Research On Reliability Evaluation Of Bulk Power System Based On Gaussian Mixture Model And Cross Entropy

Power system reliability refers to a kind of measure of ability to satisfy power consumers with sufficient electrical power and energy with acceptable quality standards. Reliability evaluation of bulk power system supplies significant reference information to power system planning and operation, and thus becomes an important auxiliary tool of power system planning and operation. It is a significant subject to evaluating reliability of power system more accurately and efficiently.Various uncertain factors exist in power system operation, such as malfunction of electrical equipment, random fluctuation of load demand and renewable energy sources. It is via quantitative diagnosis of impact of uncertain factors on power system operation that reliability assessment of power system reveals the level of risk and conducts risk identification. Therefore, the modeling accuracy of uncertainty factors turns into the foundation and application premise of reliability assessment of power system. On the other hand, bulk power system is a multi-constrained, non-linear, high-dimensional and complex system on account of its large scale, randomness and hard modelling. Therefore, such a huge amount of computation is needed that it is an urgent problem to improve computational efficiency of bulk power system reliability evaluation without losing precision.In consideration of the contradiction of accuracy and efficiency of the current models in probabilistic modeling of multivariate in power system reliability evaluation, a Gaussian mixture model(GMM) for multiple random variables is proposed in this paper. Based on GMM which is terse in form, arbitrary continuous random variables can be modeled flexibly and efficiently and the correlation between variables is also apt to be considered. A free split and merge expectation maximum(FSMEM) algorithm is used for parameters solution of GMM, which is able to determine the optimal number of Gaussian components adaptively and avoid being caught into local optimum. In addition, a two-stage complex sampling method is employed to generate random samples of GMM efficiently. Taking the probabilistic modeling of electric load and wind speed for example, RBTS and IEEE-RTS79 are used to demonstrate the accuracy and efficiency of proposed model.For Monte Carlo simulation(MCS) method is really sensitive to the sparsity of failure accident, the importance sampling(IS) method is able to sampling more failure states by altering the probability density function(PDF) of input variables, thereby improves efficiency of MCS method. As a valid IS method, cross entropy based Monte Carlo simulation(CE-MCS) method is an attractive method recently. However, CE-MCS is still restricted with variables following binomial distribution, which is obviously impractical. Therefore, a CE algorithm incorporating various types of distribution is proposed in this paper. The method is able to optimize the parameters of PDF of both discrete and continuous variables, and of course expends the application of CE-MCS. On the basis, a composite reliability index which combines the pre-samples and optimal samples of system states, which could improve the accuracy and efficiency of CE-MCS significantly with a little more computation. Considering the derating state of generators and randomness of electric load, RBTS and IEEE-RTS79 with a wind farm are used to demonstrate the accuracy and efficiency of proposed model.