A 1000 kVA, three-phase, Y-connected, 4160 V, 60 Hz synchronous gererator has an armature resis

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A 1000 kVA, three-phase, Y-connected, 4160 V, 60 Hz...

A $1000 \mathrm{kVA}$, three-phase, $Y$-connected, 4160 $\mathrm{V}, 60 \mathrm{~Hz}$ synchronous gererator has an armature resistance and synchronous reactance of $0.14 \Omega$ and $2.5 \Omega$ per phase, respectively. If the power factor is 0.77 lagging, determine the full load generated voltage per phase.

Key Concepts

Three?Phase Y-Connected Systems

In Y-connected (star) three-phase power systems, each phase’s voltage is found by dividing the line-to-line voltage by the square root of three. This reduction to per-phase analysis simplifies the study of the circuit, making it easier to apply electrical principles like Ohm’s law and phasor analysis to each individual branch of the system.

Synchronous Generator Equivalent Circuit

The synchronous generator can be represented by an equivalent circuit in which an internal generated (or excitation) voltage is in series with the armature impedance, comprising both the resistance and the synchronous reactance. This model allows analysis of how the generator’s internal voltage must overcome both resistive and reactive drops to deliver the terminal voltage under load conditions.

Phasor Analysis and Power Factor

Phasor analysis is used to represent sinusoidal quantities as rotating vectors in the complex plane, incorporating both magnitude and phase angle. The power factor, defined as the cosine of the phase angle between the voltage and current, indicates the ratio of real power to apparent power and is essential for determining the phase relationship in the circuit, which influences the calculated internal voltage through its impact on the phasor summation.

Voltage Drop Across Impedance

The voltage drop across the generator’s armature impedance, which consists of both a resistive and a reactive component, is calculated by multiplying the load current by the complex combination of resistance and synchronous reactance. This concept is critical for determining how much additional voltage must be generated internally (the excitation voltage) to maintain the desired terminal voltage under full load conditions.

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