| There are many uncertainties in the operation of the power system. Especially nowadays, with the development of wind and solar generation, the uncertainties are becoming greater. They may cause disturbances of the power system, and even induce cascading failure, thus causing the stability problems of the system. The probabilistic load flow (PLF) studies take these uncertainties into account for system planning and operating. Therefore, compared with conventional load flow studies, the PLF can provide more valuable information.A method based on generalized Polynomial Chaos (gPC) is proposed for the PLF. Firstly, the basic knowledge of the gPC theory and the mathematical basis of the theory applying to the method is introduced. The method uses the idea of orthogonal polynomial approximation from the gPC to move the system randomness to orthogonal polynomial basis. The load flow equations in rectangle coordination are adopted to avoid high order truncation error of expending nonlinear load flow equations. Based on the stochastic Galerkin method, the probabilistic load flow equations are transformed into a set of deterministic equations. After solving these equations, the orthogonal polynomial approximation coefficients are obtained and can be used to calculate the mean and variance of the load flow state variables. Secondly, numerical results from IEEE-9bus system and IEEE-14bus system show that the method has strong ability to deal with nonlinear systems and is capable of many situations. Finally, this method is used in the probabilistic load flow calculation of systems integrated with wind and solar generations. The numerical results from IEEE-30bus distribution system further illustrate the effectiveness of the method in practical application. Besides, the method can also be used in the probabilistic load flow analysis considering dependencies among input random variables, which is proven by the numerical results of the tests in the IEEE-30bus system. |
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