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中文摘要：
综合考虑恢复初期阶段和后续阶段。提出一种扩展黑启动方案的多目标优化方法。以初期阶段内加权发电量最大化、尽快搭建系统的骨架网络和选择运行性能尽可能利于后续系统电压调整的被启动机组为优化目标。综合考虑机组启动约束和系统运行约束．建立扩展黑启动方案的多目标优化模型．然后结合快速非支配排序遗传算法（NSGA—Ⅱ）与Dijkstra法对扩展黑启动方案求解出Pareto最优解集。最后综合决策者的偏好因素和决策矩阵的客观信息。进行基于模糊熵权的Vague集多属性决策分析．选取出最满意的扩展黑启动优化方案。以新英格兰10机39节点系统为算例验证了所提方法的有效性。
英文摘要：
With the comprehensive consideration of initial and subsequent restoration stages,a multi- objective optimization model is built for the extended black-start schemes,which,with the constraints of unit startup and system operation,has three optimization objectives：maximize the weighted power generation during the initial stage,establish the system frame as soon as possible and select the black-start units beneficial to the subsequent regulation of system voltage. NSGA-I （Non-dominated Sorting Genetic Algorithm） and Dijkstra algorithm are applied to solve the model and obtain Pareto solutions,from which the best extended black-start scheme is selected by applying the fuzzy entropy weight and combining the subjective information of decision matrix. The effectiveness of the New England 10-unit 39-bus power system. Vague-set multi-attributes decision-making based on preference of decision-maker with the objective proposed method is validated by the case study of
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