ACADEMIE ROYALE DES SCIENCES D OUTRE-MER BULLETIN DES SEANCES Vol. 4 No. 3 June 2015 pp. 16-22 ISSN: 0001-4176 Application of particle swarm optimization algorithm for optimal capacitor placement problem on radial networks RezaSeyedi Marghaki, Alimorad Khajezadeh Electrical Department of Azad Kerman University, Kerman, Iran Abstract: Power generated in generating bus is transmitted in transmission network and fed to the loads through distribution terminals. The generated power distributed into the power network has some losses, which is greater in distribution system as compared to transmission section. This issue could be sited by locating capacitor at valuable terminals due to which the kW power loss may be minimized and the net savings may be improved. This article introduces an intelligent system by particle swarm optimization (PSO) algorithm for the placement of capacitors on the radial distribution systems to minimize the power losses and to enhance the voltage profile simultaneously. The proposed optimization approach suggested in this paper has been applied successfully in a real world standard system. Results achieved using computer simulation of real system, is described to validate the proposed solution approach. The computer simulation results prove that the suggested intelligent system has good performance. Key words: Capacitor PSO Optimization Power loss Voltage profile systems and the usage of non-continuous capacitors will be observed to solve it in this study. A pied of solution techniques based on classical approaches and gradient based methods [1–5] have been introduced to solve the optimal capacitor placement issue in previous years. In contrast to these classical optimization methods, soft computing algorithms science has been newly suggested in papers [6–11]. In one of the initial studies [12], the issue was divided into primary and secondary problem and solved in two independent stages. The first stage optimizes the capacitor terminals, as the second stage assigns the capacitor size values. In reference [13], authors present the optimal capacitor sizing solution using non-linear approach. In [14] authors propose the new fitness function that was classified as a non-differentiable adding more challenges to the optimization technique and simulating annealing was applied as solution algorithm. Also, more nature based optimization algorithms were applied: immune system algorithm [15], GA [16], fuzzy genetic algorithms version [17], ant colony algorithm (ACO) [18], and PSO [19]. In last decade, direct search algorithm method [20], cuckoo search algorithm [21], self-adaptive harmony search algorithm [22], ABC [23,24] and a new optimization technique known as teaching learning based INTRODUCTION In An electric power distribution system is the last stage in the delivery of electric power; it carries electricity from the transmission system to individual loads. Distribution substations connect to the transmission system and lower the transmission voltage to medium voltage ranging between 2 kV and 35 kV with the use of transformers. First distribution lines carry this medium voltage power to distribution transformers placed close to the customer's premises. Distribution transformers again lower the voltage to the utilization voltage of household instruments and typically feed several loads through secondary distribution lines at this constant voltage. Commercial and residential loads are connected to the secondary distribution lines through service drops. Loads demanding a much larger amount of power can be connected straightly to the initial distribution level or the sub-transmission level. The issue of capacitors placement in power distribution systems of electrical energy consists the assignment of the number, location, kind and size of the capacitors to be placed on the distribution feeders such that the total charge of setting and performance of the power system is minimum with respect to the consumers on the system. This issue is combinatorial in real world Corresponding Author: Seyedi, Azad Kerman University, Kerman, Iran 16 optimization [25] and many works [26- 28] are also applied in papers. The rest of paper is organized as follows. Section 2 presents the problem formulation. Section 3 presents the optimization method. Section 4 introduces the proposed method. Section 5, depicts some computer simulation results and finally Section 6 concludes the article. J Min F=K p Ploss K cj Qcj (1) j 1 Which: PROBLEM FORMULATION V min V j V max (2) THD j THD max (3) Qcj Qcmax (4) Here Qcmax L Qc0 The problem of optimal capacitor placement has many parameters consist the applied capacitor size, terminal number, capacitor charge, voltage magnitude and harmonic limits on the power system. The optimal capacitor placement is defined in this section by details. Just the lowest standard size of capacitors and several of this standard size are permitted to be installed at the terminals to have more realistic optimal out. The capacitor sizes are considered as non-continuous parameters and the charge of the capacitor is not linearity symmetric to the capacitor size, this makes the mathematical problem a complex issue. The target of the capacitor placement issue is to lessen the general power losses of the electrical system while striving to minimize the charge of capacitors placed in the power system. The fitness function includes of two main parts. The first is the charge of the capacitor installation and the second one is the charge of the general power losses. The charge related with capacitor installation is made of a fixed installation charge, a purchase charge and operational charge (keeping and depreciation). The charge mathematical formulation described in this approach is a step-like function rather than a continuously differentiable function since capacitors in practice are grouped in banks of standard discrete capacities with charge not linear symmetric to the capacitor bank size. It should be hinted that since the fitness function is nondifferentiable, all nonlinear optimization methods become unskillful to use. The second part in the fitness function represents the general charge of power losses. This part is gained by summing up the annual real power losses for the network. Voltages along the feeder are wanted to remain within maximum and minimum constraints after the addition of capacitors on the feeder. Voltage limits may be taken into account by specifying the maximum and minimum ranges of the amplitude of the voltages. The oscillation of voltage is considering by specifying for maximum total harmonic distortion (THD) of voltages and the maximum number of banks to be placed in one terminal is taken into account. The optimal capacitor placement issue is defined mathematically as given follow: (5) More details regarding the applied system can be found in [29]. The parameters of fitness function are presented in Table 1. F Table 1: The parameters of fitness function The total annual cost function. Kp Annual cost per unit of power losses. Ploss The total power losses. (Result from ETAP PowerStation Harmonic Load Flow Program). Number of buses. J K cj The capacitor annual cost/kvar Qcj The shunt capacitor size placed at bus j. Vj The rms voltage at bus j. (Result from ETAP PowerStation Harmonic Load Flow Program). V min Minimum permissible rms voltage. V max Maximum permissible rms voltage. THD j The total harmonic distortion at bus j. (Result from ETAP PowerStation Harmonic Load Flow Program). THD max Maximum permissible total harmonic distortion. Qcmax L Qc0 Maximum permissible capacitor size. An integer. Smallest capacitor size. PSO In soft computing science, particle swarm optimization (PSO) is an intelligent calculation approach that optimizes a problem by iteratively effort to enhance nominate with regard to a given measure of quality. PSO optimizes an issue by having a population of nominate solutions, here dubbed birds, and moving these birds about in the search-boundary according to easy mathematical formulae over the particle's position and velocity. Each bird's motion is affected by its local best known location but, is also guided toward the best known location in the search-space, as are updated as better locations are discovered by other birds. This strategy moves the crowd toward the best outs. 17 PSO is primary introduced to Kennedy, Eberhart and Shi [30] and was first intended for simulating social behavior, as a stylized representation of the motion of organisms in a bird population. PSO is a met heuristic as it makes few or no assumptions about the issue being optimized and may investigate numerous spaces of nominate solutions. But, met heuristics such as PSO do not guarantee an optimal solution is ever discovered. Furthermore, PSO is a pattern search approach which does not apply the gradient of the problem being improved, which means PSO does not need that the optimization issue be differentiable as is essential by traditional optimization techniques such as gradient descent and quasi-newton algorithms. PSO may therefore also be applied on optimization cases that are partially irregular, noisy, nonlinear, oscillate over time, etc. A main variant of the PSO works by having a crowd (called a swarm) of nominate solutions (called particles). These birds are moved about in the searchspace according to a few easy strategies. The motions of the birds are governed by their own best known location in the search-space as well as the entire swarm's best known location. When enhanced location are being found these will then come to guide the movements of the population. The procedure is repeated and by doing so it is hoped, but not guaranteed, that a good solution will finally be found. is added in the terminal(i). Thus a particle may be described as shown in Fig. 1: Terminal number Particle 1 2 3 …. …. m-2 3 0 1 …. …. 4 Fig. 1: Sample of particle in PSO-CPP m-1 m 1 2 SIMULATION RESULTS The benchmark standard power system applied in this article is IEEE 37 buses test feeder. One line diagram of this standard power network has been depicted in Fig. 2. This system is a real world feeder placed in USA. Some features of the feeder are as presented here: Three wire delta working at a rated voltage of 4.8kV. All cables are underground cables. All consumers are “spot” consumers and include of fixed PQ, fixed current and fixed impedance value. The consumers are significantly unbalanced [32]. It is considered that nonlinear consumers are placed at buses 2, 15, 22 with the weight factor of 0.5 furthermore the node 35 with the weight factor of 0.25. Weight factor of nonlinear consumers at a special terminal means the ratio of nonlinear consumers to general consumer of that terminal. In this paper we apply 25 KVAR capacitors banks. PROPOSED METHOD Because of its effectiveness, generality, powerfulness and ability to cope with practical limits, a PSO has been suggested to solve the general optimal capacitor placement problem (OCPP).The following notes shed some guidance on the draft faces of the proposed method as applied to the OCPP: The number of particles (n) is a constant value and the same is determined empirically by trial and error way. The fitness function itself is applied to generate fitness values of the newly generated outs. The proposed method is designed to stop after nominative number of iterations. Based on the above texts, a PSO-based solution strategy used to the OCPP has been applied. The proposed approach implementation (PSO-CPP) may be described as follows: In this study the representation by means of strings of integers was selected. Each variable (represent terminal numbers) of the bird (its length is equal to the total number of the system terminals (m)) may save a zero, which indicates absence of capacitors on the corresponding terminal or an integer different from zero that indicates the number of placed capacitor sizes that Fig. 2: One line diagram of IEEE 37 terminals standard benchmark network WITHOUT CAPACITOR PLACEMENT Table 1 indicates the described indices before capacitor placement in investigated power network. Voltage amplitude profile of all terminals in three phases, without capacitor placement, is illustrated in Fig. 3. 18 Furthermore voltage THD of all terminals in three phases, without capacitor placement, is illustrated in Fig. 4. 0.075 0.07 Table 1: Described indices without Capacitor placement Index Value 62.4659 Active Power Loss 0.8242 Voltage Unbalancing Index 1.1737 Voltage Profile Index 5.6729 Voltage THD Index 1.005 0.065 THD 0.06 0.055 0.05 Phasea Phaseb Phasec 1 Phasea Phaseb Phasec 0.045 0.995 0.04 0 5 10 15 0.99 20 NodeNo. 25 30 35 40 Fig. 4: Voltage THD of used network without capacitor installation 0.98 PERFORMANCE AFTER OPTIMIZATION Voltagemagnitude(P.U) 0.985 In this experiment, the suggested method is used in test standard benchmark power network. Table 2 depicts the PSO variables. Table 3 shows the defined indices with capacitor installation in test standard benchmark power network. Voltage value profile of all terminals in three phases, with capacitor installation, is illustrated in Fig. 5. Furthermore voltage THD of all terminals in three phases, with optimal capacitor installation, is depicted in Fig. 6. 0.975 0.97 0 5 10 15 20 NodeNo. 25 30 35 40 Fig. 3: Voltage amplitude profile of applied network Table 2: Parameters used in the PSO Number of particles, n 20 1.6 2 100 C1 C2 Number of iterations, R It may be noticed from the Tables 1 and 3, the common active power loss in power network is decreased significantly from 62.46 KW to 52.42 KW, the voltage profile index is decreased significantly from 1.1737 to 0.933, voltage unbalancing index is gained to 0.785 from 0.8242 and voltage THD index is decreased to 5.012 from 5.6729. Voltage amplitude profile of all terminals in three phases, with capacitor installation, is illustrated Fig. 5. Furthermore voltage THD of all terminals in three phases, with capacitor installation, is illustrated in Figs 6. 1.005 Phasea Phaseb Phasec 1 Voltagemagnitude(P.U) 0.995 0.99 0.985 0.98 Table 3: Defined indices for standard benchmark power network with capacitor installation Index Value 52.42 Active Power Loss 0.785 Voltage Unbalancing Index 0.933 Voltage Profile Index 5.012 Voltage THD Index 0.975 0 5 10 15 20 NodeNo. 25 30 35 40 Fig. 5: Voltage magnitude profile of all terminals in three phases, with capacitor installation 19 0.065 1 Phasea Phaseb Phasec GA IBA 0.9 0.06 0.8 0.055 Normalizedfitnessvalue 0.7 THD 0.05 0.6 0.5 0.045 0.4 0.04 0 0 5 10 15 20 NodeNo. 25 30 35 40 1 0.9 Normalizedfitnessvalue 0.7 0.6 0.5 0.4 50 Iteration 60 70 80 90 100 1. Grainger JJ, Lee SH. Optimum size and location of shunt capacitors for reduction of losses on distribution feeders. IEEE Trans Power Apparatus Syst 1981;100(3):1105–18. 2. Grainger JJ, Lee SH. Capacity release by shunt capacitor placement on distribution feeders: a new voltage-dependent model. IEEE Trans Power Apparatus Syst 1982;101(5):1236–44. 3. Salama MMA, Chikhani AY. A simplified network approach to the var control problem for radial distribution systems. IEEE Trans Power Deliv1993;8(3):1529–35. 0.8 40 50 Iteration REFERENCES run1 data2 data3 data4 data5 30 40 Optimal capacitor installation problem is an issue that helps towards discovers a lowest of defined fitness function through solving a combinatorial problem in which the placement and size values of capacitor banks are to be selected. There are many of articles where independent mathematical formulations and definition of the optimal capacitor allocation issue along with solution approaches have been introduced. The target in common, is to discover optimal terminal numbers and sizes of parallel capacitors such that the cost of general real power/energy losses and that of parallel capacitors are minimized. Also, acceptable voltage profile has to be gained throughout the whole electrical power network. This paper investigated the optimal capacitor allocation issue by a PSO called as PSO-CPP. The proposed method demonstrated the quality of the PSO through the test standard benchmark network. The PSO shows excellent properties in terms of accuracy and simulation running time. In this part of paper, for investigating the performance of the optimization algorithm, several independent runs have been done. Fig. 7 depicts a typical improve of the fitness function (Eq. 1) of the best particles fitness of the crowd gained from suggested method for several independent runs. In this Fig., for simplicity, objective function value is normalized between [0, 1]. As illustrated in this Fig., its fitness values gradually enhanced from iteration 0 to 100, and exhibited no noticeable enhancement after iteration 50 for the all independent runs. The optimal stopping iteration to get best fitness for the all independent runs was about iteration 40–50. In Fig. 7, the accuracy and the speed of genetic algorithm (GA) [31] and PSO are compared. The obtained curves depict the average of 50 independent runs for both optimization algorithms. As illustrated in this Fig., the PSO has better operation and velocity of convergence compared with GA. 20 30 CONCLUSION INVESTIGATION OF PROPOSED METHOD IN SEVERAL RUNS 10 20 Fig. 8: Operation comparisons of GA and PSO Fig. 6: Voltage THD of all terminals in three phases, with capacitor installation 0 10 60 70 80 90 100 Fig. 7: Investigation of proposed methods in several runs 20 4. Baghzouz Y, Ertem S. Shunt capacitor sizing for radial distribution feeders with distorted substation voltages. IEEE Trans Power Deliv 1990;5(2):650–7. 5. Singh SP, Rao AR. Optimal allocation of capacitors in distribution systems using particle swarm optimization. Int J Electr Power Energy Syst 2012;43(1):1267–75. 6. Sundhararajan S, Pahwa A. Optimal selection of capacitors for radial distribution systems using a genetic algorithm. IEEE Trans Power Syst 1994;9(3):1499–507. 7. Su CT, Tsai CC. A new fuzzy reasoning approach to optimum capacitor allocation for primary distribution systems. In: Proceedings IEEE on industrial technology conference, Shanghai, China; 1996. p. 237–41. 8. Su CT, Lee CS, Ho CS. Optimal selection of capacitors in distribution systems. In: Proceedings of IEEE power tech conf, Budapest, BPT99-171-42; 1999. 9. Su CT, Lee CS. Modified differential evolution method for capacitor placement of distribution systems. In: Proceedings of IEEE/PES T&D conference Asia and Pacific; 2002. p. 208–13. 10.Taher SA, Bagherpour R. A new approach for optimal capacitor placement and sizing in unbalanced distorted distribution systems using hybrid honey bee colony algorithm. Int J Electr Power Energy Syst 2013;49:430–48. 11.Baran ME, Wu FF. Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans Power Deliv 1989;4(1):735–43. 12.Baran M, Wu F. Optimal capacitor placement on radial distribution systems. IEEE Trans Power Del 1989;4(1):725–34. http://dx.doi.org/10.1109/61.19265. 13.Baran M, Wu F. Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans Power Del 1989;4(1):735–43. http://dx.doi.org/10.1109/ 61.19266. 14.Chiang H-D, Wang J-C, Cockings O, Shin H-D. Optimal capacitor placements in distribution systems. I. A new formulation and the overall problem. IEEE Trans Power Del 1990;5(2):634–42. http://dx.doi.org/10.1109/61.53065. 15.Huang S-J. An immune-based optimization method to capacitor placement in a radial distribution system. IEEE Trans Power Del 2000;15(2):744–9. http:// dx.doi.org/10.1109/61.853014. 16.Das D. Reactive power compensation for radial distribution networks using genetic algorithm. Int J Elect Power Energy Syst 2002;24(7):573–81. http:// dx.doi.org/10.1016/S0142-0615(01)00068-0. 17.Das D. Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method. Int J Elect Power Energy Syst 2008;30(6–7):361–7. http:// dx.doi.org/10.1016/j.ijepes.2007.08.004. 18.Annaluru R, Das S, Pahwa A. Multi-level ant colony algorithm for optimal placement of capacitors in distribution systems. In: Proc. 2004 evol. comput. congr., vol. 2; 2004. p. 1932–1937. http://dx.doi.org/10.1109/CEC. 2004. 133 1132. 19.Prakash K, Sydulu M. Particle swarm optimization based capacitor placement on radial distribution systems. In: Proc. 2007 IEEE power eng. soc. general meeting; 2007. p. 1–5. http://dx.doi.org/10.1109/PES.2007.386149. 20.Raju MR, Murthy KR, Ravindra K. Direct search algorithm for capacitive compensation in radial distribution systems. Int J Elect Power Energy Syst 2012;42(1):24–30. http://dx.doi.org/10.1016/j.ijepes.2012.03.006. 21.Arcanjo D, Pereira J, Oliveira E, Peres W, de Oliveira L, da Silva Junior I. Cuckoo search optimization technique applied to capacitor placement on distribution system problem. In: 2012 10th IEEE/IAS international conference on industry applications (INDUSCON); 2012. p. 1–6. http://dx.doi.org/10.1109/ INDUSCON. 2012. 6452674. 22.Rani D, Subrahmanyam N, Sydulu M. Self adaptive harmony search algorithm for optimal capacitor placement on radial distribution systems. In: 2013 International conference on energy efficient technologies for sustainability (ICEETS); 2013. p. 1330–5. http://dx.doi.org/10.1109/ICEETS.2013.6533580. 23.El-Fergany AA, Abdelaziz AY. Capacitor placement for net saving maximization and system stability enhancement in distribution networks using artificial bee colony-based approach. Int J Electr Power Energy Syst 2014;54:235–43. http:// dx.doi.org/10.1016/j.ijepes.2013.07.015. 24.Attia El-Fergany AA. Multi-objective capacitor allocations in distribution networks using artificial bee colony algorithm. J Electr Eng Technol 2014;9(2):441–51. http://dx.doi.org/10.5370/JEET.2014.9.2.441. 25.Sultana S, Roy PK. Optimal capacitor placement in radial distribution systems using teaching learning based optimization. Int J Elect Power Energy Syst 2014;54(0):387–98. http://dx.doi.org/10.1016/j.ijepes.2013.07.011. 26.Y. Mohamed Shuaib, M. Surya Kalavathi, Christober Asir Rajan. Optimal capacitor placement in radial distribution system using Gravitational Search Algorithm. Electrical Power and Energy Systems 64 (2015) 384–397 27.Chu-Sheng Lee, Helon Vicente Hultmann Ayala, Leandro dos Santos Coelho. Capacitor placement of distribution systems using particle swarm 21 optimization approaches. Electrical Power and Energy Systems 64 (2015) 839–851 28.M.M. Aman, G .B . Jasmon, A. H. A. Bakar, H. Mokhlis, M. Karimi. Optimum shunt capacitor placement in distribution system— A review and comparative study. RenewableandSustainableEnergyReviews30(2014)4 29–439 29.http://ewh.ieee.org/soc/pes/dsacom/testfeeders.html. 30.Shi Y, Eberhart RC. A modified particle swarm optimizer. In: Proc. IJCNN. 1999. 31.K.S. Tang, K.F. Man, S. Kwong, Q. He, Genetic algorithms and their applications, IEEE Signal Processing Magazine 1996; 13: 22–37. 22

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