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Recursive Dynamic State Estimation for Power Systems with an Incomplete Nonlinear DAE Model

Milos Katanic, John Lygeros, Gabriela Hug

TL;DR

The paper addresses dynamic state estimation for power systems described by partially known nonlinear differential-algebraic equations (DAEs), where some components are unknown. It introduces a centralized recursive least-squares estimator that extends the iterated extended Kalman filter (IEKF) to under-determined nonlinear DAEs and can incorporate the addition or removal of models without redesign. A graph-theoretic notion of topological estimability is developed to guarantee unique state reconstruction and to guide PMU placement, showing that at least as many PMUs as unknown injectors are required and that placement can depend only on topology. Numerical experiments on the IEEE 39-bus system demonstrate accurate tracking under short-circuit and load disturbances with real-time-feasible computation, outperforming two-stage robust methods in some scenarios.

Abstract

Power systems are highly complex, large-scale engineering systems subject to many uncertainties, which makes accurate mathematical modeling challenging. This paper proposes a novel, centralized dynamic state estimator for power systems that lack models of some components. Including the available dynamic evolution equations, algebraic network equations, and phasor measurements, we apply the least squares criterion to estimate all dynamic and algebraic states recursively. The approach results in an algorithm that generalizes the iterated extended Kalman filter and does not require static network observability. We further derive a graph theoretic condition for placing phasor measurement units that guarantees the uniqueness of the solution. A numerical study evaluates the performance under short circuits in the network and load changes and shows superior tracking performance compared to robust procedures from the literature within computational times that are feasible for real-time application.

Recursive Dynamic State Estimation for Power Systems with an Incomplete Nonlinear DAE Model

TL;DR

The paper addresses dynamic state estimation for power systems described by partially known nonlinear differential-algebraic equations (DAEs), where some components are unknown. It introduces a centralized recursive least-squares estimator that extends the iterated extended Kalman filter (IEKF) to under-determined nonlinear DAEs and can incorporate the addition or removal of models without redesign. A graph-theoretic notion of topological estimability is developed to guarantee unique state reconstruction and to guide PMU placement, showing that at least as many PMUs as unknown injectors are required and that placement can depend only on topology. Numerical experiments on the IEEE 39-bus system demonstrate accurate tracking under short-circuit and load disturbances with real-time-feasible computation, outperforming two-stage robust methods in some scenarios.

Abstract

Power systems are highly complex, large-scale engineering systems subject to many uncertainties, which makes accurate mathematical modeling challenging. This paper proposes a novel, centralized dynamic state estimator for power systems that lack models of some components. Including the available dynamic evolution equations, algebraic network equations, and phasor measurements, we apply the least squares criterion to estimate all dynamic and algebraic states recursively. The approach results in an algorithm that generalizes the iterated extended Kalman filter and does not require static network observability. We further derive a graph theoretic condition for placing phasor measurement units that guarantees the uniqueness of the solution. A numerical study evaluates the performance under short circuits in the network and load changes and shows superior tracking performance compared to robust procedures from the literature within computational times that are feasible for real-time application.
Paper Structure (22 sections, 3 theorems, 29 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 22 sections, 3 theorems, 29 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Contributions
  4. Outline
  5. Estimation
  6. Power System Modeling
  7. Dynamic State Estimation Algorithm
  8. Estimability analysis
  9. Graphs of Structured Matrices
  10. Topological Estimability
  11. Numerical Results
  12. Simulation Setup
  13. Estimation Setup
  14. Case Study 1: Network Short Circuit
  15. Standard Measurement Noise Magnitude
  16. ...and 7 more sections

Key Result

Theorem 1

EC_full Given structured matrices $\mathcal{E} \in \mathbb{R}^{n \times n}$ and $\mathcal{C} \in \mathbb{R}^{m \times n}$, the matrix $$ is generically full column rank if and only if there exists a disjoint union of loops and $\mathcal{C}$-topped paths that span all vertices of $\mathcal{E}$ in the

Figures (6)

  • Figure 1: Graph of the structured pair $(\mathcal{E}, \mathcal{C})$
  • Figure 2: Single line diagram of the IEEE 39-bus test system. The estimation is performed on the highlighted area; shaded elements are unknown to the estimator. Voltage phasor measurements are denoted by the red circles, and current phasor measurements are denoted by the red squares.
  • Figure 3: Estimation of dynamic states of SGs during initialization and during and after the short-circuit in the network. The true state is denoted by ; the proposed IEKF with the trapezoidal rule by , and the backward Euler by . From top to bottom: rotor angle, rotor speed, turbine power, exciter voltage; from left to right: SG 33, SG 34, and SG 35.
  • Figure 4: Estimated and true voltage magnitudes during the initialization and during and after the short circuit. Full lines denote the true voltages; markers denote the estimated ones.
  • Figure 5: Results of estimated and true voltage magnitudes during and after the short circuit for elevated PMU noise levels following Laplace distribution. Red lines denote the ground truth values; blue lines denote the estimated ones.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 2
  • proof
  • Theorem 3
  • proof
  • proof
  • proof