Comments, with reply, on "An algebraic algorithm for microcomputer-based (direct) inverter pulsewidth modulation" by Y.H. Kim and M. Ehsani

Amplitude distortion compensation for voltage source dc/ac inverters

“…Kim and Ehsani (1987) also proposed a very similar algebraic algorithm for DPWM but assuming a constant utilization factor, which is the ratio of the maximum value of the desired output voltage to the input dc voltage source. However, Bowes (1988) raised several objections to Kim's paper and clearly explain that most of Kim's algorithms are not new and have been fully described previously in his papers (Bowes, 1975(Bowes, , 1981. Although it is not mentioned in Kim's or Bowes's conclusion, it is believed that the amplitude distortion error caused by the input dc voltage variation can be eliminated by modifying the computer program properly.…”

Relationship between space-vector modulation and three-phase carrier-based PWM: a comprehensive analysis [three-phase inverters]

“…1, in the linear mode, for carrier-based twolevel PWM modulators, we have (1) where and are the positive and the negative pulsewidths in the th sampling interval, respectively; is the normalized amplitude of modulation signal in the th sampling interval ( ); and the normalized peak value of the carrier signal is 1. Equation (1) is usually referred to as the Equal Voltage-Second principle [14], [18], [24]. Fig.…”

“…3 Comparing (14) with (22) leads to the relationship between length coefficient of and modulation index of the threephase carrier-based PWM as follows (23) As shown in Fig. 3, we have (24) Thus, and can be expressed as (25) Therefore, according to (21) and (25), bidirectional transformations between fundamental signals in the plane and active space vectors in the plane are derived as follows: Equations (26) and (27) are the well-known 3/2 transformation and 2/3 transformation, respectively. Because of the symmetry of space sectors, the above transformations can be extended to all other five sectors.…”