The regional grid authority makes predictions about the electrical power it can supply and the electrical power customers demand for two different autumn seasons.
The authority calculates the system margin using the equation: system margin=electrical power supplied−electrical power demanded\text{system margin} = \text{electrical power supplied} - \text{electrical power demanded}system margin=electrical power supplied−electrical power demanded
The predictions for autumn 1 are:
Calculate the percentage system margin for autumn 1.
Use the equation: percentage system margin=predicted supply−predicted demandpredicted demand×100%\text{percentage system margin} = \frac{\text{predicted supply} - \text{predicted demand}}{\text{predicted demand}} \times 100\%percentage system margin=predicted demandpredicted supply−predicted demand×100%
The predictions for autumn 2 are:
Suggest two reasons why the grid authority predicts a range of values for the system margin.
Calculate the percentage uncertainty in the predicted system margin for autumn 2.
Use the equation: percentage uncertainty=12×range of valuesmean value×100%\text{percentage uncertainty} = \frac{1}{2} \times \frac{\text{range of values}}{\text{mean value}} \times 100\%percentage uncertainty=21×mean valuerange of values×100%
Suggest why energy engineers working for the grid authority may worry if the system margin is small.
The electrical power that a hydroelectric power station is able to supply can be increased to help meet customer demand. On one autumn day:
The electrical power that the hydroelectric power station is able to supply is then increased so that the system margin is increased by 7.5%7.5\%7.5%.
Calculate the electrical power that the hydroelectric power station is able to supply after the system margin has been increased.