Power is generated at 24 kV at a generating plant located 56...

Power is generated at 24 kV at a generating plant located 56 km from a town that requires 55 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 0.10 $\Omega/$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

Transmission Efficiency

Transmission efficiency refers to the ratio of the power delivered to the load to the power generated at the source. It accounts for losses that occur during the transfer of energy, predominantly due to heat loss in the transmission lines. A required high efficiency means that these losses must be minimized, and calculations are structured to ensure that the voltage and current levels are chosen to keep the losses within acceptable limits.

Transformer Operation

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It is used to change the voltage levels between the generating station and the load, improving transmission quality and efficiency. In problems assuming an ideal or perfect transformer, the device is considered lossless, meaning it only changes voltage levels without energy loss.

Resistive Losses in Transmission Lines

Resistive losses, sometimes termed I²R losses, occur due to the resistance present in transmission lines. These losses are proportional to the square of the current flowing through the conductor multiplied by its resistance. Correct calculations require knowledge of the total resistance (which can be a function of length and resistance per unit length) to determine how much voltage drop and power is lost along the transmission path.

Voltage Drop in Conductors

Voltage drop is the reduction in voltage that occurs as current flows through a resistive element. In power transmission, the voltage at the end of the line is lower than the voltage at the source due to the inherent resistance of the conductors. Accurate assessment of voltage drop is essential when determining the necessary initial voltage that must be applied so that, after losses, the required voltage is delivered at the load.

Power Calculations and Current Determination

In power transmission problems, power calculations relate to determining current from known power and voltage levels using the relation P = VI. This calculation is crucial because the current flows influence the magnitude of resistive losses. Understanding how to derive current from the load requirement allows one to assess the power loss and subsequently the adjustment needed in the generation or transformation stage to maintain high efficiency.

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