Power is generated at 24 kV at a generating plant located 85 km from a town that requires 65 MW

step 1 Okay, so we're generating power at 24 kilovolts at a plant that's located 85 kilometers from a t

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 trans- former?

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 trans-
former?

Key Concepts

Transformer Operation

Transformers are electrical devices that change voltage levels between circuits with high efficiency. They allow power systems to operate at optimal voltage levels for different stages, such as generation, transmission, and distribution, enabling reduced energy losses and improved safety. In analysis, transformers are assumed to be ideal in many problems, meaning they have no internal losses aside from their voltage conversion function.

Resistive Loss in Transmission Lines

Transmission lines, which carry electrical power over long distances, inherently have resistance that causes power loss in the form of heat. This resistive loss is calculated using the formula based on the square of the current multiplied by the line resistance (I²R). Understanding resistive losses is crucial in designing efficient power transmission systems as it impacts the amount of power that actually reaches the end user.

Transmission Efficiency

Transmission efficiency is a measure of how effectively power is delivered from the source to the load, defined as the ratio of the power received (load power) to the power generated (input power). It takes into account losses that occur during transmission, especially due to the resistive characteristics of the conductors. Maintaining high transmission efficiency is important in power system design to minimize energy wastage.

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that relates voltage, current, and resistance through the equation V = IR. This law is essential for analyzing voltage drops across transmission lines and calculating the current flowing through the system, which, in turn, helps in understanding and minimizing energy losses during power transmission.

Power Calculations

Power calculations involve the relationship between power, voltage, and current, typically expressed by the equation P = VI, where P is power, V is voltage, and I is current. These calculations are crucial in designing and assessing power systems, as they help determine the required operating conditions and the appropriate transformer output voltage needed to meet load demands while compensating for transmission losses.

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