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

Cornell University, Ithaca NY

Investigators

Abstract

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.