In a salient pole synchronous machine, the excitation voltage for generating action is given by:

Explanation:

Excitation Voltage in Salient Pole Synchronous Machine

Definition: In a salient pole synchronous machine, excitation voltage is the voltage required at the field winding to establish the necessary magnetic flux for the machine's operation. This flux interacts with the armature winding to produce the required electromagnetic torque. The excitation voltage is also influenced by the power factor, load conditions, and machine's reactance.

Expression for Excitation Voltage:

The excitation voltage for generating action in a salient pole synchronous machine is given by:

E_o = V Cos δ + I_qR_a + I_dX_d

Where:

• E_o: Excitation voltage
• V: Terminal voltage
• δ: Power angle
• I_q: Quadrature axis component of armature current
• I_d: Direct axis component of armature current
• R_a: Armature resistance
• X_d: Direct axis synchronous reactance

Derivation:

The excitation voltage in salient pole synchronous machines depends on the phasor relationship between the terminal voltage, armature current, and the synchronous reactance. The machine's synchronous reactance is divided into two components:

• Direct axis reactance (X_d): This is associated with the magnetic flux along the direct axis.
• Quadrature axis reactance (X_q): This is associated with the magnetic flux along the quadrature axis.

The armature current can be resolved into two components:

• I_d: Direct axis component, which contributes to the direct axis magnetic flux.
• I_q: Quadrature axis component, which contributes to the quadrature axis magnetic flux.

The excitation voltage is determined by considering the power angle δ and the phasor addition of the resistive and reactive components of voltage drops across the armature resistance (R_a) and reactances.

Advantages of This Expression:

• Provides a comprehensive understanding of the relationship between excitation voltage and operating parameters such as load current and power factor.
• Helps in designing and analyzing the performance of synchronous machines under different load conditions.

Correct Option Analysis:

The correct option is:

Option 3: E_o = V Cos δ + I_qR_a + I_dX_d

This expression correctly represents the excitation voltage in a salient pole synchronous machine. The positive signs indicate the additive nature of the voltage drops due to the armature resistance and direct axis reactance.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: E_o = V Cos δ + I_qR_a - I_dX_d

This option is incorrect because the sign of the term involving I_dX_d is negative. The excitation voltage expression inherently requires the addition of the direct axis reactance component, as it contributes positively to the net excitation voltage.

Option 2: E_o = V Cos δ - I_qR_a - I_dX_d

This option is incorrect as both I_qR_a and I_dX_d have negative signs. These terms represent the voltage drops due to the resistive and reactive components, which are additive in the excitation voltage equation.

Option 4: E_o = V Cos δ - I_qR_a + I_dX_d

This option is partially correct, as it correctly includes a positive sign for the I_dX_d term. However, the negative sign for I_qR_a is incorrect, as the armature resistance contributes positively to the net excitation voltage.

Conclusion:

The excitation voltage for a salient pole synchronous machine is expressed as:

E_o = V Cos δ + I_qR_a + I_dX_d

This expression accounts for the terminal voltage, power angle, and the contributions of armature resistance and direct axis reactance. Understanding this equation is crucial for analyzing the performance and operation of synchronous machines under various load conditions. Evaluating the other options highlights the importance of correctly interpreting the signs and relationships in the excitation voltage formula.