Documentation Home Page ◇ Courseware Home Page
Pour la documentation en FRANÇAIS, utilisez l'outil de traduction de votre navigateur Chrome, Edge ou Safari. Voir un exemple.
Three-Phase Systems
Page Contents
- 1 Exercise 1: Three-Phase Passive Circuit in Steady-State Arranges in Star Configuration
- 2 Exercise 2: Three-Phase Passive Circuit in Stead-State Arranges in Delta Configuration
- 3 Exercise 3: Three-Phase Passive Balanced Circuit In Steady-State, Star-Delta Configuration
- 4 Exercise 4: Three-Phase Balanced Passive Circuit in Steady-State with Unbalanced Load, Symmetrical Components, and Neutral Influence
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:
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:
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.
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.
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: