Application of Arbitrary Polynomial Chaos Expansion to Probabilistic Power Flow Analysis of Power Systems with Renewable Energy Sources

Increasing of the electricity power generation due to some undetermined renewable energy sources i.e. photovoltaic cell or wind power plants, has affected power system performances. Probabilistic power flow analysis (PPF) based on generalized polynomial chaos (gPC) is a method for analyzing these effects, but it requires exact distribution characteristics of uncertain parameters. This paper proposes an implementation of the arbitrary polynomial chaos (aPC) expansion to solve the PPF solution. With aPC, the set of orthonormal basis polynomial is directly calculated by the available recorded data of uncertain sources. The proposed technique has been applied to the modified IEEE 39-bus system in MATLAB environment. The numerical results showed that the proposed method was not only reliable, but also reduced the computation burden compared to PPF based on Monte Carlo Simulation.