Presenting a multi-objective generation scheduling model for pricing demand response rate in micro-grid energy management

Energy Conversion and Management 106 (2015) 308–321

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Presenting a multi-objective generation scheduling model for pricing demand response rate in micro-grid energy management G.R. Aghajani a,⇑, H.A. Shayanfar b, H. Shayeghi c a

Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran Centre of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran c Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil, Iran b

a r t i c l e

i n f o

Article history: Received 9 June 2015 Accepted 17 August 2015

Keywords: Micro-grid Wind power Photovoltaic power Demand response Consumer pricing Demand response provider Energy management

a b s t r a c t In this paper, a multi-objective energy management system is proposed in order to optimize micro-grid (MG) performance in a short-term in the presence of Renewable Energy Sources (RESs) for wind and solar energy generation with a randomized natural behavior. Considering the existence of different types of customers including residential, commercial, and industrial consumers can participate in demand response programs. As with declare their interruptible/curtailable demand rate or select from among different proposed prices so as to assist the central micro-grid control in terms of optimizing micro-grid operation and covering energy generation uncertainty from the renewable sources. In this paper, to implement Demand Response (DR) schedules, incentive-based payment in the form of offered packages of price and DR quantity collected by Demand Response Providers (DRPs) is used. In the typical microgrid, different technologies including Wind Turbine (WT), PhotoVoltaic (PV) cell, Micro-Turbine (MT), Full Cell (FC), battery hybrid power source and responsive loads are used. The simulation results are considered in six different cases in order to optimize operation cost and emission with/without DR. Considering the complexity and non-linearity of the proposed problem, Multi-Objective Particle Swarm Optimization (MOPSO) is utilized. Also, fuzzy-based mechanism and non-linear sorting system are applied to determine the best compromise considering the set of solutions from Pareto-front space. The numerical results represented the effect of the proposed Demand Side Management (DSM) scheduling model on reducing the effect of uncertainty obtained from generation power and predicted by WT and PV in a MG. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Recent studies have shown that it is possible to reduce energy consumption by 20–30% without any need to change the system structure and solely through optimal performance and management. One of the methods for reducing the loss, meeting consumer’s needs and decreasing greenhouse emissions is by use of Distributed Generations (DG), particularly renewable resources of energy such as wind and solar energies [1–3]. Hence, during the recent years, MGs have been introduced as a new concept and their management has turned to a necessary issue. One of the main drawbacks in the management of some renewable resources including wind and solar energies is the issue of uncertainty in their behavior; i.e. the amount of real-time power production by these resources is different from the predicted one. In other words, ⇑ Corresponding author at: Basij Sq, Ardabil, Iran. Tel./fax: +98 4533721272. E-mail address: [email protected] (G.R. Aghajani). http://dx.doi.org/10.1016/j.enconman.2015.08.059 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

due to the presence of uncertainty in energy production by these resources, operator’s responsibility in terms of maintaining a balance between production and consumption would be faced with some problems. Then, system operators attempt to provide a certain amount of reserve in the system so that they can cover uncertainty in energy production and maintain the system security at the desired level [4]. It is true that MG operators are able to overcome the abovementioned problems by buying more energy from the utility or increasing the number of micro-resources; however, these solutions are normally accompanied by some problems in the commitment of additional units and increased emission and energy costs in the entire system [5]. Another solution to overcome this problem and provide a balance between production and consumption is via decreasing customer’s consumption during the system’s energy shortage period (caused by prediction error of wind speed and solar radiation). This demand-side reserve which is able to compete with bids offered from production units is called demand

G.R. Aghajani et al. / Energy Conversion and Management 106 (2015) 308–321

response [6]. According to the Federal Energy Regulatory Commission(FERC), DR is defined, changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized [7]. Generally, Demand Response Programs (DRPs) can be classified into two main groups: price-based and incentive-based DR programs; each of these two groups is also divided into several sub-categories (Fig. 1). For more details, see [8,9]. In general, the issue of providing reserve for power systems in order to cover the uncertainties associated with resources of wind and solar power production has been discussed as early as the emergence of these resources such that before the application of wind, solar, and other renewable energies in power systems, system operators have always had ancillary services to manage the power production shortage and provide a balance between production and consumption. However, today, with the emergence of renewable energies such as wind and solar and due to the uncertainties associated with their power production, there is a need to provide the necessary reserve and find a solution for the further cover of these uncertainties. Recently, significant studies have been conducted on MG operation management [10,11]. Since there are two main objectives in operating a MG, namely operation at the minimum possible cost and operation at the minimum amount of pollutant emissions, therefore, most of the previous studies have investigated this area from different points of view. Some of the previous studies have been focused on the uncertainties caused by renewable resources of energy resulted from the prediction error of wind speed and solar radiation in a system. An expert management system was proposed for the optimal operation of wind and solar power production beside other distributed generation resources when connected to the MG, which covered the uncertainties associated with production resources through minimizing operation cost and pollutant emissions by Motevasel and Seifi [12]. Application of a smart energy management system was also examined for the MG operation by using heuristic algorithm and predicting the photovoltaic power and its coverage by energy reserving resources by Chen et al. [13]. Role of DR programs in wind-thermal generation scheduling has been studied in [14,15] using stochastic programming as multi-objective modeling in order to reduce operation costs and pollutant emissions in a smart grid. The role of DR was investigated in the operation management of a smart distribution system in the presence of wind turbine and solar cells as a multi-objective problem using e-constraint by Zakariazadeh

309

et al. [16]. Coverage of the wind power shortage in power systems using DR and spinning reserve has been investigated in [17,18], respectively. Use of PSO algorithm was proposed by Pedro Faria et al. to minimize the operational cost for the distributed energy resources by considering the network constraints and demand response [19]. In previous studies, no precise focus has been given to the method of covering the uncertainties caused by wind turbine and solar cells by the demand-side participants as well as the method of implementing this type of programs with respect to lack of modern communicative infrastructures in distribution systems. In this study, a multi-objective scheduling model is utilized to minimize the total operation costs and pollutant emissions in a MG, which includes a WT and PV power generation with a stochastic natural behavior and their associated uncertainties and the incentive-based DR programs, were suggested to cover the uncertainties caused by these energy resources. On the other hand, since it is not possible to apply an actual open electricity market in many existing power and distribution systems due to the lack of developed communicative infrastructure, this paper recommends the use of price-offer packages and the amount of DR in simple and operation forms to solve this problem and create a competing energy market. It was considered for most of the consumers participating in demand response programs as the incentive-based programs. In this package, three load reduction intervals with three energy offer prices for residential, commercial, and industry consumers are considered, each of consumers can select from the three offer packages according to their condition and participate in DR programs. Although participation in these programs is voluntary, reasonable prices are included in the offered packages to further encourage participants to contribute to these programs. For example, if customers want to choose the offer package 100% total DRs, the price would be considered 4.5 €ct/kW h which seems a reasonable price compared to the highest market price. In this paper, the proposed offer package is based on the roulette wheel method. To sum up, the main contribution of this paper is as follows:
Using DRPs to cover the uncertainties resulted from power generation by WT and PV.
Proposing the use of price-offer packages and the amount of DR for DRPs implementation.
Considering a multi-objective scheduling model and use of MOPSO algorithm with recommending Pareto criterion with non-linear sorting based on fuzzy mechanism.

Demand Response Programs

Price Based Program (PBP)

Incentive Based Program (IBP)

Time Of Use (TOU)

Direct Control

Critical Peak Pricing (CPP)

Interruptible/Curtailable

Real Time Pricing (RTP)

Demand Bidding Emergency DR Capacity Market Ancillary Services Market Fig. 1. Classification of DRPs.

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The rest of this paper is organized as follows: Section 2 presents modeling for DR participants and Section 3 provides equations for the objective function considering the existing technical and environmental constraints. Section 4 introduces the MG model examined in this paper, Section 5 proposes the algorithm based on the Pareto criterion, and Section 5 discusses the results and studied analyses. Finally, the last section is devoted to the paper conclusion.

3.1. Objective functions The objective function of this paper is considered as the operating costs and pollutant emission costs with and without responsive loads as follows.

2. Modeling DR participants Different types of electric energy consumers with different consumption behaviors can be considered. In this paper, electricity consumers are considered to be residential, commercial and industrial which the following equations demonstrate modeling for their behavior.

RPðr; tÞ ¼ RCðr; tÞ  pr;t ;

RCðr; tÞ 6 RC max t

CPðc; tÞ ¼ CCðc; tÞ  pc;t ;

CC max t

IPði; tÞ ¼ ICði; tÞ  pi;t ;

and pollutant emissions with and without responsive residential, commercial and medium industrial loads, considering equality and inequality constraints in order to cover the uncertainties caused by the wind and solar power generation. Fig. 3 clearly shows the optimization model used in this study.

CCðc; tÞ 6

ð1Þ ð2Þ

ICði; tÞ 6 IC max t

3.1.1. Operating cost function Operating cost function consists of the cost functions for each production unit, start-up and shut-down costs, costs of energy reserve and exchange with the utility and cost of participation in the DR program. This function is expressed as:

Min f 1 ðxÞ ¼

ðcos tDG ðtÞ þ ST DG ðtÞ þ cos t s ðtÞ þ cos tGrid ðtÞ

t¼1

ð3Þ

where r, c and i represent the number of residential, commercial and industrial consumers; RC(r, t), CC(c, t) and IC(i, t) indicate the amount of load reduction planned by each residential, commercial and industrial consumer in period t; RC max , CC max and IC max indicate t t t the maximum load reduction proposed by each consumer in period t, respectively; pr,t, pc,t and pi,t indicate the amount of incentive payment to each consumer in period t; and RP(r, t), CP(c, t) and IP(i, t) represent the cost due to load reduction by residential, commercial and industrial consumers in period t for the proposed load reduction, respectively. Fig. 2 shows the model used for the incentivebased DR program according to the price offer packages considering the level of load reduction.

T X

cos t DG ðtÞ ¼

þ cos tDR ðtÞÞ

ð4Þ

Ng X ui ðtÞPDGi ðtÞBDGi ðtÞ

ð5Þ

i¼1

ST DG ðtÞ ¼

Ng X SDGi jui ðtÞ  ui ðt  1Þj

ð6Þ

i¼1

cos t s ðtÞ ¼

Ns X ½uj ðtÞPsj ðtÞBsj ðtÞ þ Ssj ðtÞjuj ðtÞ  uj ðt  1Þj

ð7Þ

j¼1

cos t Grid ðtÞ ¼ uBuy ðtÞPGrid-Buy ðtÞBGrid-Buy ðtÞ  usell ðtÞP Grid-sell ðtÞBGrid-sell ðtÞ ð8Þ

3. Problem formulation

cos t DR ðtÞ ¼ PDR ðtÞBDR ðtÞ The considered MG scheme is based on planning the existing units to supply demand by wind and solar energy generation elements with a natural stochastic behavior and the way these stochastic power generation elements is covered by the DRPs. Energy is supplied within the 24-h period by the power generation resources consisting of utility, MT, WT, PV, FC, battery, and responsive loads. The optimization goal is to minimize operating costs Offered Price(€Cent/KWh)

3

2

PDR ðtÞ ¼

ð9Þ

X X X RCðr; tÞ þ CCðc; tÞ þ ICði; tÞ r

c

ð10Þ

i

where PDGi(t) and Psj(t) are the real power output of ith generator and jth storage in period t, respectively. BDGi(t) and Bsj(t) are the bids of the DGs and storage devices in period t, as shown in Table 1. SDGi(t) and Ssj(t) represent the start-up or shut-down costs for ith DG and jth storage, PGrid-Buy(t) and PGrid-sell(t) are the active power which are bought and sold with the utility in period t, BGrid-Buy(t) and BGrid-sell(t) are the bid bought and sold with the utility in period t as shown in Table 1,respectively, PDR(t) and BDR(t) is the active power and the bid price for participate in the DRP’s in period t, as shown in Table 3, respectively. When implementing the objective function, X is considered as the decision variable vector, consisting of the unit’s output power the amount of exchange power with utility, amount of load reduction of DRPs and on/off mode in a vision planned for the day ahead, which are expressed as follows:

X ¼ ½Pg ; U g 12nT Pg ¼ ½PDG1 ; PDG2 ; . . . ; PDGNDG ; Ps1 ; Ps2 ; . . . ; PsNs ; PGrid ; P DR 

1

U g ¼ ½U DG1 ; U DG2 ; :::U DGNDG ; U s1 ; U s2 ; . . . ; U sNs ; U Grid ; U DR 

ð11Þ

n ¼ NDG þ Ns þ 2 1 DR 3

2 DR 3

DR

Fig. 2. DRP’s offer package.

DR quanty (KW)

where n is the number of decision variables, NDG and Ns are the total number of generation and storage units, respectively, T denoted total number of periods, Pg is the active power vector including of all DGs and storage units, utility power and active power participate

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Multi-Optimal Configuration

DR Participants

Environmental Cost and Emission

Operating Cost: Cost function/constraints

Sources: MT,PAFC,PV,WT,Batt,Grid

Residential Customer

Commercial Customer

Industrial Customer

Optimization Model

Objective Function

MOPSO Fig. 3. Optimization model structure.

Table 1 Bids and emissions coefficient of the DG sources. Unit

Type

Bid (€ct/kW h)

Start-up/shut-down cost (€ct)

CO2 (kg/MW h)

SO2 (kg/MW h)

NOx (kg/MW h)

P min (kW)

P max (kW)

1 2 3 4 5 6

MT PAFC Bat PV WT Grid

0.457 0.294 0.38 2.584 1.073 –

0.96 1.65 0 0 0 0

720 460 10 0 0 950

0.0036 0.003 0.0002 0 0 0.5

0.1 0.0075 0.001 0 0 2.1

6 3 30 0 0 30

30 30 30 25 15 30

in the DRP’s, Ug is the state vector indicating the ON or OFF states of all units during in period t. 3.1.2. Pollutant emission function Pollutant emission function consists of emissions function caused by generation units, energy-reserving resources, and emissions resulted from grids when making a purchase. The considered pollutants include CO2 (carbon dioxide), SO2 (sulfur dioxide), and NOx (nitrogen dioxide). The mathematical model for the pollutant functions can be expanded as follows: Min f 2 ðxÞ ¼

T X

EmissionðtÞ ¼

t¼1

¼

T X femissionDG ðtÞ þ emissions ðtÞ þ emissionGrid ðtÞg t¼1

(N ) g Ns T X X X ½ui ðtÞPDGi ðtÞEDGi ðtÞ þ ½uj ðtÞPsj ðtÞEsj ðtÞ þ PGrid ðtÞEGrid ðtÞ t¼1

i¼1

j¼1

where PDemandL is the amount of Lth demand level and NL is the total number of demand levels. 3.2.2. Real power generation limit The active power output of each DG’s, storage unit and the utility are limited by lower and upper bounds as follows:

PDGi;min ðtÞ 6 P DGi ðtÞ 6 PDGi;max ðtÞ Psj;min ðtÞ 6 Psj ðtÞ 6 Psj;max ðtÞ

ð14Þ

PGrid;min ðtÞ 6 P Grid ðtÞ 6 PGrid;max ðtÞ where PDG,min(t), Ps,min(t) and PGrid,min(t) are the minimum active power of ith DG, jth storage and the utility at period t, respectively. PDG,max(t), Ps,max(t) and PGrid,max(t) are the maximum active power units in period t.

ð12Þ

where EGi(t), Esj(t) and EGrid(t) are amount of pollutants emission in kg MW h1 for each generator, storage device and utility in period t, respectively.

The constraints of the objective functions are described as. 3.2.1. Load balance Ng Ns X X PDGi ðtÞ þ Psj ðtÞ þ uBuy ðtÞPGrid-Buy ðtÞ

¼

j¼1 NL X L¼1

PDemandL ðtÞ þ usell ðtÞPGrid-sell ðtÞ  PDR ðtÞ

wj ðtÞ ¼ wj ðt  1Þ  k1Dj uDj ðtÞPsj ðtÞ þ kCj ðtÞuCj ðtÞPsj ðtÞ uDj ðtÞ þ uCj ðtÞ 6 1

3.2. Constraints

i¼1

3.2.3. Battery limit

ð13Þ

wmin 6 wj ðtÞ 6 wmax

ð15Þ

wj ðtÞ ¼ we The first equation indicates the battery capacity which can vary from hour to hour depending on the charging and discharging level, while the second equation shows that the battery can be charged or discharged in each hour; their co-occurrence is irrelevant. wj(t) and wj(t  1) indicate the reserved energy at current and previous times. PDsj(t) (PCsj(t)) is the permitted rate of charge (discharge) during a definite period of time. kDj and kCj are the convertor’s efficiency at the times of charge and discharge, respectively.

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4. MOPSO algorithm Since the problem in this paper was a continuous one and also considering results of the conducted studies, PSO algorithm had a high level of accuracy and higher rate of convergence than other intelligent algorithms. Therefore, it is recommended to use this algorithm for solving the problem. This section describes the algorithm. Multi-objective problems contain multiple inconsistent objective functions, and equality and inequality constraints, like the one written below, which needs to be optimized.

! ! ! ! T Min Fð X Þ ¼ ½f 1 ð X Þ; f 2 ð X Þ; . . . ; f N ð X Þ Subject to : ! g i ð X Þ < 0 i ¼ 1; 2; . . . ; Nueq ! hi ð X Þ ¼ 0 i ¼ 1; 2; . . . ; Neq

ð16Þ

The space within which the objective function is defined is called objective space. In multi-objective optimization, every two solutions can have two different forms with respect to each other: one solution can dominate the other one and no solution can dominate the other solution, as expressed in (17).

! ! f jð X 1Þ 6 f jð X 2Þ ! ! 9 k 2 f1; 2; . . . ; ng; f k ð X 2 Þ < f k ð X 2 Þ

8 j 2 f1; 2; . . . ; ng;

ð17Þ

By applying the Pareto optimal concepts using fundamental principles in Particle Swarm Optimization (PSO) algorithm [20,21], this algorithm can be used to solve multi-objective problems called Multi-Objective Swarm Particle Optimization (MOPSO) [22]. In MOPSO algorithm, a repository is used to save solutions. Repository means an external memory on which the dominated solutions are saved. This algorithm first starts to work using a series of random particles. All the population particles are compared with each other during a repeated procedure and position of the dominated particles is saved on the repository. New velocity and position of the ith particle in the dth dimension and t + 1 repetition are updated using the following relation. See [21,22] for more details. t v tþ1 id ¼ w  v id þ c 1 rand1 

   g tbestrd  xtid



 Ptbestid  xtid þ c2 rand2

tþ1 ¼ xtid þ v tþ1 xid id

ð18Þ

Step 5: Separating non-dominated solutions and saving them in the repository. Step 6: Choosing the best particle from the non-dominated solution repository as the leader. The process of selecting the leader is done by first dividing the discovered search space into equal parts, then allocating probability distribution to each part of the discovered search space, and finally selecting the best particle as the leader using the roulette wheel. Step 7: New velocity and position of each particle is calculated using (18) and (19). Step 8: Updating the best position for each particle. To update the best position for each particle, the new particle position is compared with the previous particle position.

8 P best;i ðtÞ  X i ðt þ 1Þ Pbest;i ðtÞ > > > < X ðt þ 1Þ X i i ðt þ 1Þ  P best;i ðtÞ Pbest;i ðt þ 1Þ ¼ > select randomly > > : ðPbest;i ðtÞ or X i ðt þ 1ÞÞ otherwise

Step 9: Adding the current non-dominated solutions to the repository. Step 10: Eliminating the dominated solutions from the repository. Step 11: If the number of members in the repository is larger than the pre-specified capacity, the excessive members would be omitted. Step 12: If the maximum number of repetitions is satisfied, the optimization process would end; otherwise, go back to the Step 6. Fig. 5 shows the flowchart of the proposed algorithm for solving the optimization problem. 4.1. Finding the best interactive solution After obtaining the Pareto optimal set, planners might need to choose the final solution from among the set of optimal solutions.

ð19Þ

The algorithm implemented on the studied problem can be carried out according to the following steps.

Ng

Ns

i =1

j =1

ΔP = ∑ PDGi (t ) + ∑ Psj (t ) + u Buy (t ) PGrid − Buy (t ) NL

− ∑ PDemand L (t ) − usell (t ) PGrid − sell (t ) + PDR (t ) L =1

Step 1: Defining the input data.

Yes

At the beginning of the program, the required input data are carefully defined which includes: MG structure, operating characteristics of DGs and utility, the PV and WT predicted output power for each study period, real time price offer for DGs and utility, pollutant emission coefficients and the daily demand curve.

ΔP = 0

X 0 ¼ ½X 1 ; X 2 ; . . . ; X N T

Stop

No Select

k th unit randomly

Pk ,new = Pk ,old − ΔP

Step 2: Generating the Initial Population. In this step, an initial population is considered according to the limitations applied to the problem based on the following relation:

Yes

Pk ,min ≤ Pk ,new ≤ Pk ,max

ð20Þ No

In which X vector is defined as in (11). Step 3: In this step, power dispatch algorithm, specified in Fig. 4, is implemented for each of the generated populations and then the fitness is calculated based on (4) or (12). Step 4: Specifying the non-dominated solutions.

ð21Þ

if

Pk ,new ≤ Pk ,min

then Pk ,new = Pk ,min

if

Pk ,new ≥ Pk ,max

then Pk ,new = Pk ,max

Fig. 4. Flowchart of power dispatch algorithm.

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START Update best posion of each parcle-Eq. (21)

Input data definition Generate initial population

Add non-dominated soluon to the repository

A Calculate objecve funcon

Eliminate excess members of repository

N Repository > N Identified

Determine non-dominated soluon (Pareto- Front)-Eq. (17)

Is the max number of iteration satisfied?

Separang and saving nondominated soluon in the repository

End

B

Select a leader for each parcle and the parcle moves- Eq. (18-19)

Fig. 5. Flowchart of MOPSO algorithm.

B

Dominated Solution Non-dominated Solution Pareto-Front

f2

× × ×× ×× × × f1

Fuzzy mechanism for best comparison

ζi 1

fi min

fi max

fi

B Fig. 6. Impalement fuzzy decision making for chooses better solution from Pareto-front set.

Therefore, to achieve such an important goal, a fuzzy decision making function with a membership function is introduced, on which the exact values of variables can be saved. Fig. 6 shows the clear concept of the optimization problem along with the fuzzy decision making function. The membership function fki indicates the optimality of the objective function i among the Pareto optimal solution k, which is formulated as follows:

fki ¼

8 1 > > < max fi

min

fi 6 fi f i

f max f min > i > : i 0 max

max

fi

min

< fi < fi

ð22Þ

max

fi P fi min

where f i and f i are minimum and maximum values of the ith objective function among all non-dominated solutions, respectively. fki ranges from 0 to 1, where fki ¼ 0 indicates incompatibility of the

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Distribution System Operator (DSO) Power Utility Grid

20kV/400 Micro-Grid central Controller

PCC

Feeder1 Residential Load

Feeder2 Commercial Load LC

Feeder3 Industrial Load LC

LC MT (30kW)

LC

PAFC (30kW)

WT (15kW)

PV (25kW) LC LC

Bat (30kW)

Fig. 7. MG schematic configuration.

5

55

Resindential

Industrial

Commercial

4.5

Real Time Market Price (Cent/kWh)

50 45 40

Load (kW)

35 30 25 20 15 10

4 3.5 3 2.5 2 1.5 1 0.5

5 0

0

2

4

6

8

10

12

14

16

18

20

22

0

24

5

10

15

20

25

Time (h)

Time (Hour) Fig. 9. The real-time market prices. Fig. 8. Daily load curves for the three load types of the MG.

fki

solution with the set, while ¼ 1 means full compability. For each Pareto front solution k, the normalized membership function is calculated:

Pm

fk ¼

fki Pn i¼1 Pm k k¼1 i¼1 fi

ð23Þ

where n is the number of non-dominated solutions and m is the number of objective function. The maximum value of the membership function is the best compromise solution. In this paper, it was

conducted by the simultaneous fuzzy minimization of two inconsistent functions, namely operational cost and pollution emissions. 5. Case study The MG connected to the utility, shown in Fig. 7, was analyzed as the test system in this paper. In this system, three feeders, namely medium industrial, commercial, and residential consumers, were considered such that the maximum electricity demand was assumed as 50%, 16%, and 33% of the total energy demand in the system per period, respectively.

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G.R. Aghajani et al. / Energy Conversion and Management 106 (2015) 308–321 Table 2 The forecasted value of WT and PV. Hour

WT (kW)

PV (kW)

Hour

WT (kW)

PV (kW)

1 2 3 4 5 6 7 8 9 10 11 12

1.7850 1.7850 1.7850 1.7850 1.7850 0.9150 1.7850 1.3050 1.7850 3.0900 8.7750 10.410

0 0 0 0 0 0 0 0.200 3.750 7.525 10.45 11.95

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

3.9150 2.3700 1.7850 1.3050 1.7850 1.7850 1.3020 1.7850 1.3005 1.3005 0.9150 0.6150

23.90 21.05 7.875 4.225 0.550 0 0 0 0 0 0 0

Therefore, the daily curve load for the three feeders is shown in Fig. 8. The total energy consumption during the day was equal to 1695 kW h [11]. Also, it was assumed that the reactive power required by the loads was compensated for by locally capacitor placement in the relevant buses. This system contained technologies as MT, WT, PV, FC and battery whose installation details are presented in Table 1 that DG bids and start-up/shut-down costs, greenhouse emission caused by system and DGs, as well as minimum and maximum power generation limits for each unit [11]. In this system, most of the DGs were installed in the residential feeder. Also, power factor for all the DGs was assumed to equal one. In the typical system, the battery of 30 kW h was considered, where the maximum charging capacity for the residential feeder assuming the residential electricity supply of 230 V and 16 A was considered to be 4 kW h. Also, lower and upper limits on the amount of energy storage inside the battery were respectively

10% and 100% of battery capacity and efficiency of the battery during charge and discharge was assumed to be 94% [13,23]. Real-time market price was assumed to be equal to APX hourly market price, as shown in Fig. 9, and the output power from the WT and PV are presented in Table 2 based on the predicted values. Price offer packages proposed for the demand response programs are presented in Table 3. Simulation results were analyzed in six different case studies. During all the cases, it was assumed that all the generation units participated in the MG considering their corresponding electrical features and the excessive electricity generation and demand in the system was exchanged with the utility through point of common coupling (PCC). In cases 1 and 2, operating costs of all the units were considered along with the problem constraints such that case 1 was aimed to obtain the minimum value for the operating costs without DR participation. In case 2, beside minimizing the operating costs via participation in the DR program, the uncertainties resulted from the power generation by the WT and PV were covered using this type of DR in such a way that the participants can register in one of the three modes of demand reduction as provided in Table 3. Furthermore, since the participation in this program was voluntary and also demands were delivered in three forms, namely demands which can be interrupted (or reduced), and shifter and loads that cannot be altered. Therefore, it was assumed that 40% of the total consumers would participate in these programs. In cases 3 and 4, the pollutant emissions were assumed without and with responsive loads, respectively. Cases 5 and 6 were aimed to simultaneously optimize the objective functions relating to the operating costs and pollutant emissions without and with responsive loads, respectively. Table 5 presents the results of islanding performance of the micro-grid without demand responses.

Table 3 Price-quantity offer package for RC, CC and IC. The store value DR Energy cost (€ct/kW h)

33% of total response 2.5

66% of total response 3.5

100% of total response 4.5

Table 4 Economic power dispatch for case 1 (without DR). Hour

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

Units MT (kW)

PAFC (kW)

WT (kW)

PV (kW)

Batt (kW)

Utility (kW)

9.5335 6 8.0095 6 7.0713 7.0021 6.0000 25.9720 29.9719 30 30 30 29.9870 30 30 30 30 19.1125 22.5324 24.2994 29.9996 21.6007 9.1837 26.7621

23.5693 30 22.4317 28.9535 5.7000 26.3207 22.8271 22.9524 28.5555 30 30 30 30 30 29.7784 30 29.9324 28.2711 30 30 30 29.9711 21.7484 27.30

0 0 0.4167 0.0169 0.4998 0.6011 0.1785 0.4205 1.7270 3.09 8.3762 10.41 3.915 2.2209 1.785 1.305 1.5176 0.2106 0.3906 0.9540 1.0067 1.3005 0.4320 0.6150

0 0 0 0 0 0 0 0.18 3.2437 7.5249 9.6237 3.59 0 9.6644 7.0875 4.2035 0.2743 0 0 0 0 0 0 0

5.4700 15.4764 10.8579 13.7025 16.4577 5.10665 12.5727 14.0498 30 29.9996 30 30 29.8944 30 30 29.9999 29.9997 14.2696 16.7978 21.4849 29.9944 26.9955 3.6356 7.5793

13.4271 29.4764 30 29.7319 26.2710 23.9693 28.4216 11.4251 17.4983 20.6146 30 30 21.7965 29.8854 22.6509 15.5085 6.7241 26.1360 20.2790 10.2616 13.0008 8.8678 30 8.9022

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Table 5 Economic power dispatch for island mode (without DR).

100 BeforDR

90

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

Units

AfterDR

80

MT (kW)

PAFC (kW)

WT (kW)

PV (kW)

Batt (kW)

22.1055 15.6518 20.2309 8.63875 9.31568 26.6985 21.3415 21.5249 28.8977 20.7471 28.2483 20.4458 16.3313 22.7177 16.3119 21.5400 24.3149 29.0091 28.698 29.8919 25.2023 23.4437 16.2925 10.9881

19.4366 18.0606 17.1757 23.3260 27.3898 28.1646 26.7464 27.4179 23.5938 29.2864 29.0252 24.5700 29.0096 24.3118 30 29.1454 30 30 30 27.4754 27.0925 29.2471 30 30

0.0147 0 0.1788 0.0698 0.8275 0.1987 0.1063 0.2309 0 0.21138 0 0 0.0696 0.3453 0.3690 0.01363 0.357 0.3093 1.302 0 0.1056 0.1620 0.0020 0.4228

0 0 0 0 0 0 0 0.1976 0.0049 0 0.5869 0.0125 0.7311 0 0.5295 0.90568 0.3280 0 0 0 0 0 0 0

10.4430 16.2875 12.4144 18.9652 18.4668 7.9381 21.8056 25.6285 23.5033 29.7550 20.1394 28.9715 25.8581 24.6250 28.7893 28.3952 30 28.6815 30 29.6325 25.5995 18.1470 18.7054 14.5890

Demand (KW)

Hour

70 60 50 40 30 20 10 0 0

5

10

15

20

25

Time (h) Fig. 11. The load demand before and after DR implement.

Table 6 Economic power dispatch for case 2 (with DR). Hour

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

5.1. Cases 1 and 2: Operating costs without and with responsive load In this case, results of the minimization of operating costs were analyzed without and with responsive loads. Unit’s optimal power generation allocation without and with the responsive loads are presented in Tables 4 and 5. Numerical results, presented in Table 4, which are related to the case without the responsive loads, indicated that during the first hours of day when the price was low, the battery started to charge, while during the peak-demand hours when the price was at its highest level, the utility was making a purchase from the MG in which the power consumption was supplied by the price offer from the distributed generation resources; the results in [11] could verify these results. According to the obtained results, when there were responsive loads available in the system (Table 5), the same condition existed with the difference that there was a significant decrease in the power generation by the WT and PV, particularly in the peak-

Units MT (kW)

PAFC (kW)

WT (kW)

PV (kW)

Batt (kW)

Utility (kW)

18.3466 17.2249 12.6986 19.2521 26.5306 16.2433 14.6743 30 30 29.9999 30 29.8611 29.5951 29.1307 30 29.9996 27.9692 11.5206 20.6331 14.0873 29.9674 24.7678 16.7823 22.0410

19.8461 21.2220 7.6801 24.8593 27.3998 24.2030 22.1115 13.5362 30 30 29.5188 27.6948 29.5801 30 30 29.9985 28.6141 17.5520 29.7375 30 30 21.0790 12.5165 28.1346

0 0.0539 0.1785 0.4561 0.357 0.549 0 0 1.785 3.0899 4.1887 1.4940 0 1.3714 1.785 1.305 0.8881 1.2495 0.1302 0.0355 1.3005 0.1080 0.183 0

0 0 0 0 0 0 0 0.04 3.7498 7.525 10.2923 11.95 10.7680 7.1351 7.875 4.0808 0.4640 0 0 0 0 0 0 0

12.2865 27.5783 17.6651 6.71784 22.2875 8.4136 9.3690 7.5935 29.9999 30 30 30 28.0567 28.3626 29.9991 29.9958 30 26.9061 11.7536 22.4774 30 24.1800 20.4607 12.4345

28.0937 14.0793 13.7775 23.1707 30 12.5909 28.7830 19.8302 23.5348 27.6149 30 30 30 30 28.6591 19.3798 7.9355 24.7716 22.7453 16.3997 5.2679 6.8648 25.0573 29.2588

12

forecast

withoutDR

withDR

forecast

25

withoutDR

withDR

10

PV Power (kW)

Wind Power (kW)

20

8

6

4

10

5

2

0

15

0

5

10

15

20

25

0

0

5

10

15

Time (h)

Time (h)

(a)

(b)

Fig. 10. (a) Wind power with considering operating cost and (b) PV power with considering operating cost.

20

25

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G.R. Aghajani et al. / Energy Conversion and Management 106 (2015) 308–321 Table 7 Environmental power dispatch for case 3 (without DR). Hour

Units

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

MT (kW)

PAFC (kW)

WT (kW)

PV (kW)

Batt (kW)

Utility (kW)

11.0424 8.1288 14.9198 13.9688 10.3824 21.6969 12.4437 21.5255 30 29.5761 22.9531 6.4473 11.6480 16.9108 18.2833 27.0838 16.8772 19.6293 13.3928 8.7059 15.1842 7.3815 7.6022 6.8718

30 30 29.2625 29.9654 29.9670 29.7246 30 29.4450 30 29.9239 28.5767 29.6877 29.2975 29.0558 29.9050 29.9261 29.5912 29.9630 29.9997 22.4880 30 30 29.7116 29.8051

1.7747 1.5631 1.7295 1.785 1.6065 0.6405 1.5725 1.305 1.785 2.9627 8.5212 9.9980 3.7389 2.3415 1.785 1.3047 1.785 1.7849 1.2754 1.5520 1.2553 1.3005 0.8476 0.6110

0 0 0 0 0 0 0 0.1876 3.75 7.525 10.45 11.9465 23.9 21.05 7.875 4.1728 0.55 0 0 0 0 0 0 0

30 29.9017 30 28.8708 29.9953 30 29.9947 30 30 29.9999 29.9982 29.9896 29.8442 30 30 29.7405 29.8254 29.9083 29.5468 30 30 30 30 29.8525

20.8171 19.5937 25.9118 23.5901 15.9513 19.0620 4.0109 7.4632 19.535 19.9878 22.4993 14.0693 26.4287 27.3582 11.8483 12.2282 6.3710 6.7143 15.7851 24.2585 1.5604 2.3179 3.1616 11.1406

700

800

650

Operating Cost (Ect)

600

600

500

Min Operating Cost without DR

400

500 450 400

Min Operating Cost with DR

350

X: 1000 Y: 241.3

0

100

200

300

400

500

600

700

800

X: 1500 Y: 231.3

250 200

900 1000

0

500

1000

Iteration

Iteration

(a)

(b)

1500

Fig. 12. Convergence characteristic of propose algorithm (a) in the case 1 (without DR) and (b) in the case 2 (with DR).

12

forecast

withoutDR

withDR

withoutDR

withDR

20

8

6

4

15

10

5

2

0

forecast

25

10

PV Power (kW)

200

550

300

300

Wind Power (kW)

Operating Cost (Ect)

700

0

5

10

15

20

25

0

0

5

10

15

Time (h)

Time (h)

(a)

(b)

Fig. 13. (a) Wind power output and (b) PV power output with considering pollutant emission.

20

25

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G.R. Aghajani et al. / Energy Conversion and Management 106 (2015) 308–321 750

600

700 550

650

500

Emission (Kg)

Emission (Kg)

600 550 500

Min Emission Without DR

450 400 350

X: 1500 Y: 299.7

300

450 400 350

Min Emission with DR

300 X: 1500 Y: 234

250

250 0

500

1000

1500

Iteration

200 0

500

1000

1500

Iteration

(a)

(b)

Fig. 14. Convergence characteristic of propose algorithm (a) in the case 3 (without DR) and (b) in the case 4 (with DR).

Table 8 Environmental power dispatch for case 4 (with DR).

310 Operating cost

252

308

Emission

250

306

248

304

246

302

244

300

242 240

298

238

296

Hour

Emission (kg)

Operating Cost (Ect)

254

294

236 1

2

3

4

5

6

7

8

9

10

Algorithm Run for without DR

244 242 240 238 236 234 232 230 228 226 224

Operating cost Emission

1

2

3

4

5

6

7

8

9

246 244 242 240 238 236 234 232 230 228

Emission (kg)

Operating Cost (Ect)

(a)

10

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

Units MT (kW)

PAFC (kW)

WT (kW)

PV (kW)

Batt (kW)

Utility (kW)

6 6.4442 11.6244 13.4673 10.3311 19.7514 30 29.5861 7.0728 30 6 6 6 11.5734 6.6235 7.6190 20.2955 15.3916 30 20.9228 20.1260 14.6694 6 9.5054

30 25.8718 29.4249 30 27.3707 28.1725 26.5993 28.2874 28.7119 30 22.4403 27.8278 21.8106 28.1917 29.9912 27.9768 30 30 30 30 29.8144 28.9340 30 27.8620

0.0393 0.6103 1.785 1.785 1.7669 0.549 1.6714 1.305 1.785 3.09 8.4500 10.2935 3.915 2.3531 1.785 1.305 1.7848 1.6265 1.302 1.785 1.2055 1.2296 0.7146 0.3075

0 0 0 0 0 0 0 0.2 3.75 7.525 10.2881 11.9483 23.9 20.4111 7.875 3.9028 0.55 0 0 0 0 0 0 0

30 30 29.5321 30 30 30 30 30 30 30 30 29.9973 29.8156 30 30 29.5650 30 30 29.9999 30 29.5484 29.5242 30 30

17.0393 15.9265 25.3665 27.2523 17.4688 19.4730 23.2707 19.3785 0.3197 25.615 4.1785 17.0669 18.4412 25.5295 5.2748 4.6311 3.6304 4.9817 7.3019 1.7078 7.6909 8.3574 5.7146 15.6750

Algorithm Run for with DR

(b) Fig. 15. Operating cost and emission obtained in ten runs of the algorithm for (a) without DR and (b) with DR.

demand period, which is also clearly illustrated in Fig. 10a and b. Also, according to Fig. 10a, it can be observed that, due to the low price of power generation by the WT compared to the PV, participation of this power type without the responsive loads was very close to that of the predicted values. Furthermore, it is observed from Fig. 11 that DR not only affected reduction in the power generation by the WT and PV, but also resulted in peak shaving in the daily load curve and load shifting in the off-peak period. However, from the perspective of operating costs, due to the convergence characteristics resulted from the proposed algorithm in Fig. 12a and b, it can be noticed that implementing the DR programs decreased the operating costs by 5%, which was completely dependent on the price offer package. By comparing the results in this table with those in Table 4, it can be reported that, in the

islanding mode without demand responses, the battery was in the discharge mode during all the times, while other generations during most of the operation hours had values close to their maximum values, which led to an increase in the operational cost and decrease in the system safety. Therefore, use of the islanding mode is not recommended for achieving minimum operational cost. 5.2. Cases 3 and 4: Pollutant emissions without and with responsive loads In this part, results of minimizing pollutant emissions were analyzed without and with the participation of the responsive loads. The unit’s optimal power allocation in these two cases is presented in Tables 6 and 7, respectively. Power generation by the wind turbine and photovoltaic cells, demonstrated in Tables 6 and 7, was not-significantly different from the predicted values presented in Table 2, which could be due to the fact that these types of power generation are devoid of any pollutant. For this reason, battery

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600

X: 260.2 Y: 587.4

600

X: 228.3 Y: 593.1

Min Operating Cost

580

Min Operating Cost

550

540

Emission (Kg)

Emission (Kg)

560

520

Best Solution With out DR 500

Min Emission

480

500

Best Solution With DR 450

400

X: 336.1 Y: 458.9

440 420 260

Min Emission

X: 270.5 Y: 394.4

460

280

300

320

350

X: 455.2 Y: 428.9

340

360

380

400

420

440

X: 368.3 Y: 310.2

300 220

460

240

260

280

Operating Cost (Ect)

300

320

340

360

380

Operating Cost (Ect)

(a)

(b)

Fig. 16. Convergence characteristic of propose algorithm (a) in the case 5 (without DR) and (b) in the case 6 (with DR).

540

580 560

530

540 520 Best Solution with out DR (NSGA-II)

Emission (Kg)

Emission (Kg)

520 500 480 460

X: 385.6 Y: 466

Best Solution with DR (NSGA-II)

510 500 490 X: 296.7 Y: 488.5

440 480 420 470

400 380 360

370

380

390

400

410

420

430

440

450

460

460 270

280

290

300

310

Operating Cost (Ect)

Operating Cost (Ect)

(a)

(b)

320

330

340

Fig. 17. Convergence characteristic of NSGA-II algorithm (a) in the case 5 (without DR) and (b) in the case 6 (with DR).

source was in its maximum power generation mode during most of the periods. The obtained results indicated that, during most of the operating periods, the utility was making purchase from the MG because of having a high level of pollutant emissions. Also, by comparing Fig. 13, it can be observed that, when the pollutant emission was minimized, the DRP had a significant effect on covering the uncertainties associated with the wind and solar power generation. From the perspective of pollutant emission, considering the convergence characteristics resulted from the proposed algorithm in Fig. 14a and b, it is noticed that implementing the DR program decreased the pollutant emission by 21%. The operating cost and the emission were calculated for each of the obtained best compromise solutions for without/with DR and shown in Fig. 15. The results show small range of variations for the cost and emission objectives (see Table 8).

5.3. Cases 5 and 6: Considering both operating costs as well as pollutant emissions without and with responsive loads In this case, results of minimizing two inconsistent functions, namely operating costs and pollutant emissions, without and with

Table 9 Comparison of best compromise solution. Approach

MOPSO

NSGA-II

Without DR

Operation cost (€ct) Emission (kg)

336.1 458.9

385.6 466

With DR

Operation cost (€ct) Emission (kg)

270.5 394.4

296.7 488.5

the participation of the responsive loads were analyzed. Since the objectives of operating costs and pollutant emissions were opposite, therefore, according to Fig. 16, moving from the initial points on the curve toward the final points along the Pareto path was the same as changing the operating model from lower costs and higher pollutions to higher costs and lower pollution, where the optimal location can be determined using the fuzzy mechanism. Results in Fig. 16 indicate that, when the DR programs were implemented, location of the optimal operation can be improved such that the operating costs and pollutant emissions could be decreased by 24% and 16%, respectively. In order to demonstrate efficiency of MOPSO algorithm, the results were compared with

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35

CostOptimization Multi-objectiveOptimization EmissionOptimization

30 25

10

PV Power (kW)

WTPower (kW)

CostOptimization Multi-objectiveOptimization EmissionOptimization

5

20 15 10 5

0

0

5

10

15

20

25

0

0

5

10

15

Time (h)

Time (h)

(a)

(b)

20

25

Fig. 18. (a) Wind power output and (b) PV power output for the multi-objective optimization.

those of NSGA-II algorithm. However, according to Figs. 16 and 17, it can be said that MOPSO algorithm had better performance in finding the optimal interaction point between operational cost and pollution emissions in both cases of with and without demand response, compared with NSGA-II algorithm. Table 9 shows the results of this comparison. Fig. 18 shows the power generation by the WT and PV considering the minimization of the operating cost function and pollutant emission function as well as simultaneous minimization of both operating cost and emission functions when responsive loads were available. As shown in Fig. 18, the maximum power generation by wind and solar energies was related to the case when the pollutant emission was considered and therefore a balance can be maintained by selecting the simultaneous optimization mode. 6. Conclusion In this paper, the problems of operating a MG were implemented considering the responsive loads as coverage for the uncertainties associated with the wind and solar power generation as an optimization function with two inconsistent objectives where the total MG operating costs and the associated pollutant emission were analyzed in six different cases. In order for the MG to have better performance, the possibility of energy exchange with the utility was assumed. Furthermore, the consumption side could be actively involved in energy generation and consumption management. For the consumption management, it was assumed that consumers could participate in incentive-based DRPs. In order to obtain the optimal result or a set of optimal results, MOPSO methods based on fuzzy technique was used. According to the obtained results, it was observed that, among the analyzed cases, simultaneously considering the operating costs and pollutant emissions with the participation of responsive loads, which decreased the operating costs and pollutant emission by 24 and 16%, respectively, yielded the best results. Also, results of simulation indicated that the proposed model not only had a simple structure, but also was very powerful in yielding the optimal result such that consumer’s participation in the DRP not only covered the shortage caused by the uncertainties resulted from the wind and solar power generation, but also decreased the total operating costs and pollutant emission in the system, because using the DR caused the application of expensive generation units (including distributed, renewable and utility generation resources), some of which could cause environmental pol-

lution. Among the most important results obtained in the study was the use of price-offer packages which made it possible to apply a competitive market among consumers in a simple way.

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