Hosting an increasing share of distributed generation and flexible consumers, distribution systems are being more often considered as providers of ancillary services among which are reactive power support and voltage control. For the purpose of reliable and efficient planning and operation of a transmission system, information about reactive power capabilities of connected distribution systems would be beneficial. These capabilities are subject to uncertainties especially with a presence of intermittent distributed generation and stochastic loads. To capture these uncertainties, this paper introduces probabilistic capability charts using the concept of probabilistic curves. These curves analytically represent reactive power support limits of distribution systems as a family of random variables with their associated probabilistic density functions. As such, they carry more information about states of the system than deterministic curves. The proposed capability charts can be easily applied in probabilistic studies of the overlaying transmission system. By providing analytical expressions of stochastic power injections of connected distribution systems, the use of these charts can speed up time and memory demanding probabilistic calculations of transmission systems planning and operation studies. Not containing sensitive system information, the charts can be used to exchange data between distribution and transmission system operators.

中文翻译：

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DSO / TSO接口上的概率无功功率图表

托管着越来越多的分布式发电和灵活的用户，配电系统通常被认为是辅助服务的提供者，其中包括无功功率支持和电压控制。为了可靠和有效地规划和运行传输系统，有关已连接配电系统无功功率能力的信息将是有益的。这些功能特别是在存在间歇性分布式发电和随机负载的情况下会受到不确定性的影响。为了捕获这些不确定性，本文使用概率曲线的概念介绍了概率能力图。这些曲线从理论上将配电系统的无功功率支持极限表示为一组随机变量及其相关的概率密度函数。这样，它们比确定性曲线携带更多有关系统状态的信息。所提出的能力图可以很容易地应用于叠加传输系统的概率研究中。通过提供连接的配电系统的随机功率注入的分析表达式，这些图表的使用可以加快时间和内存需求，从而对传输系统的规划和运行研究进行概率计算。这些图表不包含敏感的系统信息，可用于在配电和传输系统运营商之间交换数据。通过提供连接的配电系统的随机功率注入的分析表达式，这些图表的使用可以加快时间和内存需求，从而对传输系统的规划和运行研究进行概率计算。这些图表不包含敏感的系统信息，可用于在配电和传输系统运营商之间交换数据。通过提供连接的配电系统的随机功率注入的分析表达式，这些图表的使用可以加快时间和内存需求，从而对传输系统的规划和运行研究进行概率计算。这些图表不包含敏感的系统信息，可用于在配电和传输系统运营商之间交换数据。