最优协调电压控制直接Radau配置算法

根据准稳态假设，建立含连续-离散时间微分-代数方程约束的最优协调电压控制模型, 并采用现代最优控制理论中的直接法求解该动态优化问题。根据Radau配置法将动态优化问题转化为连续变量与离散变量并存的非线性规划问题。为考虑有载调压变压器变比、可投切电容器组和待切除负荷的离散特性，引入离散变量的罚函数处理机制，并采用非线性原对偶内点算法求解。新英格兰10机39节点系统的仿真结果表明，所提出方法能有效地协调各种控制设备动作，从而增强系统的长期电压稳定性。

Direct Radau Collocation Algorithm Applied to Optimal Coordinated Voltage Control

Based on the quasi-steady-state assumption, an optimal coordinated voltage control model consisting of the constraint of continuous and discrete time differential-algebraic equations is established, and a direct method from the modern optimal control theory is applied to solving this dynamic optimization problem.Then, according to Radau collocation method, the dynamic optimization problem is converted to a nonlinear programming one that contains continuous and discrete variables.Moreover, in order to consider the discrete characteristics of the turn ratio of on-load regulating transformer, the switchable capacitor bank and the shedding load, a nonlinear primal-dual interior-point algorithm incorporating the penalty function mechanism for discrete variables is used during the solving of this problem.Simulated results on New England 10-machine 39-bus system demonstrate that the proposed method improves the long-term voltage stability of power systems because it effectively coordinates the actions of different control devices.