The national grid makes predictions about the electrical power it can supply and the electrical power customers demand for two different winters.
The national grid 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 winter 1 are:
Calculate the percentage system margin for winter 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 winter 2 are:
Suggest two reasons why the national grid predicts a range of values for the system margin.
Calculate the percentage uncertainty in the predicted system margin for winter 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 people working for the national grid may worry if the system margin is small.
The electrical power that a gas turbine power station is able to supply can be increased to help meet customer demand. On one winter's day:
The electrical power that the gas turbine power station is able to supply is then increased so that the system margin is increased by 6.0%6.0\%6.0%.
Calculate the electrical power that the gas turbine power station is able to supply after the system margin has been increased.