In today’s drive to save energy on heating and protect the environment, heat pumps are increasingly coming to the fore. They are a genuinely viable alternative to conventional types of heating; however, the initial costs of adopting this technology are higher, so the return on such an investment needs to be weighed across the whole spectrum of economic considerations.
The first theoretical foundations for the future design of heat engines were defined as early as the beginning of the 19th century by Léonard Sadi Carnot, who established the fundamental relationships between energy and work in a closed system. These relationships are universally valid and to this day form the framework that limits the theoretical maximum efficiency of heat engines, which include heat pumps as well as, for example, combustion engines or thermal power plants.The basic idea is that if a gas is compressed in an enclosed space, the total amount of thermal energy it contains increases by the energy supplied in the form of the mechanical work needed for compression. Since the volume of the gas decreases after compression and its energy increases, the result is a higher gas temperature. Conversely, when the gas expands, mechanical work is performed, its energy decreases and its volume increases, so the gas cools down.
From the theoretical basis defined by Carnot, it took more than 100 years to arrive at a functional, commercially usable heat pump. The first heat pumps were built by the Slovak physicist Aurel Stodola, and one of them heated the Geneva town hall from 1928. Thermal energy can only be transferred from a place with a higher potential (temperature) to a place with a lower potential. From a heating point of view this is unfavourable, but a heat pump makes it possible to get around this.
In their closed circuit, heat pumps have one part of the gas under extremely high pressure, and therefore at a high temperature, and a second part of the circuit under low pressure, and thus at a low temperature.The pressure difference between one part and the other is achieved using a compressor and an expansion valve. By moving the gas around the circuit, heat can then be transferred from the colder environment to the warmer one. Part of the heat is also transferred in the form of latent heat during condensation on the warm exchanger and evaporation on the cold exchanger.
If the temperature of the cold part of the circuit is lower than the temperature of the medium from which we want to draw heat (e.g. outdoor air, well water…), and the temperature of the hot part of the circuit is higher than the temperature of the space we want to heat, we can thus, in winter, pump thermal energy from the cold outdoor environment into the heated building.
It might therefore seem that a heat pump is a perpetuum mobile, because the energy needed to compress the gas is lower than the heat energy it actually delivers. In reality, the heat supplied by the heat pump was first extracted from the outdoor environment – we simply do not pay for it, because it comes, for example, from the outside air. As mentioned above, when assessing efficiency we are only interested in the energy we must supply to run the heat pump itself and the actual heat energy it delivers to the heating system. The energy taken from the outdoor environment is not counted, because it costs us nothing. The theoretical efficiency defined by Carnot can be expressed with a simple formula:
In reality, this value is lower, because heat pumps do not operate with an ideal Carnot cycle and an ideal gas. The temperature difference considered must also be increased by the temperature gradients of the heat exchangers, which do not have an infinite surface area. Another element that significantly reduces overall efficiency is the compressor.
For example, with heat pumps that extract heat from the air, at lower outdoor temperatures the overall balance is further reduced by the energy needed to defrost the evaporator fins.
So how can the real efficiency be increased? There is room for improvement in enlarging the surface area of the heat exchangers, improving the properties of the refrigerant mixtures, better compressor design, or adding a supplementary heat exchanger that uses the residual heat after condensation to preheat the vapour drawn into the compressor. This is also where the differing efficiency of heat pumps from different manufacturers comes from. However, these improvements should be economically justified, so that a relatively small gain in efficiency does not significantly increase the price of the unit.
We might assume that a heat pump pays off in all circumstances whenever its efficiency exceeds 100 %. That would hold true if energy prices were the same regardless of the energy carrier. Since the compressor and other components of a heat pump run on electricity, the economics of operation must be based on the difference between the price of electricity and other fuels that can be used to heat buildings.
In the European Union, thermal power plants burning fossil fuels account for a significant share of electricity generation. This method is not very efficient, because due to the limits of the Carnot cycle the resulting efficiency of these plants is relatively low. As a result, the average efficiency of electricity generation in the European Union is ~40 %. This is also reflected in the price of the “heating” electricity tariff, at 2 – 2.5 times the price of natural gas. This means that if a heat pump does not achieve a seasonal efficiency of at least 200 – 250 %, it will be more expensive to run than heating with natural gas.
From the basic relationship defined by Carnot follows an important fact: the smaller the temperature difference required from a heat pump, the higher its efficiency. Precisely because of this, installing a heat pump makes the most sense with underfloor heating or another low-temperature heating system.
On the side of the medium from which heat is extracted, the situation is more complicated, because not everyone is lucky enough to have subsoil that allows a borehole to be drilled or a well with sufficient yield to be dug. A ground collector can be a compromise solution, but the plot must be large enough. The simplest solution is extracting heat from the ambient air, although due to Slovakia’s climatic conditions the resulting efficiency over the heating season is lower.
Heat pumps have undeniable advantages, but when designing a specific application, the economic aspects of the solution need to be considered alongside the energy balance.
If a medium with a relatively high temperature is available in the given location (e.g. water at +12 °C) and the building’s heating is low-temperature (water at +35 °C), then using a heat pump is more than desirable, because in such an application a real efficiency of around 600 – 700 % can be expected. Such heating will be by far the cheapest compared with other available fuels. The other side of the coin is that the cost of a borehole capable of supplying a sufficient amount of water at the required temperature can considerably increase the initial investment.
The solution requiring the lowest investment is a heat pump extracting heat from the ambient air, but when used with low-temperature heating (water at +35 °C), its resulting efficiency over the heating season in our climate will be around 280 – 310 %. The overall efficiency of such a heat pump also depends on the location and the specific heat loss of the building.
At current energy prices, using a heat pump that extracts heat from the ambient air in a heating system running on higher water temperatures (e.g. +55 °C) is economically justified mainly in locations where natural gas is not available for heating.
With this kind of application, a real efficiency of 240 – 280 % can be expected. When using a heat pump whose output does not cover the building’s heat loss across almost the entire range of outdoor temperatures during the heating season, the efficiency calculation must also include direct supplementary heating at times when the heat pump’s output is lower than the building’s heat loss. Such an analysis should also include the overall economics of running the building, taking into account the synergy of using a two-tariff electricity supply for the household’s total electricity consumption.
The general principle of how heat pumps work
High efficiency is a prerequisite for savings
COP = Tmax [°K]/ (Tmax [°K] – Tmin [°K]),
so in theory, with the temperature of the medium from which we extract heat (Tmin) at +2 °C and a heating water temperature (Tmax) of +55 °C, the efficiency could be 6.19 (i.e. 619 %).
As a result of these limitations, real heat pumps achieve only about half the theoretical efficiency.
Proper use of a heat pump should be preceded by an analysis of how such a heat source interacts with the specific building.
Text: Ing. Valér Fabčin
