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# Synchronous Machines - 5. Exercise 2

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

# Section Content

# 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:

- Continuous voltage supplies SC1, SC2, SC3 set to 0 V.
- Continuous voltage supply SC4, in the "Measurement Resistors" tab, set to 0 V.
- Alternative power SA1, in the tab "AC Grid" tab, set to 0 V.
- Switches K
_{1}, K_{2}, K_{3}, K_{4}opened: synchronous generator armature has no load. See Table 4. - Switch K
_{6}disabled: the synchronous machine rotor is driven by the DC motor. See Table 4. - Switch K
_{5}disabled: voltage source SC3 powers the synchronous machine field winding. See Table 4. - Trigger switches K
_{10}, K_{11}, K_{12}, K_{13}, K_{14}, 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 K_{3} 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

- 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 K_{5}is disabled and the voltage source SC3 supplies the synchronous machine's field winding.

Select the "RLC load" tab in the panel. - 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. - 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. - Close switch K
_{3}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. - 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. - Disconnect the RLC load using switch K
_{3}.

Reset the setup to its original state described in Section 5.2. - 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}. - Disconnect the RLC load using switch K
_{3}.

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

- 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 K
_{5}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. - 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. - 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. - Close switch K
_{3}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. - 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. - Disconnect the RLC load using switch K
_{3}. Reset the setup to its original state described in Section 5.2. - 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. - 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

- 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 K_{5}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. - 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. - 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. - Close switch K
_{3}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. - 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. - Disconnect the RLC load using switch K
_{3}.

Reset the setup to its original state described in Section 5.2. - 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. - 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

- 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. - 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? - 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? - 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. - 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? - 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. - 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.

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