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Data-Driven Dynamic State Estimation of Photovoltaic Systems via Sparse Regression Unscented Kalman Filter

Elham Jamalinia, Zhongtian Zhang, Javad Khazaei, Rick S. Blum

TL;DR

This work tackles dynamic state estimation for PV systems under model uncertainty by introducing a two-phase data-driven framework: (i) identify a nonlinear transition function via sparse regression (STLS) to obtain $\dot{\mathbf{x}}=\Theta(\mathbf{x},\mathbf{u})\bm{\Xi}$, and (ii) perform state estimation with an adaptive unscented Kalman filter that augments inputs to track changing system parameters. The method is validated for both single-stage and two-stage PV configurations, showing coefficients that align with physics-based models and robust performance under process and measurement noise. Adaptivity is demonstrated via online model updates (within $0.5\,\text{s}$) in response to grid-impedance changes and faults, outperforming traditional physics-based DSE in scenarios with parameter variation. System-level tests on a PV microgrid with mixed PV types confirm scalability and resilience to faults such as equipment disconnections and under-voltage conditions, highlighting practical applicability for real-time grid monitoring and protection.

Abstract

Dynamic state estimation (DSE) is vital in modern power systems with numerous inverter-based distributed energy resources including solar and wind, ensuring real-time accuracy for tracking system variables and optimizing grid stability. This paper proposes a data-driven DSE approach designed for photovoltaic (PV) energy conversion systems (single stage and two stage) that are subjected to both process and measurement noise. The proposed framework follows a two-phase methodology encompassing ``data-driven model identification" and ``state-estimation." In the initial model identification phase, state feedback is gathered to elucidate the dynamics of the photovoltaic systems using nonlinear sparse regression technique. Following the identification of the PV dynamics, the nonlinear data-driven model will be utilized to estimate the dynamics of the PV system for monitoring and protection purposes. To account for incomplete measurements, inherent uncertainties, and noise, we employ an ``unscented Kalman filter," which facilitates state estimation by processing the noisy output data. Ultimately, the paper substantiates the efficacy of the proposed sparse regression-based unscented Kalman filter through simulation results, providing a comparative analysis with a physics-based DSE.

Data-Driven Dynamic State Estimation of Photovoltaic Systems via Sparse Regression Unscented Kalman Filter

TL;DR

This work tackles dynamic state estimation for PV systems under model uncertainty by introducing a two-phase data-driven framework: (i) identify a nonlinear transition function via sparse regression (STLS) to obtain , and (ii) perform state estimation with an adaptive unscented Kalman filter that augments inputs to track changing system parameters. The method is validated for both single-stage and two-stage PV configurations, showing coefficients that align with physics-based models and robust performance under process and measurement noise. Adaptivity is demonstrated via online model updates (within ) in response to grid-impedance changes and faults, outperforming traditional physics-based DSE in scenarios with parameter variation. System-level tests on a PV microgrid with mixed PV types confirm scalability and resilience to faults such as equipment disconnections and under-voltage conditions, highlighting practical applicability for real-time grid monitoring and protection.

Abstract

Dynamic state estimation (DSE) is vital in modern power systems with numerous inverter-based distributed energy resources including solar and wind, ensuring real-time accuracy for tracking system variables and optimizing grid stability. This paper proposes a data-driven DSE approach designed for photovoltaic (PV) energy conversion systems (single stage and two stage) that are subjected to both process and measurement noise. The proposed framework follows a two-phase methodology encompassing ``data-driven model identification" and ``state-estimation." In the initial model identification phase, state feedback is gathered to elucidate the dynamics of the photovoltaic systems using nonlinear sparse regression technique. Following the identification of the PV dynamics, the nonlinear data-driven model will be utilized to estimate the dynamics of the PV system for monitoring and protection purposes. To account for incomplete measurements, inherent uncertainties, and noise, we employ an ``unscented Kalman filter," which facilitates state estimation by processing the noisy output data. Ultimately, the paper substantiates the efficacy of the proposed sparse regression-based unscented Kalman filter through simulation results, providing a comparative analysis with a physics-based DSE.
Paper Structure (28 sections, 1 theorem, 28 equations, 11 figures, 3 tables, 1 algorithm)

This paper contains 28 sections, 1 theorem, 28 equations, 11 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our contribution
  3. Problem Formulation
  4. Single Stage PV system
  5. Two Stage PV system
  6. Data-Driven Model Identification
  7. Data Collection
  8. Library of Candidate Functions
  9. Identification by Sparse Regression
  10. Validation of Single Stage and Two Stage PV Models
  11. Adaptive Sparse Regression Unscented Kalman Filter
  12. Feature Selection Sparse Regression
  13. Observability
  14. Adaptive Unscented Kalman Filter with Augmented Input
  15. Discrete Time Model
  16. ...and 13 more sections

Key Result

Theorem 4.1

A linear system with state space as $\dot{\textbf{x}}=\mathbf{A}\textbf{x}+\mathbf{B}\textbf{u}$, and measurement $\textbf{y}=\mathbf{C}\textbf{x}$ is observable if and only if the observability matrix $\mathcal{O}$ has full rank. The observability matrix is defined as:

Figures (11)

  • Figure 1: The schematic of sparse regression UKF for data-driven dynamic state estimation of PV systems.
  • Figure 2: Circuit diagram of single stage and two stage PV systems
  • Figure 3: Flowchart of sparse regression UKF for DSE.
  • Figure 4: Sparse Regression UKF for single stage PV.
  • Figure 5: Effect of $\gamma$ on DSE normalized error via sparse regression UKF in two stage PV
  • ...and 6 more figures

Theorems & Definitions (1)

  • Theorem 4.1