PARAMETER IDENTIFICATION FOR THE STEADY-STATE SYNCHRONOUS MACHINE MODEL

4.1 Objective

This exercise presents the implementation of standardized reduced-power tests that allow the user to identify the synchronous machine's steady state model parameters.
Load tests of high-power synchronous machines are difficult to perform in real life before they are commissioned in power plants or factories since they require high-power test facilities.
In power engineering, we prefer to estimate load tests using synchronous machine models determined in low power tests to overcome this problem.
The four identification tests used in this exercise are:  (i) no-load (ii) steady state (iii) short-circuit, and (iv) slip and measuring windings resistance.
The results of these tests will allow users to calculate the synchronous machine's steady state model parameters: no load characteristic E-Jf at nominal speed and frequency, armature reactances X_d and X_q and resistance R_s.

4.2 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 "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
8. Select the "AC Grid" tab in the simulator panel.

4.3 Starting and Setting the Driving Speed Using the DC Motor

1. Set the variable voltage supply SC2 to provide maximum voltage to the DC motor field, to start with maximum exciter current I_f.
2. Slowly start the drive using the DC motor by gradually increasing SC1 up to V_a= 460 V.
   Caution: at startup, the speed and electromotive force in the DC motor armature are null.
   Current is only limited by the small resistance R_a of the motor armature. I_a must be limited at startup by manually increasing V_a proportionally to the motor speed rising time, otherwise, fuse F_ia is blown and the drive stops.
   If this happens, it is necessary to wait until the speed returns to null, then return to the initial settings specified in section 4.2.
   Then, and only then, can we simulate replacing fuses by resetting the protection system using switch K₈.
3. To set the drive speed, voltage V_a, which is supplied by the variable continuous voltage SC1 must be maintained at its nominal value, V_an = 460 V. Speed is set by adjusting the exciter current I_f, with SC2.
   When the I_f is reduced the drive speed increases and vice versa.
   Precise speed setting is achieved using the slider bar below SC2.

4.4 No Load Test, Constant-speed Characteristics (E-J_f) of the Synchronous Generator

4.4.1 Setup Diagram

In this exercise, the synchronous machine is operating in generator mode and is driven by the DC motor.
To adjust generator speed, SC1 is used in conjunction with supply SC2, as described in section 4.3.
Synchronous machine armature windings are open (no-load).
This is a low power test since there is no current in the armature.

Figure 6: Electrical diagram of synchronous generator with no-load, driven by the DC motor

4.4.2 Exercise

1. Drive the synchronous machine at its nominal speed of 1800 rpm using the DC motor, following the procedure set out in section 4.3.
2. Starting at 0, gradually increase current Jf supplied by SC3, which fed the synchronous machine's field winding.
   During this test, it is imperative to maintain a constant speed of 1800 rpm to maintain the synchronous machine's armature voltage frequency at 60 Hz.
   Since the DC motor is not regulated automatically, speed must be manually adjusted at each operating point.
   Take note of each operation point value: (i) RMS voltage line-line U_s and (ii) field current J_f.
   Since the synchronous machine's armature is open, the RMS voltage line-line U_s is equal to the no-load electromotive line-line force E.
   Continue the exercise until maximum J_f is reached, which is achieved with SC3.
3. Take note of the current J_fo which makes possible to obtain, at 1800 rpm, an RMS value for the line-line voltage E equal to the synchronous machine's nominal voltage U_sn (see the machine's data plate).
4. Using the previously measured operating points, we can plot the synchronous machine's no-load characteristic E-J_f at 1800 rpm.
   The synchronous machine's equivalent circuit in a steady state corresponds to a line-neutral diagram.
   Calculate the line-neutral electromotive force from the measured line-line value.

4.5 Steady-state short-circuit test, constant-speed characteristic of the synchronous generator I_sc-J_f

4.5.1. Setup Diagram

Figure 7 : Electrical diagram of the short-circuited synchronous generator driven by the DC motor

In this exercise, the synchronous machine is driven by the DC motor.
Supply SC1 and SC2 are both used to control generator speed, as described in section 4.3.
Synchronous machine armature windings are short-circuited.
Switch K₂ is closed.
This is a low power tests since the voltage at armature terminals are zero.

4.5.2. Exercise

1. Reset the setup to its original state, as described in section 4.2, by bringing voltage sources SC3, SC1 and SC2 back to 0 V and by resetting switches to their default settings.
2. With all machines stopped, use switch K₂ to short-circuit all three armature windings.
3. Start the DC motor, as shown in section 4.3, and drive the synchronous machine at 1800 rpm.
4. Gradually increase current J_f starting from 0 A provided by SC3, which supplies the synchronous machine field winding by using the RMS value of I_s and the current in the field J_f. In this test I_s corresponds to the short-circuit current and is typically called I_ssc.
   Continue to increase J_f until the current of the short-circuited windings reaches the value of the synchronous machine's nominal current I_sn.
   Be sure to maintain the speed at 1800 rpm throughout the exercise.
5. Using the previously measured operating points, we can plot the synchronous machine's steady state short-circuit characteristic I_ssc - J_f at 1800 rpm.

4.6 Slip Test, Saliency Measurement

4.6.1. Setup Diagram

Figure 8: Electrical diagram of the slip test on the synchronous machine driven by the DC motor

In this exercise, the synchronous machine's rotor is driven by the DC motor at a slightly slower speed than the synchronous speed (1800 rpm).
The synchronous machine armature is fed at reduced voltage from the grid, and switch K₁ is closed.
Since switch K₅ is open, the synchronous machine's field is not powered and is in parallel with the starting resistor.
This is an asynchronous operating mode during which the machine reactance varies between X_d and X_q at a frequency equal to the difference between the rotor frequency multiplied by the pairs of poles and the grid frequency.
Since the test is conducted at low voltage levels to limit the RMS current in the armature windings, this is a reduced power test.

4.6.2. Exercise

1. Reset the setup to its original state, as described in section 4.2, by bringing voltage sources SC3, SC1 and SC2 back to 0 V and resetting switches to their default conditions.
2. Select the "AC Grid" tab at the right of the panel.
   Adjust SA1 to 0 V and f_s to 60 Hz if they are not already set to these values.
3. Enable switch K₅: the synchronous machine field is no longer powered by SC3 and is connected to the starting resistor.
4. Start the DC machine using the procedure described in section 4.3
5. Set the drive speed to approximately 1790 rpm using the DC motor, following the procedure described in section 4.3.
6. Close switch K₁ to connect the synchronous machine armature to the grid.
   Energize and gradually increase the voltage at stator terminals to approximately 100 V, using transformer SA1 in the "AC Grid" tab.
7. Select the "Oscilloscope2" tab and enable switch K₁₁ to observe the current waveform that circulates in phase 1 of the synchronous machine's armature.
8. Observe the current in the armature: it varies at f_s, but its amplitude is modulated by reluctance variations.
   These variations are due to rotor saliency and oscillate in a low frequency resulting from the difference between the armature power frequency and the rotor electrical frequency multiplied by the pairs of poles.
   The armature reactance seen from the voltage source SA1, varies at low frequency between X_d and X_q.
   Take note of the minimal (I_s=I_smin) and maximal (I_s=I_smax) peak values of I_s from the amplitude modulated current signal.
   We can deduce that the X_d /X_q ratio is essentially equal to the I_smax / I_smin ratio.
9. Use Autotransformer SA1 in the "AC Grid" tab to bring the voltage at the stator terminal back to 0 V.
   Open switch K₁ to disconnect the synchronous machine's armature from the grid.
   Stop the DC motor by bringing the SC1 voltage down to 0 V.
   Close switch K₅ and disable switch K₁₁.

4.7 Armature Resistances Measurement

4.7.1. Setup Diagram

Figure 9: Wiring diagram for the synchronous machine's armature resistance measurement

During the synchronous machine armature windings resistance test, two phases are connected to the continuous voltage source SC4 and the third phase remains open.
Adding external resistances in series with SC4 the circulating current is limited in the machine windings, each of which present a very low resistance R_s.
The synchronous machine rotor is blocked and the source SC3 is at 0 V.

4.7.2. Exercise

1. Reset the setup to its original state, as described in section 4.2, by bringing voltage sources back to 0 and resetting switches to their default conditions.
2. With all machines stopped, use switch K₆ to block the synchronous machine rotor.
3. Close switch K₄ and select the "Measurement Resistance" tab at the right of the panel. In this configuration, two phases of the synchronous machine armature are powered by the DC source SC4.
   Since the synchronous machine armature winding resistance R_s is low, two limiting resistances were added in series with SC4 to limit the current I_dc circulating in the windings.
   A voltmeter directly measures voltage U_dc at both phase terminals of the armature in which I_dc is flowing.
   Gradually increase SC4, starting from 0, so that the DC current I_dc does not surpass the synchronous machine armature's nominal value I_sn (see the machine data plate). Measure U_dc and I_dc.
   Calculate the value of resistance R_s of the armature winding from:
    

4.8 Lab report

1. Present the no-load test results in tables (SI units).
2. Plot the synchronous machine's no-load characteristic E-J_f at 1800 rpm.
   Make sure to calculate the no-load electromotive force E line-neutral from the line-line value measured in the exercise.
3. Present the results of the short-circuit test in tables (SI units).
4. Plot the synchronous machine's steady state short-circuit characteristic I_scc - J_f at 1800 rpm.
5. Calculate the synchronous machine armature's winding resistance R_s based on the test performed in section 4.7.
6. Use the theory learned during the course to show that we can deduce the armature's reactance X_d from the two previous characteristics (we will calculate the impedance Z_d from the short-circuit ratio)_.
7. Calculate the saliency value X_d /X_q based on the slip test in section 4.6 and find the value of X_q.