47 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.
48 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, r s Vdc 1 I 2 dc (5.1) where V dc - Input dc voltage applied I dc - 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, P ohmic = 3 I 2 nl r s (5.2) where I nl - No load phase current r s - Stator resistance losses are Therefore the power loss due to friction and windage losses and core P fwc = P nl P ohmic (5.3) where P nl - No load power P ohmic - Ohmic losses
49 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, X ls X m Vnl 1.732 I nl (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, P br = 3 I 2 br (r s + r r ) (5.5) From which r r P 3 I br 2 br r s (5.6) where P br - Blocked rotor power r r - Rotor resistance The magnitude of the blocked rotor input impedance is Z br Vbr 1.732 I br (5.7) Now, f (r r ) j (X X ) Z br s r ls lr br fnl (5.8) where f br = Frequency during blocked rotor test f nl = Frequency during no load test
50 X ls = Stator leakage reactance X lr = Rotor leakage reactance From the above equation the values of X ls and X lr are calculated. Generally X ls 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 (r s ) 0.435 2 Rotor Resistance (r r ) 0.816 3 Mutual Inductance (Xm) 26.13 4 Stator Leakage Reactance (X ls ) 0.754 5 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.
51 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
52 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 T e and r - Implementation of torque and speed equations v) Subsystem I abcs - Two phase to three phase conversion (stator) vi) Subsystem I abcr - 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, V qdos = K s V abcs (5.9) where [V qdos ] T = [ V qs V ds v os ] [V abcs ] T = [V as V bs V cs ] K s is transformation factor Cos Cos ( 2 / 3) Cos ( 2 / 3) 2 Ks Sin Sin ( 2 / 3) Sin ( 2 / 3) 3 ½ ½ ½
53 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, V qdor = K r V abcr (5.10) where [V qdor ] T = [ V qr V dr V or ] [V abcr ] T = [V ar V br V cr ] K r is transformation factor Cos Cos ( 2 / 3) Cos ( 2 / 3) 2 Kr 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
54 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
55 Figure 5.5 Implementation of dynamic modeling equations Figure 5.6 Implementation of overall flux equations in terms of D-Q form
56 (a) Subsystem 411 (b) Subsystem 412 Figure 5.7 Implementation of stator flux equations in terms of D-Q form
57 (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)
58 The subsystem T e and (4.11) are implemented as shown in Figure 5.10. r represented by the equations (4.20) and d r P dt (2 J) (T T ) e L (5.11) where P - number of Poles J - Moment of inertia T e - Electrical output Torque T L - Load Torque r - Rotor angular electrical speed The subsystem I abcs describes the conversion of two phase (D-Q) variable into three phase variables (ABC) in stator side. It may be expressed as, I abcs = K -1 S I qdos where [I qdos ] T = [I qs I ds I os ] [I abcs ] T = [I as I bs I cs ] K -1 S is Inverse transformation factor 1 s Cos Sin ( 2 / 3) 1 K 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.
59 Figure 5.10 Implementation of speed and torque equations Figure 5.11 Two phase to three phase variables conversion (stator) The subsystem I abcr describes the conversion two phase (D-Q) variable into three phase variables (ABC) in rotor side. It may be expressed as, I abcr = K -1 r I qdor (5.13) where [I qdor ] T = [I qr I dr I or ] [I abcr ] T = [I ar I br I cr ] K -1 r is Inverse Transformation factor 1 r Cos Sin ( 2 / 3) 1 K Cos( 2 / 3) Sin ( 2 / 3) 1 Cos( 2 / 3 Sin ( 2 / 3) 1
60 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.
61 ii) iii) iv) Single phasing: Anyone of the phase is cut down or anyone of the phase voltage is zero. Voltage unbalance: By providing different magnitude of voltages in all the three phases of supply. Under voltage: Providing phase voltage less than the rated voltage. v) Over voltage: Providing phase voltage greater than the rated value. vi) vii) viii) Earth fault: Creating leakage current in three phase supply by certain percentage simulates ground fault. Phase reversal: By inter changing any two phases of the supply. 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:
62 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
63 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) iii) iv) Under voltage unbalance /over voltage unbalance Single phasing Variable frequency v) Phase reversal Load Conditions i) No load ii) iii) 25%, 50%, 75%, 100% and 125% of rated loads 2, 2.5 and 3 times rated current
64 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). current) Case (v) Over load condition (2, 2.5, 3 and 4 times of rated 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.
65 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.