Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning

Distribution system state estimation is essential for real-time monitoring and control of distribution systems. In recent years, an increasing number of Automated Meter Reading (AMR) systems have been installed to provide customer consumption information. The deployment of smart meters in low voltage (LV) distribution networks, within the context of Advanced Metering Infrastructure (AMI) systems, will enhance the electric energy consumption data storage, processing and analysis capabilities. Because of the limited number of real-time measurements in distribution systems, increased smart metering data availability from LV consumers is necessary to provide load estimates, which can be treated as pseudo-measurements to guarantee the network observability and estimate the system states. This paper presents two distinctive load estimation methods which utilize near real-time consumption data and short past consumption data, respectively. The accuracy of estimated loads is tested with a combined load and state estimation approach. Numerical results with a distribution system will show the effectiveness of the proposed algorithms.

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A Comparison of Moving Horizon and Bayesian State Estimators with an Application to a pH Process

Automated image classification is an essential task of the computer vision field. The tagging of images into a set of predefined groups is referred to as image classification. The implementation of computer vision to automate image classification would be beneficial because manual image evaluation and identification can be time-consuming, particularly when there are many images of different classes. Deep learning approaches are proven to overperform existing machine learning techniques in many fields in recent years, and computer vision is one of the most notable examples. The very deep neural network (VDCNN) is a powerful deep learning model for image classification, and this paper examines it briefly using MNIST handwritten digit dataset. This dataset is used to prove the efficacy of very deep neural networks over other deep learning models. The proposed study aims to comprehend the very deep neural network architecture used to accomplish a handwritten digit recognition task. The feasibility of the proposed model is evaluated using mean accuracy, validation accuracy, and standard deviation. The study results of the very deep neural network model are compared to a convolutional neural network and convolutional neural network with batch normalization. According to the results of the comparison study, very deep neural networks achieve high accuracy of 99.1% for a handwritten dataset. The outcome of the proposed work is used to interpret how well a very deep neural network performs when compared to the other two models of deep neural networks. This proposed architecture may be used to automate the classification of handwritten digits dataset.

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.

Estimation of internal states in a Li-ion battery using BiLSTM with Bayesian hyperparameter optimization

A solution to the state estimation problem of systems with unmeasurable non-zero mean inputs/disturbances, which do not satisfy the disturbance decoupling conditions, is given using the Kalman filtering and Bayesian estimation theory. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle filtering technique. The extra step, called supervisory layer, numerically solves the measurement equations for the portion of the state vector that cannot be estimated by the Kalman filter. First, it produces N randomly generated state vectors, the particles, which are distributed based on the Kalman filter’s last updated estimate. Then, the estimated measurement vector associated with each particle is compared to the actual measurement vector to identify the particle’s probability to be a solution. Finally, a so-called resampling stage is implemented to refine the particles with higher likelihoods. The effectiveness of the SKF is demonstrated by comparing its estimation performance with that of the standard Kalman Filter and the particle filter for a vehicle state estimation problem. The estimation results confirm that the SKF precisely estimates those states of the vehicle that cannot be estimated by either the Kalman filter or the particle filter, regardless of the unknown disturbances from the road. The filtering methodology offered in the article has a potential to improve performance of the systems presented in the patents WO2011115960, WO2010024751, US8073528, and US20110299730. Keywords: Bayesian state estimation, disturbance decoupling conditions, inputs/disturbances, particle filtering, state estimation, systems with unknown kalman filtering, unscented kalman filtering

Learning-based state estimation in distribution systems with limited real-time measurements

The presence of an accurate and efficient system state estimator is a precondition for supervision and closed-loop-control of low voltage grids. Such an estimator has to perform in consecutive periods of minutes. Between two periods in most cases, only the measurement values will change, but sometimes also the measurement model. This paper gives suggestions on how to improve the computationally efficiency of state estimation algorithms that have to perform in such an environment. The efficiency improvements are achieved by the application of advanced matrix inversion methods. Further the use of a linear measurement model and the application of the standard augmented matrix approach for solving the state estimation formula is suggested. However, these improvements can also be applied to other measurement models and estimation methods. The efficiency of the improvements is benchmarked against standard methods for different real grid operation cases. In particular, cases when new measurements are added or measurement values get lost are considered. The final result of the paper is an adjustable, robust and efficient algorithm for low voltage state estimation, presented in a way to support manufacturers and operators to implement and maintain it. The paper is a contribution in the field of static state estimation and short-term operation in distribution systems, in particular, low voltage grids.

This article proposes a forecasting-aided medium-voltage (MV) distribution system state estimation (SE) method using a robust ensemble Kalman filter (REnKF). In the proposed solution, low-voltage (LV) measurements at the LV side of secondary substations are used together with the mathematical model of the MV/LV substations to derive new equivalent MV measurements. This yields the improvement of measurement redundancy and robustness of the REnKF to bad data and unknown system process noise. Specifically, we rely on the temporal correlations of the constructed innovation vector as well as the projection statistics (PS) to detect and modify the measurement error covariance matrix. Furthermore, the system process noise covariance matrix is updated adaptively to mitigate the impacts of uncertainties ON-state forecasting and measurement filtering. Extensive comparisons have been carried out with both the traditional EnKF and other SE formulations under balanced and unbalanced distribution system conditions. The results reveal that our proposed REnKF is able to obtain accurate SE results under various operation conditions, including the presence of intermittent renewable energy sources, bad data, and system unbalance.

State estimation plays a critical role in power dis-tribution systems. However, the conventional state estimation commonly used in transmission systems cannot be applied to the distribution systems because of insufficient measurements. Even though machine learning methods have begun to demonstrate their capabilities to overcome this challenge, they are not capa-ble of explicitly incorporating distribution systems' topological information. This paper proposes EleGNN, an electrical-model-guided graph neural network (GNN), to perform power distri-bution system state estimation (DSSE). By explicitly considering physical topology, EleGNN enhances GNN with original node and edge feature propagation methods, allowing us to obtain accurate estimation results despite insufficient measurements and various topologies. Evaluations of six different power systems demonstrate significant improvement in state estimation accuracy than the method relying on general neural networks. Specifically, node-level mean square errors introduced by EleGNN are at least one order of magnitude smaller, even with up to 50% of missing measurements.

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

Monitoring and controlling the electrical distribution system for real time is becoming very important to improve its operating performance after transition to active distribution systems. So, many sensors are needed to monitor all parts in the systems. But if sensors are installed at all buses, investment cost becomes huge. To reduce the number of sensors, state estimation approach can be used to estimate the voltage of buses, which do not have sensors. State Estimation (SE) algorithms are broadly classified into Static State Estimator (SSE) and Dynamic State Estimator (DSE). This chapter classifies most algorithms used in active distribution networks, also State estimation in unbalanced distribution systems, and Role of PMU in Distribution System State Estimation.

Learning ability is the basic characteristic of human intelligence. The July 1, 2005 issue of Science published a list of 125 important questions in science. Among them, the question 94 “What are the limits of learning by machines?”. The annotation “Computers can already beat the world’s best chess players, and they have a wealth of information on the Web to draw on. But abstract reasoning is still beyond any machine”. In recent artificial intelligence has made great progresses. In 1997, the rise of the man-machine war, IBM Supercomputer Deep Blue defeated the chess master Garry Kasparov. On February 14, 2011, IBM’s Watson supercomputer won a practice round against Jeopardy champions Ken Jennings and Brad Rutter. In March 2016, Google DeepMind’s AlphaGo sealed a 4-1 victory over a South Korean Go grandmaster Lee Se-dol. This paper focuses on the machine learning methods of AlphaGo, including reinforcement learning, deep learning, deep reinforcement learning, analysis of the existing problems and the latest research progress. Deep reinforcement learning is the combination of deep learning and reinforcement learning, which can realize the learning algorithm from the perception to action. Simply said, this is the same as human behavior, input sensing information such as vision, and then, direct output action through the deep neural network. Deep reinforcement learning has the potential to learn a variety of skills for the robot to achieve full autonomy. Even though reinforcement learning is practiced successfully, but feature states need to manually set, for complex scene is a difficult thing, especially easy to cause the dimension disaster, and expression is not good. In 2010, Sascha Lange and Martin Riedmiller proposed deep auto-encoder neural networks in reinforcement learning to extract feature, which is used to control the visual correlation. In 2013, DeepMind proposed deep Q-network (DQN) in NIPS 2013, using convolution neural network to extract features, and then applied in reinforcement learning. They continue to improve and published an improved version of DQN on Nature in 2015, which has aroused widespread concern. In order to break through the limits of learning by machines, cognitive machine learning is proposed, which is the combination of machine learning and brain cognition, so that the machine intelligence is constantly evolving, and gradually reaches the human level of artificial intelligence. A cognitive model entitled Consciousness And Memory (CAM) is proposed by author, which consists of memory, consciousness, high-level cognitive functions, perception and motor. High-level cognitive functions of the brain include learning, language, thinking, decision making, emotion, and so on. Learning is a course to accept the stimulus through the nervous system and obtain new behavior, habits and accumulation experience. According to the current research progress of brain science and cognitive science, cognitive machine learning may be interested in learning emergence, procedural memory knowledge learning, learning evolution and so on. For intelligence, so-called evolution is refers to the learning of learning and the structure also follows the change. It is important to record the learning result by structure changing and improve the learning method.

Due to low levels of observability and automation in active distribution networks (ADNs), the deployment of accurate measurement devices would be inevitable to increase the network observability. This work develops an optimal framework for phasor measurement unit (PMU) placement considering the accuracy of the distribution system state estimation (DSSE) process. In this regard, first, considering the significance of active power in supplying network loads, an active power sensitivity analysis is conducted in which the accuracy of active power injection at each bus is multiplied by its value of lost load. In this way, the accuracy of active power estimation could be transformed into a monetary value. Then, based on the determined sensitivity criterion, the optimal placement of PMUs has been performed with the aim of appropriate accuracy for the DSSE. On the other hand, the accuracy of the results obtained in the state estimation procedure can affect the estimation of line-loadings and lead to load shedding due to the low accuracy of estimated line-loadings. It is noteworthy that due to the high integration of distributed energy resources in distribution systems, ADNs would be prone to congestion issues. Therefore, in the next stage, this perspective is also used for determining the optimal number and location of PMUs in ADNs to improve their observability based on the operational conditions of the network. Finally, the developed algorithm is applied on the 77-bus-UK-test distribution network to investigate its effectiveness in improving the DSSE accuracy and mitigating interrupted loads. The numerical results indicate that implementing the proposed framework not only increases the DSSE accuracy but also decreases the cost of compensating the accuracy of active power by 7% compared to the typical network without PMUs. Further, the results show that the proposed model significantly mitigates the total curtailed loads due to the low accuracy of estimated line-loadings.