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Page Contents
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List of Figures
Figure 1:Symmetrical Three-Phase RL Load Connected in Star Configuration
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Figure 4:Asymmetrical three-phase circuit considered
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Exercise 1: Three-Phase Passive Circuit in Steady-State Arranges in Star Configuration
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THREE-PHASE PASSIVE CIRCUIT IN STEADY STATE ARRANGED IN STAR CONFIGURATION
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Objective
We have a balanced three-phase load connected in a star (Y) configuration, consisting of an inductance L = 12 mH and a resistance R = 10 Ω. This load, which could be a motor, is supplied by a direct symmetrical three-phase network with a line voltage U = 400 V and a frequency f = 50 Hz. The reference for the voltage will be placed on the phase voltage
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Preparatory Activities
In order to set up the requested circuit and gain a better understanding of the basics, theoretical exercises are required. The values of the circuit elements are as follows:
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Calculate the current flowing in each of the three phases, provide the phasor representation as well as the instantaneous value of the three currents. Visualize the currents using the oscilloscope in the virtual laboratory and compare them with the calculated currents.
Calculate the current flowing in the three lines, provide the phasor representation and instantaneous value. Visualize the line currents on the oscilloscope. Compare them with the results from question 1.
Calculate the power factor of the circuit and validate it by visualizing the functions and/or measurements on the oscilloscope in the virtual laboratory.
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Setup initialization
When the virtual laboratory is launched, the initial settings in the "Network and Transformer" tab under "Fundamental" and "Harmonic" are configured as follows:
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g) Under the "Passive load" tab, choose the configuration "Star".
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Question 1
In the first exercise, you are asked to calculate the current flowing in each of the three phases.
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The Setup
The requested setup can be created in the "Passive load" tab as follows:
Set the impedance Z_1_Series to balanced mode and choose component A as an RL impedance with values R = 10 Ω and L = 12 mH.
The other three impedances are balanced circuits with component A short-circuited.
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Take Measurements
Once the setup is complete, you need to take measurements:
In the "Network and Transformer" tab, activate the "Power On" button.
Open the "Measurements and Calculations” tab and measure "Rés Z_1 U" and "Rés Z_1 I" for each phase. Observe the magnitudes and phase angles of voltages and currents, as well as the phase shift. Compare with the theoretical values.
Observe the signals using measurements and the "Oscilloscope" tab.
Observe the behavior in case "Phase Inversion" is not activated.
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Question 2
In this question, you are asked to calculate the current flowing in the three lines.
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The Setup
The requested setup can be created in the "Passive load" tab as follows:
Set the impedance Z_1_Series to balanced mode and choose component A as an RL impedance with values R = 10 Ω and L = 12 mH.
The other three impedances are balanced circuits with component A short-circuited.
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Take Measurements
Once the setup is complete, you need to take measurements:
In the "Network and Transformer" tab, activate the "Power On" button.
Open the "Measurements and Calculations" tab and measure "Rés Z_1 U" and "Rés Z_1 I" for each phase. Observe the magnitudes and phase angles of voltages and currents, as well as the phase shift. Compare with the theoretical values.
Observe the signals using measurements and the "Oscilloscope" tab.
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Question 3
In this question, you are asked to calculate the power factor of the circuit.
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Take Measurements
The setup remains the same, and you need to take measurements:
In the "Network and Transformer" tab, activate the "Power On" button.
Open the "Measurements and Calculations" tab and observe the active and apparent power, and deduce the power factor.
Compare the phase angle obtained from the power factor with the calculated angle.
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Laboratory Report
a) Perform the preparatory activities.
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c) Compare the theoretical values with the measured values.
Exercise 2: Three-Phase Passive Circuit in Stead-State Arranges in Delta Configuration
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THREE-PHASE PASSIVE CIRCUIT IN STEADY STATE ARRANGED IN DELTA CONFIGURATION
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Objective
In this exercise, we will consider a balanced three-phase load connected in a delta configuration, consisting of a capacitance and a resistance per phase with values of R=100 Ω and C=40 μF. This load is supplied by a symmetrical three-phase network with a line voltage of
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Preparatory Activities
To create the requested circuit and gain a better understanding of the fundamentals, theoretical exercises are required. The values of the circuit elements are as follows:
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Calculate the current flowing in the three phases. Visualize and compare the currents using the oscilloscope in the virtual lab.
Calculate the current flowing in the three lines. Visualize and compare the currents using the oscilloscope in the virtual lab. What observations can be made?
Determine the power factor analytically and compare it with the virtual lab. Do the same for the active, reactive, and apparent power supplied by the source.
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Setup Initialization
When the virtual lab is launched, the initial settings in the "Network and Transformer" tab under "Fundamental" and "Harmonic" should be adjusted as follows:
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g) Under the "Passive load" tab, choose the configuration "Delta."
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Question 1
In this exercise, you are asked to calculate the current flowing through the three phases.
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The Setup
The requested setup can be performed under the 'Passive load' tab:
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b) The other three impedances are balanced circuits with component A in short-circuit
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Take Measurements
Once the setup is done, it's time to take measurements:
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c) Observe the signals using the measurements and the "Oscilloscope" tab.
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Question 2
For question 2, the line currents are requested, and the setup remains the same.
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Take Measurements
a) In the "Network and Transformer" tab, activate the "Power On" (Power On) button.
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c) Observe the signals using the measurements and the "Oscilloscope" tab.
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Question 3
For question 2, the power factor and powers need to be observed. The setup remains the same.
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Take Measurements
a) In the "Network and Transformer" tab, activate the "Power On" (Power On) button.
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d) Observe the signals using the measurements and the "Oscilloscope" tab.
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Laboratory Report
a) Perform the preparatory activities.
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c) Compare the theoretical values with the measured values.
Exercise 3: Three-Phase Passive Balanced Circuit In Steady-State, Star-Delta Configuration
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THREE-PHASE PASSIVE BALANCED CIRCUIT IN STEADY-STATE, STAR-DELTA CONFIGURATION
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Objective
In this exercise, we will consider a symmetrical three-phase source connected in a star configuration with a phase voltage of
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Preparatory Activities
To set up the requested circuit and gain a better understanding of the basics, theoretical exercises are required. The values of the circuit elements are as follows:
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Calculate the line current and visualize and compare the currents using the oscilloscope in the "Virtual Laboratory."
Repeat the calculations with a frequency of f = 100 Hz.
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Setup Initialization
When the virtual laboratory is launched, the initial settings in the "Network and Transformer" tab under "Fundamental" and "Harmonic" are configured as follows:
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f) Under the "Passive load" tab, choose the "Delta" configuration.
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Question 1
In this exercise, you are asked to measure the line current of the circuit.
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The Setup
The requested setup can be performed under the "Passive load" tab as follows:
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c) The other two impedances should be set to balanced circuits with component A in short-circuit mode.
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Take Measurements
Once the setup is complete, you need to take the measurements as follows:
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d) Use the measurements to observe the signals under the "Oscilloscope" tab.
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Question 2
For question 2, you are asked to repeat the previous exercise with a frequency of f = 100 Hz. The setup remains the same.
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Take Measurements
a) In the "Network and Transformer" tab, under "Fundamental," set the frequency to 50Hz.
b) In the "Network and Transformer" tab, activate the "Power On" button.
c) Open the "Measurements and Calculations" tab and measure the currents "Rés I," "Z_1 I," and "Z_2 I" for phase A. Observe the magnitudes and phases (arguments) of these currents.
d) Use the measurements to observe the signals under the "Oscilloscope" tab.
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Laboratory Report
a) Perform the preparatory activities.
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c) Compare the theoretical values with the measured values.
Exercise 4
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THREE-PHASE BALANCED PASSIVE CIRCUIT IN STEADY-STATE WITH UNBALANCED LOAD, SYMMETRICAL COMPONENTS, AND NEUTRAL INFLUENCE
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: Three-Phase Balanced Passive Circuit in Steady-State with Unbalanced Load, Symmetrical Components, and Neutral Influence
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Objective
In this exercise, we will consider a symmetrical three-phase source, connected in a star configuration with a phase voltage of
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Preparatory Activities
In order to carry out the requested circuit and better understand the fundamentals, theoretical exercises are required. The values of the circuit elements are as follows:
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Calculate the line currents and the homopolar, direct, and inverse currents using the inverse Fortescue matrix. Compare the line currents and the symmetrical components measured in the virtual laboratory with those calculated. Visualize the line currents as well.
Calculate the current in the neutral
and compare it with the homopolar currentMathinline body --uriencoded--\underline%7BI_N%7D
. Visualize the current in the neutral.Mathinline body --uriencoded--\underline%7BI_h%7D What happens to the currents of the symmetrical components, namely homopolar, direct, and inverse, when
? Compare with the result of question 1 as well as with the values obtained from the virtual laboratory.Mathinline body --uriencoded--\underline%7BZ_1%7D = \underline%7BZ_2%7D = \underline%7BZ_3%7D= 100Ω Calculate the apparent, active, and reactive powers using the symmetrical components. Also, compare them with the powers measured in the virtual laboratory.
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Setup Initialization
When the virtual laboratory is launched, the initial settings in the "Network and Transformer" tab under "Fundamental" and "Harmonic" are configured as follows:
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g) Under the "Passive load" tab, choose the "Star" configuration.
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Question 1
In this exercise, you are required to measure line currents and the homopolar, direct, and indirect currents. The Fortescue transformation is used for this purpose.
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The Setup
The requested setup can be achieved under the "Passive load" tab:
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b) The other three impedances are balanced circuits with component A in short-circuit mode.
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Take Measurements
Once the setup is complete, you need to take measurements:
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e) Compare the results with your calculations.
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Question 2
For question 2, you will observe the neutral current and the homopolar current. The setup remains the same.
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Take Measurements
a) In the "Network and Transformer" tab, activate the "Power On" button.
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c) Observe the signals using the measurements and the "Oscilloscope" tab. The signals to observe are "Rés Z_1 U" and "Z_N_I."
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Question 3
In this exercise, you are asked to make modifications to the circuit and make it symmetric by setting
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The Setup
The requested setup can be achieved under the "Passive load" tab:
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b) The other three impedances are balanced circuits with component A in short-circuit mode.
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Take Measurements
Once the setup is complete, you need to take the appropriate measurements:
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d) Next, measure the symmetrical components using the Fortescue transformation of the network.
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Question 4
In this exercise, you are asked to measure the powers in the circuit. The setup is the same as in question 1.
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Take Measurements
a) In the "Network and Transformer" tab, activate the "Power On" button.
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c) Next, measure the symmetrical components using the Fortescue transformation of the network.
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Laboratory Report
a) Perform the preparatory activities.
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