arXiv 2203.166862022-03-30math.OC

电力系统仿射约束下的分散凸优化控制

Decentralized convex optimization under affine constraints for power systems control

Demyan Yarmoshik, Alexander Rogozin, Oleg. O. Khamisov, Pavel Dvurechensky, Alexander Gasnikov

摘要：

现代电力系统正处于持续的巨大变化过程中。分布式发电、能量存储和可控需求的日益普及需要引入一种新的控制范式，这种范式不依赖于集中式方法所需的大量信息交换。分布式算法可以仅依赖于有限的邻域信息来获得各种最优化问题的最优解，如最优潮流，机组组合等。作为这些问题的推广，我们考虑了在耦合$\sum_{k=1}^l (A^k x^k - b^k) \leq 0$和共享$\tilde{A} \tilde{x} - \tilde{b} \leq 0$仿射约束下光滑凸部分可分函数$f = \sum_{k=1}^l f^k(x^k,\tilde x)$的分散极小化问题，其中关于$A^k$和$b^k$的信息仅可用于计算网络的第$k$节点。以分布式方式处理耦合约束的一种方法是使用通信图的拉普拉斯矩阵和辅助变量以分布式友好的形式重写它们（Khamisov，CDC，2017）。而不是使用这种方法，我们重新制定的约束最优化问题作为一个鞍点问题（SPP），并利用共识约束技术，使其分布友好。然后，我们提供了一个国家的最先进的SPP求解算法应用于这个SPP的复杂性分析。

英文摘要：

Modern power systems are now in continuous process of massive changes. Increased penetration of distributed generation, usage of energy storage and controllable demand require introduction of a new control paradigm that does not rely on massive information exchange required by centralized approaches. Distributed algorithms can rely only on limited information from neighbours to obtain an optimal solution for various optimization problems, such as optimal power flow, unit commitment etc. As a generalization of these problems we consider the problem of decentralized minimization of the smooth and convex partially separable function $f = \sum_{k=1}^l f^k(x^k,\tilde x)$ under the coupled $\sum_{k=1}^l (A^k x^k - b^k) \leq 0$ and the shared $\tilde{A} \tilde{x} - \tilde{b} \leq 0$ affine constraints, where the information about $A^k$ and $b^k$ is only available for the $k$-th node of the computational network. One way to handle the coupled constraints in a distributed manner is to rewrite them in a distributed-friendly form using the Laplace matrix of the communication graph and auxiliary variables (Khamisov, CDC, 2017). Instead of using this method we reformulate the constrained optimization problem as a saddle point problem (SPP) and utilize the consensus constraint technique to make it distributed-friendly. Then we provide a complexity analysis for state-of-the-art SPP solving algorithms applied to this SPP.

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摘要：

英文摘要：

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