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中文摘要：
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。该模型综合考虑长期电压稳定性和控制成本因素，协调不同地理位置和不同种类的控制手段。根据Pontryagin极大值原理建立该协调电压控制问题的1阶最优性条件，该条件是一个典型的两点边值问题。在此基础上采用拉道（Radau）排列法求解这个两点边值问题。该算法具有计算精度高、数值稳定性好等特点。此外，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，还在控制模型中引入了二次罚函数的处理方法。以新英格兰39节点系统为基础构造算例，算例结果表明了该方法的有效性。
英文摘要：
Based on quasi-steady-state （QSS） approximation, an optimal coordinated voltage control （OCVC） mode/including continuous and discrete time differential-algebraic equations （DAEs） was established. This model considered long-term voltage stability and costs of controls synthetically, which could coordinate different kinds of controls distributed over different locations. This OCVC problem was converted to a typical two-point boundary-value problem （TPBVP） according to Pontryagin maximum value principle, and this TPBVP was a first order optimality condition which could be solved by Radau collocation method. Radau collocation method has high accuracy and good numerical stability. Besides, in order to consider discrete characteristics of transformer tap control, capacitor switching and load shedding, a quadratic penalty function mechanism was incorporated to this control model. The simulation results on New England 39-bus system demonstrate the merits of this proposed method.
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