In this study, a time-domain methodology for the harmonic state estimation (HSE) assessment of power networks is proposed. The time domain HSE solution is based on the application of the Kalman filter, Poincaré map and extrapolation to the limit cycle using a numerical differentiation procedure. The noisy state variables measurements to be used for HSE are taken from a simulation of the network harmonics propagation. The estimated harmonic magnitudes are obtained applying the discrete Fourier transform. The results obtained with the proposed time-domain HSE methodology are validated against the actual system response and against the solution obtained with the power systems computer aided design/electromagnetic transients including direct current (PSCAD/EMTDC) simulator, widely accepted by the power industry, a close agreement between the results is obtained.

A methodology is developed to assess the time-domain power quality state estimation (PQSE) in electrical systems based on the Kalman filter implemented using parallel processing techniques through graphics processing units (GPUs) to reduce the execution time. The measurements used by the state estimation algorithm are taken from the simulation and transient propagation response of the power network. The parallel Kalman filter (PKF) state estimation obtains the waveforms for busbar voltages and line currents with several sources of time-varying electromagnetic transients. The PKF is evaluated using the compute unified device architecture (CUDA) platform and the CUDA basic linear algebra subprograms library, the parallel filter is executed on GPU cards. Case studies are applied to solve the time-domain state estimation using the proposed PKF-PQSE method, obtaining an execution time reduction and including time-varying harmonics, short circuit faults, and load transient conditions. The speed-up depends on the number of state variables modeling the electrical system under analysis. The PKF-PQSE results are successfully compared and validated against the power systems computer aided design/electromagnetic transients including direct current simulator.

This paper proposes a time-domain methodology based on the unscented Kalman filter to estimate voltage sags and their characteristics, such as magnitude and duration in power systems represented by nonlinear models. Partial and noisy measurements from the electrical network with nonlinear loads, used as data, are assumed. The characteristics of voltage sags can be calculated in a discrete form with the unscented Kalman filter to estimate all the busbar voltages; being possible to determine the rms voltage magnitude and the voltage sag starting and ending time, respectively. Voltage sag state estimation results can be used to obtain the power quality indices for monitored and unmonitored busbars in the power grid and to design adequate mitigating techniques. The proposed methodology is successfully validated against the results obtained with the time-domain system simulation for the power system with nonlinear components, being the normalized root mean square error less than 3%.

State estimation is one of the most important processes to perform a reliable monitoring and control of the steady-state operating condition of modern electric power systems; thus, it is currently a fundamental part in the development of research to enhance the monitoring and security of the smart grids operation. This important topic is taught in advanced courses of operation and control of power systems, for graduate and undergraduate power engineering students. However, the most used software packages for simulation and analysis of power systems by researchers, students, and educators have put little attention on the state estimation module. Due to this fact, this paper proposes an approach to develop the computational implementation of a practical educational tool for state estimation of electric power systems using the MATLAB optimization toolbox. In this proposal, the formulation of the state estimation problem consists of developing a general digital code to implement an objective function based on the weighted least squares method. While the lsqnonlin function of the MATLAB optimization toolbox solves the formulated state estimation problem. Simplifying both research and educational processes, this tool helps graduate and undergraduate students to improve learning, understanding, and the times of implementation and development of research in state estimation. Simulations of an equivalent model of the Mexican interconnected power system consisting of 190 buses and 46 machines are used to test and validate the proposal performance.

This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among other issues, of microgrids with PV sources. The results are successfully validated through direct comparison against those obtained with the PSCAD/EMTDC simulator, widely accepted by the power industry.