EGH448 - Power Electronics Selective Harmonic Mitigation Assignment

Assignment Task

Project Summary

As some students intend to take EGH448 while staying overseas, this project has been designed so that it can be carried out individually and remotely. To that end, the project has been drafted to be more conceptual, and the students need to analyse, simulate, and report their observations in a way that is explained in this instruction manual. The necessary documents required for this project are as follows:

• Instruction Manual (that you are currently reading)
• MATLAB Simulink file and its initializing m-file
• Excel Record File
• Report Template

This instruction manual elaborates how to use the listed materials to complete this project. The project focuses on a specific selective harmonic mitigation technique known as the three-angle control scheme. To complete this project, the instructions, concepts, and analyses detailed in each section must be followed. Finally, the provided Excel file must be completed, and the achievements must be explained in the project report in the style and format provided in this instruction manual and in the report template.

The manual is organized as follows. The second section elaborates on the main principles of selective harmonic mitigation with three-angle control scheme. In the third section, the mathematical principles required for the numerical analysis of this project are explained. The fourth section illustrates how to use the provided MATLAB Simulink file to set the input variables and to collect the output results. In Section 5, the guidelines to generate and record data in the Excel file are provided. Section 6 provides some guidelines to write the report. Finally, the submission details are provided in Section 7.

Selective Harmonic Mitigation with Three-Angle Control Scheme

This project focuses on the principles of three-angle control technique to mitigate some specific harmonics in the output voltage of an H-bridge inverter [see Fig. 1] [1]. A generalized technique for harmonic elimination of a voltage-sourced inverter was first proposed in [2]. Although the selective harmonic mitigation (SHM) is usually used in multilevel converters, a crude version of SHM, the three- angle control scheme for harmonic mitigation is chosen for this project [3].

In this subsection, elaborate on the principles of the H-bridge converter, and how it can convert a DC voltage to an AC voltage. For this purpose, use some figures for the converter, its PWM gate signals and output voltage waveform (as provided in the figure below)

Using the Fourier transform of each individual sub-signal [see Fig. 4], the Fourier transform of the output signal is obtained as follows:

In this equation, is a function of (harmonic order) and (angle vector ]). Together with forms a four ariable function to selectively tune (or eliminate) different harmonics. Amongst these variables can be chosen as the target harmonic to be tuned. For example and can be used to control the amplitude of three different odd harmonics. If one needs to tune the amplitudes of the fundamental, third and fifth harmonics to  and respectively, from the equation, we can see that the following system of non-linear equations need to be solved.

In this equation, is a function of (harmonic order) and  (angle vector]). Together with forms a four variable function to selectively tune (or eliminate) different harmonics. Amongst these variables, can be chosen as the target harmonic to be tuned. For example, 

Numerical Analysis

This section introduces the mathematical principles required to carry out the project. Fourier transforms (explained earlier in Section 2), calculation of RMS values, total harmonic distortion (THD), active and apparent powers from RMS values of current and voltages, as well as power factors will be covered here. To start the analysis, the harmonic contents of the output voltage are broken down. Then we show how to calculate the RMS value of the output voltage mathematically. Similar steps are taken for the output current analysis. We use the RMS values of the output voltage and current to explain the power calculations. For example, assume that the obtained output voltage waveform has amplitude and angular characteristics for the first eight odd harmonic.

By performing the RMS calculations on the output waveform using the above equation, the of the output voltage is obtained as. It is worth noting that due to sharp edges in the waveform, high values for high order contents are seen in TABLE I. Approximating the output voltage RMS for the first eight odd harmonics may not be enough in certain situations. Having the RMS value of the output voltage and its fundamental ( | in Table I), the THD can be calculated as follows.

For the given example, the THD of the output voltage is The FT equation indicates that the output voltage only has odd harmonics. To find the respective current harmonics, the influence of each voltage harmonic on the output load impedance (where  is the fundamental frequency and is the harmonic order) needs to be considered. For example, the test student (Nikola Tesla) with an ID 9833333 receives the value of the load with the specifications of Rl= 833333

From Tables I and II, the harmonics of the output current can be extracted by dividing the harmonic contents of the output voltage by their respective impedance. Table III shows the obtained harmonic content using this method. The obtained output current waveform and its harmonic spectrum are shown in Figs. 7 and 8, 

MATLAB Simulink File

In this section, the principles necessary to complete the simulations of this project are explained:

• PWM Generator
• Power Circuitry (DC-Link Voltage, Power Converter, and Load)
• Data Acquisition
• Data Processing
• Measurements

Fig. 11 shows a virtual H-Bridge system (As seen in Fig. 1) with its multiple subsections within the MATLAB environment. The PWM generator subsection in this integrated system takes the three angles of the SHM technique and generates respective gate pulses for the power converter to generate the desired output voltage. With the use of the three-angle control scheme, the PWM generator subsection makes sure the power converter generates the chopped output voltage shown in Fig. 3. The R-L Load is connected across the output nodes [see nodes 1 and 2 in Fig. 11] of the power converter which synthesizes the output voltage using the supplied DC Link Voltage depending on gate signals from the PWM Generator subsection. In this assignment, the output signals of the Power Converter are analysed ⁵ . These signals are collected in the data acquisition subsection. RMS and power calculations of the obtained signals are performed by the data processing subsection. Additional necessary information required for the simulation can be observed in the measurement subsection.

Power Circuitry

The power circuitry subsection consists of a DC-link power supply with the voltage of a full-bridge inverter and an R-L load as shown in  resistance (????L) and inductance of this subsection are obtainable from the Excel file. If all parameters are correctly calculated and setup, the converter should generate an output voltage like that given in Fig

Data Acquisition

In this subsection, the electrical variables from the power circuitry subsection are measured by measurement units. This can be achieved by setting “Measurements” in R-L load menu to “Branch voltage and current” as shown in the right side of Fig. 14. By double clicking blocks in Part 3.A, window of the measurement unit appears with a list of “Available Measurements” which contains signals chosen earlier. By selecting any of these signals from the left side list and pressing button, that signal is inserted in the “Selected Measurements” list at the right side and activated as the output signal of the measurement block. In the Simulink file, this procedure has already been done for and  . The block in stores data from the chosen signals in the MATLAB Workspace to be used in the M-File. The processed RMS values of and are sent.

Data Processing

The Data Processing subsection outputs important information, such as the RMS values of the output voltage  and output current as shown in Fig. 16. This module also calculates the load power factor active power and the apparent power absorbed by the load. Students can analyse frequency content of a signal using either m-file code or the explained later. They must ensure that the figures are properly scaled. In the block , Fast Fourier Transform (FFT) analysis can be used to extract the harmonic content of the selected signal. Double- click on the and click on “FFT Analysis” as shown in Fig. 16 and the FFT analysis window appears as shown in Fig.

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