V and Inverted V Curves of Synchronous Machines: Experimental Setup and Analysis

Introduction 

The V and Inverted V curves of a synchronous machine illustrate the relationship between armature current and excitation current under constant power conditions. These curves help analyze the machine's power factor and stability.

1. Experimental Setup

Equipment Required

Synchronous machine (alternator or motor)

DC source for field excitation

Three-phase power supply

Ammeter (for armature and field currents)

Voltmeter (to measure line voltage)

Wattmeter (to measure power)

Rheostat (to vary field excitation)

Load (resistive or inductive)

Circuit Diagram 

2. Procedure

V Curve (Armature Current vs. Field Excitation for Constant Load)

1. Set up the synchronous machine with a connected load.

2. Start the machine as an induction motor and apply DC field excitation to achieve synchronization.

3. Adjust the excitation current (If) gradually from under-excited to over-excited conditions.

4. Record the armature current (Ia) at each excitation level while maintaining constant load.

5. Plot a graph of armature current (Ia) vs. excitation current (If).

6. The resulting curve will have a characteristic "V" shape, where minimum armature current corresponds to unity power factor.

Inverted V Curve (Power Factor vs. Field Excitation for Constant Load)

1. Using the same setup, measure the power factor using a wattmeter or calculate it using the power triangle (cos 𝜙 = P / (√3 * V * Ia)).

2. Vary the field excitation (If) from under-excited to over-excited conditions while maintaining a constant load.

3. Record the power factor at each excitation level.

4. Plot power factor vs. excitation current (If).

5. The resulting curve has an "Inverted V" shape, with unity power factor at the peak and lagging/leading power factor on either side.

3. Analysis and Observations

V Curve Interpretation

Under-Excited Region: High armature current, lagging power factor.

Optimum Excitation (Unity Power Factor): Minimum armature current.

Over-Excited Region: Higher armature current, leading power factor.

Inverted V Curve Interpretation

Under-Excited: Lagging power factor (inductive behavior).

Optimum Excitation: Unity power factor.

Over-Excited: Leading power factor (capacitive behavior).

Practical Applications

Power factor correction in industries.

Stability analysis of synchronous generators in power systems.

Improving efficiency and reducing losses in synchronous motors.

Reference 

1. P. S. Bimbhra, Electrical Machinery, Khanna Publishers.

2. A. E. Fitzgerald, Charles Kingsley Jr., and Stephen D. Umans, Electric Machinery, McGraw-Hill.