离散粒子群优化：布局优化、电容大小、基于谐波共振问题的分布式发电(IJISA-V5-N7-6).doc

I.J. Intelligent Systems and Applications, 2013, 07, 42-49 Published Online June 2013 in MECS http//www.mecs-press.org/ DOI 10.5815/ijisa.2013.07.06 Optimal Placement and Sizing of Capacitor and Distributed Generation with Harmonic and Resonance Considerations Using Discrete Particle Swarm Optimization M. Heydari E-mail S.M. Hosseini Faculty of electrical engineering, Babol University, Iran E-mail mehdi.hosseininit.ac.ir S.A. Gholamian Faculty of electrical engineering, Babol University, Iran E-mail gholamiannit.ac.ir AbstractPresence of distributed generation DG in distribution systems has significant impacts on the operational characteristics of these systems, also using capacitor for reactive compensation and loss reduction is so common. Injected harmonic currents from non-linear loads into distribution system distort all of voltages and currents and must be considered when placing the capacitor banks so that the resonance will not occur. In this paper discrete particle swarm optimization DPSO approach is used for the optimal placement and sizing of distributed generations and capacitors in distribution systems for simultaneous voltage profile improvement, loss and total harmonic distortion THD reduction. There is a term in the objective function which prevents harmonic resonance between capacitor reactance and system reactance. Constraints include voltage limit, voltage THD, number/ size of capacitors and generators. For uating the proposed algorithm, the IEEE 33-bus test system is modified and employed. Index TermsCapacitor, Distributed Generation, Optimal Placement, Harmonic, Resonance,Discrete Particle Swarm Optimization I.Introduction Centralized Power plants deliver the electricity to the end-user via transmission system. Distribution system makes a link between the high voltage transmission system and consumers. In distribution system, the voltage levels are low but current levels are high in the compare of transmission system, so the loss, in distribution system is greater than in transmission system. Most of loads connected to distribution systems are induction loads which make the system power factor will be lag and the voltage drop to a lower level even lower than the acceptable range. Any components connected to power system for working properly and safely must receive voltage in the defined range, any voltage out of this boundary can damage these components. In power system, operator is obligated to maintain voltage level of each costumer bus within the required limit. A most acceptable voltage variation is within the range of [1]. As mentioned above, drop of voltage is unavoidable, so this drop should be compensating somehow. One of the most widely is using shunt capacitors. In addition improving voltage profile, shunt capacitors can reduce loss, enhance power factor and voltage stability of the system [2]. Another is using distributed generation DG.DG is playing an increasing role in distribution system. Improving voltage profile, reducing system losses, reinforcing grid and improving system reliability are some advantages of using DG[3]. All of these advantages will be achieved only on the condition, these DG capacitor placed in proper buses. Any improper placing may adverse system condition.There have been some studies for optimal placing such as tabu search [4], analytical approaches [5, 6], second-order algorithm [7], meta-heuristic approaches[8,4],fuzzy-GA algorithm[10],etc. Most of these techniques suffer from the inability to escape local optimal and burden heavy computational time.Psoparticle swarm optimizationis a good which is fast and have ability to escape local optimal.Pso is a self-adaptive search optimization was introduced by Kennedy and Ebhart[11]. Pso has been applied to many optimization problems such as dynamic systems [12], optimal capacitor placement in distribution system [13], constrained optimization [14], multi-objective optimization problems [15], etc. Some works have used pso for optimal placing of capacitors, it was considered as a continuous problem but as we know capacitors are commercially available in discrete sizes, so in this paper a modified version of pso which is suitable for discrete problems and is called discrete particle swarm optimization DPSO or binary particle swarm optimization is used .Most of these works consider all of loads are linear and exclude the effect of harmonic in the objective function. But in practice, a portion of loads are none linear because of wide speared use of electronic devices, so it can lead to improper placing because of probation of resonance at some harmonic frequencies. In this paper, there is a term in the objective function which prevents harmonic resonance. The rest of this paper is organized as follows in section 2modeling of network components at harmonic frequencies is discussed. Problem ulation for the objective function for improving voltage profile and minimization of loss and THD is presented in section3.In section 4 the pso algorithm is described briefly. The results of DG and capacitor placement on 33-bus test system are presented and discussed in section5. Finally, section 6 summarizes the main points and results of this paper. II.Model of Network Components at Harmonic Frequencies In this paper for modeling of network components at harmonic frequencies, some practical and approximation of references [16,17] is used. 2.1 Cable For very accurate model of cable at high frequency some modifications need to be applied to the resistance and inductance of cable. But for practical harmonic analysis a simple model is enough. For the harmonic order the line impedance can be written as 2.2 Transer Because of non-linear magnetizing properties of transer it is difficult to model it at harmonic frequencies and because of core saturation it produces harmonic itself. For harmonic study in this paper we assume transer operates in normal condition. So the impedance of transer at harmonic frequency can be written as 2.3 Capacitor and Inductor Capacitor and inductor can be modeled similarly and their impedance at harmonic frequency can be expressed by ⁄ where f is the main frequency of the system. III.Problem ulation In this paper the following assumptions are made Capacitors are fixed type. Both linear and non-linear loads are presented in a balanced 3-phase system. 3.1 Constraints Voltage constraint will be defined as follows √ where is lower , is upper bounds of rms voltage and is harmonic order of voltage at bus i . In this paper 0.95 and 1.05. THD Total harmonic distortion of voltage THD should be less than the maximum of allowable [√ ] ⁄ In this paper according to IEEE-519, 0.05. 3.2 Indexing For ing of objective function some inds are defined. 3.2.1 Voltage deviation index This index is for improving of voltage profile and defined as follows ∑ Where is the nominal of system voltage 1 , is the voltage at node i and n is number of busses. 3.2.2 Active and reactive power loss index PL-I, QL-I Where ,are active and reactive power losses after installation of DG and capacitor respectively and , are active and reactive power loss before installation. 3.2.3 THD index This index is for minimizing of total harmonic distortion ∑ Where is the total harmonic distortion of bus i. 3.2.4 Resonance index RES-I Many works concerning capacitor placement, consider all loads are linear, recently some works take non-linear loads into account, so the capacitor placement problem mixed with harmonic consideration, but as it is shown in [18] even in these works, capacitor placement led to harmonic resonance at one or some harmonic frequencies. In this paper there is a term in the objective function which prevents harmonic resonance. So resonance index is defined as follow ∑∑ ∑∑ Where , are the voltage and current of bus I at harmonic order after installation and , are before installation of DG and capacitor. When resonance occurs, voltage or current at resonance frequency will increase and may go much more than the nominal amplitude of main frequency. So if resonance occurs, the amplitude of this term will increase and capacitors which make resonance will be omitted automatically in the minimization progress of the algorithm. 3.3 Objective Function By introducing above inds objective function is defined as follows where is the index weight, these weights indicate the importance of each index in the placement problem. They depend on the required analysis. ∑[] In table 1 these weights is defined, for selecting these weights, the guides of [19,20] is used. Table 1 index weights IV.PSO Algorithm Particle swarm optimization is an algorithm developed by Kennedy and Ebhart. This algorithm is based on social behaviors of bird flocking or fish schooling and the s which they use to find food sources. In a simple way this algorithm is defined as follows The search space is d-dimensional Particle Each member is called particle and is presented by d-dimensional vector and described as [ ] Where is the I-th particle. Population a set of n particles in the swarm is called population and described as [ ] pbest the best previous position for each particle is called particle best pbest and described as [ ] gbest the best position among all of particle is called global best gbest and described as [ ] velocity the rate of position change for each particle is called particle velocity and described as [ ] updating velocity at iteration k the velocity for d-dimension of i-particle is updated by Where w is the inertia weight, and are the acceleration constants, and , are two random values in range [0,1]. The acceleration constants , control how far a particle will move in a single iteration. Typically these both are set to a value of 2. The inertia weight w is used to control the convergence of behavior of pso. Small values of w lead to more rapid convergence usually on suboptimal position, but large value may prevent divergence. In general the inertia weight is set according to the following equation updating position The i-particle position is updated by For binary discrete search space, Kennedy and Ebhart [21] have adopted the pso to search in binary space by applying a sigmoid transation to the velocity component given in 21 to squash the velocities into a range [0,1],and force the component values of position to be 0 or 1. The equation for updating positions in 20 then is replaced by 22 Fig.1 shows the flowchart of this algorithm Fig. 1 flowchart of pso algorithm V.Simulation Results The presented algorithm was implemented and coded in Matlab computing environment. In order to uate the proposed algorithm, the 12.6 kv 33-bus IEEE distribution system is modified and applied, such that the objective function given in [16] is minimized. The single diagram of this system is shown in Fig.2. The specification of this system is given in[22] .two none-linear loads are replaced with loads in buses 5 and 26.This loads are two six-pulse converter with active and reactive power of 1MW and 0.75MVAR.the harmonic current spectra of these converters is given in table 2. Fig. 2 single line diagram of 33-bus IEEE distribution system Table 2 six-pulse converter harmonic spectra Capacitors and Distributed generations are commercially available in discrete sizes. In table 3and 4 the size of capacitor bank and DG are given Table 3 capacitor sizes Table 4 DG sizes In table 5, rms voltages and THD of all buses for the base case no installation are demonstrated. As observed in table 5, the voltage level of some buses drop to level lower than acceptable limit and THD of some buses go to level higher than upper limit of defined range by IEEE-519 standard. Table 5 bus voltage and THD before installation The DPSO algorithm is applied in this system for placement of capacitor and distributed generation for improving voltage profile and reducing loss and THD. In table 6 the locations and sizes of capacitors and Distributed generations are given. In table 7, rms voltages and THD of all buses after installation of capacitor and DG are demonstrated, as observed in table 7, after placement of capacitor and DG by this algorithm, no voltage and THD violation is observed in any buses. Optimal Placement and Sizing of Capacitor and Distributed Generation with Harmonic and Resonance Considerations Using Discrete Particle Swarm Optimization 47 TABLE 6 the locations of capacitors and DGs with proposed Bus number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 CapacitorKVAR 1350 750 1500 0 0 2700 DGKW 3000 800 Bus number 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 CapacitorKVAR 1050 900 900 1050 DGKW 5000 - Table 7 bus voltage and THD after installation of capacitor and DG Bus number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1.003 1.004 1.008 1.010 1.022 1.030 1.033 1.044 1.044 1.043 1.042 1.036 1.034 1.033 1.032 1.030 0.08 0.51 0.83 1.16 2.33 2.31 2.31 2.28 2.28 2.28 2.29 2.30 2.30 2.30 2.31 2.31 Bus number 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1.029 1.009 1.014 1.016 1.015 1.003 0.996 0.993 1.020 1.017 1.018 1.018 1.018 1.026 1.027 1.027 2.31 0.08 0.08 0.08 0.08 0.51 0.51 0.52 2.17 1.96 1.96 1.96 1.96 1.94 1.94 1.94 RESULTS Table 8 comparison results Before installation 578 8.55 1 0.86 After installation 349 2.33 1.04 0.99 In table 8 and Fig.3 and 4 the results of two cases before installation and after installation are compared. As observed in table 8, after optimization by proposed , power loss was decreased by 39.61 and maximum THD was decreased by 72.74. Copyright 2013 MECS Fig. 3 voltage comparison I.J. Intelligent Systems and Applications, 2013, 07, 42-49 48 Optimal Placement and Sizing of Capacitor and Distributed Generation with Harmonic and Resonance Considerations Using Discrete Particle Swarm Optimization [6] N. Acharya, P. Mahat, N. Mithulananthan, “An analytical approach for DG allocation in primary distribution network, Int. J. Electr. Power Energy Syst. 2006, PP.669-678. [7] K.H. Kim, Y.J. Lee, S.B. Rhee, S.K. Lee, S.-K. You, “Dispersed generator placement using fuzzyGA in distribution systems“, in IEEE PES Summer Meeting, vol. 3 July, 2002, pp. 1148 – 1153. [8] Y.A. Katsigiannis, P.S. Georgilakis,“ Optimal sizing of small isolated hybrid power systems using tabu search“, Journal of Optoelectronics and Advanced Materials 10 5 2008 1241–1245. Fig. 4 THD comparison VI. Conclusion In this paper a modified version of pso algorithm DPSO which is suitable for discrete problems is applied for optimal placing and sizing of capacitor and DG in distribution system. In some works in spite of taking harmonic into account like [17] resonance occurs at some freque