Energy Storage Optimization Method for Flexible Interconnected Low-voltage Distribution Network Based on Positive Semi-definite Programming

Abstract

With the fast development of the electricity market, the number of small and medium-sized new energy generation in the urban low-voltage distribution networks is increasing. These “retail investors” hope to sell the extra electricity for financial gain. However, these renewable energy generation units have small capacity and obvious intermittent output. Thus, they can not be added to the operation of the power system alone. In this paper, the model is understood from the perspective of optimization theory, and the solution method is given. The optimization problem of the model is given, and the required gradient and Hessian functions are defined. By applying mathematical induction and the properties of the special matrix column, a decomposition formula of the matrix column is derived. Through using this inequality and the standard decomposition of a positive semi-definite matrix, a feasible scheme is formed. The eigenvalue relationship between the sum of elements of a positive semi-definite block matrix and its quasi-diagonal block is given under certain conditions, while the number of such blocks is not required. The standard form of the dual problem is drawn by the method of Lagrange multipliers, and the relationship between the dual solution and the solution of the original problem is studied. The stability of the system is further improved, which provides reference significance for improving the utilization rate of photovoltaic new energy, optimizing the charging and discharging of the energy storage system, and ensuring the safe and reliable operation of the distribution network.