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A synchronous motor operating at rated voltage draws 1.0 pu current at 1.0 power factor . the machine parameters are synchronous reactance 1.0 pu armature resistance negligible . Apart from supplying this rated power if the motor has to supply an additional reactive power of o.8 pu then the field current has to be increased by?
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A synchronous motor operating at rated voltage draws 1.0 pu current at...
Question: What is the increase in field current required for a synchronous motor operating at rated voltage to supply an additional reactive power of 0.8 pu?

Solution:

Given:

  • Synchronous reactance = 1.0 pu

  • Armature resistance = negligible

  • Rated voltage = V

  • Rated current = I = 1.0 pu

  • Power factor = 1.0

  • Additional reactive power = 0.8 pu



Steps to Find the Increase in Field Current:

  1. Calculate the rated apparent power of the motor.

    S = V*I = V*1.0 = V pu

  2. Calculate the rated active power of the motor.

    P = S*power factor = V*1.0 = V pu

  3. Calculate the rated reactive power of the motor.

    Q = sqrt(S^2 - P^2) = sqrt(V^2 - V^2) = sqrt(0) = 0 pu

  4. Calculate the total reactive power that the motor has to supply.

    Q_total = Q + additional reactive power = 0 + 0.8 = 0.8 pu

  5. Calculate the field current required to supply the additional reactive power using the formula:

    Q_total = (3*V^2*E_f)/(2*pi*f*X_s)

    Where E_f is the field voltage, f is the frequency, and X_s is the synchronous reactance.

    E_f = (2*pi*f*X_s*Q_total)/(3*V^2) = (2*pi*50*1.0*0.8)/(3*V^2) = 0.0265/V

  6. Calculate the increase in field current required using the formula:

    delta(I_f) = (E_f - E_rated)/X_s

    Where E_rated is the rated field voltage.

    E_rated = V/X_s = V/1.0 = V

    delta(I_f) = (0.0265/V - V)/1.0 = -V^2 + 0.0265



Answer: The increase in field current required for the synchronous motor to supply an additional reactive power of 0.8 pu is -V^2 + 0.0265.
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A synchronous motor operating at rated voltage draws 1.0 pu current at 1.0 power factor . the machine parameters are synchronous reactance 1.0 pu armature resistance negligible . Apart from supplying this rated power if the motor has to supply an additional reactive power of o.8 pu then the field current has to be increased by?
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