The Model And Modification Of Probabilistic Load Flow Based On Uncertainty Quantification

As a complex giant nonlinear system, the power system has a lot of uncertain factors, such as the fluctuations of loads, generators outage and the change of power system operation mode etc. Nowadays, with the increasing depletion of fossil fuels and increasing environmental pressure, the growing penetration of renewable energy, such as wind power and solar power, has brought trough intermittency and volatility, which brings new challenges to power system operation and control. Therefore, uncertainty quantificationis (UQ) for the power system operation and dispatching has becoming an important subject for power system researchers.UQ theory is based on the tool-generalized polynomial chaos (gPC), its basic idea is to approximate random variables by using the series expansion of gPC, and utilize the orthogonal property of gPC to further convert the problem of solving complex function into calculating the deterministic gPC coefficients. This method is in fact a spectral algorithm, which can be divided into two categories:stochastic collocation (SC) method and stochastic Galerkin (SG) method. The gPC based spectral method has excellent computing performance, which has now widely applied into the uncertainty analysis fields of electric and electronic, computer analysis, while rarely used in the UQ study of power system. Therefore, this paper applied the UQ theory to solve the load flow and optimal load flow considering the uncertainty factors in power system.Firstly, based on the nonintrusive SC method, this paper proposed spectral methods to study the load flow and the optimal power calculation considering the uncertain variables in power system:probabilistic load flow (PLF) and probabilistic optimal power flow (POPF). The SC method is an nonintrusive spectral method, which regards the original system as a black box, and run deterministc solver at all the collocation points of inputs, obtaining the gPC coefficients from the calculation results by postprocessing. The principle of SC method is simple, the calculation process is decoupled and the calculation speed is very fast. However, the aliasing error introduced by SC method will reduce its computational accuracy significantly.According to the charateristic of SC that its calculation speed and accuracy are greatly depend on the location of collocation nodes, we modified the candidate node construction method to improve its calculation performance, and respectively, proposed PLF method and POPF method based on the modified SC method.Secondly, we propsed a PLF method based on the SG method which offers the higher accuracy. The SG method is an intrusive method which needs to construct an orgonal coupling Galerkin system, which guarantees that when project the gPC approximation errors to the gPC orthogonal polynomial space, the projection in each direction of the polynomial space is minimized. Then, the gPC coefficients of all outputs can be calculated by one calculaton. The SG method achives high accuracy but the calculation process is very cumbersome, even unsolvable for some complex system.Considering the shortcomings of these two methods, this paper proposed a modified SG method. Due to the derived Galerkin system equations are usually coupled and to implement, we utilize the P-Q decoupling property of power system to form two pre-calculated constant sparse Jacobian matrices, which can significantly reduce the computational burden.At last, the calculation accuracy and efficiency of all the proposed methods are verified in their corresponding test system, such as the 5-bus, IEEE14-bus and IEEE 118-bus test systems.