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objective Optimal Operation. Management of Distribution Network. T. Niknam1, H. Zeinoddini-Meymand2*. 1 Electrical and Electronic Engineering Department, ...
DOI: 10.1002/fuce.201100167

T. Niknam1, H. Zeinoddini-Meymand2* 1 2

Electrical and Electronic Engineering Department, Shiraz University of Technology, Shiraz, Iran. Islamic Azad University, Kerman Branch, Kerman, Iran.

Received October 10, 2011; accepted March 08, 2012

Abstract This paper presents an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and differential evolution (MHBMO-DE) to solve the multiobjective optimal operation management (MOOM) problem, which can be affected by fuel cell power plants (FCPPs). The objective functions are to minimize total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources, and deviation of bus voltages. A new interactive fuzzy satisfying method is presented to solve the multi-objective problem by assuming that the decisionmaker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolution-

1 Introduction The large scale development of renewable electricity generation will require the integration of renewable electricity supplies within the current electricity networks. Investigation of the impact of such supplies on the performance and robustness of the electricity supply chain is of critical importance for development of future electricity networks. Fuel cells are electrochemical devices that convert the chemical energy of a fuel directly and efficiently into electricity. Fuel cell is considered as an emerging technology that can deliver clean, quiet, and potentially renewable energy for primary, base-load, and back-up power. However, this technology needs to be commercialized [1–5]. In the last decade the fuel cell has emerged as one of the most promising renewable energy technologies. Because of

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ary methods are used to solve this problem because of their independence from type of the objective function and constraints. Recently researchers have presented a new evolutionary method called honey bee mating optimization (HBMO) algorithm. Original HBMO often converges to local optima, in order to overcome this shortcoming, we propose a new method that improves the mating process and also, combines the modified HBMO with DE algorithm. Numerical results for a distribution test system have been presented to illustrate the performance and applicability of the proposed method. Keywords: Fuel Cell Power Plant (FCPP), Hybrid Modified Honey Bee Mating Optimization and Differential Evolution (MHBMO-DE), Interactive Fuzzy Satisfying Method, MultiObjective Optimal Operation Management (MOOM), MultiObjective Optimization

their modular capabilities, fuel cells can be built in a wide range of sizes from 200 kW units, which provide electricity for an individual building, to 100 megawatt plants, which are used to add base-load capacity to an electric utility system. Small plants can operate with efficiencies similar to those of large plants. They produce high grade waste heat, which can be used in cogeneration or in space heating applications, yielding total energy efficiencies approaching 85%. Their reliability makes them useful as uninterruptible power systems for hospitals and hotels as well as communication and computer companies. They are quiet, safe, and generally acceptable in close quarters. They can use a variety of fuels

– [*] Corresponding author, [email protected]

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Impact of Fuel Cell Power Plants on Multiobjective Optimal Operation Management of Distribution Network

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants and change out between fuels can be performed rapidly. They can provide VAR control, have a quick ramp rate, and can be remotely controlled in unattended operation [1–5]. Since the FCPPs are usually connected to distribution networks, it is necessary to study the effect of FCPPs on this part of the power systems. MOOM is one of the most significant schemes in the distribution networks, which can be affected by fuel cell power plants (FCPPs); because the X/R ratio of distribution lines is small and the structure of distribution network is radial. X and R are reactance and resistance of the transmission line, respectively. Many researchers have investigated optimal operation of the distribution network considering reactive power and voltage control in distribution networks. For instance, Lu and Hsu [6] presented an approach for reactive power/voltage control in a distribution substation, which minimizes the reactive power flow. Hatziargyriou and Karakatsanis [7] proposed a method for the adjustment of voltage and reactive power control devices in distribution networks based on probabilistic constrained load flow. Lu and Hsu [8] developed a fuzzy dynamic programming approach to reactive power/voltage control. Hsu and Lu [9] presented a combined artificial neural network-fuzzy dynamic programming technique to control voltage profile and reactive power in a distribution substation. Yoshida et al. [10] proposed a particle swarm optimization for reactive power and voltage control considering voltage security assessment. Liu et al. [11] presented an approach to optimal Volt/Var control with a comprehensive consideration of control means at the substation and along feeders of the distribution network. Liang and Wang [12] proposed a simulated annealing approach to fuzzy-based reactive power and voltage control in a distribution system. Viswanadha Raju and Bijwe [13] presented a method for real power loss or total real power demand minimization. Vlachogiannis and Østergaard [14] solved the reactive power and voltage control problem by means of a quantum computing inspired genetic algorithm. Some of the reported works in the literature have studied optimal operation of distribution network considering the effect of distributed generations (DGs). For example, Katiraei and Iravani [15] presented a real and reactive power management strategy of electronically interfaced DG units in the context of a multiple DG system. Kim and Kim [16] proposed a voltage regulation coordination method of DG system. Vovos et al. [17] presented the comparison of the centralized and distributed approaches for controlling distribution network voltages in terms of the capacity of DG. Kashem and Ledwich [18] presented the optimal use of voltage support DG to support voltage in distribution feeders. Carvalho et al. [19] proposed the problem of voltage rise mitigation in distribution networks with DG. Senjyu et al. [20] presented the optimal control of distribution voltage with coordination of distribution installations. Viawan and Karlsson [21] presented the voltage and reactive power control in distribution systems in the presence of synchronous machine-based DG. Madureira and Lopes [22] described a methodology for coordinated volt-

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age support in distribution networks with large integration of DG and micro-grids. Niknam et al. [23–27] presented the methods for the Volt/Var control in radial distribution networks considering DGs. Niknam et al. [28] presented a method for optimal operation management of distribution network including FCPPs. In the above-mentioned studies, the optimal operation is considered as a single-objective problem. A multi-objective daily MOOM problem in distribution networks regarding FCPPs is solved in this paper that the objective functions are the total electrical energy losses, the total cost of electrical energy generated by FCPPs and distribution companies, the total emission of FCPPs and distribution companies and voltage deviations during the next day. The control variables are the active power of FCPPs and tap of transformers in the next day. Multi-objective optimization is a design methodology that optimizes a set of objective functions systematically and simultaneously. It is used for optimization with multiple conflicting objectives. One traditional method to solve multiobjective optimization problems is to select only one objective and combine other objectives as constraints. The other traditional method is to combine all the objectives into a single objective function [29]. There are disadvantages associated with these methods, for example, the first approach limits the choices available to operators. Both of the methods require a priori selection of weights or targets for each of the objective functions and the operator’s preferences are usually ignored to some extent. Because of the existence of such equipments as static var compensators (SVCs), FCPPs, load tap changers (LTCs), and voltage regulators (VRs), the MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods do not depend on the type of the objective function and constraints and therefore, are good candidates for solving this problem. Recently, a new optimization algorithm based on honey-bee mating proposed by Afshar et al. [30] has been used to solve challenging optimization problems such as optimal reservoir operation [30, 31], clustering [32], distribution state estimation [33], and distribution feeder reconfiguration [34, 35]. Honey-bee mating may also be considered as a typical swarm-based approach to optimization in which the search algorithm is inspired by the marriage process of real honey bee. However, the performance of original honey bee mating optimization (HBMO) greatly depends on the mating process, and it often suffers from the problem of being trapped in local optima. In order to overcome local optima problems, first we propose a new mating process and then, combine the modified HBMO with the differential evolution (DE) algorithm. Therefore, in this paper an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and DE (MHBMO-DE) for multi-objective optimal operation management (MOOM) problem considering the effect of FCPPs is proposed and implemented to solve the MOOM problem. In the proposed algorithm, the objective functions are modeled with fuzzy sets. Fuzzy sets were first introduced by

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants  is the state vector including active power of FCPPs where, X and tap positions of transformers for the next day, Ng the number of FCPPs, Nt the number of transformers, Nd the number of load variation steps, Nb the number of branches, Ri the resistance of the ith branch, Iit the current of the ith branch for the tth load level step, PG the active powers of all FCPPs during the day, Pgi the active power of the ith FCPP during the day, and Ptg is the active power of the ith FCPP for i the tth load level step. Tap is the tap vector representing the tap positions of all transformers in the next day, Tapi the tap vector including the tap position of the ith transformer in the next day, Tapti the tap position of the ith transformer for the tth load level step, and n is the number of state variables. 2.1.2 Total Electrical Energy Costs Generated by FCCPs and Distribution Companies The total energy cost of FCCPs and distribution companies are modeled as follows [37]: min

 ˆ f2 …X†

Nd X

Costt ˆ

tˆ1

Nd X

CtFC ‡ Ctsubstation



tˆ1

X Ptgj Ng

CtFC ˆ 0:04$=kWh ×

jˆ1

PLRtj ˆ

gj

Ptg

j

P maxj

For PLRj < 0:05 ⇒ gj ˆ 0:2716 For PLRj ≥ 0:05 ⇒ gj ˆ

2 Optimal Operation Management of Distribution Networks Considering the Effect of FCPPs This section presents the objective functions, constraints, and fuzzy modeling of the objective functions for the MOOM problem. 2.1 Objective Functions The objective functions of MOOM problem are defined as: 2.1.1 Electrical Energy Losses of Distribution Network in the Presence of FCPPs min

 ˆ f1 …X†

Nd X

PtLoss ˆ

tˆ1

Nd X Nb X

0:9033 PLR5j

Ctsubstation ˆ pricet × Ptsub (2† where gj is the electrical efficiency of the jth FC, PLRtj is part load ratio of the jth FC for the tth load level step, Ptsub the active power generated at the substation bus of distribution feeders for the tth load level step, CtFC the cost of electrical energy generated by FCPPs for the tth load level step, Ctsubstation the cost of power generated at the substation bus for the tth load level step, and pricet is the energy price for the tth load level step.

min

tˆ1 iˆ1

 ˆ f3 …X†

Nd X

Emissiont ˆ

tˆ1

Nd X

EtFC ‡ EtGrid



tˆ1

EtFC ˆ NOtxFC ‡ SOt2FC ˆ …0:03 ‡ 0:006†lb=MWh ×

Ng X

Ptg

jˆ1

(1†

n ˆ Nd × …Ng ‡ Nt †

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2:0704 PLR2j ‡ 0:3747

2.1.3 Summation of FCPPs and Substation Bus Emissions

2 Ri × Iit

   ˆ PG ; Tap X 1 ×n h i PG ˆ Pg1 ; Pg2 ; . . . ; PgN g h i d Pgi ˆ P1g ; P2g ; . . . ; PN i ˆ 1; 2; 3; :::; Ng gi ; i i h i Tap ˆ Tap1 ; Tap2 ; . . . ; TapNt h i d Tapi ˆ Tap1i ; Tap2i ; . . . ; TapN ; i ˆ 1; 2; 3; :::; Nt i

2:9996 PLR4j ‡ 3:6503 PLR3j

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EtGrid

ˆ

NOtxGrid

‡

SOt2Grid

ˆ …5:06 ‡ 7:9†

lb=MWh

(3†

j

× Ptsub

where, EtFC is the emission of FCPP, EtGrid the emission of large scale sources (the substation bus connected to grid), NOtxFC is nitrogen oxide pollutants of FCPP, SOt2FC is sulfur oxide pollutants of FCPP, NOtxGrid is nitrogen oxide pollu-

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Zadeh [36] as an effective method of solving non-probabilistic problems. The different objectives are easily integrated because all the membership function values of these objectives are in the same range [0, 1]. It is assumed that the decision-maker (DM) has imprecise or fuzzy goals for each of the objective functions. The fuzzy goals are quantified by defining their corresponding membership functions. The DM then, indicates the reference membership values for each of the objective functions and the corresponding best-compromising solution can be obtained. Through the interaction, the DM’s reference membership values are updated by considering the current values of the membership functions as well as the objectives until a satisfying solution for the DM is obtained. The main contributions of the paper are as follows: (i) It presents a new multi-objective approach for the daily optimal operation management in distribution networks considering FCPPs. (ii) It presents a modified HBMO (MHBMO). (iii) It combines MHBMO with the DE algorithm. The rest of the paper is organized as follows. In Section 2, the MOOM problem formulation is developed. A suitable FCPP modeling and its effect on the voltage profile of distribution networks is presented in Section 3. In Section 4 the interactive fuzzy satisfying method is illustrated. Section 5 deals with the proposed HBMO-DE algorithm. Application of the proposed approach to MOOM problem is demonstrated in Section 6. Finally, in Section 7, the feasibility of the proposed algorithm is shown by the implementation on a distribution system.

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants tants of grid and SOt2Grid is sulfur oxide pollutants of grid for the tth load level step. 2.1.4 Deviation of Bus Voltages Voltage deviation is also considered as the objective function. It determines the difference between the voltages in nodes with respect to the nominal voltage. The voltage deviation is calculated as follows: Nd N bus t  P P Vi Vi Vi  ˆ tˆ1 iˆ1 minf4 …X† (4† Nd where, Vi  is the desired voltage of network at the bus i, Vit is the voltage magnitude of the ith bus during time t and Nbus is the number of buses. In this problem, it is assumed that tap position of transformers change stepwise.

Since the mentioned objective functions are imprecise, they are formulated as fuzzy sets. A fuzzy set is generally shown  The higher value of the by a membership function lfi …X†. membership function implies a greater satisfaction with the solution. The membership function comprises of lower and upper boundary values together with a continuous strictly monotonically decreasing function. Figure 1 shows the graph of the possible shape of a strictly monotonically decreasing membership function. The lower and upper bounds, fimin , fimax of each objective function under given constraints are established to extract a  for each objective function, fi …X†.  membership function l …X† fi

The i membership function is now defined as:  ˆ lfi …X†

8 > < > :

1

 fimax fi …X† fimax fimin

 ≤ f min fi …X† i  ≤ f max f min ≤ fi …X† i

0

i

Constraints are defined as follows: Active power constraints of FCPPs: i

(6†

where P min;FCi and P max;FCi are the minimum and maximum active power of the ith FCPP, respectively.

Fig. 1 A membership function for objective functions.

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where Tapti is the current tap positions of the ith transformer during time t, Tapimin and Tapimax are the minimum and maximum tap positions of the ith transformer, respectively. ● Unbalanced three-phase power flow equations. ● Maximum allowable daily operating times of transformers: (9†

is daily operating times of the ith transformer and DOTTrans i Trans MADOTi is maximum allowable daily operating times of the ith transformer. ● Substation power factor Pf min ≤ Pf t ≤ Pf max

(10†

Pfmin, Pfmax, and Pft are the minimum, maximum, and the current power factor at the substation bus during time t. ● Bus voltage magnitude V min ≤ Vi t ≤ V max

(11†

where Vi t , Vmax and Vmin are the voltage magnitudes of the ith bus during time t and the maximum and minimum values of voltage magnitudes, respectively.

3 Fuel Cell Power Plant Modeling and Considering Its Effect on Voltage Profile of Distribution Network

2.3 Constraints

P min;FCi ≤ Ptg ≤ P max;FCi

(8†

(5†

 ≥ f max fi …X† i

fimin is calculated by optimizing each objective separately.



Tapimin < Tapti < Tapimax

DOTTrans ≤ MADOTTrans i i

2.2 Fuzzy Modeling of Objective Functions

th

Distribution line limits: Line t (7† Pij < PLine ij; max t Line where PLine ij and Pij; max are the absolute power flowing over distribution lines and maximum transmission power between the nodes i and j, respectively. ● Tap of transformers: ●

Generally, FCPPs in distribution networks can be modeled as PV or PQ models. Since distribution networks are unbalanced three-phase systems, FCPPs can be controlled and operated in two forms: (i) Simultaneous three-phase control, and (ii) Independent three-phase control or single-phase control. Considering the control methods and FCPP models, four different models can be used for simulation of these sources as follows: (a) PQ model with simultaneous three-phase control. (b) PQ model with independent three-phase control. (c) PV model with simultaneous three-phase control. (d) PV model with independent three-phase control. It should be noted that when FCPPs are considered as the PV models; they should be able to generate reactive power to maintain their voltage magnitudes. Many researchers have proposed several procedures to model generators connected to distribution networks as the PV buses [33, 38, 39]. In this

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paper, the FCPPs are modeled as the PQ model with simultaneous three-phase control. Connecting an FCPP to the distribution network will affect the power flow and the voltage profiles. Since the X/R ratio of the distribution lines is small, the FCPP has a significant impact on voltage profiles. To explain this, consider a twobus test system (Figure 2). The voltage drop along the line from bus 1 to bus 2 is calculated as follows: DV ˆ V1 ∠d1 P jQ Iˆ V2*

V2 ∠d2 ˆ …R ‡ jX†I

P ˆ Pg ‡ PLoad

(12†

Q ˆ Qg ‡ QLoad jDVj2 ˆ

…RP ‡ XQ†2 ‡ …XP V22

RQ†2 …RP ‡ XQ†2 ≈ V22

where Vi and di are the magnitude and angle of voltage at the ith bus, and Pg, Qg, PLoad, and QLoad are the active and reactive powers of the FCPP and load, respectively. R + jX is the line impedance. As it was shown in the above equation, RP and XQ are not negligible. Also, since the X/R ratio is small and Q is less than P, the effect of FCPPs’ active power is more than their reactive power.

4 Interactive Fuzzy Satisfying Method In this section an interactive fuzzy satisfying method has been proposed to obtain the satisfying solution for the DM from the non-inferior solution set in the multi-objective optimization. Typically, an infinite number of non-inferior points exist in a given multi-objective problem. After defining the membership functions, the DM is asked to specify the desirable levels of achievement of the membership functions, called the reference membership values lri ; i ˆ 1; . . . ; p where, p is the number of objective functions. The reference value is a real number in the interval [0,1], and represents the importance of each objective function. The following minimax problem is solved to obtain the optimal solution. It is the best compromise and satisfactory solution, which is close to the requirements for the DM’s reference values:    ˆ min max l  f…X† lfi …X† (13† ri X∈X

iˆ1;:::;n

where, X is the set of non-inferior solutions, lfi is the ith membership function, lri is the ith reference membership value. The optimization technique can now be described as follows:

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5 The Proposed MHBMO-DE Algorithm 5.1 Basic HBMO The HBMO algorithm simulates the mating process of the queen of a hive. The mating process of the queen starts when the queen flights away from the nest performing the mating flight during which the drones follow the queen and mate with her in the air. The algorithm is a swarm based algorithm since it uses a swarm of bees, where there are three kinds of bees: the queen (reproductive female), the drones (male), and the workers (non-reproductive female). There are a number of procedures that can be applied inside the swarm. In the original HBMO algorithm, the procedure of mating of the queen with the drones has been described in Ref. [30–35]. A drone mates with a queen probabilistically using an annealing function as follows [32–34]:  Prob…D† ˆ exp

D…f† S…k†

 (14†

where, Prob(D) is the probability of adding the sperm of drone D to the spermatheca of the queen, D(f) is the absolute difference between the fitness of D and the fitness of the queen and S(k) is the speed of the queen at iteration k. The probability of mating is high when the queen is with the high speed level, or when the fitness of the drone is as good as the queen’s. After each transition in space, the queen’s speed decreases according to the following equation: S…k ‡ 1† ˆ a × S…k†

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(15†

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Fig. 2 A two-bus test system.

Step 1: Input the data and set the interactive pointer q = 0. Step 2: Determine the upper and lower bounds for every objective function fimin , fimax and extract a strictly monotonically decreasing function to formulate the membership func tions lfi …X†. Step 3: Set the initial reference value of each objective …0† function lri ˆ 1 for i = 1,..., p. Step 4: Solve the minimax problem (Eq. 13) using a suitable algorithm.  fi …X†;  l …X†,  and proStep 5: Calculate the values of X; fi ceed to the next step if they are satisfactory. Otherwise, set the interactive pointer q = q + 1 and choose a new reference …q† value lri , i = 1,..., p. Then, go to Step 4. Step 6: Output the most satisfactory feasible solution  fi …X†;  l …X†,  i = 1,..., p. X; fi The DM determines the new reference value at each iteration. The sequence of this program is processed automatically afterwards, and the DM does not need to provide an accurate goal for each objective. The reference value of an objective is estimated from the DM’s experience or by trial and error according to the current values of the membership and objective functions. Thus, the DM can determine the most satisfactory solution for the minimax problem using the interactive fuzzy satisfying algorithm.

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants where, a is a factor ∈[0,1] and is the amount of speed reduction after each transition and each step. The speed of the queen is initialized randomly. A number of mating flights are then realized. At the start of a mating flight drones are generated randomly and the queen selects a drone using the probabilistic rule in Eq. (14). If the mating is successful (i.e., the drone passes the probabilistic decision rule), the drone’s sperm is stored in the queen’s spermatheca. By using the crossover of the drone’s and the queen’s genotypes, a new brood (trial solution) is generated, which can be improved later by employing workers to conduct local search. 5.2 Modified HBMO (MHBMO) The main difference of the HBMO algorithm from the classic evolutionary algorithms is that since the queen stores a number of different drones’ sperm in her spermatheca, she can use parts of the genotype of different drones to produce a new solution, which gives the possibility to have fitter broods. In the original HBMO algorithm, initially, the queen flies with her maximum speed. A drone is randomly selected from the population of drones. The mating probability is calculated based on the objective function values of the queen and the selected drone. A number between 0 and 1 is randomly generated and compared with the calculated probability. If it is less than the calculated probability, the drone’s sperm is sorted in the queen’s spermatheca and the queen speed is decreased. Otherwise, the queen speed is decreased and another drone from the population of drones is selected until the speed of the queen reaches to her minimum speed or the queen’s spermatheca is full. Then, a population of broods is generated based on mating between the queen and the drones stored in the queen’s spermatheca. The jth brood is generated by using the following process:    best ˆ x1 ; x2 ; . . . ; xn X best best best   Spi ˆ s1i ; s2i ; . . . ; sni   best ‡ b × X  best Spi ; Broodj ˆ X

(16† j ˆ 1; 2; . . . ; NBrood

where, b is a random number between 0 and 1 and Broodj is the jth brood. In this paper, in order to overcome the local optima problem of the original HBMO algorithm, we propose a new approach to improve the brood generation that is described as follows.  Initially, three drones Spm1 ; Spm2 ; Spm3 are randomly selected from the queen’s spermatheca so that m1 ≠ m2 ≠ m3. Then, an improved drone position vector is calculated as follows:

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Ximproved;1 ˆ Spm1 ‡ rand…† × Spm2 h i Ximproved;1 ˆ x1im1 ; x2im1 ; . . . ; xnim1 h i XBrood;1 ˆ x1br1 ; x2br1 ; . . . ; xnbr1 ( i xim1 ; if c1 ≤ c2 xibr1 ˆ sim1 ; otherwise  best ‡ rand…† × Spm Ximproved;2 ˆ X h i 2 Ximproved;2 ˆ x1im2 ; x2im2 ; . . . ; xnim2 h i XBrood;2 ˆ x1br2 ; x2br2 ; . . . ; xnbr2 ( i xim2 ; if c3 ≤ c2 xibr2 ˆ xibest ; otherwise

Spm3



Spm3



(17†

where, rand(·) is a random function generator, and c1, c2, c3 are the random numbers in the range [0,1]. 1 2 The best individual between XBrood and XBrood is considered as a new brood. To apply the MHBMO algorithm in the MOOM problem, the following steps have to be taken: Step 1: Define the input data. In this step, the input data including the network configuration, line impedance, characteristics of FCPPs, emission functions and prices of Fuel cells and substation bus, fimin , fimax , the speed of queen at the start of a mating flight (Smax), the speed of queen at the end of a mating flight (Smin), the speed reduction schema (a), the number of iterations, the number of drones (NDrone), the size of the queen’s spermatheca (NSperm), and the number of broods (NBrood) are defined. Step 2: Transfer the constrained optimization problem to an unconstrained one. Step 3: Generate the initial population. Step 4: Calculate the augmented objective function value. Step 5: Sort the initial population based on the objective function values. In this step, the initial population is sorted in ascending order based on the values of the objective functions. Step 6: Select the queen. The individual that has the minimum objective function  best † should be considered as the queen. …X Step 7: Generate the queen speed. The queen speed is randomly generated as: Squeen ˆ rand…† × …S max

S min † ‡ S min

(18†

where, rand(·) is a random function generator, Smax and Smin are the maximum and minimum values of queen speed, respectively. Step 8: Select the population of the drones. The population of drones is selected from the sorted initial population as:

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants D1

3

over, and selection. The main procedure of DE is illustrated in detail as follows.

6 D 7 2 7 6 7 Drone population ˆ 6 6 .. 7 4 . 5 DNDrone   i ˆ 1; 2; . . . ; NDrone Di ˆ PG ; Tap 1 × n ;

(19†

where, Di is the ith drone. Step 9: Generate the queen’s spermatheca matrix (mating flight). This step is described in detail at this section. The queen’s spermatheca matrix is generated as follows. 2

3 Sp1 6 7 6 Sp2 7 6 7 Spermatheca matrix ˆ 6 7 .. 6 7 . 4 5 SpNSperm   i ˆ 1; 2; :::; NSperm Spi ˆ ‰sj Š1 × n ˆ PG ; Tap ;

(20†

th

where, Spi is the i individual in the queen’s spermatheca. Step 10: Breeding process. As described in the beginning of this section, the breeding process in the original HBMO algorithm is performed according to Eq. (16). In this paper, the mating process has been improved and it is performed according to Eq. (17). Step 11: Feed selected broods and queen with the royal jelly by workers. The broods have been improved by employing different heuristic functions and mutation operators as follows: At first, ten individuals are randomly generated around the ith brood. Then, the values of the objective functions are evaluated for each individual. If the ith brood is better than the best individual, the brood is replaced with it. Step 12: Calculate the objective function value for the new generated solutions. The objective function for the new population is calculated as mentioned in step 4. Step 13: Check the termination criteria. If the termination criterion is satisfied, finish the algorithm, else select the N best individuals among the broods and initial population, consider them as the new initial population, and return to Step 4 until convergence criterion is met.

Mutation: When mutation is implemented, several differential vectors obtained from the difference of several randomly chosen parameter vectors are added to the target vector to generate a mutant vector. A perturbed individual is therefore, generated on the basis of the parent individual in the mutation process. At each step, algorithm mutates vectors by selecting three vectors m1, m2, m3 from initial population as m1 ≠m2 ≠m3 ≠j in order to cover the entire searching region uniformly. For each target vector Xjk …j ˆ 1; 2; . . . ; N† at iteration k, a k mutant vector Xmut;j is generated as: h i k ˆ xkmut;1 ; xkmut;2 ; . . . ; xkmut;n Xmut;j   k k k k Xmut;j ˆ Xm ‡ rand…† × X X m m 1 2 3

where, rand(·) is a random function generator between 0 and 1, and N is the number of populations. Crossover: In order to extend the diversity of the new individuals in the next generation, the perturbed individual xknew;z and the current individual are selected from a binomial distribution to perform the crossover operation. In this crossover operation, the gene of an individual at the next generation is produced from the perturbed individual and the present individual, determined by a parameter called crossover probability (CR∈‰0; 1Š): h i k Xnew;j ˆ xknew;1 ; xknew;2 ; . . . ; xknew;Ng ( k xmut;z if …rand…† ≤ CR† k xnew;z ˆ otherwise xkindividual; z

(22†

Selection: k competes against the target indiThe trial individual Xnew;j k vidual Xindividual;j using the greedy criterion and the survivor enters the next generation. k‡1 Xindividual;j

ˆ

8 < Xk

new;j : Xk individual;j

    k k if f Xnew;j ≤ f Xindividual;j otherwise

5.3 Basic DE

(23†

Differential evolution (DE) is a simple population based stochastic and powerful evolutionary algorithm. It requires a few control variables and converges fast. DE was proposed by Storn and Price [40] for finding the global optimal solutions. DE creates new candidate solutions by disturbing the parent with a weighted difference of several other randomly chosen individuals of the same population. A candidate replaces the parent only if it is better than its parent. Afterwards, DE guides the population toward the vicinity of the global optimum through repeated cycles of mutation, cross-

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(21†

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where, f(·) is the function to be minimized. If the child yields a better value of the fitness function, it replaces its parent in the next generation; otherwise, the parent is retained in the population. Hence the population either gets better in terms of the fitness function or remains the same but it never becomes worse. To apply the DE algorithm to the MOOM problem, the following steps should be taken: Step 1: The input data should be defined.

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants In this step, the input data including the network configuration, line impedance, characteristics of FCPPs, emission functions, and prices of Fuel cells and substation bus, fimin , fimax , the number of populations N, crossover probability CR are defined. Step 2: The constrained optimization problem should be transferred to an unconstrained one. Step 3: Randomly initialize the population for DE. Step 4: Evaluate the objective values of all individuals, and determine the individual, which has the best objective value (Xbest). Step 5: Perform mutation operation for each individual according to Eq. (21) in order to obtain each individual’s mutant counterpart. Step 4: Perform crossover operation between each individual and its corresponding mutant counterpart according to Eq. (22) in order to obtain each individual’s trial individual. Step 5: Evaluate the objective values of the trial individuals. Step 6: Perform selection operation between each individual and its corresponding trial counterpart according to Eq. (23) so as to generate the new individual for the next generation. Step 7: Determine the best individual of the new population with the best objective value. If the objective value is better than the objective value of Xbest, then update Xbest and its objective value. Step 8: If a stopping criterion is met, then output Xbest and its objective value; otherwise go back to Step 5.

Fig. 3 Schematic representation of the hybrid MHBMO-DE algorithm.

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6 Application of MHBMO-DE Algorithm to MOOM Problem The algorithm proposed in this paper combines MHBMO with DE to form a hybrid algorithm. The hybridization of the algorithms combines their advantages and remedies their disadvantages. For instance, MHBMO is a very efficient procedure for small-scale problems but when the number of variables increases, this algorithm does not work properly and does not achieve a unique solution in several runs. DE is simple, efficient, and works with only a few control parameters. In DE, fitness is a one-to-one competition between an offspring and its parent. This evolution process of one-to-one competition, which is different from the other evolutionary algorithms, can speed up the convergence and increase the exploitation of the best solution for possible improvement [40]. However, the faster convergence may lead to a higher probability toward a local optimum because the diversity of the population descends faster. This drawback could be overcome by using a larger population, which increases the computational burden. The MHBMO algorithm also suffers from the mentioned disadvantage and dependence on the initial population. In order to avoid the use of a larger population, exploitation of the best solution and exploration of the promising space are performed simultaneously. The proposed hybrid method is not sensitive to the choice of the initial points and has a faster convergence rate compared to MHBMO and DE. Also, it maintains the population diversity and avoids local optima. This section discusses the infrastructure and rationale of the hybrid algorithm and presents its application to the MOOM problem. Figure 3 depicts the schematic representation of the proposed hybrid MHBMO-DE for solving the MOOM problem. Both MHBMO and DE work with the same initial population. When an N-dimensional problem is solved, the hybrid approach takes 2N individuals that are randomly generated. These individuals are regarded as drones in the case of MHBMO, or as chromosomes in the case of DE. The top N drones are then fed into the MHBMO method to improve the N chromosomes. The other N chromosomes are adjusted by the DE method. To apply the MHBMO-DE algorithm to the MOOM, the following steps are taken:

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0  ˆ f …X†  ‡ k1 @ F…X†

Neq  X

 hj …X†

2

1

7 Simulation Results

A

jˆ1

0 1 Nueq  h i2 X  A Max 0; gj …X† ‡ k2 @

(24†

jˆ1

 is the objective function described in Eq. (13). Neq where f…X† and Nueq are the number of equality and inequality con and gj …X†  are the equality and straints, respectively. hj …X† inequality constraints, respectively. k1 and k2 are the penalty factors. Since the constraints should be met, the values of these parameters should be high (10,000,000 in this case). Step 3: Generate the initial population. In this step, an initial population based on the state variables is generated randomly: 2 3 X1 6X 7 6 2 7 6 population ˆ 6 . 7 7 4 .. 5 N X h i    i ˆ xj ˆ PG ; Tap ; i ˆ 1; 2; 3; :::; N X 1 ×n   xj ˆ rand…  † × xjmax xjmin ‡ xjmin

In this section, the multi-objective daily OOM in distribution networks considering FCPPs is tested on a practical distribution network of TPC. The system is shown in Figure 4, and the related data can be found in Ref. [41]. It is a threephase, 11.4-kV system that consists of 83 buses. It is also assumed that a distribution company operates this network and supplies the demand power in its feeding substation via 11 feeders A, B, C, D, E, F, G, H, I, J, K. Table 1 shows the specifications of FCPPs used in the network. It is also assumed that there are two transformers. They have 21 tap positions ( [–10,–9,...,0,1,2,...,10] ) and their MADOT in a day is 30. They can change voltage from –10 to +10%. In the daily MOOM problem, it is assumed that daily load variations and daily energy price variations are changed as shown in Figure 5.

7.1 Interactive Fuzzy Multi-Objective Optimization Method (25†

n ˆ Nd × …Ng ‡ Nt † where, xj is the position of the jth state variable, rand (·) is a random function generator between 0 and 1, N is the number of populations. Step 4: Calculate the augmented objective function value. In the MOOM problem, the augmented objective function is calculated as follows: The augmented objective functions (Eq. 24) are evaluated for each individual by using the result of the distribution load  i ), the membership values of flow. Also, for each individual (X all the different objectives are evaluated. A fuzzy decision for overall satisfaction may be defined as the choice that satisfies all of the objectives. The DM then specifies the reference membership values for each of the objective functions and the corresponding best compromising solution is obtained by solving the minimax problem (Eq. 13). Step 5: Sort the initial population based on the augmented objective function values. Step 6: Select the N generated population that have the best objective function value for the MHBMO and select the N remained generated population for the DE. Step 7: Go to MHBMO algorithm.

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Step 8: Go to DE algorithm. Step 9: In this step, results of MHBMO and DE are combined. Step 10: Check the termination criteria. If the termination criteria are satisfied, finish the algorithm, else return to Step 4.

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At first, the total electrical energy losses (f1), the total cost of electrical energy (f2), the total emission (f3), and voltage deviation (f4) objectives are separately optimized. The best results obtained by separately optimizing the objectives are shown in Table 2. This table presents a comparison among the results obtained from PSO, DE, HBMO, and MHBMO-DE algorithms for 100 random tails for these four objective functions. In Table 2, the smallest and the largest values of the minimized objective functions are indicated as the “Best Solution” and the “Worst Solution”, respectively. Comparison of the best and the worst solutions obtained by the proposed optimization algorithm with the corresponding values of other methods confirm the effectiveness of the proposed method. In addition to the best and the worst solutions, this table provides the standard deviation and average values of the objective functions for different methods. The best solutions obtained by separately optimizing f1, f2, f3, and f4 are 3226.99245 (kWh), 30827.25804 ($), 1.5930097610578E + 09 (lb) and 0.72220 (p.u), respectively. These solutions were obtained by considering the effect of FCPPs. These values are 7753.63678 (kWh), 30827.25804 ($), 7.5222899096514E + 09 (lb), and 0.98055 (p.u) in the case that there are not FCPPs. It is obvious that the total electrical energy losses, total emission, and voltage deviation are greatly reduced by controlling FCPPs. The total cost of electrical energy is the same for these two cases because the FCPPs have high prices compared to substation price or if their loca-

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Step 1: Define the input data. Step 2: Transfer the constrained optimization problem to an unconstrained one. The proposed MOOM problem needs to be transformed into an unconstrained one by constructing an augmented objective function incorporating penalty factors for any value violating the constraints:

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Fig. 4 Single line diagram of Taiwan Power Company distribution system.

Table 1 Characteristic of FCPPs. No. of FCPP

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

Capacity (kW) × 250 2 Location 3

5 6

4 12

3 13

3 14

3 16

2 18

4 19

7 28

7 31

3 34

3 45

3 51

2 52

2 53

2 54

2 58

1 68

7 71

4 75

8 78

2 81

Fig. 5 Daily load variations and energy price.

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Average

Standard deviation

Worst solution

Best solution

Method

MHBMO-DE

HBMO

DE

PSO

PLoss (kWh) Cost ($) Emission (lb) Voltage deviation (p.u) PLoss (kWh) Cost ($) Emission (lb) Voltage deviation (p.u) PLoss (kWh) Cost ($) Emission (lb) Voltage deviation (p.u) PLoss (kWh) Cost ($) Emission (lb) Voltage deviation (p.u)

3226.99245 30827.25804 1.5930097610578E+ 09 0.72220 0 0 0 0 3226.99245 30827.25804 1.5930097610578E + 09 0.72220 3226.99245 30827.25804 1.5930097610578E + 09 0.72220

3641.79540 39046.94298 1.5972194418057E 0.89348 245.39801 2674.38753 1.7589412520604E 0.05175 4053.63902 40605.71581 1.6014291225537E 0.92857 3462.11838 34637.21080 1.5930097610578E 0.80481

4633.06901 46506.44202 4.4272813952484E 0.99149 495.48300 5242.21913 5.9533876070258E 0.08971 4958.18494 48500.95585 4.8121792753335E 1.01458 3867.26727 38876.12439 2.9918222930655E 0.85216

5892.69291 47837.93186 6.7482686166882E 1.01788 910.59458 5514.86470 5.4326769901621E 0.10117 6165.36832 49038.40970 7.1302455760228E 1.08269 4378.88681 39932.62904 3.7916414716066E 0.86777

tions are not optimal. It other words, for minimizing cost objective function, the generation of FCPPs would be equal to zero. Figures 6–10 show the convergence characteristics of MHBMO-DE, HBMO, and DE algorithms for the best solution, when reference membership values are equal to one (lr1 = lr2 = lr3 = lr4 = 1). The above figures show that the minimum values of the objective functions are reached by the proposed algorithm after 392 iterations. However, the HBMO algorithm converges to the global optimum after 597 iterations and the DE algorithm converges after 627 iterations. Table 3 shows the daily variations of the four mentioned objective functions for the best solutions in two cases (with and without FCs), when reference membership values are equal to one (lr1 = lr2 = lr3 = lr4 = 1). The results given in Table 3 show that the summation of losses, cost, emission, and voltage deviation are 4749.30085

+ 09

+ 04

+ 09

+ 09

+ 09

+ 06

+ 09

+ 09

+ 09

+ 08

+ 09

+ 09

(kWh), 46749.70838 ($), 4.3384699158E + 09 (lb), and 2.99609 (p.u), respectively, for case 1 with FCPPs. For case 2 without FCPPs, the corresponding values are 8079.85865 (kWh), 31959.36781 ($), 7.8204505304E+09 (lb), and 6.31419 (p.u), respectively. The results illustrate that the losses, emission, and voltage deviation in case1 are much less than the other case. On the other hand, it can be concluded that the system performance can be improved with FCPPs. In this problem, cost objective function conflicts with other objectives because the population that minimizes this objective cannot minimize other objectives. Therefore, it has a higher value in case 1 compared to case 2. Table 4 shows the daily optimal active power dispatch of FCPPs and tap positions of transformers. Table 4 shows that in order to minimize the objective function when reference membership values are equal to one (lr1 = lr2 = lr3 = lr4 = 1), the active power (kW) components of all FCPP units should be changed during the day.

Fig. 6 Convergence characteristics of the MHBMO-DE, HBMO, and DE algorithms for the best solution.

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Table 2 Comparison of average and standard deviation for 100 trails.

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Fig. 7 Convergence characteristics of the MHBMO-DE, HBMO, and DE algorithms for the best solution (PLoss).

Fig. 8 Convergence characteristics of the MHBMO-DE, HBMO, and DE algorithms for the best solution (Voltage deviation).

Tap1 and Tap2 are the tap positions of LTC transformers. In the initialization of the interactive process, the minimax problem is solved to find a global non-inferior solution for the initial reference membership values lri ˆ 1. The DM terminates the interactive steps if he is satisfied with the solution; otherwise, he selects and inputs a set of new reference memberships for the following interactive steps. The interactive steps are repeated until the algorithm generates the desired solution. In the interactive fuzzy satisfying method, the DM evaluates the values of the membership and objective functions. This procedure continues according to this scheme until the DM is satisfied with the solution. In this multi-objective optimization problem, the objectives are typically non-commensurable and conflict with each

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other. Therefore, it is impossible to reach a common optimal solution by simultaneously optimizing all of the objectives. The proposed method resolves this issue by allowing the DM to settle for a tradeoff between conflicting objectives. The proposed algorithm can extract one optimal non-inferior solution in the first run of the interactive program. If the DM is not satisfied with the results of this interactive program, then he or she can obtain other solutions from the following interactive steps of this program. The reference values of the objectives are changed after the first run according to the situation of the network or the policies of the utilities. Table 5 shows the values of the membership and objective functions, that the DM evaluates at the interactive steps.

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Fig. 9 Convergence characteristics of the MHBMO-DE, HBMO, and DE algorithms for the best solution (Emission).

Fig. 10 Convergence characteristics of the MHBMO-DE, HBMO, and DE algorithms for the best solution (Cost).

It can be seen from the above table that DM with considering his (her) past experience can change the reference membership value until he (she) reaches the desired solutions. In this simulation, the operator decreases the values of lri from 1 to 0.8 with step size 0.05. The results show that f1 and f3 decrease and increase together. Therefore, when FCPPs generations are high, the total losses and emission decrease and vice versa. If the operator decides to decrease the cost and voltage deviation objective functions, first he (she) should reduce lr1 from 1 to 0.95 (Interaction 1). In this state, f2 and f4 are decreased 5.17 and 11.62%, respectively. However, as shown in Table 2, the minimum values of f2 and f4 are 30827.258039 ($) and 0.722201 (p.u), respectively, which are much less than

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the value obtained from Interaction 1. Thus, the DM reduces lr1 from 0.95 to 0.9 (Interaction 2). In this state, f2 and f4 are reduced 6.13 and 8.04%, respectively compared to Interaction 1. At the next interaction, lr1 is reduced from 0.9 to 0.85 (Interaction 3). In this case, f2 and f4 are reduced 5.03 and 20.57%, respectively, compared to Interaction 2. At last, with reducing lr1 from 0.85 to 0.8 (Interaction 4), f2 and f4 are decreased 3.42 and 4.34%, respectively, compared to Interaction 3. Similarly, when the operator wants to reduce the power losses and emission objective functions, first he (she) should reduce lr4 from 1 to 0.95 (Interaction 13). In this state, f1 and f3 are decreased 7.47 and 12.77%, respectively. As shown in Table 2, the minimum values of f1 and f3 are 3226.992451

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Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants Table 3 Daily variations of the objectives in two cases. With FCPP Hour

f1 (kWh)

f2 ($)

f3 (lb)

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

109.56040 109.56040 162.43723 139.15447 139.15447 162.43723 162.43723 187.39814 206.59038 206.59038 228.26827 260.23662 287.91038 287.91038 287.91038 260.23662 260.23662 228.26827 228.26827 206.59038 187.39814 162.43723 139.15447 139.15447 4749.30085

1784.06644 1784.06644 1716.54601 1600.83103 1600.83103 1716.54601 1716.54601 1817.57353 2012.78144 2012.78144 2123.43927 2268.11530 2354.63742 2354.63742 2354.63742 2268.11530 2268.11530 2123.43927 2123.43927 2012.78144 1817.57353 1716.54601 1600.83103 1600.83103 46749.70838

9.1324894696E 9.1324894696E 1.7337593151E 1.5686999665E 1.5686999665E 1.7337593151E 1.7337593151E 1.8697340528E 1.8708966390E 1.8708966390E 2.0459216292E 2.2486420833E 2.3608931276E 2.3608931276E 2.3608931276E 2.2486420833E 2.2486420833E 2.0459216292E 2.0459216292E 1.8708966390E 1.8697340528E 1.7337593151E 1.5686999665E 1.5686999665E 4.3384699158E

+ + + + + + + + + + + + + + + + + + + + + + + + +

07 07 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 09

f4 (p.u)

Without FCPP f1 (kWh)

f2 ($)

f3 (lb)

3.44400 3.44400 2.83971 2.56063 2.56063 2.83971 2.83971 2.84993 2.90731 2.90731 3.01042 3.37178 3.28278 3.28278 3.28278 3.37178 3.37178 3.01042 3.01042 2.90731 2.84993 2.83971 2.56063 2.56063 2.99609

207.44938 207.44938 277.32067 244.57085 244.57085 277.32067 277.32067 311.67367 350.70848 350.70848 389.07438 432.71144 478.85452 478.85452 478.85452 432.71144 432.71144 389.07438 389.07438 350.70848 311.67367 277.32067 244.57085 244.57085 8079.85865

886.38789 886.38789 1129.60136 1058.19720 1058.19720 1129.60136 1129.60136 1201.02378 1402.01789 1402.01789 1535.55465 1646.45480 1760.42273 1760.42273 1760.42273 1646.45480 1646.45480 1535.55465 1535.55465 1402.01789 1201.02378 1129.60136 1058.19720 1058.19720 31959.36781

2.5987974065E 2.5987974065E 2.9752686766E 2.7873163224E 2.7873163224E 2.9752686766E 2.9752686766E 3.1634287907E 3.3521956495E 3.3521956495E 3.5408758062E 3.7302390790E 3.9199271031E 3.9199271031E 3.9199271031E 3.7302390790E 3.7302390790E 3.5408758062E 3.5408758062E 3.3521956495E 3.1634287907E 2.9752686766E 2.7873163224E 2.7873163224E 7.8204505304E

f4 (p.u) + + + + + + + + + + + + + + + + + + + + + + + + +

08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 09

7.10748 7.10748 6.07640 6.01111 6.01111 6.07640 6.07640 6.35545 6.23596 6.23596 6.51540 6.39538 6.27480 6.27480 6.27480 6.39538 6.39538 6.51540 6.51540 6.23596 6.35545 6.07640 6.01111 6.01111 6.31419

Table 4 Daily optimal dispatch of FCPPs and transformers. Hour

No. of FCPP

(h)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

1

Tap 2

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

221 221 452 360 360 452 452 278 390 390 419 416 426 426 426 416 416 419 419 390 278 452 360 360

811 811 1163 1142 1142 1163 1163 1161 1145 1145 1204 1184 1212 1212 1212 1184 1184 1204 1204 1145 1161 1163 1142 1142

543 543 267 353 353 267 267 319 631 631 369 675 472 472 472 675 675 369 369 631 319 267 353 353

366 366 148 257 257 148 148 470 448 448 316 459 353 353 353 459 459 316 316 448 470 148 257 257

417 417 126 304 304 126 126 445 478 478 362 256 351 351 351 256 256 362 362 478 445 126 304 304

587 587 189 151 151 189 189 132 218 218 167 100 96 96 96 100 100 167 167 218 132 189 151 151

429 429 4 217 217 4 4 432 328 328 347 209 310 310 310 209 209 347 347 328 432 4 217 217

477 477 561 456 456 561 561 328 745 745 627 658 681 681 681 658 658 627 627 745 328 561 456 456

778 778 643 377 377 643 643 675 984 984 758 593 755 755 755 593 593 758 758 984 675 643 377 377

1151 1151 490 670 670 490 490 394 688 688 817 581 858 858 858 581 581 817 817 688 394 490 670 670

448 448 609 515 515 609 609 368 272 272 600 589 532 532 532 589 589 600 600 272 368 609 515 515

399 399 0 40 40 0 0 0 121 121 6 196 14 14 14 196 196 6 6 121 0 0 40 40

605 605 313 468 468 313 313 439 322 322 440 250 447 447 447 250 250 440 440 322 439 313 468 468

429 429 191 190 190 191 191 375 275 275 338 365 260 260 260 365 365 338 338 275 375 191 190 190

473 473 406 185 185 406 406 252 227 227 322 276 390 390 390 276 276 322 322 227 252 406 185 185

409 409 302 291 291 302 302 375 234 234 323 341 318 318 318 341 341 323 323 234 375 302 291 291

335 335 332 378 378 332 332 395 144 144 402 378 395 395 395 378 378 402 402 144 395 332 378 378

250 250 222 130 130 222 222 250 134 134 157 0 183 183 183 0 0 157 157 134 250 222 130 130

971 971 949 1142 1142 949 949 947 1267 1267 1330 1581 1390 1390 1390 1581 1581 1330 1330 1267 947 949 1142 1142

825 825 467 202 202 467 467 170 427 427 303 183 438 438 438 183 183 303 303 427 170 467 202 202

1695 1695 1304 1099 1099 1304 1304 1372 1453 1453 1401 1542 1547 1547 1547 1542 1542 1401 1401 1453 1372 1304 1099 1099

323 323 355 394 394 355 355 309 385 385 399 458 445 445 445 458 458 399 399 385 309 355 394 394

1 1 6 6 6 6 6 7 5 5 7 8 8 8 8 8 8 7 7 5 7 6 6 6

9 9 4 3 3 4 4 3 6 6 4 4 4 4 4 4 4 4 4 6 3 4 3 3

(kWh) and 1.5930097610578E + 09 (lb), respectively, that are much less than the values obtained from Interaction 13. Thus, the DM reduces lr4 from 0.95 to 0.9 (Interaction 14). In this

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state, compared to Interaction 13, f1 and f3 are reduced 7.89 and 19.84%, respectively. At the next interaction, lr4 is reduced from 0.9 to 0.85 (Interaction 15). In this case, com-

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Interaction

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Reference membership value lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

1.00 1.00 1.00 1.00 0.95 1.00 1.00 1.00 0.90 1.00 1.00 1.00 0.85 1.00 1.00 1.00 0.80 1.00 1.00 1.00 1.00 0.95 1.00 1.00 1.00 0.90 1.00 1.00 1.00 0.85 1.00 1.00 1.00 0.80 1.00 1.00 1.00 1.00 0.95 1.00 1.00 1.00 0.90 1.00 1.00 1.00 0.85 1.00 1.00 1.00 0.80 1.00 1.00 1.00 1.00 0.95 1.00 1.00 1.00 0.90

Membership function lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

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0.86046 0.85073 0.98394 0.85813 0.82706 0.86705 0.98068 0.87863 0.79752 0.88541 0.97811 0.89115 0.76147 0.89957 0.97547 0.92064 0.72289 0.90870 0.97357 0.92558 0.86130 0.85133 0.98307 0.81086 0.86230 0.85449 0.98274 0.77530 0.86649 0.85614 0.98232 0.72307 0.86876 0.85939 0.98234 0.68466 0.85993 0.85167 0.98350 0.87394 0.85757 0.85262 0.98340 0.85910 0.85903 0.85409 0.98331 0.87043 0.85877 0.85541 0.98298 0.86593 0.88332 0.82482 0.98685 0.88435 0.90567 0.79510 0.99079 0.91736

Objective function f1 (kWh), f2 ($), f3 (lb), f4 (p.u) f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

4749.30085 46749.70838 4.3384699157776E 2.99609 5267.42690 44334.32778 4.9585207891444E 2.64789 5725.57191 41617.96526 5.4489356799328E 2.43510 6284.74560 39522.83280 5.9513267755994E 1.93412 6883.03371 38172.20196 6.3134835040953E 1.85017 4736.29628 46660.99584 4.5038875205097E 3.79913 4720.75331 46192.79975 4.5676236741744E 4.40322 4655.84232 45948.40869 4.6474226933513E 5.29067 4620.59050 45468.67766 4.6434710138148E 5.94326 4757.56562 46610.62621 4.4223353284653E 2.72744 4794.11898 46469.30806 4.4404290160123E 2.97953 4771.50684 46252.82055 4.4583765707409E 2.78707 4775.49862 46056.33659 4.5210890970341E 2.86354 4394.70604 50583.81488 3.7845999223075E 2.55064 4048.08995 54980.31413 3.0335939678405E 1.98975

Interaction

15 + 09

16 + 09

+ 09

+ 09

Reference membership value lr1 lr2 lr3 lr4 lr1 lr2 lr3 lr4

= = = = = = = =

1.00 1.00 1.00 0.85 1.00 1.00 1.00 0.80

Membership function lf1 lf2 lf3 lf4 lf1 lf2 lf3 lf4

= = = = = = = =

0.91164 0.77619 0.99277 0.91537 0.91424 0.76125 0.99433 0.92153

Objective function f1 (kWh), f2 ($), f3 (lb), f4 (p.u) f1 f2 f3 f4 f1 f2 f3 f4

= = = = = = = =

3955.49758 57779.09862 2.6563799270448E + 09 2.02368 3915.16734 59989.31914 2.3578582750777E + 09 1.91891

pared to Interaction 14, f1 and f3 are reduced 2.29 and 12.43%, respectively. At last, with reducing lr4 from 0.85 to 0.8 (Interaction 16), f1 and f3 are decreased 1.02 and 11.24%, compared to Interaction 15. The simulation results confirm that the proposed method can be implemented in large scale practical systems. 7.2 Pareto Optimization Multi-Objective Method

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

+ 09

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In this section we want to present the relation of objectives with each other, that when one particular objective is minimized what happens for the other objectives. So the problem was expressed as a multi-objective problem where all objectives were optimized simultaneously with the proposed MHBMO-DE approach. The three-dimensional Pareto front for the objectives with MHBMO-DE algorithms is shown in Figures 11–14. Also in order to demonstrate the relation between PLoss and Voltage deviation objectives, a two-dimensional Pareto front for these two objectives is shown in Figure 15, where as it can be seen the minimum value of objectives shown with cursor in the figure, are placed in two different location of Pareto-optimal solutions. In this problem with four objective functions, four three-dimensional Pareto front would be obtained with the objectives Emission, Cost, PLoss, and Voltage deviation. It is worth mentioning that the Pareto optimal set has 200 nondominated solutions generated by a single run. Out of them, the non-dominated solutions that represent the best solutions of objective functions given in Tables 3–6, are shown in Figures 10–13 with the cursor. These solutions are quite close to those of individual optimization in terms of objective function values. The best solutions for objectives Emission, Cost, PLoss and Voltage deviation are closely 1.593E + 09 (lb), 3.083E + 04 ($), 3227 (kWh), and 0.7222 (p.u) respectively, which shown in Figures 11–15 with cursor. 7.3 Locating of FCPPs In this section locating FCPPs as the optimization problem will be studied [42]. In the previous section the simulation was performed with the specified location of FCPPs given in Table 1, but we can consider FCPPs location as the parameters for optimization procedure and obtain the optimal locations. This approach is implemented for minimization of PLoss objective function and the results are shown in Table 6. In this table, step loads of Figure 5 are used in order to show daily

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Table 5 Results of the interactive fuzzy satisfying procedure.

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Fig. 11 Three-dimensional Pareto front of MHBMO-DE algorithm (Emission, Cost, PLoss).

Fig. 12 Three-dimensional Pareto front of MHBMO-DE algorithm (PLoss, Voltage deviation, Cost).

load variations. For example, the step load of 0.7 is for hours 1, 2 and 0.75 is for hours 4, 5, 23, 24. So the number of FCPPs for each step load is given in Table 6. The value of PLoss objective function before FCPPs locating is 3226.99245 kWh (Table 2) and after locating is 3110.07055 kWh.

8 Conclusion In this paper, a multi-objective algorithm based on the interactive fuzzy satisfying method and Hybrid MHBMO-DE

502

© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

technique was developed to solve the multi-objective daily optimal operation management problem in distribution networks considering the effect of FCPPs. Total electrical energy losses, total electrical energy cost, total emission, and voltage deviation have been considered as objectives. Using FCPPs for active power generation is very appealing because of reduction of losses, emission, and voltage deviation although, they are relatively expensive. MHBMO-DE was used to find the non-inferior optimal solution because of its ability to handle problems with nonlinear and non-differentiable objective functions. Through the interactive process, the DM updates the membership values by considering the current values of

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Fig. 13 Three-dimensional Pareto front of MHBMO-DE algorithm (Emission, Voltage deviation, Cost).

Fig. 14 Three-dimensional Pareto front of MHBMO-DE algorithm (Emission, Voltage deviation, PLoss).

the membership functions and objectives until a satisfactory solution is obtained. Finally, the proposed method was implemented and tested on a large-scale distribution system and it can be concluded that: (i) the proposed method can efficiently yield the optimal non-inferior solution for the tested system with a large search space, (ii) the interactive fuzzy satisfying method, based on the proposed algorithm, enables a DM to choose the most satisfactory solution from the multiple objectives, (iii) the human interaction in the solu-

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tion process can handle multiple competing objective problems using a tradeoff design.

Acknowledgments The financial support given by Iran Renewable Energy Organization (SUNA) is gratefully acknowledged by the authors.

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Fig. 15 Two-dimensional Pareto front of MHBMO-DE algorithm (PLoss, Voltage deviation).

Table 6 FCPP locating with PLoss objective function. Node of FCPP location

Capacity of FCPP (×250 kW) @ Daily step load (Figure 5)

4 6 10 12 13 18 19 28 31 34 41 45 51 54 58 64 68 71 75 79 81 Sum (number of FCPPs)

0.70 2 3 5 2 8 5 5 5 7 1 2 1 2 5 1 3 1 8 2 6 5 79

0.75 2 6 4 3 7 3 5 5 7 2 1 1 2 7 0 4 4 4 2 6 4 79

0.80 1 7 3 2 5 2 7 9 5 2 3 0 3 4 1 3 0 8 2 6 6 79

0.85 1 5 5 4 2 2 7 6 6 3 3 2 2 6 1 2 2 6 3 4 7 79

References [1] M. Y. El-Sharkh, M. Tanrioven, A. Rahman, M. S. Alam, J. Power Sources 2006, 161, 1198. [2] F. Jurado, Fuel Cells 2004, 4, 378. [3] H. J. Jahn, W. Schroer, Fuel Cells 2004, 4, 276. [4] F. Marechal, F. Palazzi, J. Godat, D. Favrat, Fuel Cells 2005, 5, 5.

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0.90 1 6 4 5 4 5 7 3 6 2 3 0 1 5 1 4 1 6 2 7 6 79

0.95 1 7 4 1 7 2 7 6 7 2 2 0 3 5 0 3 0 9 3 5 5 79

1.00 3 7 4 2 5 3 7 5 7 2 1 0 1 6 1 5 1 7 3 2 7 79

1.05 1 4 7 5 4 0 8 6 5 3 1 2 2 6 1 2 3 6 1 6 6 79

[5] M. Y. El-Sharkh, M. Tanrioven, A. Rahman, M. S. Alam, J. Power Sources 2006, 153, 136. [6] F. C. Lu, Y. Y. Hsu, IEE Proc. Gen. Transm. Distrib. 1995, 142, 639. [7] N. D. Hatziargyriou, T. S. Karakatsanis, IEE Proc. Gen. Transm. Distrib. 1997, 144, 363. [8] F. C. Lu, Y. Y. Hsu, IEEE Trans. Power Syst. 1997, 12, 681.

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FUEL CELLS 12, 2012, No. 3, 487–505

Niknam, Zeinoddini-Meymand: Impact of Fuel Cell Power Plants [25] T. Niknam, A. M. Ranjbar, A. R. Shirani, Iran J. Sci. Technol. 2005, 29, 1. [26] T. Niknam, A. M. Ranjbar, A. R. Shirani, Int. J. Sci. Technol Sci. Iran. 2005, 12, 34. [27] T. Niknam, B. Bahmani Firouzi, A. Ostadi, Appl. Energy 2010, 87, 1919. [28] T. Niknam, H. Zeinoddini-Meymand, M. Nayeripour, Renew. Energy 2010, 35, 1696. [29] C. A. Coello, A. D. Christiansen, Comput. Struct. 2000, 75, 647. [30] A. Afshar, O. B. Haddad, M. A. Marino, B. J. Adams, J. Franklin Inst. 2007, 344, 452. [31] O. B. Haddad, A. Afshar, M. A. Marino, Water Resour. Manag. 2006, 20, 661. [32] M. Fathian, B. Amiri, A. Maroosi, Appl. Math. Comput. 2007, 190, 1502. [33] T. Niknam, J. Zhejiang Univ. Sci. A 2008, 9, 1753. [34] T. Niknam, J. Olamaie, R. Khorshidi, World Appl. Sci. J. 2008, 4, 308. [35] T. Niknam, Energy Conv. Manag. 2009, 50, 2074. [36] L. A. Zadeh, Fuzzy Sets Inf. Control 1965, 8, 338. [37] M. Y. El-Sharkh, M. Tanrioven, A. Rahman, M. S. Alam, J. Power Sources 2006, 161, 1198. [38] T. Niknam, Energy Conv. Manag. 2008, 49, 3417. [39] A. Losi, M. Russo, IEEE Trans. Power Deliv. 2005, 20, 1532. [40] R. Storn, K. Price, J Global Optim. 1997, 11, 341. [41] C. T. Su, C. S. Lee, IEEE Trans. Power Deliv. 2003, 18, 1022. [42] R. A. Jabr, B. C. Pal, IET Gen. Transm. Distrib. 2009, 3, 713.

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505

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[9] Y. Y. Hsu, F. C. Lu, IEEE Trans. Power Syst. 1998, 13, 1265. [10] H. Yoshida, K. Kawata, Y. Fukuyama, Sh. Takayama, Y. Nakanishi, IEEE Trans. Power Syst. 2000, 15, 1232. [11] Y. Liu, P. Zhang, X. Qiu, Int. J. Electric Power Energy Syst. 2004, 24, 271. [12] R. H. Liang, Y. Sh. Wang, IEEE Trans. Power Deliv. 2003, 18, 610. [13] G. K. Viswanadha Raju, P. R. Bijwe, IET Gen. Transm. Distrib. 2008, 2, 752. [14] J. G. Vlachogiannis, J. Æstergaard, Expert Syst. Appl. 2009, 36, 6118. [15] F. Katiraei, M. R. Iravani, IEEE Trans. Power Syst. 2006, 21, 1821. [16] T. E. Kim, J. E. Kim, Proc IEEE Power Eng. Soc. Summer Meeting 2001, 1, 480. [17] P. N. Vovos, A. E. Kiprakis, A. R. Wallace, G. P. Harrison, IEEE Trans. Power Syst. 2007, 22, 476. [18] M. A. Kashem, G. Ledwich, IEEE Trans. Energy Conv. 2005, 20, 676. [19] P. M. S. Carvalho, P. F. Correia, L. A. F. M. Ferreira, IEEE Trans. Power Syst. 2008, 23, 766. [20] T. Senjyu, Y. Miyazato, A. Yona, N. Urasaki, IEEE Trans. Power Deliv. 2008, 23, 1236. [21] F. A. Viawan, D. Karlsson, IEEE Trans. Power Deliv. 2008, 23, 1079. [22] A. G. Madureira, J. A. Pecas Lopes, IET Renew. Power Gen. 2009, 3, 439. [23] T. Niknam, H. Zeinoddini Meymand, H. Doagou Mojarrad, Renew. Energy 2011, 36, 1529. [24] T. Niknam, H. Zeinoddini Meymand, H. Doagou Mojarrad, Energy 2011, 36, 119.