Table of Contents

List of Figures

Figure 1: RL circuit

Figure 2: RC circuit

Figure 3: RLC resonance series circuit

Figure 4: RLC resonance parallel circuit

Exercise 1: Single-Phase RL and RC Circuit in Steady-State

Objective

This exercise aims to highlight the relationships between voltage and current in the case of a passive load consisting of inductive and capacitive elements under single-phase alternating voltage in steady-state conditions.

Part 1: Single-Phase RL Circuit in Steady-State

In the first part, the circuit to observe consists of a series combination of a resistor and an inductance.

Open

Figure 1: RL circuit

Preparatory Activities

To create the requested circuit and better understand the fundamentals, theoretical exercises are requested. The values of the circuit elements are as follows:

• Voltage source:

• Source frequency:

• 

• 

1. Calculate the instantaneous value of the current and display the obtained function on the virtual laboratory’s oscilloscope.

2. Same as question 1 but with a source frequency of . Visualize the current obtained on the virtual laboratory’s oscilloscope.

3. Calculate the value of the resistance so that the phase difference φ between the voltage and the current is 45° for a source frequency of . Also, visualize the current obtained on the virtual laboratory’s oscilloscope.

Setup Initialization

When the virtual laboratory is launched, the initial parameters in the “Network and Transformer” tab under “Fundamental” and “Harmonic” are set as follows:

a) Set the frequency to 50 Hz.

b) Choose the network as a single-phase network with a phase A voltage of 230 V (since it’s a single-phase network, the phases are set as unbalanced) and no phase shift.

c) Set the transformer in short-circuit mode because it’s not being used.

d) The circuit breaker is not being 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 configuration “A1 + B1//C1.”

Question 1

In the first question, you are asked to calculate the instantaneous value of the currentand visualize the obtained function on the virtual laboratory’s oscilloscope.

1- The Setup

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

a) Set impedance Z_1_Series to non-balanced mode (as it’s a single-phase circuit) and choose component A as an RL impedance with values R=20 Ohms and L=100 mH. Components B and C are short-circuited.

b) The other three impedances are balanced circuits with component A short-circuited; they are not used.

2- Take Measurements

Once the setup is completed, the remaining steps are as follows:

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, observe phase A.

c) Observe the signals using the measurements in the “Oscilloscope” tab.

Question 2

For question 2, it’s the same process, but with a source frequency of . Visualize the current obtained on the virtual laboratory’s oscilloscope.

In this exercise, the setup from the previous exercise remains the same, but the frequency of phase A is changed to 100Hz. Take the same measurements as in question 1 and compare them.

Question 3

For question 3, you are asked to calculate the value of the resistance so that the phase difference φ between the voltage and the current is 45° for a source frequency of . Then, visualize the current obtained on the virtual laboratory’s oscilloscope.

1- The Setup

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

a) Set impedance Z_1_Series to non-balanced mode and choose component A as an RL impedance with the value L=100mH and the value of R as calculated. Components B and C are short-circuited.

b) The other three impedances are balanced circuits with component A short-circuited.

2- Take Measurements

Once the setup is complete, it remains to take the measurements:

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

b) Open the “Measurements and Calculations” tab and choose “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, phase A is observed.

c) Observe the signals using the measurements in the “Oscilloscope” tab, and verify the requested phase difference in the exercise.

Part 2: Single-Phase RC Circuit in Steady-State

In the second part, the circuit to observe consists of a circuit composed of a resistance R2 in parallel with a capacitor C. This element is in series with a resistance R1.

Open

Figure 2: RC circuit

Preparatory Activities

To create the required circuit and better understand the fundamentals, theoretical exercises are requested. The values of the circuit elements are as follows:

• Voltage source:

• Source frequency:

1. Calculate the current at time = 8 ms and the current I. Visualize the current on the oscilloscope of the virtual laboratory. The circuit is in a steady-state.

Setup Initialization

When the virtual laboratory 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 50 Hz.

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

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

d) The circuit breaker is not used; the “Without protection” button is enabled.

e) Under the “Harmonic” tab, no harmonics are added. The “A” button is disabled.

f) In the “Passive load” tab, choose the configuration “A1 + B1//C1”.

Question 1

In this exercise, you are asked to calculate the current at the time = 8 ms and the current I. Then, you need to visualize the current on the oscilloscope of the virtual laboratory.

1- The Setup

The requested setup can be created in the “Passive load” tab as follows:

a) Set the impedance Z_1_Series to non-equilibrium mode and choose component A as a pure ohmic resistance with R = 5 Ohms. Components B and C are short-circuited.

b) Set the impedance Z_1_Parallels to non-equilibrium mode and choose component A as an RC impedance with the values R = 10 Ohms and C = 318.6 μF.

c) The other two impedances are balanced circuits with component A short-circuited

2- Take Measurements

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

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, observe phase A.

c) Observe the signals using the measurements and in the “Oscilloscope” tab.

Laboratory Report

The tasks to be performed for each part are as follows:

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: Single-Phase RLC Circuit in Steady-State, Power Factor Correction

Objective

This second exercise aims to explore and acquire the necessary knowledge for a better understanding of power factor correction in a single-phase RLC alternating current circuit.

Preparatory Activities

In order to set up the required circuit and gain a better understanding, theoretical exercises are required. The values of the circuit elements are as follows:

For the initial questions 1 and 2, the capacitance (C) is neglected.

1. Calculate the power factor cos⁡(φ), the phase angle (φ) between current and voltage, the apparent power (S), and the reactive power (Q) of the circuit.

2. What are the values of the components R and L?

3. Calculate the value of the compensating capacitance needed to achieve a power factor of 0.95 and inductive, while keeping the active power constant. Also, calculate the current after compensation.

4. Create a qualitative representation of the power triangle and visualize the various currents and phase angles on the oscilloscope before and after compensation.

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 single-phase network with the phase A voltage of 230 V and no phase shift.

c) Set the transformer to 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 “A1 + B1//C1” configuration.

A) Before Compensation

In the first question, you are asked to calculate the power factor cos(φ), the phase angle φ between current and voltage, the apparent power S, and the reactive power Q of the circuit. Then, based on these calculations, you need to determine the values of the components R and L. Compensation will be applied in a subsequent step.

1- The Setup

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

a) Set impedance Z_1_Series to unbalanced mode and choose component A as a short circuit, component B as an open circuit (as it is used later), and component C as an RL impedance with the previously calculated values.

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

2- Take Measurements

Once the setup is complete, it’s time to take measurements:

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, observe phase A.

c) Examine the signals using the measurements and the “Oscilloscope” tab, and compare the measured phase angle with the theoretical value.

B) After Compensation

In a second step, it is requested to apply the compensation with the calculated capacitance value. The capacitor is inserted in parallel with the existing circuit.

1- The Setup

The requested setup can be done under the “Passive load” tab:

a) Set the impedance Z_1_Series to non-balanced mode and choose component A as a short circuit, component B as a capacitor, and component C as an impedance RL. Use the previously calculated values.

b) The other three impedances are balanced circuits with component A short-circuited.

2- Take Measurements

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

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, phase A is observed.

c) Observe the signals using the measurements and in the “Oscilloscope” tab, and compare the measured phase shift after compensation with the theoretical value.

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 in both situations: without and with compensation.

Exercise 3: Single-Phase Series RLC Resonant Circuit in Steady-State

Objective

In this exercise, it’s a single-phase RLC circuit with the aim of achieving resonance behavior.

Preparatory Activities

To create a resonant circuit, some preliminary calculations need to be performed. Consider the circuit above with the following data:

1. Calculate the value of inductance L and determine the source frequency for the voltage across the capacitor to be maximum.

2. What should be the source voltage for the voltage across the capacitor to be = 200 V?

3. In this case, what is the current I, and what is the maximum energy stored in the inductance and the capacitance, denoted as and ? Also, visualize the current function .

4. Considering the maximum available inductance is 2 mH, what is the frequency value for the voltage across the capacitor to remain maximum? In this case, what are the values of current I and voltage ?

Setup Initialization

When the virtual laboratory is launched, the initial settings in the “Network and Transformer” tab under “Fundamental” and “Harmonic” are set as follows:

a) Set the frequency to 50 Hz.

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

c) Set the transformer to 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 ’A1 + B1//C1’ setup.

Questions 1, 2, and 3

In this section, you are first asked to calculate the value of the inductance L and determine the frequency of the source for the voltage across the capacitor to be maximum. The value of the inductance is defined to achieve a resonant behavior. With these calculated values, you need to find the source voltage for the voltage across the capacitor to be =200 V. In the final question, the energies stored in the inductance and in the capacitor are discussed.

1- The Setup

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

a) Set the impedance Z_1_Series to non-balanced mode and choose component A as an impedance RLC with the values R=1Ohm, C=4mF, and L as calculated before. The components B and C are short circuits.

b) The three other impedances are balanced circuits with component A short-circuited.

2- Take Measurements

Once the setup is complete, it remains to take measurements:

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, phase A is observed.

c) Observe the signals using the measurements and in the “Oscilloscope” tab. Compare the phase shift with the calculated value.

Question 4

In the last part, you are asked to repeat the first question but with a constraint on the inductance, which should be a maximum of 2mH. You need to determine the frequency for which the voltage across the capacitor remains maximum, as well as the voltage to be applied.

1- The Setup

The requested setup can be done under the “Passive load” tab as follows:

a) In the “Network and Transformer” tab, set the frequency and phase A voltage to the previously calculated values.

b) Set the impedance Z_1_Series to the unbalanced mode and choose component A as an RLC impedance with the values R=1Ohm, L=2mH, and C=4mF. Components B and C are short circuits.

c) The other three impedances should be balanced circuits with component A as a short circuit.

2- Take Measurements

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

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

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. Make sure to observe phase A for both measurements.

c) Observe the signals using the measurements and in the “Oscilloscope” tab. Verify the phase shift.

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.

d) What is the advantage of having a variable-frequency voltage source?

Exercise 4: Single-Phase Parallel RLC Resonant Circuit in Steady-State

Objective

To better understand the resonance phenomenon in a single-phase RLC parallel circuit under an alternating monophasic voltage, we will perform this final exercise, which will help us grasp the theoretical foundations and gain a solid understanding of the topic.

Preparatory Activities

To achieve a resonant circuit, we need to perform some preliminary calculations. Let’s consider the given circuit with the following parameters:

1. Calculate the value of inductance (L) in such a way that the apparent power consumed by the circuit is minimized.

2. In the case of question 1, where the apparent power is minimized, calculate the power consumed by the resistance (R), the inductance (L), and the capacitance (C). Also, calculate and visualize the current drawn from the voltage source .

Setup Initialization

When the virtual laboratory 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 50 Hz.

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

c) Set the transformer to 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, select the configuration “A1 + B1//C1.”

Questions 1 and 2

In these questions, you are asked to first calculate the value of inductance L in such a way that the apparent power consumed by the circuit is minimized. Then, you need to calculate the power consumed by each component.

1- The Setup

The requested setup can be done under the “Passive load” tab as follows:

a) Set the impedance Z_1_Series to non-equilibrium mode and choose component A and C as short circuits, and component B as an open circuit. This impedance is not used in this exercise, but to avoid influencing the circuit, these settings need to be adjusted.

b) Set the impedance Z_1_Parallels to non-equilibrium mode and choose component A as an RLC impedance with the values R=10Ohm, L=2.53mH, and C=4mF.

c) The other two impedances are balanced circuits with component A as a short circuit.

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 select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, phase A is observed.

c) Observe the signals using the measurements and under the “Oscilloscope” tab, and verify the phase difference.

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.