  Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) is an
important technique to solve PWM problems, which control the output voltage of
an inverter via selecting appropriate switching angles. Based on the Rational
Univariate Representation (RUR) theory for solving polynomial systems, the
paper presents an algorithm to compute a "nearly parametric" solution to a
SHEPWM problem. When the number of switching angles N is fixed, a "nearly
parametric" solution can be considered as functions of the modulation index m.
So we can adapt the amplitude of the output voltage with the same source
voltage by changing the modulation index. When m is given as a specific value,
complete solutions to the SHEPWM problem can be obtained easily using
univariate polynomial solving. Compared with other methods, m is considered as
a symbolic parameter for the first time, and this can help avoid totally
restarting when m changes. The average time for computing complete solutions
associated to 460 modulation indexes based on a "nearly parametric" solution
when N=5 is 0.0284s, so the algorithm is practical. Three groups of switching
angles associated to N=5, m=0.75 is simulated in MATLAB, and it verifies the
algorithm's correctness.
