Fuzzy multi-objective decisions in the problem of optimal distribution load flow

Abstract

Abstract This paper presents an iterative method for the calculation of load flows and decisions making in multi-objective procedure for optimal solution in distribution systems in the presence of uncertain and/or low precision input data. Uncertainty of node active and reactive loads and source–node voltage are given through the linguistic description transformed to trapezoidal membership functions fuzzy variables. System topology and element parameters, as well as, locations and capacities of switched-on capacitors are assumed to be certain (crisp) variables. The same assumption is applied for tap-change positions of transformers. Calculations of load flows are performed by using rules of interval arithmetic. For the determination of optimal defuzzified solution based on minimum active power losses, the minimum operator procedure is applied. Constraints of voltage profile are ‘soft’ and specified through corresponding linguistic descriptions, translated to the form of the membership functions. The methodology for the multi-objective decisions is developed, by using the calculation of the satisfactory degree with achieved solutions with or without weighting factors (thresholds), set to particular criteria. Finally, for verification of fuzzy optimal distribution load flow model, a real-life three-voltage level distribution system, is used.