A Newton solution for the harmonic phasor analysis of AC/DC converters

Abstract

The steady state equations that describe the converter and dc system in the harmonic domain are solved by means of Newton's method, in a manner suitable for embedding in an iterative harmonic analysis of the complete power system. The solution includes the interaction of the converter with the dc system, and the effect of variation in the firing and end of commutation angles caused by ac voltage and dc current harmonics. The convergence of Newton's method is investigated, and methods for accelerating the solution are implemented. Finally, the solution obtained is validated by means of time domain simulation. J. Arrillaga FIEEE. commutating current dc side current (sum of phasors) commutating reactance number of harmonics to be analysed dc voltage (sum of phasors) commutating voltage (sum of phasors) thyristor forward voltage drop dc shunt admittance instantaneous alpha order (sum of phasors) average firing order timing reference for i'th firing angle of firing angle of end of commutation Le + L b -Q t = the i'th sampling function (sum of phasors) W

A contribution for modeling controlled and uncontrolled AC/DC converters in harmonic power flows

“…According to these methods, the firing angle is adjusted to satisfy the specified dc current. They avoid the aforementioned convergence problems but they force the detailed representation of the dc current controller [5] or the formulation of a complicated expression of the mean value of the dc current in function of the ac magnitudes [6], [7]. In these cases, power specifications on the ac side are not considered.…”

“…Iberdrola S.A. Gardoqui 8,Bilbao (Spain) defined in terms of dc magnitudes (dc current and emf) in other papers [5], [6], [7]. According to these methods, the firing angle is adjusted to satisfy the specified dc current.…”

“…For uncontrolled rectifiers with dc ripple, obtain a = to by solving iteratively (5). For ideal dc smoothing, estimate a = t', by solving iteratively (6).…”

“…In these cases, power specifications on the ac side are not considered. The dc side structure used in [5], probably the most elaborated model, allows for any degree of complexity. However, the converter steady state calculation involves the simultaneous solution of 113 nonlinear equations.…”

Iterative harmonic analysis for controlled and uncontrolled AC/DC converters under unbalanced conditions: a compromise between model accuracy and flexibility

“…From the point of view of model accuracy, the proposals of [2], [3] seem to be the most elaborated attempt to provide a detailed representation of the whole system. In particular, the dc controller and dc side structure admits any degree of complexity.…”