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Mats Bengtsson

Temperature based form, including water temperature effects, for calculating heat savings yourself

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 and also on the Temperature based form for calculating heat savings yourself. It is meant to be used to provide information enough to make buying decisions, but can also be used to try out and understand alternative choices and the effects of changing size on radiators or other factors affecting the heating water temepratures. The form, just like the temperature based, basically only needs three values in order to do meaningful calculations (where you live, how much heat the house needs, and what heat pump to model). Basically, in order to use the form, be shure to have pressed each read conversion and calculate button at least once, or that you have manually provided the data needed.

There is a lot of possible further extensions of detailing the calculations, a number of them defined below, but also with a lot of additions specifically to handle calculations based on the effects of having varying temperatures in the forward water, and predefined temperatures in the warm household water heating, defined further down. The calculations independent of varying forward temperatures are:

  • 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 in the first part of the form is that all calculations assume that the radiators are large enough to deliver the needed heating without needing water temperatures above the heat pumps forward water temperature limits, and all calculations are done at the temperature for which the hea pump factors, like COP and powers, are defined. This can all be seen as calculations based on fixed condensation (in fact very strict fixed condensation, there are no varying of the forward water temeprature at all during the seasons of the year).

For the second part of the form, results are shown after including effects from varying the heat forward temperature need, decided hot household water temperature and adjusting for passingmax heat pump temperatures.

Extensions in calculations effects from varying temperatures in the forward water, and predefined temperatures in the warm household water

The results of these calculations are shown in the later part of the form. The calculations are based on the same information as is used for the rest of the form, plus:

  • The forward water temperature is assumed to be varying with the outside temperature, thus taing into account that the radiators need to be warmer the colder it is outside, and that the heat pumps deliver lower COP and less power the warmer the forward water need to be.
  • The hot household water temperature is assumed to be predefined, and at another level than the forward water. Thus effectively leading to a worse COP than for the forward water while heated
  • The maximum temperature possible to produce with the heat pump is taken into account. Thus adding increased electrical heating need when the forward water exceeds what the heat pump can produce

There is a number of limitations in the calculations:

  • The assumption is that the change of COP due to the change of water temperature is proportional to the distance from the known COP/Input/Output curve for the heat pump (which may be non linear). This assumption is good, but not exact
  • If the hot household water temperature wanted exceeds the heat pump maximum temperature, assumption is that the hot water consumption empties and refills the hot water tub, or preheats the water to the heat pump maximum and then adds to that temperature in a second storage. No estimates are made of energy losses from the tank to the surrounding environment, or for germ fighting increases ot the hot water temeprature. Thus the calculations are using the heat pump for a part of the heating and eletric addition for the rest. In real world, this might not be the case, and the cost for heating the hot water when passing the maximum temperature for the heat pump will be higher than shown in the calculations. Maybe a future addition will add assumptions on the hot water tank size.
  • If the forward water temperature needed exceeds the heat pump maximum temperature, the assumption is made that the water heating needed takes place in the heat pump up to its maximum temperature and that additional electric heating is used afterwards to achieve the desired temperature. It assumes the control system to work well and never stopping the heat pump (except when minimum outside temperature is passed) if the heat pump is not enough for the heating. It also assumes the electrically added heating to be well regulated (a fairly stable output temperature instead of the on/off behavoiur used in some heat pumps). The last means that the input temperature to the heat pump after its maximum temperature is exceeded will be the needed forward temperature minus the temparature drop over the radiators (assumed to be 10 degrees Celcius). A control system not behaving like described above will lead to higher costs than calculated when passing the heat pump maximum temperature. Also, not only the maximum output temperature but also the maximum input temperature of the heat pump could be considered in the calculations in the future.

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
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 unless you want to start over again.
House curve definition
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. Calculations are based on daily temperatures and house needs depending on temperatures. Even though the heat pump is defined using a COP curve as well as the output power curve, these values are for the geothermal heat pump assumed to be independent of outside temperature, thus easily defined as constants.

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 Geothermal pump, and pressing the button to convert the heat pump model selected to heat pump data. The fields defining the Geothermal 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 outside temperature independent heat pump model you want to do calculations on.
  • Just like with the house curve, if you want to define the curve data manually, do not press the conversion button after having changed data manually unless you want to start over again.
  • 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).
Geothermal heat pump model selection
Geothermal heat pump model to take data from
Yearly power needed for circulation pump above what is included in stated COP (kWh)


(or If you select to open and change Geothermal heat pump data manually, do not after that press the above key to convert geothermal heat pump model to heat pump data unless you want to start over again).

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. Unlike the Geothermal heat pump, these curves are very much depending on the outside temperature, in fact, modelling them as straight lines would not work very well, and thus the data to define these dependencies use enough factors to be able to model a curve instead of a line.

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. Another good way to do the modelling is to first take data from one of the provided heat pumps, and then change only the constant factors (thus keeping the curve shapes, but altering their levels)
  • Just like with the house curve, if you want to define the curve data manually, do not press the button after having changed them unless you want to start over again.
  • The specified output power is not used in the calculactions (it is derived from the input power and the COP). The value is provided for reference only.
  • The specified forward temperature is the forward temperature for the water for which the data is 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 50-30 degrees Celcius.
Air-To-Water Heat Pump Model Selection
Air-To-Water heat pump model to take data from
Yearly power needed for circulation pump above what is included in stated COP (kWh)


(or If you select to open and change air-to-water heat pump data manually, do not after that press the above key to convert air-to-water heat pump model to heat pump data unless you want to start over again).

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, and from which temperatures it need additional assistance (in this form calculated as need for electrical additional heating).

  • 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.
  • If there is no curve for the house need, air-to-water heat pump, or for the Geothermal heat pump, or the curves are steady at 0, then you have not yet pressed the corresponding calculation buttons for those respective areas above.
  • Please note, the lines are unfortunately having a pixel resolution, and thus sometimes drawn a little bit above or below where they should be.
Chart.

Investment costs

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

Base cost assumptions for calculations
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 is too narrow, then there will be many starts and stops every day. The below values are used to calculate number of starts and stops.

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

Savings and pay back times excluding effects from varying water temperatures

Below is calculated the needed time to get back the investment for the alternatives, assuming that the cost per kwh is 1 SEK (so the output could just as well be viewed as being in kWh).

  • 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 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 7.0 22,024 14,071 0.0 814 0.0
1880 7.2 22,019 14,045 0.0 805 0.0
1890 8.7 21,351 13,648 0.0 735 0.0
1900 6.6 20,996 13,579 0.0 695 0.0
1910 7.8 19,983 12,987 0.0 625 0.0
1920 6.8 20,752 13,485 0.0 611 0.0
1930 6.3 19,046 12,504 0.0 537 0.0
1940 9.2 20,203 12,844 0.0 658 0.0
1950 7.4 19,676 12,798 0.0 598 0.0
1960 6.4 19,759 12,827 0.0 614 0.0
1970 6.6 19,133 12,542 0.0 531 0.0
1980 8.0 19,314 12,507 0.0 564 0.0
1990 6.1 18,339 12,093 0.0 459 0.0
2000 6.4 17,766 11,698 0.0 449 0.0

temperature location: Copenhagen

Chart.


Savings and pay back times including hot household water but excluding effects from varying water temperatures

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.
Base assumptions for hot water calculations
Factors used to define heat pump Factors independent of varying water temperature effects Factors used to handle varying water temperature effects
Yearly hot water heating need (kW) As defined to the left
Desired standard hot water temperature (fixed hot water temperature for household hot water, degrees Celcius) Not applicable
Geothermal hot water additional investment, above gethermal heating investment (SEK) As defined to the left
Air-To-Water investment, including all (SEK) As defined to the left

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 27,024 17,404 0.0 511 0.0
1880 27,019 17,352 0.0 520 0.0
1890 26,351 16,969 0.0 503 0.0
1900 25,996 16,941 0.0 445 0.0
1910 24,983 16,377 0.0 432 0.0
1920 25,752 16,845 0.0 418 0.0
1930 24,046 15,929 0.0 381 0.0
1940 25,203 16,158 0.0 429 0.0
1950 24,676 16,194 0.0 396 0.0
1960 24,759 16,213 0.0 363 0.0
1970 24,133 15,960 0.0 346 0.0
1980 24,314 15,879 0.0 371 0.0
1990 23,339 15,529 0.0 306 0.0
2000 22,766 15,139 0.0 279 0.0

temperature location: Copenhagen

Chart.
Chart.


Savings and payback times including effects from varying water temperatures

The calculations done so far in this form (all above this line) are all done based on the water heating temperature is fixed (the base data fetched for the heat pumps using the drop downs above default at 50 degree Celcius). However, when the outside temperature varies, so does the temperature needed to heat the house. There is two ways to handle this:

  • Fixed condensation (as calculated above based on the temperature for which the heat pump factors are given). All water is always heated to a fixed temperature, and then that water is used for the heating and the hot water
  • Floating condensation (as calculated below). The water is heated to the temperature needed for the current circumstances.

Floating condensation has a number of advantages:

  • There is no need for the additional circulation pump needed for the fixed condensation
  • The heat pump always works against a water temperature that is as low as it can be for the need, meaning it produces the best COP during the circumstance

The calculations for floating condensation is harder to do. They also need more data in order to be done in the correct way (for example the heat pump input power and COP does not only vary based on outside temperature, but also based on current water temperature. The below calculations takes part of this into consideration. However, since more assumptions need to be made, these calculations are less reliable, and should thus only be used as comparison figures, not as absolute figures.

Water temperatures needed for water temperature based heating calculations
Low outside temperature forward water temperature targeted by heat pump (temperature known to be needed at a low outside temperature, at as low temperature as is known, in degrees Celcius)
Outside temperature at which above forward water temperature targeted by heat pump is valid (degrees Celcius)
Inside house temperature aimed at (Celcius)
Resulting forward water need curve (degrees Celcius needed to increase the forward water per degree Celcius the outside temperature is lower than the outside temperature below which heating is needed
Results for water temperature based Heat Pump heating calculations
Year Max heat need (kW) Electric Heater Cost (SEK) Air-To-Water water temperature based Heat Pump Saving (SEK) Air-To-Water water temperature based Heat Pump years to payback Geothermal water temperature based saving above Air-To-Water (SEK) Geothermal water temperature based heat pump above Air-To-Water years to payback
1870 7.0 22,024 14,322 0.0 2,907 0.0
1880 7.2 22,019 14,311 0.0 2,873 0.0
1890 8.7 21,351 14,143 0.0 2,533 0.0
1900 6.6 20,996 14,202 0.0 2,413 0.0
1910 7.8 19,983 13,835 0.0 2,047 0.0
1920 6.8 20,752 14,348 0.0 2,113 0.0
1930 6.3 19,046 13,626 0.0 1,656 0.0
1940 9.2 20,203 13,245 0.0 2,394 0.0
1950 7.4 19,676 13,648 0.0 1,998 0.0
1960 6.4 19,759 13,460 0.0 2,223 0.0
1970 6.6 19,133 13,559 0.0 1,763 0.0
1980 8.0 19,314 13,264 0.0 1,994 0.0
1990 6.1 18,339 13,250 0.0 1,506 0.0
2000 6.4 17,766 12,745 0.0 1,530 0.0


Resulting payback times for Water temperature based calculations including both heating and hot water
Year Electric Heater Cost including hot water (SEK) Air-To-Water water temperature based Heat Pump Saving including hot water (SEK) Air-To-Water water temperature based Heat Pump years to payback including hot water Geothermal water temperature based saving above Air-To-Water including hot water (SEK) Geothermal water temperature based heat pump above Air-To-Water years to payback including hot water
1870 27,024 16,600 0.0 3,894 0.0
1880 27,019 16,596 0.0 3,819 0.0
1890 26,351 16,550 0.0 3,391 0.0
1900 25,996 16,590 0.0 3,326 0.0
1910 24,983 16,342 0.0 2,885 0.0
1920 25,752 16,849 0.0 2,930 0.0
1930 24,046 16,254 0.0 2,422 0.0
1940 25,203 15,780 0.0 3,072 0.0
1950 24,676 16,183 0.0 2,813 0.0
1960 24,759 15,965 0.0 3,039 0.0
1970 24,133 16,192 0.0 2,500 0.0
1980 24,314 15,863 0.0 2,707 0.0
1990 23,339 15,993 0.0 2,155 0.0
2000 22,766 15,484 0.0 2,181 0.0
Chart.


Headlines

Never trade stocks without having tested your system. In fact, most trading systems are not profitable if tested over many stocks. full story...

Do not invest in heating equipment without having compared the alternatives, not only to current situation, but also to each other. Full story...

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