Optimal operation of microgrids through simultaneous scheduling of electrical vehicles and responsive loads considering wind and PV units uncertainties

Renewable and Sustainable Energy Reviews 57 (2016) 721–739

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Optimal operation of microgrids through simultaneous scheduling of electrical vehicles and responsive loads considering wind and PV units uncertainties Abdorreza Rabiee a,n, Mohammad Sadeghi b, Jamshid Aghaeic c, Alireza Heidari d a

Department of Electrical Engineering, Faculty of Engineering and Technology, Shahrekord University, Shahrekord, Iran Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran c Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran d School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia b

art ic l e i nf o

a b s t r a c t

Article history: Received 7 January 2015 Received in revised form 29 November 2015 Accepted 3 December 2015

This paper deals with the simultaneous scheduling of electrical vehicles and responsive loads to reduce operation cost and emission in presence of wind and PV powers in microgrid. In the proposed method, the electrical vehicles are used for peak shaving and load curve modification while the responsive loads are employed to supply the reserves needed to compensate the intrinsic uncertainties of wind and PV powers. Furthermore, a developed two-stage model is proposed to determine the expected operation cost of microgrid (energy and reserve). In the first stage, the generation and reserve power costs are minimized while in the second stage, the costs associated with unit scheduling changes resulting from wind and PV power variations are minimized. The proposed model is implemented in a microgrid with various distributed generations. The simulation results have shown that the incorporation of electrical vehicles and responsive loads leads to decrease the system operation costs and emissions while the uncertainties related to wind and PV are compensated. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Renewable energy Microgrid Electrical vehicles Responsive load Uncertainty

Contents 1. 2.

3.

4.

5.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722 Modeling of microgrid components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 2.1. Modeling of demand response program (DRP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 2.2. Implementation of electrical vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 2.2.1. Modeling and constraints of electrical vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 2.3. Uncertainties modeling of wind and PV powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 3.1. Cost-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 3.2. Emission function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726 3.3. Single-objective function for optimal operation of microgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 3.4. First stage constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 3.5. Second – stage constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 3.6. Constraint linking the first and second stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728 Solution methodology: the PSO algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728 4.1. Binary PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729 4.2. The proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730 5.1. Scenario 1: optimal operation of microgrid without load response and electrical vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732

Corresponding author. E-mail addresses: [email protected] (A. Rabiee), [email protected] (M. Sadeghi), [email protected] (J. Aghaeic), [email protected] (A. Heidari).

http://dx.doi.org/10.1016/j.rser.2015.12.041 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

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5.2. Scenario 2: optimal operation of microgrid with load response and 5.3. Scenario 3: optimal operation of microgrid with load response and 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction In the past few decades, researchers have considered operation of distributed generations and renewable energies to reduce power generation cost and improve the system reliability and efficiency [1–3]. So far minimum fuel cost was the dominant strategy for electric power dispatching; however, environmental issues must be taken into account. Thus, decreasing pollution of power plants is a priority for electric utilities [4]. Sulfur dioxide and nitrogen oxides are the most crucial contaminants due to their adverse effect on all forms of life, global warming and natural resources. Such condition necessitates new strategies for environmental/economic dispatch as it provides commercial benefits as well as reducing emission [5]. In this regard, microgrids can meet the above requirements to supply future demands of power grids. Microgrid is a set of components which may be either connected to the grid or isolated from it. Its components include low-voltage distribution network, distributed generation units, storage devices and controllable loads [6,7]. The presence of increasing number of renewable resources (e.g. wind and solar) as well as variations in the price of energy (resulted from deregulation of electricity market) have made microgrid management a difficult task. So, some schemes are needed to provide efficient management of such systems in presence of uncertainties [8]. In [9] a novel scheduling is proposed which guarantees optimal operation of microgrid which includes renewable energy resources. The authors have included a micro-turbine/fuel cell/battery hybrid system which is responsible for power consumption fluctuations. A nonlinear constraint multi-objective optimization method is exploited to fulfill operating cost and emission requirements. The work in [10] models the microgrid management as a multi-objective optimization problem to decrease of NOx, SO2 and CO2 in addition to operation and maintenance costs. In [11], the power generation of a grid-connected microgird is optimized using heuristic optimization. The optimized cost-functions include both emissions and fuel consumption. To obtain an efficient energy management, artificial intelligence techniques are employed together with linear-programming-based multi-objective optimization in [12]. To consider intermittency, Weibull and Beta PDFs are exploited in [13] to model the uncertainty of wind speed and solar irradiation. The resulted nonlinear optimization problem is solved via differential evolution algorithm. Another scheme which could be substituted for deterministic models of uncertainties is a fuzzy set modeling approach, using chaos clonal evolutionary programming [14]. In [15] an expert energy management system for optimal scheduling of wind turbine (WT) is proposed in which an artificial neural network predicts wind power generation. The uncertainties are modeled based on confidence interval concept. The expert system is formulated and Modified Bacterial Foraging Optimization algorithm optimizes the problem while considering both operating cost and emission. In order to examine effect of uncertainty on microgrid management, a stochastic framework is introduced in [16]. This twophase approach considers various uncertainties simultaneously, including load prediction error, wind turbine generation, PV generation and market price. In its first phase, the stochastic behavior of uncertainties is converted to deterministic problems with

without electrical vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . electrical vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................................... .....................................................

733 734 734 738

different probabilities. For this purpose, PDF of variables and roulette wheel mechanism are utilized. The generated problem is solved using Adaptive Modified Firefly Algorithm (AMFA) in the second phase. In [17], cost and emission are minimized in a scenario based stochastic programming model. Moreover, similar to [16], the stochastic problem is converted to a deterministic one, using roulette wheel mechanism and PDF of input variables. The same uncertainties are dealt with in [18], using a proposed probabilistic Energy Management system. The system is based on Point Estimate Method (PEM). In this method cost-minimization is obtained using an optimal operational planning which is realized through AMFA. Battery management is investigated in [19]. The included uncertainties consist of wind power and solar energy is addressed using PEM. However, this method lacks power loss and reliability cost in its objective function. In [20], PEM is employed to model uncertainties associated with wind and solar energy in which robust optimization technique models uncertainties of load demand variations. An energy management system (EMS) is proposed in [21], aiming at managing power demand of the main grid via controlling microgrid generation. The EMS which controls the microgrid in grid-connected mode is capable of providing optimal operating strategies. It achieves minimized energy cost and emission as well as maximized output of renewable energy. Autoregressive Integrated Moving Average (ARIMA) is used to model wind power uncertainty using interval prediction [22]. Fluctuations and variations in different components of a microgrid, such as storage devices, energy resources and loads are handled by a stochastic method proposed in [23], considering power losses and operational cost-minimization. In [24], a stochastic operational scheduling is proposed to schedule energy and reserve in a system with dominant wind generation. To deal with uncertainties and including their effect on optimal management of microgrid, a probabilistic framework based on 2m PEM is proposed in [25]. To include m uncertain variables in terms of three moment of corresponding PFD, 2m runs of the framework are needed. It facilitates simultaneous consideration of load demand, grid bid variations, and fluctuations of WT and PV. Because of the unpredictable and variable nature of wind and PV powers, it is always possible that the real-time values of these variables are different from the corresponding planned values. Therefore, grid operators try to have a certain level of spinning and non-spinning reserve in the grid. Thus they would be able to compensate for the uncertainty in the output power of these sources to preserve the system security [26,27]. Reserve of power plants, pumped hydro storage (PHS), compressed air energy storage, flywheel energy storage, superconducting magnetic energy storage, super capacitor energy storage and battery energy storage are used to compensate for the uncertainty of wind and PV powers [28]. The implementation of demand response program can be another method of providing the required energy storage for the grid. This method is based on reducing customers' consumption rather than increasing power generation at power plants. Thus, balance can be restored between power generation and consumption if the system encounters power shortages (arising from wind and PV prediction errors) [29]. Due to lower costs, the

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

Nomenclature EC t C tsi C tsimn T Ng U ti P tGi C tGi RtGi:u RtGi:d λtGi:u λtGi:d rCDRtL

ECDRtL

NEV P tEV j C tEV j P tw C tw P tPV C tPV P tgrid C tgrid Nm

expected cost of the system at time t start-up cost of unit i at time t the actual start-up cost incurred by unit i in scenario m; n at time t. total number of hours total number of generating units status of the unit i in period t (ON/OFF) active power output unit i at time t cost of energy offered by unit i at time t spinning reserve up of unit i at time t spinning reserve down of unit i at time t cost of spinning reserve up offered by unit i at time t cost of spinning reserve down offered by unit i at time t capacity cost-reserve provided by DRP L at time t that is just calculated for the sets of DRPs which provide up rd and down reserve (Sru DRP and SDRP ) cost of energy provided by DRP L in period t at time t the considered for set of DRPs which provide energy (SeDRP ) number of electrical vehicle aggregators power output of aggregator j at time t cost of energy offered by aggregator j at time t wind power output at time t cost of the energy offered by wind producer at time t PV output power at time t (charge or discharge) cost of the energy offered by the PV at time t active power absorbed/injected from/to the utility at time t bid of utility at time t number of wind power scenarios (equal to 3 in this article, representing upper limit, lower limit, and predicted power)

responsive loads can be a serious rival for the power plant reserves in providing the reserve power for the grids. Recently, this field has been noticed by many researchers. In [30,31] a comprehensive review on demand response (DR) integration is provided mentioning obstacles and achievements of this field. DR programs are handled in [32] using a Virtual Power Player. Its objective is to minimize operation cost while consumption shifting is applied. Responsive loads and distributed generation units are both involved in providing reserve requirement in the method introduced by [33]. This is performed via a two-stage stochastic objective function. All different types of load consisting of residential, commercial and industrial ones play their role in DR program. A methodology is proposed in [34] to support Virtual Power Players (VPPs) in DR program management. The proposed method which is based on locational marginal prices (LMP) values that considers all energy resources (generation and storage). Using Demand Side Management (DSM) scheme is investigated in [35]. Data extracted from digital measurement units is exploited to obtain load patterns and simulate the system. Subsequently, the obtained load data is employed to train an ANN which, in turn, is used to classify new data. The results of this study revealed that DSM could be implemented using intelligent network while an acceptable performance could be achieved using ANN. In [36], DSM is examined in a heuristic manner in an off-grid system including specific requirements. The proposed system is tested and analyzed using smart house platform developed in

723

Nn

number of PV power scenarios (equal to 3 in this article, representing upper limit, lower limit, and predicted power) P rmn occurrence probability of the m-th scenario for wind power and the nth scenario for PV power r tGimn reserve deployed of energy offered by unit i in the m,n scenario at time t. rEDRtLmn energy cost of reserve provided by DRP L in the m,n scenario at time t VOLLtL value of lost load for customer L in period t NL number of load r tEV mn reserve deployed of energy offered by aggregator j in the m,n scenario at time t P twsmn wind power generation spillage in the m,n scenario at time t C tws cost of wind power spillage in the m,n scenario at time t P tPV smn PV power generation spillage in the m,n scenario at time t C tPVs cost of PV power spillage in the m,n scenario at time t P tgridmn active power absorbed/injected from/to the utility in the m,n scenario at time t P Gi; min ðtÞ lower power limit of DGs at time t P Grid; min ðtÞ lower power limit of main-grid at time t P Gi; max ðtÞ upper power limit of DGs at time t P Grid; max ðtÞ upper power limit of main-grid at time t EE t expected pollution of the system at time t EGi pollution coefficient of unit i at time t Egrid pollution coefficient of the main grid (due to energy exchange with the main grid). The pollution coefficients for units are obtained from the sum of released CO2 , SO2 , and NOx gases.

VSB-Technical University of Ostrava, Czech Republic. Reduction of peak demand was the objective of a study presented in [37]. It considers four power demand scheduling scenarios. It is assumed that each consumer has a definite number of appliances with different power consumptions in various operational times. The proposed model consists of the percentage of consumers who are available for demand scheduling program. A fuzzy subtractive clustering technique is utilized in [38] to model DR. The proposed model has considered the trade-off between imposed consumption necessities and economic benefits resulted from reshaping and rescheduling. The loads might be also considered as extra resources as is the case in an integrated electricity system. In [39], such system is modeled using an agentbased modeling. Since the model includes load and generator controllers, it provides Real-Time Pricing (RTP) for demanders and suppliers. The peak load could be managed to minimize total energy consumption cost. For this purpose some loads might be shifted to off-peak hours in a house-hold scale. In [40], an autonomous energy scheduling approach is presented to obtain this goal. It is probable that there is more than one supplier in a smart grid. In such cases, the DSM problem might be modeled as a two non-cooperative games as suggested in [41]. The first game guarantees maximum profit for a supplier using supply function biding mechanism and the second game provides optimal load profile for customers. To obtain the best condition, Nash equilibrium is explored using a tractable distributed algorithm.

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A method is presented in [42] to manage and optimize interaction between a commercial building and the grid. To forecast possible variations in power demand of the building, a simplified thermal storage model is introduced. It is used concurrent with a model which predicts normal power consumption profile of the building. In [43], a DSM and DR programs are deeply investigated in China, considering deregulation of China's power industry. Another challenge in power systems operation is related to electrical vehicles with grid-connection capabilities (EV). These vehicles can be used as loads while being charged, and as generators while being discharged, and as potential reserves (storage) otherwise. Avoiding grid overload and other problems posed by electrical vehicles would require a coordinated charging scheduling program. In [44], the operation of power plants in the presence of electrical vehicles is studied. The obtained results have indicated a considerable reduction in the costs and emissions, and increased spinning reserve which thereby improves grid reliability. In [45,46], the electrical vehicles are considered to compensate the uncertainty of the wind power. Many research works focused on the optimal management of EV charge and discharge. An encompassing review on research topics and various approaches to PHEV integration is presented in [47–49]. Furthermore, the reader may find a survey of research works conducted on Grid-Integrated Vehicle systems including their modeling and their influence on the grid in [50]. The common types of EVs and their charging systems are briefly explained. Then, their effect on low voltage distribution systems is analyzed. Vehicle-to-grid (V2G) operation of PEVs is a promising topic which must be investigated. It is a prominent approach because it may improve efficiency and reliability of the grid. Moreover, it is able to decrease operating cost while reducing greenhouse gas emission. Since EVs may be in trip, they cannot be considered as a secure ESS. In [51], an event-triggered scheduling method is proposed for V2G to overcome this problem, based on stochastic PEV connection. An Automatic Generation Control (AGC) scheme is proposed in [52] which take distributed generation units and EVs into considerations. The methodology is capable of designing an AGC in distribution level. In the system model presented in [53], V2G is considered as a distributed storage device considering battery lifetime. Moreover, using this model, G2V owners may obtain an efficient cost-benefit analysis to assess whether their participation in the program is useful or not. A multi-objective optimization algorithm is used to handle EVs management [54]. The objectives are minimizing operation costs and minimizing the difference between minimum and maximum value of system demand. In [55], a nonlinear complementarity optimization model is proposed. It aims at bidirectional coordinating dispatch of largescale PEVs based on a hierarchically coordinated operation framework. Top level Independent System Operator's (ISO) operation module of the framework is exploited in this model. In this module PEV is a type of dispatchable demand response and energy storage resource. Charging operations of EVs in smart grid are managed using an event driven model predictive control in [56]. The objectives include minimizing power consumption cost, meeting EV drivers' expectations, satisfying market and grid constraints (it is done via following a reference load profile defined by operator) and avoiding technical bounds violation. This control method encourages EV users to take part in DSM which accordingly improves the efficiency and stability of grid. In this paper, optimal operation of microgrids in the presence of electrical vehicles and responsive loads is proposed. The electrical vehicles are used for peak shaving as well as load curve correction, and the responsive loads are used to supply a part of

the required grid reserve to compensate wind and PV uncertainties. The simulation results confirm the effect of this scheduling in reducing operation costs and environmental pollution. Moreover, a two-stage optimization model is proposed to determine the expected operation cost of microgrid. In the first stage, the power generation and reserve power costs are calculated while in the second stage, the costs associated with generating rescheduling due to variations in wind and PV powers, are determined. The contributions introduced in this paper are briefly as follows: 1. Simultaneous scheduling of the electrical vehicles and responsive loads to peak shaving and supporting the uncertainties associated with wind and PV powers. 2. Presenting a developed two-stage model to calculate expected operation cost of microgrid with considering of wind and PV powers uncertainties. The remainder of the paper is organized as follows. In Section 2, the modeling of microgrid components is discussed. The objective function formulation is presented in Section 3. Section 4, reviews the PSO algorithm, and Section 5 includes the simulation results and discussions. Finally, conclusions are drawn in Section 6.

2. Modeling of microgrid components In this section, the required formulations of demand response programs and electric vehicles have presented. 2.1. Modeling of demand response program (DRP) In this paper, it is assumed that the values of consumed load and its price are arranged by load response providers (who are responsible for collecting minor consumers' response) into a scheme (Fig. 1) and presented at the next day's market [57]. The load decrease and proposed price are shown by mSL and π SL , respectively. Therefore, the load response program model can be described as: DRLt ¼

NSL X

ΔSLt Z SLt

ð1Þ

S¼1

where ΔSLt ¼ mSLt  mSLt 1

;

S ¼ 1; 2; ; …; NSL

ð2Þ

where ¼ 0, and NSL is the number of discrete points presented to grid operator in the proposed scheme on the next day market. Z SLt is a binary variable with a value of 1 for responsive scheduling in time t and 0 if such scheduling is not available during time t. m0Lt

Fig. 1. Proposed pricing scheme of demand response provider.

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

725

ETripðV;tÞ : Energy consumption during a trip of the electric vehicle V in period t (W h). The energy stored in the batteries in each period t must be lower than or equal to the battery capacity (Eq. (4)). Eq. (5) ensures that the battery of each electric vehicle V always contains a minimum amount of energy. This can be seen as a reserve energy which can be used for an unexpected travel in each period t, and to avoid the fast degradation of EVs' batteries [59]. EStoredðV ;tÞ r EBatCapðvÞ ;

8 t A f1; …; Tg;

EStoredðV ;tÞ Z EMinChargðv;tÞ ; 8 t A f1; …; Tg;

8 V A f1; …; N V g 8 V A f1; …; N V g

ð4Þ ð5Þ

where Fig. 2. Evolution of the state of charge (s.o.c.) of a BV for a typical day [58].

2.2. Implementation of electrical vehicles In spite of the stochastic nature of electrical vehicles displacement, a pattern can be defined to predict these displacements on a daily basis. For a day during which the battery vehicle (BV) owner goes to work in the morning, parks the BV, goes back home in the late afternoon and then plugs the BV for charging during the night, the state of charge (s.o.c) will evolve along a pattern illustrated in Fig. 2 [58]. It is assumed in this paper that from 8 a.m. to 6 p.m., the electrical vehicles are parked in office parking lots, and at the other times are plugged at home parking lots [58]. About forty percent of the vehicle power is lost in commuting between home and office and the remaining 60% can be exchanged with the grid [58]. The vehicles are fully charged during the night. In this paper, the charging/discharging schedule of the vehicles is determined based on the mean load. Therefore, during the lower-than-mean load periods of the grid, the vehicles are charged so the grid base load could be increased and base load generators can generate more power. Thus, the costs related to switching-off and restarting operations are eliminated. For the peak shaving during above-mean load periods of the grid, the vehicles can return their stored power to the grid, thus, prevents to operate the high cost-units. The recommended energy and reserve prices for the electric vehicles in the electricity market are assumed to be $0.83 and $0.07, respectively. 2.2.1. Modeling and constraints of electrical vehicles Eq. (3) is used to determine the amount of energy stored at the end of period t. The battery balance also needs to consider the energy remaining from the previous period, and the charge/discharge in period t. The efficiency of charge ðηcðVÞ Þ and discharge ðηdðVÞ Þ processes is also considered for each electric vehicle [59]. EStoredðV ;tÞ ¼ EStoredðV;t  1Þ  ETripðV ;tÞ þΔt  ηcðV Þ  P chðV ;tÞ  8 t A f1; …; T g;

1 ηdðV Þ

8 V A f1; …; N V g;

t ¼ 1-EStoredðV;t  1Þ ¼ EInitialðVÞ

!

 P DchðV;tÞ Δt ¼ 1; ð3Þ

where: Δt: Elementary period ηcðVÞ : Grid-to-vehicle efficiency ηdðV Þ : Vehicle-to-grid efficiency EInitialðV ;tÞ : Energy stored of the electric vehicle V at the beginning of period 1 (W h) EStoredðV;tÞ : Energy stored in electric vehicle V at the end of period t (W h)

EBatCapðvÞ : Battery energy capacity of electric vehicle V (W h) EMinChargðv;tÞ : Minimum stored energy to be guaranteed at the end of period t, for electric vehicle V (W h). The EVs discharge process is limited by technical constraints of charging/discharging sites (Eqs. (6) and (7)). According to this, it is important to limit the maximum discharging rate to the maximum allowed rate by the charging/discharging points [59]. P Dchðv;tÞ r P DchLimitðV;tÞ  X ChðV ;tÞ 8 t A f1; …; Tg; 8 V A f1; …; NV g;

X chðV ;tÞ A 0; 1

ð6Þ

1  P Dchðv;tÞ  Δt rEStpredðV;t  1Þ  EtripðV ;tÞ ηdðvÞ 8 t A f1; …; T g;

8 V A f1; …; NV g;

ð7Þ

where P DchLimitðV ;tÞ : Maximum active power discharge of electric vehicle V in period t (W) The charge rates are also limited by the technical characteristics of the charging/discharging site (Eqs. (8) and (9)) [59]. P chðv;tÞ r P chLimitðV;tÞ  X DchðV;tÞ 8 t A f1; …; Tg; 8 V A f1; …; NV g;

X DchðV;tÞ A 0; 1

ð8Þ

ηdðvÞ  P Chðv;tÞ  Δt r EBatcapðV Þ  EStoredðV;t  1Þ EtripðV;tÞ 8 t A f1; …; T g;

8 V A f1; …; NV g;

ð9Þ

where P chLimitðV;tÞ : Maximum active power charge of electric vehicle V in period t (W). 2.3. Uncertainties modeling of wind and PV powers To model the stochastic nature of the wind (PV), the probability density function needs to be divided into three parts: the upper limit, the predicted value, and the lower limit set for the wind (PV) power [60,61]. Then, based on this function, the scenario tree will form which is used as the input parameter in the stochastic optimization problem. The probabilities of selecting the predicted power, the upper and lower limit would then be 50 percent, 25 percent, and 25 percent, respectively. Fig. 3 shows the structure of the scenario tree.

3. Problem formulation 3.1. Cost-function Once wind and PV powers have been probabilistically modeled, a proper energy reserve must be considered in the grid to support

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A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

Fig. 3. The structure of scenario tree [60].

their relevant uncertainties. Also, the operation and reserve costs of energy reserves need to be calculated [61,62]. The cost-function can be expressed as Eq. (10). This function comprises two parts. The first part is related to the generated and reserve power costs, and the second part gives the cost-pertaining to the variations of the scheduling of the units caused by changes in the behaviors of wind and PV powers. Also, in this equation, the uncertainty of wind and PV power are considered. ( N Ng Ng g T T X X X X X F ðP i Þ ¼ EC t ¼ C tsi þ U ti P tGi C tGi þ U ti RtGi:u λtGi:u t¼1

þ

Ng X

t¼1

þ

j¼1

þ

L A Sru DRP

P tEV j C tEV j

Nm X Nn T X X

X L A Sru DRP

or

or

i¼1

(

Ng X

P rmn

i¼1

rEDRtLmn Srd DRP

þ

X

rCDRtL þ

)

þ P tgrid C tgrid

C tsimn þ

NL X L¼1

ECDRtL

L A SeDRP

Srd DRP

þ P tw C tw þ P tPV C tPV

t ¼1m¼1n¼1

7

i¼1

X

U ti RtGi:d λtGi:d þ

i¼1 N EV X

i¼1

Ng X i¼1

r tGimn C tGi t

VOLLtL shedLmn þ

þ P twsmn C tws þ P tPVsmn C tPV s þP tgridmn C tgrid

)

N EV X j¼1

r tEV jmn C tEV j ð10Þ

3.2. Emission function Similar to the cost-function, the emission function must also be formulated in two stages due to the uncertainties associated with wind and PV powers. In the first stage, the pollution resulting from the scheduled power generation for load and reserve supplies is calculated. In the second stage, the pollution pertaining to the variations of scheduling of the units caused by changes in the behaviors of wind and PV powers is calculated.

Fig. 4. The flowchart of the proposed algorithm for the simultaneous scheduling of electrical vehicles and responsive loads.

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

C ðP i Þ ¼

T X

t

EE ¼

t¼1

þ

T X

(

t¼1

Nm X Nn T X X

Ng X

)

 Demand response (DR) costs:

U ti P tGi EGi þP tgrid Etgrid

i¼1

(

P rmn

t ¼1m¼1n¼1

Ng X

i¼1

r tGimn EGi þ P tgridmn Etgrid

NSL X

rCDRtL ¼

) ð11Þ

OF ¼ ω1 F ðP i Þ þω2 Q r;i CðP i Þ ¼ ω1

T X

Cos t

t

þ ω2

T X

NSL X

Q r;i Emissiont

ð12Þ

t¼1

ð20Þ



where π sLt and πesLt are the capacity and energy cost of point S of DRP L in period t, respectively. Generating unit start-up cost

C tsi Z 0 where

where OF is the value of the objective function, Q r;i is defined as the i-th unit price penalty factor [63] and ω1 and ω2 are the nonnegative coefficients used for adjusting the cost and emission ratios in the objective function. The values of coefficients can be adjusted between ω1 ¼ 1 ; ω2 ¼ 0 and ω1 ¼ 0 ; ω2 ¼ 1. Also, for cost and emission pollution to be observed equally in the objective function, the equality ω1 ¼ ω2 ¼ 0:5 must hold.

8 t; L A SeDRP

ΔsLt πesLt zsLt

t t1 Þ C tsi Z ηSU it ðU i  U i

t¼1

ð19Þ

s¼1

3.3. Single-objective function for optimal operation of microgrid The single-objective function for optimal operation of the microgrids is proposed as follows [63]:

rd 8 t; L A Sru DRP or SDRP

ΔsLt π sLt zsLt

s¼1

ECDRtL ¼

Min

727

8 i; t

ð21Þ

8 i; t ηSU it

ð22Þ

presents the start-up cost of unit i in period t.

3.5. Second – stage constraints

 Power balance in the mn scenario: Ng X i¼1

P tGimn þ P twmn þ P tPV mn 7 P tEV mn 7 P tGridmn þ

NL X

t

ðshedLmn  LC tLmn Þ ¼ P L ðtÞ

L¼1

ð23Þ

3.4. First stage constraints The constraints are as follows:

 Production limits in scenarios:

 Market balance Ng X

P tGi þP tw þ P tPV 7 P tEV 7P tGrid ¼ P tL

ð13Þ

i¼1



 ð14Þ

uit

P Grid; min uit r P tGi r P Grid; max

P tGimn r P Gimax yti;mn

8 i; t; mn

ð25Þ

is a binary variable that will be 1 if unit i is schedwhere uled at time t and scenario mn. DR reserve: dr tLmn ¼

ð16Þ

P tPV;LB r P tPV r P tPV;UB



ð24Þ

ð15Þ

uit

P tw;LB r P tw r P tw;UB

P tw;LB

8 i; t; mn

yti;mn

where P L ðtÞ is the load demand at time t. Power generation capacity P Gi; min uit r P tGi r P Gi; max

P tGimn Z P Gimin yti;mn

ð17Þ

0 rRtGi:u r ðP Gi; max P tGi Þ uit

8 i; t

0 rRtGi:d r ðP tGi  P Gi; min Þ uit

8 i; t

ð18Þ



ΔsLt vsLtk

rd 8 t; k; L A Sru DRP or SDRP

ð26Þ

s¼1

rEDRtLmn ¼

P tw;UB

and are lower and upper limits of wind power where at time t, respectively. P tPV;LB and P tPV ;LB represent lower and upper limits of PV power at time t. uit is a binary variable (1 if unit i is scheduled in period t and 0 otherwise). Spinning reserve limit:

NSL X

NSL X

ΔsLt π sLt vsLtk

rd 8 t; k; L A Sru DRP or SDRP

ð27Þ

s¼1

where dr tLmn is the deployed reserve of DRP L in period t and scenario mn and vsLtk is a binary variable associated with point S of DRP L at time t and scenario mn. Load shedding and wind and PV spillage: 0 r shed r LC tLmn LC tLmn ¼

X L A SeDRP

ð28Þ !

X

DRtL 7

L A Sru DRP

or

dr tLmn

8 L2 = SPBDR ; t; k

Srd DRP

ð29Þ Table 1 The limits, bids, reserve and emission coefficient of DG sources. Type

Min power (kW) Max power (kW) Bid ($/kW) Reserve cost (up and down) ($/kW)

Start-up cost ($) CO2 (kg/MW h) NOx (kg/MW h) SO2 (kg/MW h)

DSG MT FC WT PV EVa(  40)

2 6 3 0 0 0

1.82 0.96 1.65 0 0 0

a

50 30 30 15 30 1.5

The number of vehicles is assumed 40.

0.187 0.457 0.294 1.073 2.548 0.83

0.11 0.316 0.19 0 0 0.07

840 720 460 0 0 0

0.2 0.1 0.0075 0 0 0

0.0071 0.0036 0.003 0 0 0

728

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

0 rP twsmn rP twmn

ð30Þ

 Generating units start-up cost-adjustments in scenarios:

0 rP tPVsmn r P tPV mn

ð31Þ

C tsimn ¼ CC tsimn  C tsi

In Eq. (29), if DRPs provide up reserve (decrease their consumption), negative sign will be used.

where mn.

 Disintegration of generator power outputs P tGimn ¼ P tGi þ r tGi:umn  r tGi:dmn r tGi:umn



8 i; t; k

ð32Þ

r tGi:dmn

and are the up and down reserve deployed where by unit i in period t, scenario mn, respectively. Spinning reserve 0 rr tGi:umn r RtGi:u

8 i; t; k

ð33Þ

0 rr tGi:dmn r RtGi:d

8 i; t; k

ð34Þ

 DR reserve 0 rdr tLmn r DRtL

t t 1 CC tsimn Z λSU it ðyimn  yimn Þ

CC tsimn Z 0

3.6. Constraint linking the first and second stage

rd 8 i; t; k; L A Sru DRP or SDRP

ð35Þ

Eqs. ((33)–(35)) express that the amount of reserve in each scenario must be lower than the amount of scheduling reserve in the first stage.

8 i; t; k

CC tsimn

ð36Þ

8 i; t; k

ð37Þ

8 i; t; k

ð38Þ

is the actual start-up cost of i in period t and scenario

4. Solution methodology: the PSO algorithm The general principles observed in PSO algorithm are as follows [64]: Assume an n-dimensional search space. Therefore, the i-th particle can be represented with an n-dimensional position vector X i ¼ ½X i1 ; X i2 ; …; X in T and the velocity vector V i ¼ ½V i1 ; V i2 ; …; V in T , where i ¼ 1; 2; …; N, and N is the size of the population. Each particle in the swarm refines its search through its present velocity, previous experience, and the experience of the neighboring particles. The best position of particle i found so far is called personal best and is denoted by P i ¼ ½P i1 ; P i2 ; …; P in T and the best position in the entire swarm is called global best and is denoted by Gi ¼ ½g 1 ; g 2 ; …; g n T . First, the velocity of the i-th particle on the nth dimension is updated by using Eq. (39), and then, Eq. (40) is used to modify the position of that particle: V iðt þ 1Þ ¼ ωðtÞV i ðtÞ þ c1 r 1 ðP i ðtÞ  X i ðtÞÞ þ c2 r 2 ðGðtÞ  X i ðtÞÞ

Table 2 Offer prices of load response provider. Value reserve of responsive loads

ð39Þ

X iðt þ 1Þ ¼ X i ðtÞ þμV i ðt þ 1Þ

33% of total load

66% of total Load

100% of total load

Reserve cost (π SLt )

2.5

3.5

4.5

Energy cost (π eSLt )

20

28

36

ð40Þ

where ωðt Þ is the inertia coefficient (the value of which gradually reduces linearly during the course of calculations from 1 to an insignificant value close to zero), μ is the coefficient of contraction applied to limit velocity (set to 0.8 in this paper). C 1 and C 2 are cognitive and social parameters, respectively (equal to 2.05 in this

Table 3 The upper limit, lower limit, and predicted values for wind and PV powers. Time

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

Load demand

52 50 50 51 56 63 70 75 76 80 78 74 72 72 76 80 85 88 90 87 78 71 65 56

Wind power

PV power

Forecasted

Upper limit

Lower limit

Forecasted

Upper limit

Lower limit

1.78554 1.78554 1.78554 1.78554 1.78554 0.91324 1.78554 1.30166 1.78554 3.08541 8.77236 10.4132 3.92283 2.37655 1.78554 1.30166 1.78554 1.78554 1.30166 1.78554 1.30166 1.30166 0.91203 0.61244

4.1623 4.1623 4.1623 4.1623 4.1623 3.2371 4.1623 3.7369 4.1623 6.2971 12.1743 14.7396 7.5473 5.7451 4.1623 3.7369 4.1623 4.1623 3.7369 4.1623 3.7369 3.7369 2.9783 2.3154

0.7192 0.7192 0.7192 0.7192 0.7192 0.5371 0.7192 0.6172 0.7192 1.9326 5.4316 7.4473 2.3871 1.1173 0.7192 0.6172 0.7192 0.7192 0.6172 0.7192 0.6172 0.6172 0.4971 0.2617

0 0 0 0 0 0 0 0.19374 3.75395 7.52793 10.4411 11.9640 23.8929 21.0493 7.86474 4.22076 0.53879 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0.53271 6.2173 12.4116 15.21731 17.2314 29.7116 27.6391 12.4386 9.6317 2.6378 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0.0519 1.2146 3.3117 5.2369 6.7823 15.1643 13.2714 3.5623 1.6329 0.1276 0 0 0 0 0 0 0

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

729

Table 4 Beast solution obtained for optimal operation of microgrid (scenario 1). Time Status of DGs

Power of DGs for supplying load

Power of DGs for supplying reserve

n

MT

FC

DSG

MT

FC

DSG

WT

PV

MT

FC

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

0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1

1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1

0 0 0 16.53 0 15.07 25.36 0 10.88 17.80 0 14.561 18.623 20.728 11.708 18.499 18.869 20.922 27.065 16.253 17.466 0 17.082 11.103

20.517 21.527 24.650 0 16.640 0 0 25.702 19.643 14.010 22.719 0 19.688 0 21.188 0 23.866 16.008 27.297 19.936 17.935 25.572 17.471 0

27.012 24.332 23.690 30.344 35.277 45.025 43.228 45.374 37.533 34.322 28.067 27.216 0 17.609 31.230 48.285 37.976 46.874 31.849 46.383 41.135 41.916 27.219 42.663

4.1623 4.1623 1.7855 4.1623 4.162 3.2371 1.7855 3.7369 4.1623 6.2971 12.174 14.739 3.9228 5.7451 4.1623 3.7369 1.7855 4.1623 3.7396 4.1623 1.3017 3.7369 2.9783 2.3154

0 0 0 0 0 0 0 0.1937 3.7560 7.5279 15.217 17.231 29.711 27.639 7.8647 9.6317 2.6378 0 0 0 0 0 0 0

0 0 0 1.0622 0 0 0.4666 0 0.9278 1.7200 0 0.1758 10.875 5.8189 0.5972 10.696 0.0016 0.8253 0 0 0.4078 0 0.9985 0

3.4555 2.1196 1.0622 0 1.6252 0 0 1.6270 2.9202 0.7699 4.5348 0 5.2071 0 1.8063 0 1.0612 1.8231 0.3369 1.0643 0 2.0767 0.5808 0

DSG

Generation cost Reserve cost Start up cost – – –

–

0 1.3302 0 2.3784 1.8118 2.6991 0.5967 1.6417 2.1563 6.0929 12.204 17.561 0 13.153 5.3462 0.4150 1.6281 0.7974 2.7872 2.3759 0.2788 1.0433 0.9102 2.0531

15.549 15.345 13.593 17.696 15.955 18.781 21.590 20.551 31.935 44.881 64.312 72.085 95.283 90.349 42.208 46.381 31.473 27.499 30.359 26.428 22.344 19.366 21.229 15.536

33.723 32.440 31.732 40.153 39.566 50.952 55.422 52.075 52.235 54.813 46.374 48.235 32.694 44.964 50.170 61.942 58.969 63.917 61.304 62.332 55.918 48.813 44.959 45.566

0.6566 0.5941 0.2018 0.5920 0.5081 0.2969 0.2131 0.4897 1.0852 1.3600 2.2042 1.9873 4.4260 3.2857 1.1200 3.4258 0.6610 0.6949 0.3706 0.4636 0.1595 0.5093 0.5260 0.2258

3.47 0 0 0.96 0 0.96 0 0.65 0.96 0 0 0.96 1.65 1.82 1.65 0 1.65 0 0 0 0 0 0.96 0

Emission

Fig. 5. Energy resources scheduling of the scenario 1.

paper). r 1 and r 2 are random real numbers. In this paper, the number of iterations and particles (population) are considered to be 300 and 60, respectively.

¼

if

> :

Otherwise

0;

randð U Þ o ρðV i ðK þ 1Þ Þ ð41Þ

where randð U Þ is a uniform distribution in [0, 1]. Dimension of particles is defined as follows:

4.1. Binary PSO To extend the real-valued PSO to discrete space where it is needed, Kennedy and Eberhart calculate probability from the velocity to determine whether X i K þ 1 will be in ON state or OFF (0/ 1). They squashed V i K þ 1 using the following logistic functions [9]: ρðV i ðK þ 1Þ Þ ¼

Xi

ðK þ 1Þ

8 > < 1;

1 1 þ expð V i ðK þ 1Þ Þ

where X, is the state variables vector which includes active power of units and their related states. P Gi ðtÞ and U Gi ðtÞ are the output active power and status (denoting the ON or OFF state) of i-th unit at hour t, respectively. P Ri ðtÞ is the reserve power of i-th unit at hour t, and P Grid ðtÞ is the power of main grid at hour t (exchanged power with main grid).

730

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

2

U G1 ð1Þ; 6 U ð2Þ; 6 G1 X¼6 6⋮ 4 U G1 ðtÞ;

⋯; U Gi ð1Þ

P G1 ð1Þ ; ⋯; P Gi ð1Þ

⋯ ; U Gi ð2Þ

P G1 ð2Þ; ⋯ ; P Gi ð2Þ ⋮

⋯ ; U Gi ðtÞ

P R1 ð1Þ ; ⋯; P Ri ð1Þ

P Grid ð1Þ

P Grid ð2Þ 7 7 7 7 5 P Grid ðtÞ

P R1 ð1Þ ; ⋯; P Gi ð1Þ ⋮

P G1 ðtÞ; ⋯ ; P Gi ðtÞ

⋮ P R1 ð1Þ ; ⋯; P Gi ð1Þ

4.2. The proposed algorithm In the proposed scheduling, the electrical vehicles are used for peak shaving and load curve modification, and responsive loads are employed to supply the reserves needed to compensate the intrinsic uncertainties of the wind and PV powers. The proposed algorithm for the simultaneous scheduling of responsive loads and electrical vehicles in order to optimal operation of microgrids is as follows: 1. Input problem data including load demand, generations' data, etc. 2. Calculating mean of grid load via the following formula: T P

PLMean ¼ t ¼ 1

PLðtÞ ð43Þ

T

where T is the number of hours under study and PL(t) is the load required by the grid at hour t 3. t ¼ 1. 4. If PLðtÞ Z PLMean , electric vehicles can be discharge. ð44Þ

Thus PLðtÞ ¼ PLðtÞ  V2GðtÞdisch 5. If PLðtÞ〈PLMean , electric vehicles can be charge.

ð45Þ

Thus PLðtÞ ¼ PLðtÞ þ V2GðtÞchar

6. Initiating generators to supply load PL(t) 7. If load PL(t) is supplied, go to 8; otherwise, go back to 6. 8. Calculating reserve power to optimally support wind and PV powers via Eq. (46) P reserve ¼ ðWTðtÞ  WT LB ðtÞÞ þ ðPVðtÞ  PV LB ðtÞÞ

ð46Þ

3

9. 10. 11. 12. 13. 14. 15.

ð42Þ

where P reserve is the reserve required by the grid, WT(t) and PV(t) are scheduled wind and PV powers at time t, and WTLB(t) and PVLB(t) are the lower bound of wind and PV powers at time t. Initiating generators and responsible loads to supply the required reserve If the reserve is supplied, go to 11; otherwise, go back to 9 Calculating operation cost including the startup, power generation and reserve costs at time t Calculating the pollution of units at time t t¼t þ 1 If t r T, go back to 4; otherwise, go to 15 End

The proposed algorithm to solve the problem of optimal operation of microgrids in presence of electrical vehicles and responsive loads is presented in Fig. 4. 5. Simulation results

The studied microgrid in this paper is taken from [7]. Table 1, presents the generation limitations, sale and reserve cost and emission coefficient of the generation units of the microgrid. The demand response data are shown in Table 2. It is assumed that 10% of the subscribers participate in the demand response program. The upper limit, lower limit, and predicted values for wind and PV powers as well as the load demand are presented in Table 3. To observe the effect of simultaneous scheduling of the electrical vehicles and responsive loads on operation costs and emissions costreduction, three scenarios are implemented as follows: Scenario 1: Microgrid operation without load response and electrical vehicles.

Fig. 6. Reserve resources scheduling of the scenario 1.

Table 5 Beast solution obtained for optimal operation of microgrid (scenario 2). Status of DGs

n

Power of DGs for supplying load

Power of DGs for supplying reserve

MT

FC

DSG

MT

FC

DSG

WT

PV

MT

FC

DSG

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

1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0

0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1

18.216 0 19.016 0 0 15.098 0 15.062 15.075 14.995 0 24.655 11.868 19.037 9.2451 0 16.703 20.240 27.687 19.579 19.505 19.748 22.013 25.170

29.614 20.015 26.906 16.905 20.469 17.691 19.131 17.703 17.573 14.268 20.802 0 0 19.474 16.915 21.307 14.345 16.886 8.2474 22.902 19.949 15.128 0 0

0 25.541 0 29.969 31.294 26.846 46.735 37.802 35.481 34.992 33.124 22.662 32.372 0 37.917 44.948 48.709 46.754 49.825 40.343 35.041 31.162 39.256 28.675

4.163 4.162 4.162 4.162 4.162 3.327 4.162 3.736 1.785 3.085 8.772 14.739 3.9228 5.7451 4.1623 3.7369 1.7855 4.1623 3.7369 4.1623 0 3.7369 2.9783 2.3154

0 0 0 0 0 0 0 0.5327 6.2173 12.411 15.217 11.964 23.892 27.639 7.864 9.631 2.637 0 0 0 0 0 0 0

1.6488 0 0 0 0 0 0 0.8896 0.2587 0 0 1.8051 4.6150 4.8275 0.0735 0 0 0 0.0588 0.0440 0.1750 0.0912 0.3356 0.0934

0.0751 1.7942 1.7764 0.4002 1.6494 0.6200 0.8637 0 1.6423 2.2755 3.9545 0 0 6.9568 3.4081 6.2579 0 0.2138 0 0 0.3633 0.6959 0 0

0 0 0 1.3274 0 0 0.2456 0.2480 1.6547 0 1.5529 8.2231 0.8975 0 1.7655 2.2287 0.7907 0.3144 0.0912 0.5011 0 0 0 0.1195

Generation cost

Reserve cost

Start up cost

Emission

DR

–

–

–

–

1.7160 1.6500 1.6500 1.6830 1.8480 2.0790 2.3100 2.4750 2.5080 8.0000 7.8000 2.4220 4.7520 7.2000 2.5080 2.6400 2.8050 2.9040 2.9700 2.8710 2.5740 2.3430 2.1450 1.8480

4978.21 1270.15 21.0670 15.0407 16.3361 20.5951 18.8305 24.5434 36.6723 52.9737 61.0445 62.2360 77.4259 92.0097 41.0774 43.5680 29.6918 27.4240 28.4049 27.6915 25.3417 23.3102 20.5970 19.3499

0.621 0.423 0.4200 0.3062 0.4058 0.2217 0.3066 0.4322 0.7012 1.2323 1.7022 1.5971 1.9372 3.5673 0.9904 1.5662 0.2272 0.2204 0.1771 0.2126 0.2019 0.2782 0.2133 0.1351

2.61 1.82 0.96 1.82 0 0.96 0 0.96 0 0 0 0.96 0 1.65 1.82 0 0.96 0 0 0 0 0 0 0

9604.27 4877.31 26.8880 34.2570 36.4684 41.8528 48.6721 51.6011 51.0831 47.8098 40.5244 45.0045 39.8232 29.3441 49.4015 52.3195 60.2181 61.9898 65.7143 58.9840 53.0506 47.7495 49.0776 42.3869

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

Time

731

732

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

Fig. 7. Energy resources scheduling of the scenario 2.

Fig. 8. Reserve resources scheduling of the scenario 2.

Scenario 2: Microgrid operation with load response, but without electrical vehicles. Scenario 3: Microgrid operation with both load response and electrical vehicles. 5.1. Scenario 1: optimal operation of microgrid without load response and electrical vehicles In this scenario, the load demand of the grid is supplied by micro-turbine, fuel cell, diesel generator, wind and PV resources. Since the wind and PV powers are intermittent, the required reserve power is provided by micro-turbine, fuel cell, and diesel generator. Table 4 shows the output of generation units. As can be seen from the economic/emission dispatch results, low-cost diesel generator is used as the base generator to supply the load demand and reserve power. This generator can be operated during the most hours of the day, to reduce the overall system costs.

However, diesel generator produces the greatest emissions among generators. Solving this problem requires implementation of units with reduced emission units such as fuel cell, micro-turbine, or wind and PV resources (emission free). But, in spite of their reduced emission, these units are more costly. Since the objective is Economic – Emission dispatch, a suitable compromise between costs and pollution should be obtained. In this scenario, the wind power is set at the upper limit for most of the 24 h to reduce emission. Due to the higher cost as compared with the wind power, the PV power is utilized at its predicted value and so the reserve power required by the grid can be reduced. Also, the PV power is set at its upper limit at peak load to reduce emission from highlypolluting units. The generation, startup, and reserve generator costs in this scenario are obtained as $847.3967, $15.69, and $24.7746, respectively. The amount of emission is 1169.278 kg. Figs. 5 and 6 show the output power and reserve power of generating units in this scenario.

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

733

Fig. 9. Percent of the load participation and generation units in reserve market.

Fig. 10. Comparison of the reserve of generation units with and without DR.

5.2. Scenario 2: optimal operation of microgrid with load response and without electrical vehicles As the level of wind power generation increases, the need for spinning and nonspinning reserves increases [20], and this increase translates into higher operation cost. To decrease the operational costs, it is necessary to decrease the cost of reserve considered to cope with the uncertainty of wind and PV powers. In this scenario, the responsive loads are employed alongside with the other power generators, and the subscribers act as a grid reserve resource in the market by participating in the demand response program. Due to the lower cost, responsive loads are considered as a serious rival for generators in the ancillary services market and this allows the operator to use the

wind and PV powers which provide no emission. Table 5 shows the results of power distribution among the generators in this scenario. Note that, the demand response, along with supplies provided by other generators, compensates the uncertainty of the wind and PV powers. It is assumed that only 10 percent of the consumers are willing to participate in the demand response program. Load response and generators reserve are adjusted in such a way to compensate the power shortages if the wind and PV powers decrease to their lower limits. The maximum load response capacity is scheduled by the operator to occur at 10:00, 11:00, and 14:00 h during the day. During these hours, the demand response program (DRP) acceptability is 100 percent, whereas at 13:00 h, DRP acceptability reduces to 66% and on other times to 33%. Providing cheaper reserve compared with

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Fig. 11. Comparison of the reserve cost with and without DR.

generators, the responsive loads make it possible to utilize wind and PV powers at their peak values during most of the 24 h resulting in emission reduction. The generation, reserve, and startup costs values in this scenario are obtained as $821.8561, $18.0522, and $14.52, which are $1.17, $6.6783, and $75.61 which are lower than those of scenario 1. Also, the amount of emission is 1093.668 kg, which is 25.5406 kg lower than that of previous scenario. These results reflect the positive role of subscribers in the ancillary services load response program. Figs. 7 and 8 show the output and reserve power of the generating units. As can be seen from Fig. 9, the responsive loads provides a considerable portion of the needed reserve in the network which can decrease the reserve and operation cost of the network. The comparison of the used spinning reserve in the generating units is shown in Fig. 10. It can be observed that the participation of the responsive loads in the ancillary service market can decrease the reserve powers of the generating units due to their higher cost. In Fig. 11, the costs of reserve in the scenarios 1 and 2 are also compared.

fill up the load curve hollows. Thus, the need for switching off the base load generators and consequently the costs associated with re-operating would be eliminated. The decrease of the operating cost of generating units in the presence of the electrical vehicles is presented in Fig. 14. Also, Fig. 15 shows the modified load curve in the presence of electrical vehicles. The cost of operation and emission derived by the three scenarios with and without electrical vehicles are compared in Figs. 16 and 17, respectively. Similar to scenario 2, load response provides a part of the required reserve power, thus encouraging the operator to use more wind and PV powers. The generation, reserve and startup costs in this scenario are obtained as $748.3654, $10.5278, and $6.35, which are considerably lower than those obtained for the previous two scenarios. As mentioned before, the reason for operation costs reduction is the modification of the load curve by the electrical vehicles which eliminates the unnecessary switching on/off of the certain units. Also, the amount of emission is 1086.956 kg in this scenario. Fig. 18 compares the operation costs and emission of these three scenarios.

5.3. Scenario 3: optimal operation of microgrid with load response and electrical vehicles

6. Conclusions

In this scenario, the presence of electrical vehicles is considered. An efficient scheduling of the electrical vehicles and responsive loads can improve the performance of the microgrids. The responsive loads and electrical vehicles are modeled as the reserve suppliers and generators/controllable loads, respectively. Table 6 shows the Economic – Emission dispatch results of this scenario. The output and reserve powers are shown in Figs. 12 and 13. During peak load hours, the electrical vehicles that connected to the grid are discharged, and thus, the operation of the more costly units like micro-turbines can be delayed. The peak consumption hours, determined by the grid loads, are from 9:00 to 12:00 and from 18:00 to 20:00. During these periods, the electrical vehicles would supply the peak loads through discharging. However, once the grid loads have subsided during the evening hours, the vehicles start charging to

In this paper, the optimal operation of microgrids in the presence of electrical vehicles and responsive loads is studied. In the proposed scheduling, the electrical vehicles used for peak shaving as well as load curve correction, and the responsive loads used to supply a part of the required grid reserve to compensate wind and PV uncertainties. The simulation results confirmed the positive effect of the proposed scheduling in reducing the operation costs and emission. Moreover, a twostage optimization model is proposed to determine the operation costs. In the first stage, power generation and reserve power costs are calculated, and in the second stage, the costs associated with re-scheduling of generating units due to the variations in wind and PV powers are determined. The proposed method decreases the system emission and also increases the incentives of the owner of electric vehicle and responsive loads as well as wind and PV for the dollars obtained.

Time

Status of DGs

Power of DGs for supplying load

Power of DGs for supplying reserve

*

MT

FC

DSG

MT

FC

DSG

WT

PV

VG

MT

FC

DSG

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

0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 13.890 0 0 0 0 0 13.288 0 16.565 10.022 9.4744 9.5909 14.892 0 0

14.1222 15.7676 15.8461 12.7615 13.4488 18.1393 16.1372 20.0703 22.0200 18.1865 26.4039 23.822 21.925 27.151 28.186 25.719 25.337 19.307 24.363 22.032 23.069 22.827 28.824 26.092

42.73968 39.08186 38.983 42.9421 45.39132 46.6331 49.69887 49.99998 44.97487 30.1148 31.6924 27.62225 22.25724 22.68997 33.58139 30.06684 49.96138 42.46561 45.88062 45.31762 39.60238 29.54085 38.19501 40.92637

4.1623 4.1623 4.1623 4.1623 4.1623 3.2371 4.1623 3.7369 1.78554 6.2971 12.1743 14.739 3.9228 1.1173 1.7855 1.3016 4.1623 4.1623 3.7369 4.1623 3.7369 3.7369 2.9783 2.9783

0 0 0 0 0 0 0 0.19374 6.2173 7.52793 5.2369 6.7823 23.892 21.049 12.438 9.6317 0.5387 0 0 0 0 0 0 0

 8.972  9.011  8.987  9.131  6.985  4.993 0 0.0996 1.0013 4.0123 2.5007 1 0 0 0 2.0023 4.9917 5.5003 6.0162 5.9913 1.9785 0  5.001  2.985

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.16390 0 0 0 0 0.10789 0.89811 0.81958 0 0 1.75982 0.18901 0.17750 0.57789 1.16776 0.68392 1.19242 0 0 0 0.12334 0.77657 0.17116 0.04692

1.2665 1.4964 1.4960 1.4627 1.3640 0.3480 0.2349 0 1.1195 0.9812 0 2.2806 2.8854 0 1.1751 0 0.0219 0.7205 0.3472 0.7692 0.4880 0 0 0.1243

Generation cost

Reserve cost

Start up cost

Emission

DR









2.013 1.947 1.947 1.98 2.079 2.244 2.31 2.442 4.95 7.6 4.983 4.818 7.2 7.2 7.6 8 2.64 2.7225 2.772 2.673 2.508 2.343 2.31 2.31

16.6051 16.4101 16.4147 16.2727 16.9082 17.5267 18.5041 20.5909 33.6955 46.855 42.3594 46.340 76.556 67.815 48.623 47.201 26.800 30.219 29.312 28.727 32.710 23.050 18.812 18.520

0.2711 0.2619 0.2619 0.2599 0.2539 0.1709 0.3119 0.2778 0.5191 0.8679 0.733 0.6722 1.0711 0.8297 1.1111 0.9299 0.3609 0.2153 0.1767 0.2182 0.2025 0.2646 0.1480 0.1380

3.47 0 0 0 0 0 0 0 0 0.96 0 0 0 0 0 0.96 0 0.96 0 0 0 0 0 0

42.9806 40.8054 40.7581 42.7478 44.9287 47.3257 49.2491 51.0779 48.3162 43.9534 39.0418 35.628 30.7507 31.2782 42.1639 46.4351 53.6582 56.5539 56.7235 55.1382 50.7175 45.8605 44.8879 45.9734

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Table 6 Beast solution obtained for optimal operation of microgrid (scenario 3).

735

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Fig. 12. Energy resources scheduling of the scenario 3.

Fig. 13. Reserve resources scheduling of the scenario 3.

Fig. 14. Operating cost of generating units in the presence of the electrical vehicles.

A. Rabiee et al. / Renewable and Sustainable Energy Reviews 57 (2016) 721–739

Fig. 15. Modified load curve in presence of electrical vehicles.

Fig. 16. Comparison of the total operation cost of the three scenarios.

Fig. 17. Comparison of the Emission of the three scenarios.

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Fig. 18. Comparison of the operation cost and Emission of the three scenarios.

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