Hybrid State Estimation Research Articles

Event‐triggered state estimation for stochastic hybrid systems with missing measurements

This study is concerned with the event-triggered state estimation problem for a class of stochastic hybrid systems with missing measurements in a networked environment. Two independent Markov chains are introduced to, respectively, characterise the stochastic measurement missing and the possible modal (or mode) transition of the system. In consideration of the constrained bandwidth and limited power resources of networked systems, a closed-loop event-triggered mechanism based on the measurement innovation is designed to trigger data transmission only when trigger conditions are satisfied. To keep the exponentially increasing number of full hypothesis sequences in optimal estimation to bounded computational complexity, the interacting multiple model framework is extended to tackle event-triggered sampling with the statistical information implicit in event-triggered conditions sufficiently explored and the possible measurement missing taken into account. A Monte Carlo simulation involving tracking a two-dimensional manoeuvring target with two operational modes is provided to demonstrate the effectiveness and efficiency of the proposed event-triggered hybrid state estimation in the presence of missing measurements.

Hybrid State Estimation in Complex Variables

Power system state estimation is classically formulated as a weighted least squares (WLS) optimization problem over the real domain, with the state variables being the voltage magnitudes and angles or the voltage real and imaginary parts. Although the voltages in ac networks are complex variables, a solution in the complex domain has not been previously reported; this is because a real function of complex variables is nonanalytic in its arguments, i.e., the Taylor series expansion in its arguments alone does not exist. By making use of the Wirtinger calculus, this paper presents a new implementation of the WLS state estimation problem in complex variables. The partial derivatives employed in the method give rise to a structure that is very simple to implement. The method can straightforwardly handle both legacy and phasor measurements; particularly, the processing of phasor current measurements does not require any special provisions, unlike previously reported hybrid state estimator implementations over the real domain. Numerical results are reported on networks with up to 9241 nodes, and they demonstrate that the accuracy of the complex variable implementation is competitive with that of the real variable constrained hybrid state estimator, while being significantly faster.

A Hybrid State Estimator Based on SCADA and PMU Measurements for Medium Voltage Distribution System

With the increasing importance of renewable energy and flexible loads, the operation of the distribution system is becoming more stochastic and complex, and it is necessary to monitor the power system in real-time. Considering the gradual applications of intelligent electronic devices in the distribution systems, a hybrid state estimator based on supervisory control and data acquisition (SCADA) and phasor measurement unit (PMU) measurements is proposed in this paper, which consists of the improved robust estimation and linear state estimation. At the time of SCADA data acquisition, the improved robust estimation combining the SCADA measurements with PMU measurements is performed. To eliminate the effect of bad data, the internal student residual method is introduced, and the robust thresholds are adjusted adaptively. Then the linear state estimation is performed at the time of PMU data acquisition based on the results of the previous estimation time and the PMU measurements, which can quickly correct the robust estimation results and track the changes of the distribution system. Finally, the effectiveness and performance of the proposed method are verified in a modified IEEE 33-bus distribution system and a real distribution system in China.

Distributed state estimation for a stochastic linear hybrid system over a sensor network

In this study, the authors consider the distributed state estimation problem of a stochastic linear hybrid system (SLHS) observed over a sensor network. The SLHS is a dynamical system with interacting continuous state dynamics described by stochastic linear difference equations and discrete state (or mode) transitions governed by a Markovian process with a constant transition matrix. Most existing hybrid estimation algorithms are based on a centralised architecture which is not suitable for distributed sensor network applications. Further, the existing distributed hybrid estimation algorithms are restrictive in sensor network topology, or approximate the consensus process among connected sensor agents. This study proposes a distributed hybrid state estimation algorithm based on the multiple model based approach augmented with the optimal consensus estimation algorithm which can locally process the state estimation and share the estimation information with the neighbourhood of each sensor agent. This shared information comprises local mode-conditioned state estimates and edge-error covariances, and is used to bring about an agreement or a consensus across the network. The proposed distributed hybrid state estimation algorithm is demonstrated with an illustrative aircraft tracking example.

Mode discernibility and bounded-error state estimation for nonlinear hybrid systems

State estimation is a key engineering problem when addressing control or diagnosis issues for complex dynamical systems. The issue is still challenging when the latter systems must be modelled as hybrid discrete–continuous dynamics, which is true for many complex and safety-critical systems. In this paper, we investigate nonlinear hybrid state estimation in a bounded-error framework using reliable and robust methods. We first establish a testable condition for current mode location discernibility. Then we build our hybrid state estimator which relies on a prediction–correction approach. An illustrative example is presented.

State Estimation of Power System Embedded with FACTS devices and PMUs

In recent days, the power system is incorporated with Flexible AC Transmission System (FACTS) devices for compensation of reactive power to maintain the stability of the system. The stability of the system is highly dependent on the state variables which are the outcomes of a state estimator in the power system. To improve the efficiency of a state estimator, high precision measuring devices such as Phasor Measurement Units (PMUs) are installed in the power system. Hence a state estimator embedded with these compensatory devices and PMUs is necessary for estimation of state variables. The present work has been carried out in three steps. Step 1: Considering the cost of PMUs and the availability of the communication network in the particular location, PMUs are optimally placed in the nodes of the system so that all critical measurements are transmuted into redundant ones using differential evolution (DE) algorithm to perform observability analysis. Step 2: A hybrid state estimation is performed by including the mathematical model of FACTS devices and PMUs. Step 3: It is shown that by installing optimal number of PMUs at desired location, multiple bad data detection and identification capability of residual method is considerably improved. Lastly, numerical simulation with standard IEEE 14 bus system, IEEE 118 bus system and a practical 246 bus system of northern region power grid (NRPG) is presented to confirm the effectiveness of the proposed approach in assessing the estimation of the system state variables.

A Decentralization Method for Hybrid State Estimators

Hybrid state estimation determines the states of systems monitored both by conventional SCADA measurements and PMUs. This paper proposes a decentralization method in order to improve the computational performance of hybrid state estimators with minimum loss of accuracy. The proposed method utilizes sensitivity matrix that relates measurement errors to state estimates in order to form the so-called isolated bus groups and observable subislands. Although the proposed decentralization method can be applied to any state estimator, the paper is developed using a least absolute value (LAV) estimator for demonstration purposes, which is known to be robust against bad data. The high computational burden of LAV estimator compared to the well-known weighted least squares estimator is eliminated, thanks to the proposed decentralization method.

A Performance Evaluation Algorithm of Stochastic Hybrid Systems Based on Fuzzy Health Degree and Its Application to Quadrotors

A stochastic hybrid system (SHS) is a type of model describing real-world systems, who are both dynamic and hybrid. System performance evaluation is a key technology related to mission accomplishment and safety, where a rational selection of performance indicators is an important guarantee of truly and accurately evaluating system performance. This paper proposes a performance evaluation algorithm of SHS. First, the concept of fuzzy health degree is proposed and the SHS model studied in this paper is established. Then, the procedure of the algorithm is presented in detail, including hybrid state estimation based on a modified interacting-multiple-model algorithm, discretization of continuous variables, and quantitative calculation of fuzzy health degree. In order to validate the effectiveness of the proposed algorithm, an experiment of a quadrotor with sensor anomalies is made where the system performance is quantitatively described by using the fuzzy health degree. Comparative studies are also made and discussed.

Bayesian hybrid state estimation for unequal-length batch processes with incomplete observations

This paper investigates state estimation problem for batch processes with unequal-length batches as well as incomplete observations. A Bayesian hybrid state estimation method is proposed based on two dimensional (2D) correlations of states. The states of equal-length segment of time are estimated according to both within-a-batch and batch-to-batch correlations, and the states of unequal-length segment are obtained according to the correlations within the batch. In this way, the batch process states can be achieved in both equal-length and unequal-length situations, of which the latter one is a more general case. In order to approximate state distribution of nonlinear system and to deal with the problem of incomplete observations, particle filter (PF) is employed. The proposed method shows its superiority with a nonlinear system and a gas-phase reaction process. Compared to a typical existing method, the proposed method provides better estimation accuracy in the situation of equal-length batches, also it shows less sensitivity to incomplete observations.

A hybrid method for power system state estimation using Cellular Computational Network

Several heuristic optimization methods including Particle Swarm Optimization (PSO) have been studied for power system state estimation and these perform quite well for small systems. However, in case of larger systems with hundreds of states, these suffer from the curse of dimensionality. To overcome this problem, a hybrid state estimator that consists of a Cellular Computational Network (CCN) and the Genetic Algorithm (GA) is proposed in this study. CCN is a framework that distributes the whole computation to computation cells and the cells execute local estimation. The result of CCN is further improved using GA. To compare the performance of the proposed estimator, two acclaimed variants of PSO, Comprehensive Learning PSO, and Orthogonal Learning PSO, which are specialized in multimodal high dimensional systems, are also implemented both individually and in conjunction with CCN. Through simulation, it is shown that the proposed CCN-GA outperform all direct and hybrid methods in terms of accuracy. Typical results on an IEEE 16-machine 68-bus power system are presented to illustrate the effectiveness of the CCN-GA over other methods.

A Hybrid State Estimator using Current based Estimator and PMU Measurements

The increasing use of synchronized phasor measurements in modern power systems has made it necessary to consider its effects on the state estimation algorithm. Accuracy of the measurements used has a great impact on the output of state estimators. Thus including the highly accurate phasor measurements into the existing state estimators can be highly beneficial. With the advent of synchrophasors, modifications in the existing state estimators have to be considered as most of the existing estimators rely primarily on conventional measurements from SCADA system. The conventional state estimators are traditional Power based estimators. The faster convergence of current based estimators as against the traditional power based estimators has already been proved in the literature. This necessitates the need for modifying current based estimators to incorporate PMU measurements. This paper investigates a technique to incorporate the PMU measurements into a current based state estimator. The model used for incorporating the PMU measurements is a linear model and hence can be solved non-iteratively. The result is being discussed for standard IEEE 14 bus test case. The results indicate that the output obtained from the estimator using both PMU data and conventional data is much more efficient than the existing current based state estimator.

A health evaluation method of multicopters modeled by Stochastic Hybrid System

For multicopters, failures may abort missions, crash multicopters, and moreover, injure or even kill people. In order to guarantee flight safety, a system of prognostics and health management should be designed to prevent or mitigate unsafe consequences of multicopter failures, where health evaluation is an indispensable module. This paper proposes a health evaluation method of multicopters based on Stochastic Hybrid System (SHS). In the SHS model, different working conditions (health statuses) of multicopters are modeled as discrete states, and system behaviors of different working conditions are modeled as continuous dynamics under discrete states. Then, the health of multicopters is quantitatively measured by a definition of health degree, which is a probability measure describing an extent of system degradation from an expected normal condition. On this basis, the problem of multicopter's health evaluation is transformed to a hybrid state estimation problem. In this case, a modified interacting-multiple-model algorithm is proposed to estimate the real-time distribution of hybrid state, and evaluate multicopter's health. Finally, a case study of multicopter with sensor anomalies is presented to validate the effectiveness of the proposed method.

Efficient multiple model particle filtering for joint traffic state estimation and incident detection

This article proposes an efficient multiple model particle filter (EMMPF) to solve the problems of traffic state estimation and incident detection, which requires significantly less computation time compared to existing multiple model nonlinear filters. To incorporate the on ramps and off ramps on the highway, junction solvers for a traffic flow model with incident dynamics are developed. The effectiveness of the proposed EMMPF is assessed using a benchmark hybrid state estimation problem, and using synthetic traffic data generated by a micro-simulation software. Then, the traffic estimation framework is implemented using field data collected on Interstate 880 in California. The results show the EMMPF is capable of estimating the traffic state and detecting incidents and requires an order of magnitude less computation time compared to existing algorithms, especially when the hybrid system has a large number of rare models.

Multiple Model Particle Filter for Traffic Estimation and Incident Detection

This paper poses the joint traffic state estimation and incident detection problem as a hybrid state estimation problem, in which a continuous variable denotes the traffic state and a discrete model variable identifies the location and severity of an incident. A multiple model particle smoother is proposed to solve the hybrid estimation problem, in which the multiple model particle filter is used to accommodate the nonlinearity and switching dynamics of the traffic incident model, and the smoothing algorithm is applied to improve the accuracy of the estimate when data are limited. The proposed algorithms are evaluated through numerical experiments using CORSIM as the true model. The proposed algorithm is also compared with a standard macroscopic traffic estimator via particle filtering and the California incident detection algorithm. The results show that jointly estimating the state and incidents in one algorithm is better than two dedicated algorithms working independently.

A Synchrophasor Assisted Hybrid State Estimator

Abstract The paper presents a Synchrophasor Assisted Hybrid State Estimator that utilizes the conventional SCADA measurements and the synchrophasors obtained from Phasor Measurement Units (PMUs). To take advantage of the high sampling frequency of the multiple sets of synchrophasors they are preprocessed in a recursive algorithm that provides the state estimate for the power system part observable by PMUs. The results are forwarded to an iterative procedure in which they are combined with SCADA measurements. The given solution was applied on the IEEE test systems with 14, 30 and 57 buses and its performance was compared with other state estimators. The filtering of measurement errors and convergence, while providing improved accuracy of the final state estimates of the developed methodology can be compared with other hybrid state estimators.

Comparison of state estimation techniques for nonlinear hybrid systems

Modern real-world engineering systems exhibit complex hybrid behaviors, which are composed of continuous nonlinear plant dynamics interspersed with discrete mode switching. State estimation of hybrid systems for accurate and timely online monitoring and diagnosis applications is a difficult task. A number of different methods have been proposed, and we develop a conceptual framework to perform a comparative study of four different hybrid state estimation algorithms in this paper: (1) the switched extended Kalman filter; (2) focused hybrid estimation; (3) multiple-modal particle filtering; and (4) the one-step look-ahead particle filtering. The conceptual comparison is followed by an empirical evaluation, where we study the effectiveness of these algorithms in tracking the behaviors of a Reverse Osmosis Subsystem of an Advanced Water Recovery System that was developed at the NASA Johnson Space Center. We discuss our results, which show the strengths and weaknesses of each of these algorithms, and propose topics for further research into this important problem.

Hybrid state estimator considering SCADA and synchronized phasor measurements in VSC-HVDC transmission links

This paper proposes a practical approach for implementing a hybrid state estimator by considering SCADA and PMU measurements in VSC-HVDC transmission links under a unified framework of reference. A proposed formulation for the PMU measurements associated with the VSC-HVDC state variables is derived from the first principles and is implemented into a weighted least square-based state estimation algorithm. In order to avoid numerical problems of convergence of the proposed state estimation approach, the set of current phasor measurements is represented in rectangular coordinates, such that their corresponding variances are also recalculated according to the uncertainty propagation theory. The state estimation process uses the measurement of one voltage phase angle as the global reference for the rest of voltage phase angles estimated at network buses and VSC-HVDC's voltage source converters. The proposed formulation improves the accuracy at which both network and VSC-HVDC state variables are simultaneously estimated based on the measurements provided by a SCADA system and PMUs. A Mexican interconnected 190-bus equivalent system is used as the test system in order to validate the effectiveness of the proposed hybrid state estimator.

Hybrid State Estimation Model Based on PMU and SCADA Measurements

Abstract: In this paper, a new method of hybrid non-linear state estimation with PMU and SCADA measurements will be proposed. PMU measurements, the voltage and current phasors, are used for real time transmission line parameters (impedance and admittance) calculation. Transmission line parameters are input data for the conventional state estimator. Calculated parameters of the transmission lines based on the real time PMU measurements are compared with the measured impedance and admittance. The simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and used to quantify the impact of PMU measurements on power system state estimation by using proposed hybrid model. Software for the proposed hybrid model was developed and it is compatible with PMUs form different vendors. This research was made possible by implementation of 5 PMUs and restoration of wide area monitoring (WAM) system in Croatian power system. Those PMUs were implemented during the reconnection process - reintegration of the 1 st and 2 nd UCTE synchronous zone.

A new hybrid state estimation based on pseudo‐voltage measurements

This paper presents a new hybrid state estimation method based on the concept of pseudo‐voltage measurements for a power system containing both conventional and synchronizing phasor measurements. Actual measurement data is employed to calculate the magnitude and phase of the pseudo‐voltage. In the proposed formulation, the measurement matrix describing the relations between the measured data and the state variables contains only 0 or 1. Then the state estimation problem is formulated based on the weighted least‐squares criterion, and its solution can be obtained without using iterative procedures. Comparisons with previous hybrid state estimation methods have been performed on IEEE 14‐bus, 57‐bus, and 118‐bus systems. Numerical experimental results indicate that the proposed approach yields solutions of comparable accuracy with other methods but with shorter computation times. Moreover, the proposed method also provides superior results in the presence of bad data. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Coordinated Cyber-Attacks on the Measurement Function in Hybrid State Estimation

The paper assesses the cyber-security of power systems static state estimation (SE) in the possible presence of phasor measurement units (PMUs). Attacks are considered in the Jacobian matrix or the measurement function of the state estimation leading to the presence of coordinated leverage points. Leverage points, which are outliers, constitute a very challenging attack configuration even if randomly present. It is shown that coordinated cyber-attacks when applied to the Jacobian matrix raise major concerns about robust SE. The vulnerability of the least trimmed squares (LTS) estimator, which is robust towards leverage points, is shown. More generally, the weaknesses of robust regression equivariant estimators are discussed if attacks are developed and optimized based on a projection framework. Attack scenarios are outlined considering the number of attacked Jacobian elements, a decomposition of the system to maximize robustness, and whether a DC or AC formulation is used by the operator. Stealthy attacks that stay undetected with respect to the robust LTS are studied. Masked attacks are defined as well. Some possible solutions and remedial actions are proposed. Robust state estimation methods are evaluated and compared in the presence of different configurations of attacks through Monte Carlo simulations on the IEEE 14- and 30-bus test beds.