Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 6740261, 14 pages

http://dx.doi.org/10.1155/2016/6740261

## Model of Transient Process Where Three-Phase Transducer Feeds Induction Motor Equivalent as a Variable Active-Inductive Load

^{1}Advanced Polytechnic School of Vocational Studies Uroševac, 24 Novembre, 38218 Leposavić, Serbia^{2}Faculty of Technical Sciences, University of Priština, Kneza Miloša 7, 38220 Kosovska Mitrovica, Serbia^{3}Faculty of Technical Sciences Čačak, University of Kragujevac, Svetog Save 65, 32000 Čačak, Serbia^{4}Business College of Vocational Studies, Kralja Petra I 70, 18420 Blace, Serbia^{5}Faculty of Economics, University of Priština, Kolašinska 156, 38220 Kosovska Mitrovica, Serbia

Received 12 March 2016; Accepted 18 July 2016

Academic Editor: Yan-Wu Wang

Copyright © 2016 Nenad Marković 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

The paper presents a new approach in the analysis of a transient state in a system where the feeding source is a transducer-IGBT inverter and load is introduced through the induction motor with its parameters. Induction motors with different parameters of powers and power factors are tested. MATLAB simulation of the three-phase inverter that feeds the induction machine has replaced the missing lab equipment with which mathematical model of this system was verified. According to the selected parameters of the inverter and induction machine and through the simulation in the MATLAB program, the results are obtained in the form of diagrams that verify the model of a transient state of the induction machine operation when it operates as a motor which is presented as a variable load. The transient process of the system three-phase bridge inverter whose active-inductive load is the induction machine in the conditions of the change of the load parameters is analyzed. The model of the transient process in the system formed by the inverter in PWM (Pulse Width Modulation) converter and induction machine is developed in the time domain and phase coordinates.

#### 1. Introduction

When there was a need for the analysis of a wave current in a system in which the three-phase induction motor was fed from a three-phase bridge inverter it appeared that there were no adequate mathematical models of such a system in available literature. The models of three-phase induction motors, mostly derived by Park’s coordinate system, are quite common in the literature. However, the mathematical model which unites the processes in the system of polyphase motor-polyphase inverter in the time domain could not be found. Therefore, during the formation of the transient state model an idea emerged to present an induction machine in such system as an active-inductive () load which significantly simplifies the whole process.

The analysis of stationary processes in the inverter during the operation with active-inductive () load can be performed using the different methods. However, for the analysis of the transient states it is necessary to compose differential equations and to implement boundary conditions for each time interval of operation. If the form of phase voltage in the electrical circuit is known, then the inverse Laplace transform applies. By applying the different methods it is possible to determine instantaneous values of currents for each part of the voltage, respectively, independent of some other part during the given time interval, while the substitution of initial conditions in obtained relations is not necessary. The use of thyristors that block the passage in electric circuit of the voltage inverter can simplify its typology since there is no need to add capacitance, inductance, and additional thyristor elements for commutation [1].

The induction machines are suitable for operation through the inverter transducers, because the winding insulation of standard induction motors tolerates certain voltage overload but at higher speeds of rotation, that is, higher frequencies; they have higher noise level and additional losses [2–4], which affect the motor output torque, depending on the regulation range of the speed of rotation and power factor correction [5–9]. The induction machines can be connected to transducers for the purpose of asymmetry elimination and electric networks harmonics reduction [10, 11].

The paper is organized in the following way: Section 2 describes the operation of the three-phase bridge with active-inductive load. Section 3 presents the analysis of the transient processes and the transducer-IGBT inverter is proposed as the feeding source. Section 4 presents the selected example of the three-phase inverter with the frequency of 2000 Hz and modulations frequency of 50 Hz. Following the presentation of analytical considerations in Section 4 presentation and verification of a model on a selected type of the induction motor are given. The optimal type of the inverter with which the desired correction can be achieved in relation to the power factor and the power of the motor is determined. Section 5 presents the concluding remarks.

#### 2. Description of the System Transducer-Induction Motor

The operation of three-phase bridge inverter with active-inductive load at given time interval and activation of active valves is described in [1, 12], but the type of the receiver, such as induction machine, has not been stated.

Scheme of bridge voltage inverter (Figure 1(c)) is characterized by the fact that each time it activates two oppositely orientated and parallel valves. This is necessary for voltage inverter through load that contains reactive component each time to yield both currents (Figure 1(e)). If in the first semiperiod () valves and are open, the load is connected to feeding sources.