An Approach Inspired by Quantum Mechanics for the Modeling of Large Power Systems

Abstract

The ever increasing complexity of power systems mandates a further improvement of the numerical methods used for their simulation. We propose a new approach that is inspired by an exact analogy with quantum mechanics, but requires no specific knowledge of quantum physics. This approach allows in particular to use local methods commonly applied in quantum mechanics, such as Lanczos' algorithm. It is applied to computing the load flow and extended to simple dynamic studies where the nodes are described by swing equations. The first set of results are for an ideal 2D-lattice grid to illustrate the method and its main features. Then a contingency analysis by the proposed approach is performed for various realistic power systems, including a model of the European network. This demonstrates the interest of the new approach and its efficiency when compared with stateof-the-art methods, especially for large power system.

Fast load-flow calculations based on spanning trees

“…where θ is the vector storing the phase angles at every node. Rather than solving this Laplacian system for θ, an effective strategy has been to define the new variables (ψ L l ) on the lines of the network (such as done in figure (1))…”

“…That is why we will not use in this paper techniques relying on the full inversion of matrices (such as the nodal laplacian matrix of the network), nor spectral based methods [8]. Rather, we extend here a method presented in [1] that doesn't rely on the full resolution of a linear system and presents a substantial gain, as the number of arithmetic operations is only O(N ). It is based on the computation of load flows relative to specific power injections, that are dipoles.…”

“…Focusing on the DC load flow equations [5], [8], we have proposed an approach avoiding the full resolution of linear systems, by taking the physical properties of the load flow to its advantage [1]. The DC load flow equations are rewritten in the Hamiltonian formalism well known from quantum physicists.…”

“…This paper is divided into three sections after the present introduction. The first two sections briefly recall the main results stated in [1]. Section (II) specifically details the electrical model of the power system and the equivalence between the usual Laplacian formalism of the DC load flow equations and the new Hamiltonian formalism introduced in [1].…”

“…The first two sections briefly recall the main results stated in [1]. Section (II) specifically details the electrical model of the power system and the equivalence between the usual Laplacian formalism of the DC load flow equations and the new Hamiltonian formalism introduced in [1]. Section (III) recalls the Lanczos algorithm and how a local resolution is by design provided by this method.…”