Minimizing operational losses in transmission systems through the Optimal Reactive Dispatch (ORD), a non-convex mixed-integer nonlinear programming problem, is crucial for operational cost reduction, resource optimization, and greenhouse gas emission mitigation. Besides all intricacies associated with solving ORDs, transmission system operators encounter the challenge of determining sequences in which ORD control adjustments must be implemented before significant changes occur in generators scheduled power output and system loading. Sequencing ORD control adjustments, in spite of not being novel, remains modestly scrutinized in the literature. This paper introduces a two-phase framework that tackles the globally optimal sequencing of ORD control adjustments over potential paths by solving the ORD to minimize operational losses in transmission systems in the first phase, and optimally sequencing ORD control adjustments employing fast power flow calculations, graph shortest path, parallel computing, and dynamic programming in the second phase. We discuss the framework’s second phase asymptotic time complexity, which is exponential over factorial for brute-force approaches, and its capability to guarantee globally optimal paths toward minimal operational losses determined in the framework’s first phase. ORD control adjustments for transmission systems with up to 27 controllable variables are benchmarked against two mixed-integer nonlinear programming solvers: BARON, a global non-convex solver, and Knitro, a local solver (assuming convexity around local optima). Globally optimal sequences of ORD control adjustments over potential paths (more than for sequencing 27 control adjustments) and average algorithm runtimes validate the straightforward application and, more importantly, effectiveness of such a comprehensive framework.

中文翻译：

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通过图最短路径、并行计算和动态规划，对最优无功调度控制调整进行全局最优排序，以最大限度地减少输电系统的运行损失


通过最优无功调度 (ORD)（一种非凸混合整数非线性规划问题）最大限度地减少输电系统的运营损失，对于降低运营成本、优化资源和减少温室气体排放至关重要。除了与解决 ORD 相关的所有复杂问题之外，输电系统运营商还面临着确定顺序的挑战，即在发电机预定功率输出和系统负载发生重大变化之前必须实施 ORD 控制调整的顺序。排序 ORD 控制调整尽管并不新颖，但在文献中仍然受到适度的审查。本文介绍了一个两阶段框架，该框架通过求解 ORD 来最小化第一阶段输电系统的运行损失，并采用快速潮流计算来优化排序 ORD 控制调整，从而解决潜在路径上 ORD 控制调整的全局最优排序问题。第二阶段的最短路径、并行计算、动态规划。我们讨论了该框架的第二阶段渐近时间复杂度（对于暴力方法来说，它是阶乘的指数），以及它保证框架第一阶段确定的全局最佳路径实现最小运营损失的能力。具有多达 27 个可控变量的传输系统的 ORD 控制调整以两个混合整数非线性规划求解器为基准：BARON（全局非凸求解器）和 Knitro（局部求解器）（假设围绕局部最优的凸性）。 潜在路径上的 ORD 控制调整的全局最优序列（超过 27 个控制调整的排序）和平均算法运行时间验证了简单的应用程序，更重要的是，验证了这种综合框架的有效性。