Comparing Kalman Filters and Observers for Power System Dynamic State Estimation with Model Uncertainty and Malicious Cyber Attacks

Kalman filters and observers are two main classes of dynamic state estimation (DSE) routines. Power system DSE has been implemented by various Kalman filters, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). In this paper, we discuss two challenges for an effective power system DSE: (a) model uncertainty and (b) potential cyber attacks. To address this, the cubature Kalman filter (CKF) and a nonlinear observer are introduced and implemented. Various Kalman filters and the observer are then tested on the 16-machine, 68-bus system given realistic scenarios under model uncertainty and different types of cyber attacks against synchrophasor measurements. It is shown that CKF and the observer are more robust to model uncertainty and cyber attacks than their counterparts. Based on the tests, a thorough qualitative comparison is also performed for Kalman filter routines and observers.Comment: arXiv admin note: text overlap with arXiv:1508.0725

A partially linearized sigma point filter for latent state estimation in nonlinear time series models

A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process

A new algorithm for latent state estimation in nonlinear time series models

We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples

Implementation of Bivariate Unspanned Stochastic Volatility Models

Unspanned stochastic volatility term structure models have gained popularity in the literature. This dissertation focuses on the challenges of implementing the simplest case – bivariate unspanned stochastic volatility models, where there is one state variable controlling the term structure, and one scaling the volatility. Specifically, we consider the Log-Affine Double Quadratic (1,1) model of Backwell (2017). In the class of affine term structure models, state variables are virtually always spanned and can therefore be inferred from bond yields. When fitting unspanned models, it is necessary to include option data, which adds further challenges. Because there are no analytical solutions in the LADQ (1,1) model, we show how options can be priced using an Alternating Direction Implicit finite difference scheme. We then implement an Unscented Kalman filter — a non-linear extension of the Kalman filter, which is a popular method for inferring state variable values — to recover the latent state variables from market observable dat

Dynamic State Estimation of Microgrid With Imperfect Data Communication

Dynamic state estimation of power systems is essential for wide area control purposes. In this thesis, we present the results of dynamic state estimation for a grid-connected microgrid including two synchronous generators and three loads. The Unscented Kalman filter (UKF) and the Extended Kalman filter (EKF) are implemented using a classical generator model connected to a Thevenin equivalent of the remainder of the microgrid. The model is used to estimate the six states variables of the generator; namely, rotor angle, speed variant, d- and q- axis transient voltages, d-axis damper flux, and q-axis second damper flux. Both real power and reactive power are used as measurements in our state estimation algorithm. The estimation results are compared with the true values to demonstrate the accuracy of the state estimator. In addition to data loss or delay, sensor measurements may include outliers that distort state estimation. We utilized the Generalized Maximum Likelihood-extended Kalman filter (GM-EKF), as a robust estimator, which exhibits good tracking capabilities suppressing the effects of bad data (outliers). We also used two methods of state estimation on UKF to deal with bad data. Simulation results obtained from the UKFs are compared with those of GM-EKF. We present simulation results at a high frequency of 1 kHz of state estimation for different scenarios that include normal operation, fault at Point of Common Coupling (PCC), loss of generator, and loss of load. We also developed a scheme to use delayed data in Kalman filter estimation and used it to simulate the effect of data loss and/or delay in the communication system of the microgrid. For the same scenarios, we also present simulation results at 50 Hz, which is compatible with Phasor Measurement Units (PMU), including bad data as well as data loss or delay. Our results demonstrate that while both filters successfully detect bad data, the UKF methods provide better estimates than those of the GM-EKF

Sensor Placement Algorithms for Process Efficiency Maximization

Even though the senor placement problem has been studied for process plants, it has been done for minimizing the number of sensors, minimizing the cost of the sensor network, maximizing the reliability, or minimizing the estimation errors. In the existing literature, no work has been reported on the development of a sensor network design (SND) algorithm for maximizing efficiency of the process. The SND problem for maximizing efficiency requires consideration of the closed-loop system, which is unlike the open-loop systems that have been considered in previous works. In addition, work on the SND problem for a large fossil energy plant such as an integrated gasification combined cycle (IGCC) power plant with CO2 capture is rare.;The objective of this research is to develop a SND algorithm for maximizing the plant performance using criteria such as efficiency in the case of an estimator-based control system. The developed algorithm will be particularly useful for sensor placement in IGCC plants at the grassroots level where the number, type, and location of sensors are yet to be identified. In addition, the same algorithm can be further enhanced for use in retrofits, where the objectives could be to upgrade (addition of more sensors) and relocate existing sensors to different locations. The algorithms are developed by considering the presence of an optimal Kalman Filter (KF) that is used to estimate the unmeasured and noisy measurements given the process model and a set of measured variables. The designed algorithms are able to determine the location and type of the sensors under constraints on budget and estimation accuracy. In this work, three SND algorithms are developed: (a) steady-state SND algorithm, (b) dynamic model-based SND algorithm, and (c) nonlinear model-based SND algorithm. These algorithms are implemented in an acid gas removal (AGR) unit as part of an IGCC power plant with CO2 capture. The AGR process involves extensive heat and mass integration and therefore, is very suitable for the study of the proposed algorithm in the presence of complex interactions between process variables

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed