Optimized Solutions for an Optimization Technique ... - IEEE Xplore

1st Int’l Conf. on Recent Advances in Information Technology | RAIT-2012 |

Optimized Solutions for an Optimization Technique Based on Minority Charge Carrier Inspired Algorithm Applied to Selective Harmonic Elimination in Induction Motor Drive Madichetty Sreedhar, Navin Mani Upadhyay, Sambeet Mishra KIIT University Bhubaneswar Abstract: Multidimensional scaling is a technique for exploratory analysis of multidimensional data, whose essential part is optimization of a function possessing many adverse properties including multi objectivities, multimodality, and non differentiability etc., In this paper, global optimization algorithms for multi Objective problems are chosen for different kind of problems especially in the IT Industry and power Industry. In this Paper it have been given the detail analysis of new algorithm with comparison of other algorithms. This new algorithm is tested and it is applied to an induction motor drive to eliminate selective harmonics for an voltage source inverter. The results have been compared with other algorithms and improvement in the performance has been observed. Keywords: Multi Objective optimization, charge carrier based algorithm, optimization, Power Industry.

I.

INTRODUCTION

Now a days it have a lot of algorithms for optimization. There are some drawbacks in respective algorithm. At the same time some excellent features are there, in those respective algorithms. So, in the present algorithm we want to combine those algorithms advantages and by discarding the disadvantages to make a new algorithm, which has the fast rate of convergence with very less number of particles. It have some of the algorithms are based on behavior of Fish, bats, and other called as swarm intelligence[5,6,8]. Those algorithms we are calling it as a particle swarm optimization. The algorithm which is based on the cooling stimulant process of metals called as Simulated annealing(SA)[1]. This process converges to a best position by updating its velocities. It have some other different type of algorithms such as the harmony search, firefly and bat algorithms. By taking the advantages of all algorithms, we want to develop a new algorithm, with reasonable good result. This technique is compared with the existing algorithms and finding the optimum solution with less time and less number of iterations[13]. The algorithm ,we are introducing is Minority Charge Carrier Inspired Algorithm(MCCIA).Modern meta heuristic algorithms such 978-1-4577-0697-4/12/$26.00 ©2012 IEEE

as the Ant Colony Optimization and the harmony search start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems[9,11]. But some of them have drawbacks and advantages. So, In this paper, we will implement a new algorithm which will eliminate the drawbacks and combine the advantages of those algorithms which shows better and efficient result. II. BRIEF HISTORY OF OPTIMIZATION Alan Turing was probably the first to use optimization algorithms during the second World War[5] . Turing called his search method heuristic search, as it could be expected it worked most of time, but there was no guarantee to find the correct solution, but it was a tremendous success. John Holland and his collaborators at the University of Michigan developed the genetic algorithms in 1960s [5]. Then, in 1966, L. J. Fogel, together A. J. Owen and M. J. Walsh, developed the evolutionary programming technique by representing solutions as finite-state machines and randomly mutating one of these machines. Artificial neural networks are now routinely used in many applications[7,12]. In 1943, W. McCulloch and W. Pitts proposed the artificial neurons as simple information processing units A systematical summary in Vapnik’s book on the Nature of Statistical Learning Theory was published in 1995.The next big step is the development of simulated annealing (SA) in 1983, an optimization technique, pioneered by S. Kirkpatrick, C. D. Gellat and M. P. Vecchi, inspired by the annealing process of metals[18]. In 1992, Marco Dorigo work on optimization and natural algorithms, in which he described his innovative work on ant colony optimization (ACO). Slightly later in 1995, another significant progress is the development of the particle swarm optimization (PSO) by American social psychologist James Kennedy, and engineer Russell C. Eberhart. In 1997[8], the publication of the ‘no free lunch theorems for optimization’ by D. H. Wolpert and W. G. Macready sent out a shock way to the optimization community First Zong Woo Geem et al. in 2001 developed the harmony search (HS) algorithm, which has been widely


applied in solving various optimization problems such as water distribution, transport modelling and scheduling. In 2004, S. Nakrani and C. Tovey proposed the honey bee algorithm and its application for optimizing Internet hosting centers, which followed by the development of a novel bee algorithm by D. T. Pham et al. in 2005 and the artificial bee colony(ABC)by by D. Karaboga in 2005.FireFly algorithm was introduced by XIN SHE –Yang in 2008. III. INTRODUCTION TO ALGORITHM This technique is based on the charge movement. Simply we can call it as charge carrier algorithm(CCM). We are not using the exact behavior of Electron, instead we are assuming some assumptions of our convenient purpose. Where as, here we are considering a basic PN Semiconductor device with reverse bias condition. When the P terminal of the device is connected negative terminal of the supply , and the positive terminal of the device is connected N terminal of the supply.The electrons are always choosing low resistance path. I=Q/T (1) In ‘P’ type semiconductor device , it has excessive holes and ‘N’ type semiconductor device, it has excessive electrons. It also consist of minority charge carriers. Due to the presence of minority charges it will moves with a certain velocity to reach the destination. Each electron will move with certain velocity Vi and it will update the position Xi and due to the presence of supply voltages . It will moves towards the destiny, Through which is having low resistance path. This will choose only low resistance path, even several paths are available. It will constantly update its velocity and position. Q=I.T=V/Q-T (2) Q=V.T/R (3) The charge will locate the low resistance path. Since it has the capability of available range E [0,1] and R=0, Q=∞ .That will indicate that convergence will be takes place in very little time. The pseudo code of the developed algorithms as follows with some assumptions. (I) In this all electrons are moving with some velocity in spite of the other lot of obstacles are present, constantly it will changes its direction with constant velocity.This will be the main advantage of this one. In PSO ,Even though Particle(Swarm) knows the destination, the swarms will fly, first fast and slow as the target is reaching. Where as in this technique, it will reach definitely the target with the same speed. So the velocity component is constant. Hence these will be no change in the velocity. By this we can predict the speed of convergence is high. This component is independent of velocity Vi. (II).In normal case, as the electron will pass through certain path it loses its energy in the form of heat. Here we are considering this one as the loss less competent. (III).Even the electrons will move with the constant velocity Vi at the positions Pi with a fixed charge on the positive -

1.602 x 10-19 coulombs and they will search for the low resistance path. They can automatically adjust the position to go the target which will be in the range r[0,1]. (IV)All though the resistance varies from time to time we will assume that the resistance is a constant value which will not change with the time and this will be lies in between minimum Amin and Amax. (V) Here are main important consideration is that as the voltage varies the number of electrons will increases. we are consider that it will be as charges. So that the voltage changes with [Volmin, Volmax] corresponding the resistance values changes [Rmin,Rmax] with a fixed number of charges. The Algorithm as follows (I)Objective function F(X), Where X =(x1, x2, x3, … xn).Initialize the number of electrons that are present in the space x1, x2, x3 … xn with a velocity ‘V’.Now we will choose the voltage and resistance range. I=Q/T Q=I*T=V.T/R As the V,R,T are defined at the starting. While (TRi) Select a solution among all the best solution. Generate a local solution around and select the best solution End if Generate a new solution by going in different paths. If (rand < Ai & f(xi) I α1/P Where A=Area of cross section, p=Resistivity of the material,R=Resistance of the material.


Here the current is inversely proportional to the resistivity. As the resistivity increases the current flowing capability decreases. There are many standard test functions for validating new algorithms. In the current benchmark validation, we have chosen the well-known Rosenbrock’s function. In addition, we have also used other standard test functions for numerical global optimization [10] such as Ackley’s function Comparison with Other Algorithms. In order to compare the performance of the new algorithm, we have tested it against other heuristic algorithms, including genetic algorithms (GA) [5, 6, 11], and particle swarm optimization (PSO) [7, 8]. There are many variants of PSO, and some variants such as the mean PSO could perform better than the standard PSO [3]. However, the standard PSO is by far the most popularly used. Therefore, we are also using the standard PSO in our comparison. There are many ways to carry out the comparison of algorithm From the table, we can see that PSO performs much better than Genetic Algorithms, while the MCCBA algorithm is much superior to other algorithms in terms of accuracy and efficiency. This is no surprising as the aim of developing the new algorithm was to try to use the advantages of existing algorithms and other interesting feature inspired by the fantastic behavior of electrons. If we replace the variations of the velocity Vi by a random parameter and setting Ai = 0 and ri = 1, the MCCBA algorithm essentially becomes the standard Particle Swarm Optimization (PSO). Similarly, if we do not use the velocities, but we use fixed frequency and rate Ai and ri. This algorithm is virtually reduced to a simple Harmony Search (HS) as the frequency/wavelength change is essentially the pitch adjustment, while the rate of pulse emission is similar to the harmonic acceptance rate in the harmony search algorithm [4, 15]. The current studies implies that the proposed new algorithm is potentially more powerful and thus should be investigated further in many applications of engineering and industrial optimization problems[17]. V. IMPLEMENTATION TO SELECTIVE HARMONIC ELIMINATION PROBLEM APPLIED TO AN INDUCTION MOTOR DRIVE The Harmonic elimination problem is formulated as a set of transcendental equations that must be solved to determine the angles for turning the switches [13,14] ON and OFF in a full bridge inverter .So as to produce a desired fundamental amplitude while eliminating those harmonics. The transcendental equations are then solved using iterative numerical techniques to compute the switching angles. In this paper it have been determined that the switching angles for both the single phase and three phase inverter by using the MCCBA optimization technique and compared with other techniques and shown better results so far[14].The harmonic elimination problem in PWM inverter is treated as an Optimization problem and solved using MCCBA. The derived equations for computation of THD of the output

performance, and two obvious approaches are to compare the numbers of function evaluations for a given tolerance or accuracy, or to compare their accuracies for a fixed number of function evaluations. Here we are using the first approach In our simulations, it use a fixed tolerance e 10−5, and it run each algorithm for 100 times so that it can do meaningful statistical analysis. Comparison of MCCBA with GA, and PSO. TABLE1: SHOWS ,COMPARATIVE PERFORMANCE OF TECHNIQUE Functional Algorithm Multiple Peak’s Rosen Brock’s Ackley’s

GA

PSO

MCCBA

54124 55023 30720

3880 32056 20407

1052 17903 15933

voltage of PWM inverter is used as the objective function. The switching angles are calculated by using MCCBA for Bipolar case and objective function is minimized to obtain in minimum THD. Genetic algorithms[5] and Artificial Neural Networks [6] are also recently employed for inverter harmonic elimination. On many applications PSO has been reported to have better performance than GA. . In Selective harmonic elimination the switching angles are calculated so that the desired amplitude of fundamental voltage is obtained and simultaneously the harmonics are selectively eliminated[7]. This is achieved by mathematically generating the exact instant of turn on and turn off the power valves[8]. Here the number of nonlinear equations in terms of un known switching angles depends on number of harmonic components to be eliminated, have to be solved for each value of modulation index using numerical minimization approach. The fundamental component is assigned a desired output value and other selected orders of harmonics are equated to zero to form the set of transcendental equations[11]. Harmonics can be eliminated for both single phase as well as three phase inverter by using selective harmonic elimination technique. Here we are using two types of switching techniques. In that Unipolar switching scheme and Bi polar switching scheme. VI. BIPOLAR SWITCHING SCHEME The main objective is to obtain a sinusoidal ac output voltage waveform where the fundamental component can be adjusted arbitrarily with in a range and intrinsic harmonics selectively eliminated. The ac output voltage features odd half and quarter wave symmetry. Therefore the even harmonics are absent. Moreover, the per phase voltage waveform should be chopped N times per half cycles in order to adjust the fundamental and eliminate N-1 harmonics in the ac output voltage wave for[16].


VII. RESULTS AND DISCUSSION

Fig. 1. Bi polar Switching Scheme for elimination of 3rd, 5th, 7th harmonics in single phase inverter.

The above technique is implemented in MATLAB. Firstly it had applied, algorithm for non linear equations ,thus finding angles. Thus obtained angles are applied in the SIMULINK and the results is compared with existing technique and thus concluded as the results are far better than previous work[11]. In the fig(4) it shows that the ,all the lower order harmonics are eliminated. FFT Analysis of Single Phase inverter showing the dominant harmonic is 15 th ,Fundamental Frequency is 50 Hz and THD is 11.27% .

Fig. 4. Harmonic analysis of the 3-phase inverter. Fig. 2.Three Phase Voltage Source Inverter for Unipolar and Bipolar Switching mode

A. Comparison with Sinusoidal Pulse Width Modulation Pulse Width Modulation is a bit different compared to the Sinusoidal Pulse Width Modulation(SPWM). In case of sinusoidal pulse width modulation, all the pulses are modulated individually. Each and every pulse is compared to a reference sinusoidal pulse and then they are modulated accordingly to produce a waveform which is equal to the reference sinusoidal waveform. Thus, sinusoidal pulse width modulation modulates the pulse width sinusoidally.[6] .

To eliminate the 3rd ,5th ,7th ,9th ,11th Harmonics and to perform fundamental magnitude control, If V01is the Fundamental value, the equations to be solved are the following. The anglesα1