多直流馈入受端系统负荷恢复分布鲁棒优化

在含风电的多直流馈入受端系统中，直流系统和风电提供功率支撑可以加快负荷恢复，但不可避免的风电和负荷不确定性问题会给恢复安全带来挑战。为此，提出了一种可以充分利用现有数据降低不确定性风险的恢复决策方法。该方法首先分析直流系统的功率调控特性，建立多回直流功率调控约束模型。其次，构建基于Wasserstein距离的风电出力和负荷模糊集来描述源荷双侧的不确定性。然后，定义恢复风险指标描述不确定性导致的安全越限风险，建立两阶段分布鲁棒优化模型，最小化最恶劣概率分布下的恢复风险。最后，利用对偶理论和big-M方法，将该模型转化为混合整数线性规划问题求解。该方法可充分利用已有数据，提供鲁棒性灵活可调的最优负荷恢复方案，能够平衡恢复过程中的经济性与安全性。算例分析结果表明，所提出的方法可以有力保障各直流传输功率的协调优化和负荷的安全有序接入，消除不确定性带来的运行风险。

Distributionally robust optimization of load recovery for a multi-infeed HVDC receiving end system

In a multi-infeed HVDC receiving system with wind power, the power support provided by the HVDC system and wind power can accelerate load recovery, but the inevitable uncertainty of wind power and load will bring challenges to recovery security. Therefore, a restoration decision-making method that can make full use of existing data to reduce the risk of uncertainty is proposed. First, this method considers the power control characteristics of an HVDC system and establishes a power control constraint model of multiple HVDC links. Secondly, the ambiguity sets of wind power output and load based on Wasserstein distance are constructed to describe the source-load uncertainty. Then a restoration risk index is defined to describe the risk of security violations caused by uncertainty. A two-stage distributionally robust optimization model is established to minimize the recovery risk under the worst-case probability distribution of ambiguity sets. Finally, by using dual theory and the big-M method, the model is transformed into a deterministic mixed integer linear programming problem. The method can make full use of the existing data, provide a robust and flexible and adjustable optimal load recovery scheme, and balance the economy and safety in the recovery process. The results show that the proposed method can effectively guarantee the coordinated optimization of HVDC transmission power and the safe and orderly access of load, and eliminate the operational risk caused by uncertainty.This work is supported by the National Key Research and Development Program of China (No. 2016YFB0900100).