On the Holomorphic Embedding Power Flow Method: Theoretical Foundation, Limitations, Extensions and Implementation

潮流研究在电力系统运行和规划中有着广泛的应用。它涉及求解一组非线性潮流（代数）方程。潮流发散问题是电力系统潮流研究中的一个重大挑战。这是一个长期存在的问题。新型电力系统设备与可再生能源的结合，使得潮流发散问题更加突出。由于可再生能源的发展，未来的电网必须支持各种各样的潮流模式。目前可用于克服潮流发散的传统选择是相当有限的。此外，当潮流发散发生时，需要解决以下问题：-问题EN（存在）：潮流解确实存在，但数值方法（例如常用的牛顿法）无法从给定的初始猜测计算它，或-问题NE（不存在）：在指定的网络拓扑和负载条件下不存在潮流解。最近，一种全纯嵌入潮流（HEPF）方法被提出，获得了美国专利，并宣布是智能和鲁棒的。具体而言，提出了以下三个主要且重要的声明：（i）它是确定性的且非迭代的;（ii）如果确保其存在，则它始终计算正确的潮流解;（iii）如果它不能找到正确的潮流解，则它明确地发出潮流解不存在的信号。然而，上述三大主张鲜有理论依据和技术分析支撑。如果HEPF如所声称的那样工作，则可以解决长期存在的潮流发散问题。然而，当前版本的HEPF方法存在一些局限性、缺陷和七个未解决的问题，上述主张是不合理的。本项目旨在为HEPF方法建立理论基础，研究HEPF方法的局限性，研究其适用范围，并将HEPF方法扩展到处理可再生能源的大规模电力网络。拟议的工作将包括一系列理论基础开发，解决方案设计和实际数值实现。一个智能和强大的潮流求解器及其理论基础将被开发和应用于大规模电网与可再生能源。在工程和科学的许多实际应用中，鲁棒且高效地计算一组非线性方程的解是一项重要任务。因此，所提出的研究的发展具有广泛的影响，在许多实际应用中，如计算直流（DC）的超大规模集成电路（VLSI）的工作点。这是VLSI电路模拟器中最重要也是最困难的任务之一。克服潮流发散问题的困难将具有深远的意义，因为该问题是电力系统研究的核心，如功率传输能力计算，静态安全评估，最优潮流，动态安全评估等。

Power flow study is used extensively in power system operations and planning. It involves solving a set of nonlinear power flow (algebraic) equations. A great challenge in power flow study is the problem of power flow divergence. This is a long standing problem. The integration of new power system devices and renewable energy aggravates the power flow divergence problem. Future power grids have to support a wide variety of power flow patterns due to renewable energies. The conventional options currently available to overcome power flow divergence are quite limited. In addition, the following issues need to be addressed when the power flow divergence occurs: -Issue EN (existence): a power flow solution does exist, but the numerical method, such as the commonly used Newton method has failed to compute it from a given initial guess, or -Issue NE (non-existence): no power flow solution exists with the specified network topology and loading conditions. Recently, a Holomorphic Embedding Power Flow (HEPF) method was proposed, awarded a U.S. patent, and declared to be smart and robust. Specifically, the following three major and yet important claims were made (i) it is deterministic and non-iterative, (ii) it consistently computes the correct power flow solution if its existence is ensured, (iii) it unambiguously signals the nonexistence of a power flow solution if it cannot find the correct power flow solution. However, there is little theoretical basis and technical analysis to support the above three major claims. HEPF, if works as claimed, can resolve the long-standing power flow divergence problem. However, the current version of HEPF method has several limitations, deficiencies and seven unresolved issues and the above claims are unjustified. This proposal aims to establish a theoretical foundation for the HEPF method, examine the limitations of HEPF, study the scope of its applicability and extend the HEPF method to deal with large-scale power networks with renewable energy.The proposed work will cover a range of theoretical foundation development, solution methodology design and practical numerical implementation. A smart and robust power flow solver and its theoretical foundation will be developed and applied to large-scale power grids with renewables. Robust and efficient computation of the solutions of a set of nonlinear equations is an important task in many practical applications in engineering and sciences. Hence, the development of the proposed study has broad impacts on many practical applications such as computation of direct current (DC) operating points of very large scale integration (VLSI) circuits. This is one of the most important and yet difficult tasks in VLSI circuit simulators. Overcoming the difficulties of power flow divergence problems will have a far-reaching benefit since the problem is at the heart of several power system studies such as power transfer capability calculations, static security assessment, optimal power flow, dynamic security assessment, etc.