A transmission line with impedance of 0.08+j 0.25 Ωis used...

A transmission line with impedance of $0.08+j 0.25 \Omega$ is used to deliver power to a load. The load is inductive, and the load voltage is $220 / 0^{\circ} \mathrm{V}$ rms at $60 \mathrm{Hz}$. If the load requires $12 \mathrm{kW}$ and the real power loss in the line is $560 \mathrm{W}$, determine the power factor angle of the load.

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Key Concepts

Complex Power Analysis

Complex power analysis combines both real (active) and reactive power into a unified framework expressed as a complex number. This approach is essential in AC power systems because it helps to account for the phase relationship between voltage and current, allowing engineers to evaluate and optimize system performance under varying load conditions.

Real Power Loss

Real power loss refers to the actual energy dissipated as heat in the system, predominantly due to the resistance present in the transmission line. This loss is calculated using the square of the current multiplied by the resistance, and it serves as an important metric in assessing the efficiency of power transmission.

Transmission Line Impedance

Transmission line impedance represents the combination of resistance and reactance in a power delivery system. It models how both energy dissipation (resistive losses) and energy storage (reactive effects) occur along the line, impacting voltage drops and overall system performance.

Load Power Factor

Load power factor is the cosine of the phase angle between the applied voltage and the resulting current. It quantifies the proportion of electrical power that is converted into useful work versus the power that circulates as reactive power, affecting both efficiency and the degree of power loss in the system.

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