Robust state estimation for distribution networks with generation

In this paper a new approach to state estimation in distribution networks is proposed. This approach is more robust against large uncertainties of the state estimation inputs than the conventional method. Traditionally, the goal of state estimation was to estimate the exact value of network parameters, such as voltages and currents. This works well in transmission networks where many real time measurements are available. In distribution networks, however, only few real-time measurements are available. This means that the estimated state can be significantly different from the actual network state. Therefore, the focus of the proposed robust state estimation is shifted from estimating the exact values of the network parameters to the confidence that these parameters are within their respective constraints. This approach is able to provide useful results for distribution network operation, even if large uncertainties are present in the estimated network state.

This paper proposes a robust three-phase state-estimation method that is applicable to both balanced transmission networks and unbalanced distribution networks with nonlinear measurements. We extend the recently introduced bilinear formulation of state estimation problems to a robust three-phase model. The original nonlinear state estimation is solved by resorting to two auxiliary linear model and a nonlinear transformation in between. Bad measurements are further suppressed by introducing a robust state estimation model. Numerical tests on IEEE benchmark systems, including a distribution network and a transmission network, demonstrate the robustness and efficiency of the method.

The measurements given by Supervisory Control And Data Acquisition (SCADA) systems are generally insufficient for Distribution network State Estimation (DSE). The accuracy of DSE seriously relies on the pseudo measurements, which are generally inaccurate. In historical scene, measurements given by smart distribution transformer meter (SDTM) can be used to enrich the measurements for DSE. The hybrid measurements of SCADA and SDTM can satisfy the observability of DSE with certain redundancy. By using rectangular coordination and introducing intermediate variables and quadratic equalities, the SCADA/SDTM hybrid DSE is modeled as quadratic constrained quadratic estimation (QCQE) problem, which can be solved by traditional state estimation methods with sparse techniques efficiently and conveniently. Simulations on the IEEE 33-bus system show the accuracy of the hybrid DSE. The proposed DSE has been implemented in distribution networks in Zhejiang and shows good efficiency and accuracy.

Today's power system predominantly employing the weighted least squares (WLS) technique for estimating the state of the power system over robust state estimation techniques. The computational inexpensiveness of WLS made it a good choice for the operators compared to the robust state estimators. When the system is completely observable by PMUs, the relationship between measurements and state variables changes from non-linear to linear. This made robust state estimators computationally competitive with the WLS estimator (WLSE). In this paper, quadratic-constant (QC) robust estimator has been improved to make it suitable for linear state estimation. The constant part of the estimator after the break-even point is changed to decaying exponential. The proposed quadratically- decaying exponential criterion (QE) is tested on IEEE 14, 30, 57 and 118- bus systems for two cases. (a) measurement data having only Gaussian noise (b) with corrupt measurement data. It is demonstrated that the proposed estimator is able to suppress the bad data and exhibiting better estimation accuracy and computational performance compared to least absolute value (LAV) and WLSE.

Global state estimation for whole transmission and distribution networks

State estimation of distribution network based on hybrid measurement combined with multi-source asynchronous data

This paper tackles the growing uncertainty in distribution networks caused by distributed generation, load fluctuations, and frequent topological changes. It proposes a multi-source data fusion framework using enhanced selective convolution (SKNet) and graph attention networks (GAT). First, heterogeneous measurement data, including Phasor Measurement Unit (PMU) and Supervisory Control and Data Acquisition (SCADA) data, are processed through a unified normalization and outlier elimination technique to ensure data quality. Second, SKNet is utilized to extract spatiotemporal multi-scale features, improving the detection of both rapid disturbances and long-term trends. Third, the extracted features are fed into GAT to model node electrical couplings, while power flow residual constraints are embedded in the loss function to enforce the physical validity of the estimated states. This physics-informed design overcomes a key limitation of pure data-driven models and enables an end-to-end framework that integrates data-driven learning with physical mechanism constraints. Finally, comprehensive validation is performed on the improved IEEE 33-node and IEEE 123-node test systems. The test scenarios include Gaussian measurement noise, data outliers, missing measurements, and topological changes. The results show that the proposed method outperforms baseline models such as Multi-Scale Graph Attention Network (MS-GAT), Bidirectional Long Short-Term Memory (BiLSTM), and traditional weighted least squares (WLS). It achieves Root Mean Square Error (RMSE) reductions of up to 18% and Mean Absolute Error (MAE) reductions of up to 15%. The average inference latency is only 10–18 ms. Even under unknown topological changes, the estimation error increases by only 15–25%. These results demonstrate the superior accuracy, robustness, and real-time performance of the proposed method for intelligent distribution network state estimation.

Many of the past work on distribution state estimation have been focused on the adoption of a transmission state estimation approach, without necessarily accounting for specific requirement distribution networks analysis. On distribution networks, typically, there are very few real-time measurements, and power consumption of each load is very uncertain. This paper presents an alternative approach to distribution state estimation with limited Real-Time Measurements Points (RTMP). This method includes two steps; in the first step Correlation Coefficient (CC) between power consumption of each LP and RTMP with usage of least squares (LS) is determined. In the second step; with data of RTMP, CC and forward backward load flow modification, excellent state estimation of electrical distribution networks can be determine.

The state estimation of an active distribution network (ADN) in the absence of enough measurements, and with the presence of distributed energy resources (DERs) located behind-the-meter (BTM), is a significant challenge. The operational philosophy of power distribution networks (DNs) is also changing from “generation following demand” to “demand following generation.” Consequently, emerging demand and generation patterns are difficult to handle through standard state estimators. This article introduces a profiling framework that characterizes responsive/flexible demands and BTM DERs to represent nonconventional load power. The impact of these nonconventional load power on DN monitoring and the challenges of system observability are addressed using a deep learning-based forecaster. This forecaster utilizes weather and other relevant input features to tackle the irregularities in demand profiles. Additionally, the framework includes proposing a strategy for time-varying smoothing parameters in forecasting-aided state estimation (FASE) to address the uncertainties associated with loads and the outputs of DERs. The framework is validated on a modified IEEE-123 bus unbalanced three-phase DN for demonstrating improved accuracy of the estimation.

The volatile and intermittent nature of distributed generators (DGs) in active distribution networks (ADNs) increases the uncertainty of operating states. The introduction of distribution phasor measurement units (D-PMUs) enhances the monitoring level. The trade-offs of computational performance and robustness of state estimation in monitoring the network states are of great significance for ADNs with D-PMUs and DGs. This paper proposes a second-order cone programming (SOCP) based robust state estimation (RSE) method considering multi-source measurements. Firstly, a linearized state estimation model related to the SOCP state variables is formulated. The phase angle measurements of D-PMUs are converted to equivalent power measurements. Then, a revised SOCP-based RSE method with the weighted least absolute value estimator is proposed to enhance the convergence and bad data identification. Multi-time slots of D-PMU measurements are utilized to improve the estimation accuracy of RSE. Finally, the effectiveness of the proposed method is illustrated in the modified IEEE 33-node and IEEE 123-node systems.

The distribution of measurement noise applied in practical power system state estimation (PSSE) can deviate from the assumed Gaussian model, and the performance of an estimator becomes bad if the Gaussian model is still used. This article proposes a new distributed robust PSSE method for multiarea power systems. The non-Gaussian model is utilized to fit the measurement noise distribution to reach high model accuracy. The proposed distributed method is derived based on the maximum correntropy criterion to further reduce the impact of non-Gaussian measurement noise and outliers. The influence function combined with the finite-time average consensus algorithm is used to implement the proposed distributed robust method in a fully distributed manner. Simulations conducted on the IEEE 30-bus, 118-bus and 300-bus systems and the Polish 2383-bus system demonstrate the robustness and effectiveness of the proposed distributed method. Each local area can get the system-wide robust state estimation solution by only using local information and small amounts of data from neighboring areas. Our proposed distributed robust method has at least 12% improvement in reducing the mean squared error under Gaussian-Uniform noise. It is verified the communication network applied for the proposed method is fairly flexible while the existing distributed approaches use a fixed communication network when the power systems are partitioned. The simulation results also verify the robustness of the proposed method to bad data and communication failure.

A bilinear robust state estimation method for electric thermal integrated energy system (IEHS) is proposed. First, the linear weighted least absolute value (WLAV) model of IEHS is constructed by introducing auxiliary variables, and then the state variables are estimated by solving a quadratic programming model with a nonlinear transformation. The advantage of the proposed method is that it has a high calculation efficiency. The effectiveness of the proposed method is verified on the IEHS test system.

Aiming at the interaction between the distribution network and electric vehicles(EVs) during the charge-discharge process, based on the complex network theory, the dynamic evolution model of distribution network under Vehicle-to-Grid(V2G) mode is proposed, which can analyze the relationship between the distribution network topological statistical and electrical characteristics. Considering both the distance and access number of charge stations, EV chooses the optimum charge station, then the access mode of EV in the distribution network is obtained. The model is used to study the impact of the spatial-temporal distribution of EV load on the two distribution network characteristics under three charge-discharge modes. Simulation results show that this method can reflect the interactive evolution process between the distribution network and EVs. The consistency between the distribution network topological statistical and electrical characteristics during peak-valley period is verified by comparative analysis. The method provides a theoretical basis for studying the charge-discharge strategy of EVs based on network topological statistical characteristics.

A novel method is proposed for solving online nodal load estimation of middle voltage distribution networks systematically. Firstly the solution strategies are introduced, and then the algorithm is presented. The proposed method consists of three phases that are crude load estimation, load forecasting and robust load estimation. Three load allocation methods are offered in crude load estimation phase which can provide crude load values. A case-based fuzzy-neural network is utilized in load forecasting phase for supplying nodal load forecasting values. Robust load estimation has been robustified synthetically in both structure space and measurement space, which can effectively withstand the influence of gross errors and many small errors. The three phases of load estimation cooperate closely and form a closed-cycle information flow. The proposed method can run online and can provide reliable and consistent load data set for control and management of distribution networks.

Chapter 4 - Kalman Filtering and Robust Estimation