# A Passivity Interpretation of Energy-Based Forced Oscillation Source Location Methods

## TL;DR

This paper introduces a passivity-based framework to analyze and improve energy-based methods for locating forced oscillation sources in power systems, highlighting limitations and proposing a simulation-free performance prediction algorithm.

## Contribution

It provides a systematic passivity interpretation of the DEF method, identifies its deficiencies, and develops a new algorithm for predicting its performance without simulations.

## Key findings

- The DEF method's deficiencies are mathematically characterized.
- No universal passivity transformation exists for all power system components.
- The proposed algorithm accurately predicts DEF performance on standard test systems.

## Abstract

This paper develops a systematic framework for analyzing how low frequency forced oscillations propagate in electric power systems. Using this framework, the paper shows how to mathematically justify the so-called Dissipating Energy Flow (DEF) forced oscillation source location technique. The DEF's specific deficiencies are pinpointed, and its underlying energy function is analyzed via incremental passivity theory. This analysis is then used to prove that there exists no passivity transformation (i.e. quadratic energy function) which can simultaneously render all components of a lossy classical power system passive. The paper goes on to develop a simulation-free algorithm for predicting the performance of the DEF method in a generalized power system, and it analyzes the passivity of three non-classical load and generation components. The proposed propagation framework and performance algorithm are both tested and illustrated on the IEEE 39-bus New England system and the WECC 179-bus system.