Machine Learning-Based Predictive State Estimation
This talk presents the machine-based predictive state estimation method developed in Grid Optimization with Solar (GO-Solar) project.
41 EE - Solar Energy Technologies Office (EE-4S)↗
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Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches
With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. Furthermore, the comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.
97 MATHEMATICS AND COMPUTING↗
Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids
Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Dynamic Matrix Completion Based State Estimation in Distribution Grids
The power distribution network is undergoing tremendous transformation due to an increase in the penetration of renewable energy resources and electric vehicles. These changes have resulted in greater uncertainty and dynamics in the distribution grid states. Therefore, the ability to track and monitor system states has become a critical need for accurate and timely control actions. In this paper, we propose two dynamic sparsity-based state estimation approaches for distribution systems: (1) locally weighted matrix completion (LW-MC) and (2) Bayesian matrix completion with Kalman filter prediction (BMC-KF). The performance of the proposed dynamic state estimation strategies is compared with the classic/static matrix completion (static-MC) approach using the IEEE 37 and IEEE 123 bus test systems. Finally, results indicate that BMC-KF approach outperforms both LW-MC as well as static-MC even when 30% of the measurement data is available. Computational complexity associated with both approaches is quantified.
42 ENGINEERING↗
Secure State Estimation with Asynchronous Measurements for Coordinated Cyber Attack Detection in Active Distribution Systems
Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data.
asynchronous measurements↗
A Scalable Meter Placement Method for Distribution System State Estimation
This paper studies the optimal meter placement problem for distribution system state estimation given limited measurement resources. We formulate the problem as a mixed integer semi-definite programming that minimizes the worst case estimation errors over a set of operating points. To solve the problem, we first relax the problem as a convex optimization problem. Motivated by the lack of scalability of existing solvers, we next leverage the special structure of the cost function and propose an algorithm based on barrier method that solves the problem with significantly better numerical performance. The proposed method has been validated on the IEEE 13-bus, IEEE 123-bus, and IEEE 8,500-bus feeders.
barrier method↗
Solving Optimal Power Flow for Distribution Networks with State Estimation Feedback
Conventional optimal power flow (OPF) solvers assume full observability of the involved system states. However in practice, there is a lack of reliable system monitoring devices in the distribution networks. To close the gap between the theoretic algorithm design and practical implementation, this work proposes to solve the OPF problems based on the state estimation (SE) feedback for the distribution networks where only a part of the involved system states are physically measured. The SE feedback increases the observability of the under-measured system and provides more accurate system states monitoring when the measurements are noisy. We analytically investigate the convergence of the proposed algorithm. The numerical results demonstrate that the proposed approach is more robust to large pseudo measurement variability and inherent sensor noise in comparison to the other frameworks without SE feedback.
distirbution systems↗
High Impedance Fault Detection Through Quasi-Static State Estimation: A Parameter Error Modeling Approach
This paper presents a model for detecting high impedance faults using parameter error modeling and a two step per-phase weighted-least squares state estimation process. The proposed scheme leverages the use of Phasor Measurement Units and synthetic measurements to identify per-phase power flow and injection measurements which indicate a parameter error through ?2 Hypothesis Testing applied to the composed measurement error. Although current and voltage waveforms are commonly analyzed for high-impedance fault detection, wide area power flow and injection measurements, which are already inherent to the state estimation process, also show promise for real-world high-impedance fault detection applications. The error distributions after detection share the measurement function error spread observed in proven parameter error diagnostics and can be applied to high-impedance fault identification. Further, this error spread across measurement functions related to the fault will be clearly discerned from measurement error. Case studies are performed on the IEEE 33-Bus Distribution System along with the proposed model in Simulink.
Cooper, Austin↗
A practical and efficient approach for Bayesian quantum state estimation
Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Real Time Applications Using Linear State Estimation Technology (RTA/LSE)
Electric Power Group, LLC (EPG) was awarded DOE OE0000849 to design, develop, and demonstrate three real-time applications for monitoring power system stability. The applications use phasor measurements and processing by a linear state estimator (LSE) to improve system visibility and accuracy. These applications leverage the large and expanding phasor measurement systems being deployed by utilities throughout the world, and specifically in the United States. Phasor measurements provide a much more detailed view of the power systems than traditional SCADA systems, so can provide better visibility of events and an early warning of developing problems. These three applications are real-time contingency analysis (RTCA), area angle monitoring (AAM), and a voltage stability index (VSI). The project was fully completed as proposed. All three applications were successfully implemented and demonstrated. There were challenges the caused project delays, however. While the RTCA is based on well-known concepts and readily available tools, its deployment using phasor measurements meant it needed to be adapted to sometimes sparse measurements and limited coverage areas. EPG met these challenges with extensive modeling and testing. The AAM is based on unproven research, so EPG had to deal with a lot of unknowns and develop additional methods for practical implementation. These activities took more time than anticipated, so required extra time for development. In addition, there was difficulty getting adequate measurement locations for successful deployment and utility installation delays. Consequently, the project required a time extension to complete. These three real-time applications, RTCA, AAM, and VSI, use only phasor measurement input. Since they do not require the EMS or other measurement systems, they can serve as a backup and security check for the EMS. Phasor measurements are validated and extended by an LSE. The LSE will always produce an output even when some inputs are impaired, so the RT applications will operate even when the EMS state estimator does not converge and the applications it supports cannot function. Consequently, these RT applications can provide valuable additional reliability for control center operation.
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Optimal Power Flow With State Estimation in the Loop for Distribution Networks
Here in this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy "pseudomeasurements." We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.
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Multiarea Distribution System State Estimation via Distributed Tensor Completion
Here, this paper proposes a model-free distribution system state estimation method based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Multi-Area Model-Free State Estimation via Distributed Tensor Decomposition
This paper proposes a model-free method for distribution system state estimation based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A third-order tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. To demonstrate the efficacy of the developed algorithm, numerical simulations are carried out using an IEEE test system.
alternating direction method of multipliers↗
Physics-guided Deep Learning for Power System State Estimation
In the past decade, dramatic progress has been made in the field of machine learning. This paper explores the possibility of applying deep learning in power system state estimation. Traditionally, physics-based models are used including weighted least square (WLS) or weighted least absolute value (WLAV). These models typically consider a single snapshot of the system without capturing temporal correlations of system states. In this paper, a physics-guided deep learning (PGDL) method is proposed. Specifically, inspired by autoencoders, deep neural networks (DNNs) are used to learn the temporal correlations. The estimated system states from DNNs are then checked against physics laws by running through a set of power flow equations. Hence, the proposed PGDL is both data-driven and physics-guided. The accuracy and robustness of the proposed PGDL method are compared with traditional methods in standard IEEE cases. Simulations show promising results and the applicability is further discussed.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Robust Adaptive Decentralized Dynamic State Estimation with Unknown Control Inputs using Field PMU Measurements
This paper proposes a robust adaptive decentralized dynamic state estimation method for power system with unknown inputs of the highly detailed synchronous machine model. The temporal and spatial correlations among the unknown inputs are used to derive a vector auto-regressive model. The latter is further integrated together with state transition and measurement models for joint state and unknown inputs estimation. Thanks to the consideration of implicit cross-correlations between the states and the unknown inputs, only generator terminal voltage and current phasors are needed. Test results on the US WECC system using the field PMU measurements show that the proposed method is able to track both the system dynamic states and unknown controller inputs. These information could significantly benefit the validation and calibration of generator controller parameters.
Zhao, Junbo↗
A General Decentralized Dynamic State Estimation With Synchronous Generator Magnetic Saturation
We report the saturation of the nonlinear magnetic circuit of synchronous generators is often neglected when performing Kalman filter-based dynamic state estimation (DSE), yielding significant estimation bias. This letter addresses this problem and proposes a generalized DSE framework to handle magnetic saturation. Moreover, this letter derives a state initialization procedure that improves the Kalman filter tracking speed. The framework is flexible in dealing with different saturation functions and generator models. Numerical results on the Texas 2000-bus system verify the effectiveness of the proposed method.
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Distribution System State Estimation With High Penetration of Demand Response Enabled Loads
Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A Hybrid-Learning Algorithm for Online Dynamic State Estimation in Multimachine Power Systems
With the increasing penetration of distributed generators in the smart grids, having knowledge of rapid real-time electromechanical dynamic states has become crucial to system stability control. Conventional Supervisory Control and Data Acquisition (SCADA)-based dynamic state estimation (DSE) techniques are limited by the slow sampling rates, while the emerging phasor measurement units (PMUs) technology enables rapid real-time measurements at network nodes. Using generator bus terminal voltages, we propose a hybrid-learning DSE (HL-DSE) algorithm to estimate the synchronous machine rotor angle and speed in real time. The HL-DSE takes the power system model into account and trains neuroestimators with real-time data in an online manner. Compared with traditional DSE methods, the HL-DSE overcomes limitations by using a data-driven approach in conjunction with the physical power system model. The time efficiency, accuracy, convergence, and robustness of the proposed algorithm are tested under noises and fault conditions in both small- and large-scale test systems. Simulation results show that the proposed HL-DSE is much more computationally efficient than widely used Kalman filter (KF)-based methods while maintaining comparable accuracy and robustness. In particular, HL-DSE is over 100 times faster than square-root unscented KF (SR-UKF) and 80 times faster than extended KF (EKF). The advantages and challenges of the HL-DSE are also discussed.
24 POWER TRANSMISSION AND DISTRIBUTION↗