An industrial plant at the end of a transmission line consumes 144 kW at 0.88 PF lagging. The l

step 1 In this problem I can write the value of p line is equal to PS minus PL which is equal to 100k m

An industrial plant at the end of a transmission line...

An industrial plant at the end of a transmission line consumes $144 \mathrm{~kW}$ at 0.88 PF lagging. The line voltage at the plant is $480 \angle 0^{\circ} \mathrm{V}$ rms. The resistance of the transmission line is $0.13 \Omega$. Determine the voltage and power factor at the input of the transmission line.

Key Concepts

Power Factor

Power factor is the cosine of the phase angle between voltage and current in an AC circuit. It quantifies the efficiency with which the circuit converts electric power into useful work. A lagging power factor indicates that the current lags the voltage, typically due to inductive loads, and affects how much apparent power is required to deliver a given amount of real power.

Complex Power

Complex power in AC circuits represents the combination of real power (which does work) and reactive power (which oscillates between the source and load). It is expressed in the form S = P + jQ, where P is the real power and Q is the reactive power. Understanding complex power is essential for analyzing how power is utilized and distributed in systems with non-unity power factors.

Transmission Line Voltage Drop

When electric power is transmitted over a line with inherent resistance, some of the voltage is dropped across the line due to the resistive losses. This voltage drop must be accounted for to ensure that the load receives the required voltage, and it is calculated based on the current flowing through the line and its resistance.

Ohm’s Law in AC Circuits

Ohm’s law in AC circuits extends the familiar relationship between voltage, current, and resistance to include the effects of phase difference. In the phasor domain, voltage drop across a resistor is found using V = IZ, where Z represents impedance. This principle is used to determine how the transmission line resistance affects the overall voltage applied to the load.

Phasor Analysis

Phasor analysis is a method used in AC circuit analysis that simplifies the calculation of voltages and currents by representing sinusoidal functions as rotating vectors (phasors) in the complex plane. It allows for the straightforward handling of phase differences and is crucial for solving problems involving AC power flow and voltage drops in transmission lines.

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