Probabilistic Load Flow Considering Wind Generation Uncertainty

Renewable energy sources, such as wind, solar and hydro, are increasingly incorporated into power grids, as a direct consequence of energy and environmental issues. These types of energies are variable and intermittent by nature and their exploitation introduces uncertainties into the power grid. Therefore, probabilistic analysis of the system performance is of significant interest. This paper describes a new approach to Probabilistic Load Flow (PLF) by modifying the Two Point Estimation Method (2PEM) to cover some drawbacks of other currently used methods. The proposed method is examined using two case studies, the IEEE 9-bus and the IEEE 57-bus test systems. In order to justify the effectiveness of the method, numerical comparison with Monte Carlo Simulation (MCS) method is presented. Simulation results indicate that the proposed method significantly reduces the computational burden while maintaining a high level of accuracy. Moreover, that the unsymmetrical 2PEM has a higher level of accuracy than the symmetrical 2PEM with equal computing burden, when the Probability Density Function (PDF) of uncertain variables is asymmetric. Keywordsprobabilistic load flow; two point estimation method; uncertainty; wind turbine generator (WTG). NOMENCLATURE The notation used throughout the paper is stated below for quick reference. c The weibull scale factor [ s m / ]. h The nonlinear function that relates Y to X , here, the LF problem. k The weibull shape factor. ) ( ' 3 k X M 3th moment of the k x PDF.. n The number of uncertain variables. 1 , k p The weight associated to 1 , k ε . 2 , k p The weight associated to 2 , k ε . P The wind turbine generator (WTG) output power [ MW ]. D P The demand active power [ pu ]. DG P The distributed active power generation [ pu ]. D i P The active power demanded at bus i [ . .u p ]. G i P The active power generation at bus i [ . .u p ]. net i P The net active power injection at bus i [ . .u p ]. r P The WTG rated power [ MW ]. slack P The power generated by the slack bus [ pu ]. D Q The demand reactive power [ pu ]. DG Q The distributed reactive power generation [ pu ]. net i Q The net reactive power injection at bus i [ . .u p ]. ij S The power transmitted between buses i and j [ pu ]. v The wind speed [ sec / m ]. V The bus voltage magnitude vector [ pu ]. i V The magnitude of voltage at bus i [ . .u p ]. i v The wind turbine generator (WTG) cutin speed [ sec / m ]. r v The WTG rated speed [ sec / m ]. o v The WTG cutout speed [ sec / m ]. X The uncertain input variable. Y The uncertain output variable. ij Y The admittance magnitude between buses i and j [ . .u p ]. δ The bus voltage angle [ rad ]. i δ The bus voltage angle [ . rad ]. ij θ The angle of ij Y [ . rad ]. 1 , k ε The location of concentration for variable number k above the mean, n k ,..., 2 , 1 = . 2 , k ε The location of concentration for variable number k below the mean, n k ,..., 2 , 1 = . μ Mean value of the x k x, μ The mean of k x σ Standard deviation of the x k x, σ The standard deviation of k x ETASR Engineering, Technology & Applied Science Research Vol. 1, o. 5, 2011, 126-132 127