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# Heat loss calculation for heat networks

Heat losses play an important role in the planning of heat networks. Especially for 5th generation district heating and cooling networks, heat gains from the ground must also often be estimated. On this page you find a short documentation of the calculation method used in the nPro tool.

## Heat losses: calculation and equations

Various calculation approaches are available in nPro for calculating heat losses: For classic heat networks, rough estimates for heat losses are often sufficient in an early planning phase. For this purpose, the losses can be specified in nPro as a relative share of the heat generation in the energy hub or as absolute power loss. Alternatively, the sections of the heat network can also be defined in more detail. For a detailed calculation, the insulation layer, the installation depth, the distance between supply and return pipe, pipe diameters, etc. must then be described for each pipe section. In this case, the calculation is based on the Standard DIN EN 13941. The formulae of DIN EN 13941 calculate heat losses or gains for a quasi-stationary operation of a heating network for different temperature levels with a high degree of accuracy. For a detailed description of the formulae, we refer to the standard.

In the nPro tool, heat losses can be calculated for different network temperatures, installation depths and soil conditions depending on pipe diameter and insulation thickness.

## Heat gains and cold gains

In conventional, hot heat networks with a high supply temperature, there is only a heat transfer from the heat transfer medium (pipe) to the surrounding ground. Since the network is only used for heating, this heat transfer to the surroundings automatically represents heat losses. However, in 5GDHC networks with very low network temperatures, the surrounding ground may be warmer than the fluid in the pipe at some point. In this case, heat is transferred from the ground to the pipe. If heating is predominant at this time, this heat transfer represents a heat gain because less heat has to be fed into the heating network at the energy hub. In the case of only heat supply, the concept of heat gains and losses is simple to understand. However, it becomes more complex when additional cooling is provided with the (cold) heat network. For example, in summer, heat from the buildings is fed into the heating network for cooling purposes. In this case, if there is a heat transfer from the pipe to the ground, the energy hub has to remove less heat from the network (provide less cooling). The transferred heat would therefore be called cooling gain. If, on the other hand, there is a heat flow from the ground into the heating network, this would be a cooling loss because the energy hub has to generate more cooling as a result. This means, whether a heat flow represents a gain or a loss depends not only on its direction (pipe to ground or ground to pipe), but also on whether the energy hub is in heating or cooling mode. There are therefore 4 cases to distinguish. These are shown as examples in Table 1. The first and second columns describe the heating and cooling demand of all buildings excluding ground gains/losses. The third column describes the heat flow from the pipe to the ground (positive), or from the ground to the pipe (negative). The fourth column is the net demand, i.e. heat demand minus cooling demand plus heat flow (from pipe to ground). If the value in the 4th column is positive, it is transferred to the 5th column. If, on the other hand, the value is negative, it is transferred to the 6th column. The last two columns describe whether the heat flow from the pipe to the ground increases or decreases the heat or cooling demand at the energy hub. In the first row, the heat demand increases from 10 kW to 12 kW due to the losses. The value in the penultimate column is therefore negative and there is a heat loss.

Table 1: Calculation approach for heat losses and gains and cooling losses and gains.
Heat demand Cooling demand Heat flow from pipe to ground Heating demand - cooling demand + heat flow Heat demand with losses Cooling demand with losses Heat gains/losses Cooling gains/losses
10 kW 0 kW 2 kW 12 kW 12 kW 0 kW -2 kW 0 kW
10 kW 0 kW -2 kW 8 kW 8 kW 0 kW 2 kW 0 kW
0 kW 10 kW 2 kW -8 kW 0 kW 8 kW 0 kW 2 kW
0 kW 10 kW -2 kW -12 kW 0 kW 12 kW 0 kW -2 kW
2 kW 0 kW 5 kW 7 kW 7 kW 0 kW -5 kW 0 kW
2 kW 0 kW -5 kW -3 kW 0 kW 3 kW 2 kW -3 kW
0 kW 2 kW 5 kW 3 kW 3 kW 0 kW -3 kW 2 kW
0 kW 2 kW -5 kW -7 kW 0 kW 7 kW 0 kW -5 kW

The last two columns (heat gains and losses, and cooling gains and losses) can now be split into pure gains and losses: If the number is positive, there are heat gains (e.g. 2nd row: 2 kW), if it is negative, there are heat losses (e.g. 1st row: 2 kW). Similarly for cooling gains and losses: If the number in the last column of the table is positive, cooling gains are present (e.g. 3rd row), if it is negative, cooling losses are present (4th row).

## Validation of the loss calculation

For the comparison with other calculation approaches, the scientific study by Madan et al.  is used. In this study, the network losses are determined for different network parameters with different outdoor conditions (summer/winter case). The investigated temperature range from high-temperature heat networks with temperatures above 100 °C to 5th generation district heating and cooling networks with temperatures of around 10 °C. For the calculation, a thermal conductivity of the ground of 1.2 W/(m K), a thermal conductivity of the insulation of 0.027 W/(m K) and an installation stiffness of 0.9575 m were assumed. The exact calculation parameters can be found in the study. The ground temperatures were also taken from the data in the study. Tables 2 and 3 show the heat losses for the winter and summer cases, respectively. It can be seen that the method for calculating heat loss according to the DIN EN 13941 standard practically corresponds to the model according to Kvisgaard/Hadvig and the results obtained are almost identical. The Wallenten model  differs from the Kvisgaard/Hadvig model in the choice of ground temperature, which leads to minor but significant deviations in the results. It should be noted that the calculation approach described in the standard should only be used for heating networks up to a length of about 20 km, as it assumes that the network temperatures do not change significantly over the length of the network. In very large networks with high losses, however, the losses in the branches of the network are lower, as the losses here result in a lower network temperature.

Table 2: Comparison of the length-specific heat losses for the winter case between the data from the scientific article by Madan et al.  and the methodology implemented in nPro according to DIN EN 13941.
Network temperatures nPro
(DIN EN 13941)
Wallenten
133/60 °C 69 W/m 69 W/m 72 W/m
100/55 °C 54,8 W/m 55 W/m 58 W/m
80/45 °C 43,5 W/m 45 W/m 49 W/m
56/35 °C 30,7 W/m 30 W/m 34 W/m
8/15 °C 5,2 W/m 5 W/m 9 W/m
Table 2: Comparison of the length-specific heat losses for the summer case between the data from the scientific article by Madan et al.  and the methodology implemented in nPro according to DIN EN 13941.
Network temperatures nPro
(DIN EN 13941)
Wallenten
90/20 °C 30,1 W/m 30 W/m 27,5 W/m
69/20 °C 22,2 W/m 22,5 W/m 19,5 W/m
70/45 °C 32 W/m 32,5 W/m 29,5 W/m
56/35 °C 23 W/m 23 W/m 20,5 W/m
12/6 °C -4,4 W/m -4,5 W/m -7 W/m

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