Virtual power plants (VPPs) have become an effective technique to manage a growing number of flexible resources, which have posed great technical challenges to distribution system operators (DSOs). This article proposes a bi-level programming approach for the collaborative management of an active distribution network (ADN) with multiple VPPs by designing comprehensive prices for active and reactive power. The upper layer aims to minimize the overall operation cost of the ADN considering the system security and economic operation and the interactions among the power market, ADN and VPPs. The lower layer aims to maximize the benefits of each VPP agent considering various flexible resources. Then, the bi-level model is transformed into a tractable single-level problem by using a linearization method, the Karush–Kuhn–Tucker (KKT) optimality conditions, the Fortuny-Amat transformation and the strong duality theorem. Case analyses indicate that the proposed strategy can effectively enhance the system security and improve the system economic performance by introducing reactive power pricing. The implementation effect and superiority of the proposed strategy are profoundly analyzed under different scenarios and conditions, which indicates its promising application value in the industrial field.

中文翻译：

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具有多个虚拟电厂的有源配电网最佳运行的双层编程

虚拟电厂（VPP）已成为管理越来越多的灵活资源的有效技术，这对配电系统运营商（DSO）提出了巨大的技术挑战。本文提出了一种双层编程方法，用于通过设计有功和无功功率的综合价格来对具有多个VPP的有源配电网（ADN）进行协作管理。考虑到系统安全性和经济运行以及电力市场，ADN和VPP之间的相互作用，上层旨在使ADN的总体运行成本最小化。下层旨在通过考虑各种灵活资源来最大化每个VPP代理的收益。然后，通过使用线性化方法，Karush–Kuhn–Tucker（KKT）最优性条件，将双层模型转化为可处理的单层问题，Fortuny-Amat变换和强对偶定理。案例分析表明，该策略通过引入无功电价可以有效地提高系统安全性，提高系统经济性能。在不同的场景和条件下，对该策略的实施效果和优越性进行了深入分析，表明了该策略在工业领域的应用前景。