Power Flow Studies in Stochastic Framework
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- Institutt for elkraftteknikk 
Power flow studies are indispensable in power system planning studies. Deterministic load flow calculations are performed with constant network parameters such as load and generation, but these parameters are uncertain of nature. Probabilistic load flow analysis can be performed in order to avoid the large computational burden required to cover all possible combinations of loads, generators and network topologies. This thesis has evaluated the Point Estimate Method and the Cumulant Method in terms of accuracy and efficiency for solving the probabilistic load flow applied on Roy Billinton s Test System. The Point Estimate Method substitutes the probability distributions of the input variables with a certain number of concentrations in which weighted deterministic load flow solutions are reached. Specifically, the number of simulations in this work has been 2n +1 where n is the number of uncertain input variables. Concentrations are points located on the individual probability density function of the input variables. Furthermore, the concentrations of variables are determined by their expected value, standard deviation, skewness and kurtosis. The Cumulant Method, on other hand, runs one deterministic solution in order to obtain the sensitivity matrices of the state vector and line flows to the power injections. Cumulants are closely related to statistical moments since the Cumulant Generating Function is the logarithm of the Moment Generating Function. The procedure is to calculate the cumulants of output variables based on the sensitivity matrices and cumulants of the input variables. Both methods are efficient compared to a Monte Carlo Simulation with 10 000 trials. The Cumulant Method has, as expected, proven to be the most efficient solution with total time consumption equal to 1.984 % of a Monte Carlo Simulation with 10 000 trials. In comparison, the corresponding performance for the Point Estimate Method is 3.678 %. On the other hand, the Point Estimate Method has an overall better accuracy in estimation of statistical parameters for the unknown variables. The suggested method for further analysis depends on whether accuracy or efficiency is the motivation of study. Nevertheless, the Cumulant Method is the recommended solution if the parameters are weighted equally.