Observability analysis for state estimation using Hachtel’s augmented matrix method

State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, which is useful for security-constrained dispatch and power system control. For nonlinear AC power systems, SE amounts to minimizing a weighted least-squares cost that is inherently nonconvex, thus giving rise to many local optima. As a result, estimators used extensively in practice rely on iterative optimization methods, which are destined to return only locally optimal solutions, or even fail to converge. A semidefinite programming (SDP) formulation for SE has been advocated, which relies on the convex semidefinite relaxation (SDR) of the original problem and thereby renders it efficiently solvable. Theoretical analysis under simplified conditions is provided to shed light on the near-optimal performance of the SDR-based SE solution at polynomial complexity. The new approach is further pursued toward complementing traditional nonlinear measurements with linear synchrophasor measurements and reducing computational complexity through distributed implementations. Numerical tests on the standard IEEE 30- and 118-bus systems corroborate that the SE algorithms outperform existing alternatives, and approach near-optimal performance.

Inferential measurement of SAG mill parameters II: state estimation

We propose a state estimation approach, enhanced with prior information, for dynamic magnetic resonance imaging (MRI). In state estimation the time series of system states are estimated, utilizing the observation and state evolution models and the dynamic time-varying measurements. In this work the state estimation algorithm is the Kalman filter (KF), where the state estimation formulation is complemented with an anatomical structural prior. In our previous work we used two different methods to include prior information to KF. In the first method the observation matrix was augmented with anatomical prior information and in the second method a heuristic total variation (TV) denoising was applied to each Kalman recursion. While the TV method was faster and better than the augmented one, the TV method lacked a sound mathematical background. In this work, we include the prior information in the state evolution model allowing for significantly faster computation compared to the previous augmented method, yet retaining the solid mathematical background and the same quality of the estimate.The proposed approach is evaluated using simulated functional MRI (fMRI) data and experimental, golden angle sampled, small animal dynamic contrast-enhanced MRI data from a rat brain. When using a state estimation method, we can improve the temporal resolution compared to conventional methods by using only one spoke of radial data for each estimate. We compare the results to the augmented Kalman filter and a sliding window method. The results show that the proposed method produces equally good results when compared to the augmented Kalman filter, but allows for over five times shorter computational times.

A block-partitioned (blocked) sparse formulation for the solution of equality-constrained power system static-state estimation is presented. The blocked structure is formed based on a new formulation of Hachtel's augmented matrix method, which preserves several desired features of the conventional normal equations with equality constraints approach. The proposed formulation treats the constraints by the method of Lagrange multipliers, but allows triangular factorization to proceed in a positive-definite manner. A mixed-size blocked structure is proposed for the internal solution, while a formulation composed exclusively of (2*2) blocks is proposed for the external solution. The method is well suited to the implementation of regulation schemes and limit enforcement, necessary in the state-emission-based external solution. The pairing of equations with state variables in the observable state-estimation solution is tightly linked to the results of a topological observability algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this chapter, a wide-area integrated method including a set of algorithms for transmission lines fault analysis is introduced. The proposed method is based on extension and modification of state estimation formulation. Thus, the method is applicable to both symmetrical and asymmetrical networks as well as all fault types including symmetrical and asymmetrical ones. The method exploits the capacities of state estimation formulation and the solution algorithm of weighted least squares (WLS) to reduce the effect of inherent errors on the fault location accuracy and detection and elimination of bad data in the measurement vectors. For this purpose, an error model of the measurement chain including instrument transformers and PMUs is proposed. This model is used to design measuring errors covariance matrix in the state estimation formulation. The performance of the proposed method has been investigated through numerous fault events simulated on different locations of all transmission lines of the IEEE 118-bus test system.KeywordsAsymmetrical faultsBad data detectionFault locationMeasurement chain errorState estimationUntransposed transmission lines

This paper is concerned about the state estimation of power systems, which contain flexible ac transmission system devices. Specifically, the formulation of state estimation in order to incorporate the detailed steady state models of the unified power-flow controller (UPFC) is investigated. This formulation involves the use of equality and inequality constraints that account for the limits associated with the device operation and ratings. Furthermore, in addition to its use as an estimator, the developed estimator can also be used to determine the required settings for the control parameters of UPFCs for a given operating condition. Computational issues concerning initialization, step length, and matrix conditioning are also discussed and practical solutions are offered. Simulations on IEEE test systems of sizes ranging from 14 to 118 buses are presented to demonstrate the use of the developed program both as a state estimator and as a tool for setting the parameters of unified power-flow controllers.

Combined heat and power networks effectively improve energy efficiency. It is necessary to get a global solution with high accuracy for the combined networks, which is the basis of the subsequent analysis and optimization. State estimation has been widely adopted in the power system to decrease errors caused by measurements. Similarly, state estimation can also be used in the district heating network. State estimation for the district heating network is developed in this paper with a simplified dynamic model by the weighted least-square method. However, the state estimation for each network individually doesn't give a global solution. So, it is necessary to take coupling components into consideration. The proposed state estimation is for the entire combined power and heat networks. Because of the increased coupling constraints equations, the redundancy of the state estimation increases, which helps to improve the accuracy. This paper shows the comparison between the combined state estimation and the individual state estimation. The combined state estimation gives a global solution with higher precision, which helps the subsequent analysis and optimization.

In this paper a new approach for a three-phase Distribution System State Estimator (DSSE) is presented. It utilizes the most types of analog real time measurements (including voltage and current magnitude, active and reactive power measurements). The correct utilization is supported by topology analysis and creation of measurement areas. Loads are modeled based on historical or AMR information. The estimation problem is solved by weighted least squares error method. Applying traditional state estimation on distribution networks, by using load data as pseudo measurement, causes state estimation formulations that have very large size. Approach presented in this paper is based on network reduction which reduces size of the problem. The approach is very fast and provides feasible results.

This paper describes an approach by which the status of circuit breakers which are not directly monitored can be determined. The approach combines a previously proposed circuit breaker model with the least absolute value (LAV) state estimation method for this purpose. The ability of the LAV estimators to reject inconsistent measurements is exploited in order to decide whether a circuit breaker is closed or open. The formulation of the LAV state estimation is accordingly modified to include the circuit breaker models and associated constraints. The proposed approach is implemented and tested. Simulation results for single and multiple circuit breaker configurations are given. Robustness of the approach against analog measurement errors is also demonstrated by examples. >

According to principle of model reference adaptation, a model reference fault diagnosis approach for on-orbit satellite attitude control system was proposed based on measurement and calculation of environmental torques acted on satellite. With satellite kinematics and attitude dynamics, a linear model for satellite attitude control system is established. On the basis of system parameter and structural characteristics, satellite attitude control system reference model modified by measurement and calculation of environmental torques is built. With fault residual vector generated by comparing output of reference model with real system, sensor fault detection and isolation is accomplished. Extended state observer is designed to estimate system disturbance using augmented matrix method. According to disturbance estimation and environment torque calculation, actuator fault residual vector is obtained to detect and isolate actuator fault. The simulation experiment result demonstrates that the proposed approach is effective and efficient for real-time fault diagnosis of on-orbit satellite attitude control system.

This paper investigates how the efficiency of Weighted Least Squares (WLS) State Estimation changes according to both the uncertainty of network parameters and the uncertainty of measurements. Performance of State Estimator based mainly on the accuracy of its inputs and it is very important for the power system planners to improve the state estimation by determining whether to invest on increasing the measurement preciseness or improve the power network model. For this purpose, an algorithm for simulation of the uncertainty effects on the state estimator is proposed and tested on IEEE 14-Bus power network test case. The implementation of this algorithm enables us to analyze how much the state estimator's output is affected according to the network parameters uncertainty by means of state errors distribution versus the network parameters uncertainty. On the other hand, a serious defect in an estimator is the lack of unbiasedness. Hence a new prominent analysis is performed to find how network parameters uncertainty can affect the state estimator's bias by using distribution of the ratio between the absolute value of state errors mean and the related standard deviations versus the network parameters uncertainty and comparing it with a predefined threshold. Moreover, this analysis is also performed considering correlation in the network parameters, to investigate the effect of parameters correlation on the state estimator.

Lagrangian Point State Estimation with Optimized, Redundant Induction Coil Gauges

The state estimator (SE) was originally developed to deal with transmission networks (TN). Hence, its application in distribution networks (DN) requires the classical methods to be modified. The main aim of this work was to evaluate the methods available in the literature for state estimation in DN and to explore in depth a chosen method. The chosen approach was the one that uses the complex branch currents as state variables. This approach aims to take advantage of the specific characteristics of DN, and presents a superior computational performance when compared to solutions that use voltages as state variables. However, this method is still little explored in the literature, so that several limitations have been identified. The main limitation was in terms of the presence of transformers in the system, which was neglected in the papers found in the literature. In order to increase the reliability of the estimation, in addition to the branch currents, it was considered the posibility of including the substation voltage variables in the state vector. In the presence of transformers, such expansion in the state vector generated a coupled mathematical model. In this work, solutions were proposed to deal with different transformer connections using the branch current SE while keeping one of its main characteristics, that is the decoupling between phases. When the substation voltage is being estimated, an optimal combination of state variables was proposed in order to circumvent the coupling in the mathematical model. IEEE test systems were used to evaluate the performance of the implemented algorithm. The results showed that the chosen methodology was able to estimate the DN state with adequate accuracy in the presence of different types of measurements and topologies. The models proposed in this work proved to be effective in the incorporation of transformers with different connections in the SE formulation. Finally, the proposed method to decouple the branch current SE when dealing with substation voltage estimation in the presence of transformers was validated and proved to be computationally more efficient when compared to its coupled version.

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.

With the development of computer and network communication technology, substation comprehensive automation system has been widely applied in power network, thus power dispatching center can collect and monitor a lot of power network operation information. How to draw useful diagnosis rules from history and real time operational state data of power network, how to use these rules to find important information and exceptional situation from power network real time state data and give early warning of potential fault in time and correctly, become a significant and urgent research problem of dispatching automation system. This paper presents a framework of SOM-DBN based fault early warning system for dispatching automation, including data monitoring, diagnosis and warning, rule drawing, management control center, memory unit. Data monitoring module is used to monitor real time operational data of power network; diagnosis and warning module is designed to build diagnosis model, identify important information and exceptional situation, and send out warning information according to diagnosis rules; rule drawing module uses data mining methods find potential knowledge and rules from history and real time data; management control center as the system backbone aims at the whole management and cooperation; storage unit, composed of database, knowledge-base and rule-base, is used to store operational state data, expert domain knowledge and diagnosis rules. The proposed system can monitor power network state and realize early fault warning through two stages. In the first stage, it constructs fault diagnosis model for power network. Firstly, it clusters history data by SOM and finds clustered feature variables; secondly, through rule drawing module, it can identify fault zone and work out corresponding measures according to clustered feature variables combined with expert domain knowledge; then it uses LVQ algorithm to train SOM network model; next it uses the fault zone sample data to train diagnosis Bayesian network model and learns model parameters. In the second stage, the system can monitor power network state and realize fault diagnosis and warning. Through data monitoring module, it monitors the environment state variables and determines the need for situation assessment; through diagnosis and warning module, it propagates event cues, projects events, diagnoses situation, warns fault and prorides decision-marking. The SOM-DBN based fault early warning system has been applied into dispatching automation system ON2000, and effectively improved the diagnosis and warning capability of dispatching automation system.