Refrigeration is an essential sector in our daily lives, accounting for 15-20% of global energy consumption, according to data presented by the European Cool-Save project. It therefore accounts for a significant fraction of the CO2 emissions emitted worldwide and, at the same time, plays an essential role in the progress of society.

As in other sectors, we are increasingly looking for greater energy efficiency in our refrigeration systems, with the aim of reducing our costs while reducing our energy demand and greenhouse gas emissions. To know the efficiency of our installation, the most representative indicator is the instantaneous efficiency of a refrigeration machine or heat pump (η), defined as the quotient between the cooling capacity, or heating capacity in the case of a heat pump (Q), and the electrical power of the compressor (W_{comp}):

In the case of the efficiency of a refrigeration machine, it is usually called EER (Energy Efficiency Ratio); and in the case of a heat pump, it is called COP (Coefficient of Performance).

When it comes to calculating this instantaneous efficiency in practical terms, two methods can be distinguished: the direct method and the indirect method.

**Direct Method**

The direct method consists of taking operational data corresponding to the refrigerant fluid that evolves inside the refrigerating machine or heat pump.

To understand this, it is necessary to take a look at the Pressure-Enthalpy diagram of the refrigerant and at the enthalpy evolution at the different points of the refrigeration system or heat pump:

As it can be seen in the diagram, each point corresponds to a state of the refrigerant in the circuit:

- 1: Evaporator outlet and compressor inlet.
- 2: Compressor outlet and condenser inlet
- 3: Condenser outlet and expansion valve inlet
- 4: Expansion valve outlet and evaporator inlet

As it can be seen, the specific heat of the condenser **(Q**_{cond}** , [kW/kg])** is equal to the enthalpy difference between point 2 and 3. Similarly, the specific heat of the evaporator **(Q**_{evap}** , [kW/kg])** is equal to the enthalpy difference between points 1 and 4.

In the previous picture, an isoenthalpic expansion has been assumed in the expansion valve (3🡪4), therefore, the enthalpy at point 3 is the same as at point 4. Furthermore, it is also assumed that the losses in the condenser and evaporator are insignificant, and the pressure at point 2 is the same as at point 3, as well as the pressure at point 4 is the same as at point 1.

To know the enthalpy of the refrigerant, it is necessary to know two state properties at each point. The easiest properties to measure are pressure and temperature, using temperature and pressure probes at the inlet and outlet of the compressor. Furthermore, if we assume that the pressure in the condenser hardly changes (as described above), it is only necessary to add an additional temperature probe at the condenser outlet. A network analyser is also required for each compressor.

To calculate the total heating and cooling heat **(Q**_{heat}** [kW] and Q**_{heat }**[kW])**, it is necessary to know the refrigerant mass flow rate (mref):

**Q _{heat} = m_{ref} (h_{2} – h_{3}), Q_{cool} = m_{ref} (h_{4} – h_{1})**

There are several strategies to calculate the refrigerant mass flow rate:

- Invasive or non-invasive flowmeter measurement.
- Performing an energy balance to the compressor and assuming heat losses to clear the mass flow rate; or using flowmeters and temperature probes to calculate the external cooling of the compressor to close the energy balance.
- Modelling the refrigerant flow rate as a function of the compressor pressure-volume curve provided by the manufacturer.
- Using the manufacturer’s software to model the compressor in order to calculate the heat losses and thus close the energy balance.

Once the above values are known, it is possible to calculate the efficiency of a heat pump (**COP**) or a refrigeration machine (**EER**):

The **advantages **of this method are:

- It allows to analyze the performance in installations without an external circuit, such as cold rooms, freezer tunnels, etc.
- It provides a better analysis of compressor efficiency, such as isentropic efficiency.

And the main **disadvantages **are:

- It is sometimes difficult to calculate the refrigerant flow rate, being a further instrumentation required to calculate it.
- It is possible to apply this method easily at a given point in time. But, to be able to monitor the performance dynamically, modelling of the thermodynamic properties of the refrigerant and more complex mathematical methods are required.

Currently, there are some systems suitable to thermodynamically model the properties of the refrigerant, such as the**PilotE**^{2}** HVACR****,** method from Articae Smart Technologies. It is possible to monitor the performance of refrigeration systems with this technology.

**Indirect Method**

This method consists of taking data and measurements of the fluids outside the machine. This is the most widely used and easiest method to apply. However, it is not more precise than the direct method and sometimes presents difficulties in data collection.

With this method, we calculate the difference in enthalpy between the input and output of the external fluid of the evaporator, in the case of a refrigerating machine; or of the condenser, in the case of a heat pump. Applying the energy balance we obtain:

Where:

Q_{cond} , Q_{evap} are the heating heat in the condenser, and cooling heat in the evaporator, respectively.

H_{e cond} , H_{s cond} , H_{e evap} , H_{s evap} are the enthalpies at the inlet and outlet of the condenser, and at the inlet and outlet of the evaporator, respectively.

T_{e cond} , T_{s cond} , T_{e evap} , T_{s evap} are the condenser inlet and outlet temperatures, and the evaporator inlet and outlet temperatures, respectively.

m_{f. ext. cond.}, m_{f. ext. evap.} are the condenser and the evaporator external fluid flow rates, respectively.

Ce_{f. ext. cond.}, Ce_{f. ext. evap.} are the specific heat of the external fluid of the condenser and the evaporator, respectively.

For performance measurement in a simple refrigeration or heat pump circuit, it is necessary to install 1 flowmeter and 2 temperature probes for each external circuit in the condenser or evaporator, and a network analyzer for each compressor.

The main **advantages **of this method are:

- Ease of installation of data collection equipment. Data can be obtained with liquid flowmeters, temperature probes, pressure probes and a network analyzer or electric meter.
- In the case of using ultrasonic flowmeters, it is possible to use this method in a non-invasive way.
- It is a simple method, and the most used for performance measurement.

However, it has the following **disadvantages**:

- In systems where the external fluid is air, the measurements are very complicated or unfeasible. In the case of air conditioners, it is possible to measure the air flow with an anemometer, trying to achieve a flow rate as stable and uniform as possible throughout the air outlet. In the case of industrial and commercial refrigeration, this is not possible and it is necessary to use to the direct method.
- In many cases, to measure the overall performance of the installation, a single primary circuit may have several exchangers with an external fluid (desuperheaters, subcoolers, etc.); and it is then necessary to use a flow meter and two additional temperature probes for each secondary circuit.

To be continued…