Probabilistic Static Voltage Stability Analysis Based On Regularized Low-Rank Approximation

With the increasing scale of grid-connected renewable energy generation represented by wind power and photovoltaic,and the increasing number of various new types of loads,the operation of power system will become more complex and variable.Static voltage stability is the basic condition for safe and reliable operation of power system,but in the current background of high-dimensional random variables into the system,the traditional deterministic static voltage stability analysis can no longer comprehensively assess the operating situation of power system,and the probabilistic static voltage stability analysis considering the uncertainty of random variables is often difficult to balance the calculation accuracy and calculation efficiency.Therefore,this paper takes uncertainty quantification analysis as the entry point to investigate the probabilistic static voltage stability analysis method for power systems with random variables.Therefore,this paper takes uncertainty quantification analysis as the entry point to investigate the probabilistic static voltage stability analysis method of power system with random variables.A probabilistic static voltage stability analysis method based on Latin hypercube sampling is adopted to address the current situation that the number of random variables in power systems is increasing year by year.The method establishes a static voltage stability analysis model based on the basic principle of continuation power flow,and probabilistic modeling of random variables in power systems.Then,based on the basic principle of Latin hypercube sampling,the steps of the probabilistic static voltage stability analysis method based on Latin hypercube sampling are established.The results of the algorithm simulation analysis show that the proposed method has high practicality in small-scale power systems with few random variables.In order to achieve effective probabilistic static voltage stability analysis in power system with high-dimensional random variable access,a probabilistic static voltage stability analysis method based on the conventional low-rank approximation(LRA)is proposed.The method uses small-scale deterministic continuation power flow calculation samples and establishes the LRA proxy model based on the traditional parameter solution method to achieve fast and accurate probabilistic static voltage stability analysis.The simulation results show that the proposed method has high computational efficiency and can be applied to more complex power systems with high-dimensional random variable access without higher requirements for computational accuracy.In order to further improve the accuracy of the probabilistic static voltage stability calculation with high-dimensional random variables,a probabilistic static voltage stability analysis method based on improved LRA is proposed.The method improves the way of solving the LRA model parameters according to the regularization theory,and uses the least angle regression algorithm to solve for the polynomial coefficients and weight coefficients in it,so the method can also be called the regularized LRA method.At the same time,the optimal rank is determined by the generalization error together with the relative empirical error with a predetermined value of the highest degree.The results of the simulation analysis of the algorithm show that the proposed method has higher computational accuracy and similar computational speed compared with the traditional LRA method,and has higher application value in more complex power systems with high-dimensional random variables access.