Steady-State Security Region-Based Voltage/Var Optimization Considering Power Injection Uncertainties in Distribution Grids

Solving the power injection uncertainties of wind power generation, photovoltaic power generation, and demand response is a challenge for voltage/var optimization in distribution grids. An effective solution is to establish a chance-constrained optimization model. However, there is no fast and efficient method to determine the chance constraints, and the established models are difficult to solve. Therefore, this paper establishes a steady-state security region-based chance-constrained model. First, we find that the boundaries of the steady-state security region, which satisfy the voltage and current constraints, can be approximated by the union of a few hyperplanes in complex power injection spaces. Additionally, the expressions for hyperplanes are uniquely determined by the grid topology and are irrelevant to power injections. Then, we set the power injection adjustments as variables and propose a fast generation method for the linear expressions of the chance constraints. Because the variables of constraints and the objective function are identical, the computational burden for optimization is significantly reduced. Meanwhile, using the minimum power loss as the objective function, we present a quadratic optimization model that is easily solved by the quadratic programming method. Optimization results for IEEE 33-bus and PG&E 69-bus distribution grids are presented to verify the effectiveness of the proposed method.