Laboratory Manual For Electric Energy Engineering EE-360 Electrical Engineering Department King Fahd University of Petroleum & Minerals Dhahran, Saudi Arabia Table of Contents Experiment Title No. 1 Three Phase Circuit Page No. 3 2 Three Phase Power Measurement 6 3 Magnetic Circuit 9 4 Equivalent Circuit of Transformer 12 5 Regulation and efficiency of a single phase Transformer 16 6 Load Characteristic of shunt and compound DC generator 19 7 Torque Speed Characteristic of DC shunt and compound motors 22 8 Determination of Parameters of Synchronous Generators 26 9 Torque Speed Characteristics of 3Φ Induction Motors 29 10 Determination of Induction Motor Parameters 32 2 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#1 THREE PHASE CIRCUITS Objectives: • • • To learn how to make wye (Y) and delta (∆) connections To study the relationship between voltage and current in three phase circuits. To make power calculations. Apparatus: • • • • 2 AC voltmeters 2 AC Ammeters 1 3Φ- load 1 3Φ variable AC power supply Theory : In a Y connection , the line and the phase quantities are related by: Vp=VL/√3 (1) Ip=IL (2) Whereas the relationships for a delta connection are Ip=IL/√3 (3) Vp=VL (4) The real and reactive powers for a 3 Φ circuit (either Y or ∆ connection) are given as 3 P=√3 VL IL cos θ (5) Q=√3 VL IL sin θ (6) Where θ is the power factor angle of the balanced load Procedure: A: Y – Connection 1. Connect the three-phase load in Y as shown in Fig. 1. Ask your instructor to check your connections. a A A V V 3 Phae Ac B b C c Fig. 1 : The Y - Connection 2. Switch the load to unity power factor mode 3. Select the balanced load from each phase 4. With the load switch off turn the power supply on and adjust the line to neutral voltage to 120 volt or VL = 208 volt 5. Measure the line and phase voltages and currents. Make the table similar to table1 on a separate page and enter your readings in the first 4 columns Table 1: Y connecteds load VL Vp IL Ip VL / Vp IL Ip / P 4 Q Remarks Take three readings, one at the rated value of the load current (8A), one at ½ rated load and one at ¼ rated. 6. Repeat step 5 for 0.8 and 0.8 leading power factor loads B: ∆ Connection 1. Connect the three phase load as shown in fig. 2 A A a 3 Phae ac N V N b N B A C c Fig. 2 : The Delta- Connection 2. Turn the power supply on and adjust for 120V A.C (Note: Vp=VL for ∆) 3. Repeat step 5 of the Y connection for unity, 0.8 lagging and 0.8 leading power factors and enter in a table similar to table 1, call it table 2. Report 1. Complete tables 1 and 2. 2. Calculate the total real and reactive powers. 3. Draw phasor diagrams showing the line and phase voltages and currents for both Y and ∆ connections. Draw only for rated load, unity power factor condition. 4. Verify the relationships for the phase and the line voltages and currents and state reasons for any errors. 5 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electrical Engineering Department EE 360 Electric Energy Engineering - Experiment # 2 THREE PHASE POWER MEASUREMENT Objectives: 1. Measure power in balanced Y and ∆ systems. 2. Determine power factor of 3Φ systems. Apparatus: 2 Wattmeters 1 Voltmeter 1 3Φ load 1 Ammeter 1 3Φ variable AC power supply (Variac) Theory: a M A V1 A Three Phase Load V B b V1 c C M Fig.1: Two Wattmeter Connection If two wattmeters are connected to measure the power of any 3Φ load, it can be shown that the wattmeters will read V1 6 P1 = VL IL cos ( 30 – θ ) P2 = VL IL cos ( 30 + θ ) (1) (2) Where θ the power factor angle of the load. From (1) and (2) we can show that the total power PT = P1 + P2 = 3 VL IL cosθ (3) tanθ = 3 ( P1 - P2 ) / ( P1 + P2 ) (4) Procedure 1. Connect the circuit as shown in fig 1. Connect the 3Φ load in Y. 2. Before you switch on, have your connections cheeked by the instructor. 3. Set the supply voltage to 200 V from a variac 4. Select the load power factor to be unity 5. On a separate sheet of paper make a table with 11 columns as shown in table.1. Pf P1 P2 VAB VCB IA PT (Watt) (Watt) (Watt) (Volt) (Volt) (amp) Pf calc. Pf Error (%) PT Calc. Power Error calc. Table.1: Results for Y connection 6. Take three sets of readings, one for the rated load 8 A, one for ½ rated and one for ¼ rated loads. 7. Repeat step 6 for 0.8 lagging as well as leading power factor conditions. 8. Connect the three phase load in ∆. 9. Set the supply voltage to 100 volts (VL= VP for ∆). 10. Repeat step 6 for unity, 0.8 lagging and 0.8 leading power factor conditions. Enter the results in a table similar to table 1.call table 2. 7 Note: At a certain power factor, one of the wattmeters may try to read backwards. Switch the supply off, reverse the voltage OR the current coil connection. Mark the reading as negative. Report 1. Using the wattmeter readings, compute the power factor from equation (4). Enter it as pf (calculated) in tables.1 and 2. Calculate the percent error between the calculated and the recorded power factors. 2. Use equations (1) and (2) to calculate the total power. Compare it to the measured total power and enter the percent error in the tables. 3. Comment on the levels of error between the computed and measured values. State any sources of error. 4. Draw a phasor diagram and show why equations (1) and (2) can be used to calculate the total power. 8 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#3 MAGNETIC CIRCUITS Objective: 1. To determine the B-H characteristics of an iron core 2. To find the relative permeability (µr) 3. To calculate the reluctance “R” Apparatus: 1 Rectangular laminated core 1 coil 1 voltmeter 1 ammeter 1 variable AC supply Theory: I A N V Fig. 1 : A simple rectangular core If a current of 1 A, flows from a supply of E volts through a coil of N turns, as shown in fig 1, the magnetic field intensity can be written as H = NL / LC 9 (1) From faraday’s law of electromagnetic induction, the rms values of the induced voltage across the coil (E) is E = ωNΦ = ωNAB (2) B=µH (3) From (1), (2) and (3) it is clear that E-I characteristic of the core is equivalent to the B-H characteristic. Further, it can be shown that E = ωN2A µ I Lc (4) Where, the permeability can be written as: µ = µr µo; µo = 4 π x 10-7 (H/n) The reluctance of the core can be expressed as: R= NI / Φ = Lc / (µA) (5) Procedure 1. Find the typical dimensions of the core. The instructor may help you to get the accurate numbers. 2. Connect the circuit as in fig 1 3. On a separate sheet of paper make a table as shown below: Table 1 E I K= E / I µr R 4. Set the input voltage of 10V. Record the current and enter them in table 1. 5. Repeat step 4 up to 150 volts in steps of 10 volts. 10 Report 1. Plot E Vs I on a graph paper. 2. Find K, and R for each reading and complete the table. Here, K=E/I µ r= KLc 2 π fN2A µo 3. Plot µ and R as functions of I 4. Derive equations (4) and (5) Core Dimensions: Lc = 40 cms N = 400 turns A = 9 Sq. cms 11 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#4 EQUIVALENT CIRCUIT OF TRANSFORMER Objectives: 1. To determine the equivalent circuit of a single phase transformer 2. To verify the voltage current relationship Apparatus: 1 Single-phase transformer 1 Variable AC power supply 1 AC voltmeter 2 AC ammeters 1 Wattmeter 1 Variable load resistance Theory The approximate equivalent circuit of a transformer is given in Fig. 1. Req Xeq Xm Rc Fig 1. Equivalent Ciruict of transformer Where, Rc =1/g and xm =1/b. These quantities are obtained from the open circuit power, voltage and current measurements. These are 12 and, Y = g - jb = Io / Vo (1) g = Po / Vo2 (2) b = √ |Y|2 – g2 (3) The equivalent resistances and reactances (Req, Xeq) are obtained from the current, voltage and power measurements in the primary winding when the secondary is shorted. These are written as Req = Psc / I2sc |Zeq| = Vsc / Isc Xeq = √|Zeq|2 - Req2 (4) (5) (6) Procedure 1. Note the current, voltage and volt-ampere ratings of both windings of the transformer. Note the turns ratio 2. Connect the circuit as shown in Fig2. with the high voltage side open circuited 3. Adjust the supply voltage until the voltage on the primary side is the rated value. 4. Record the current, voltage and power in this condition. Take another reading at 110 % of the rated value. 5. Next, connect the transformer for the short circuit test as given in Fig 3. The variable supply will be on the high voltage side. 13 L Variable AC Source Digital Wattmeter 220V side Open Circuit 110 / 220 V N Fig. 2 : The Open Circuit Test connection 6. Gradually increase the supply voltage from zero until the rated current flows in the shorted secondary winding 7. Record the current, voltage and power. Repeat step 6 for 110 % of rated current and record the values. A L Variable AC Source Digital Wattmeter 110V side short Circuit 220 / 110 V N Fig. 3 : The Short Circuit Test connection 8. Connect the circuit as shown in Fig. 4 for a load test 9. Adjust the supply voltage and the resistive load such that rated current flows through the load at rated voltage Measure the voltages and currents on both sides of the transformer 14 A L Variable AC Source Digital Wattmeter Load V 220 / 110 V N Fig. 4 : The Load Test connection Report 1. Calculate Rc, Xm, Req and Xeq from the open circuit and short circuit tests. 2. Draw the approximate equivalent circuit diagrams and label the parameter values. Note that some of the values have to be transferred to the other side of the winding by multiplying with approximate constant. 3. For the unity power factor loading condition of Fig 4, calculate the primary current and voltage using the equivalent circuit you obtained. Start with the measured values of current and voltage on the load side. 4. Compare the calculated quantities with measured ones and compute the percent error 5. State the possible sources of errors, if any. 15 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#5 REGULATION AND EFFICIENCY OF A SINGLE PHASE TRANSFORMER Objectives: 1. To determine the regulation of a transformer 2. To determine the efficiency of a transformer Apparatus: 1 Single-phase transformer 1 Variable AC power supply 2 Voltmeters 2 Ammeters 2 Wattcmeters 1 Variable load Theory The voltage regulation of transformer at rated load is defined as: VR = (Vno load - Vrated) / Vrated (1) If the approximate equivalent circuit of a transformer is used then for a lagging pf load V1= Vno load = Vrated <0o + I (cos θ – j sin θ) (Req + j Xeq) = Vrated <0o + (Req cos θ + I Xeq sin θ) + j (- I Req sin θ + I Xeq cos θ) Neglecting the imaginary part on the right hand side, 16 (2) VR = I (Req cos θ + Xeq sin θ) Vrated (3) The efficiency of the transformer can be written as η = Power output / Power input (4) Or η = Power Output___ Power output + Loses The losses are, Core loss = No load power input – No load copper loss Copper loss = I22 Req Procedure : L Load Variable AC Source Digital Wattmeter Digital Wattmeter 220 / 110 V N Fig. 1 : A Transformer with Load 1. Record the ratings of the transformer 2. Note down the parameters of the approximate equivalent circuit from the previous experiment. If you are using a different transformer, perform the open circuit and short circuit test again. 3. Connect the circuit as shown in Fig.1. 4. Make a table on the separate page as table.1. 5. Select unity power factor load. 6. Adjust the input voltage so that the load voltage is the rated value for a certain load current. Record Pi, Po, V2 and I2. Switch the load off and record V2. This is V2 (no load) 7. Repeat step 6 for various loads until you have reached the rated current. Take about 10 readings. Make sure that you have taken readings at ¼, ½, and ¾ of full load and rated load (8A) condition. 17 8. Select 0.8-power factor lag. Repeat step 6 for rated current 9. Repeat step 8 for 0.8 p.f . leading. Table 1 P.f V2 I2 Pi Po V2 (No load) η= P2/Pi VR Η (cal) VR from eq3 Report 1. Calculate efficiency and voltage regulation fro your test results. Enter them in columns 7 and 8 in table 1 2. Plot efficiency as function of load current for the unity power factor load 3. For rated, ½ and ¼ rated load, Calculate the efficiency from the equivalent circuit. Enter them in table 1. Compare with measured values 4. Calculate the voltage regulation for rated load at unity, 0.8 lagging and 0.8 leading power factors using equation 3. Enter them in the table. Compare your results with measured values. 5. State reasons of any discrepancy between the measured and the calculated values 18 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#6 Load Characteristics of Shunt and Compound DC Generators Objectives: 1. To study the load voltage vs. current characteristics of shunt connected DC generator. 2. Study the load characteristics of a compound generator. Apparatus: 1 DC motor-generator set 1 Tachometer 1 DC Voltmeter 2 DC Ammeters 1 Power Supply 1 Resistive load Theory: The terminal voltage of a shunt generator is written as: Vt = Ea – Ia Ra (1) Where Ia = If + IL If is the shunt current and IL is the load current For a short shunt compound generator, the terminal equation is modified to Vt = Ea – Ia Ra - IL Rsc (2) Where Rsc is the resistance of the series winding. 19 Procedure: 1. Record the rated currents and voltages of the DC generator and the motor. Record the rated speed of the motor and generator. 2. Make the connection as shown in fig.1. + R + LINE If - rheostat rheostat + + + M - DC SUPPLY A Ia + G - Ea SHUNT Vt V LOAD - SHUNT + - A - Fig.1: Connection Diagram For Shunt Generator 3. Set the generator shunt field rheostat to its maximum value. 4. Set the motor shunt field to its minimum value. 5. Adjust the motor speed to almost rated value. You can go slightly higher than the rated one. The motor speed can be adjusted by changing the resistance in the motor field winding or with series resistance RLine. 6. Adjust the generator voltage to its rated value by controlling the field rheostat. Keep the load disconnected during the voltage buildup. 7. Gradually change the load resistance from no load to about 120 % rated load. Maintain the motor speed to same value. 8. Record the speed of the motor. Enter the load voltage, load current and field current as in table.1 for different loading conditions. Take at least 10 sets of readings. Table.1 20 VL IL If 9. Repeat the procedure for the compound generator given in fig.2. + 10. Enter your readings in table similar to table.1. A + R LINE SERIES Ia + M - DC SUPPLY + G - IL If + Ea V - SHUNT + - LOAD A - Fig.2: Connection Diagram for Compound Generator REPORT: 1. Plot the load voltage and field current of the shunt generator against the load current. 2. Repeat the above for the compound machine. 3. Find the voltage regulation at rated load from your experimental results for both shunt and compound machines. 4. Comment which generator is better in terms of load characteristics and why? 21 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electrical Engineering Department EE 306 Electric Energy Engineering - Experiment#7 Torque Speed Characteristics of DC Shunt and Compound Motors Objectives: 1. To study the variation of speed of shunt motor when load is changed. 2. To study speed vs. load characteristics of a compound motor. Apparatus: 1 DC motor- generator set 1 Tachometer 1 DC Voltmeter 2 DC Ammeters 1 Power supply 1 Resistance Theory: For DC shunt and long shunt compound motors, current and flux are related by: Vt = Ea + Ia Ra (1) Ea = Ka ω m Φ (2) Which gives ωm = Vt − I a Ra KaΦ (3) Using the equation Ia = Tdev / (KaΦ) (4) We can write 22 ωm = Ra 1 Vt − Tdev KaΦ ( K a Φ) 2 (5) Equation (5) shows the relation between torque, speed, terminal voltage and flux of the motor. Procedure: 1. Record the rated voltage, current and speed of the motor and the generator. The generator is used to load the motor. 2. Connect the circuit as shown in fig.1 A A + DC SUPPLY Ia + M - + G - Ea + DC FIELD SUPPLY - V LOAD - Fig.1: The Shunt Motor Generator Connection 3. Adjust the generator field resistance to maximum and motor field to minimum. 4. Start the motor and bring the speed to slightly more than rated. 5. Apply the generator field and buildup the voltage to its rated value. 6. Load the generator from no load to approximately 120 % full load by switching in the load rack. Adjust the generator terminal voltage to the rated value every time by varying the field rheostat and/or the field supply voltage. 7. Record the motor speed n (rpm) and the motor armature current Ia for every load value of load. 8. Make connection as given in fig.2 for the compound motor. 23 A A + DC SUPPLY SERIES FIELD + M - + DC FIELD SUPPLY - + G - V LOAD - Fig.2: The Compound Motor Generator Connection 9. Repeat steps 3 thru 7 for the compound motor. Report: 1. Plot the speed vs. motor armature current for the DC shunt motor. 2. Repeat 1 for the compound motor. 3. Calculate the speed regulation from no load to full load of the DC shunt motor. 4. Repeat 3 for the compound motor. Compare the torque-speed characteristics of the two motors and note your observation. 24 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#8 Determination of Parameters of Synchronous Generators Objectives: 1. To determine the synchronous impedance of an alternator. 2. To determine its voltage regulation. Apparatus 1 3Φ alternator 1 DC motor 1 AC Voltmeter 1 DC Ammeter 1 DC voltmeter 1 DC power supplies 1 Tachometer Theory: For a certain excitation the synchronous impedance per phase of a synchronous machine can be calculated as Zs = Ea / Ia (1) Where Ea is the open circuit voltage per phase and Ia is the short circuit current. The synchronous reactance then can be calculated as (2) X s = Z s2 − Ra2 Ra is considered as 1.5 times the armature DC resistance Rdc .Xs is the saturated reactance when Ea is taken from the open circuit characteristics and Ia is the corresponding short circuit current for the same excitation. For a certain load current Ia, the internal voltage per phase can be written as 25 Ea = Vt + Ia ( Rs + jXs ) (3) Where Vt is the terminal voltage per phase. Note, Ia is a complex number The voltage regulation of the generator at the rated load is given as: VR = (VNL-VFL)/VFL X 100% (4) Where, VNL = Ea and VFL = Vt (rated) Procedure: 1. Note the rated values of current, voltage and speed of the synchronous generator as well as the motor that will drive the generator. 2. Connect the motor generator set as shown in fig.1 for the open circuit test. A + + DC FIELD SUPPLY - FIELD DC SUPPLY E A - C DC MOTOR B SYN. ALTERNATOR Fig.1: The Open Circuit Test 3. Adjust the alternator field rheostat to the maximum value and that for the motor to the minimum value. 4. Adjust the motor speed to the synchronous speed of the alternator. You can control the speed by the resistors in the line or in the motor field circuit. 5. Vary the field current in steps by varying the rheostat in the field circuit and/or the supply voltage. Record the line-to-line voltage (E) and the filed current If. Make sure that the speed remains constant through the whole test. 6. Take the readings upto 110 % of the rated voltage of the alternator. 7. Stop the motor and connect as in fig .2 for the short circuit test of the alternator 26 IA A A A + DC FIELD SUPPLY - FIELD DC MOTOR C B DC MOTOR SYN. ALTERNATOR Fig.2 The Short Circuit Test 8. With the generator exciter off, bring DC motor upto synchronous speed. Close the 3Φ switch and gradually increase the excitation. Record the field current If and the armature current Ia. Take readings upto 120 % of the rated generator current. 9. Switch the alternator exciter off. Stop the motor and make connection as given in fig.3 for measurement of DC resistance of the armature. B A + + DC POWER SUPPLY V - - C A Fig.3: DC Resistance measurement Of The Alternator 10. Adjust the DC power supply so that the current flowing through the alternator winding does not exceed the rated value. The DC resistance is given as Rdc = Vdc / 2Id c The armature resistance Ra can be considered to be 1.5 times Rdc Note: the armature DC resistance can also be measured by an accurate millimeter, or by some resistance measurement bridge. 27 Report: 1. Using the OCC and SCC test results, plot EA and IA against If on the same graph paper. 2. From the plotted graphs, determine Zs and Xs using equations (1) and (2). Calculate only the saturated value. 3. Calculate, analytically, the voltage regulation of the generator for the following loading conditions: One. Rated load, unity power factor Two. Rated load, 0.8 lagging p.f Three. Rated load, 0.8 leading p.f Use equations (3) and (4). 28 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering - Experiment#9 Torque Speed Characteristics of 3Φ Induction Motors Objectives: 1. To determine the torque speed characteristics. 2. To determine slip-torque characteristics. 3. To observe variation of efficiency. APPARATUS: 1 3Φ induction motor 1 Prony brake 2 Wattmeters 1 3Φ variable power supply 1 Tachometer 1 Single pole switch 1 Digital Torquemeter Theory: The slip of an induction motor is defined as s= ns − nr ns where ns is the synchronous speed nr is the rotor speed The efficiency of the motor is calculated from the ratio of the output mechanical power to input electrical power as η= Pout x 100% P 29 Procedure: 1. Record the rated values of the induction motor. Note the synchronous speed. 2. Couple the induction motor to the prony brake as shown in fig.1, adjust the prony brake belt so that it is not very tight. 3. Connect the two wattmeters to read the total power. 4. Start the motor and perform a load to 5 Nm in steps of 0.5 Nm. a P1 M A 3Φ ac A T V1 ROTOR B b C A c INDUCTION MOTOR Prony Brake Fig.1: Connection of 3Φ Induction Motor 5. Prepare a table similar to table.1 on a separate sheet of paper. Record the motor speed n (rpm) and load T(Nm) and the wattmeter readings P1 and P2 (watts). Report 1. Calculate the total input power, the slip and the output power for each reading. Pout = 2 ( π / 60) Tn Slip s = ( ns – n ) / ns watts ns = 1800 rpm ( syn. Speed ). 2. 3. 4. 5. Plot torque vs speed and torque vs slip. Calculate efficiency of the motor and enter it in table.1. Plot efficiency vs torque. Find maximum torque and slip conditions. 30 Table.1 Torque-T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Speed P1 P2 Ptotal (P1+P2) 31 Slip Pout (watts) KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 306 Electric Energy Engineering-Experiment#10 DETERMINATION OF INDUCTION MOTOR PARAMETERS Objective The goal of this experiment is to determine the electrical parameters of a 3-ϕ induction motor (primary and secondary resistance and reactance and the magnetization branch values). APPARATUS 1) 1 Three-Phase Induction Motor. 2) 1 Prony Brake. 3) 2 Digital Wattmeters. 4) 1 Three-Phase Variable AC Power Supply. 5) 1 DC Power Supply. 6) 1 DC Ammeter. 7) 1 DC Voltmeter. 8) 2 Three Phase Switches. Introduction Induction motor is an AC machine in which an alternating current is supplied to the stator armature windings directly and to the rotor windings by induction. Because it operates at balanced conditions, only a single phase is necessary. So, the per-phase equivalent circuit of the induction motor in which the rotor parameters are referred to the stator side is shown in Figure 1. It can be seen from Figure 1 that the core loss represented by RC is neglected since its effect is lumped with the rotational losses. The following equations can be derived: V1 = E1 + (R1 + jX 1 )I 1 ................................................... (1) ⎛R ⎞ E1 = ⎜ 2 + jX 2 ⎟ I 2 ...................................................... (2) ⎝ s ⎠ To determine the parameters of the equivalent circuit of the three-phase induction motor, it is subjected to three tests. 32 j X1 R1 I1 j X2 I2 + + j Xm V1 R2 / s E1 _ _ Figure 1: Per-phase equivalent circuit of a three-phase induction motor referred to the stator Proceedure A. DC Test Connect the circuit as shown in Figure 2 (while the motor is at standstill), apply the dc voltage Vdc until the current Idc flowing in the induction motor is the rated value. The stator resistance per phase can be calculated as R1 = Vdc / (2 Idc).. I dc A V Vdc A R1 R1 B R1 C Figure 2: DC test for the determination of the stator resistance B. No Load Test Rated balanced voltage at rated frequency is applied to the stator, and the motor is allowed to run on no-load. When the machine runs on no-load, the slip is close to zero, and the circuit to the right of the shunt branch in Figure l is taken to be an open circuit. Thus the equivalent circuit to the no-load test conditions is given in Figure 3. Because of the relatively low value of rotor frequency, the rotor core loss is practically negligible at no-load. From Figure 3, it follows that Protational = Pnl − 3I nl2 R1 ................................................... (3) P Rnl = nl2 = R1 + lumped losses .................................... (4) 3 I nl Vnl Z nl = = Rnl2 + X nl2 ............................................ (5) 3 I nl X nl = Z nl2 − Rnl2 = X 1 + X m ......................................... (6) 33 No load power factor = cos ϕ 0 = Inl Pnl 3 Vnl I nl ..................... (7) j X1 R1 + j Xm Vnl /sqrt(3) _ Figure 3: Approximate equivalent circuit for no load test Perform the following: 1. 2. 3. 4. 5. Connect the circuit as shown in Figure 4. Apply the rated voltage. Measure the rated voltage Vo = Vnl. Measure the line current (Ia = Ib = Ic = Inl). Measure the wattmeters powers W1 and W2, so Pnl = W1 + W2. Calculate Rnl, Xnl, Znl, and φ0 from equations (4)−(7). W1 a Ia b A V0 3 Phase Supply Rated Voltage Ib c B C Ic W3 2 Figure 4: Schematic diagram for the no load test C. Blocked-Rotor Test In this test, the rotor of the induction motor is blocked so that the slip is equal to unity, and a reduced voltage value is applied to the machine stator terminals so that the rated current flows through the stator windings. The iron losses are assumed to be negligible in this test. Also, the shunt branch is neglected for this test since the excitation current is small. The equivalent circuit corresponding to the blocked rotor test condition is given in Figure 5. From Figure 5, it then follows that Rbl = Pbl = R1 + R2 .................................................... (8) 3 I bl2 34 Z bl = Vbl 3 I bl = Rbl2 + X bl2 ............................................ (9) X bl = Z bl2 − Rbl2 = X 1 + X 2 .......................................... (10) The following assumption can be taken: X1 = X 2 = 1 X bl ......................................................... (11) 2 Finally, the magnetization reactance can be found: X m = X nl − X 1 ............................................................ (12) j X1 R1 Ibl j X2 + Vbl /sqrt(3) R2 _ Figure 5: Approximate equivalent circuit for blocked rotor test Perform the following: 1. Connect the circuit as in Figure 6. Keep the applied voltage to zero at starting. 2. Increase the applied voltage until the rated current flows in the stator winding. 3. Measure the applied voltage VS = Vbl. 4. Measure the line current (Ia = Ib = Ic = Ibl). 5. Measure the wattmeters powers W1 and W2, so Pbl = W1 + W2. 6. Apply equations 8−12 to calculate the parameters X1, X2 , Xm , R2 . W1 a Ia b A V VS 0 3 Phase Supply Ib c B W32 Ic Figure 6: Schematic diagram for the blocked-rotor test 35 C Brake Report 1. Record the ratings of the induction motor and determine the number of its poles. 2. Find the parameters of the equivalent circuit of the three-phase induction motor. 3. Draw the equivalent circuit of the induction motor and put the values of the parameters that you found in the previous question along with their symbols. 4. Determine the no load power angle. 5. Determine the combined rotational losses of the motor. 36 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Electric Engineering Department EE 360 LAB – EXP # 1 & 4 Loading Combination for different power factors (New load banks). 1. Y CONNECTION Pf Loading 0.8 lag 480W+420W+120W 480W+420W 480W+120W 480W 480W+420W+420W +all inductance (22.9) mH 480W+420W+420W +all capacitors (22.9) mH 0.8 Lead P1 (W) P2 (W) PT (W) VAB (V) VCB (V) IA (A) P.f Cal. 2. DELTA (∆) CONNECTION For the above combinations of loading in ∆ connection reduce the applied voltage (60 V) to limit the line current (same as in Y connected load). 37 P.f

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