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Electrical Power and Energy Systems 60 (2014) 34–44 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes Optimal location and sizing of DSTATCOM in distribution systems by immune algorithm Seyed Abbas Taher ⇑, Seyed Ahmadreza Afsari Department of Electrical Engineering, University of Kashan, Kashan, Iran a r t i c l e i n f o Article history: Received 16 March 2013 Received in revised form 28 January 2014 Accepted 18 February 2014 Available online 21 March 2014 Keywords: Optimal location Sizing DSTATCOM Immune algorithm (IA) Objective function (OF) Distribution system a b s t r a c t In this paper, optimal location and sizing of DSTATCOM for the sake of power loss reduction, and improvement of current and voltage proﬁle in distribution networks are investigated. An effective biologically inspired algorithm (Immune Algorithm) is used to search the best location and determine the size of DSTATCOM. By keeping voltage and current proﬁle improvements in mind, minimum cost of installation of DSTATCOM and maximum power loss reduction are integrated into an objective function through appropriate weighting factors. Comparative results are obtained on two standard distribution systems (IEEE 33-bus and IEEE 69-bus) with encouraging optimization as far as location and size of DSTATCOM and objective function minimization are concerned. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Distribution networks have increasingly found more importance in recent years as they play essential roles in power system quality and planning. By introducing deregulation in power systems, it has become necessary to use advanced equipments for quality improvement of the distribution networks. Complete utilization of lines capacity in these networks is not possible for several reasons including allowable voltage sag and restrictions of stability. These lead to power loss increase, slower response time and decreasing of power ﬂow limits [1,2]. Modern techniques and power electronic devices such as ﬂexible AC transmission systems (FACTS) have improved in these regards considerably. Development of such networks requires provision of reactive power by appropriate sources and additive usage of FACTS compensators. Desirable control methods for improving the distribution system are possible with the aid of power electronic technology such as custom power (CP) devices. These are elements that are used for power quality improvement, loss reduction and voltage proﬁle improvement in distribution networks and include equipments such as SSTS (Solid State Transfer Switch), DVR (Dynamic Voltage ⇑ Corresponding author. Address: Department of Electrical Engineering, University of Kashan, Kashan 87317-51167, Iran. Tel.: +98 9131614352; fax: +98 3615559930. E-mail address: [email protected] (S.A. Taher). http://dx.doi.org/10.1016/j.ijepes.2014.02.020 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. Restorer), DSTATCOM (Distribution STATic COMpensator) and UPQC (Uniﬁed Power Quality Conditioner) [3–5]. DSTATCOM as a shunt connected voltage source converter (VSC) is frequently employed to compensate power quality concerns. During the voltage sag and over loading, the load voltage of the bus in which the DSTATCOM is connected can be regulated by injection of compensating current into the system [6]. The injected current is evaluated using bus voltage and reactive power required for regulating/balancing voltage in the desired value. The design of a prototype DSTATCOM for voltage sag mitigation in an unbalanced distribution system is presented by [7]. A new cascade loop control strategy to regulate and balance the voltage at a distribution bus using a DSTATCOM is proposed by [8]. Design and operating fundamentals and characteristics of a DSTATCOM as well as its basic control strategy are described in [9]. Implementation and experimental details of a real-time digital simulator designed for representing a DSTATCOM interfaced with a digital controller is also described by [10]. Balancing of source currents, power factor correction and harmonic mitigation in three-phase, three-wire distribution system supplying delta connected load under various source voltage conditions is done by using DSTATCOM in [11]. In [12] performance of the DSTATCOM using an control strategy based on improved instantaneous active and reactive current component theory for generating reference currents has been evaluated under various source and load conditions. The performance of the proposed control strategy has been evaluated in terms of load balancing, reactive power compensation, compensator rating 35 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Nomenclature Vi voltage of ith bus IDSTATCOM current of DSTATCOM Ri + jXi impedance between ith and i + 1th bus Pi + jQi local loads are connected in ith and i + 1th bus Ii current between ith and i + 1th bus hi angle of Vi di angle of Ii V 0i voltage of ith bus after installing DSTATCOM h0i angle of Vi after installing DSTATCOM QDSTATCOM reactive power injecting to the network by DSTATCOM Ke energy cost of losses Ti time duration of ith load level Kci time duration proportion of ith load level to the total time duration Ploss i power losses in ith load level nbus number of buses CostDSTATCOM year annual cost of DSTATCOM CostDSTATCOM cost of investment in the year of allocation and harmonic mitigation. Ref. [13] analyses the negative sequence equivalent circuit of DSTATCOM in unbalanced distribution networks. A comparative evaluation of three different control techniques (instantaneous reactive power, symmetrical component, and improved instantaneous active and reactive current component) for DSTATCOM installed in three-phase four-wire distribution system has been presented in [14]. In [15] a three-phase three-wire DSTATCOM which is fed by Photovoltaic array or battery operated DC–DC boost converter and controlled by I Cos/ algorithm is proposed for power quality improvement in the distribution system. A number of works [16–18] have been carried out on optimal location of STATCOM using techniques such as particle swarm optimization (PSO) and genetic algorithm (GA). Immune algorithm (IA) is also considered as one of the best evolutionary algorithms (EA) [19–28] and is widely used to solve the optimization problems in general as well as in power system [29–36]. Ref. [37] presents the application of immune algorithm (IA) to ﬁnd optimal location of uniﬁed power ﬂow controller (UPFC) to achieve optimal power ﬂow (OPF) and congestion management. Then in [38] the application of hybrid immune algorithm such as immune genetic algorithm and immune particle swarm algorithm to ﬁnd optimal location of UPFC to achieve optimal power ﬂow has been investigated. Ref. [39] proposes a two-stage immune algorithm that embeds the compromise programming to perform multi-objective optimal capacitor placement. A new approach using immune algorithms to solve thermal generation scheduling problems is proposed in [40]. Ref. [41] propose the application of artiﬁcial immune systems as bio-inspired optimization technique to reconﬁgure radial distribution networks and to minimize the total energy losses in these systems. In [42] an integrated algorithm proposed for forecasting annual electrical energy consumption based on artiﬁcial immune system, genetic algorithm and particle swarm optimization. Artiﬁcial immune system method with the clonal selection algorithm shows satisfactory results when applied with simulated data and has been selected as the preferred method. This paper proposes an application of IA approach to solve the optimal location and sizing of DSTATCOM in distribution systems to reduce power and energy losses, improve voltage proﬁle and decrease the line current. A newly deﬁned objective function is introduced for this optimization, which includes installation cost of DSTATCOM and cost of energy losses. NDSTATCOM longevity of DSTATCOM B asset rate of return OC line over current factor OV voltage stability index for buses Imax maximum current that can ﬂow in the network lines k small positive constant l small positive constant OF objective function TCS total cost saving Pi total power loss before installation of DSTATCOM PDSTATCOM total power loss after installation of DSTATCOM i Pr probability of replacement Pc probability of cloning Pm probability of mutation Rand a random number Abi ith anti-body IMAX maximum allowable current of lines 2. DSTATCOM structure and modeling in distribution load ﬂow DSTATCOM is a shunt device that injects or absorbs both active and reactive current at a point of common coupling connection. DSTATCOM is also a DC/AC converter consisting of a dc-link capacitor or a dc energy storage device that provides constant dc-link voltage, and a 3-phase PWM voltage source converter (VSC) bridge. All these are usually connected to the network via a coupling transformer [43]. A DSTATCOM can work as a synchronous voltage source with a variable magnitude and phase angle. Hence, it is capable of controlling its bus voltage and correcting the power factor. Fig. 1 shows a bus in a distribution system equipped with a proposed DSTATCOM. Switch changing can absorb or generate the current by considering control strategy and depend on voltage of common coupling bus. In steady-state operation with heavy loading or some short-circuit events, DSTATCOM typically injects appropriate compensating current to the point of coupling connection, and thus voltage at the load bus regulated by the DSTATCOM will be lifted close to the nominal or a given value [1,44–46]. Generally, DSTATCOM has the ability of exchanging active and reactive power simultaneously. The amount of active power exchanging depends on the capacity of energy source. In this paper, only DSTATCOM application for reactive power exchanging is considered and exchange of active power with the network is neglected. Bus i V i IDSTATCOM VSC Energy Storage Fig. 1. A typical DSTATCOM connected to bus i. 36 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Fig. 2. Single line diagram of two consecutive buses of a distribution system. 2.1. System model Backward/forward sweep load ﬂow calculations are used in this work, in conjunction with a suitable steady state model for DSTATCOM as presented by [47]. Many distribution networks have radial structures which only feed from one side. A section of a sample distribution network is shown in Fig. 2 [48,49] which assumes that three phase radial distribution network is in balance. Impedance between buses i and i + 1 are shown with Ri + jXi. Local loads are connected in buses i and i + 1 are named Pi + jQi and Pi+1 + jQi+1, respectively. Vi and Vi+1 are voltages of these buses. The phasor diagram for Fig. 2 is presented in Fig. 3. KVL equation can be stated as below: V iþ1 \hiþ1 ¼ V i \hi ðRi þ jX i ÞIi \d ð1Þ Values of variables are derived from load ﬂow. Usually in traditional networks, the buses voltage is less than 1 pu, in which case, one can assume that voltage of bus i + 1 is also less than 1 pu. A DSTATCOM device is installed in this study in order to compensate voltage of bus i + 1 to a desired value. As noted earlier, DSTATCOM is used for voltage regulation and loss reduction in steady state condition and can inject only reactive power to the system. Consequently, IDSTATCOM must be kept in quadrature with respect to the system voltage. As shown in Figs. 4 and 5, by installing DSTATCOM in bus i + 1, currents Ii and IDSTATCOM ﬂow in branch simultaneously. \IDSTATCOM ¼ V 0iþ1 \h0iþ1 ¼ p 2 þ h0iþ1 V 0i \h0i p ðRi þ jX i Þ Ii \d þ IDSTATCOM \ þ h0iþ1 2 ð2Þ ð3Þ By separating the real and imaginary parts of Eq. (3) and some computation we have: pﬃﬃﬃﬃ B D x¼ 2A Fig. 4. DSTATCOM installation in bus i + 1 of proposed distribution system. ð4Þ That: x ¼ sin h0iþ1 ð5Þ A ¼ ða1 a3 a2 a4 Þ2 þ ða1 a4 þ a2 a3 Þ2 ð6Þ B ¼ 2ða1 a3 a2 a4 Þ V 0iþ1 ðRi Þ ð7Þ 2 C ¼ V 0iþ1 R ða1 a4 þ a2 a3 Þ2 ð8Þ Fig. 5. Phasor diagram of voltage and current of system shown in Fig. 4. a1 ¼ Real V 0i \h0i RealððRi þ jX i Þ ðIi \dÞÞ ð9Þ a2 ¼ Imag V 0i \h0i ImagððRi þ jX i Þ ðIi \dÞÞ ð10Þ a3 ¼ X i ð11Þ a4 ¼ Ri ð12Þ As seen from Eq. (4), there are two roots for the variable x, and therefore two values are calculated for \IDSTATCOM and |IDSTATCOM|. In order to determine the correct answer, the boundary conditions are examined in these roots. V 0iþ1 ¼ V iþ1 ) IDSTATCOM ¼ 0 h0iþ1 ¼ hiþ1 pﬃﬃﬃ D Results show that x ¼ Bþ is the correct answer of Eq. (4). There2A fore \IDSTATCOM can be determined as below: \IDSTATCOM ¼ p 2 þ h0iþ1 ¼ p 2 1 þ sin x ð13Þ Current magnitude of DSTATCOM can be calculated by the appropriate separated real and imaginary equations as below: jIDSTATCOM j ¼ V 0iþ1 cos h0iþ1 a1 a4 sin h0iþ1 a3 cos h0iþ1 ð14Þ Thus IDSTATCOM and voltage of common coupling bus are calculated using Eqs. (13), (14), and (3). Finally reactive power injected to the network by DSTATCOM for voltage correction of connected bus up to V 0iþ1 can be expressed as: p jQ DSTATCOM ¼ V 0iþ1 \h0iþ1 IDSTATCOM \ þ h0iþ1 2 Fig. 3. Phasor diagram of voltage and current of the system shown in Fig. 2. Such that, symbol ‘‘*’’ denotes complex conjugate. ð15Þ 37 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 2.2. Installing model in load ﬂow suggested answers loop. Details of calculation for each component of Eq. (16) are expressed in below. To evaluate load ﬂow considering DSTATCOM in a distribution network with any iteration in forward sweep, voltage magnitude of the compensated node can be assumed to be any desired value (for example 1 pu). The phase angle of the compensated node, reactive power and also the size of DSTATCOM can now be calculated using above equations. The updated voltage and injected reactive power by DSTATCOM are used for continuing forward sweep in order to determine load currents in the next backward sweep load ﬂow. This procedure is repeated until load ﬂow converge [48,50,51]. 3. Problem formulation In this work the optimal location (bus number) and reactive power (kV Ar) of DSTATCOM in a distribution system are obtained, in a steady state condition. Minimizing the size of DSTATCOM and power loss in distribution network, are considered in the objective function (OF). The voltage and current constraints are formulated as a penalty function to the OF. 3.2. Cost of DSTATCOM Cost of investment can be extracted from cost of DSTATCOM as Eq. (19) [54]: CostDSTATCOMyeari ¼ CostDSTATCOMi OC ¼ OV ¼ " 3 3 X X O:F: ¼ K e ðT i P lossi Þ þ ðK ci Cost DSTATCOMyeari Þ i¼1 i¼1 ! 3 4 OC OV 5 i¼1 j¼1 j¼1 i 2 3 Y # nl Y nb Y ð16Þ where i, nb and nl indicate the number of load level, the number of bus and number of lines respectively. Ke corresponds to the energy cost of losses, Ti is the time duration of ith load level and Kci is the proportion of ith load level time duration to the total time duration [52], determined as Ti K ci ¼ P3 i¼1 T i : Plossi ¼ nl X Rj jIj j2 : 8 < 1; if Ij 6 Imax Ij : exp k1 I ; if Ij > Imax max j¼1 A straight forward approach is to convert a constraint optimization problem into a non-constrained optimization problem by adding penalty for violation of constraints [38]. The ﬁrst term in the R.H.S. of Eq. (16) corresponds to the total costs (in US$) of power loss and DSTATCOM installations, needs to be minimized. The second term deals with the voltage and current limitations of the network, whose quantity should be bounded within desired limits. The latter act as a penalty factor assigned in a constant ratio to the ﬁrst term, in response to the deviation from speciﬁc boundary conditions, and is equals to 1 when all limitations are secured for buses voltages and lines currents. The ultimate goal is to minimize proposed OF so that all boundary conditions be satisﬁed. Loss minimization and minimum size of DSTATCOM utilization are represented as their cost in ﬁrst part of OF which should be minimized. Over current and over voltage boundaries are represented as a coefﬁcient for the ﬁrst part of OF. Violation from proposed constraints by the suggested candidates for best answer, greatly increase the value of related OF and thus lead to exclusion of inappropriate candidate from if V min 6 V b 6 V max ð20Þ ð21Þ where Ij is the current magnitude ﬂows in jth line and Imax is the maximum current that can ﬂow in the network lines, k and l are small positive constants, and Vb is the voltage magnitude of the bth bus. If all lines currents are less than Imax, OC will then be equal to 1, and if all buses voltages are within the desired boundaries, OV would equal unity. In all other conditions, OC or OV will acquire a value (larger than unity) that acts as a penalty factor in OF. Total cost saving (TCS) is the difference between total energy loss cost before installation and total energy loss cost and annual cost of DSTATCOM after installation in three load levels and is given by Eq. (22). TCS ¼ K e 3 3 X X T i Plossi K e T i PWith lossi i¼1 ð18Þ 1; expðlj1 V b jÞ; otherwise ð17Þ The power losses in ith load level (P lossi ), can be described as Eq. (18) [53]. ð19Þ where CostDSTATCOMyeari is the annual cost of DSTATCOM in ith load level and CostDSTATCOMi is the cost of investment in the year of allocation in ith load level. nDSTATCOM is the longevity of DSTATCOM and B is the asset rate of return. Minimizing the deviation of node’s voltage and line’s current are formulated in the second term of OF. OC denotes line over current factor and OV denotes voltage stability index for buses [55] deﬁned as 3.1. Objective function The proposed OF has been mathematically formulated as expressed by Eq. (16) ð1 þ BÞnDSTATCOM B : ð1 þ BÞnDSTATCOM 1 DSTATCOM i¼1 3 X K ci CostDSTATCOMyeari ð22Þ i¼1 4. Immune algorithm Artiﬁcial immune systems (AIS), have been deﬁned as ‘‘adaptive systems, inspired by theoretical immunology and observed immune functions, principles and models, which are applied to problem solving’’ [56,57]. The immune system is considered to provide both defense and maintenance of the body. When an animal is exposed to an Ag (foreign invader) (Ag), some of it’s bone marrow derived cells respond by producing antibodies (Ab) [19]. The immune system has a fundamental ability to produce new types of Ab or ﬁnd the best-ﬁtting Ab to attack an invading Ag [36]. Many properties of the immune system (IS) are of great interest for computer scientists and engineers, such as: uniqueness, recognition of foreigners, anomaly detection, distributed detection, imperfect detection (noise tolerance), and reinforcement learning and memory [58]. Immune response reﬂects on how antibodies learn antigenic structure pattern and eliminate Ags ultimately [59]. Pattern recognition is carried out by white blood cells (lymphocytes) of two types: B-cells, and T-cells. Both B-cells and T-cells have receptors, present on their surfaces that are responsible for recognition antigenic patterns. However, B- and T-cells detect different features of 38 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 pathogens [60], and function quite differently: B-cells can recognize isolated Ags from outside the Ag-cell, while T-cells operate on Ag-cell complex and can recognize parts of the complex presented by organic molecules [20]. The size of subpopulations of these cells is controlled by a process termed clonal selection. After successful recognition, cells with capability of binding with non-self Ags are cloned. The elements of this subpopulation also undergo mutations resulting in a subpopulation of cells that are slightly different. In addition, in thymus the cells which recognize self-Ags are removed (negative selection) [20]. The Ag can be regarded as a problem to be solved and the Ab a solution vector that best ﬁts to solve the problem. In this article, an objective function is deﬁned aiming to be optimized in its minimum value. This OF is however assigned to the IA as an Ag and IA calculates the optimized OF as an Ab to ﬁt the problem as best as possible. Start Input Data (Generating first random Population) (Location and Three Desired Voltage) Calculate population affinity (Run Load Flow and Calculating OF.) iteration < max iteration N Output (Best Population With Minimum OF.) End 4.1. Initialize repertoire Y An Ag or an Ab, can be represented as an attribute string m [61]. At ﬁrst a population of Abs is randomly selected (strings of real or binary forms) as candidate for the solution result. Random value > Pr 4.2. Evaluation Random value > Affinity (Abi) N Y Degree of binding between Ag and Ab string can be described as afﬁnity. In this paper the inverse of Objective Function (OF) is deﬁned as afﬁnity. Greater afﬁnity means the better Ab for solving the problem and minimizing OF [20]. Y Replace Antibody by maximum affinity in new population Replace this Antibody in new population 4.3. Adaptation In this section, n attribute strings with highest afﬁnity are selected to proliferate by cloning, hyper-mutation and replacing. Three variables are tuned for these purposes: probability of replacement Pr, probability of cloning Pc and probability of mutation Pm which are deﬁned as constant values in IA. For any Ab (i), an afﬁnity value (afﬁnity (Abi)) is deﬁned, equal to inverse of OF. Any Ab with higher afﬁnity (i.e. lower OF) is a better candidate to remain in repertoire. A random number (e [0, 1]) is generated and compared to Pr. If rand 6 Pr, hence a new Ab is generated and placed in new repertoire. Else if rand > Pr, an Ab from the current repertoire is selected for cloning. If randnew 6 afﬁnity(Abi), the Ab is cloned and put into the new generation with probability of cloning Pc. If randnew 6 afﬁnity(Abi) but Abi has not been cloned due to the stochastic character of the cloning process, the Ab is submitted to hyper mutation. In hyper-mutation each attribute of Ab string replaced with a new randomly-generated value by the probability of mutation (Pm) [20]. This procedure is repeated until a complete new repertoire has been created. In this way high-afﬁnity (low OF) Abs can be cloned and/or mutated several times and low afﬁnity (high OF) Abs can be skipped several times and be implicitly replaced by newly generated ones. The algorithm proceeds iteratively until a stopping criterion is met. Fig. 6 shows the ﬂowchart of immune algorithm. Artiﬁcial immune systems provide superior performances in dealing with multi-modal, combinatorial, time dependent, and inventory optimization problems [62]. According to [17,18] the capability of IA method for pattern recognition and memorization does provide a more efﬁcient way to solve the optimization problem as compared to the GA. In [17] by comparing the proposed IA with the standard EA, is stated that IA (clonal selection) can reach a diverse set of local optima solutions, while the conventional EA tends to bias the whole population of individuals toward the best candidate solution. Essentially, their encoding schemes and N Y Random value > Pc N Mutate this Antibody Y Random value > [Pm/NormAffi,1] N N Complete new population Y Fig. 6. Flowchart of immune algorithm. evaluation functions are similar, but their evolutionary search processes differ from the viewpoint of inspiration, vocabulary, and sequence of steps. It is also remarkable to note that the IA (clonal form) version for optimization implicitly accounts for the search of multiple solutions. Thus, its computational cost is reduced when compared to that has to explicitly evaluate the degree of similarity among the individuals of the population [17]. Another important aspect of IA model, when compared with the standard EA, is the fact that the IA takes into account the cell afﬁnity, corresponding to the ﬁtness of the individuals, in order to deﬁne the proliferation and mutation rates to be applied to each member of the population. It is shown in [63] that IA is superior to the other algorithms in most of cases except smooth shaped functions and IA will be useful for wide optimization aspects. Both IA and GA are immanent in parallel action and being random and both of them have the ability to escape from local optima [64]. The learning process of IA is implemented by an evolutionary process which is similar to GA. 39 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Here, at ﬁrst a random population, each consisting location and three desired voltages (for three load levels) is produced and assigned to IA as the ﬁrst repertoire. IA, then runs load ﬂow for each Ab to evaluate the OF and associated afﬁnity of each Ab candidate within the population (repertoire). IA will ﬁnally run the internal calculation to obtain the best Ab deﬁned by its minimum OF (or maximum afﬁnity) based on the presented ﬂowchart (see Fig. 6). 5. Implementation of IA for ﬁnding optimal location and size of DSTATCOM The purpose of the IA in this paper is to determine the size of DSTATCOM at the candidate locations for each load level in order to minimize power loss, size, cost of DSTATCOM, and deviation of voltages/currents from the desired values. Hence, DSTATCOM is located and tuned to achieve the minimum OF. In other words, attempts were made to decrease the total power loss and size of installing DSTATCOM and maintaining voltages and currents of network in desired boundaries as much as possible. For examine applicability of the proposed approach, it was applied to two standard sample distribution networks. Examined IEEE networks have 33 and 69 bus that work at 12.66 kV and have radial structure [50,51]. The single line diagrams are shown in Figs. 7 and 8, respectively. Line data and nominal load data of study systems are given in Appendix A. In order to model the annual load proﬁle, three load levels are selected (Light, Medium and Peak). Table 1 shows the time duration and total load for each load level. In order to evaluate the effectiveness of IA, its performance is compared with GA, run on the same basis. To ﬁnd the optimum set of parameters for IA (and GA), 50 trials are performed for each possible set of parameters. For each trial, the optimum OF is recorded and the appropriate statistical measures are compared in continue. Maximum iteration and initial population size are set to 100 and 50, respectively. Initial binary strings (chromosomes) are randomly produced, containing a number of selected bus for compensation as well as three values for voltages of compensated node in three load levels. The IA and GA settings are shown in Table 2. After running the load ﬂow in three levels, OF is calculated for each chromosome. The OF parameters applied are indicated in Table 3 [65,66]. It should be noted that the constraint of injected reactive power by DSTATCOM, voltage of buses and current of lines are as indicated below in steady state: Ar kV Ar 0 6 Q kV DSTATCOM 6 10; 000 ð23Þ 0:9pu 6 V pu 6 1:1pu ð24Þ Table 2 Parameters setting of the IA and GA methods. IA GA Fig. 7. Single line diagram of IEEE 33-bus distribution system. Pr Pc Pm Mutation rate Selection rate 0.3 – 0.9 – 0.1 – – 0.3 – 0.5 Fig. 8. Single line diagram of IEEE 69-bus distribution system. Table 1 Load level and load duration time in 33 and 69 bus IEEE test systems. Load level Light Medium Peak Duration (h) Total load (kV Ar) 2000 3715 + j2300 3802.2 + j2694.6 202.68 225 5260 4829.5 + j2300 4942.8 + j2694.6 305.86 342.99 1500 5944 + j2300 6083.5 + j2694.6 442.41 502.52 Total power loss (kW) 33-bus 69-bus 33-bus 69-bus 40 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Table 3 OF parameters setting for optimization. CostDSTATCOM US($/kV Ar) nDSTATCOM (year) B Ke US ($/kW h) k l 50 30 0.1 0.06 2 1 IMax 6 520A ð25Þ 6. Simulation results The effectiveness of proposed approach is illustrated using IEEE 33-bus, and IEEE 69-bus test systems. It is tried to obtain the optimal solution using the objective function given by Eq. (16) in two sample networks; the simulation results are described in the following sections. 6.1. IEEE 33-bus system Table 4 shows the placement and size of DSTATCOM, and also the minimum objective function using IA and GA methods in 33 buses distribution system in three load levels. As can be seen, compared with GA, IA offers an improved optimal solution with its lower size of DSTATCOM and lower OF. In this system, the 12th bus is selected for DSTACOM installation by both IA and GA methods for compensating in light, medium and heavy load levels. It is worth noting that the OF value is reduced by 22.5% and size of DSTATCOM is also reduced by at least 13.62% in three load levels. For IA it is multi-focused and can implement Table 4 Comparison results of OF value, optimal location and sizing of DSTATCOM in IEEE 33bus test system. OF IA GA IA GA Location Size (kV Ar) IA GA 2.5 2.4 Light 962.49 1114.21 149149.1 192456.04 12 12 Medium 1008.18 1376.97 Peak 1222.66 1845.48 Kci Load level 1 2 3 0.22831 0.60046 0.17123 search for multiple optimal points with certain decentralization and independence concerning for its search objectives so IA covers global and local search simultaneously. Meanwhile, GA focuses on one optimal solution due to singleness and exclusion concerning its search objective and emphasizes global search while ignores local search [64]. For IA, it is running based on memory units and guarantees its convergence whereas in GA, it is running based on parent population and in some cases standard GA cannot guarantee its convergence [64]. The proposed method has been implemented on a quad computer with 2.8 GHz CPU. The convergence curves for the OF obtained by GA and IA algorithms in the IEEE 33-bus network are presented in Fig. 9. As shown after 50th iteration, solution convergence takes place in IA quicker than that of GA, even after 75th iteration. Also, IA has reached a better answer (i.e. lower OF and nearer to the global optima) compared with GA. For IA, it incarnates the self-adjustment of immune response by accelerating and suppressing the generation of antibodies and so it can guarantee the diversity of individuals. While for GA, it only chooses individuals from parent generation according to ﬁtness and does not adjust the diversity of individuals [64]. Table 5 shows CPU time for each algorithm. In this optimization, CPU time is reduced by 12.2% using IA compared with GA method. Therefore, optimal solution found by the IA was better than the GA method. Table 6 presents comparison of power loss, annual cost of DSTATCOM, no. of under voltage buses and no. of over current lines pre and post installation using proposed method in three different load levels, in 33 buses distribution system. Table 5 CPU time for optimization in IEEE 33-bus test system. Algorithm IA GA CPU time (s) 21,220 24,157 x 106 OF Convergence by IA (33 bus) OF Convergence by GA (33 bus) 2.2 2 1.8 1.6 OF 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 Iteration Fig. 9. Comparison of convergence between GA and IA. 41 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Results indicate a power loss reduction in all three load levels, and in general, the total power loss is reduced by 10.9%, while all voltages and currents are within the desired limits. Table 7 presents the annual results of economic evaluations. As can be seen, total cost saving is around 115,209 ($). Voltage of buses pre and post DSTATCOM installation using proposed method are presented in Table 8. It can be seen that all voltages are within the desired limits (Vmin = 0.9 pu and Vmax = 1 pu). Table 6 Summary results of IEEE 33-bus test system. Load level Total power loss (kW) CostDSTATCOM year ($) No. of under voltage buses No. of over current lines B.I. A.I. A.I. B.I. A.I. B.I. A.I. Light Medium Peak 202.68 171.81 5105.1 0 0 0 0 305.86 272.04 5347.4 7 0 0 0 442.41 407.71 6485 14 0 2 0 B.I., Before installation; A.I., After installation. Table 7 Comparison of annual costs of IEEE 33-bus test system. Total Total Total Total energy loss cost before installation ($) energy loss cost after installation ($) annual cost of DSTATCOM ($) cost saving ($) 160,670 143,160 5989.1 115,209 6.2. IEEE 69-bus system Table 9 shows the placement and size of DSTATCOM, as well as the minimum objective function using IA and GA methods in 69 buses system in three load levels. Similar to the ﬁrst case study, IA offers better optimal solution here (i.e. lower DSTATCOM size and lower OF) compared to GA. In this 69 buses distribution system, the 61st bus is selected for DSTATCOM installation by both IA and GA methods for compensating in light, medium and heavy load levels. OF value is evidently reduced by 6.54% and size of DSTATCOM is also reduced by at least 9.58% in three load levels. For IA, it often integrates afﬁnity with concentration to evaluate the quality of an individual, thus reﬂects the diversity of real immune system. While for GA, it simply uses ﬁtness as the only standard to evaluate the quality of an individual [64]. Table 10 shows CPU time for each algorithm. It can be seen that IA has a faster convergence than GA and optimal solution found by the IA is better than the GA method. Table 11 shows the results for the 69 buses distribution system. Minimum voltage and maximum current of the system has improved and the system losses are reduced in each load level. Generally total power loss is reduced by 18%. Annual results of economic evaluation for the 69 bus system, is presented in Table 12 with total cost saving of 21,972 ($). Table 9 Comparison results of OF value, optimal location and sizing of DSTATCOM in IEEE 69bus test system. OF IA GA IA GA Location Table 8 Voltages of 33 bus distribution network before and after DSTATCOM installation. Medium Size (kV Ar) IA GA Bus no. Light Peak B.I. A.I. B.I. A.I. B.I. A.I. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1.0000 0.9970 0.9829 0.9754 0.9680 0.9496 0.9461 0.9413 0.9350 0.9292 0.9283 0.9268 0.9207 0.9185 0.9170 0.9157 0.9136 0.9130 0.9965 0.9929 0.9922 0.9915 0.9793 0.9726 0.9693 0.9477 0.9451 0.9337 0.9255 0.9219 0.9177 0.9168 0.9165 1.0000 0.9973 0.9848 0.9786 0.9724 0.9585 0.9590 0.9556 0.9541 0.9530 0.9526 0.9519 0.9460 0.9438 0.9424 0.9411 0.9391 0.9385 0.9968 0.9932 0.9925 0.9918 0.9812 0.9746 0.9713 0.9566 0.9541 0.9428 0.9346 0.9311 0.9270 0.9261 0.9258 1.0000 0.9963 0.9787 0.9695 0.9603 0.9381 0.9341 0.9279 0.9200 0.9127 0.9116 0.9097 0.9021 0.8993 0.8975 0.8958 0.8933 0.8925 0.9956 0.9913 0.9904 0.9897 0.9743 0.9661 0.9620 0.9357 0.9326 0.9192 0.9096 0.9053 0.9002 0.8991 0.8988 1.0000 0.9966 0.9808 0.9728 0.9649 0.9475 0.9477 0.9431 0.9403 0.9381 0.9375 0.9364 0.9290 0.9263 0.9246 0.9229 0.9205 0.9198 0.9959 0.9916 0.9907 0.9900 0.9764 0.9682 0.9641 0.9452 0.9421 0.9289 0.9194 0.9152 0.9101 0.9090 0.9087 1.0000 0.9955 0.9744 0.9633 0.9522 0.9260 0.9215 0.9138 0.9043 0.8955 0.8941 0.8917 0.8825 0.8792 0.8770 0.8749 0.8720 0.8711 0.9948 0.9896 0.9886 0.9878 0.9692 0.9594 0.9546 0.9232 0.9195 0.9041 0.8930 0.8880 0.8819 0.8806 0.8802 1.0000 0.9959 0.9769 0.9673 0.9578 0.9375 0.9380 0.9324 0.9290 0.9265 0.9257 0.9245 0.9156 0.9124 0.9103 0.9083 0.9054 0.9045 0.9951 0.9900 0.9890 0.9881 0.9716 0.9619 0.9571 0.9348 0.9311 0.9159 0.9050 0.9001 0.9000 0.9000 0.9000 158500.15 169600.36 61 61 Light 1704.42 1918.39 Medium 1911.23 2223.28 Peak 2606.83 2883.00 Table 10 CPU time for optimization in IEEE 69-bus test system. Algorithm IA GA CPU time (s) 32,305 45,588 Table 11 Summary results of IEEE 69-bus test system. Load level Total power loss (kW) CostDSTATCOM year ($) No. of under voltage buses No. of over current lines B.I. A.I. A.I. B.I. A.I. B.I. A.I. Light Nominal Peak 225 157.50 9040.2 0 0 0 0 343 274.4 10137.1 6 0 0 0 502.5 472 13826.5 8 0 4 0 B.I., Before installation; A.I., After installation. Table 12 Comparison of annual costs of IEEE 69-bus test system. Total Total Total Total energy loss cost before installation ($) energy loss cost after installation ($) annual cost of DSTATCOM ($) cost saving ($) 180,470 147,980 10,518 21,972 42 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Table 13 shows voltage of buses pre and post installation of DSTATCOM in each load level in 69-bus distribution network, in which all voltages are again within the upper and lower bounds. Table 13 Voltages of 69 bus distribution network before and after DSTATCOM installation. Bus no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 Light Medium Peak B.I. A.I. B.I. A.I. B.I. A.I. 1.0000 0.9999 0.9999 0.9998 0.9990 0.9900 0.9807 0.9785 0.9774 0.9724 0.9713 0.9681 0.9652 0.9623 0.9594 0.9589 0.9580 0.9580 0.9575 0.9572 0.9568 0.9568 0.9567 0.9565 0.9564 0.9563 0.9563 0.9999 0.9998 0.9997 0.9997 0.9996 0.9993 0.9990 0.9989 0.9999 0.9997 0.9995 0.9995 0.9997 0.9990 0.9987 0.9987 0.9986 0.9985 0.9985 0.9997 0.9985 0.9946 0.9941 0.9785 0.9785 0.9746 0.9714 0.9669 0.9625 0.9400 0.9290 0.9247 0.9197 0.9123 0.9120 0.9116 0.9097 0.9091 0.9712 0.9712 0.9678 0.9678 1.0000 0.9999 0.9999 0.9999 0.9994 0.9926 0.9856 0.9839 0.9831 0.9781 0.9770 0.9739 0.9710 0.9681 0.9652 0.9647 0.9638 0.9638 0.9634 0.9631 0.9626 0.9626 0.9625 0.9623 0.9622 0.9621 0.9621 0.9999 0.9998 0.9997 0.9997 0.9996 0.9993 0.9990 0.9989 0.9999 0.9997 0.9996 0.9995 0.9997 0.9990 0.9987 0.9987 0.9987 0.9986 0.9986 0.9998 0.9986 0.9947 0.9942 0.9839 0.9839 0.9813 0.9793 0.9765 0.9738 0.9579 0.9500 0.9470 0.9434 0.9392 0.9389 0.9385 0.9367 0.9361 0.9770 0.9770 0.9735 0.9735 1.0000 0.9999 0.9999 0.9998 0.9988 0.9877 0.9762 0.9734 0.9720 0.9657 0.9643 0.9604 0.9567 0.9530 0.9494 0.9487 0.9476 0.9476 0.9470 0.9467 0.9461 0.9460 0.9460 0.9458 0.9455 0.9455 0.9454 0.9999 0.9998 0.9996 0.9996 0.9995 0.9992 0.9987 0.9987 0.9999 0.9997 0.9995 0.9994 0.9996 0.9988 0.9985 0.9984 0.9984 0.9983 0.9983 0.9997 0.9983 0.9941 0.9935 0.9734 0.9734 0.9685 0.9645 0.9589 0.9534 0.9249 0.9108 0.9054 0.8989 0.8897 0.8893 0.8888 0.8865 0.8857 0.9643 0.9643 0.9600 0.9600 1.0000 0.9999 0.9999 0.9998 0.9992 0.9906 0.9816 0.9794 0.9784 0.9721 0.9708 0.9668 0.9631 0.9595 0.9559 0.9553 0.9542 0.9541 0.9536 0.9532 0.9526 0.9526 0.9525 0.9523 0.9521 0.9520 0.9520 0.9999 0.9998 0.9997 0.9996 0.9995 0.9992 0.9988 0.9987 0.9999 0.9997 0.9995 0.9995 0.9997 0.9988 0.9985 0.9985 0.9985 0.9983 0.9983 0.9998 0.9984 0.9941 0.9935 0.9794 0.9794 0.9760 0.9734 0.9697 0.9661 0.9450 0.9347 0.9307 0.9260 0.9204 0.9200 0.9195 0.9172 0.9165 0.9707 0.9707 0.9664 0.9664 1.0000 0.9999 0.9999 0.9997 0.9986 0.9852 0.9713 0.9680 0.9663 0.9587 0.9571 0.9523 0.9478 0.9434 0.9390 0.9382 0.9368 0.9368 0.9361 0.9357 0.9349 0.9349 0.9348 0.9346 0.9343 0.9342 0.9342 0.9999 0.9998 0.9996 0.9996 0.9994 0.9990 0.9985 0.9984 0.9998 0.9996 0.9994 0.9994 0.9996 0.9987 0.9983 0.9982 0.9982 0.9981 0.9981 0.9997 0.9982 0.9935 0.9928 0.9680 0.9680 0.9621 0.9572 0.9504 0.9438 0.9088 0.8915 0.8848 0.8769 0.8657 0.8653 0.8647 0.8618 0.8609 0.9570 0.9570 0.9518 0.9518 1.0000 0.9999 0.9999 0.9998 0.9992 0.9890 0.9784 0.9759 0.9746 0.9671 0.9655 0.9607 0.9563 0.9519 0.9476 0.9467 0.9454 0.9454 0.9447 0.9442 0.9435 0.9435 0.9434 0.9432 0.9429 0.9428 0.9428 0.9999 0.9998 0.9996 0.9996 0.9994 0.9991 0.9986 0.9985 0.9999 0.9997 0.9995 0.9994 0.9996 0.9987 0.9983 0.9983 0.9982 0.9981 0.9981 0.9998 0.9983 0.9936 0.9929 0.9758 0.9758 0.9719 0.9688 0.9646 0.9605 0.9355 0.9233 0.9187 0.9131 0.9070 0.9066 0.9060 0.9033 0.9024 0.9654 0.9654 0.9602 0.9602 7. Conclusion This paper presents a new approach for optimization problem of DSTATCOM placement and sizing in radial distribution systems using IA method for obtaining minimum power loss and minimizing cost of DSTATCOM installation with pre-determined voltage and current constraints in network. Energy and power losses due to installed DSTATCOM as well as its associated cost are used to deﬁne the objective function. For system solution, backward/forward sweep load ﬂow is applied. Simulation results show that utilizing DSTATCOM reduce objective function. Using IA method, the optimal location and size of DSTATCOM is obtained in order to decrease power loss, cost of DSTATCOM and current proﬁle, and improve voltage of buses. Compared with GA, IA technique provides minimum DSTATCOM size, CPU time, and objective function. Installation of DSTATCOM by the proposed approach leads to 10.9% and 18% power loss reductions, in 33 and 69 buses distribution systems, respectively. All buses voltage and current of lines are within the desired boundaries. Total energy loss cost reduction were 10.89% and 18% in 33 and 69 buses distribution network, respectively. Total cost saving as a result of this exercise are estimated to be of the order of 7.17% and 12.17%, in 33 and 69 buses distribution network, respectively. Appendix A Tables A1 and A2 show the line and bus data in IEEE-33 and 69 bus distribution networks in light loading. Table A1 IEEE 33-bus distribution network data. Bus Send Receive 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 19 20 21 3 23 24 6 26 27 28 29 30 31 32 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 P kW Receive Ar Q kV Receive R (X) X (X) 100 90 120 60 60 200 200 60 60 45 60 60 120 60 60 60 90 90 90 90 90 90 420 420 60 60 60 120 200 150 210 60 60 40 80 30 20 100 100 20 20 30 35 35 80 10 20 20 40 40 40 40 40 50 200 200 25 25 20 70 600 70 100 40 0.0922 0.4930 0.3660 0.3811 0.8190 0.1872 0.7114 1.0300 1.0440 0.1966 0.3744 1.4680 0.5416 0.5910 0.7463 1.2890 0.7320 0.1640 1.5042 0.4095 0.7089 0.4512 0.8980 0.8960 0.2030 0.2842 1.0590 0.8042 0.5075 0.9744 0.3105 0.3410 0.0470 0.2511 0.1864 0.1941 0.7070 0.6188 0.2351 0.7400 0.7400 0.0650 0.1238 1.1550 0.7129 0.5260 0.5450 1.7210 0.5740 0.1565 1.3554 0.4784 0.9373 0.3083 0.7091 0.7011 0.1034 0.1447 0.9337 0.7006 0.2585 0.9630 0.3619 0.5302 S.A. Taher, S.A. Afsari / Electrical Power and Energy Systems 60 (2014) 34–44 Table A2 IEEE 69-bus distribution network data. Bus Send Receive 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 3 28 29 30 31 32 33 34 3 36 37 38 30 40 41 42 43 44 45 4 47 48 49 8 51 9 53 54 55 56 57 58 59 60 61 62 63 64 11 66 12 68 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 43 References P kW Receive Ar Q kV Receive R (X) X (X) 0 0 0 0 2.6 40.4 75 30 28 145 145 8 8 0 45.5 60 60 0 1 114 5.3 0 28 0 14 14 26 26 0 0 0 14 19.5 6 26 26 0 24 24 1.2 0 6 0 39.22 39.22 0 79 384.7 384.7 40.5 3.6 4.35 26.4 24 0 0 0 100 0 1244 32 0 227 59 18 18 28 28 0 0 0 0 2.2 30 54 22 19 104 104 5.5 5.5 0 30 35 35 0 .6 81 3.5 0 20 0 10 10 18.6 18.6 0 0 0 10 14 4 18.55 18.55 0 17 17 1 0 4.3 0 26.3 26.3 0 56.4 274.5 274.5 28.3 2.7 3.5 19 17.2 0 0 0 72 0 888 23 0 162 42 13 13 20 20 0.0005 0.0005 0.0015 0.0251 0.3660 0.3811 0.0922 0.0493 0.8190 0.1872 0.7114 1.0300 1.0440 1.0580 0.1966 0.3744 0.0047 0.3276 0.2106 0.3416 0.0140 0.1591 0.3463 0.7488 0.3089 0.1732 0.0044 0.0640 0.3978 0.0702 0.3510 0.8390 1.7080 1.4740 0.0044 0.0640 0.1053 0.0304 0.0018 0.7283 0.3100 0.0410 0.0092 0.1089 0.0009 0.0034 0.0851 0.2898 0.0822 0.0928 0.3319 0.1740 0.2030 0.2842 0.2813 1.5900 0.7837 0.3042 0.3861 0.5075 0.0974 0.1450 0.7105 1.0410 0.2012 0.0047 0.7394 0.0047 0.0012 0.0012 0.0036 0.0294 0.1864 0.1941 0.0470 0.0251 0.2707 0.0619 0.2351 0.3400 0.3450 0.3496 0.0650 0.1238 0.0016 0.1083 0.0696 0.1129 0.0046 0.0526 0.1145 0.2475 0.1021 0.0572 0.0108 0.1565 0.1315 0.0232 0.1160 0.2816 0.5646 0.4873 0.0108 0.1565 0.1230 0.0355 0.0021 0.8509 0.3623 0.0478 0.0116 0.1373 0.0012 0.0084 0.2083 0.7091 0.2011 0.0473 0.1114 0.0886 0.1034 0.1447 0.1433 0.5337 0.2630 0.1006 0.1172 0.2585 0.0496 0.0738 0.3619 0.5302 0.0611 0.0014 0.2444 0.0016 [1] Somsai K, Kulworawanichpong T. 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