CHAPTER 5 PERFORMANCE EVALUATION OF SYMMETRIC H- BRIDGE MLI FED THREE PHASE INDUCTION MOTOR

Transcription

1 85 CHAPTER 5 PERFORMANCE EVALUATION OF SYMMETRIC H- BRIDGE MLI FED THREE PHASE INDUCTION MOTOR 5.1 INTRODUCTION The topological structure of multilevel inverter must have lower switching frequency for each switching device. Power switches used in the multilevel inverter must be capable of withstanding very high input voltage for medium and high power applications. Modified phase disposition sinusoidal pulse width modulation technique uses the high switching frequency for switching operation. Modified H-bridge inverter proposed with MPD-SPWM technique may have lower efficiency than the inverter operating at a low switching frequency. This chapter describes the operation of symmetric cascaded H-bridge and modified H-bridge multilevel inverter with selective harmonic elimination technique. Fourier analysis of symmetric multilevel inverter output voltage wave form is also derived. Switching angles are calculated using Newton Raphson method and Genetic Algorithm and are tabulated in section 5.3.The performance of three phase cascaded H-bridge and modified H-bridge seven level inverter with equal DC source is simulated using MATLAB/Simulink software and is compared. Harmonic analyses of three phase symmetric H-bridge and modified H-bridge seven level inverter are also presented.

2 SYMMETRIC CASCADED H- BRIDGE MLI TOPOLOGY Symmetric cascaded H-bridge multilevel inverter consists of series connected H-bridge inverter cells. The general function of a multilevel inverter is to synthesize a desired voltage from separate DC sources, which may be obtained from solar cells, fuel cells, batteries or ultra-capacitors (Leon Tolbert et al 2002, Venkatachalam Kumar Chinnaiyan et al 2013). The advantage of this topology is that the modulation technique, control algorithm and protection requirements of each bridge are modular (Ebrahim Babaei et al 2012). Unlike the diode clamped and flying capacitor topologies, in this topology isolated DC sources are required for each cell. If all the DC voltage sources are equal then the inverter is known as symmetric multilevel inverter. Figure 5.1 Single phase structure of symmetric cascaded H-bridge seven level inverter

3 87 Table 5.1 Switching table of symmetric cascaded H-bridge seven level inverter Switches Voltage Levels 0 0 * S S S S S S S S S S S S Single phase structure of cascaded seven level inverter with three H-bridges is shown in Figure 5.1 and its switching table is given in Table 5.1. A separate DC source is connected to each H-bridge of a single phase multilevel inverter. AC output voltage of each level is series connected in such a way that the synthesized voltage waveform is the sum of the H-bridge outputs. V 1, V 2 and V 3 are respectively the output voltages of the first H-bridge, second H-bridge and third H-bridge. Output voltage of this cascaded multilevel inverter is denoted in Equation (5.1). V 0 = V 1 + V 2 + V 3 (5.1)

4 88 The effective number of output voltage levels (N L ), number of switches (N S ) and the maximum possible output voltage (V omax ) in symmetric multilevel inverter are related to the number of DC voltage source (h) are given in Equations (5.2) to (5.4). N L = 2h+1 (5.2) N S =4h (5.3) V omax = hv dc (5.4) For symmetric topology using (5.2) and (5.3), the relation between number of output voltage levels and number of switching devices can be obtained as Equation (5.5). N L = (N S -2h) +1 (5.5) 5.3 FOURIER ANALYSIS OF SYMMETRIC MLI OUTPUT VOLTAGE WAVEFORM For a symmetric multilevel inverter, the switching angles at fundamental frequency are obtained by solving non-linear transcendental equations in such a way that the fundamental voltage is obtained as desired and specific lower order harmonics are eliminated (Ebrahim Babaei et al 2013). The output voltage waveform of a seven level cascaded H-bridge inverter is shown in Figure 5.2. It is possible to define three switching angles in correspondence with the rising edges which describe the wave due to its symmetrical properties. The output voltage waveform of seven level inverter is odd and quarter waveform symmetric, with three positive steps of equal magnitude each, V dc /3. Fourier series for a periodic function V( t) is expressed in Equation (5.6).

5 89 ( ) = + cos( ) + sin( ) (5.6) Figure 5.2 Output voltage waveform of symmetric cascaded H-bridge seven level inverter Sinusoidal function is odd. The Fourier series for odd functions contain only sine terms. Due to quarter wave symmetry a 0 = a n = 0 for all n. The constant b n is given in Equation (5.7). = sin( ) (5.7) V ( t) can therefore be expressed in Equation (5.8). ( ) = sin( ) (5.8) Let = t.

6 90 The constant b n is determined in equations (5.9) to (5.11). = ( ) sin( ) (5.9) = sin( ) + sin( ) + sin( ) (5.10) = [ ( ) + ( ) + ( )] (5.11) The periodic function V( t) is obtained by substituting Equation (5.11) in (5.8) which is given in equation (5.12) ( ) = [ ( ) + ( ) + ( )],, sin( ) (5.12) Due to quarter wave symmetry along x-axis, the even harmonic voltages are absent. 1, 2 and 3 are the switching angles to be calculated and they must satisfy the condition 0< <( /2). For desired fundamental voltage V 1, determination of switching angles 1, 2 and 3 is possible. So V( t) = V 1 sin( t) and specific lower order harmonics are equal to zero. The peak value of the fundamental output voltagev 1 should be controlled. Fifth and seventh harmonics should be eliminated. The resulting harmonic equations are expressed in Equations (5.13) to (5.15). = [ ( ) + ( ) + ( )] = (5.13) = [ (5 ) + (5 ) + (5 )] = 0 (5.14) = [ (7 ) + (7 ) + (7 )] = 0 (5.15) Here the third harmonic has not been eliminated because the triplen harmonics can be automatically cancelled in the line to line voltages for

7 91 balanced three phase systems. Therefore, the triplen harmonics are not chosen for elimination in the phase voltage. These harmonic voltages (5.13) to (5.15) are transcendental equations (Carlo Cecati et al 2010). The fundamental voltage and the maximum obtainable voltage are related via the modulation index. Modulation index m a is defined as the ratio of fundamental voltage V 1 to the maximum obtainable voltage V 1max. The maximum fundamental voltage (V 1max = 4V dc /3 ) is obtained when all the switching angles are zero. The expression for m a is given in Equation (5.16). = (5.16) Where s is the number of switching angles which also equals the number of DC sources. By substituting the value of m a from the equation (5.16) in Equations (5.13) to (5.15), the following transcendental equations are obtained. [ ( ) + ( ) + ( )] = 3 (5.17) [ (5 ) + (5 ) + (5 )] = 0 (5.18) [ (7 ) + (7 ) + (7 )] = 0 (5.19) Equations (5.17) to (5.19) represent a system of three transcendental equations. For given values of m a from 0 to 1, complete and all possible solutions for (5.17) to (5.19) are required with minimum computational burden and complexity. One approach to get the solution for the set of nonlinear transcendental equations is by applying an iterative method such as the Newton Raphson method. To select the set generating the lowest harmonic distortion, the solution sets are examined for their corresponding total harmonic distortion.

8 Algorithm for Newton Raphson Method to Find the Switching Angles of Symmetric H-Bridge Seven Level Inverter The set of nonlinear transcendental equations can be solved by an iterative method such as Newton Raphson (NR) method. If the number of equations increases, the time and the amount of calculations to obtain the conduction angles also increase. The step by step procedure to solve the nonlinear transcendental equations are as follows. Step 1: Define a switching angle matrix. All switching angles must lie within 0 to ( /2) = [ ] (5.20) Step 2: Specify the value of modulation index m a and the number of voltage level N L Step 3: Define a non-linear matrix F as given below: = cos( ) + cos( ) + cos( ) cos(5 ) + cos(5 ) + cos(5 ) cos(7 ) + cos(7 ) + cos(7 ) (5.21) Step 4: Define the corresponding harmonic amplitude matrix as = ( ) 0 0 (5.22)

9 93 Step 5: Define dervf which is the derivative of the matrix F with respect to x 1, x 2 and x 3. Step 6: Initial values for the switching angles are entered as 0 = [ ] (5.23) Step 7: Solve for F and dervf at the initial values of 0 As on linearizing the Equation (5.22), we get + ( ) = (5.24) Where DelX is the change in the switching angle. Step 8: Solve for DelX from Equation (5.24) as = ( ) ( ) (5.25) Step 9: Update the value of the switching angle. = + (5.26) Step 10: The process is repeated until the desired condition is satisfied. The above equations are solved with N L =7 for various modulation indexes. Fifth and seventh harmonic values are calculated for the switching angles 1, 2 & 3 and presented in Table 5.2. It is observed that the switching angle values given in Table 5.2 are greater than 0 and less than /2 radians.

10 94 Table 5.2 Switching angles of symmetric H-bridge seven level inverter using NR method Modulation Switching Angles in radians Magnitude of 5 th Harmonic Magnitude of 7 th Harmonic Index,m a (V 5 ) (V 7 ) Genetic Algorithm to Calculate Optimum Switching Angles of Symmetric H-Bridge Seven Level Inverter Genetic Algorithm (GA) was developed based on the Darwinian s principle of the survival of the fittest and the natural process of evolution through reproduction. A solution to a given problem is represented in the form of a string called chromosome, consisting of a set of elements called genes that hold a set of values for the optimization variables. The fitness of each chromosome is determined by evaluating it against an objective function. To simulate the natural survival of the fittest process, best chromosomes exchanges information to produce offspring chromosomes. The offspring solutions are then evaluated and used to evolve the population if they provide better solutions than weak population members. Usually, the process is continued for a large number of generations to obtain a best fit

11 95 solution. Four main parameters that affect the performance of GAs are population size, number of generations, crossover rate and mutation rate. Larger population size and large number of generations increase the likelihood of obtaining a global optimum solution, but substantially increase processing time. In crossover, the exchange of parent s information produces an offspring. As opposed to crossover, mutation is a rare process that resembles a sudden change to an offspring. This can be done by randomly selecting one chromosome from the population and then arbitrarily changing some of its information. The benefit of mutation is that it randomly introduces new genetic material to the evolutionary process, perhaps thereby avoiding stagnation around local minima. Genetic algorithm is a computational model that solves optimization problems by imitating genetic processes and the theory of evolution. It imitates biological evolution by using genetic operators referred to as reproduction, crossover, mutation etc. The GA is simple and applicable to the harmonic problems with any number of voltage levels, without the extensive derivation of analytical expressions for both eliminating and minimizing harmonics. The steps for formulating a problem and applying GA are as follows. Step 1: Find the number of variables specific to the problem; this number will be the number of genes in a chromosome. In this application, the number of variables is the number of controllable switching angles which is the number of H-bridges in a symmetric cascaded multilevel inverter. A seven level inverter requires three switching angles. Thus each chromosome for this application will have three switching angles 1, 2 & 3.

12 96 Step 2: Set a population size and initialize the population. Higher population might increase the rate of convergence but it also increases the execution time. The selection of an optimum-sized population requires some experience in GA. The population in this work has 20 chromosomes each containing three switching angles. The population is initialized with random angles between 0 and /2 taking into consideration the quarter wave symmetry of the output voltage waveform. Step 3: The most important parameter in GA is the cost function to evaluate the fitness of each chromosome. The objective of this study is to minimize specified lower order harmonics. Therefore the cost function has to be related to these harmonics. In this work, the fifth and seventh harmonics at the output of a seven level inverter has to be minimized or eliminated. Then the cost function (f) can be selected as the Equation (5.27) (,, ) = (5.27) Step 4: For each chromosome, a multilevel output voltage waveform is created using the switching angles and the required harmonic magnitudes are calculated using Fast Fourier Transform (FFT) techniques. Step 5: In this case, The fitness value (FV) is calculated for each chromosome insertion. (,, ) = (5.28) Step 6: The switching angle set producing the maximum FV is the best solution of the first iteration.

13 97 Step 7: The GA is usually set to run for a certain number of iterations (100 in this case) to find an answer. After the first iteration, FVs are used to determine new offspring. These go through crossover, mutation operations and a new population is created which goes through the same cycle starting from FV evaluation. The flow chart for calculation of switching angles is shown in Figure 5.3. Start Find No. of Variables Set population size Evaluation of fitness If No. of Iterations < 100 No Yes Reproduction Cross over Mutation No If cost function <1 Yes Stop Figure 5.3 Flow chart for calculation of switching angles The MATLAB code is written for achieving switching angle. The GA program is written using MATLAB/Simulink software. The parameters

14 98 of GA such as crossover and mutation probability, population size and number of generations are usually selected as common values given in the literature. It is observed that a value of is ideal for population size; a lesser value increases the number of iterations. The population size of GA is 20. The number of iterations is rst xed at 100, and increased to 1000 in steps of 100. In most of the operating points, an optimum solution is obtained around iterations. The probability of mutation is rst xed at 0.1. An increased value yields poor results. In addition, the number of iterations for each run is 100 and it is assumed as a termination criterion. The values of calculated switching angles, magnitudes of 5 th and 7 th harmonics are presented in Table 5.3. Comparing the value of 5 th and 7 th harmonic given in Table 5.2 and Table 5.3, magnitude obtained from the GA method is very closer to zero. It shows the superiority of the GA optimization method when compared to the NR method. Table 5.3 Switching angles of symmetric H-bridge seven level inverter using GA Modulation index Switching Angles in Radians Magnitude of 5 th Harmonic (V 5 ) Magnitude of 7 th Harmonic (V 7 )

15 SIMULATION STUDY The simulation of three phase symmetric cascaded H-bridge and modified H-bridge seven level inverter fed three phase induction motor are modelled in MATLAB/Simulink environment. All the switches in the simulations are considered to be ideal. The DC voltage sources used in the simulation studies are separate DC sources. These DC voltage sources are available via distributed energy resources like photovoltaic panels, fuel cells and ultra- capacitors in practice. If the available source is an AC source then the required DC voltage sources can be obtained by rectifiers fed by a transformer with multiple secondary windings. Figure 5.4 Simulation diagram of three phase symmetric cascaded H-bridge seven level inverter In this work, the fundamental switching frequency scheme is used. Voltage of each switch is limited to the value of DC source in the case of symmetrical type.simulation is carried out using the switching angles shown in Table 5.3. The simulation parameters of the three phase cascaded

16 100 multilevel inverters are furnished in Table 5.4. The simulation diagram of three phase cascaded H-bridge seven level inverter fed induction motor is shown in Figure 5.4. Single phase structure of the cascaded H-bridge seven level inverter is shown in Figure 5.5. Twelve switches are used to obtain seven level output voltage for each phase.the frequency of output voltage is 50Hz. Figure 5.5 Subsystem of symmetric cascaded H-bridge seven level inverter for phase A

17 101 Table 5.4 Simulation parameters of symmetric cascaded H-bridge seven level inverter Description Parameter Value DC Supply DC Voltage Sources 107V Frequency Switching Frequency 50Hz Three phase Squirrel cage induction motor Load Rated Voltage Rated Current Rated Power Rated Speed Rated Torque 400V 10A 5.4HP(4.03KW) 1430rpm 26.9 N-m Stator Resistance Rotor Resistance Number of Poles 4 Moment of Inertia (J) kg.m 2 Friction co-efficient (B) N-m-s Results and Discussions of Symmetric Cascaded H-bridge Seven Level Inverter The switching pulse waveform for each switch of symmetric cascaded H-bridge is presented in Figure 5.6. The switching pulses are given in such a way that the switches connected in the same arm should not be turned ON at the same time. The simulation results of phase voltage for each phase are shown in Figure 5.7. It can be seen that each phase is phase shifted by 120 o. The Figure 5.7 clearly shows that all of the desired voltage levels are generated.

18 102 (a) Switching pulse waveform for switches S 1 -S 4 (b)switching pulse waveform for switches S 5 -S 8

19 103 (c)switching pulse waveform for switches S 9 -S 12 Figure 5.6 Switching pulse waveform of symmetric cascaded H-bridge seven level inverter Figure 5.7 Phase voltage waveform of symmetric cascaded H-bridge seven level inverter

20 104 Phase current of the induction motor when it is fed by three phase cascaded H-bridge seven level inverter is shown in Figure 5.8. From Figure 5.7 and Figure 5.8, it is clear that the output current waveform is smoother than the output voltage waveform. It is evident from Figure 5.8 that the currents fluctuate up to 0.1 sec and after that they attain a constant value. The extremely high value of current at the starting points of the simulation is due to the fact that before the rotor gains any type of momentum or speed, the stator acts as a very high power load. The fluctuations in the stator current die out at about 0.15 sec and the currents attain a fairly constant value to reach their full speed of 1430 rpm. Figure 5.8 Phase current waveform of symmetric cascaded H-bridge seven level inverter Figure 5.9 depicts the electromagnetic torque characteristic of the induction motor supplied by three phase cascaded H-bridge seven level inverter. Torque has an oscillating characteristic at the starting instant. A nearly constant electromagnetic torque is obtained after a time of 0.65 sec. It is observed that as the stator currents settle to a constant value, the

21 105 electromagnetic torque also reaches a fairly constant value. Torque reaches a mean value of about 26.9 N-m at steady state. Figure 5.9 Electromagnetic torque of three phase induction motor fed by symmetric cascaded H-bridge seven level inverter Figure 5.10 shows the speed characteristic of the induction motor when it is fed by cascaded H-bridge seven level inverter. The rated speed of 1430 rpm is reached at 0.4 sec. The speed curve shows that the motor is started from stall and very quickly reaches its speed of about 1430 rpm at 0.45 sec. The speed then settles down to a fairly constant value at its rated speed. Observation also shows that the stator current is quite noisy. The noise introduced by the inverter is also observed in the electromagnetic torque waveform shown in the Figure 5.9. However the motor inertia prevents this noise from appearing in the motor speed waveform.

22 106 (a) Rotor speed at no load (b) Rotor speed at 50% of full load (c) Rotor speed at full load Figure 5.10 Rotor speed of three phase induction motor fed by symmetric H-bridge seven level inverter

23 107 Settling time of the three phase induction motor operating at different loading is given in Table 5.5. From the table 5.5, it is observed that the settling time increases with load. Table 5.5 Settling time of symmetric cascaded H-bridge seven level inverter fed induction motor settling time for different loading conditions Load Settling Time No load 0.18s 50% of load 0.2s Full load 0.45s Line voltage waveform is taken to determine the voltage THD of the inverter. The simulation results of line voltages and their corresponding harmonic spectrum are presented in the Figure 5.11 and Figure From the normalized harmonic analysis shown in Figure 5.12, it can be seen that the magnitudes of lower order harmonics are very low and the magnitudes of higher order harmonics are nearly equal to zero. Figure 5.11 Line voltage waveform of symmetric cascaded H-bridge seven level inverter

24 108 (a) Harmonic analysis of line voltage V AB (b) Harmonic analysis of line voltage V BC (c) Harmonic analysis of line voltage V CA Figure 5.12 Harmonic analysis of line voltages for symmetric cascaded H-bridge seven level inverter

25 109 The simulation results of line currents and their corresponding harmonic spectrum of the symmetric seven level inverter are presented in the Figure 5.13 and Figure Figure 5.13 Line current waveform of symmetric cascaded H-bridge seven level inverter From the harmonic analysis shown in Figure 5.14, it can be viewed that the magnitude of 5 th and 7 th harmonics are eliminated and the magnitude of higher order harmonics are minimized. Triplen harmonics are cancelled automatically in three phase system. THD contents of line currents measured are 3.15%, 3.15% and 3.17% respectively.

26 110 (a) Harmonic analysis of line current I A (b) Harmonic analysis of line current I B (c) Harmonic analysis of line current I C Figure 5.14 Harmonic analysis of line current for symmetric cascaded H-bridge seven level inverter

27 Results and Discussions of Modified H-bridge Seven Level Inverter Switching pulses of modified H-bridge seven level inverter are produced using selective harmonic elimination technique. These switching patterns are given in Figure All the switching devices operate at fundamental frequency. It can be seen that all the switches are turned ON and OFF very few times. (a) Switching pulse waveform for switches S 1 -S 6 (b) Switching pulse waveform for switches S 8 -S 10 Figure 5.15 Switching pulse waveform of modified H-bridge seven level inverter

28 112 The simulation result of level generation part when it is operated by fundamental frequency SHE method is shown in Figure This is the input voltage of the fundamental frequency polarity generation part. Figure 5.16 Three phase voltage waveform of level generation part of modified H-bridge seven level inverter Figure 5.17 Three phase voltage waveform of modified H-bridge seven level inverter

29 113 Output of the level generation part is fed to the polarity generation part to produce the desired seven level output voltage. The simulation result of phase voltage is shown in Figure It can be seen that each phase is phase shifted by 120 o. Figure 5.17 shows that all of the desired voltage levels are generated using the modified multilevel inverter. Stator current of the induction motor when it is fed by three phase modified H-bridge seven level inverter is given in Figure From Figure 5.17 and Figure 5.18, it is clear that the output current waveform is smoother than the output voltage waveform. It is evident from Figure5.18 that the currents fluctuate up to 0.1 sec and after that it reach a constant value. The extremely high value of current at the starting points of the simulation is due to the fact that before the rotor gains some speed, the motor acts like a transformer with short circuited secondary winding. The fluctuations in the stator current die out at about 0.15 sec and the currents attain fairly constant value at the rated speed of 1430 rpm. Figure 5.18 Phase current waveform of modified H-bridge seven level inverter

30 114 Figure 5.19 describes the electromagnetic torque characteristic of the induction motor when supplied by three phase modified H-bridge seven level inverter. At starting instant, the torque has an oscillating characteristic. A nearly constant electromagnetic torque is obtained after a time of 0.35 sec. It is observed that as the stator currents settle to a constant value, the electromagnetic torque also attains a fairly constant value. Torque attains a mean value of about 26.9N-m at steady state. Figure 5.19 Electromagnetic torque of three phase induction motor fed by modified H-bridge seven level inverter Figure 5.20 shows the speed characteristic of the induction motor when it is fed by modified H-bridge seven level inverter. Rated speed of 1430 rpm is reached at 0.35 sec. The speed curve shows that the motor is started from stall and very quickly reaches its rated speed of about 1430 rpm at 0.35 sec. The speed then settles down to a fairly constant value at its rated speed. Observation also shows that the stator current is quite noisy. The noise introduced by the inverter is also observed in the electromagnetic torque waveform shown in the Figure However the motor inertia prevents this noise from appearing in the motor speed waveform.

31 115 (a) Rotor speed at no load (b) Rotor speed at 50% of full load Figure 5.20 (c) Rotor speed at full load Rotor Speed of three phase induction motor fed by modified H-bridge seven level inverter

32 116 Settling time of the three phase induction motor operating at different loading is tabulated in the Table 5.6. For the increase in the load, settling time also increases. Table 5.6 Settling time of modified H-bridge seven level inverter fed induction motor for different loading conditions. Load Settling Time No load 0.18s 50% of full load 0.2s Full load 0.25s Figure 5.21 Line voltage waveform of modified H-bridge seven level inverter The simulation results of line voltages and their corresponding harmonic spectrum of the modified inverter are presented in Figure 5.21 and Figure It can be observed from the Figure 5.22 that the magnitude of 5 th and 7 th harmonics are eliminated as expected and the magnitude of higher order harmonics are nearly equal to zero.

33 117 (a) Harmonic analysis of line voltage V AB (b) Harmonic analysis of line voltage V BC (c) Harmonic analysis of line voltage V CA Figure 5.22 Harmonic analysis of line voltages for modified H-bridge seven level inverter

34 118 From the harmonic analysis of line voltage waveform, it is seen that the triplen harmonics are cancelled automatically in three phase system. It also shows that the THD content of all the line voltages are 6.02%, 6.02% and 6.03% which are similar to the symmetrical cascaded H-bridge seven level inverter. The same performance is achieved using the modified topology with less number of switches. The simulation results of line current and their corresponding harmonic spectrum of the modified inverter when fed by fundamental frequency SHE scheme are presented in Figure 5.23 and Figure Figure 5.23 Line current waveform of modified H-bridge seven level inverter From the harmonic analysis shown in Figure 5.24, it can be viewed that the magnitude of 5 th and 7 th harmonics are eliminated as expected and the magnitude of higher order harmonics are nearly equal to zero. It is also observed that the triplen harmonics are cancelled automatically in three phase system. As in the symmetrical cascaded H-bridge seven level inverter, THD content of line currents measured are 3.16%, 3.16% and 3.15%. It is concluded from the above observation that the same performance is achieved using the modified topology with less number of switches.

35 119 (a) Harmonic Analysis of line current I A (b) Harmonic Analysis of line current I B (c) Harmonic Analysis of line current I C Figure 5.24 Harmonic analysis of line current for modified H-bridge seven level inverter

36 Performance Analysis between Symmetric Cascaded and Modified H-Bridge Seven Level Inverter The performance parameters of symmetric cascaded and modified H-bridge seven level inverter operated by low frequency SHE method are given in Table 5.7. Modulation index of 0.8 is taken to calculate the performance parameters of both the topologies. From Table 5.7, it can be seen that the calculated parameters match with the simulated parameters. Table 5.7 Performance parameters of symmetric cascaded and modified H-bridge seven level inverter Phase Voltage Analysis Line Voltage Analysis Parameters Calculated Simulated (CHMLI) Simulated (MHMLI) Calculated Simulated (CHMLI) Simulated (MHMLI) THD (%) V 1 (Volts) WTHD (%) DF (%) HF 3 (%) HF 5 (%) HF 7 (%) HF 9 (%) HF 11 (%) HF 13 (%) HF 15 (%) HF 17 (%) HF 19 (%) LOH (>3%) 9 th 9 th 9 th 9 th 13 th 13 th

37 121 The total harmonic distortion in three phase system is less than the single phase system. The lower order harmonic in the single phase system is the 9 th harmonic. In three phase system, the triplen harmonics get cancelled automatically. So the lower order harmonic in the three phase system for both the topologies is the 13 th harmonic. From the above comparative analysis, it is concluded that the same performance is achieved using the modified topology with less number of switches. But the fundamental line voltage of the modified H-bridge is less than the cascaded H-bridge topology. 5.5 SUMMARY In this chapter, a detailed analysis of symmetrical cascaded and modified H-bridge seven level inverter is presented. Fourier analysis of seven level output voltage is derived. The nonlinear transcendental equations obtained by the Fourier analysis are solved by NR method and GA optimization method. GA based solution of switching angles give minimum THD in the output voltage waveform when compared with the conventional Newton Raphson method. The designed simulation model is presented to validate the performance of three phase symmetrical cascaded and modified H-bridge seven level inverter fed induction motor.