Analysis and Verification of Synchronous Machine Characteristics: EMF Method and Phasor Diagrams

          CO:1 Determining Synchronous Impedance: EMF Method Explained with Examples

Introduction

The Electromotive Force (EMF) Method, also known as the Synchronous Impedance Method, is used to determine the synchronous impedance () of an alternator. It involves performing Open Circuit Test (OCT) and Short Circuit Test (SCT) on a synchronous machine and using the test data to compute synchronous impedance. This method is widely used for voltage regulation calculations and machine performance analysis.

                                   

Steps to Determine Synchronous Impedance Using the EMF Method

1. Open Circuit Test (OCT)

The alternator is driven at rated synchronous speed by a prime mover.

The field winding is excited, and the open circuit voltage (Voc) is measured at different field currents.

The results are plotted as an Open Circuit Characteristic (OCC) curve.

Since the armature current is zero, the voltage drop across the synchronous impedance is negligible.

2. Short Circuit Test (SCT)

The alternator terminals are short-circuited through an ammeter.

The field current is gradually increased, and the short circuit current (Isc) is measured.

The plotted Short Circuit Characteristic (SCC) curve shows that the short-circuit current varies linearly with field current.

In this test, the terminal voltage is nearly zero, so the excitation voltage is dropped mostly across synchronous impedance.

3. Determine the Synchronous Impedance ()

The synchronous impedance is calculated using:

Z_s = \frac{E_{oc}}{I_{sc}}

where:

 = Open Circuit Voltage (for the same field current)

 = Short Circuit Current (for the same field current)

Since synchronous impedance consists of armature resistance () and synchronous reactance (), we express:

Z_s = R_a + jX_s

If  is small (which is often the case), then .

Example Calculation

Given Data:

Open Circuit Voltage () = 230 V (for a specific field current)

Short Circuit Current () = 10 A

Armature Resistance () = 1 Ω

Calculation:

Z_s = \frac{V_{oc}}{I_{sc}} = \frac{230}{10} = 23 \, \Omega

X_s = \sqrt{Z_s^2 - R_a^2} = \sqrt{(23)^2 - (1)^2} = \sqrt{529 - 1} = \sqrt{528} \approx 22.98 \, \Omega

Thus, the synchronous reactance .

4. Determine the Voltage Regulation

Voltage regulation is an important parameter that indicates the change in terminal voltage from no-load to full-load conditions. It is given by:

\text{Voltage Regulation} =Eb - Vb / Vb *100

where:

 = No-load excitation EMF per phase

 = Full-load terminal voltage per phase

Using phasor relationships and synchronous impedance values, the voltage regulation can be computed for different power factor loads.

Advantages of the EMF Method

• Simple and easy to perform using basic laboratory equipment.
• Provides a good approximation of synchronous impedance.
• Useful for voltage regulation calculations in synchronous machines.

Limitations of the EMF Method

• It assumes the synchronous reactance is constant, which is not always accurate.
• It does not consider armature reaction effects accurately at different load conditions.
• The results may deviate at high saturation levels of the machine.

Conclusion

The EMF method provides a practical way to determine the synchronous impedance of an alternator by conducting open circuit and short circuit tests. Though it has limitations, it is widely used for estimating voltage regulation and analyzing machine performance under different load conditions.

References:

1. "Electrical Machines" by I.J. Nagrath and D.P. Kothari.
2. "Theory of Alternating Current Machinery" by Alexander S. Langsdorf.
3. "Electric Machinery Fundamentals" by Stephen J. Chapman.

                C0:2 Experimental Verification of Synchronous Machine Phasor Diagrams

Introduction

A synchronous machine (generator or motor) operates with a fixed relationship between voltage and current, which can be represented using phasor diagrams. These diagrams help in understanding how different parameters such as voltage, current, synchronous reactance, and power factor interact in different operating conditions.      

 

                                               

This experiment verifies the theoretical phasor diagrams by measuring real-time electrical parameters under various load conditions.

Objectives of the Experiment

1. To experimentally analyze the phasor relationships in a synchronous machine.

2. To verify the phasor diagrams for different load conditions (lagging, leading, and unity power factor).

3. To compare experimental and theoretical phasor diagrams.

Equipment Required

Synchronous generator (Alternator)

DC motor or prime mover (to run the generator at synchronous speed)

Load bank (Resistive, Inductive, and Capacitive loads)

Voltmeter & Ammeter (for measuring voltage and current)

Wattmeter & Power factor meter (for real power and power factor measurement)

Oscilloscope (for waveform and phasor observation)

Procedure

Step 1: Open Circuit Test (No Load Condition)

The alternator is run at synchronous speed using a prime mover.

The field current is adjusted to get the rated voltage at the output terminals.

The generated EMF () is measured and noted.

The phasor diagram is drawn, where  is in phase with the field flux.

Step: 2 Phasor Diagram for Unity Power Factor Load (Resistive Load)

A pure resistive load is connected.

The armature current  is measured using an ammeter.

The terminal voltage  is measured.

The phasor diagram is drawn, where  is in phase with , and  leads  by a small angle due to internal resistance and reactance.

Step 3: Phasor Diagram for Lagging Power Factor Load (Inductive Load)

An inductive load is connected to the alternator.

The armature current  is noted, which lags behind the terminal voltage .

The phasor diagram is drawn, showing:

 lagging behind  by an angle .

 leading  by a larger angle due to the increased reactance drop.

Step 4: Phasor Diagram for Leading Power Factor Load (Capacitive Load)

A capacitive load is connected.

The armature current  is measured, which leads the terminal voltage .

The phasor diagram is drawn, showing:

 leading  by an angle .

 still leading , but by a smaller angle compared to the inductive case.

Analysis of Experimental Results

• The phasor diagrams obtained experimentally are compared with theoretical phasor diagrams.
• Differences are analyzed, considering factors such as armature reaction, saturation effects, and measurement inaccuracies.
• The variation in excitation voltage  for different loads confirms the theoretical behavior of synchronous machines.

Conclusion

The phasor diagrams of a synchronous machine were experimentally verified under different loading conditions. The results confirm that:

1. For a resistive load, current and voltage are in phase.

2. For an inductive load, current lags voltage.

3. For a capacitive load, current leads voltage.

This experiment helps in understanding alternator performance and is useful in power system analysis and machine design.

References

1."Electric Machinery Fundamentals" by Stephen J. Chapman – This textbook covers the theoretical aspects of synchronous machines and provides insight into phasor diagram construction.

2."Electrical Machines" by I.J. Nagrath and D.P. Kothari – It includes both theoretical and experimental analysis of synchronous machines, including phasor diagrams.

3."Theory of Alternating Current Machinery" by Alexander S. Langsdorf – A detailed source for understanding the phasor diagram and experimental methods for verifying machine performance.

4."Synchronous Generators and Motors" by P.C. Sen – Provides in-depth theoretical background and practical methods for verifying synchronous machine operation, including phasor diagrams.