A robust bilinear three-phase state estimation method for power 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 robust state estimation method of distribution network is proposed based on robust estimation theory. The estimator operates on a pi-section branch model, utilizes voltage magnitude and phase angle of each node as state variables, and provides a steady state solution for a balanced three-phase distribution network with generation. According to characteristics of complex distribution networks with generation, a novel equivalent weight function is proposed based on the influence function theory. Moreover, a procedure is designed which can determine correlative parameters of the equivalent weigh function automatically and self-adaptively. The proposed estimator is robustified synthetically in both factor space and measurement space. Test results are very promising. (4 pages)

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.

Robots and particularly drones are especially useful in exploring extreme environments that pose hazards to humans. To ensure safe operations in these situations, usually perceptually degraded and without good GNSS, it is critical to have a reliable and robust state estimation solution. The main body of literature in robot state estimation focuses on developing complex algorithms favoring accuracy. Typically, these approaches rely on a strong underlying assumption: the main estimation engine will not fail during operation. In contrast, we propose an architecture that pursues robustness in state estimation by considering redundancy and heterogeneity in both sensing and estimation algorithms. The architecture is designed to expect and detect failures and adapt the behavior of the system to ensure safety. To this end, we present HeRO (Heterogeneous Redundant Odometry): a stack of estimation algorithms running in parallel supervised by a resiliency logic. This logic carries out three main functions: a) perform confidence tests both in data quality and algorithm health; b) re-initialize those algorithms that might be malfunctioning; c) generate a smooth state estimate by multiplexing the inputs based on their quality. The state and quality estimates are used by the guidance and control modules to adapt the mobility behaviors of the system. The validation and utility of the approach are shown with real experiments on a flying robot for the use case of autonomous exploration of subterranean environments, with particular results from the STIX event of the DARPA Subterranean Challenge.

A new approach to the unmeasurable state reconstruction problem for nonlinear chemical reaction systems in the presence of model uncertainty is proposed. In particular, a new robust nonlinear state estimation method is developed that explicitly uses all the available useful information associated with: (i) a dynamic model inevitably characterized by uncertainty, and (ii) a set of sensor measurements in order to accurately reconstruct other key quantities/variables that cannot be measured on-line due to physical and/or technical limitations. The problem of interest is conveniently formulated and addressed within the context of singular partial differential equations (PDE) theory, leading to a nonlinear state estimator that possesses a state-dependent gain computed through the solution of a system of first-order singular PDEs. A set of necessary and sufficient conditions is presented that ensure the existence and uniqueness of a locally analytic solution to the aforementioned system of singular PDEs, and a series solution method that can be easily implemented via a MAPLE code is developed. Under these conditions, the convergence of the estimation error or the mismatch between the actual unmeasurable states and their estimates is analyzed and characterized in the presence of model uncertainty. Finally, the performance of the proposed nonlinear etimator and its convergence properties are evaluated in an illustrative biochemical reaction system that exhibits nonlinear behavior coupled with parametric uncertainty, and the estimation objective is to accurately reconstruct the unmeasurable substrate concentration using the available cell mass concentration measurements and the model of the system under consideration.

This paper adresses the problem of simultaneously estimating the state and the fault of nonlinear discrete-time stochastic systems in light of the unknown input filtering framework. The fault and unknown disturbances which may cause great estimate errors and even divergence of conventional filters, affect both the system state and the measurements. Inspired by the robust two stage Kalman filter for linear discrete-time system, a nonlinear robust state and fault estimator is derived. In order to achieve the aim, the nonlinear system with fault and unknown disturbances is first transformed into an equivalent descriptor system. Next, it is shown that the previously proposed robust two stage Kalman filter can be applied to yield a robust state and fault estimation. Simulation results for a robotic manipulator show the effectiveness of the proposed method.

Chapter 4 - Kalman Filtering and Robust Estimation

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.

With the application and development of combined heat and power (CHP) techniques, the coupling of electrical and heat energy is gradually increasing. State estimation (SE) is essential to achieve the comprehensive and accurate operating status in an integrated electricity-heat system (IEHS). This article proposes a robust SE method based on second-order conic programming (SOCP) for IEHS. Firstly, auxiliary state variables and measurements are introduced to obtain the exact linear measurement equations for IEHS. Then, a robust SE model based on weighted least absolute values (WLAV) for IEHS is proposed. To further improve the estimation performance, the constraint conditions satisfied by auxiliary state variables are relaxed into second-order cone constraints and added to the proposed WLAV model, leading a SOCP-based robust SE method. Simulations demonstrate that the proposed method ensures a global optimal solution and has good robustness and high estimation accuracy.

Robust three-phase state estimation for PV-Integrated unbalanced distribution systems

Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty

Network Topology Error Identification in Robust State Estimation for Power Systems

Smart grid is built by combination of electric and information technologies and achieves the two-way interaction between power utilization and power generation. Unfortunately, new security threats appears together with cyber-physical communication systems. In order to properly monitor power network, an effective cyber attack detection and state estimation method are required to know attack and system states. This article considers the problem of robust grid state estimation and suggests a technique for distributed state estimation in power networks. First, the distribution power system incorporating multiple synchronous generators is modeled as a state-space framework, where attack occurs in measurements. Basically, the false data injection attacks can interfere with state estimation process by tampering with sensor measurements. Using mean squared error principle, the distributed dynamic state estimation algorithm is designed where local and neighboring gains are obtained using optimal filter and graph theory. For local gain computation, the attack parameter is obtained using the Bayesian learning process. The convergence condition of the proposed approach is derived. Extensive simulation results show that the proposed approach is able to estimate the system state within a short period of time. Hopefully, the proposed methodology can be used to tolerate the cyber attacks for improving the confidence of the grid state estimation process.

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.

The robot localization problem is typically solved using state estimation techniques, where process and sensing inaccuracies are invariably present. Moreover, disturbances in the sensing and actuating mechanisms add to the uncertainties. Any system may degrade over time, and its parameter values may be ambivalently known. Cumulatively, all these sources of errors and uncertainties are considered as unknown inputs. This work aims to address the unknown inputs using a robust state (pose in the robot localization problem) estimator. The proposed robust state estimator deals with the unknown inputs such that the solution of the estimator is constrained in a way that warrants unbiased state estimates in the presence of the unknown inputs. This article explores the formulation of these constraints and the development of a constrained state estimator for a system, where the unknown inputs appear in both the state transition map (i.e., system model) and the state-output map (i.e., measurement model). The theoretical development of such a strategy stems from the localization problem of a wheeled mobile robot. The residuals of the constrained state estimator developed contain information about the unknown inputs. We conceive a recursive least squares strategy to estimate the unknown inputs simultaneously with the states using this information. Using simulations and experimental studies, we demonstrate the adequacy of our strategy for a differential drive robot.