Residual harmonics in voltage unbalanced power systems

The analysis of residual harmonics requires combining linear and nonlinear analysis into a computer algorithm. The mathematical techniques are to apply state space methods to solve the nonlinear loads such as converters in a time domain format, analyze the resulting waveform with a Fourier analysis to convert the data to the frequency domain, and then solve the linear portion of the circuit with a linear algebra method, preferably utilizing sparsity techniques to speed the solution. The key model in a power system is that for the three-phase transformer. It is of consequence to note that the phase angle of any harmonic is a function both of the fundamental and of the particular harmonic