A 960 hp synchronous motor is fed by a 2300 V, three-phase supply at 0.75 pf lagging. If the rot

step 1 solving part of this problem so let us calculate the value of P naught which is equal to 10 HP t

A 960 hp synchronous motor is fed by a 2300 V, three-phase...

A $960 \mathrm{hp}$ synchronous motor is fed by a 2300 $\mathrm{V}$, three-phase supply at $0.75 \mathrm{pf}$ lagging. If the rotational losses are known to be $20 \mathrm{~kW}$, the armature resistance is negligible and the synchronous reactance is $2.2 \Omega$, determine the excitation voltage at full load.

Key Concepts

Synchronous Motor Operation

Synchronous motors operate at a speed that exactly matches the frequency of the AC supply, meaning the rotor rotates in synchronism with the stator's rotating magnetic field. Their operation depends on maintaining a constant field via excitation, which directly influences the motor's ability to maintain system stability under varying load conditions.

Excitation and Field Voltage

Excitation in a synchronous motor involves supplying DC current to the rotor windings to generate a magnetic field. The magnitude of the excitation (or field voltage) determines the internal generated emf, which, when balanced against voltage drops due to reactance, ensures proper motor performance at full load.

Synchronous Reactance

Synchronous reactance is the combination of the stator leakage reactance and the armature reaction effects in a synchronous machine. It is responsible for the voltage drop between the internal excitation voltage and the terminal voltage, playing a critical role in determining the motor's operating characteristics in response to load changes.

Phasor Analysis

Phasor analysis involves using vector representations of sinusoidal voltages and currents to simplify the analysis of AC circuits. In synchronous motors, it provides a clear method to account for the phase relationships between the excitation voltage, the induced voltage, and the drops across reactances, aiding in the calculation of the required excitation level.

Power Factor

Power factor, defined as the cosine of the phase angle between voltage and current, indicates the efficiency of power usage. In a lagging power factor scenario, such as in many induction or synchronous motors under load, the current lags the voltage mainly due to inductive components, which necessitates careful adjustment of the excitation to maintain efficient and stable motor operation.

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