Power loss in transmission
Modelling power transmission
Consider the problem a farming family has in supplying power to a milking shed 10 km away from their house. (They have a big farm!) Knowing that there will be energy losses in the wires connecting the 240 V generator at the house to the shed, the family decide to install a step-up transformer (1:20 turns ratio) at the generator, and a step-down transformer of the inverse ratio (20:1) at the shed.
What energy loss will be incurred over this distance for a power generation of, say, 1000 W? What if the transformer ratios are changed? Will the voltage at the shed be adequate to run 240 V appliances? If the family bought the neighbouring farm, could they run the wires across to its milking shed 50 km away?
This situation can be explored using a spreadsheet to model the electrical system.
Designing the spreadsheet
The ‘Milking shed’ worksheet is divided into three areas: the house transformer, the transmission wires, and the shed transformer. We will assume that the power generated and its voltage are fixed, and we will aim to calculate the voltage at the shed as well as power losses in the transmission lines. The diagram below gives definitions of the variables used. The calculations are explained in the text that follows. Work through these, referring to the spreadsheet and diagram, before answering the questions that follow.