# Temperature based form for calculating heat savings yourself

This form extends a little on the simple calculations done on heat savings without looking at daily temperatures. It is meant to be used to provide information enough to make buying decisions, but can also be used to try out alternative choices. The form basically only needs two values in order to do meaningful calculations (where you live and how much heat the house needs), but then the basics in the simpler calculations are extended to:

• Use outside daily temperatures to decide if additional heating will be needed
• Use outside daily temperatures to decide utilised COP for an Air-To-Water pump
• Use the house's energy need curve based on outside temperatures to decide needed heating energy
• Use the Air-To-Water input power and COP to determine if additional heating is needed, and then include that in the cost
• Use the Geothermal maximum Power to determine if additional heating is needed, and then include that in the cost

It delivers cost saving payback times utilising comparisons between the alternatives. The shown alternatives are

• Using an eletric heater only
• Using an Air-To-Water heat pump
• Using a geothermal heat pump, compared to an Air-To-Water pump
• Using the heat pumps with or without the production of hot water

The way the calculations are done are described here. An important assumption for all calculations is that the radiators are large enough to deliver the needed heating without needing water temperatures above the heat pumps forward water temperature limits.

# Select temperature location

The below input data is to define the outside temperatures to be used, some calculations are then provided to help understand how they affect the results.

 Location to use temperatures from CopenhagenFalunGothenburgHammer OddeHaparandaHärnösandJönköpingKarlstadKvikkjokkMalungÖstersundStenseleStockholm
 Decade Yearly DegreeNeed*Days as heat need Yearly number of days with heat need Min Day Average Daily Average outside temperature Average heated temperature 1870 3,930 342 -11.8 7.17 6.51 1880 3,929 338 -12.9 7.38 6.36 1890 3,810 340 -19.4 7.68 6.80 1900 3,747 338 -10.4 7.87 6.93 1910 3,566 333 -15.2 8.40 7.29 1920 3,703 346 -11.3 7.95 7.31 1930 3,399 329 -9.0 8.85 7.68 1940 3,605 330 -21.4 8.32 7.06 1950 3,511 333 -13.8 8.53 7.45 1960 3,526 339 -9.4 8.46 7.60 1970 3,414 329 -10.3 8.86 7.61 1980 3,447 333 -16.1 8.73 7.66 1990 3,273 326 -8.1 9.28 7.97 2000 3,170 321 -9.4 9.57 8.13

# Define house heating needs

The below input data is to define the heating needs of the house, and to understand how the need affect the results. The selection can be done in two different ways:

• Select an average heat consumption per year (for a definition of the heat consumption, see the simple temperature calculation form).
• Select the highest outside temperature at which heating is still needed for the house (heating a house is partly done by being in it, and by using household appliances in the house). Thus, normally a house having a temperature of around 20-21 degrees does not need any specific heating above around 16-18 degrees.
• Then press the button below, which converts the given house data plus the selected temperature location to a house heat need curve.
• If so desired, it is instead possible to enter the heat need curve directly. This can be interesting to do to simulate either changed outside temperatures, or changes to the house isolation, or if curve is known through some means. If you specify the house curve yourself, by entering the effect needed per degree celcius in the third box below, then do not press the button below.
 Average heat consumption per year (kwh) Max outside temperature needing heating Average heating need per degree Celsius below Max temperature needing heating (Watt)

(or instead enter degree factor manually and do not press above button)

# Geothermal heat pump definition

The geothermal heat pump is straight forward. It is defined by:

• The COP, which is assumed to be constant for all outside temperatures
• By its maximum output power (again assumed constant for all outside temperatures).
• For the COP calculations presented in the detailed tables available further down, the COP reduction caused by the power needed for circulation pumps, if not included in the stated COP figure, can be included by stating how much yearly consumption the pumps are expected to have. (Some vendors include this in their COP, some do not, most do not).
 Output Power for geothermal heat pump (kW) Average COP per year for geothermal pump Yearly power needed for circulation pump above what is included in stated COP (kWh)

# Heat Pump Effect and COP curve for Air-To-Water

Here the Air-To-Water heat pump is defined. Since the calculations are based on daily temperatures and house needs depending on temperatures, the heat pump must be defined using a COP curve as well as the input power curve for the heat pump.

In order to provide the possibility to calculate on more heat pumps than those for which I have provided data, the data is fetched in two steps.

• By selecting the Air-To-Water pump, and pressing the button to convert the heat pump model selected to heat pump data, the fields defining the Air-To-Water heat pump curves are filled with data from the selection.
• These data can then be altered at will, allowing you to define any behaviour of any heat pump model you want to do calculations on. The curve is based on a third degree curve, and the factors can easily be taken from a diagram using Excel or similar tools. Also, by setting the second and third degree factors to zero, a simple linear curve is easily defined.
• Just like with the house curve, if you want to define the curve data manually, do not press the button after having changed them.
• The specified output power is not used in the calculactions (it is derived from the input power and the COP). Ther value is provided for reference only.
• The specified forward temperature is the forward temperature for the water for which the data are taken. To compare different pumps fairly, the same temperature should be used. A rough estimate is that the COP is improved with about 15 percent per 10 degrees lower forward temperature, in the range of 50-35 degrees Celcius.
 Air-To-Water heat pump model to take data from NIBE F2120-12NIBE F2120-16NIBE F2120-20NIBE F2120-8NIBE Fighter 2020-10NIBE Fighter 2020-14NIBE Fighter 2020-8
 Specified output power for Air-To-Water heat pump (kW) Water Forward temperature data is valid at (Celcius) Minimum operational outside temperature Yearly power needed for circulation pump above what is included in stated COP (kWh)

(or change values manually and do not press the key)

 Factor used to build temperature response curve Input Power (kW) COP Constant Proportional to Outside temperature Proportional to outside temperature squared Proportional to outside temperature raised by three

# Heating curves for house and heat pumps

One important need is to understand at what temperatures the heat pump can meet the heating need of the house.

• The power need curve of the house is plotted below, and compared to the power outputs of the heat pumps selected. The diagrams are shown over a fixed intervall of temperatures. If you experiment with defining your own curves, the diagrams helps verifying the curves.
• Please note, the lines are unfortunately having a pixel resolution, and thus sometimes drawn a little bit above or below where they should be.
mibChart.

# Investment costs

The investment costs are the same as for the simple form for heat cost calculations, and are defined there.

 Geothermal investment, including all (SEK) Air-To-Water investment, including all (SEK)

# Starts and stops

Heat pumps without adjustments of their speed, will be regulated by starting and stopping the heat pump, thus either producing full output, or not producing any heat at all. If there is too little water in the system compared to the size of the pump, or if the difference between the minimum and maximum forward temperature aimed at by the regulator, then there will be many starts and stops every day. The below values are used to calculate number of starts and stops.

 Amount of water circulated in the heating system (liters) Difference between start temperature and stop temperature when regulating the heat pump

# Resulting pay back time

Below is calculated the needed times to get back the investment for the alternatives, assuming that the cost per kwh is 1 SEK.

There is a factor that should be added to the calculations below. If you are situated in a place where the temperature is likely to go below the temperature of the air-to-water heat pump, then the need for additional heating will increase in a jump (from a little extra to using only additional heating). This additional heating might at that time mean you need a larger connection for the house to the power company than with the geothermal heater. The price for that additional connection is not yet included in below calculations, but can easily amount to 750 SEK per year, and even more.

• The electric heater is included as worst case reference, and is thus calculated without an investment in a new electric heater.
• The columns "Air-To-Water heat pump Saving" and "Air-To-Water heat pump years to payback" shows the yearly saving and the number of years it takes to get back the investment for the Air-To-Water alternative, compared to keeping an electric heater. Observe that the less energy is needed for heating, the longer time it takes to get back profit after an investment
• The column "Geothermal saving above Air-To-Water" and "Geothermal heat pump above Air-To-Water years to payback" looks at the additional yearly saving and number of years to achieve a payback for the decision to buy a geothermal pump, compared to buying an Air-To-Water pump. It is thus comparing the time it takes to get back the additional investment for the geothermal pump (the difference in investment) by the improved COP produced by that pump. A more thorough explanation for the reason for doing this kind of comparison is given.
• There are two buttons below, allowing to view more details on both the Air-To-Water pump, and the Geothermal pump. Most essentially, allowing to see needed amount of additional heating, needed due to either the pump being to small for handling all heat, or for the pump not being able to work during all outside temperatures.
• When looking at those details, COP is shown in two columns, one column indicating COP for the output produced by the heat pump, where the only factor reducing the COP is if a value has been defined in the input for circulations pump power not included in stated COP. The other factor shows that COP, further reduced by the additional heating needed by the electrical furnace to achieve the targeted power output.
 Year Max heat need (kW) Electric Heater Cost (SEK) Air-To-Water Heat Pump Saving (SEK) Air-To-Water Heat Pump years to payback Geothermal saving above Air-To-Water (SEK) Geothermal heat pump above Air-To-Water years to payback 1870 6.2 19,616 12,413 5.6 1,001 50.0 1880 6.4 19,612 12,401 5.6 992 50.4 1890 7.8 19,017 12,032 5.8 925 54.1 1900 5.9 18,701 11,951 5.9 872 57.3 1910 6.9 17,799 11,424 6.1 778 64.2 1920 6.1 18,484 11,858 5.9 800 62.5 1930 5.6 16,964 10,985 6.4 670 74.6 1940 8.2 17,995 11,334 6.2 884 56.5 1950 6.6 17,525 11,243 6.2 765 65.4 1960 5.7 17,599 11,265 6.2 803 62.2 1970 5.9 17,042 11,012 6.4 691 72.4 1980 7.1 17,203 10,995 6.4 754 66.3 1990 5.4 16,335 10,608 6.6 615 81.4 2000 5.7 15,824 10,253 6.8 612 81.7

temperature location:

mibChart.

# Resulting pay back times including hot water

Below are similar calculations as those above, but this time assuming that hot water is part of the production from the heat pumps.

• As before, when the heat pumps are not capable to deliver the need, the remaining need is calculated as filled with additional heating from an electric heater.
 Yearly hot water heating need (kW) Geothermal hot water additional investment, above gethermal heating investment (SEK) Air-To-Water hot water additional investment, above Air-To-Water heating investment (SEK)

 Year Electric Heater Cost including hot water (SEK) Air-To-Water Heat Pump Saving including hot water (SEK) Air-To-Water Heat Pump years to payback including hot water Geothermal saving above Air-To-Water including hot water (SEK) Geothermal heat pump above Air-To-Water years to payback including hot water 1870 24,616 15,642 5.1 1,050 47.6 1880 24,612 15,600 5.1 1,039 48.1 1890 24,017 15,238 5.3 990 50.5 1900 23,701 15,191 5.3 942 53.1 1910 22,799 14,672 5.5 877 57.0 1920 23,484 15,098 5.3 879 56.9 1930 21,964 14,255 5.6 790 63.3 1940 22,995 14,525 5.5 915 54.7 1950 22,525 14,494 5.5 862 58.0 1960 22,599 14,508 5.5 885 56.5 1970 22,042 14,278 5.6 793 63.0 1980 22,203 14,228 5.6 836 59.8 1990 21,335 13,885 5.8 724 69.1 2000 20,824 13,523 5.9 725 68.9

temperature location:

mibChart.