Holomorphic embedding load flow method

Abstract: This paper describes a simple, very reliable and extremely fast load-flow solution method with a wide range of practical application. It is attractive for accurate or approximate off-and on-line routine and contingency calculations for networks of any size, and can be implemented efficiently on computers with restrictive core-store capacities. The method is a development on other recent work employing the MW-?/ MVAR-V decoupling principle, and its precise algorithmic form has been determined by extensive numerical studies. The paper gives details of the method's performance on a series of practical problems of up to 1080 buses. A solution to within 0.01 MW/MVAR maximum bus mismatches is normally obtained in 4 to 7 iterations, each iteration being equal in speed to 1? Gauss-Seidel iterations or 1/5th of a Newton iteration. Correlations of general interest between the power-mismatch convergence criterion and actual solution accuracy are obtained.

Abstract: The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.

Abstract: In this paper, a load flow calculation method for ill-conditioned power systems is developed. The proposed method is very simple, has no mathematical approximations, and requires almost no additional storage and computation time when incorporated into the normal Newton-Raphson program. Using the method, the load flow solution never diverges, and also the existence of the solution from the initial estimate can be easily judged. To examine the effectivenesst two ill-conditioned power systems, i.e., 11 and 43 bus systems are studied by the method, and it is found that the solution does not exist for the 11 bus system though the given data are said to be operational, and also that the solution does exist for the 43 bus system but does not converge with the single precision due to the precision deficiency of the computer.

Abstract: The Holomorphic Embedding Load Flow is a novel general-purpose method for solving the steady state equations of power systems. Based on the techniques of Complex Analysis, it has been granted two US Patents. Experience has proven it is performant and competitive with respect established iterative methods, but its main practical features are that it is non-iterative and deterministic, yielding the correct solution when it exists and, conversely, unequivocally signaling voltage collapse when it does not. This paper reviews the embedded load flow method and highlights the technological breakthroughs that it enables: reliable real-time applications based on unsupervised exploratory load flows, such as Contingency Analysis, OPF, Limit-Violations solvers, and Restoration plan builders. We also report on the experience with the method in the implementation of several real-time EMS products now operating at large utilities.