SYNCHRONOUS GENERATOR, NOT CONNECTED TO THE GRID, FEEDING A PASSIVE LOAD

5.1 Objective

This exercise presents the implementation of the synchronous machine operating as an autonomous generator, not connected to an AC grid and supplying a balanced, three-phase passive load.
When the passive load varies, the output frequency of the synchronous generator is kept constant at its nominal value by adjusting the DC motor speed.
We are performing two load tests for different power factors: (i) a purely resistive load at unity power factor, and (ii) inductive and capacitive load at power factor equal to 0.7.
The first test is performed with a constant field current and shows the evolution of the synchronous generator load's voltage drop on a variable passive load with a constant power factor.
In the second test, we maintained a constant generator output voltage by varying the field current when the load varies.
Thus, we will get the current regulation curves of the synchronous generator's field that keeps a constant output voltage on a variable passive load with a power factor applied.
These regulation curves can be used to sizing the generator field's power source voltage.
The results obtained serve to analyze the generator's exchange of Q with the passive load.
The tests are also used to validate the synchronous machine's steady state model, whose parameters were determined using the low power test from Exercise 1.

5.2 Initialization of the Setup

When the simulator is started up, the initial settings on screen are as follows:

1. Continuous voltage supplies SC1, SC2, SC3 set to 0 V.
2. Continuous voltage supply SC4, in the "Measurement Resistors" tab, set to 0 V.
3. Alternative power SA1, in the tab "AC Grid" tab, set to 0 V.
4. Switches K₁, K₂, K₃, K₄ opened: synchronous generator armature has no load. See Table 4.
5. Switch K₆ disabled: the synchronous machine rotor is driven by the DC motor. See Table 4.
6. Switch K₅ disabled: voltage source SC3 powers the synchronous machine field winding. See Table 4.
7. Trigger switches K₁₀, K₁₁, K₁₂, K₁₃, K₁₄, in the tab "Oscilloscope", disabled. See Table 4.

5.3 Description of the RLC Passive Load

This is a passive series RLC, three-phase, wye-configured, balanced load that can be connected to the synchronous generator's stator (see Fig.10).
The complex impedance Z per phase at 60 Hz is variable and the user can independently adjust the resistive, inductive and capacitive components using R, X_L and X_C settings. (Z=R+j(X_L-X_C)).
By controlling R, X_L and X_C settings, we can also modify the power factor value displayed in the "Load RLC" tab.
Note that the X_L, X_C and the power factor values are only valid when the synchronous generator's frequency output is 60 Hz.
The minimum setting values for R, X_{L (60Hz)} and X_{C (60Hz)} are 10 Ω, 5 Ω and 5 Ω respectively, and the maximum values are equal to 300 Ω. The overall reactance value is: X = X_L-X_C.

5.4 Test of the Synchronous Generator Feeding a Resistive Load

5.4.1 Setup Diagram

Figure 10: Diagram of the synchronous generator driven by the DC motor and supplying the passive RLC load

In this exercise, the synchronous machine is operating in generator mode and is driven by the DC motor.
Use sources SC1 and SC2, as described in Section 4.3, to control the generator drive speed and the armature output voltage frequency.
The synchronous generator is feeding a passive RLC load. Switch K₃ is closed.
This is a load test: the synchronous generator converts the mechanical power supplied to its shaft by the DC motor, into electrical power that is dissipated by the load and the losses.

5.4.2 Exercise

1. Reset the setup to its original state, as described in Section 5.2 by bringing voltage sources SC3, SC1 and SC2 back to 0 and resetting switches to their default conditions.
   Thus, the synchronous machine's rotor is driven by the DC machine, switch K₅ is disabled and the voltage source SC3 supplies the synchronous machine's field winding.
   Select the "RLC load" tab in the panel.
2. Follow the procedure described in Section 4.3 of Exercise 1 to start the DC motor and set the drive speed to 1800 rpm so that the generator's output voltage frequency is 60 Hz.
3. Adjust the synchronous machine current field J_f with the voltage source SC3 so that the RMS line-line value of the armature is U_s= 460 V at 1800 rpm with no load.
4. Close switch K₃ to connect the RLC load to the synchronous machine armature's winding.
   During this resistive load exercise, the inductive reactance value X_L and the capacitive reactance X_c must be adjusted to 5Ω (X_L-X_C =0) for the duration of the test.
   Thus Z=R+j(X_L-X_C)=R, the load is resistive, and its power factor is unitary.
   In this case, we can adjust I_s from 0 to I_sn varying the resistance R from 300 Ω to 10 Ω.
5. Without changing current J_f adjusted in step c and by maintaining constant speed and frequency using SC2, gradually vary the resistance so that I_s varies from 0 to I_sn.
   For each steady state operating point, take note of the values of the line-line RMS voltage U_s and the RMS current I_s.
   It is important to maintain a constant frequency or the test results will be unusable.
   Calculate the RMS line-neutral voltage V_s for each operating point and determine the characteristic V_s vs I_s at constant frequency and field current on a resistive load.
6. Disconnect the RLC load using switch K₃.
   Reset the setup to its original state described in Section 5.2.
7. Repeat steps 1 to 4 then, starting with step 5, adjust the value of J_f using SC3 at each new R and I_s value to compensate the voltage drop and maintain a constant generator RMS voltage output value equal to Us = 460 V.
   Make sure to maintain constant speed (1800 rpm) and frequency (60 Hz) using SC2, otherwise the test results will be unusable.
   Thus, we obtain the synchronous generator's field current regulation curve J_f vs I_s which maintains a constant voltage on a variable resistive load.
   Take note of the regulation curve J_f vs I_s until the nominal value for I_sn.
8. Disconnect the RLC load using switch K₃.
   Reset the setup to its original state described in Section 5.2.

5.5 Test of the Synchronous Generator Feeding an Inductive Load

The wye-connected passive load, as in the previous exercise, is now a variable inductive load that absorbs active and reactive power (the load is studied as receptor convention, so the current phasor I_s lags the line neutral voltage V_s).
When this load varies, we must maintain the frequency at 60 Hz and the power factor constant at 0.707.
In this case, we use this procedure:

• Set the capacitive reactance X_c to its minimum value of 5 Ω and maintain this value throughout the test.
• Vary resistance R and inductive reactance X_L to adjust the module of the complex impedance Z and modify the current I_s from 0 to I_sn while keeping the constant power factor at 0.707.
  To maintain the power factor value, note that Z=R+j(X_L-X_C)= R+jX.
  Thus, it is sufficient to vary R and X_L so that R = X = X_L-X_C (example: R= 295 Ω, X_L = 300 Ω and X_C = 5 Ω, which gives R = X_L-X_C = 300 – 5 = 295 Ω)

5.5.1 Exercise

1. Return to the initial state, as described in Section 5.2 by bringing voltage sources SC3, SC1 and SC2 back to 0 and resetting switches to their default conditions. Thus, the synchronous machine's rotor is driven by the DC motor, switch K₅ is closed and the voltage source SC3 supplies the synchronous machine's field winding. Switch K3 is open. Select the "RLC load" tab in the panel.
2. Follow the procedure described in Section 4.3 of Exercise 1 to start the DC motor and set the drive speed to 1800 rpm so that the generator's output voltage frequency is 60 Hz.
3. Adjust the synchronous machine current field J_f with the voltage source SC3 so that the RMS line-line value of the armature is U_s= 460 V at 1800 rpm with no load.
4. Close switch K₃ to connect the RLC load to the synchronous machine armature's winding. During this test on an inductive load, it is necessary to adjust resistance R and reactive inductance X_L to modify the complex impedance module Z and vary the current I_s from 0 to I_sn, while keeping a constant power factor of 0.707 at 60 Hz. Use the passive load adjusting method described in Section 5.5 to achieve this.
5. Without changing current J_f adjusted in the step c, and maintaining constant speed and frequency using SC2, gradually vary the resistance R and inductive reactance X_L so that I_s varies from 0 to a value as close as possible to the nominal I_sn, while keeping a constant power factor of 0.707 at 60 Hz. For each steady state operating point, take note of the RMS value of the line-line voltage U_s and the RMS value of the current I_s. It is important to maintain a constant frequency, otherwise the test results will be unusable. For every point calculate the RMS line-neutral voltage V_s value and determine the characteristics V_s I_s at constant frequency and field current on an inductive load with a power factor of 0.707.
6. Disconnect the RLC load using switch K₃. Reset the setup to its original state described in Section 5.2.
7. Repeat steps a to d, then, starting with step e, adjust the value of J_f using SC3 at each new R, X_L and I_s value to compensate the voltage drop and maintain a constant generator RMS voltage output value equal to U_s = 460 V. Make sure to maintain constant speed (1800 rpm) and frequency (60 Hz) using SC2, otherwise the test results will be unusable. Thus, we obtain the synchronous generator's field current regulation curve J_f vs I_s which maintains a constant voltage on a variable inductive load. Take note of the regulation curve J_f vs I_s until the closest value to the nominal I_sn is reached.
8. Reset the setup to its original state described in Section 5.2 by bringing voltage sources back to 0 and disabling all switches.

5.6 Test of the synchronous generator feeding a capacitive load

The wye-connected passive load, as in the previous exercise, is now a variable capacitive load that absorbs active power and produces reactive power (the load is studied as receptor convention, so the current phasor I_s leads the line neutral voltage V_s). When this load varies, we must maintain the frequency at 60 Hz and the power factor constant at 0.707. In this case, we use this procedure:

• Set the capacitive reactance X_L to its minimum value of 5 Ω and maintain this value throughout the test.
• Vary the resistance R and capacitive reactance X_C to adjust the module of the complex impedance Z and to modify the current I_s from 0 to I_sn while keeps constant power factor at 0.707. To maintain the power factor value, note that Z=R+j(X_L-X_C)= R+jX. Thus, it is enough to vary R and X_C so that R = -X = X_C-X_L (example: R= 295 Ω, X_C = 300 Ω and X_L = 5 Ω, which gives R = X_C-X_L = 300 – 5 = 295 Ω)

5.6.1 Exercise

1. Return to the initial state, as described in Section 5.2, by bringing voltage sources SC3, SC1 and SC2 back to 0 and resetting switches to their default conditions.
   Thus, the synchronous machine's rotor is driven by the DC motor, switch K₅ is closed and the voltage source SC3 supplies the synchronous machine's field winding.
   Switch K3 is open.
   Select the "RLC load" tab in the panel.
2. Follow the procedure described in Section 4.3 of Exercise 1 to start the DC motor and set the drive speed to 1800 rpm so that the generator's output voltage frequency is 60 Hz.
3. Adjust the synchronous machine current field J_f with the voltage source SC3 so that the RMS line-line value of the armature is U_s= 460 V at 1800 rpm with no load.
4. Close switch K₃ to connect the RLC load to the synchronous machine armature's winding.
   During this test on a capacitive load, it is necessary to adjust resistance R and reactive inductance X_C to modify the complex impedance module Z and vary the current I_s from 0 to a value as close as possible to the nominal I_sn, while keeping a constant power factor of 0.707 at 60 Hz.
   Use the passive load adjusting method described in Section 5.6 to achieve this.
5. Without changing current J_f adjusted in the step 3 and maintaining constant speed and frequency using SC2, gradually vary the resistance R and capacitive reactance X_C so that I_s varies from 0 to a value as close as possible to the nominal I_sn, while keeping a constant power factor of 0.707 at 60 Hz.
   For each steady state operating point, take note of the RMS value of the line-line voltage U_s and the RMS value of the current I_s.
   It is important to maintain a constant frequency, otherwise the test results will be unusable.
   For every point calculate the RMS line-neutral voltage V_s value and determine the characteristics V_s vs I_s at constant frequency and field current on an inductive load with a power factor of 0.707.
6. Disconnect the RLC load using switch K₃.
   Reset the setup to its original state described in Section 5.2.
7. Repeat steps 1 to 4 then, starting with step 5, adjust the value of J_f using SC3 at each new R, X_C and I_s value to compensate the voltage drop and maintain a constant generator RMS voltage output value equal to Us = 460 V.
   Make sure to maintain constant speed (1800 rpm) and frequency (60 Hz) using SC2, otherwise the test results will be unusable.
   Thus, we obtain the synchronous generator's field current regulation curve J_f vs I_s which maintains a constant voltage on a variable capacitive load.
   Take note of the regulation curve J_f vs I_s until the closest value to the nominal I_sn is reached.
8. Reset the setup to its original state described in Section 5.2 by bringing voltage sources back to 0 and disabling all switches.

5.7 Lab Report

1. Present the results in tables (SI units) for all three curves V_s vs I_s at constant frequency and field current on: (i) a resistive load with unitary power factor (ii) an inductive load with lagging power factor of 0.707 and (iii) a capacitive load with leading power factor of 0.707.
2. Plot all characteristics V_s vs I_s on the same graph (SI units).
   What can we see with respect to the voltage drop for the current I_s = 0.5 I_sn?
   What can we deduce, in general, about synchronous machine voltage output variations when the load absorbs or produces reactive power while the current field J_f is constant?
3. Show that if we extrapolate the 3 characteristics V_s vs I_s, they converge on point I_s=0 for the same voltage value U_s.
   What does this voltage represent?
4. Present the results in tables (SI units) for the 3 synchronous machine's current field regulation curves J_f vs I_s measured at constant frequency and voltage on: (i) a variable resistive load with unity power factor (ii) a variable inductive load with lagging power factor of .707 and (iii) a variable capacitive load with leading power factor of .707.
5. Plot all characteristics J_f vs I_s on the same graph (SI units).
   For the same current value I_s, what do we notice in terms of field current J_f values that are required to maintain a constant V_s for the following three operation points: (i) the load does not have any exchange of reactive power with the synchronous generator (ii) the load consumes reactive power from the synchronous generator, and (iii) the load supplies reactive power to the synchronous generator?
   Does this behavior correspond to the curves plotted at step 2?
6. Using the synchronous machine's steady state model, whose parameters E(Jf), X_d, X_q and R_s were determined using the low power tests of Exercise 1, is it possible to predict and calculate characteristics V_s vs I_s and J_f vs I_s in this exercise?
   Using the theoretical machine model, its parameters and circuit methods learned in the class (Kirchhoff and Ohm's laws, phasor diagram, etc.) determine the expressions of the characteristics V_s vs I_s and J_f vs I_s for: (i) lagging power factors (ii) unity power factor, and (iii) a leading power factor.
   Use these expressions to calculate theoretical characteristics V_s vs I_s and J_f vs I_s corresponding to this exercise.
   To compare these curves, superimpose on a single graph the theoretical calculated and measured characteristics.
   What can we deduce about the synchronous machine's steady state model validity?
   Discuss.
7. Show qualitatively, how we can control the RMS voltage of a node connected to an AC grid injecting or absorbing reactive power to/from this node.