Point estimate schemes for probabilistic harmonic power flow

There is an increasing interest in standards and technical literature to the probabilistic characterization of voltage and current harmonics in multi-convertor power systems. The characterization requires to express the input data of the harmonic penetration modelling by random variables and to apply probabilistic techniques of analysis. Among probabilistic approaches, Monte Carlo simulation is widely applied even if it requires high computational efforts. This paper describes a probabilistic approach for harmonic analysis of a multi-convertor power system which takes into account the interactions among the grid voltage distortions and the converter current harmonics. In order to reduce the computational efforts, the Point Estimate Method (PEM) is applied as an alternative to Monte Carlo simulation. PEM permits to account for the uncertainties that affect the evaluation of the steady state operating conditions in the presence of non linear loads and allows us to obtain the first moments of the output random variables of interest through the solution of only few deterministic harmonic power flows. Numerical applications to a test system are presented to demonstrate the accuracy and speed of the proposed method.