissions per hour by CHP units, heat-only units and the main grid generation system are calculated by Eqs. (42)-(44), respectively [20]. It should be noted that the amount of main grid generation system emissions are considered only when electricity is purchased from the power market, as expressed in Eq. (44).

Echp t;p



¼ NOX

chp

þ SO2

chp

þ CO2

chp





uncertain parameter and assuming a standard deviation of 10%, the Probability Distribution Function (PDF) of uncertain parameters is formed. The beta and Weibull PDFs are chosen for modeling solar radiation and wind speed, respectively. Also normal PDF is used for modeling electric load power and market price. The PDF of each uncertain parameter is split into some sections called scenarios, and then a specific weight called probability is assigned to each scenario. In this paper, seven scenarios are considered for each uncertain parameter. As the total number of scenarios is equal to the Cartesian product of the number of scenarios of each uncertain parameter, which will be a large number equal to 74, the calculation of this large number of scenarios will be very time-consuming, so a scenario

P chp t;p

(42)

  ho ho ¼ NOX ho þ SO2 ho þ CO2 ho  Ht;p Et;p

(43)

 n  o grid þ SO2 grid þ CO2 grid  max  P grid Egrid s;t ¼ NOX s;t ; 0

(44)

4.10. Scenario generation and reduction There exist uncertain parameters that affect the optimal operation of power systems. The first step in investigating the uncertainty issue related to VPPs is to identify the uncertain parameters. The most important uncertain parameters of a VPP scheduling are wind power, solar radiation, load and market price [5]. Scenario-based decision making is used to model uncertainties in this paper based on Ref. [23]. Using the hourly average of historical data for each

(40)

reduction method has been used. Thus, the number of reduced scenarios in this paper is equal to seven (Ns ¼ 7). 5. Implementation The presented model was implemented using PSO and multiobjective PSO algorithms for single-objective and multi-objective optimization, respectively. The code is very carefully developed to reduce runtime. For all case studies, 288 real variables are required. The number of particles and iterations in PSO algorithm are considered to be 100 and 1,000, respectively. It should be noted that the number of particles and iterations are selected using trial and error method. With regard to the use of a computer with Intel® Core™ i5-M430 2.37 GHZ CPU and 4 GB RAM specifications, the average calculation time is mentioned in each case study. 6. Case study Three different cases have been investigated for evaluating the proposed model for day-ahead scheduling of VPP as follows:  Case 1: Single-objective scheduling of VPP to maximize profit.  Case 2: Single-objective scheduling of VPP to minimize emission.  Case 3: Multi-objective economic/emission scheduling of VPP. The proposed scheduling model is applied to a large scale VPP composed by 4 (Np ¼ 4) plants (Fig. 2) in a radial network (Fig. 1). The scheduling of VPP is done for a 24-h period with 1-h time step. Table 2 provides the hourly average values of electricity price and electrical load power, as well as VPP's retail rate and thermal load power. Also, electrical and thermal loads of each plant are shown in Fig. 6. The hourly electricity price of open market is taken from Ref. [24]. Also, the hourly retail rates of VPP are available in Ref. [7]. The sales price of heat to consumers is assumed to be 80% of VPP's electricity retail rates. VOLL is considered to be 2000 ($/MWh) for all hours. The input data for solar radiation is according to the monthly average of data in Ref. [25] for each hour in August. The data for ambient temperature and wind speed are taken from Ref. [26]. The required technical input data for DERs and power lines are provided in Table 3-Table 9. The input data for wind

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

639

Table 2 The hourly average values of electricity price, electrical load power, as well as VPP's retail rate and thermal load power. Hour

Electricity price

Retail rate

Plant 1

Plant 2

Electrical load

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Thermal load

Plant 3

Electrical load

Thermal load

Electrical load

Plant 4 Thermal load

Electrical load

Thermal load

$/MWh

$/MWh

MW

MWth

MW

MWth

MW

MWth

MW

MWth

33 27 20 17 17 29 33 54 215 572 572 572 215 572 286 279 86 59 50 61 181 77 43 37

76 76 76 76 76 76 76 116 116 116 116 53 53 53 53 116 116 116 116 76 76 76 76 76

1.3340 1.3280 1.3340 1.3340 1.2800 1.4400 1.8880 2.0800 2.2560 2.3520 2.3680 2.0480 1.5840 1.5360 1.7440 2.1600 2.3200 2.4000 2.3040 2.1280 1.4720 0.9600 1.0080 0.9920

1.5840 1.5840 1.5840 1.5840 1.5840 1.600 1.4720 1.3440 1.4240 1.4080 1.4080 1.3280 1.4720 1.5520 1.5520 1.5520 1.5520 1.5200 1.5200 1.5200 1.5360 1.5200 1.5040 1.4880

0.6080 0.5920 0.6080 0.5760 0.5920 0.5280 0.9280 1.2480 1.5200 1.5520 1.4720 1.5200 1.4560 1.5360 1.4400 1.5840 1.6000 1.6000 1.3120 1.0560 0.7200 0.5440 0.4800 0.4640

0 0 0 0 0 0 0.0320 1.5680 1.7920 1.6800 1.8720 1.6000 1.3760 1.8720 1.6800 1.8400 1.8720 1.7920 1.7760 1.6320 0.0320 0 0 0

1.1200 1.1680 1.2000 1.1680 1.1680 1.1680 1.2000 1.1840 1.0880 1.1360 1.1520 1.1840 1.1680 1.1360 1.1200 1.1200 1.2640 1.2800 1.2320 1.1520 1.1680 1.1200 1.0560 1.0720

0.5280 0.5280 0.5280 0.5280 0.5280 0.5280 0.5440 0.5600 0.8000 0.9760 1.0880 1.1200 1.1200 1.0400 1.0400 1.0880 1.0720 0.9280 1.8000 0.6400 0.7040 0.5280 0.5120 0.5120

0.2880 0.2880 0.2880 0.2880 0.2880 0.2720 0.3040 0.3360 0.4960 0.6400 0.5920 0.6080 0.5760 0.5600 0.6240 0.5920 0.5760 0.5120 0.4800 0.4320 0.3360 0.3040 0.3040 0.3040

0.9600 0.9600 0.9440 0.9600 0.9600 0.9600 0.9440 0.9600 0.9600 0.9440 0.9440 0.9440 0.9440 0.9600 0.9600 0.9600 0.9600 0.9440 0.9440 0.9440 0.9440 0.9600 0.9600 0.9600

2.5

2

Power (MWth)

Power (MW)

2 1.5 1

1.5

1

0.5

0.5 0

0 5

10

15

20

5

Time (hour) (a)

10

15

20

Time (hour) (b)

Plant 1 Plant 2 Plant 3 Plant 4

Fig. 6. The power pattern of the (a) electrical and (b) thermal load at each plant.

Table 6 Parameters of heat-only units.

Table 3 Parameters of wind turbines. Plant

P wt rated (kW)

vcin (m/s)

vcout (m/s)

vrated (m/s)

N wt p

1, 2, 3, 4

150

3.5

25

13.5

3




$ MWth2






$ MWth

Plant

Hho max;p ðMWthÞ

ap

1, 2, 4 3

1.2 0.6

0.052 0.038

3.0651 2.0109

bp



gp ð$Þ 4.8 9.5

Table 4 Parameters of PV modules. Plant

V OC (V)

I SC (A)

K i (I/ C)

K v (V/ C)

I MPPT (A)

V MPPT (V)

N OT ( C)

Nppv

1, 2, 3, 4

21.98

5.32

0.00122

0.0144

4.76

17.32

43

2240

Table 5 Parameters of CHP units.



    sd Plant cp ð$Þ Feasible region coordinates [P,H] $ $ $ $ $ C su p ; C p ð$Þ ap bp ep fp dp 2 2 MW MWth MW: MWth MW MWth 1, 2 3, 4

0.0345 0.0435

44.5 56

26.5 12.5

0.03 0.027

4.2 0.6

0.031 0.011

20 20

[1.258,0], [1.258,0.324], [1.102,1.356], [0.4,0.75], [0.44,0.159], [0.44,0] [2.47,0], [2.15,1.8], [0.81,1.048], [0.988,0]

640

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Table 7 Parameters of EES systems. Plant

P st p;max;dch ðMWÞ

P st p;max;ch ðMWÞ

Est p;max ðMWhÞ

Est p;min ðMWhÞ

Est p;initial ðMWhÞ

Est p;final ðMWhÞ

hst p;dch (%)

hst p;ch (%)

1, 2, 3, 4

0.4

0.4

1.2

0.24

0.375

0.375

75

75

turbines is provided in Table 3 [27]. Also, the input data for PV modules is given in Table 4 [7]. The operational parameters of CHP units are presented in Table 5 [20]. The parameters of heat-only units and EES systems are provided in Table 6 and Table 7, respectively. The assumed parameters for the thermal limit of power lines are presented in Table 8. Emission factors are given in Table 9. The emission factors for CHP units and grid generation system are taken from Ref. [20]. In addition, the emission factors for gas-fired heat-only units are according to Ref. [28].

Table 10 Maximum, mean, and minimum profit for 20 independent runs for case 1.

6.1. Case 1

the electric power generation and the power values below the horizontal axis indicate the electric power consumption. It should be noted that the power generation and consumption of VPP is the result of the accumulation of power in the four plants. As seen in Fig. 8 (a), the VPP purchases electricity from the energy market like a consumer in periods with low electricity price; while during periods with high electricity price, the VPP sells electricity to the energy market like a real power plant. When electricity prices are low, the purchase of electricity from the energy market is more economical than generating electricity by CHP units; therefore these units are not committed or reduce their output powers. However, in some periods with low electricity price, when heat-only units are not able to fully supply the thermal demand, CHP units must be committed (Fig. 9). The thermal power balance in the local network of VPP is shown in Fig. 9. Given that the thermal load demand is locally supplied, the thermal power balance in each plant is displayed separately. The heat values above and below the z axis indicate the production and consumption of heat, respectively. As seen in Fig. 9, thermal load demand in four plants and at all hours is fully supplied by CHP and heat-only units. Due to the lower cost of heat-only units compared to the cost of CHP units, heat-only units have a larger share in supplying heat demand. EES devices have a very good performance with regard to electricity prices. They are charged at low prices and discharged at

Convergence curve of PSO algorithm for case 1 is shown in Fig. 7. As it is seen in this figure, the VPP net daily profit converges to the optimum value of 23,302.8271 ($) after 1000 iterations (100,000 number of function evaluations). Statistical results of the proposed method for 20 independent runs are provided in Table 10. The electrical power balance per hour is well presented in Fig. 8. The left and right axes represent the power and the electricity price, respectively. The power values above the horizontal axis represent

Table 8 Parameters of power lines. Plant

Plant 1

Plant 2

Plant 3

Plant 4

P line p;max

2.5

3.5

4

7

Table 9 Emission factors related to NOx , CO2 and SO2 . Emissions

Grid

CHP

Heat-only

NOx CO2 SO2

2.295 921.25 3.583

0.1995 723.93 0.0036

0.3145 401.4284 0.0027

Value

$ $ $ $ s

22,600.1679 22,955.3462 23,302.S8271 176.9387 148.0945

104 13

104

2.4

Net profit ($)

Unit

Minimum profit Mean profit Maximum profit Standard deviation Runtime

2.2

12

2

11

1.8

10

1.6

9

1.4

8

1.2

7

1 0

100

200

300

400

500

600

700

800

Iteration Fig. 7. Convergence characteristics of PSO algorithm for case 1 and case 2.

900

6 1000

Emissions (kg)

(MW)

Output

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

641

600 10

5

Power (MW)

200

0

0

-200 -5

Electricity price ($/MWh)

400

-400 -10 Wind turbine PV CHP EES Energy market Electric load Electricity price

-600 0

1

2

3

4

5

6

7

8

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

Hour (h) (a) 600 10

5

Power (MW)

200

0

0

-200 -5

Electricity price ($/MWh)

400

-400 -10 -600 0

1

2

3

4

5

6

7

8

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

Hour (h) (b) Fig. 8. Electrical power balance in the local network of VPP for (a) case 1 and (b) case 2.

high prices, which means that the VPP purchases electricity at low prices and sells at high prices to increases its profit. The SoC of EES devices is shown in Fig. 10. Details of costs and revenues of VPP are illustrated in Fig. 11 (a). Revenues are displayed above the horizontal axis and costs are shown below the horizontal axis. Revenues include the sale of electricity and heat to consumers and the sale of electricity to the energy market. During periods 8 to 18 and 20 to 22, the VPP earns profit by selling electricity to the energy market. Particularly during periods 10 to 12 and 14, when the highest electricity prices occur, the VPP earns the most. Also, costs include the cost of purchasing electricity from the energy market and the cost of CHP and heatonly units. The cost of purchasing electricity from the energy market is relatively low due to the purchase at low prices. The VPP net hourly profit, which is the sum of revenues and costs per hour,

is shown in Fig. 12. 6.2. Case 2 Convergence curve of PSO algorithm for case 2 is shown in Fig. 7. As it is observed in Fig. 7, the amount of daily emission converges to the optimum value of 64,432.3217 (kg) after 1000 iterations (100,000 number of function evaluations). Statistical results of the proposed method for 20 independent runs are provided in Table 11. The electrical power balance for case 2 is shown in Fig. 8 (b). Due to the fact that the goal of this case is minimizing emissions, the scheduling of DERs is done in a different way compared to case 1. Since the emissions of committed power plants in the main grid are higher than the emissions from the VPP resources, The VPP operator meets the demand by DERs in its territory and does not

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Thermal power (MWth)

642

2

0

-2 0 3 6

4 9 12

3

15 18

Time (hour)

CHP Heat-only Surplus heat Thermal load

2

21 24

Plant

1

Fig. 9. Thermal power balance in the local network of VPP for case 1.

600 SOC - Plant 1 SOC - plant 2 SOC - Plant 3 SOC - Plant 4 Market price

Energy (MWh)

1.2

500

1

400

0.8

300

0.6

200

0.4

100

0.2 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

Price ($/MWh)

1.4

0 24

Time (hour) Fig. 10. SoC of EES devices for case 1.

purchase electricity from energy market. Also, the thermal power balance in four plants is illustrated in Fig. 13. According to this figure, CHP units have greater contribution to supply thermal load demand compared to case 1. Also, details of costs and revenues in the second case are shown in Fig. 11 (b). The VPP net day-ahead profit in this case is 9,883.6889 ($), which has decreased compared to the first case by 57.59%. Moreover, the day-ahead emission in the second case is 64,432.3217 (kg), which has decreased by 47.60% compared to the first case. 6.3. Case 3 In the third case, the multi-objective energy management of VPP is carried out. The Pareto-based approach is presented to get a set of non-dominated solutions. The number of repository members is

considered to be 200. The Pareto-optimal solutions for case 3 are shown in Fig. 14. The maximum day-ahead profit and the minimum day-ahead emissions, which have been obtained by single-objective optimization in case 1 and case 2 respectively, are presented in Table 12. After generating the Pareto front, VPP operator selects a compromise solution in accordance with regulatory restrictions related to emissions and economic constraints associated with the distribution system operation. The VPP operator can also apply Multi Attribute Decision Making (MADM) approach which assists in choosing the best compromise solution. Examples of MADM include Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) used to extract the best solution for multi-objective generation scheduling in Ref. [29], fuzzy set employed to facilitate selection of the best solution for Economic-environmental energy and reserve scheduling

4000

4000

3000

3000

Cost/Revenue ($)

Cost/Revenue ($)

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

2000 1000

643

2000 1000 0

0

-1000

-1000 0

5

10

15

20

25

Time (hour) (a)

0

5

Electric power sale Heat power sale Energy market Heat-only CHP

10

15

20

25

Time (hour) (b)

Fig. 11. Expected costs and revenues of VPP for (a) case 1 and (b) case 2.

3500 Case 1 Case 2

3000

profit ($)

2500

2000

1500

1000

500

0 0

1

2

3

4

5

6

7

8

9

10

11 12 13 14

15 16 17

18 19 20

21 22 23

24

Time (hour) Fig. 12. The hourly expected day-ahead profit of the VPP for case 1 and case 2.

Table 11 Maximum, mean, and minimum amount of emission for 20 independent runs for case 2. Output

Unit

Value

Minimum emission Mean emission Maximum emission Standard deviation Runtime

kg kg kg kg s

64,432.3217 66,070.1682 67,077.3937 556.6522 171.4826

of smart distribution systems in Ref. [30], max-min method used to determine the final compromise solution for the choice of distributed generation capacity within existing networks in Ref. [31], and

Knee set presented for multi-objective planning with uncertainty in Ref. [32]. 7. Conclusion Due to the fact that the greenhouse gas emissions are one of the critical environmental issues, this paper addresses the operational scheduling of DERs of a VPP focusing on both maximization of the expected day-ahead profit and minimization of the expected day-ahead emissions. A stochastic non-linear model is proposed for the energy management of a VPP including renewable energy and conventional distributed generations as well as EES systems. The VPP energy management with the aim of maximization of

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

Thermal power (MWth)

644

2

0

-2 0 5

4 10 3 15 CHP Heat-only Surplus heat Thermal load

2

20

Time (hour)

25

Plant

1

Fig. 13. Thermal power balance in the local network of VPP for case 2.

13

104

12

Emission (kg)

11

10

9

8

7

6 0.8

1

1.2

1.4

1.6

1.8

Net Profit ($)

2

2.2

2.4 104

Fig. 14. The Pareto-optimal solutions for case 3.

Table 12 Payoff table of the multi-objective PSO multi-objective method. Objective function

Profit

Emission

$

kg

maxF profit

23,302.8271

122,963.4634

minF emission

9,883.6889

64,432.3217

the day-ahead profit leads to 23,302.8271 ($) net daily profit and 122,963.4634 (kg) daily emissions. However, consideration of the

emissions reduction as the objective function leads to about 60% reduction in daily profit and about 50% reduction in daily emissions. Moreover, the multi-objective economic/emission operational scheduling has been implemented for generating the Pareto front in order to provide the possibility of selecting a compromise solution for the VPP operator in accordance with environmental limitations and economic constraints. Finally, the contributions of our future work would be modeling more grid constraints such as reactive power consideration and implementing different types of demand response programs in the VPP energy management.

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

645

Appendix Table 13 Optimal scheduling of CHP units Hour

Case 1 chp P t;p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Case 2 chp Ht;p ðMWthÞ

ðMWÞ

chp

chp

P t;p ðMWÞ

Ht;p ðMWthÞ

Plant1

Plant 2

Plant 3

Plan4

Plant1

Plant2

Plant3

Plan4

Plant1

Plant2

Plant3

Plan4

Plant1

Plant2

Plant3

Plan4

0.4352 0.4340 0.4065 0.4011 0.4042 0.7294 0.4402 1.2323 1.2580 1.2580 1.2580 1.2580 1.2347 1.2270 1.2519 1.2436 1.2232 1.2494 1.1160 1.2392 1.2320 1.2570 0.5121 0.4461

0 0 0 0 0 0 0 1.2208 1.1768 1.2344 1.2053 1.2154 1.2580 1.2054 1.2295 1.1892 1.1139 1.1836 1.1775 1.2311 1.2580 0 0 0

0 1.1337 0 0 0 0 0 1.4814 2.4127 2.3910 2.3774 2.3756 2.3771 2.3913 2.3572 2.3816 2.2180 2.2261 1.9268 2.3201 2.4417 2.1717 0 0

0 0 0 0 0 0 0 1.5749 2.4700 2.4700 2.4700 2.4699 2.4693 2.4700 2.4698 2.4698 2.4672 2.1629 0.8408 1.1687 2.4700 2.4655 0 0

0.6033 0.6058 0.7280 0.7420 0.7285 0.4009 0.4556 0.1898 0.2248 0.2269 0.2211 0.1497 0.2719 0.3519 0.3524 0.3538 0.3538 0.3426 0.7170 0.3250 0.3403 0.3267 0.8468 0.4085

0 0 0 0 0 0 0 0.4110 0.5923 0.4802 0.6721 0.4006 0.2898 0.6720 0.4815 0.6400 0.6763 0.5989 0.5793 0.4956 0.0320 0 0 0

0 0.5292 0 0 0 0 0 0.5701 0.2000 0.3765 0.4880 0.5241 0.5222 0.4402 0.4441 0.4964 1.0731 0.9285 0.8013 0.6408 0.1016 0.5288 0 0

0 0 0 0 0 0 0 0.9601 0 0 0 0 0 0 0 0 0 0.8993 0.9440 0.9458 0 0.0164 0 0

0.9010 1.0366 0.9082 0.8484 0.7060 0.8512 1.0863 0.8710 0.8162 0.5594 1.0699 1.0320 0.4001 0.6785 0.4000 0.5144 0.8698 0.7844 1.0158 1.0697 0.9482 0.8512 0.9655 1.1020

0 0 0 0 0 0.6808 0 1.0789 1.0734 1.0799 1.0979 1.0624 0.8555 1.0998 0.8061 0.6213 1.0993 1.0896 0.7416 1.0833 0.7226 0.6031 0 0

0.9285 1.2169 0 0.9607 1.1955 0 0 0 1.1982 1.7917 0.8225 0.9428 0.8103 1.4221 1.1265 1.7671 1.6422 2.2235 1.4814 0.9589 0.8982 0 0 0

0.8418 0 0.8702 0 0 0 1.3220 1.0139 0.8599 0.8544 1.2004 0.8608 1.0740 0 0.8514 0.8502 1.0231 0.8173 1.5253 1.2958 1.3560 0.8403 1.0189 0.8492

1.1818 1.2977 1.1864 1.1371 1.0138 1.1393 1.3319 1.1560 1.1092 0.8875 1.3283 1.2914 0.7498 0.9904 0.7500 0.8441 1.1556 1.0812 1.2699 1.3271 1.2233 1.1390 1.2377 1.3477

0 0 0 0 0 0.0036 0 1.3346 1.3306 1.3368 1.3520 1.3217 1.1432 1.3541 1.0992 0.9410 1.3533 1.3452 1.0438 1.3399 0.0320 0.0033 0 0

0.5279 0.5280 0 0.5281 0.5280 0 0 0 0.8000 0.9764 1.0439 1.1204 1.0473 1.0400 1.0401 1.0880 1.0718 0.9279 0.8001 0.6400 0.7040 0 0 0

0.9601 0 0.9440 0 0 0 0.9377 0.9600 0.9600 0.9440 0.9440 0.9457 0.9443 0 0.9600 0.9597 0.9601 1.0048 0.9440 0.9440 0.9440 0.9603 0.9600 0.9597

References [1] Li B, Shen J, Wang X, Jiang C. From controllable loads to generalized demandside resources: a review on developments of demand-side resources. Renew Sustain Energy Rev 2016;53:936e44. [2] Fan S, Ai Q, Piao L. Fuzzy day-ahead scheduling of virtual power plant with optimal confidence level. IET Gener, Transm Distrib 2016;10:205e12. [3] Papaefthymiou SV, Papathanassiou SA. Optimum sizing of wind-pumpedstorage hybrid power stations in island systems. Renew Energy 2014;64: 187e96. [4] Dietrich K, Latorre JM, Olmos L, Ramos A. Modelling and assessing the impacts of self supply and market-revenue driven Virtual Power Plants. Electr Power Syst Res 2015;119:462e70. [5] Nosratabadi SM, Hooshmand R-A, Gholipour E. A comprehensive review on microgrid and virtual power plant concepts employed for distributed energy resources scheduling in power systems. Renew Sustain Energy Rev 2017;67: 341e63. [6] Skarvelis-Kazakos S, Rikos E, Kolentini E, Cipcigan LM, Jenkins N. Implementing agent-based emissions trading for controlling Virtual Power Plant emissions. Electr Power Syst Res 2013;102:1e7. [7] Zamani AG, Zakariazadeh A, Jadid S, Kazemi A. Stochastic operational scheduling of distributed energy resources in a large scale virtual power plant. Int J Electr Power Energy Syst 2016;82:608e20. [8] Arslan O, Karasan OE. Cost and emission impacts of virtual power plant formation in plug-in hybrid electric vehicle penetrated networks. Energy 2013;60:116e24. [9] Zamani AG, Zakariazadeh A, Jadid S. Day-ahead resource scheduling of a renewable energy based virtual power plant. Appl Energy 2016;169:324e40. [10] Zapata J, Vandewalle J, D'haeseleer W. A comparative study of imbalance reduction strategies for virtual power plant operation. Appl Therm Eng 2014;71:847e57. [11] Tascikaraoglu A, Erdinc O, Uzunoglu M, Karakas A. An adaptive load dispatching and forecasting strategy for a virtual power plant including renewable energy conversion units. Appl Energy 2014;119:445e53. [12] Kardakos EG, Simoglou CK, Bakirtzis AG. Optimal offering strategy of a virtual power plant: a stochastic bi-level approach. IEEE Trans Smart Grid 2016;7: 794e806. [13] Tajeddini MA, Rahimi-Kian A, Soroudi A. Risk averse optimal operation of a virtual power plant using two stage stochastic programming. Energy 2014;73: 958e67.

i [14] Pandz c H, Kuzle I, Capuder T. Virtual power plant mid-term dispatch optimization. Appl Energy 2013;101:134e41. [15] Dabbagh SR, Sheikh-El-Eslami MK. Risk-based profit allocation to DERs integrated with a virtual power plant using cooperative Game theory. Electr Power Syst Res 2015;121:368e78. [16] Pand zi c H, Morales JM, Conejo AJ, Kuzle I. Offering model for a virtual power plant based on stochastic programming. Appl Energy 2013;105:282e92. [17] Giuntoli M, Poli D. Optimized thermal and electrical scheduling of a large scale virtual power plant in the presence of energy storages. IEEE Trans Smart Grid 2013;4:942e55. [18] Shabanzadeh M, Sheikh-El-Eslami M-K, Haghifam M-R. A medium-term coalition-forming model of heterogeneous DERs for a commercial virtual power plant. Appl Energy 2016;169:663e81. [19] http://www.fenix-project.org. [20] Nazari-Heris M, Abapour S, Mohammadi-Ivatloo B. Optimal economic dispatch of FC-CHP based heat and power micro-grids. Appl Therm Eng 2017;114:756e69. [21] Nazari-Heris M, Mehdinejad M, Mohammadi-Ivatloo B, BabamalekGharehpetian G. Combined heat and power economic dispatch problem solution by implementation of whale optimization method. Neural Comput Appl 2017:1e16. [22] Nojavan S, Zare K, Mohammadi-Ivatloo B. Application of fuel cell and electrolyzer as hydrogen energy storage system in energy management of electricity energy retailer in the presence of the renewable energy sources and plug-in electric vehicles. Energy Convers Manag 2017;136:404e17. [23] SoltaniNejad A, Hadayeghparast S, Mehdinejad M, Shayanfar H. A novel stochastic energy management of a microgrid with various types of distributed energy resources in presence of demand response programs. Energy; 2018. [24] Zakariazadeh A, Jadid S, Siano P. Stochastic multi-objective operational planning of smart distribution systems considering demand response programs. Electr Power Syst Res 2014;111:156e68. [25] http://weather.uwaterloo.ca/data.html. [26] Nojavan S, allah Aalami H. Stochastic energy procurement of large electricity consumer considering photovoltaic, wind-turbine, micro-turbines, energy storage system in the presence of demand response program. Energy Convers Manag 2015;103:1008e18. [27] Raoofat M, Saad M, Lefebvre S, Asber D, Mehrjedri H, Lenoir L. Wind power smoothing using demand response of electric vehicles. Int J Electr Power Energy Syst 2018;99:164e74. [28] https://www3.epa.gov/ttnchie1/ap42/ch01/final/c01s04.pdf.

646

S. Hadayeghparast et al. / Energy 172 (2019) 630e646

[29] Falsafi H, Zakariazadeh A, Jadid S. The role of demand response in single and multi-objective wind-thermal generation scheduling: a stochastic programming. Energy 2014;64:853e67. [30] Zakariazadeh A, Jadid S, Siano P. Economic-environmental energy and reserve scheduling of smart distribution systems: a multiobjective mathematical programming approach. Energy Convers Manag 2014;78:151e64.

[31] Harrison GP, Piccolo A, Siano P, Wallace AR. Exploring the tradeoffs between incentives for distributed generation developers and DNOs. IEEE Trans Power Syst 2007;22:821e8. [32] Burke WJ, Merrill HM, Schweppe FC, Lovell BE, McCoy MF, Monohon S. Trade off methods in system planning. IEEE Trans Power Syst 1988;3:1284e90.