Optimal Sizing of Heat Pumps and Thermal Storage for District Heating
– A Cost and Performance Analysis Using Perfect Forecast Optimisation
Why Read This Article?
The shift towards electrification in district heating creates opportunities to reduce carbon emissions and operating costs, if systems are sized and operated correctly. This white paper examines the optimal sizing of a heat pump and accumulation tank for supplying heat to a single average household with an annual heat demand of 18.1 MWh, based on scaled real-world data from 2020-2024.
Using a perfect forecast of weather (driving demand) and electricity prices, we optimise operation to determine cost-optimal heat pump capacity and tank size. Results are presented for Western Denmark (DK1) first, then Eastern Denmark (DK2).
Introduction
In district heating, the sizing of key components like heat pumps and thermal-storage tanks has a major impact on capital expenditure (CAPEX), operating expenditure (OPEX), and overall heat prices. Oversizing increases investment costs unnecessarily, while undersizing can force reliance on more expensive backup systems.
We model a system where a heat pump is supported by a 6 kW electric boiler, capable of covering the observed peak demand of 5.32 kW. The model evaluates a grid of heat-pump and tank sizes to balance upfront costs and operational efficiency.
System Configuration and Methodology
The simulated system uses the following assumptions:
- Total annual heat demand: 18.1 MWh
- Peak observed load: 5.32 kW
- Electric boiler capacity: 6 kW (covers peak load)
- CAPEX for heat pump: 6.5 million DKK per MW
- Annual maintenance cost for heat pump: 38,000 DKK per MW
- CAPEX for tank: 2,000 DKK per m³
Operation is optimised with perfect foresight of electricity prices and heat demand, deciding when to produce heat with the heat pump and/or electric boiler and when to charge/discharge the tank. We compute net present cost (NPC) over a lifetime of 20 years at a discount rate of 4%, and report average OPEX and average heat price accordingly.
Results
For each price area, we present a single figure that contains three subplots across the same sizing grid: (i) CAPEX, (ii) average OPEX, and (iii) average heat price. In all figures, the x-axis is tank size (m³) and the y-axis is heat-pump size (kW).
Western Denmark (DK1)
Eastern Denmark (DK2)
Key Findings
- DK1 (Western Denmark): Optimal configuration is a 3.5 kW heat pump with a 1.5 m³ tank.
- DK2 (Eastern Denmark): Optimal configuration is a 3.5 kW heat pump with a 2 m³ tank.
- Configurations around the optimal configuration provide a similar average heat cost, highlighting that small deviations from optimal sizing can be viable to meet other requirements such as security of supply.
- The addition of a thermal storage tank increases CAPEX but can also decrease OPEX if balanced with the heat-pump capacity and demand.
- Using production optimisation shifts production to low-price/high-COP hours, lowering the average heat price.
Additional Insights
Scaling to District Heating Networks
Since the data is scaled to a representative household, results can be linearly extrapolated for a larger network if the number of households is known. For example, with the DK1 optimal configuration (3.5 kW heat pump and 1.5 m³ tank) and 800 households, the aggregated sizing would be:
This provides a quick method for preliminary planning of larger district heating systems.
Rule of Thumb Limitations
The results presented here should be considered a rule of thumb that assumes all consumers on the network are average households. In reality, the optimal sizing can vary significantly depending on the actual mix of consumers, including the proportion of industrial or commercial users and seasonal variations in demand.
Potential for Energy Balancing
The system could also be used for energy grid balancing by operating the heat pump when electricity demand is low and supply is high, storing surplus heat in the tank, and reducing production during high-demand, low-supply periods. In such a strategy, the optimal tank size will likely be larger than the values found in this study, as more storage capacity enables greater flexibility. This would also be expected to reduce the average heat price further.
Conclusion
Careful co-sizing of the heat pump and accumulation tank yields substantial savings in district heating. For the average-load case analysed here, compact storage volumes paired with a modest 3.5 kW heat pump are cost-optimal in both DK1 and DK2, with slightly larger storage favoured in DK2. Under perfect foresight, the system reliably exploits low-price periods while meeting peak demand via the storage tank and 6 kW boiler.
Contact Clean Heat Partners at contact@cleanheatpartners.com.