Full Paper Proc. of Int. Conf. on Advances in Electrical & Electronics 2012
Particle Swarm Optimization based Selective Harmonic Elimination In PWM AC-AC Converter Dr. S. Muralidharan1, Bindu J2, S Selvaperumal2, M Muhaidheen2 1
Mepco Schlenk Engineering College,EEE Dept, India Email:yes_murali@yahoo.com 2 Mepco Schlenk Engineering College,EEE Dept, India Email:jbindunair@gmail.com harmonics like Phase shifting transformer, Passive harmonic filters, Active harmonic filters, DC Choke, Line Reactor Harmonic Trap Filters, Broadband Filters, SHE-PWM etc. Among this Selective Harmonic Elimination (SHE) Pulse-width modulation (PWM) technique can be used for the selective elimination of harmonics. The main challenge involved in SHE-PWM is to solve nonlinear equations involved, which are transcendental in nature and therefore have multiple solutions. The common characteristic of the selective harmonic elimination pulse width modulation (SHE–PWM) method was that the waveform analysis were performed using Fourier theory. Sets of nonlinear transcendental equations were derived, and the solution is obtained using an iterative procedure, mostly by Newton–Raphson method. To avoid this cumbersome procedure, this paper proposes PSO based method to find the switching pattern to eliminate rectifier low input current harmonics, without having initial guess for the switching pattern. PSO was adopted to reduce the lower order line current harmonics by developing N number of pulse per half cycle. The optimal pulse pattern was used to suppress harmonics in PWM inverter. In concise, this paper introduces a technique which reduces the computational burden related with the nonlinear transcendental equations of the SHE–PWM technique by the application of intelligent based technique like Particle Swarm Optimization (PSO) method. By this technique switching angle can be calculated efficiently ensuring in rapid convergence. The results obtained were compared and analyzed.
Abstract -Power Electronics is the field which combines Power, Electronic and Control systems. It deals with the study and design of Thyristorised power controllers for variety of application like Heat control, Illumination control, High voltage power supplies, Vehicle propulsion systems, High voltage direct current (HVDC) transmission. Harmonics were produced due to these devices. Such harmonics leads to switching loss which affects the performance of the system. Hence elimination of these harmonics is essential. This paper analyzes a technique to eliminate pre-specified order of harmonics from the output waveform of AC/AC converters. Selective Harmonic Elimination (SHE) in Pulse-width modulation (PWM) technique was proposed for the elimination of harmonics. This necessitates solving systems of nonlinear equations that are transcendental in nature and therefore have multiple solutions. To minimize the computational burden associated with the nonlinear transcendental equations of the SHE–PWM method, intelligent based techniques was suggested in this paper. Particle Swarm Optimization (PSO) technique was analyzed and compared for calculating the switching angles. Keywords- Particle Swarm Optimization (PSO), Pulse-width modulation (PWM), Selective Harmonic Elimination (SHE).
I. INTRODUCTION Advent of power electronics and proliferation of nonlinear loads in industrial applications, power harmonics and their effects are of great concern. Harmonics are electric voltages and currents that appear on the electric power system as a result of certain kinds of electric loads. Harmonic frequencies in the power grid were a frequent cause of power quality problems. The harmonic distortion travels back into the power source and can affect other equipment connected to the same source. The harmonic currents also resulted in the heating of the connected devices. This heat over a period of time, will raise the temperature of the neutral conductor causing nuisance like tripping of circuit breakers, overvoltage problems, blinking of Incandescent Lights, computer malfunctions etc. High levels of harmonic distortion may lead to problems for the utility’s distribution system. This can cause spurious operation of equipment to a shutdown of important plant equipment. All electrical utilities do not have the same order of harmonics. So it is essential to eliminate those dominant orders of harmonics from the output waveform of AC/AC converters. Several techniques were available to reduce these © 2012 ACEEE DOI: 02.AETAEE.2012.3.20
II. LITERATURE SURVEY The recent developments in the field of power electronics has made it possible to improve the performance of electrical system utilities. An AC voltage regulator can be used to control an output AC voltage due to its simplicity and the ability to control large amount of power economically. Microprocessor based control scheme can be employed to control the firing instance for eliminating harmonics [1]. Selective harmonics can be reduced by Programmed PWM techniques, but this method is derivative-dependent and may end in local optima [2]. Solving linear algebraic equations instead of solving nonlinear transcendental equations using Walsh transformation for harmonic elimination is proposed in [3]. [4] Describes two-phase hybrid optimization algorithm 47
Full Paper Proc. of Int. Conf. on Advances in Electrical & Electronics 2012 to solve non-linear constrained optimization problems. Harmonic distortion is minimized through numerical techniques in [5]. Number of cost functions has been studied in eliminating selected harmonics minimizing THD is mentioned in [6]. In [7], NPC inverter configuration is chosen and piece-wise linear representations of PWM-SHE switching angles are developed to formulate the on-line linear equations. Determine optimum switching angles for eliminating some higher order harmonics while maintaining the required fundamental voltage is described in [8]. A novel neural network for generation of optimal switching patterns in voltage-controlled inverters is suggested in [9]. [10] Facilitates linear control of the fundamental output voltage and eliminates harmonic contents up to a specified order. A Newton algorithm to find the solutions is suggested in [11]. The nonlinear equations of the problem can be solved using computer is suggested in [12]. [13] Suggests that GA can be used to reduce the low order harmonic content in PWM output voltage. The effect of power system harmonics on equipment is described in [14]. Harmonic elimination problem in PWM inverter is treated as an optimization problem and solved using particle swarm optimization (PSO) technique is proposed in [15]. [16] Presents accurate solutions for nonlinear transcendental equations of the selective harmonic elimination technique used in three-phase PWM inverters feeding the induction motor by particle swarm optimization. Elimination of considerable amount of lower order line voltage harmonics in Pulse Width Modulation (PWM) inverter using PSIM software package is recommended in [17]. Signal processing methods like modified adaptive selective harmonic elimination algorithms is suggested in [18]. Harmonic elimination problem in PWM inverter is treated as an optimization problem and solved using particle swarm optimization (PSO) technique is proposed in [19]. [20] Recommends PSO technique to obtain the solutions for non-linear transcendental equations.
derived from PSO.
Figure 1. Circuit Diagram of Ac/Ac Converter
IV. PWM-SHE TECHNIQUE Using Fourier series Output Voltage would be expressed as
vO (t ) An cos nt Bn sin nt
(1) Due to odd function and half-wave symmetry the output voltage can be reduced to n 1
v 0 ( t )
n
sin n t
(2)
Where Bn is the Fourier Coefficient The magnitude of the harmonic components including the fundamental can be written as: B1 1
2 N sin 2 ( 1)i i 2 i i 1
(3)
2 N sin( n 1) i sin( n 1) i n 1 n 1 (4) i 1 where n = 3, 5, . . . , 2N 1, N denotes the number of switching angles per-quarter cycle and αi is the ith switching angle. The objective function of PWM-SHE technique was to minimize the harmonic content in the inverter line voltage and it is given in “(5)” Bn
III. PROPOSED SYSTEM AC voltage converters were widely used in power electronic systems to control an output ac voltage where a variable ac voltage was obtained from a fixed ac voltage, for power ranges from few watts up to fraction of megawatts. They were used in light dimmers and in starting systems of large induction motors. It consists of two switches the switching loss is less and is more flexible. The schematic representation of the power circuit configuration which had a load connected to an ac source through an ac voltage controller was provided in Fig.1. During the positive half cycle, switch S1 turns on and the diodes D1 , D4 will be forward biased and the diodes D3 , D2 will be reverse biased, at that moment the switch S2 will be at off state, thus delivering power to the load. During the negative half cycle , Switch S2 turns on, the diodes D5, D8 will be forward biased and the diodes D7 , D6 will be reverse biased thus feeding back the inductive energy to the source. The switches are triggered at particular angles using Pulse width modulation technique and those switching angles are © 2012 ACEEE DOI: 02.AETAEE.2012.3.20
B
n 1 , 3 , 5
2 F (1, 2 ,......, N ) ( B1 mi ) 2 B 2 B 2 ..... Bn 3
5
(5)
Where, mi- is modulation index mi=V1/Vm V1-Value of fundamental component Vm -Value of peak input voltage Minimizing “(5)” subjected to the constraint “(6)”, for Quarter-wave symmetric pulse pattern. These switching angles are generated for different values of modulation index and used to control the converter for certain operating point. 0 1 2 ....... N
48
2
(6)
Full Paper Proc. of Int. Conf. on Advances in Electrical & Electronics 2012 The main challenge involved was solving nonlinear equations, which are transcendental in nature and therefore had multiple solutions. Hence a convenient method to find the solution was needed with less computational effort. In this paper an attempt had been made to solve the transcendental equations using Particle Swarm Optimization (PSO). Fig. 2 show the simulated model of the circuit. It consisted of Diodes and two switches. The switches were triggered at particular switching angles which were generated using PSO.
B. Steps for PSO Algorithm The PSO algorithm has the following steps: 1. PSO parameters were initialized randomly 2. Objective function was computed at the initial position 3. Position and velocity were updated. (8)&(9) 4. The updated position was evaluated; the local best (L) and global best (G) particles are updated. 5. Repeat the algorithms for the fixed number of iterations 6. Best values were obtained (G). V. PROPOSED SYSTEM To obtain an optimum result the following parameters were used: Swarm size 100 Maximum iterations 100 Inertia weight factor 0.9 A. Simulated Results for R-Load and Induction Motor Load The circuit was simulated using a dynamic load. The asynchronous load used here was a 220V,1420 rpm,0.37KW capacitor start-run induction motor. Fig. (3) shows the input and output voltage waveform for Motor Load.
Figure.2. Simulink Model
IV. PARTICLE SWARM OPTIMIZATION Particle swarm Optimization is a computational method used for optimizing a problem by iteratively solving the candidate solution. It is a metaheuristic approach as it makes few or no assumptions about the problem to be optimized. The system was initialized with a population of random solution and optimized by updating generations. PSO had no evolutionary operators such as crossover and mutation. The advantages of PSO were that PSO was easy to implement and there were few parameters to adjust. PSO had been successfully applied in many areas like function optimization, artificial neural network training, fuzzy system controller etc. A. PSO Algorithm PSO was initialized with a group of random solutions and then searches for optima by updating generations. In every iteration, each particle was updated by two best values. The first one would be the best solution achieved called pbest. Another best value was tracked by the particle swarm optimizer. This best value was called global best or gbest. After finding the two best values, the particle updates its velocity and positions (8)(9).
v[] v[] c1 * rand () * ( pbest[] present[]) c 2 rand () * ( gbest[] present[])
present [] present [] v[]
Figure.3 Input and Output Voltage Waveform for Motor Load
SHE-PWM technique was compared with EAC technique for R-Load and Dynamic Load and % of voltage and current harmonics for various harmonic orders were presented in Table 1 and Table 2 respectively. As expected, from Table 1 and Table 2 it can be noted that the percentage of individual voltage harmonics, current harmonics and overall THD was comparatively low when using PSO technique.
(8) (9)
v[] is the particle velocity present [] is the current solution. pbest[] and gbest[] are defined as stated before. rand () is a random number between (0,1). c1, c2 are learning factors. © 2012 ACEEE DOI: 02.AETAEE.2012.3. 20
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Full Paper Proc. of Int. Conf. on Advances in Electrical & Electronics 2012 TABLE I. COMPARISON O F PWM VS EAC FOR % VOLTAGE H ARMONICS USING PSO T ECHNIQUE FOR R-LOAD AND MOTOR LOAD
Figure.5 Harmonic spectrum of output voltage
VII. CONCLUSION Selective harmonic elimination/control had been widely explored as alternative to traditional pulse-width modulation techniques. In this paper, a selective harmonic elimination control based on Particle Swarm Optimization was proposed for PWM AC/AC voltage Controllers. The algorithm was developed using MATLAB m-file and simulated using Simulink. With the proposed PSO method, elimination of desired harmonics was ensured. The outputs were then compared with the Extinction Angle control Technique (EAC) which proves the effectiveness and robustness of these techniques over the other conventional techniques. A complete analysis was done using the result obtained from PSO.
TABLE II. C OMPARISON OF PWM VS EAC FOR % CURRENT H ARMONICS USING PSO T ECHNIQUE FOR R-LOAD AND MOTOR LOAD
REFERENCES [1] Addoweesh KE, Mohamadein AL,” Microprocessor based harmonic elimination in chopper type AC voltage regulators”, IEEE Trans Power Electron 5th ed.,vol.2.1990,pp.191–200 [2] Enjeti PN, Ziogas PD, Lindsay JF, “Programmed PWM techniques to eliminate Harmonics A critical evaluation”. IEEE Trans Industrial Application 26th ed.,vol.2.1990,pp.302 -316 [3] Liang TJ, O’Connnell RM, Hoft RG, “Inverter harmonic reduction using Walsh function harmonic elimination method”. IEEE Trans Industrial Electronics 12th ed.,6th vol.,1997,pp.971– 982 [4] Baskar S, Subbaraj P, Rao MVC,” Performance of hybrid real coded genetic algorithms”. International Journal Computer Engineering Science 2nd ed.,4th vol. 2001,pp.583–601 [5] Deib DA, Hill HW, “Optimal Harmonic Reduction In Ac/Ac Chopper Converters” In Proceedings of 24th annual IEEE power electronics specialist conference, 1993, pp. 1055–1060. [6] Holmes DG, Lipo TA, “Pulse-width modulation for power converters principles and practice”. IEEE press series on power engineering, New York (2003) [7] Maswood AI, Rashid MH, Jian L, “Optimal PWM–SHE switching on NPC inverter: a winning match for high power conversion”. Electrical Power System Res 1998,pp19–24 [8] Sun J, Beineke S., Grotstollen H, “Optimal PWM based on real-time solution of harmonic elimination equations”. IEEE Trans Industrial Electronics 1996,pp.612–621 [9] Trzynadlowski AM, Legowski S, “Application of neural networks to the optimal control of three-phase voltagecontrolled inverters”. IEEE Trans Power Electronics 1994, pp.397–404
VI. PROPOSED SYSTEM In order to validate the proposed method, experiments were carried out in the laboratory. The pulses for the switches are programmed using AT89C51 microcontroller. An optocoupler was used to isolate the power circuit from the microcontroller. Eliminating 3rd and 5th order Harmonics Fig 4 shows the output voltage obtained experimentally. Fig 5 shows the harmonic spectrum of output voltage waveforms for N=3 measured using Power Quality Analyzer.
Figure 4. Output Voltage Waveform for N=3
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Full Paper Proc. of Int. Conf. on Advances in Electrical & Electronics 2012 [10] Jian Sun, Horst Grotstollen, “Solving Nonlinear Equations for Selective Harmonic Eliminated PWM Using Predicted Initial Values”. IEEE Trans Power Electronics, 1992,pp.259260 [11] Hasmukh S. Patel and Richard G. Hoft, “Generalized Techniques Of Harmonic Elimination And Voltage Control In Thyristor Inverters: Part I-Harmonic Elimination”. IEEE Transactions On Industry Applications, 1973, Vol. Ia-9, No. 3,pp.310-373 [12] J. C. Balda D. C. Griffitki A. McEachern,” Effects of Harmonics on Equipment”,.IEEE Transactions on Power Delivery, Vol. 8, No. 2, April 1993,pp.672-680 [13] Pattaraporn Jitta, Somyot Kaitwanidvilai and Atthapol Ngaopitakkul, “Switching Angle Design for Pulse Width Modulation AC Voltage Controller Using Genetic Algorithm and Distributed Artificial Neural Network”. Proceedings of International Multi conference of Engineers and computer scientists vol II, March 2011.
© 2012 ACEEE DOI: 02.AETAEE.2012.3. 20
[14] Ramkumar, S.; Kamaraj, V.; Thamizharasan.S,” GA based optimization and critical evaluation SHE methods for threelevel inverter”. Electrical Energy Systems (ICEES), 2011,pp. 115 – 121. [15] Rup Narayan, Ray Debashis Chatterjee, Swapan Kumar Goswami, “An application of PSO technique for harmonic elimination in a PWM inverter”, Journal of applied soft computing archive Vol.9 , No.4,2009 [16] Mohamed Azab,”Harmonic Elimination in Three-Phase Voltage Source Inverters by Particle Swarm Optimization”. Journal of Electrical Engineering & Technology Vol. 6, No. 3, 2011, pp.334-341. [17] R. Lynn Kirlin, Cristian Lascu and Andrzej M. Trzyn, “Shaping the Noise Spectrum in Power Electronic Converters”, IEEE Transactions On Industrial Electronics, 2011, Vol. 58, No. 7,pp: 2780- 2788. [18] H. Taghizadeh and M. Tarafdar Hagh “Harmonic Elimination of Cascade Multilevel Inverters with Nonequal DC Sources Using Particle Swarm Optimization” IEEE Transactions On Industrial Electronics, 2011, Vol. 57, No.11,pp: 3678- 3684
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