On the Calculation of the Variance of Algebraic Variables in Power System Dynamic Models with Stochastic Processes

TL;DR

This paper introduces a Lyapunov-based method to efficiently compute the variance of algebraic variables in stochastic power system models, validated on IEEE and Irish transmission system models.

Contribution

It presents a novel technique using Lyapunov equations for variance calculation in stochastic power system models, improving computational efficiency over Monte Carlo simulations.

Findings

High accuracy of the proposed method demonstrated on IEEE 14-bus system.

Significant reduction in computation time compared to Monte Carlo simulations.

Effective application to large-scale Irish transmission system model.

Abstract

This letter presents a technique to calculate the variance of algebraic variables of power system models represented as a set of stochastic differential-algebraic equations. The technique utilizes the solution of a Lyapunov equation and requires the calculation of the state matrix of the system. The IEEE 14-bus system serves to demonstrate the accuracy of the proposed technique over a wide range of variances of stochastic processes. The accuracy is evaluated by comparing the results with those obtained with Monte Carlo time domain simulations. Finally, a case study based on a 1479-bus dynamic model of the all-island Irish transmission system shows the computational efficiency of the proposed approach compared to the Monte Carlo method.