Control-aware Probabilistic Load Flow for Transmission Systems: An Analytical Method

TL;DR

This paper introduces the first analytical probabilistic load flow method for transmission systems that incorporates system control actions, improving accuracy by using a high-precision linear model and Gaussian mixture models for joint probability distributions.

Contribution

It develops an analytical PLF approach considering primary and secondary frequency controls, utilizing a correction method and Gaussian mixture models for accurate, distribution-agnostic joint system state analysis.

Findings

High accuracy verified on test cases up to 1354 buses.

Method effectively captures correlations among random variables.

Applicable to any distribution of random variables.

Abstract

Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account. However, system control, as an automatic buffer between the fluctuations in random variables and the variations in system states, has a significant impact on the final PLF result. To consider control actions' influence, this paper proposes the first analytical PLF method for the transmission grid that takes into account primary and secondary frequency controls. This method is based on a high-precision linear power flow model, whose precision is even further improved in this paper by an original correction approach. This paper also proves that if the joint probability distribution (JPD) of random variables is expressed by a Gaussian mixture model (GMM), then the JPD of system states (e.g., nodal voltages) is an infinite GMM. By leveraging this proposition, the proposed method can generate the joint PLF of the whole system, is applicable to random variables obeying any distributions, and is capable of capturing their correlation. The high accuracy and satisfactory efficiency of this method are verified on test cases scaling from 14 to 1354 buses.