Modelling input parameter interactions in the possibilistic harmonic load flow

In a previous study by the authors, a possibilistic harmonic load flow (PHLF) approach was presented. The PHLF was capable of modelling, through possibility distributions, uncertainties regarding magnitude and composition in both linear (LL) and non-linear loads (NLL) connected at the linear (LL) and non-linear loads(PS). However, in that approach, possibility non-interaction between parameters for modelling LL and NLL was assumed. Such assumption is quite conservative and conduces to uncertainty overestimation. In fact, there are well-defined physical relationships among model parameters that constrain the variability of these. This study presents an improved approach which overcomes the aforementioned drawback by including both linear and non-linear equality constraints into the non-linear programming problem used to compute the PHLF. These linear and non-linear equality constraints are specifically used to model the balance of active and reactive power, respectively, at each bus of the PS. The equality constrains inclusion is supported from a possibility theory point of view by means of the `information fusion concept`. Influence of the possibility interaction consideration is evaluated in the IEEE 14-bus PS for harmonic analysis. Then, the complete PHLF is tested in a real 88-bus PS, and comparisons with Monte Carlo simulation results are performed and discussed.