This post is not original nor is it a fully thought out scheme, similar commercial concepts are available and on a scale larger than a single household they becomes a district heating schemes. For brevity and simplicity, there are some gross over simplifications.
The vast majority of households in the UK are on gas and electric grids. A home which consumes 5,000 kwh/year of electricity and 10,000 kwh/year of gas for heating, hot water and cooking might indirectly use more than 20,000 kwh of gas (contributions from other fuels are conveniently ignored). Assuming the gas fuelled plant supplying the electricity is 50% efficient, 50% of the energy input to that plant is lost. The diagram summarises the energy flows:
The house which is consuming the electricity is also acquiring 10,000 kwh of gas for space and water heating. The generating plant having dumped 5,000 kwh which might have been used to offset the heating load.
Solar PV panels are now a mature technology and a kw array is capable of generating more than 20 kwh in the south of England from spring to autumn. The downside of solar panels is that they do not work at night and output in December and January is low. Without storage, PV panel require some form of backup, in the on-grid configuration this is effectively a gas fuelled power station. Integrating storage into a household system goes some way to displacing fossil fuelled generation.
A further enhancement to the household energy system might be the addition a small gas fuelled generator, maybe a scaled down version of the system used in hybrid cars. This could operate efficiently at a constant speed, the generator would maintain the battery bank and the waste heat from the engine could be used for space and water heating.
Electricity generation has developed around large plants, but other technologies are evolving which make it possible consider scenarios which are based on the investment of thousands of pounds at the household level, rather than billions at an industrial scale.
The graph below is an approximation of the demand for energy and the availability of solar generated electricity. The generator set would have its greatest utilisation in winter when the availability of solar power is low and the demand for warmth greatest. In summer the demand for heating is low and the demand for electricity could be met by the solar panels.
With the exception of the solar panels, variations on this theme have been around for a long time, I recently came across this advert in a publication from 1911:
This “electric light plant” has most of the elements described above, gas fuelled, energy storage. As an engineering student, I was taught the basics of thermodynamics on a ancient gas engine, I have vague memories of custodian of this machine stating that it had been used as part of the heating system in a public building.