Power is generated at 24 kV at a generating plant located 85...

Power is generated at $24 \mathrm{kV}$ at a generating plant located $85 \mathrm{~km}$ from a town that requires $65 \mathrm{MW}$ of power at $12 \mathrm{kV}$ Two transmission lines from the plant to the town each have a resistance of $0.10 \Omega / \mathrm{km} .$ What should the output voltage of the transformer at the generating plant be for an overall transmission efficiency of $98.5 \%,$ assuming a perfect transformer?

Key Concepts

Power Transmission Efficiency

This concept involves the ratio of the useful power delivered to the load to the power generated or sent through the transmission system. It accounts for losses incurred in the conductors and other system components, and understanding this efficiency is crucial in designing systems that minimize wasted energy during the long-distance transmission of electrical power.

Resistive Losses in Transmission Lines

Resistive losses occur in the transmission lines due to the inherent electrical resistance of the conductors. As current flows through these resistive elements, some energy is dissipated as heat according to Joule’s law. This loss is proportional to the square of the current and the line resistance, and therefore is a key factor in system design when calculating necessary voltage levels to ensure adequate power reaches the destination.

Transformer Operation and Voltage Transformation

Transformers are critical components in power systems that alter voltage levels between the generation and distribution stages. They allow for high voltage transmission, which reduces current and, consequently, resistive losses, followed by a step-down to lower, safe distribution voltages. Understanding transformer operation is essential for achieving optimal transmission efficiency and matching the power requirements of the load.

Ohm’s Law and Voltage Drop Calculations

Ohm’s law relates the voltage drop across a conductor to the current flowing through it and its resistance. In power transmission, calculating the voltage drop is essential to ensure that the voltage delivered at the load end is sufficient to meet operational requirements, despite losses in the conductors. This concept helps determine the necessary adjustments or compensations, such as raising the generation voltage, to maintain reliable power delivery.

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