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# Diversity factors in district heating networks

Since power peaks of all consumers of a district heating networks never occur exactly at the same time, the necessary heat output of the heating center is lower than the sum of all power peaks of the consumers.

## Diversity factors

Diversity (or simultaneity) refers to the temporal dispersion of occurring power peaks of individual consumers, which leads to the fact that the power peak of the heat network supply is lower than the sum of the power peaks of all consumers. The diversity factor thus describes the ratio of the maximum load at the energy hub and the sum of the nominal powers of the consumers. This can be expressed as follows: $$DF = \frac{\sum_{i=1}^{m} P_i(t_{max})}{\sum_{i=1}^{m} P_{N,i}}$$ Here $$P_i(t_{max})$$ is the power consumed by the consumer $$i$$ at the time of the maximum power peak of the district heating network and $$P_{N,i}$$ the nominal power of the individual consumers. Usually, the diversity factor is between 0.5 and 1. Furthermore, the more consumers are supplied by a district heating network, the lower is the diversity factor. A uniform distribution of the nominal power among the consumers as well as a high temporal dispersion in the load profiles leads to a lower diversity factor. Once the diversity factor has been determined for a district heating network, it can be used to calculate the required generator output at the energy hub.

In the nPro tool, diversity factors can be taken into account to smooth district heating and cooling load profiles.

## How do diversity factors affect annual demand profiles?

The conversion of a cumulated annual profile of all consumers into an annual profile that takes the diversity factor into account is complex. A mathematical approach has been developed for the nPro tool, which makes it possible to convert annual profiles without diversity into annual profiles with a defined diversity factor. With this transformation, the maximum power of the demand profile is reduced by the defined diversity factor. At the same time, the total annual demand (area under the annual profile) remains the same. This is a necessary condition, because the consideration of diversity does not lead to a change of the total demand, but only to a reduction of the peak load. If diversity is not taken into account for district heating networks, this can lead to an oversizing of the generation capacities in the energy hub.

## What is the diversity factor?

For district heating networks with a homogeneous consumer structure (e.g. predominantly residential buildings), the diversity factor can be estimated using approximation formulas from Winter et al: $$DF = a+\frac{b}{1+(\frac{n}{c})^d}$$ Here, $$n$$ is the number of connected buildings. $$a$$, $$b$$, $$c$$ are fitted parameters from experiments. The course of the diversity factor over the number of connected buildings determined by Winter et al. is shown in Figure 1.

Figure 1: Diversity factors for different numbers of connected buildings

## Sources

1. Matthias Gaderer: Wärmeversorgung mit fester Biomasse bei kleiner Leistung. Dissertation. Technische Universität München. 2008.
2. Winter, W., T. Haslauer & I. Obernberger (2001): „Untersuchungen der Gleichzeitigkeit in kleinen und mittleren Nahwärmenetzen“. Euroheat & Power, Bd. 09&10/2001: S. 1-17
3. Arbeitsgemeinschaft QM Fernwärme: Planungshandbuch Fernwärme. EnergieSchweiz, Bundesamt für Energie BFE. 2017.
4. Untersuchungen der Gleichzeitigkeit in kleinen und mittleren Nahwärmenetzen, Euroheat & Power, 09&10/2001.

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