2017/07/13 by Antonio Trias, Trias, Antonio, J.L. Monzón Marín +1
Engineering · Mathematics · #14H50 #14H81 #30B10 #30B40 #30B70 #30E10 #94C99 #FOS: Electrical engineering #Numerical methods for differential equations #Optimal Power Flow Distribution #Power System Optimization and Stability #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1707.04064
openalex publication_date 2017/07/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A new technique is presented for solving the problem of enforcing control\nlimits in power flow studies. As an added benefit, it greatly increases the\nachievable precision at nose points. The method is exemplified for the case of\nMvar limits in generators regulating voltage on both local and remote buses.\nBased on the framework of the Holomorphic Embedding Loadflow Method (HELM), it\nprovides a rigorous solution to this fundamental problem by framing it in terms\nof \optimization. A novel Lagrangian formulation of power-flow, which is\nexact for lossless networks, leads to a natural physics-based minimization\ncriterion that yields the correct solution. For networks with small losses, as\nis the case in transmission, the AC power flow problem cannot be framed exactly\nin terms of optimization, but the criterion still retains its ability to select\nthe correct solution. This foundation then provides a way to design a HELM\nscheme to solve for the minimizing solution. Although the use of barrier\nfunctions evokes interior point optimization, this method, like HELM, is based\non the analytic continuation of a germ (of a particular branch) of the\nalgebraic curve representing the solutions of the system. In this case, since\nthe constraint equations given by limits result in an unavoidable singularity\nat s=1, direct analytic continuation by means of standard Pad 'e\napproximation is fraught with numerical instabilities. This has been overcome\nby means of a new analytic continuation procedure, denominated\nPad 'e-Weierstrass, that exploits the covariant nature of the power flow\nequations under certain changes of variables. One colateral benefit of this\nprocedure is that it can also be used when limits are not being enforced, in\norder to increase the achievable numerical precision in highly stressed cases.\n