Numerical modeling of electromagnetic transient phenomena in power system using finite element technique

Abstract

This paper sets out a theoretical basis and creates a computer program that successfully demonstrates the application of the finite element technique for harmonic and transient analysis of electrical circuits, as well as for the analysis of stationary and transient phenomena in the power system. According to the available literature, a completely new method for the analysis of transient phenomena in the power system is presented here. In Chapter 2, a simple and reliable algorithm for the analysis of both harmonic and transient electrical circuits is presented. The presented numerical algorithm is based on the finite element technique, using a solution logic analogous to the solution of fields in a continuum. In the terminology of the finite element technique, each branch of the circuit is considered as a finite element with two local nodes. The possibility of transient analysis of a linear circuit is demonstrated on a specific example of a linear circuit. The obtained numerical results are in excellent agreement with the analytical solution, which confirms the accuracy of the proposed algorithm. In Chapter 3, an algorithm for the calculation of short circuits in the power system using the finite element technique is presented. The elements of the power system are modeled on the basis of mathematical models that are natural for the stationary analysis of short circuits in the power system. For each type of finite element, a local system of equations was derived that serves to assemble the finite element with the rest of the network. On the example of a single-pole short circuit in the network, the finite element method was tested with the symmetric component method. It is important to emphasize the observed simplicity and generality in the development of a software package using the finite element technique in comparison with symmetric components. Using finite elements, it is possible to easily solve much more complicated problems, which is not the case with the symmetric component method. In Chapter 4, the possibility of applying the finite element technique in modeling electromagnetic and electromechanical transients in the power system is shown, using the logic of solving fields in a continuum. Mathematical models of finite elements are generally described by a system of differential equations. To perform the numerical integration of the above equations, we used the principle of the mean value of the integral ( -method). Each part of the system, or finite element, is represented by its local system of algebraic equations and has a certain number of local nodes, depending on the type of finite element. The number of nodes of a finite element is equal to the number of physical connections of that element to the power system. The generator model as a finite element was successfully tested with the EMTP-ATP software package on the example of a three-pole impulse short circuit. In Chapter 5, an analysis of electromagnetic and electromechanical phenomena in the power system was performed on the example of a single-pole short circuit on a double line, as well as on the example of a single-pole short circuit in the case of a power system with multiple generators. In Subchapter 5.1, we presented the short-circuit currents, overvoltages on the high-voltage side of the transformer, the electromagnetic torque of the generator, the excitation current of the generator, as well as the rotor circular frequency for the duration of the entire transient. In subsection 5.2, we have presented the results of the calculation, as a function of time, of the electromagnetic moments, reactive powers, excitation voltages, and load angles of all generators for the duration of the entire transient phenomenon. On selected examples, we have shown the possibility of applying the presented method in the analysis of various transient phenomena in the power system, as well as simple problem solving of a real power system, i.e. a system with a large number of generators, transformers, transmission lines, and other elements.

Ivica Jurić-Grgić

Full Professor | Department of Theoretical Electrical Engineering and Modelling

Researcher and full professor at the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split. His research focuses on numerical modeling of electromagnetic transients in power systems, with particular emphasis on the development of advanced numerical methods for analyzing electromagnetic transients in multi-conductor transmission lines. His work includes the application of finite element techniques for transient stability analysis of power systems, as well as the enhancement of models for harmonic and transient analysis of grounding systems.