Islamic University of Gaza Faculty of Engineering Electrical Engineering department Electric Machine Lab Eng. Omar A. Qarmout Eng. Amani S. Abu Reyala Experiment 2 THREE PHASE AC CIRCUITS: VOLTAGE AND CURRENT RELATIONS AND POWER PART1: THREE PHASE VOLTAGE AND CURRENT RELATIONSHIPS OBJECTIVE: When you have completed this assignment, you will be able to: Derive the relationship between line and phase voltages in a balanced star connected three phase supply load. Derive the relationship between line and load currents in a balanced delta connected three phase supply load. INTRODUCTION: In a typical three phase power system, the generator has a star connected output and usually includes either star or delta connected loads. Voltage relationships are considered when a star load is connected and current relationships when a delta load is connected. Figure 2-1 In power systems great care is taken to ensure that the loads of transmission lines are balanced. For balanced loads, the terminal voltages of the generator, and and the phase voltages, and at the load terminals are balanced.
Voltage relation (star load): To find the relationship between the line voltages ( line to line voltage ) and the phase voltages ( line to neutral voltages ) of a balanced three phase supply connected to a star connected load, the line to neutral voltage of phase A is arbitrarily chosen as the reference, thus: 0 120 120 Where represents the magnitude of the phase voltage (line to neutral voltage). The line voltages at the load terminals in terms of the phase voltages are found by application of Kirchhoff's voltage law: 1 0 1 120 3 30 1 120 1 120 3 90 1 120 1 0 3 150 The voltage phasor diagram of the star connected loads shown in figure 2-1 is shown in figure 2-2. The relationship between the line voltage and phase voltage is demonstrated graphically Figure 2-2 If the RMS value of any of the line voltages is denote by, and then one of the important characteristics of the star connected three phase load may be expressed as: 3 30 Thus in the case of star connected loads, the magnitude of the line voltage is 3 times the magnitude of the phase voltage, and for a positive phase sequence, the set of line voltages leads the set of phase voltages by 30 o Current relationships (Delta load): The relation between the phase and line currents of a balanced three phase supply connected to a delta connected load is considered and reference should be made to figure 2-3. It should be noted that each phase has equal impedances.
Fig 2-3 As the line currents,, and has the same magnitude and phase impedances are equal, line voltages ( ) must be the same as the phase voltages ( ): Consider the phasor diagram shown in figure 2-4, where the phase current Iab is arbitrarily chosen as refrence. Fig 2-4 Thus: 0 120 120 Where represents the magnitude of the phase current. The relationship between the phase and line currents can be obtained by applying Kirchhoff's current law at the corners of the delta load: 1 0 1 120 3 30 1 120 1 0 3 150 1 120 1 120 3 90 The relationship between the phase and line currents is demonstrated graphically in figure 2-4. If the rms of any of the line currents is denoted by, then one of the important characteristics of the delta connected three phase load may be expressed as: 3 30
Thus for delta connected loads, the magnitude of the line current is 3 times the magnitude of the phase current, and with positive phase sequence, the set of line currents lags the set of phase currents by 30 o PRACTICAL 2.1.A: VOLTAGE RELATIONSHIPS IN A BALANCED STAR SUPPLY STAR LOAD: The star connected supply is applied to a star connected load. Taken measurements are line current, voltage and phase voltage. 1. Ensure that the power supply (unit 8821-25) is switched off. 2. Make the appropriate connections either for virtual or conventional instrumentation shown in figure 2-5. 3. In the virtual instrumentation set the range of ammeters in low mode. Figure 2-5 4. Switch on all the switches in the resistive load (unit 8311-05) to get the resistor value 629Ω per phase. 5. Ensure the dial on the power supply is set to zero position. 6. Switch on the power supply unit and using the output voltage dial set the voltage to 200 V line to line as shown on the virtual or conventional voltmeter V1. 7. Measure and record parameters associated with a load of 629 ohms in each leg (table 2-1). 8. Change the condition of the switches per phase to change the value of the resistor according to the table, and then record the result for every value. Phase resistance (Ώ ) 629 733 880 1100 (ma) (V) (V) (V) (V) Table 2 1
PRACTICAL 2.1.B: CURRENT RELATIONSHIPS IN A BALANCED STAR SUPPLY DELTA LOAD: Figure 2-6 1. Ensure that the power supply (unit 8821-25) is switched off. 2. Make the appropriate connections either for virtual or conventional instrumentation shown in figure 2-5. 3. In the virtual instrumentation set the range of ammeters in low mode. 4. Switch on all the switches in the resistive load (unit 8311-05) to get the resistor value 629Ω per phase. 5. Ensure the dial on the power supply is set to zero position. 6. Switch on the power supply unit and using the output voltage dial set the voltage to 200 V line to line as shown on the virtual or conventional voltmeter V1. 7. Measure and record parameters associated with a load of 629 ohms in each leg (table 2-2). 8. Change the condition of the switches per phase to change the value of the resistor according to the table, and then record the result for every value. Phase resistance (Ώ ) 629 733 880 1100 Table 2 1 (ma) (V) ( ma ) ( ma ) ( ma ) Practical aspects: 1. In a balanced three phase system, a star connected device (transformer, Motor, etc ) carries whole line current and 1/ 3 times the line voltage. That is, the magnitude of the line voltage is 3 times the magnitude of the phase voltage. 2. A star connected supply and load provides a neutral point. 3. In a balanced three phase system, a delta connected device carries 1/ 3 times the line current and the whole line voltage. That is, the magnitude of the line current is 3 times the magnitude of the phase current. 4. A delta connected supply and load has no neutral point
PART2: BALANCED 3- PHASE RESISTIVE LOAD IN STAR AND DELTA ELEMENTS OBJECTIVE: To investigate the power dissipated in three phase circuits. INTRODUCTION: Where a 3-phase supply and load are known to be correctly balanced, it is only necessary to measure line voltage, current and power in one phase and assume that there will be corresponding values for the other phases. However, many practical systems have some imbalance. It is therefore advisable, where possible, to measure the voltage and current in all three phases, and to use either a two or three wattmeter method (as appropriate) to measure power. The two wattmeter method is widely used in three wire systems, since it can directly measure the power in both balanced and unbalanced systems, from which, with the voltage and current readings, the power factor can be calculated. Power factor can also be measured directly by a dedicated power factor meter. PRACTICAL 2.2.A: POWER AND POWER FACTOR FOR STAR CONNECTED LOAD Fig 2-7 The star connected supply is applied to a star connected load. Measurements are taken of voltage, current, power and power factor. 1. Ensure that the power supply (unit 8821-25) switched off. 2. Make the appropriate connections either for virtual or conventional instrumentation shown in figure 2-7. 3. In the virtual instrumentation set the range of ammeters in low mode. 4. Switch on all the switches in the resistive load (unit 8311-05) to get the resistor value 629Ω per phase. 5. Ensure the dial on the power supply is set to zero position. 6. Switch on the power supply unit and using the output voltage dial set the voltage to 200 V line to line as shown on the virtual or conventional voltmeter. 7. Measure and record parameters associated with a load of 548 ohms in each leg (Table 2-3).
8. Switch off supplies. Supply Star Load Star pf WA WB Table 2-3 9. Add together the two wattmeter readings WA and WB. If either of the readings is negative, its magnitude should be subtracted. 10. Compare the resulting value of power with that previously calculated. They should agree quite closely. PRACTICAL 2.2.B: POWER AND POWER FACTOR FOR DELTA CONNECTED LOAD Fig 2-8 The star connected supply is applied to a star connected load. Measurements are taken of voltage, current, power and power factor. 1. Ensure that the power supply (unit 8821-25) switched off. 2. Make the appropriate connections either for virtual or conventional instrumentation shown in figure 2-8. 3. In the virtual instrumentation set the range of ammeters in low mode. 4. Switch on all the switches in the resistive load (unit 8311-05) to get the resistor value 629Ω per phase. 5. Ensure the dial on the power supply is set to zero position. 6. Switch on the power supply unit and using the output voltage dial set the voltage to 200 V line to line as shown on the virtual or conventional voltmeter. 7. Measure and record parameters associated with a load of 548 ohms in each leg (Table 2-3). 8. Switch off supplies. Supply Star Load Star pf WA WB Table 2-3 9. Add together the two wattmeter readings WA and WB. If either of the readings is negative, its magnitude should be subtracted. 10. Compare the resulting value of power with that previously calculated. They should agree quite closely.
Practical Aspects: 1- For the star connected load in balance three-phase system, the line current is equal to the phase current but the phase voltage is 1 3 times the line voltage. 2- For the delta connected load in balance three-phase system, the line voltage is equal to the phase voltage but the phase current is 1 3 times the line current. 3- The power in three-phase system is 3 cos 4- In three lines system the power can be measured by two-wattmeter as in the Figures 2-7, 2-8. 5- The current consume in delta connection is larger than in star connection. This fact is used to reduce the starting current of the induction motor. After the motor is up to speed, the connection is changed into delta connection in order to enable the motor to develop the full power. PART3: THREE PHASE SEQUENCE DETERMINATION OBJECTIVES How to determine the sequence of a tree-phase system. INTRODUCTION: There are two sequences in three-phase systems, positive sequence like Figure 2-9a and negative sequence like Figure 2-9b. a- Positive Sequence b- Negative Sequence Figure 2-9 It's important to know the sequence before connecting any machine. For example, when we connect a motor, if the sequence is incorrect, the motor drive in reverse direction. Figure 2-10
PRACTICAL 2.3.A: THREE PHASE SEQUENCE DETERMINATION 1- Ensure that the power supply (unit 8821-25) switched off. 2- Make the appropriate connections either for virtual or conventional instrumentation shown in figure 2-7. 3- Use the virtual instrumentation in the computer to determine the sequence (Oscilloscope and Phasor analyzer) 4- In Oscilloscope, determine the voltage of every channel 5- In Phasor Analyzer, switch on the reading for the three voltages 6- The sequence can be easily determined 7- Draw the results in your report.