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CHAPTER 5

SIMULATION AND TEST SETUP FOR FAULT ANALYSIS

5.1 INTRODUCTION

This chapter describes the simulation model and experimental set up

used for the fault analysis. For the simulation set up, the d-q model proposed

by Park is taken into consideration. In this thesis, the induction motor is

modeled using the modules in the power system tool box of

MATLAB-Simulink. Mechanical load is modeled so that the load torque can

be varied externally. The module is integrated with the system using the S-

Function provided by SIMULINK. Important simulated data are sent to the

workspace of MATLAB for analysis.

Test set up for fault analysis is created using the test bench available

in the laboratory. In the present study, fault was artificially introduced in the

laboratory to new healthy motors. Specimen used was three phase and four

pole induction motor commercially available. Rated voltage, current and

output of the motor are 400 V, 4.6 A and 2.2 kW respectively. The number of

rotations is 1440 rpm. The number of slots in the stator is 36. Two stator

windings are connected in parallel for each phase. Windings of three phases

are in delta connection. 45 coils are inserted in a slot.

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5.2 DETERMINATION OF EQUIVALENT CIRCUIT

PARAMETERS

The parameters for the equivalent circuit are determined from no

load test, DC test and blocked rotor test. During the DC test, a dc voltage is

applied across two terminals while machine is at standstill. Thus,

dcs

dc

V 1rI 2

(5.1)

where Vdc - Input dc voltage applied

Idc - DC current obtained from DC test

The power input during no load test is sum of the stator ohmic losses, the core

losses due to hysteresis and eddy current losses, rotational losses due to

friction and windage. The stator ohmic losses are,

Pohmic = 3 I2nl rs (5.2)

where Inl - No load phase current

rs - Stator resistance

Therefore the power loss due to friction and windage losses and core

losses are

PfWC = Pnl – Pohmic (5.3)

where Pnl - No load power

Pohmic - Ohmic losses

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The no load impedance is highly inductive and its magnitude is

assumed to be sum of the stator leakage reactance and the magnetizing

reactance. Thus,

nlls m

nl

VX X1.732 I

(5.4)

During the blocked rotor test, the rotor is locked by some external means and

balanced three phase stator voltages are applied. The frequency of the applied

voltage is often less than rated value. From this test,

Pbr = 3 I2br (rs + r r) (5.5)

From which

brr s2

br

Pr r3 I

(5.6)

where Pbr - Blocked rotor power

r r - Rotor resistance

The magnitude of the blocked rotor input impedance is

brbr

br

V| Z |1.732 I

(5.7)

Now, brs r ls lr br

nl

f(r r ) j (X X ) Zf

(5.8)

where fbr = Frequency during blocked rotor test

fnl = Frequency during no load test

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Xls = Stator leakage reactance

X lr = Rotor leakage reactance

From the above equation the values of Xls and X lr are calculated.

Generally Xls and X lr are assumed equal. All the three tests, DC test, no load

test and block rotor test are conducted for 3 hp, 4 pole, 400 volts, 3-phase,

50 Hz and 1440 rpm induction machine. Table 5.1 shows equivalent circuit

parameters for dynamic model of induction machine.

Table 5.1 Induction motor parameters

S.No Motor Variables Value (pu) 1 Stator Resistance (rs ) 0.435

2 Rotor Resistance (r r ) 0.816

3 Mutual Inductance (Xm) 26.134 Stator Leakage Reactance (Xls) 0.7545 Rotor Leakage Reactance (X lr) 0.754

5.3 IMPLEMENTATION OF DYNAMIC MODEL IN MATLAB

SIMULINK ENVIRONMENT

Simulink is a tool in MATLAB used to simulate dynamic systems.

The Sim Power System is one of the toolbox of Simulink, which is used to

analyze steady state and transient response of the electrical and power

systems like AC motors and transformers. In this thesis, sim power system

toolbox is used to analyze the three phase induction motor performance under

different electrical fault conditions. The solver used for simulation of

induction motor performance is ODE113. This is a multi step and variable

order solver. It is recommended when function evaluation is time consuming

and tolerance is tight.

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Overall dynamic model of the three phase induction motor is

implemented in MATLAB - Simulink environment as shown in Figure 5.1.

The inputs of a squirrel cage induction motor are the three phase voltages (Va,

Vb and Vc), their fundamental frequency and load torque. The outputs are

stator currents, rotor currents, stator d-q currents, rotor d-q currents, electrical

torque and rotor speed (rpm). The d-q model requires that all the three-phase

variables have to be transformed to the two phase synchronously rotating

frame. Consequently, the induction motor model has blocks transforming the

three phase voltages to d-q frame and d-q currents back to three phases.

Figure 5.1 Overall dynamic model of three phase induction motor

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The induction motor model shown in Figure 5.1 consists of

following major subsystems:

i) Subsystem 1 - Three phase to two phase variables conversion

(stator)

ii) Subsystem 2 - Three phase to two phase variables

conversion (rotor)

iii) Subsystem 3 and 4 - Implementation of dynamic modeling

equations

iv) Subsystem Te and r - Implementation of torque and speed

equations

v) Subsystem Iabcs - Two phase to three phase conversion

(stator)

vi) Subsystem Iabcr - Two phase to three phase conversion (rotor)

The subsystem1 describes the change of variables which formulates

transformation of three phase voltage variables of stationary elements to the

arbitrary reference frame. It may be expressed as,

Vqdos = Ks Vabcs (5.9)

where [Vqdos ]T = [ Vqs Vds vos]

[Vabcs]T = [Vas Vbs Vcs]

Ks is transformation factor

s

Cos Cos ( 2 / 3) Cos ( 2 / 3)2K Sin Sin ( 2 / 3) Sin ( 2 / 3)3

½ ½ ½

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The equation (5.9) represents the transformation of three phase

variable into two phase variables in stator side. Figure 5.2 implements three to

two phase variables conversion in the stator.

Figure 5.2 Three phase to two phase variables conversion (stator)

Similarly, Vqdor = Kr Vabcr (5.10)

where [Vqdor]T = [ Vqr Vdr Vor]

[Vabcr]T = [Var Vbr Vcr]

Kr is transformation factor

r

Cos Cos ( 2 / 3) Cos ( 2 / 3)2K Sin Sin ( 2 / 3) Sin ( 2 / 3)3

½ ½ ½

The equation (5.10) represents the transformation of three phase

variables into two phase variables in rotor side. Figure 5.3 implements three

to two phase variables conversion in rotor. The subsystem 3 and subsystem 4

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represented by the equations from 4.10 to 4.18 are implemented in Simulink

platform as shown from Figure 5.4 to Figure 5.9.

Figure 5.3 Three phase to two phase variables conversion (rotor)

Figure 5.4 Mutual inductance calculation in terms of D-Q components

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Figure 5.5 Implementation of dynamic modeling equations

Figure 5.6 Implementation of overall flux equations in terms of D-Q form

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(a) Subsystem 411

(b) Subsystem 412

Figure 5.7 Implementation of stator flux equations in terms of D-Q

form

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(a) Subsystem 413

(b) Subsystem 414

Figure 5.8 Implementation of rotor flux equations in terms of D-Q form

Figure 5.9 Implementation of stator and rotor currents (D-Q Form)

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The subsystem Te and r represented by the equations (4.20) and

(4.11) are implemented as shown in Figure 5.10.

e L

d r Pdt (2 J) (T T )

(5.11)

where P - number of Poles

J - Moment of inertia

Te - Electrical output Torque

TL - Load Torque

r - Rotor angular electrical speed

The subsystem Iabcs describes the conversion of two phase (D-Q)

variable into three phase variables (ABC) in stator side. It may be expressed

as,

Iabcs = K-1S Iqdos

where [Iqdos ]T= [Iqs Ids Ios]

[Iabcs]T = [Ias Ibs Ics]

K-1S is Inverse transformation factor

1s

Cos Sin ( 2 / 3) 1K Cos( 2 / 3) Sin ( 2 / 3) 1

Cos ( 2 / 3 Sin ( 2 / 3) 1

The equation (5.12) represents the transformation of two phase

variables into three phase variables in stator side and is implemented in

Figure 5.11.

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Figure 5.10 Implementation of speed and torque equations

Figure 5.11 Two phase to three phase variables conversion (stator)

The subsystem Iabcr describes the conversion two phase (D-Q) variable

into three phase variables (ABC) in rotor side. It may be expressed as,

Iabcr = K-1r Iqdor (5.13)

where [Iqdor ]T = [Iqr Idr Ior]

[Iabcr]T = [Iar Ibr Icr]

K-1r is Inverse Transformation factor

1r

Cos Sin ( 2 / 3) 1K Cos( 2 / 3) Sin ( 2 / 3) 1

Cos ( 2 / 3 Sin ( 2 / 3) 1

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The equation (5.13) represents the transformation of two phase

variables into three phase variables in rotor side and is implemented in

Figure 5.12.

Figure 5.12 Two phase to three phase variables conversion (rotor)

5.4 SIMULATION OF ELECTRICAL FAULTS

The modeling of three-phase symmetrical induction motor is

developed in MATLAB-Simulink environment as explained above. By using

Simulink model of three phase induction motor, electrical faults such as single

phasing, voltage unbalance, current unbalance, over voltage, under voltage,

overload, earth fault and power frequency variations are all simulated.

Performance of induction motor during the above electrical faults with

various load conditions (no load, 25%, 50%, 75%, 100% and 125% of rated

full load) is obtained from simulation.

Simulation criteria for electrical faults are as follows:

i) Over load: Anyone of phase current is greater than the rated

value. It is allowed to run over certain time till the overload

fault happens.

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ii) Single phasing: Anyone of the phase is cut down or anyone

of the phase voltage is zero.

iii) Voltage unbalance: By providing different magnitude of

voltages in all the three phases of supply.

iv) Under voltage: Providing phase voltage less than the rated

voltage.

v) Over voltage: Providing phase voltage greater than the rated

value.

vi) Earth fault: Creating leakage current in three phase supply by

certain percentage simulates ground fault.

vii) Phase reversal: By inter changing any two phases of the

supply.

viii) Power frequency variation: By varying the frequency of

supply voltage.

The stator currents, rotor currents, stator and rotor d-q currents,

speed and torque during both healthy and faulty conditions are recorded.

Based on the recorded data, the performance of induction motor under various

operating conditions is analyzed.

5.5 ESSENTIALS FOR TEST SET UP

An experimental test set up was built as shown in Figure 5.13. The

test set up consists of a three phase squirrel cage induction motor with brake

drum load, 3 single phase auto transformers, ammeters, voltmeters, watt

meters, digital storage oscilloscope and a digital tachometer. Name plate

details of test motor are given below:

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Type - Squirrel Cage

Voltage - 400 to 440 V

Connection -

Class - E

Frequency - 50 Hz

Rating - 3 HP

Current - 4.6 A

Speed - 1440rpm

Figure 5.13 Experimental test set up

The motor under test are mounted on a custom built platform

designed for ease of accommodation of machines. Power is supplied to the

motors under test via a motor starter most appropriately rated for a range of

breakers. The voltages applied to the motors under test are controlled by 3

single phase auto transformers rated at 30 A, which are used for voltage

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control. The phase to neutral voltages is independently controllable between 0

and 400V. The loading is based on brake drum type. By adjusting the brake

drum arrangement load is varied. Voltage and currents are measured and

recorded through a digital storage oscilloscope and a standard power data

analyzer both sampling at 32 bits. Speed is measured using digital tachometer.

Currents and voltages are also measured using standard ammeters and

voltmeters. Power is measured using standard watt meters.

5.6 OPERATIONAL CONDITIONS FOR ANALYSIS

The adjustability of the load system and the controllability of the

auto transformer are essential for the establishment and maintenance of the

range of test conditions as follows:

Supply Variables

i) Balanced rated voltage/ under voltage /over voltage

ii) Under voltage unbalance /over voltage unbalance

iii) Single phasing

iv) Variable frequency

v) Phase reversal

Load Conditions

i) No load

ii) 25%, 50%, 75%, 100% and 125% of rated loads

iii) 2, 2.5 and 3 times rated current

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In order to get a clear and step by step idea about the induction

motor behavior during electrical faults, the following tests were carried:

Case (i) Load test on induction motor during balanced rated

voltage condition (Loads varying from no load to 125% of rated load)

Case (ii) Load test on induction motor during balanced under

voltage and over voltage conditions (Loads varying from no load to 125% of

rated load and percentage of under voltage varying from 0% to 50%)

Case (iii) Load test on induction motor during different voltage

unbalance conditions like 1-Ph, 2-Ph, 3-Ph under and over voltage

unbalances, (loads varying from no load to 125% of rated load).

Case (iv) Load test on induction motor during single phasing

condition by supplying 0V on one phase. (Loads varying from no load to

100% of rated load).

Case (v) Over load condition (2, 2.5, 3 and 4 times of rated

current)

Case (vi) Load test on induction motor during phase reversal

condition with balanced rated voltage, 1-ph under voltage unbalance and 1-ph

over voltage unbalance. (Loads varying from no load to 125% rated load).

Case (vii) Ground fault condition (Single phase, two phase line to

ground and three phase faults).

Case (viii) Various Power frequency conditions (25 Hz, 40 Hz,

50Hz, 60Hz and 100 Hz) with loads varying from no load to 125% of rated

load.

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Based on the measured and computed datas, the performance of the

three phase induction motor under various operating conditions is analyzed.

5.7 CONCLUSION

This chapter explains the simulation and test set up used for fault

analysis. Creation of faults and the operational conditions in both the cases

are explained.