PSEUDO-INVERSE-BASED PROBABILISTIC POWER-FLOW APPROACH

A probabilistic formulation of the power flow problem that includes the effects of uncertainty is given. The random variations of active and reactive loads are assumed to be normally distributed with zero mean mu(Delta PD) = 0 and some variance sigma(Delta PD) not equal 0. The resulting probabilistic active and reactive power flow equations differ from the conventional active acid reactive power flow equations due to the presence of some augmented terms. As a result, the number of equations resulting from this formulation is less than the number of the unknowns. The structure of the traditional Jacobian matrix encountered in the conventional power flow problem is altered, and the resulting problem is precisely a minimization problem. A minimal least squares based minimization technique and the Newton's method of successive approximation are proposed to obtain solutions. Test results for the IEEE 5 bus and 14 bus test systems are documented.