Simultaneity factor

The simultaneity factor is an important element in the design of collective borefields for multiple users. Think, for example, of apartment buildings with dozens of apartments connected to a central borefield. Should you take the entire installed peak power into account or not? Read the article to discover everything you need to know!

What is simultaneity?

For the design of a geothermal borefield, it is essential to know the building’s thermal demand—i.e. the peak demand in heating and cooling, as well as the annual energy demand for both. When designing a borefield for a single building (for example, 10 kW of installed heat pump capacity and 15 MWh/year of energy demand), this is straightforward: you simply take the 10 kW as the peak load and the 15 MWh as the energy demand.

Now imagine an apartment building with 25 units. Each unit has an individual heat pump with a capacity of 5 kW and a heating energy demand of 7.5 MWh per year. This gives a total installed capacity of 125 kW and a yearly demand of 187.5 MWh. The question then arises: should we size the borefield based on 100% of the installed capacity, or can we design it for a somewhat lower load?

!Hinweis
Although this article will mainly focus on the heating demand, the same reasoning can be applied to the cooling demand. However, since most of the literature focuses on heating, we use it here as the primary example.

Simultaneity factor

When combining multiple users or apartments on a central system, the peaks in demand do not typically coincide. This is because different dwellings have different occupants—some may be elderly, others may have children, and some may be occupied by individuals living alone—each with varying daily routines and behaviours. As a result, the timing of their peak loads differs. This phenomenon is quantified using the simultaneity factor: the percentage of the installed peak capacity that actually occurs simultaneously. This factor, derived from the empirical work of Winter et al. (2001), is illustrated in the figure below.

!Hinweis
The graph above is derived using the following formula:

$$f(n)=a+\frac{b}{1+\left(\frac{n}{c}\right)^d}$$

where $n$ is the number of connected users to the central system, and $a$ to $d$ are parameters fitted to measured data ($R^2 = 0.95$), with the following values:

• $a$=0.449677646267461
• $b$=0.551234688
• $c$=53.84382392
• $d$=1.76743268

The graph clearly illustrates that as the number of connected users increases, the collective system will ‘experience’ a smaller proportion of the total installed peak power. In our case with 25 apartments, the simultaneity factor is 89%, meaning that of the installed 125 kW, only 111 kW is expected to occur simultaneously. This adjusted value could therefore be used for the geothermal design.

!Hinweis
It is important to highlight that the simultaneity factor is only used to reduce the peak power. The total collective energy demand remains the simple sum of the individual users’ demands.

Historically, this simultaneity factor was developed for designing pipe diameters in collective heating systems and for sizing central boilers. In those cases, the key design parameter was the maximum peak power, regardless of how long the peak lasted. Today, however, when designing a collective borefield, the duration of the peak becomes significantly more relevant and demands additional consideration.

Peak duration

The peak duration refers to the question: “How long does the peak power occur without interruption?” In other words, if a heat pump operates at full capacity, how long will it run continuously? This duration influences both the minimum and maximum average fluid temperatures, much like the effective borehole thermal resistance (see this article for more information). For example, if the heat pump operates continuously for 20 hours, the resulting fluid temperature will be lower than if it only runs for 8 hours.

When multiple dwellings are combined on a single collective borefield, the peak duration also changes, as illustrated in the figure below.

The graph above shows the individual peak power profiles of three separate buildings. As can be seen, their peak times do not align, and the resulting collective power profile (in blue) has a lower peak power than the sum of the three. This aligns with our understanding of the simultaneity factor, which explains why the peak demand of the total system is lower than the sum of individual peak demands.

However, regarding peak durations, while each building has the same individual peak duration (as shown by the horizontal bars), the peak duration of the combined profile differs. It is neither the sum of the individual durations—which would significantly overestimate the actual value—nor equal to them.

Therefore, it is not sufficient to merely adjust the peak power using the simultaneity factor while keeping the original peak duration. Especially in larger collective systems, the true peak duration can change substantially and must be treated accordingly.

Below, we outline two possible approaches to address this:

• Dynamic simulation: This involves simulating the combined demand profiles with an hourly temporal resolution to derive a realistic, aggregate peak duration.
• Heuristic approximation: This relies on empirical or statistical rules of thumb to estimate the likely peak duration of the collective system.

Dynamic simulation

To properly address this issue, the most reliable solution is to perform a dynamic simulation of the entire building/collective system. This approach accounts for varying occupancy behaviours, thermal inertia, solar gains, and other influencing factors. The outcome of such a simulation is an hourly demand profile for both heating and cooling, like the one shown below:

When the load demand is available at this fine level of time resolution, there is no need to estimate the peak duration manually—it is inherently included within the profile itself.

However, when working with monthly load profiles, this high-resolution data is not available, and therefore the peak duration must be specified explicitly for the borefield design.

Heuristic approximation

Another way to estimate the peak duration of a collective system is to use a heuristic approach that allows us to scale the peak duration of a single user to that of the entire collective system. At present, no such heuristic is documented in the literature.

Given the importance of this parameter, we propose a first suggestion here, inspired by the Central Limit Theorem from statistics.

$$t_{duration, collective} \propto t_{duration, individual} \cdot \sqrt{n}$$ where $n$ is again the number of connected users to the collective system. This gives the graph below.

!Hinweis
The Central Limit Theorem describes the relationship between a population and the distribution of the sample means from that population. Specifically, it states that the standard deviation of the sample mean (also called the standard error) decreases with the square root of the number of independent samples $n$. Assuming that the buildings are more or less identical and behave independently, and interpreting the standard deviation as a proxy for peak duration, this same scaling factor $\sqrt{n}$​ can be used as a first-order approximation to estimate the aggregated peak duration for $n$ similar buildings.

 

Returning to the example of the 25 apartments we introduced earlier:

• Installed heating capacity: 125 kW
• Annual heating demand: 187.5 MWh
• Peak duration: 8 hours (per apartment)

By applying both the simultaneity factor and a scaling factor for the peak duration, we can design the borefield based on the following parameters:

• Effective peak load: 111 kW (using an 89% simultaneity factor)
• Annual heating demand: 187.5 MWh
• Peak duration: 40 hours (using a scaling factor of 5)

!Caution
Please note that the approach described above has not yet been validated by academic literature and should therefore be applied with caution.

Schlussfolgerung

This article explored the concept of simultaneity in the context of designing a central borefield for multiple decentralised users or heat pumps. This situation typically arises when several apartments within a single building are connected to a shared borehole system. The simultaneity factor can then be used to convert the total installed peak power into the effective power relevant for geothermal system design.

In addition, the article addressed the challenge of determining the peak duration when using a monthly simulation resolution. Although no literature currently exists on this topic, a heuristic approach based on the Central Limit Theorem was proposed. This method suggests scaling the peak duration of an individual user to that of the collective system by a factor of $\sqrt{n}$.

Literaturverzeichnis

• Sehen Sie sich unsere Videoerklärung auf unserer YouTube-Seite an, indem Sie klicken hier.
• Winter, W., T. Haslauer & I. Obernberger (2001): „Untersuchungen der Gleichzeitigkeit in kleinen und mittleren Nahwärmenetzen“. Euroheat & Power, Bd. 09&10/2001: S. 1-17