Daniel Hart Eletrônica de Potência (cap 8 Solucionário), Exercícios de Eletrônica de Potência

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CHAPTER 8 SOLUTIONS

4/24/ 8-1) 8-2)

c) PSpice results are consistent with parts (a) and (b). The current waveform reaches steady state after approximately 100 ms, corresponding to 5 time constants. Time 0s 40ms 80ms 120ms 160ms 200ms I(L) -4.0A 0A 4.0A 8.0A (158.333m,3.9485) (8.3333m,6.5486) 8-3)

n Vn Zn In,rms 1 331 29.3 8. 3 110 77 1. 5 66 127 0.

n Vn Zn In,rms 1 88.6 31.3 2. 3 29.5 61.8 0. 5 17.7 97.5 0. Using PSpice,

Using a restricted time interval of 33.33 ms to 50 ms to analyze steady-state current, the peak value is 8.26 A and the rms value is 4.77 A. The THD from the output file is 32%. Time 30ms 35ms 40ms 45ms 50ms I(R) RMS(I(R)) -10A 0A 10A 20A i(t) Peak rms (50.000m,4.7738) (35.134m,8.2603) Time 30ms 35ms 40ms 45ms 50ms I(R) V(A)/10 0

• 0 10 voltage^ (100^ V) current D3, D S3, S D1, D S1, S

n |Vn| Zn In,rms 1 90 12.5 5. 3 51.6 24.7 1. 5 4.43 39 0. 8-9)

From Eq. (8-22), Using the FFT function in Probe, the n = 7 harmonic is absent. 8-12) Letting T = 360 seconds and taking advantage of half-wave symmetry,

The VPWL_FILE source is convenient for this simulation. A period of 360 seconds is used, making each second equal to one degree. A transient simulation with a run time of 360 second and a maximum step size of 1m gives good results. The FFT of the Probe output confirms that the 3 rd^ and 5th^ harmonics and their multiples are eliminated. 0 0 30 0 30.01 1 54 1 54.01 0 66 0 66.01 1 114 1 114.01 0 126 0 126.01 1 150 1 150.01 0 210 0 210.01 - 234 - 234.01 0 246 0 246.01 - 294 - 294.01 0 306 0 306.01 - 330 - 330 0 360 0

n 1 3 5 7 9 Vn 149.5 0 -2.79 -3.04 -14. 8-15) α 1 α 2 α 3 Mi 15 25 55 0. 20 30 40 0. 10 30 50 0. 10 30 70 0. 8-16) This inverter is designed to eliminate harmonics n = 5, 7, 11, and 13. The normalized coefficients through n = 17 are n Vn/Vdc 1 4. 3 -0. 5 0.0057 ≈ 0 7 -0.0077 ≈ 0 9 -0. 11 0.0043 ≈ 0 13 -0.0078 ≈ 0 15 -0. 17 0. The coefficients are not exactly zero for those harmonics because of rounding of the angle values.

From Table 8-3, n Vn/Vdc Vn Zn In=Vn/Zn 1 0.8 76.8 33.3 2. mf 17 0.82 78.7 157 0. mf - 2 15 0.22 21.1 139 0. mf + 2 19 0.22 21.1 175 0.

The circuit “Inverter Bipolar PWM Function” is suitable to verify the design results. The parameters are modified to match the problem values. Transient Analysis and Fourier Analysis are establish in the Simulation Setup menu: The output file contains the THD of the load current, verifying that the THD is less than 10%. TOTAL HARMONIC DISTORTION = 9.387011E+00 PERCENT

Example solution: 8-22) Example solution:

Bipolar mf = 21: Bipolar mf = 41:

Unipolar, mf = 10: 8-24)