Distribution System State Estimation Research Articles

Physics-Informed Graphical Learning and Bayesian Averaging for Robust Distribution State Estimation

This paper proposes a robust topology change-aware distribution system state estimation (DSSE) method based on a physics-informed graph neural network and Bayesian Probability Weighted Averaging (BPWA). A general state estimator is first built utilizing a graph attention network to learn the nonlinear mapping functions under different distribution network topologies. During this stage, the topology information is embedded in the neural network and the attention mechanism is employed to capture collaborative signals and discriminate the importance of neighboring buses. Then, the BPWA method allows assigning proper weights for the state estimation results under different topologies, which finally yields a single consensus solution via the sparse training samples under the new topology. The physics-informed mechanism enables the proposed method to embed the topology knowledge in the neural network while fully exploiting the value of historical data. Robustness to anomalous measurements is achieved through the embedding of physics knowledge. The application of the BPWA method further allows the proposed method to achieve faster adaptation to topology change and quantification of the estimation uncertainties by measurement errors. MATLAB and Python are used to carry out the comparative tests to evaluate the performance of the proposed method.

Bibliometric study of distribution system state estimation: advances and challenges

An active distribution network with a large amount of distributed energy resources (DER) requires knowledge of the operational status of the network. In this sense, state estimation is one of the most widely used techniques and a well-developed concept in transmission systems. DERs have some monitoring, protection, and control devices. But due to the large size of the network and the number of users, the massive installation of meters is not yet economically feasible. Therefore, it is necessary to generate artificial measurements to perform all stages of distribution system state estimation (DSSE). DSSE is currently the subject of active research, so this article performs a descriptive bibliometric study, which qualitatively and quantitatively analyzes the topics found in the specialized literature in the period from 2000 to 2022 and part of the 2023. It also identifies the advances, challenges, and proposals for future lines of research in DSSE.

Distributed Dynamic State Estimation of Power Systems Considering Dynamic State Constraints based on Phasor Measurements Units

Background: Dynamic state estimation can provide detailed information about power systems. However, there is no clear, dynamic equation for the state transition of bus voltages in power systems. Currently, smoothing methods based on historical data are commonly used, but they cannot ensure accurate state prediction in power systems with a large amount of renewable energy. Moreover, the fast sampling rate of phasor measurement units generates a vast amount of real-time data for the dispatch center, making it challenging for centralized state estimation to meet real-time demands. Objective: This paper proposes a distributed power system state estimation considering dynamic state constraints to address the above issues. Methods: By incorporating the constraints between the dynamic states of the system dynamic components and the bus voltage phasors, the state transition equations for bus voltage phasors are constructed based on the predicted dynamic states and the nodal injection power equations. This allows taking the dynamic model constraints into account when predicting bus voltage phasors. Then, based on the principle of hierarchical coordination and distributed state estimation, the method of estimation-coordination-correction is adopted to acquire system state information quickly and accurately. method: By incorporating the constraints between the dynamic states of the system dynamic components and the bus voltage phasors, the state transition equations for bus voltage phasors are constructed based on the predicted dynamic states and the nodal injection power equations. This allows taking the dynamic model constraints into account when predicting bus voltage phasors. Then, based on the principle of hierarchical coordination and distributed state estimation, the method of estimation-coordination-correction is adopted to acquire system state information quickly and accurately. Results: Furthermore, an IEEE 9-bus system and an IEEE 39-bus system are used to validate the proposed method. The proposed method is compared with other algorithms to prove its superiority. result: Furthermore, an IEEE 9-bus system and an IEEE 39-bus system are used to validate the proposed method. And the proposed method is compared with other algorithms to prove its superiority. Conclusion: The simulation results show that the proposed method can effectively improve the accuracy of the state estimation results of power systems under dynamic conditions. conclusion: The simulation results show that the proposed method can effectively improve the accuracy of the state estimation results of power systems under dynamic conditions. other: None

Event-Triggered Distribution System State Estimation: Sparse Kalman Filtering With Reinforced Coupling

A novel distribution system state estimation (DSSE) method is proposed for power distribution networks with low-observablity, where the measurements come from only a few distribution-level phasor measurement units (D-PMUs). The proposed DSSE method is event-triggered, which means the state variables are updated based on the information that is extracted from the events in the power distribution system. In this regard, the estimations of the state variables during the previous events are used as priori information to predict the state variables at the current event. Accordingly, a novel data-driven method based on elastic net regression analysis is proposed to learn the event-triggered state transition matrix. The DSSE problem is formulated as a generalized group Lasso problem, which is augmented based on the knowledge on the sparsity patterns of the state variables that are extracted from the analysis of the events. Here, in the absence of direct power measurements, we enhance our ability in sparse recovery by developing a new reinforced physics-based coupling method among the state variables, in which we add a novel set of linear differential power flow equations to the DSSE problem formulation in forms of virtual measurements. Finally, two different approaches are proposed to solve the formulated sparse event-triggered DSSE problem. The first approach is exact but computationally expensive, as it requires conducting a batch alternating direction method of multipliers (ADMM) analysis. The second approach is approximate, but it is much faster as it works based on a novel modified Kalman filter/smoother in the presence of ℓ1-norm.

Allocation of Dynamic Operating Envelopes in Distribution Networks: Technical and Equitable Perspectives

A Dynamic Operating Envelope (DOE) specifies the available capacity to import/export power for Distributed Energy Resources (DERs) or connection points of a distribution network in a time interval without violating its physical and operational constraints. This paper proposes a two-stage, top-down approach to allocate DOEs in MV-LV (medium voltage-low voltage) integrated distribution networks. In the first stage, Distribution System State Estimation (DSSE) and Capacity Constrained State Optimisation (CCSO) techniques are employed to allocate DOEs at transformer connection points. Using network data from available metering infrastructure, DSSE estimates the current operational state of the network, whereas CCSO facilitates the DOE allocations at transformer connection points considering technical, soft-equitable and equitable perspectives. In the second stage, the allocated DOEs, containing available aggregate export/import power, are distributed among DERs of LV networks ensuring network integrity. Real-world data of an Australian MV-LV network is employed to demonstrate the effectiveness of proposed approach. Test results show that technical perspective can offer maximum allocated export/import power, whereas, minimum disparity of allocated power among different connection-points is attained for equitable perspective. Further, insightful performance studies of DOE and existing fixed export policies are conducted considering the condition of present as well as future power systems expecting substantial proliferations of renewables.

Forecasting-Aided Joint Topology/State Estimation for Distribution Systems via Bayesian Non-Parametric Modeling

To ensure the validity of distribution system state estimation (DSSE) in case of frequent topology changes, it is important to develop DSSE methods with topology identification capability. This paper proposes a forecasting-aided joint topology/state estimation method for distribution systems considering topology changes. The joint estimation problem is formulated under the Dirichlet-process hidden-Markov-model (DP-HMM), which requires establishing state-space models for a partial set of topologies (i.e., predefined topologies) and constructing probability distribution of the other possible topologies (i.e., unseen topologies). A particle filter (PF)-based method is proposed to resolve this joint estimation problem, which augments the particles to include both topology-related variables and nodal voltages. Its robustness against measurement outliers is enhanced by adopting the anti-zero bias modification. The base distribution for unseen topologies are constructed via probabilistic neural networks (PNNs). To improve the accuracy of PNNs, the synthetic minority oversampling technique is employed to rebalance the training data. Aiming at efficiency enhancement, a rule-based candidate set reduction method is proposed for the unseen topologies to improve topology sampling validity. Test results on the IEEE 33-bus, IEEE 123-bus, and a modified 2516-bus distribution systems show that the proposed method has good state and topology estimation accuracy while achieving good scalability.

Distribution System State Estimation with Convolutional Generative Adversarial Imputation Networks for Missing Measurement Data

Distribution System State Estimation with Convolutional Generative Adversarial Imputation Networks for Missing Measurement Data

Distribution system state estimation with Transformer-Bi-LSTM-based imputation model for missing measurements

Distribution system state estimation with Transformer-Bi-LSTM-based imputation model for missing measurements

Leveraging Behavioral Correlation in Distribution System State Estimation for the Recognition of Critical System States

State estimation for distribution systems faces the challenge of dealing with limited real-time measurements and historical data. This work describes a Bayesian state estimation approach tailored for practical implementation in different data availability scenarios, especially when both real-time and historical data are scarce. The approach leverages statistical correlations of the state variables from a twofold origin: (1) from the physical coupling through the grid and (2) from similar behavioral patterns of customers. We show how these correlations can be parameterized, especially when no historical time series data are available, and that accounting for these correlations yields substantial accuracy gains for state estimation and for the recognition of critical system states, i.e., states with voltage or current limit violations. In a case study, the approach is tested in a realistic European-type, medium-voltage grid. The method accurately recognizes critical system states with an aggregated true positive rate of 98%. Compared to widely used approaches that do not consider these correlations, the number of undetected true critical cases can be reduced by a factor of up to 9. Particularly in the case where no historical smart meter time series data is available, the recognition accuracy of critical system states is nearly as high as with full smart meter coverage.

Role of Voltage Control Devices in Low Voltage State Estimation Process

Megatrends, such as the proliferation of distributed generation, electrification, and the appearance of aggregator companies, put the low voltage power grids under intense pressure. Since the network infrastructure developments cannot keep up with the trends, distribution system operators turned to alternative solutions. Smart grid assets, such as on-load tap-changing distribution transformers or serial low voltage regulators, are promising solutions. However, the energy transition cannot be handled with the network expansive on the distribution level. Control centers are predicted to expand to this voltage level in the near future, and distribution system state estimation could be an enabler of all functionalities. On the low voltage level, data scarcity is a great challenge in observability; therefore, research must focus on the creation of pseudomeasurements and integration of available data sources. This paper examines the inclusion of smart assets from the conceptual point to the application on two sites, based on data from operational environments, both with a pseudomeasurement and an integrated metering point approach. The results showed that integrating smart assets could considerably mitigate voltage fluctuations, and reduce estimation errors by two magnitudes on the low voltage network.

An Overview of Supervised Machine Learning Approaches for Applications in Active Distribution Networks

Distribution grids must be regularly updated to meet the global electricity demand. Some of these updates result in fundamental changes to the structure of the grid network. Some recent changes include two-way communication infrastructure, the rapid development of distributed generations (DGs) in different forms, and the installation of smart measurement tools. In addition to other changes, these lead to distribution grid modifications, allowing more advanced features. Even though these advanced technologies enhance distribution grid performance, the operation, management, and control of active distribution networks (ADNs) have become more complicated. For example, distribution system state estimation (DSSE) calculations have been introduced as a tool to estimate the performance of distribution grids. These DSSE computations are highly dependent on data obtained from measurement devices in distribution grids. However, sufficient measurement devices are not available in ADNs due to economic constraints and various configurations of distribution grids. Thus, the modeling of pseudo-measurements using conventional and machine learning techniques from historical information in distribution grids is applied to address the lack of real measurements in ADNs. Different types of measurements (real, pseudo, and virtual measurements), alongside network parameters, are fed into model-based or data-based DSSE approaches to estimate the state variables of the distribution grid. The results obtained through DSSE should be sufficiently accurate for the appropriate management and overall performance evaluation of a distribution grid in a control center. However, distribution grids are prone to different cyberattacks, which can endanger their safe operation. One particular type of cyberattack is known as a false data injection attack (FDIA) on measurement data. Attackers try to inject false data into the measurements of nodes to falsify DSSE results. The FDIA can sometimes bypass poor traditional data-detection processes. If FDIAs cannot be identified successfully, the distribution grid’s performance is degraded significantly. Currently, different machine learning applications are applied widely to model pseudo-measurements, calculate DSSE variables, and identify FDIAs on measurement data to achieve the desired distribution grid operation and performance. In this study, we present a comprehensive review investigating the use of supervised machine learning (SML) in distribution grids to enhance and improve the operation and performance of advanced distribution grids according to three perspectives: (1) pseudo-measurement generation (via short-term load forecasting); (2) DSSE calculation; and (3) FDIA detection on measurement data. This review demonstrates the importance of SML in the management of ADN operation.

A co-optimized approach for state estimation based micro phasor measurement unit allocation in power distribution infrastructure

Due to the highly complex and dynamic electrical characteristics of the 3-phase unbalanced power delivery networks (PDNs), it is challenging for utilities to observe the network entirely. This impediment necessitates the PDNs to become intelligent nowadays in the presence of various smart devices. Micro-phasor measurement units (µPMUs) are expected to play a crucial role in observing the smart power distribution system due to their micro-seconds resolution and millidegree precision accuracy. The placement of µPMUs in PDNs is also very challenging due to their associated costs. So, allocating a minimal number of µPMUs in PDN with fulfilling the topological observability can elucidate the issue of real-time visibility of the entire system. This paper presents a novel co-optimized placement strategy of µPMUs (CPMP) in PDNs that minimizes the µPMU numbers and the estimation error in the buses other than the µPMU assigned nodes. This work also displays a novel dynamic heuristic distribution system state estimation (DDSSE) to estimate the system's unknown states by using only the information of bus voltage phasors at the µPMU specified buses. The DDSSE is used to estimate the root mean square error (RMSE) in estimated voltage magnitudes and angles. Besides this, the efficacy of the grey-wolf optimizer (GWO) is presented in this work to solve the newly formulated placement problem. The results are validated on an Indian 19-bus and 34-bus unbalanced radial distribution system (URDS), and a detailed comparative study of different heuristic algorithms is also analyzed in this work.

Bayesian optimization of multi-layer perceptron models for power distribution system state estimation

Abstract Feedforward multilayer perceptron models (MLPs) have been applied to power distribution system state estimation (DSSE) in the past. Existing methods usually employ an ad-hoc or trial and error approach to MLP hyperparameter selection, and thus a systematic way of selecting the optimal hyperparameters including the number of neurons per hidden layer, learning rate, number of training epochs and training batch size is desirable and needed. This paper presents an approach based on Bayesian Optimization with Gaussian Processes for selecting MLP model hyperparameters for state estimation purposes. Results of the optimized MLP models are presented alongside the unoptimized models to compare performance of training, testing, and validation in terms of root-mean-squared-error (RMSE). Additionally, machine learning pipelines were employed and total execution time (seconds) for each trial is presented. The study shows that the MLP models obtained through the proposed optimization method outperform unoptimized models in terms of generalization capability for unseen, new cases.

Distribution System State Estimation Using Hybrid Traditional and Advanced Measurements for Grid Modernization

Distribution System State Estimation (DSSE) techniques have been introduced to monitor and control Active Distribution Networks (ADNs). DSSE calculations are commonly performed using both conventional measurements and pseudo-measurements. Conventional measurements are typically asynchronous and have low update rates, thus leading to inaccurate DSSE results for dynamically changing ADNs. Because of this, smart measurement devices, which are synchronous at high frame rates, have recently been introduced to enhance the monitoring and control of ADNs in modern power networks. However, replacing all traditional measurement devices with smart measurements is not feasible over a short time. Thus, an essential part of the grid modernization process is to use both traditional and advanced measurements to improve DSSE results. In this paper, a new method is proposed to hybridize traditional and advanced measurements using an online machine learning model. In this work, we assume that an ADN has been monitored using traditional measurements and the Weighted Least Square (WLS) method to obtain DSSE results, and the voltage magnitude and phase angle at each bus are considered as state vectors. After a period of time, a network is modified by the installation of advanced measurement devices, such as Phasor Measurement Units (PMUs), to facilitate ADN monitoring and control with a desired performance. Our work proposes a method for taking advantage of all available measurements to improve DSSE results. First, a machine-learning-based regression model was trained from DSSE results obtained using only the traditional measurements available before the installation of smart measurement devices. After smart measurement devices were added to the network, the model predicted traditional measurements when those measurements were not available to enable synchronization between the traditional and smart sensors, despite their different refresh rates. We show that the regression model had improved performance under the condition that it continued to be updated regularly as more data were collected from the measurement devices. In this way, the training model became robust and improved the DSSE performance, even in the presence of more Distributed Generations (DGs). The results of the proposed method were compared to traditional measurements incorporated into the DSSE calculation using a sample-and-hold technique. We present the DSSE results in terms of Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) values for all approaches. The effectiveness of the proposed method was validated using two case studies in the presence of DGs: one using a modified IEEE 33-bus distribution system that considered loads and DGs based on a Monte Carlo simulation and the other using a modified IEEE 69-bus system that considered actual data for loads and DGs. The DSSE results illustrate that the proposed method is better than the sample-and-hold method.

Iterative Distribution System State Estimation for Integrated Primary and Split-Phase Secondary Feeder Monitoring

The observability of split-phase low-voltage (LV) secondary distribution feeders continues to pose a challenge in distribution system state estimation, which has traditionally been modeled for medium-voltage (MV) primary feeders. This work aims to improve the observability of LV feeders using smart meter data to enable a joint primary (MV) and secondary (LV) feeder state estimation. Towards this goal, a two-stage MV-LV state estimation algorithm is proposed that is iteratively executed until convergence at the MV-LV boundary. Specifically, Stage-I estimates primary feeder (MV) states using approximated load demands at the MV buses obtained from Stage-II. Stage-II estimates the secondary feeder (LV) states and improved load demands at the MV level using the MV voltage estimates obtained from Stage-I and smart meter data. black The algorithm terminates once the sequence of estimated variables from both stages at the MV-LV boundary bus, i.e., load demand (from Stage-II) and voltage (from Stage-I) have converged. The proposed algorithm is demonstrated using the IEEE 123 bus distribution test feeder modified to include secondary network extensions at 47 different nodes. The simulation results validate that the proposed approach facilitates the observability of the split-phase LV systems and enables the joint estimation of MV-LV states. Moreover, the accuracy of the primary feeder (MV) state estimation results is improved using the proposed approach to model and estimate split-phase LV feeders.

A Physics-Aware MIQP Approach to Harmonic State Estimation in Low-Observable Power Distribution Systems Using Harmonic Phasor Measurement Units

In this paper, a novel physics-aware harmonic state estimation (HSE) method is developed for power distribution systems with low-observability. The only available measurements are the harmonic synchrophasors from a small number of Harmonic Phasor Measurement Units (H-PMUs) on a power distribution feeder. The proposed HSE method provides a novel and practical application of H-PMUs, which are an emerging class of smart grid sensors, in order to address an important and challenging problem in power distribution system monitoring. More importantly, the proposed HSE method can address the highly challenging scenario, in which, not only the network has a low-observability condition, but also the number and the location(s) of the harmonic sources are unknown. The proposed HSE method captures physics-based sparsity pattern in the analysis of harmonic phasors, and then it incorporates such sparsity pattern in the formulation of a novel mixed-integer quadratic programming (MIQP) optimization which can be solved by standard solvers. The method that is proposed in this paper to address low-observability is innovative and it is specific to HSE. It does not have any similar counterpart in the literature, whether for harmonic state estimation for in ordinary (i.e., not harmonic) distribution system state estimation. The effectiveness of the proposed method is tested and confirmed in multiple case studies and compared with the existing methods.

Simultaneous Robust State Estimation, Topology Error Processing, and Outage Detection for Unbalanced Distribution Systems

This paper proposes an efficient algorithmic approach that overcomes the critical challenges in real-time unbalanced distribution system state estimation, topology error processing, and outage identification simultaneously. These challenges include (1) limited locations of measurement devices and unsynchronized measurement data as well as missing and bad data, (2) complicated mixed-phase switch actions and mutual impedances and shunt admittances, and (3) the nonlinear nature of unbalanced distribution system power flow with distributed energy resources (DERs). A single snap-shot mixed-integer quadratic programming (MIQP) optimization framework is proposed to cope with these challenges, which simultaneously identifies real-time network topology, estimates system state, and detects the outages via analytical constraints. An AC optimal power flow (ACOPF) approach is proposed to accurately model unbalanced distribution systems. In the proposed MIQP formulation, nonlinearities due to the complicated mixed-phase switch operations and the ACOPF approach are linearized. The effectiveness of the proposed approach is verified on an actual distribution feeder in Arizona. The results illustrate that the proposed model is robust, accurate, and computationally efficient for implementation in a distribution management system (DMS).

Combined unbalanced distribution system state and line impedance matrix estimation

To address the challenges that the decarbonization of the energy sector is bringing about, advanced distribution network management and operation strategies are being developed. Many of these strategies require accurate network models to work effectively. However, distribution network data are known to contain errors, and attention has been given to techniques that allow to derive improved network information. This paper presents a novel method to derive line impedance values from smart meter measurement time series, with realistic assumptions in terms of meter accuracy, resolution and penetration. The method is based on unbalanced state estimation and is cast as a non-convex quadratically constrained optimization problem. Both line lengths and impedance matrix models can be estimated based on an exact nonlinear formulation of the steady-state three-phase network physics. The method is evaluated on both the IEEE European Low Voltage Feeder (906 buses) and a real Belgian LV feeder, showing promising results.

Neutral-to-Earth Voltage (NEV) and state estimation for unbalanced multiphase distribution systems based on an optimization model

Neutral-to-Earth Voltage (NEV) and state estimation for unbalanced multiphase distribution systems based on an optimization model

Distribution System State Estimation Using PV Separation Strategy in LV Feeders With High Levels of Unmonitored PV Generation

Distribution system state estimation (DSSE) is a critical analysis tool for active distribution networks (DNs). Unlike weighted least squares techniques, which are static DSSE methods, the augmented complex Kalman filter (ACKF) is a novel technique that considers the system’s dynamic behavior. Currently, most DNs integrate a large number of unmonitored residential photovoltaic (PV) generations. Existing unmeasured PV sources violate the white noise assumption in Kalman and least-squares-based estimators, causing the estimator to be biased. Because the one-step difference of aggregated customer demand is characterized as white noise, the suggested PV estimation technique based on the differencing strategy is used to decouple PV from the measured load. Using the specified contribution factors, the new online pseudo current injections are generated. In addition, the estimator’s accuracy is improved by using a new PV-scaling-aided ACKF approach based on the PV separation strategy. For validation purposes, this method is applied to real DN case studies. This study also makes use of an actual dataset to illustrate the efficacy of the proposed technique. The proposed technique outperforms the existing snapshot and dynamic DSSE techniques, and significant improvements are achieved in terms of accuracy and computational cost.