Characterizing the Nonlinearity of Power System Generator Models

Abstract

Power system dynamics are naturally nonlinear. The nonlinearity stems from power flows, generator dynamics, and electromagnetic transients. Characterizing the nonlinearity of the dynamical power system model is useful for designing superior estimation and control methods, providing better situational awareness and system stability. In this paper, we consider the synchronous generator model with a phasor measurement unit (PMU) that is installed at the terminal bus of the generator. The corresponding nonlinear process-measurement model is shown to be locally Lipschitz, i.e., the dynamics are limited in how fast they can evolve in an arbitrary compact region of the statespace. We then investigate different methods to compute Lipschitz constants for this model, which is vital for performing dynamic state estimation (DSE) or state-feedback control using Lyapunov theory. In particular, we compare a derived analytical bound with numerical methods based on low discrepancy sampling algorithms. Applications of the computed bounds to dynamic state estimation are showcased. The paper is concluded with numerical tests.Index Terms-Synchronous generator, dynamic state estimation, phasor measurement units, Lipschitz nonlinearity, Lipschitz-based observer, low discrepancy sequence.

Computing Lipschitz Constants for Hydraulic Models of Water Distribution Networks

“…1 depicts how purely random, Sobol, and Halton points are distributed inside a unit box. It is worthwhile to mention that, however, as observed in the study [20], the advantage of LDS over random sampling can be minuscule. That is, random sampling method can yield comparable results as those obtained from LDS-even slightly better in small cases.…”

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Robust Dynamic State Estimation of Synchronous Machines With Asymptotic State Estimation Error Performance Guarantees

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“…• Based on the Lipschitz property of the generator's nonlinear model and PMU measurements [37], we propose a new robust observer framework using the concept of L ∞ stability that provides a performance guarantee for the state estimation error norm against worst case disturbance (due to uncertainty in generator inputs and noise). This performance can be assessed from a constant called the performance index or level.…”

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