Sigma algebraic approximants as a diagnostic tool in power networks

摘要

A system and method for constructively providing a set of complex-valued indices that measures the proximity of an electrical power distribution system to voltage collapse, and providing insights on general static stability issues in power networks. These indices, termed “sigmas”, are designed through a mathematical osculation of the actual load flow solution with an equivalent two-bus system at every node. The procedure for obtaining these sigmas is based on the Holomorphic Embedded Load flow Method (HELM), and the indices are, in fact, proper analytical functions of the embedding parameter, which endows them with powerful diagnostic capabilities. These indices are then used graphically on a two-dimensional chart, in order to appreciate visually the overall distance of the system to voltage collapse, while at the same time spotting the weak nodes out of the whole grid, providing new situational awareness and diagnosis tools.

主权项

1. A computer-implemented method of evaluating the state of an electrical grid, comprising:
generating a first mathematical model of load flow equations (L) representing an electric power system having an electrical grid in which all voltages are equal to a normal or designed voltage level and there is no energy flow in links of said electrical grid, using a computerized device,
said first mathematical model comprising a holomorphic embedding of said load flow equations as (L(s)), s comprising a variable in a complex domain that includes a value s=0 corresponding to a no load case (L(0)) in which all voltages are equal to a normal or designed voltage level and there is no energy flow in links of said electrical grid, and each variable of said load flow equations (L) is contained in L(s) as a function of said variable s by said holomorphic embedding; transforming said first mathematical model of said load flow equations (L), with said holomorphic embedding, to a second mathematical model comprising a dimensionless equivalent grid model for each node of said electrical grid, using said computerized device,
said second mathematical model comprising said holomorphic embedding of s in said load flow equations (L(s)) according to a sigma index function, said sigma index function comprising a σ function of s in a complex domain; transcribing said first mathematical model and said second mathematical model into software for use in a computer processor adapted to execute said software; using analytical continuation in said computer processor to perform mathematical osculation of said load flow equations at each said node of said electrical grid to calculate voltage at each said node of said electrical grid; and diagnosing an electrical state of said electrical grid by analyzing evolution of s in said sigma index function on a two-dimensional sigma plane using functional dependency of said sigma index function on said holomorphic embedding parameters, using said computerized device.