Page Contents

List of Figures

Figure 1: Symmetrical Three-Phase RL Load Connected in Star Configuration

Figure 2: Symmetrical Three-Phase RC Load Connected in Delta Configuration

Figure 3: Three-Phase RL load in star and delta configurations

Figure 4: Asymmetrical three-phase circuit considered

Exercise 1: Three-Phase Passive Circuit in Steady-State Arranges in Star Configuration

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 . The equivalent circuit is shown below:

Open

Figure 1: Symmetrical Three-Phase RL Load Connected in Star Configuration

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:

1. 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.

2. 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.

3. Calculate the power factor of the circuit and validate it by visualizing the functions and/or measurements on the oscilloscope in the virtual laboratory.

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:

a) Set the frequency to 50 Hz.

b) Choose the network as a three-phase network with a phase voltage of 230 V and no phase shift.

c) Activate the "Phase Inversion" button to obtain results equivalent to calculations (according to the convention).

d) Set the transformer to short-circuit mode as it is not used.

e) The circuit breaker is not used; the "Without protection" button is activated.

f) Under the "Harmonic" tab, no harmonics are added. The "A" button is disabled.

g) Under the "Passive load" tab, choose the configuration "Star".

Question 1

In the first exercise, you are asked to calculate the current flowing in each of the three phases.

1- 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.

2- 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.

Question 2

In this question, you are asked to calculate the current flowing in the three lines.

1- 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.

2- 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.

Question 3

In this question, you are asked to calculate the power factor of the circuit.

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.

Laboratory Report

a) Perform the preparatory activities.

b) Present and comment on the oscillogram for each question.

c) Compare the theoretical values with the measured values.

Exercise 2: Three-Phase Passive Circuit in Stead-State Arranges in Delta Configuration

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 and a frequency of 50 Hz. The diagram considered is illustrated below.

Open

Figure 2: Symmetrical Three-Phase RC Load Connected in Delta Configuration

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:

1. Calculate the current flowing in the three phases. Visualize and compare the currents using the oscilloscope in the virtual lab.

2. 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?

3. 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.

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:

a) Set the frequency to 50Hz.

b) Choose the network as a three-phase network with a phase voltage of 230V and no phase shift.

c) Activate the "Phase Inversion" button to obtain results consistent with calculations (following convention).

d) Set the transformer to short-circuit mode as it is not used.

e) The circuit breaker is not used; the "Without protection" button is activated.

f) Under the "Harmonic" tab, no harmonics are added. The "A" button is deactivated.

g) Under the "Passive load" tab, choose the configuration "Delta."

Question 1

In this exercise, you are asked to calculate the current flowing through the three phases.

1- The Setup

The requested setup can be performed under the 'Passive load' tab:

a) Set the Z_1_Series impedance to balanced mode and choose component A as an RC impedance with the values and .

b) The other three impedances are balanced circuits with component A in short-circuit

2- Take Measurements

Once the setup is done, it's time to take measurements:

a) In the "Network and Transformer" tab, activate the "Power On" (Power on) button.

b) Open the "Measurements and Calculations" tab, measure "Z_1 I" for each phase, and observe the magnitudes and arguments of the currents. Find the transformation to obtain the calculated values.

c) Observe the signals using the measurements and the "Oscilloscope" tab.

Question 2

For question 2, the line currents are requested, and the setup remains the same.

Take Measurements

a) In the "Network and Transformer" tab, activate the "Power On" (Power On) button.

b) Open the "Measurements and Calculations" tab and measure "Rés Z_1 I" for each phase. Observe the magnitudes and arguments of the currents. Find the transformation to obtain the calculated values.

c) Observe the signals using the measurements and the "Oscilloscope" tab.

Question 3

For question 2, the power factor and powers need to be observed. The setup remains the same.

Take Measurements

a) In the "Network and Transformer" tab, activate the "Power On" (Power On) button.

b) Open the "Measurements and Calculations" tab and measure P and S for the network. Deduce the reactive power Q.

c) Open the "Measurements and Calculations" tab and measure "Rés I" for phase A and observe the phase shift.

d) Observe the signals using the measurements and the "Oscilloscope" tab.

Laboratory Report

a) Perform the preparatory activities.

b) Present and comment on the oscillogram for each question.

c) Compare the theoretical values with the measured values.

Exercise 3: Three-Phase Passive Balanced Circuit In Steady-State, Star-Delta Configuration

Objective

In this exercise, we will consider a symmetrical three-phase source connected in a star configuration with a phase voltage of and a frequency of . This source will supply power to two symmetrical three-phase setups. Setup 1 consists of three resistors and three inductors connected in a star configuration. Setup 2 consists of three resistors connected in a delta (Delta) configuration. The diagram is illustrated below:

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:

• Source frequency

1. Calculate the line current and visualize and compare the currents using the oscilloscope in the "Virtual Laboratory."

2. Repeat the calculations with a frequency of f = 100 Hz.

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:

a) Set the frequency to 50Hz.

b) Choose the network as a three-phase network with a phase voltage of 230V and no phase shift.

c) Set the transformer to the short-circuit mode as it is not used.

d) The circuit breaker is not used; the "Without protection" button is activated.

e) Under the "Harmonic" tab, no harmonics are added. The "A" button is deactivated.

f) Under the "Passive load" tab, choose the "Delta" configuration.

Question 1

In this exercise, you are asked to measure the line current of the circuit.

1- The Setup

The requested setup can be performed under the "Passive load" tab as follows:

a) Set the impedance Z_1_Series to balanced mode and choose component A as an impedance R with the value .

b) Set the impedance Z_2_Series to balanced mode and choose component A as an impedance RL with the values and .

c) The other two impedances should be set to balanced circuits with component A in short-circuit mode.

2- Take Measurements

Once the setup is complete, you need to take the measurements as follows:

a) In the "Network and Transformer" tab, activate the "Power On" button.

b) 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.

c) Observe the result when the "Phase Inversion" button is activated and explain what you observe.

d) Use the measurements to observe the signals under the "Oscilloscope" tab.

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.

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.

Laboratory Report

a) Perform the preparatory activities.

b) Present and comment on the oscillogram for each question.

c) Compare the theoretical values with the measured values.

Exercise 4: Three-Phase Balanced Passive Circuit in Steady-State with Unbalanced Load, Symmetrical Components, and Neutral Influence

Objective

In this exercise, we will consider a symmetrical three-phase source, connected in a star configuration with a phase voltage of and a frequency of , which supplies two symmetrical three-phase circuits. Circuit 1 consists of three resistors and three inductors connected in a star configuration. Circuit 2 consists of three resistors connected in a Delta configuration. The diagram is illustrated below:

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:

• The frequency of the source:

1. 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.

2. Calculate the current in the neutral and compare it with the homopolar current . Visualize the current in the neutral.

3. 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.

4. Calculate the apparent, active, and reactive powers using the symmetrical components. Also, compare them with the powers measured in the virtual laboratory.

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:

a) Set the frequency to 50Hz.

b) Choose the network as a three-phase network with a phase voltage of 230V and no phase shift.

c) Activate the "Phase Inversion" button to obtain results equivalent to the calculations.

d) Set the transformer to short-circuit mode as it is not used.

e) The circuit breaker remains in the initial mode; set to 16A, class 10, and mode Z.

f) Under the "Harmonic" tab, no harmonics are added. Activate the "Équilibrées" button and set phase A to 0V.

g) Under the "Passive load" tab, choose the "Star" configuration.

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.

1- The Setup

The requested setup can be achieved under the "Passive load" tab:

a) Activate impedance Z_1_Series and choose an RL impedance for each component with the previously calculated values.

b) The other three impedances are balanced circuits with component A in short-circuit mode.

2- Take Measurements

Once the setup is complete, you need to take measurements:

a) In the "Network and Transformer" tab, activate the "Power On" button.

b) Open the "Measurements and Calculations" tab and measure the currents "Rés Z_1 I" for each phase and observe the magnitudes and phase angles of the currents.

c) Observe the signals using the measurements and the "Oscilloscope" tab.

d) Next, measure the symmetrical components using the Fortescue transformation of the network.

e) Compare the results with your calculations.

Question 2

For question 2, you will observe the neutral current and the homopolar current. The setup remains the same.

Take Measurements

a) In the "Network and Transformer" tab, activate the "Power On" button.

b) Open the "Measurements and Calculations" tab and measure the current "Z_N_I" of phase A and the homopolar current. Compare the values.

c) Observe the signals using the measurements and the "Oscilloscope" tab. The signals to observe are "Rés Z_1 U" and "Z_N_I."

Question 3

In this exercise, you are asked to make modifications to the circuit and make it symmetric by setting .

1- The Setup

The requested setup can be achieved under the "Passive load" tab:

a) Set impedance Z_1_Series in balanced mode and choose component A as an R impedance with a value of .

b) The other three impedances are balanced circuits with component A in short-circuit mode.

2- Take Measurements

Once the setup is complete, you need to take the appropriate measurements:

a) In the "Network and Transformer" tab, activate the "Power On" button.

b) Open the "Measurements and Calculations" tab and measure "Z_N_I" and "Rés Z_1 I" for phase A.

c) Observe the signals using the measurements and the "Oscilloscope" tab.

d) Next, measure the symmetrical components using the Fortescue transformation of the network.

Question 4

In this exercise, you are asked to measure the powers in the circuit. The setup is the same as in question 1.

Take Measurements

a) In the "Network and Transformer" tab, activate the "Power On" button.

b) Open the "Measurements and Calculations" tab and measure the current "Rés Z_1 I" for each phase.

c) Next, measure the symmetrical components using the Fortescue transformation of the network.

Laboratory Report

a) Perform the preparatory activities.

b) Present and comment on the oscillogram for each question.

c) Compare the theoretical values with the measured values.