Primary energy needs for households

The majority of the current domestic heat production is made by household boilers, whereas the electricity is produced in large power plants. We call this the reference situation. The reference boiler efficiency is 90% and the electricity is produced in a natural gas fired power plant with an efficiency of 40%. LHV Natural gas = 31.9 MJ/m3. An average household consumes about 3100kWh and 2200m3 gas a year.

a) How much primary energy is needed in the reference situation for an average household per year?

Besides the boiler and power plants, other technologies are available for the production of heat and/or electricity. Consider the following options:

1. Micro-cogeneration by small gas engines like a Stirling-engine. The electrical efficiency of these engines is 15%. The heat efficiency is 75%.

2. Heat pumps, with a COP (coeffiecient of performance) of 4.

b) How much primary energy is needed in these two options and how much is saved per option? So which option is the best from an energy perspective? Assume that excess electricity can be sold back to the grid and additional electricity can be purchased from the grid.