Convincing Numbers to Install a Heat-Pump for Domestic Heating

Peter Wurmsdobler
4 min readOct 16, 2024

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Being ecologically minded, I have been trying to reduce our family’s ecological footprint wherever possible, e.g. improving the thermal performance of our 1930ies house, mostly through more insulation. The next item on the list of improvements would be the installation of a heat-pump replacing a gas boiler (domestic hot water and space heating). In the past I was put off by a perhaps too simplistic reasoning only taking into account the ratio of electricity to gas price in comparison with the Coefficient of Performance (COP), until a post by Jan Rosenow and a subsequent discussion convinced me otherwise. Here I would like to share my pythonic calculations based on a spreadsheet created by Jan so that other people can warm up to the idea of having a heat-pump installed.

Initial Simplistic View

Our current annual gas consumption is about 15,000 kWh; assuming a COP of 3 as a worst case, a heat pump would consume 1/COP = 1/3 of that energy in electricity to heat the house to the same extent, i.e. 5,000 kWh. Now the price ratio of electricity to gas is about 4 with my current supplier at their standard rate. Therefore, the system would consume 1/3 of the energy in electricity, but that energy would cost me 4 times more; in other words, the running costs would be about 1/3 higher, of course only taking into account the energy price ratio at a standard rate and a conservative COP of 3.

With regards to the capital expenditure for the installation of the heat pump, the starting point is an initial quotation by an installer for £12k minus a £7.5k contributed by a grant from the UK government (actually the grant used to be £5k when I looked into heat pumps before); this still leaves me with an investment of £4.5k. Due to the operating expenditure being higher with electricity powering a heat pump given the above simplistic assumptions, the system would appear to never pay for itself.

If gas prices were higher (with the effects on the environment priced in through higher carbon taxes), or/and if electricity prices were more dynamic such that I could buy wind/solar energy when in surplus (the thermal inertia of house and water tank allowing for a demand response), then I could imagine that the electricity to gas ratio would be more in favour of heat pumps. Once the electricity to gas price ratio falls below the COP, then heating the house through a heat pump will become economical.

Jan’s Improved Model

The predictions do change however by taking into account two additional factors: 1) a non-negligible standing charge for gas, the monthly consumption independent fee to remain connected to the gas grid, and 2) alternative electricity suppliers that do accommodate heat pumps and are connected to renewable energy sources such as wind or solar farms. Building on Jan Rosenow’s spread sheet to create a small python program (listed below), it is interesting see the decreasing cost using electricity for a heat pump with increasing COP, and for different energy suppliers:

Comparison of Gas Boiler and Heat Pump Costs when disconnecting gas

The standing charge is assumed to be £115.559 with a standard gas price of 0.0624 £/kWh for 15,000kWh per annum. The electricity prices are 0.245 £/kWh for Standard, 0.2009 £/kWh for Octopus cosy, 0.1799 £/kWh for Octopus average and 0.15 £/kWh for OVO energy. It is easy to calculate the CoP break-even points for Standard, Octopus cosy, Octopus average and OVO energy: 3.34, 2.74, 2.45, and 2.04, respectively. These COPs should be easy to reach in an installation for a moderate UK climate. The capital expenditure for the £4.5k mentioned above would take about 9 years to recover on an average COP of 3, an OVO Energy tariff and with 15,000 kWh heat per annum.

In summary, taking into account more flexible electricity tariffs as well as the opportunity to disconnect gas supply all together (no standing charge), there is an economic case to replace a gas boiler with a heat pump.

Appendix

Feel free to copy & paste the following code into a python shell or jupyter notebook, then change the values to suit your needs.

import matplotlib.pyplot as plt
import numpy

Energy_annual = 15_000 # kWh/annum
Gas_price_standard = 0.0624 # £/kWh , https://www.ofgem.gov.uk/energy-price-cap
Gas_standing_charge = 115.559 # £/kWh , https://www.ofgem.gov.uk/energy-price-cap
Gas_boiler_efficiency = 0.95 # £/kWh , https://www.ofgem.gov.uk/energy-price-cap
Electricity_prices = {
"Standard": 0.245, # £/kWh , https://www.ofgem.gov.uk/energy-price-cap
"Octopus cosy": 0.2009, # £/kWh , https://cdn.sanity.io/files/lrxd4jqj/production/85b1357ec84918b3b6e42b694f60b067c3f683fb.pdf
"Octopus average": 0.1799, # £/kWh , https://agile.octopushome.net/historical-data
"OVO energy": 0.15, # £/kWh , https://www.ovoenergy.com/heat-pump-plus
}
CoPs = numpy.linspace(2, 5, num=100)

Annual_gas_cost = (
Energy_annual / Gas_boiler_efficiency * Gas_price_standard + Gas_standing_charge
)
Annual_electricity_costs = {
supplier: Energy_annual / CoPs * price
for supplier, price in Electricity_prices.items()
}
Break_even_points = {
supplier: round(Energy_annual * price / Annual_gas_cost, 2)
for supplier, price in Electricity_prices.items()
}

print(f"Annual gas cost: £{Annual_gas_cost:.2f}")
print(f"Break even CoPs: {Break_even_points}")

plt.figure(figsize=(10, 6))
for supplier in Electricity_prices:
plt.plot(CoPs, Annual_electricity_costs[supplier], label=supplier)
plt.plot(CoPs, numpy.full(len(cops), Annual_gas_cost), label="Gas boiler")
plt.grid()
plt.legend()
plt.xlabel("Coefficient of Performance")
plt.ylabel("Annual Energy Cost [£]")

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Peter Wurmsdobler
Peter Wurmsdobler

Written by Peter Wurmsdobler

Interested in sustainable mobility, renewable energy and regenerative agriculture as well as music and audio.

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