Probabilistic modeling of converters for power evaluation in nonsinusoidal conditions

This paper describes a probabilistic modeling of AC/DC static converters aimed to obtain the probability density functions of converter powers (active and reactive powers at fundamental, total active and apparent powers, and so on); the random behavior of displacement power factor and of total power factor is also considered. Both the case of a single converter and of several converters are analyzed. The influence of the main causes of converter power randomness is taken into account (supply voltages at fundamental and at harmonic order, converter firing angle, and so on). Numerical applications are presented and discussed to analyze the characteristics of the converter power probability density functions. The main conclusions of the paper are that the converter powers do not approach normal distributions and that there is a low correlation between active and reactive powers at fundamental and a high correlation between total active and apparent powers; moreover: the beta probability density function can be used to approach the active power at fundamental and the total active and apparent powers of several (up to 10) converters.