Heating Curves — Fundamentals and Application

The heating curve describes the relationship between the outdoor temperature and the required supply temperature of a heating system. As the outdoor temperature drops, the supply temperature rises to hold the desired room temperature. Typical design supply temperatures range from 30—35 °C for underfloor heating up to 70—75 °C for conventional radiators, and every Kelvin of lower supply temperature improves the heat pump COP by roughly 2—3 %. The curve therefore drives the efficiency of heat pumps, sets the network supply temperature, and shapes the achievable seasonal performance factors.

What is a heating curve?

A heating curve (also known as a supply temperature characteristic) defines which supply temperature $T_{\text{VL}}$ the heating system must provide at a given outdoor temperature $T_{\text{a}}$ in order to achieve the desired room temperature $T_{\text{Room}}$. As the outdoor temperature drops, the building’s heat demand increases, and the supply temperature must be raised accordingly.

The simplest relationship is linear:

$T_{\text{VL}} = T_{\text{VL,min}} + s \cdot (T_{\text{a,design}} - T_{\text{a}})$

with the slope (also called gradient) $s$ of the heating curve, the minimum supply temperature $T_{\text{VL,min}}$ (at the heating limit temperature) and the design outdoor temperature $T_{\text{a,design}}$.

The slope follows from the design boundary conditions:

$s = \frac{T_{\text{VL,design}} - T_{\text{VL,min}}}{T_{\text{a,design}} - T_{\text{a,heating limit}}}$

Example calculation

For an underfloor heating system with the following design data:

• Design outdoor temperature: $T_{\text{a,design}} = -12$ °C
• Design supply temperature: $T_{\text{VL,design}} = 35$ °C
• Heating limit temperature: $T_{\text{a,heating limit}} = 15$ °C
• Supply temperature at the heating limit: $T_{\text{VL,min}} = 22$ °C

the slope becomes:

$s = \frac{35 - 22}{(-12) - 15} = \frac{13}{-27} \approx -0{,}48 \; \text{K/K}$

At an outdoor temperature of 0 °C, the supply temperature is:

$T_{\text{VL}}(0\;°\text{C}) = 22 + 0{,}48 \cdot (15 - 0) = 22 + 7{,}2 = 29{,}2 \; °\text{C}$

In practice, heating curves are not always modelled as strictly linear. For radiators in particular, a slightly exponential shape is often used, which accounts for their non-linear heat transfer behaviour.

Typical heating curves in comparison

The following table shows typical design supply temperatures and the resulting heating curve slopes for various heat emission systems (at a design outdoor temperature of -12 °C):

The difference is considerable: while underfloor heating requires only 35 °C supply temperature even on the coldest day, a radiator in an older building requires 75 °C. This has direct consequences for the choice of heat generation and for network sizing.

Influence on the COP of heat pumps

The Coefficient of Performance (COP) of a heat pump depends above all on the temperature difference between the heat source and the heat sink. The theoretical Carnot COP is:

$\text{COP}_{\text{Carnot}} = \frac{T_{\text{VL}}}{T_{\text{VL}} - T_{\text{source}}}$

where the temperatures must be entered in Kelvin. In practice, heat pumps reach about 40 to 55 % of the Carnot COP (quality grade).

For a source temperature of 0 °C (273 K) and various supply temperatures, a quality grade of 0.50 yields:

Every Kelvin of lower supply temperature improves the COP by roughly 2 to 3 %. An underfloor heating system with a 35 °C supply temperature therefore reaches a COP about 75 % higher than a conventional radiator running at 70 °C. Over the year, that gap dominates the energy balance.

Heating curve and district heating network planning

Network supply temperature

The heating curve of the most critical consumer, the one with the highest supply temperature requirement, determines the required network supply temperature. In a network with mixed consumer types, such as new buildings with underfloor heating alongside existing buildings with radiators, the network supply temperature must satisfy every consumer plus the approach temperature of the transfer stations:

$T_{\text{VL,network}}(T_a) = \max_i \left[ T_{\text{VL},i}(T_a) \right] + \Delta T_{\text{approach}}$

A single consumer with a high supply temperature requirement can thus raise the temperature level of the whole network. In practice, planners then check whether local reheating for that consumer, for example via a decentralised heat pump, is more economical than lifting the network temperature for everyone.

Gliding network operation

In modern district heating networks, the network supply temperature follows the outdoor temperature (gliding operation). At mild temperatures it drops, which markedly reduces the heat losses. The network heating curve forms the envelope of all consumer heating curves:

• In winter at -12 °C: network supply temperature e.g. 75 °C
• In the transition period at 5 °C: network supply temperature e.g. 55 °C
• In summer (DHW only): network supply temperature e.g. 60 to 65 °C

The summer reduction is limited in networks that only have to provide domestic hot water, since the supply temperature for DHW preparation must be at least 58 to 65 °C.

Application in cold district heating networks

In cold district heating networks, the classical network heating curve no longer applies, since the network runs at a low, almost constant temperature level. The heating curve moves entirely to the building-side heat pump, which raises the temperature level for each building individually. Every building then generates its own optimum supply temperature, without the compromises that differing consumer requirements would otherwise force.

Optimising the heating curve

A curve set too steep produces unnecessarily high supply temperatures, and with them higher network losses, a lower heat pump COP and higher energy consumption. A curve set too flat leaves the rooms under-heated at low outdoor temperatures. Finding the optimum means tuning the curve to the building, the heat emission surfaces and the actual user behaviour. In practice, this fine-tuning happens during the first year of operation through monitoring and readjustment.

Recommended approach:

1. Perform a heat load calculation according to DIN EN 12831
2. Dimension the heat emission surfaces and derive the design supply temperature from them
3. Calculate the heating curve and store it in the control system
4. Adjust the parallel shift if necessary (vertical shift of the curve by 2 to 3 K in case of systematic under- or over-supply)

The heating curve as a planning parameter

The heating curve is more than a control setting. It is a planning parameter that governs the efficiency of the entire heat supply system. Low supply temperatures, made possible by surface heating systems and well-insulated buildings, are the key to high heat pump performance factors and low network losses. When planning a district heating network, the heating curve of every connected building should be known, because it determines the network supply temperature and therefore the network losses. VICUS Districts accounts for the heating curves of all consumers in the network design, while VICUS Buildings derives the building-side heating curve from the dynamic building simulation. Cold district heating sidesteps the problem entirely, since the decentralised heat pumps supply each building on their own.

Further reading: Sizing of Heat Transfer Stations — station control and the role of the heating curve, Network Temperatures in District Heating Networks — how supply temperature design shapes the entire network, Low-Temperature District Heating: Fundamentals — low-temperature operation where building-side heating curves become critical, Dynamic Building Simulation — using simulation to predict heating loads and derive optimal curves.

References and Standards

• DIN EN 12831 — Energy performance of buildings — Method for calculation of the design heat load
• VDI 6030 Part 1 — Designing room heating systems — Fundamentals and design of room heating systems
• DIN EN 12828 — Heating systems in buildings — Design for water-based heating systems