Power system state estimation comparison of Kalman filters with a new approach

A Review and Performance Comparison of Power System State Estimation Techniques

Abstract: State estimation is an important area required for enabling proper operation and control of the power system and its real-time monitoring. Correct knowledge of the states (like rotor angle and speed deviations) enables us to develop control schemes to enhance the system stability and reliability. Earlier the power system loads were almost constant and it was a static system as the load models became complex and the power system changed to quasi-static or sometimes dynamic it was not computationally possible to use older methods to achieve real-time monitoring. Dynamic State Estimation (DSE) techniques use the Dynamic model of the system in conjunction with the measurement model which can be used to accurately predict the states in advance. In this paper, various algorithms of traditional state estimation are presented, based on the available literature

Power system dynamic state estimation considering correlation of measurement error from PMU and SCADA

Abstract: It is well known that measurements from phasor measurement unit (PMU) or supervisory control and data acquisition (SCADA) are not generally independent. Since the correlation of measurement error is a very representative feature of the actual measurement system, traditional assumptions on error independency are not adequate. In this paper, taking the correlation of measurement error of both PMU and SCADA measurements into consideration, a novel correlated extended Kalman filter (CEKF) is proposed. The actual measurement configurations are analyzed with the consideration of measurement error transfer characteristics. Then, the modified measurement error covariance matrix is calculated by using the point estimation method, which will replace the traditional diagonal variance matrix. At last, IEEE 14‐bus system and 57‐bus system are provided to illustrate the effectiveness and superiority of the method, respectively.

Optimization-Based Estimation of Microgrid Equivalent Parameters for Voltage and Frequency Dynamics

Abstract: Microgrid parameter estimation is essential to enable optimal voltage and frequency control using distributed energy resources (DER). Microgrid parameters vary through time, e.g., when generation is re-dispatched/committed, during microgrid reconfiguration. Furthermore, sensor measurements are noisy and preservation of the fast dynamics measurements is required, which is difficult to achieve with a lowpass filter. In this paper, a moving horizon estimation (MHE) approach is applied to estimate microgrid parameters for voltage and frequency support. The proposed approach estimates the states i.e., frequency, rate of change of frequency, grid voltage and current, and system parameters i.e., inertia, damping, and equivalent impedance. The MHE is formulated as an optimization problem using data over a fixed past horizon and solved online such that the sum of the square of measurement noise and process noise is minimized. Results showed that the proposed approach was able to estimate microgrid states, parameters, and disturbances within 5% for most values, which is sufficient to use in microgrid voltage and frequency control.

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Abstract: Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

Novel approach to nonlinear/non-Gaussian Bayesian state estimation

Abstract: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.

Unscented filtering and nonlinear estimation

Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

Abstract: A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.