ELEN435_W10Lab_Anderson

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American Military University *

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435

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Electrical Engineering

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Dec 6, 2023

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Course Lab 7: Inverters: Converting DC to AC Part II Submitted by: William Anderson Course: ELEN435 Instructor: James Carmichael Date Submitted: 11/09/2023 Exercises Completed: Power Electronics by Daniel W. Hart Chapter 8 Exercise 8.18. Abstract: The experiment performed was done in order to understand the design of a bipolar inverter with an RL load and how to find the amplitude modulation and frequency modulation ratio and use them to calculate other values such as the Total Harmonic Distortion or THD.

Introduction: Using Matlab this lab demonstrates how the design of aPWM output inverter can be used to calculate the amplitude modulation ratio and THD in a circuit given the RL load, frequency, output voltage, frequency modulation ratio, and DC power supply. Problem Statement: Problem 8.18 states, “The dc source supplying an inverter with a bipolar PWM output is 96 V. The load is an RL series combination with R = 32 Ω and L = 24 mH. The output has a fundamental frequency of 60 Hz. (a) Specify the amplitude modulation ratio to provide a 54-V rms fundamental frequency output. (b) If the frequency modulation ratio is 17, determine the total harmonic distortion of the load current.” Equipment/Supplies: For this lab the supplies needed were my Acer Laptop (Windows 11) to run the Matlab software. All components were calculated, but are listed below for assistance in understanding what is required. Materials: 1 96 Volt DC power source, 1 24 milliHenry inductor, a 32 Ohm resistor, and an output frequency of 60 Hertz. Hand Calculations: First we are given a DC source voltage of 96 Volts, a RL load with R = 32 Ohms and L = 24 milliHenry, and an output frequency of 60 Hz as well as an output RMS voltage of 54 Volts, and a frequency modulation ratio of 17. For part a we are given the simple task of finding the amplitude modulation ratio. This is found with the equation ma = V 1 Vdc = √ ❑ ❑ For part b we are given the frequency modulation ratio and have to figure about what the THD is. Since we are given the frequency modulation ratio we can shorten the summation to the I15, I17, and I19 values.

First we need to understand how to calculate the In values these are calculated by the equation ¿ = Vn Zn so for I1 we can use I 1 = 76.368 √ ❑ We must also convert this to RMS so 2.297/ √ ❑ . Now given the amplitude of modulation of 0.8 for n = 1 we can use Table 8-3 to find the amplitude modulation ratio for 17 is 0.82 and the amplitude modulation ratio for 15 and 19 is 0.22. We can then multiply each of these values by 96 to get a V17 = 78.72, V15 = V19 = 21.12. To get the new frequencies we can simply multiply the 60 Hz by the new n to get f15 = 900, f17=1020, and f19 = 1140. We can then plug these values into the above equation to get I17 = 0.03, I15 = 0.01, and I19 = 0.006. Now for THD we can use THD = √ ❑ ❑ Methods: Due to having frequent issues with building these circuits in Multisim. I have decided to use Matlab for this experiment. 1. Open a new Live Script. 2. Set a variable for the voltage source equal to 96 volts. 3. Set a variable for the frequency 1 equal to 60 Hertz. 4. Set a variable for the inductor equal to 24 milliHenrys. 5. Set a variable for the resistor equal to 32 Ohms. 6. Set a variable for the output voltage equal to 56 Volts. 7. Set a variable for frequency modulation ratio equal to 17. 8. Set a variable for V1 equal to √ ❑ 9. Set a variable for amplitude modulation ratio 1 equal to V 1 Vdc 10. Set a variable for I1 equal to V 1 √ ❑ 11. Set a variable for I1 RMS equal to I1/ √ ❑ . 12.Set a variable for amplitude modulation 15 and 19 equal to 0.22

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13.Set a variable for amplitude modulation 17 equal to 0.82. 14.Set a variable for frequency 15 equal to 15*f1 15.Set a variable for frequency 17 equal to 17*f1 16.Set a variable for frequency 19 equal to 19*f1 17.Set a variable for V17 equal to ma17*Vdc. 18.Set a variable for V15 and V19 equal to ma15/19*Vdc 19. Set a variable for I15 equal to V 15 √ ❑ 20. Set a variable for I17 equal to V 17 √ ❑ 21. Set a variable for I19 equal to V 19 √ ❑ 22. Set a variable for THD equal to √ ❑ ❑ Results: Experiment 8.18 Matlab: The code was built as seen below in Figure 1 Figure 1: Experiment 8.18 Matlab Code Screenshot

The output values can be seen in Figure 2. Figure 2: Experiment 8.18 Matlab Output Screenshot

This completes the Matlab portion of Experiment 8.18.

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Discussion: As can be seen in the experiment above the values calculated were slightly off due to rounding.. I believe the computer calculations are much better due to providing more accuracy than the hand calculations with the hand calculations being rounded at 3 decimal places. Using a computer helps give confidence as well as help test various configurations with very minimal effort such as a changing of modulation or even of the load and/or output to help try out various circuits or even test to ensure that proper values are met. References: Dr, D. W. H. P. (2010). Power Electronics . McGraw-Hill Education.