Mathematical Problems in Engineering

Volume 2017, Article ID 5274517, 14 pages

https://doi.org/10.1155/2017/5274517

## Implementation of SoC Based Real-Time Electromagnetic Transient Simulator

^{1}Cinvestav, Unidad Guadalajara, Del Bosque Av. 1145, El Bajío, 45019 Zapopan, JAL, Mexico^{2}Cátedras Conacyt-Cinvestav, Unidad Guadalajara, Del Bosque Av. 1145, El Bajío, 45019 Zapopan, JAL, Mexico

Correspondence should be addressed to S. Ortega-Cisneros; xm.vatsevnic.ldg@agetros

Received 23 September 2016; Revised 23 January 2017; Accepted 29 January 2017; Published 8 March 2017

Academic Editor: Paolo Boscariol

Copyright © 2017 I. Herrera-Leandro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Real-time electromagnetic transient simulators are important tools in the design stage of new control and protection systems for power systems. Real-time simulators are used to test and stress new devices under similar conditions that the device will deal with in a real network with the purpose of finding errors and bugs in the design. The computation of an electromagnetic transient is complex and computationally demanding, due to features such as the speed of the phenomenon, the size of the network, and the presence of time variant and nonlinear elements in the network. In this work, the development of a SoC based real-time and also offline electromagnetic transient simulator is presented. In the design, the required performance is met from two sides, (a) using a technique to split the power system into smaller subsystems, which allows parallelizing the algorithm, and (b) with specialized and parallel hardware designed to boost the solution flow. The results of this work have shown that for the proposed case studies, based on a balanced distribution of the node of subsystems, the proposed approach has decreased the total simulation time by up to 99 times compared with the classical approach running on a single high performance 32-bit embedded processor ARM-Cortex A9.

#### 1. Introduction

Electromagnetic transients (EMT) in power systems [1] involve voltages and currents with very fast variations, which are produced by sudden changes in the power network and may last for only a few microseconds. Switch changes or short circuits are some of the causes that could trigger these phenomena; although they usually last only a few cycles, it is important to gather detailed information about their behavior, for example, for the design and evaluation of new control and protection devices to ensure satisfactory operation before they can be utilized in real systems. Real power systems are not accessible for testing purposes, so offline and real-time simulators represent the best alternative for testing equipment under stress conditions similar to those that they will encounter in real operating environments.

Developing real-time and even offline simulators is not a straightforward task, due to power system size and dynamic behavior of some elements, such as switches that cause modifications in the conductance matrix and nonlinear devices that make it a nonlinear problem. Modifications in the conductance matrix lead to a new matrix factorization, a time consuming process. Moreover, for real-time simulations, the complexity increases significantly when considering the limited time window usually available for processing data, generally on the order of microseconds.

Most proposals for the implementation of real-time simulators deal with the limited window of time available for computing the transient, avoiding the solution of the resulting linear system of equations that relate voltages and currents in the network [2–4], because this process is very time consuming and the computational complexity grows exponentially with the network size. Such approaches are based on prestoring the resulting inverse matrices for all possible combinations of the states of the time variant elements.

Since power electronics systems such as HVDC are widely used in power systems [5], precomputing and storing the corresponding inverse matrices in memory might not be a suitable option. In general, prestoring the possible inverse matrices is acceptable for a power system with only a few time variant elements, but in the case of many time variant elements, the memory resources can be insufficient.

This work aims to describe the implementation of an alternative offline but also real-time electromagnetic transient simulator based on a System on Chip (SoC). The simulator was designed to keep an almost invariant simulation time step independently of the number of time variant devices in the network, as the simulator performs a complete solution of the system for every simulation time step.

The architecture of the proposed simulator is based on a highly parallel implementation designed to reach multiple levels of parallelism. For the simulation transient algorithm, a topological splitting network is proposed, a technique which permits reaching a deeper degree of fragmentation than that generated by only using the well-known splitting technique using transmission lines [6, 7].

#### 2. Numerical Solution

Power systems are composed of several interconnected electric devices, like generators, transformers, transmission lines, and lumped devices, among others.

##### 2.1. Lumped Elements

Digital simulators are based on synchronous devices, such as CPU, DSP, and other digital components, which all work based on clock signals that synchronize all internal electronics, and therefore their response is limited by the clock period of the system. As a result, digital simulators cannot reproduce the natural analog response of the power network element devices (voltages and currents).

Consider the relations at terminals of an inductor and a capacitor as written in (1) and (2), respectively:In digital simulations, differential equations of lumped components, inductors, and capacitors are transformed into difference equations in the form of (3). For this, most of the software and methods for electromagnetic transient simulation work are based on a numeric integration rule, as the trapezoidal integration method. This method is one of the most widely adopted methods by engineers due to its precision and stability [8].

The resulting difference equation can be taken to a circuit representation, as in Figure 1.In (3), is an equivalent conductance. This parameter depends on the value of the element that was discretized and the specific time step chosen for the simulation; the term is a history current source, whose magnitude depends on past values of voltages at element terminals, the current through the element, or both, depending on the specific integration method used [9].