Da Meng

Estimation of the Dynamic States of Synchronous Machines Using an Extended Particle Filter

In this paper, an extended particle filter (PF) is proposed to estimate the dynamic states of a synchronous machine using phasor measurement unit (PMU) data. A PF propagates the mean and covariance of states via Monte Carlo simulation, is easy to implement, and can be directly applied to a nonlinear system with non-Gaussian noise. The proposed extended PF improves robustness of the basic PF through iterative sampling and inflation of particle dispersion. Using Monte Carlo simulations with practical noise and model uncertainty considerations, the extended PFs performance is evaluated and compared with the basic PF, an extended Kalman filter (EKF) and an unscented Kalman filter (UKF). The extended PF results showed high accuracy and robustness against measurement and model noise.

Dynamic State Estimation of a Synchronous Machine Using PMU Data: A Comparative Study

Accurate information about dynamic states is important for efficient control and operation of a power system. This paper compares the performance of four Bayesian-based filtering approaches in estimating dynamic states of a synchronous machine using phasor measurement unit data. The four methods are extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and particle filter. The statistical performance of each algorithm is compared using Monte Carlo methods and a two-area-four-machine test system. Under the statistical framework, robustness against measurement noise and process noise, sensitivity to sampling interval, and computation time are evaluated and compared for each approach. Based on the comparison, this paper makes some recommendations for the proper use of the methods.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.

Estimate the electromechanical states using particle filtering and smoothing

Accurate knowledge of electromechanical states is critical for efficient and reliable control of a power system. This paper proposes a particle filtering approach to estimate the electromechanical states of power systems from Phasor Measurement Unit (PMU) data. Without having to go through a laborious linearization procedure, the proposed particle filtering techniques can estimate states of a complex power system, which is often non-linear and has non-Gaussian noise. The proposed method is evaluated using a multi-machine system and its responses. Sensitivity studies of the dynamic state estimation performance are also presented to show the robustness of the proposed method. A promising path forward for the application of the proposed method is to reduce computational time through efficient parallel implementation owing to the inherent decoupling properties of particle filtering.

Capturing real-time power system dynamics: Opportunities and challenges

The power grid evolves towards a new mix of generation and consumption that introduces new dynamic and stochastic behaviors. These emerging grid behaviors would invalidate the steady-state assumption in todays state estimation - an essential function for real-time power grid operation. This paper examines this steady-state assumption and identifies the need for estimating dynamic states. Supporting technologies are presented as well as a proposed formulation for estimating dynamic states. Metrics for evaluating methods for solving the dynamic state estimation problem are proposed, with example results to illustrate the use of these metrics. The overall objective of this paper is to provide a basis that more research on this topic can follow.

An expectation-maximization method for calibrating synchronous machine models

The accuracy of a power system dynamic model is essential to its secure and efficient operation. Lower confidence in model accuracy usually leads to conservative operation and lowers asset usage. To improve model accuracy, this paper proposes an expectation-maximization (EM) method to calibrate the synchronous machine model using phasor measurement unit (PMU) data. First, an extended Kalman filter (EKF) is applied to estimate the dynamic states using measurement data. Then, the parameters are calculated based on the estimated states using the maximum likelihood estimation (MLE) method. The EM method iterates over the preceding two steps to improve estimation accuracy. The proposed EM methods performance is evaluated using a single-machine infinite bus system and compared with a method where both state and parameters are estimated using an EKF method. Sensitivity studies of the parameter calibration using the EM method also are presented to show the robustness of the proposed method for different levels of measurement noise and initial parameter uncertainty.

Capturing Dynamics in the Power Grid: Formulation of Dynamic State Estimation through Data Assimilation

With the increasing complexity resulting from uncertainties and stochastic variations introduced by intermittent renewable energy sources, responsive loads, mobile consumption of plug-in vehicles, and new market designs, more and more dynamic behaviors are observed in everyday power system operation. To operate a power system efficiently and reliably, it is critical to adopt a dynamic paradigm so that effective control actions can be taken in time. The dynamic paradigm needs to include three fundamental components: dynamic state estimation; look-ahead dynamic simulation; and dynamic contingency analysis (Figure 1). These three components answer three basic questions: where the system is; where the system is going; and how secure the system is against accidents. The dynamic state estimation provides a solid cornerstone to support the other 2 components and is the focus of this study.

Dynamic state estimation and parameter calibration of a DFIG using the ensemble Kalman filter

With the growing interest in the application of wind energy, doubly fed induction generators (DFIG) play an increasingly essential role in the power industry. It has been well recognized that modeling and monitoring the dynamic behavior of DFIGs are important to ensure power system reliability. Real-time estimation of the dynamic states of a DFIG is possible with high-speed measurements. But how to use such measurements to have high-quality estimation remains to be a challenge. Estimating dynamic states relies on a good dynamic model of the DFIG. Building a high-fidelity model is a problem in tandem with the dynamic state estimation problem. In this paper, we propose an ensemble Kalman filter (EnKF)-based method for the state estimation and parameter calibration of a DFIG. The mathematical formulation of state estimation combining with parameter estimation is presented. Simulation cases were studied to demonstrate the accuracy of both dynamic state estimation and parameter estimation. Sensitivity analysis is performed with respect to the measurement noise, initial state errors and parameter errors. The results indicate this EnKF-based method has a robust performance on the state estimation and parameter calibration of a DFIG.

Dynamic state estimation of a synchronous machine using PMU data: A comparative study

Accurate information about dynamic states is important for efficient control and operation of a power system. This paper compares the performance of four Bayesian-based filtering approaches in estimating dynamic states of a synchronous machine using PMU data. The four methods are Extended Kalman Filter, Unscented Kalman Filter, Ensemble Kalman Filter, and Particle Filter. The statistical performance of each algorithm is compared using Monte Carlo methods and a two-area-four-machine test system. Under the statistical framework, robustness against measurement noise and process noise, sensitivity to sampling interval, computation time are evaluated and compared for each approach. Based on the comparison, this paper makes some recommendations for the proper use of the methods.

Stochastic Operations and Planning

This document discusses PNNLs efforts to mitigate the changing patterns of electrical system behavior, how it is dispatched, and exchanges of energy.