## Dynamic State Estimation

Today’s grid operations are based on the static power flow model, which describes the steady state (or quasi-steady state) of the grid. Recent developments in phasor technology make estimating dynamic states possible with high-speed time-synchronized measurement data. Advancements in high performance computing enable the associated computation to be finished within the short time intervals required for real-time power grid operation. For future power grids with intermittent renewable energy sources and responsive loads, it is essential to establish a dynamic operation paradigm in contrast to today’s operation built on static state estimation. Such a dynamic paradigm will include three fundamental components: dynamic state estimation, look-ahead dynamic simulation, and dynamic contingency analysis as illustrated in Figure 1. Essentially, these three components answer three basic questions: where the system is; where the system is going; and what are other possible futures for the system.

Figure 1. Integrated real-time operations platform for state estimation and grid simulation. Click for a larger image.

State estimation, as a central function in power grid operations, generates critical inputs for other operational tools. Traditional state estimators receive telemetered data from a supervisory control and data acquisition (SCADA) system in the time interval of several seconds. The telemetered SCADA data is used in conjunction with a steady-state system model to estimate a set of static state variables, i.e., bus voltages and phase angles. The result of computing only the static state variables is that the state estimator generates a series of snapshots of the system conditions, in which the dynamic transition between the snapshots is not considered. Recent developments in phasor technology make estimating dynamic states (e.g., rotor angle and generator speed) possible with high-speed time-synchronized measurement data. Phasor measurement units (PMU) with a typical sampling rate of 30 samples per second currently are able to capture the major dynamics in power grids, and thus enable dynamic state estimation. Dynamic state estimation provides a full dynamic view of a power grid, which further enables look-ahead dynamic simulation and dynamic contingency analysis.

Figure 2. State tracking of one generator in the 16-generator system. The solid red line is the true value from simulation. The scattered blue dots are the estimated states from an EnKF. Click for a larger image.

Dynamic state estimation introduces dynamic models for real-time power grid operation. At Pacific Northwest National Laboratory, we have formulated the dynamic state estimation problem as a Kalman filter process. Both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) techniques have been applied to estimate dynamic states. The dynamics of a power system can be modeled as a set of non-linear differential algebraic equations. Applying EKF and EnKF, the dynamic states can be estimated using a prediction-correction process. Tests with a 16-generator system demonstrated good tracking performance of an EnKF-based dynamic state estimation (Figure 2). The test system consisted of 16 generators, 86 transmission lines, and 68 buses. A 0.05-second disturbance from a three-phase-to-ground fault at a bus at 1.1 second was simulated with 3% noise added to all simulated voltages. The estimated rotor angle and rotor speed of one generator is shown in Figure 2. As can be seen, initial errors in the state variables affect only the state variable tracking for the initial time period. After a short time, e.g., about 1s, there is no significant error for the state tracking. The disturbance does cause some deviation in the tracking. The Kalman filter can correct itself with continuous data and track the states again. Overall performance indicates that once the EnKF is locked into tracking, the accuracy of tracking is consistently good for continuous tracking.

(a) Execution time. Click for a larger image.

(b) Speedup. Click for a larger image.

Figure 3. Computational performance of EnKF-based dynamic state estimation with a 16072-bus system: (a) execution time; (b) speedup.Besides tracking accuracy, estimating dynamic states fast enough is another important aspect for real-time application. The Kalman filter has high computation demands and requires a large number of FLOPS (floating point operations per second), especially for large power grids. HPC computers with thousands to hundreds of thousands of processor cores are needed to speed up the computation. Implementing and parallelizing codes on such HPC computers is a fundamental challenge. An initial attempt (Figure 3) has shown a promising path forward to achieve the required computational performance. Figure 3(a) is the time used to compute one time step of the EnKF dynamic state estimation for a Western Electricity Coordinating Coundil (WECC)-size system. The parallel codes are based on the Global Array programming model. Although the best time, at 128 cores, is still about 1000 times longer than 0.03 second (the phasor measurement cycle), the execution time decreases consistently as more processor cores are applied. This is confirmed by the speedup curve in Figure 3(b). Dynamic state estimation is very attainable, especially for regional power systems.

## Notable Publications

K. Schneider, Z. Huang, B. Yang, M. Hauer, and Y. Nieplocha, “Dynamic state estimation utilizing high performance computing methods,” in Proceeding IEEE PES Power Systems Conference & Exposition, 2009.

J. Zhang, G. Welch, G. Bishop, and Z. Huang, “Optimal PMU placement evaluation for power system dynamic state estimation,” in Proceeding IEEE PES Innovative Smart Grid Technologies (ISGT) Europe Conference, Oct. 2010.

J. Zhang, G. Welch, G. Bishop, and Z. Huang, “Reduced measurement-space dynamic state estimation (ReMeDySE) for power systems,” in Proceeding IEEE Trondheim PowerTech., Jun. 2011.

Z. Huang, N. Zhou, Y. Li, P. Nichols, S. Jin, R. Diao, and Y. Chen, “Dynamic paradigm for future power grid operation,” in Proceeding 8th Power Plants Power System Control Symposium, 2012, pp. 218–223.

Y. Li, Z. Huang, N. Zhou, B. Lee, R. Diao, and P. Du, “Application of ensemble Kalman filter in power system state tracking and sensitivity analysis,” in Proceeding IEEE Power Energy Society Transmission and Distribution Conference and Exposition, May 2012.

D. Meng, N. Zhou, S. Lu, and G. Lin, “Estimate the electromechanical states using particle filtering and smoothing,” in Proceeding IEEE Power Energy Society General Meeting, Jul. 2012.

N. Zhou, Z. Huang, Y. Li, and G. Welch, “Local sequential ensemble Kalman filter for simultaneously tracking states and parameters,” in Proceeding North American Power Symposium (NAPS), Sep. 2012.

N. Zhou, Z. Huang, G. Welch, and J. Zhang, “Identifying optimal measurement subspace for ensemble Kalman filter,” IET Electronics Letters, vol. 48, no. 11, pp. 618–620, May 2012.

**Presentations**

Zhenyu Huang et. al. “Fusing Models and Data for a Dynamic Paradigm of Power Grid Operations,” presented at DOE Applied Mathematics Program Meeting, Washington, DC, Oct. 17-19, 2011.

Ning Zhou, Zhenyu Huang, Yulan Li, Greg Welch, Patrick Nichols, Steve Elbert, Pengwei Du, Ruisheng Diao, “Tracking Dynamic States and Parameters using an Ensemble Kalman Filter,” presented at DOE Advanced Grid Modeling Workshop, Knoxville, Tennessee, Feb. 5-6, 2013.

Zhou, Ning; Huang, Zhenyu; Chen, Yousu; Diao, Ruisheng; Elbert, Stephen T; Jin, Shuangshuang; Makarov, Yuri V, “Improving Situational Awareness for Power Grids”, presented at the 4th Annual National Science Foundation (NSF) Emerging Frontiers in Research and Innovation (EFRI) COPN Workshop, Clemson, SC, Oct 28, 2012.