3) Consider that the boost DC-DC converter, discussed in problem #1, is to feed

Question

3) Consider that the boost DC-DC converter, discussed in problem #1, is to feed a single-phase full bridge inverter with a step-up transformer to supply 120 V at 60 Hz to a 230 W resistive load. The converter operates with bipolar SPWM where the triangular carrier has a frequency of 25 kHz and peak value of 5 V. A) Select a value for the amplitude modulation index (ma) of the inverter and a turns ratio for the transformer. B) Considering the expression presented below, select a corner frequency for a second-order LC low pass filter (LPF) so that the magnitude of the dominant harmonic across the load has a peak value of 3% of the peak value of the fundamental component. C) For a filter inductor of 1 mH, compute the value of the required capacitor filter. D) Compute the angle of the fundamental component of the current in the input of the LC filter, with respect to the fundamental voltage component. This can be obtained from the overall impedance of the LPF and load. E) Compute the magnitude of the second order current harmonic drawn from the boost converter, F) Repeat part B for the converter controlled with unipolar SPWM and compare that with the filter required for bipolar SPWM. Vout_h Vin h GaindBCamli -40dB/ Dece Gain- "Gain(dB)=2010g(Gain), logfh-log fres- Note: Vout h is the magnitude of the voltage harmonic across the load (output of the LPF) Vois the magnitude of the voltage harmonic of the DC-AC converter (input of the LPF), fi is the frequency of the dominant harmonic and J is the resonant frequency of the LPF

Explanation / Answer

With the improvement on performance and the reduction in price of digital controller, the digitally controlled high-frequency switching power converter has aroused much interest.[1] In a digitally controlled system, there is a delay of sampling and calculating, so one-step-delay control is often adopted.[2] Owing to the presence of one-step-delay and the switching nonlinearity, the digitally controlled switching power converter system becomes a strongly nonlinear system.[3] Digital sinusoidal pulse width modulation (SPWM) has received increasing attention in different applications in Hbridge inverters for renewable energy systems, ac motor drives and telecommunication systems.[4–6] The modulation strategy will influence the dynamics of the system significantly.[5–7] Thus, the performances of the different modulation schemes in a digitally controlled high-frequency switching power converter should be studied in depth. The bipolar SPWM (BSPWM) has been widely used in the digitally controlled H-bridge inverter system because of its simple implementation.[6–8] However, the number of output voltage pulses and the frequency of the lowest harmonic voltage, which can also be named equivalent switching frequency, in the unipolar double-frequency SPWM (UDFSPWM) are twice those in the BSPWM with the same switching frequency.[8–11] The advantage of this method is that the filter elements needed are much less due to the fact that the equivalent switching frequency of the output voltage is twice the switching frequency. Therefore, the UDFSPWM facilitates the choice of filter and has better output waveforms.[11,12] Conventionally, the comparison of the performance between BSPWM and UDFSPWM used is based on the FFT analysis,[10,12] which cannot be used to analyze the dynamics of the system and the underlying mechanism. Up to now, by establishing the discrete-time model of the system, the performances of the UDFSPWM and BSPWM have not been studied. Generally, the discrete-time model of a piece-wise smooth system can be obtained by ‘toggling’ the topological sequence in one switching period.[13–16] However, in some cases, the topological sequence in one switching period will be changed. This means that the exact discrete-time model of the system can be obtained by analyzing all possible discretetime models, which are obtained by using the state equation of the corresponding topological sequence. Therefore, a convenient method of establishing the discrete-time model of the piece-wise smooth system is presented in this paper. The rest of this paper is organized as follows. In Section 2 BSPWM and UDFSPWM in an H-bridge inverter system are outlined. In Section 3, by the presented convenient method of establishing the discrete-time model, the discrete-time models of an H-bridge inverter system, modulated by BSPWM and UDFSPWM, are obtained respectively. In addition, the performances of the two modulation strategies are compared in detail in Section 4. Circuit simulations and experimental measurements are shown in Section 5 to illustrate and verify the theoretical results. Finally, some conclusions are given in Section 6.

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