Induction Motor Drive Matlab Simulink

International Journal of Electrical and Computer Engineering (IJECE)

584

Journal homepage: http://iaesjournal.com/online/index.php/IJECE Modeling and Simulation of VSI Fed Induction Motor Drive in

Accepted Mar 4, 2017

The theory of reference frames and switching functions are effective in analyzing the performance of the induction motor fed from VSI (Voltage Source Inverter). In this work, mathematical model of Adjustable Speed Drive (ASD) is developed by taking synchronous reference frame equations for induction motor, switching function concept for VSI and non-switching concept for diode bridge rectifier. Simulation model of induction machine is implemented using dq0 axis transformations of the stator and rotor variables in the arbitrary reference frame. The corresponding equations are given in the beginning and then the developed model is implemented using MATLAB/Simulink. In this work, the proposed model is implemented using basic function blocks. The performance of induction motor is analysed for different frequencies. The developed model is tested for the steady state behavior of machine drive. The proposed mathematical model is validated by the simulation results.

Converters

Copyright © 2017 Institute of Advanced Engineering and Science. All rights reserved.

D. Uma,

Thanjavur, Tamilnadu- 613 401, India. 1.

Introduction

In many industrial applications Adjustable speed drives (ASD) are most commonly seen workhorses. In order to supply the motor with variable AC voltage or AC current with variable frequency Variable Frequency Drives (VFD) are employed. ASDs are used in pumping applications, in sugar cane industries, conveyor applications etc. The common VFD consists of a three phase diode bridge rectifier, dc link and a pulse width modulated inverter. It is necessary to develop a model for VFD for power system dynamic studies. In literature, for the three phase diode bridge rectifier dq impedance model is employed .

State-space averaging method is used for modeling a three phase four wire diode bridge rectifier . Dynamic average value modeling methods are utilized for conventional three phase diode bridge rectifier and are validated . This can capture the steady-state and transient characteristics of the diode bridge rectifier.

An approximate switching function of the diode bridge rectifier is used in order to obtain the estimating function for the fundamental current harmonics .This method is proven to be effective in finding out the input current harmonic content. A switching function model for voltage source inverter is derived and also it is validated using MATLAB/Simulink .

Modulation function theory is effectively utilized for deriving the Pulse Width Modulated (PWM) inverter which makes use of the Iterative Harmonic and Interharmonics Analysis (IHIA) . Space vector pulse width modulation method is employed for inverter and the method is validated using MATLAB/Simulink . A three phase boost dc-ac converter is used to supply the induction motor . AC output voltage that is greater than the input dc voltage is obtained without the need of additional boost converter.

585

The effects of low switching frequencies in inverter fed ac drive are analyzed . Both the simulation and experimental results are discussed. Model predictive current control method is employed for load current control . The effectiveness of the method is validated by simulation using two level inverter.

MATLAB /Simulink model is developed for a three phase inverter with PID controller and hardware is implemented using digital signal processor . Total Harmonic Distortion (THD) is less for inverter with PID controller. A mathematical modeling of induction motor is derived and validated using MATLAB/Simulink . Fifth order differential equations are used for modeling induction motor in synchronously rotating reference frame theory . A dynamic model of three phase induction motor with double windings in the stator has been derived using space vector theory . The derived model is simulated in Simulink and the steady state and dynamic characteristics are compared with the standard three phase induction motor. Three various approaches are used to obtain the squirrel cage induction motor characteristics. They are, (a) stator resistance measurement, (b) details from the motor plate and (c) induction motor modeling . This is simple and cost effective approach . Modeling of induction motor based on object oriented methodology is employed . This model is validated on a faulty squirrel cage induction motor. A dynamic model of variable frequency drive is obtained which has the capability to ride through the fault . The same is verified using case studies. Several other models for induction motor , voltage source inverter and diode bridge rectifier are available in the literature. In literature, separate models are available for the converters and induction motor.

In modern industrial applications as the induction motor is fed from switching converters, the motor model developed must be valid for arbitrary applied voltage and current waveforms. Therefore a complete model is required for power system dynamic studies and for harmonic analysis. Also, the machine model must include the essential elements of both electromagnetic and mechanical system for both steady state and transient operating conditions. Considering this, in this work an accurate model for induction motor is developed using d-q reference frame equations. Switching function concept is used for developing a model for voltage source inverter (VSI) and a non-switching concept is employed for uncontrolled rectifier. Thereby a complete and an accurate model of VFD which is required for power system dynamic studies and harmonic analysis is developed. The accuracy of the developed model has been verified through simulation in MATLAB/Simulink.

2.

2.1. Modeling Of Induction Motor

The steady state equivalent circuit is derived from the principle of operation of induction motor. The steady state response of variable speed induction motor drive is evaluated based on the equivalent circuit. For validation of the design of the motor-drive system, the dynamic simulation is one of the important steps. This eliminates inadvertent mistakes in the design and resulting errors in prototype model. Therefore dynamic models are required for the induction motor . The dynamic model of the induction motor is obtained from the fundamentals. The dqo model makes use of two windings for the rotor and stator of the induction motor.

Transformation of abc to dqo axes employed for deriving the dynamic model is based on simple trigonometric relationship. Used in the derivation of various dynamic models are based on simple trigonometric relationships. Since the mathematical equations of induction motor are involving differential equations that are varying with respect to time which helped to choose synchronous reference frame as the scope of this work in modeling.

The assumptions that are made in order to derive the dynamic model of induction motor are as

(1) Air Gap Is Uniform

(2) Stator and rotor windings are balanced, with the mmf being distributed sinusoidally (3) Inductance versus rotor position is sinusoidal; and (4) Saturation and changes of parameter are neglected.

Three particular cases for the induction machine in arbitrary reference frames are,

(2) Rotor Reference Frames Model;

(3) Synchronously rotating reference frames model. The model of induction motor can be done effectively using the reference frames mentioned as in . Induction motor can be modeled by taking one of the generalized arbitrary reference frames, they are stator reference frame, rotor reference frame, synchronous rotating reference frames. In this work we considered implanting synchronous rotating reference frame method. Why, because the steady nature of this stator d-axis current makes this reference frame useful when a computer is used in simulation and one of advantages of this frame is speed and angular position can be taken into consideration at any instant of time.



Modeling and Simulation of VSI Fed Induction Motor Drive in Matlab/Simulink (D. Uma)

586

Since the mathematical equations of induction motor are involving differential equations that are varying with respect to time which helped to choose synchronous reference frame as the scope of this work in modeling. The model equations are derived from dqo equivalent circuit of induction motor given in Figure 1.

Figure 1. dqo equivalent circuit of three phase induction motor The flux linkage equations which are written below are obtained by applying KVL and KCL to

(7)

Current can be found by substituting flux linkages

(11)

Torque equation in terms of modified flux linkages and currents is given by

2.2. Modeling Of Voltage Source Inverter

In order to describe the function that needs to be done by the circuit, transfer function is derived. A dependent variable can be calculated in terms of its respective independent variable by using transfer function. In Pulse Width Modulation (PWM) the dependent variable is the modulated waveform and the independent variable is the waveform to be modulated. General expression of the transfer function is,

Where, Vd Is The Dependent Variable And

VI is the independent variable. There are several advantages by modelling the VSI using transfer function model. 1. Power conversion circuit can simplified into output and input variables 2. Converter topologies can be derived easily by transfer function approach 3. The strategy to implement gating pulses will become much simpler 4. Various parameters like current and voltage, load current can be calculated easily 5. For a power conversion circuits there is no need of forming real power electronic models and state

Equations

A particular transfer function has a particular switching function. The relationship between output variable and input variable is obtained by employing switching function theory. So to have a detailed account of the static power converters, a proper switching function must be obtained. Based on the theory of transfer function, in the VSI, the independent variables are the input voltage Vd and output current IA, IB, and IC and the dependent variables are input current Ii and output voltage VAB, VBC, VCA. Therefore, the output and

(15)

where TF is the Transfer Function of VSI which can expressed in the form of various switching functions.

Tf

........

(17)

For three phases VSI the switching function can be classified as SF1A, SF1B, SF1C and expressions are given

(20)

By the use of switching functions SF1A, B, C the voltages are found by

(26)

From the above mentioned theory the required variable for modeling of VSI is formed and can be realized readily. 2.3. Modeling of Three Phase Diode Bridge Rectifier The ac input power is converted into dc output power by the use of three phase diode bridge rectifier. The circuit condition determines the instant at which the diode starts conducting. The input voltages VA, VB and VC for the balanced condition can be written as follows:

(29)

where, Vm is the voltage magnitude. For this voltages, the fundamental switching functions are expressed as same as voltage source inverter SF1A, B, C as mentioned in the modeling of voltage source inverter. The correlation input and output of the diode bridge rectifier are given as

(31)

A synchronously rotating dq frame is considered with d-axis aligned with the voltage vector. By the use of transformation matrix, three phase variables FABC hence, the three phase variables FABC are expressed in terms of such dq frame.

(33)

Combining (30) and (33) following equation can be yielded

(34)

where Vd and Vq are d & q axes voltage components. The equations (30) to (34) represent the non-

Switching Model Of Diode Rectifier

3.

Matlab/Simulink Implementation

In this section, MATLAB/Simulink is used for the simulation of three phase induction motor model . The corresponding equations which are used to implement this model have been discussed in Section 1. Figure 2 shows the Simulink model of the induction motor.

Figure 2. Matlab/Simulink model 3-phase induction motor 3.1. Simulink Implementation of Voltage Source Inverter Simulink model of the voltage source inverter (VSI) is shown in Figure 3 which is implemented using the concept of switching function.

Figure 3. Voltage Source Inverter model in Matlab/Simulink

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.