Hourly Calculation Method of Air Source Heat Pump Behavior

The paper describes an hourly simplified model for the evaluation of the energy performance of heat pumps in cooling mode maintaining a high accuracy and low computational cost. This approach differs from the methods used for the assessment of the overall energy consumption of the building, normally placed in the so-called white or black box models, where the transient conduction equation is deterministically and stochastically solved, respectively. The present method wants to be the expression of the grey box model, taking place between the previous approaches. The building envelope is defined using a building thermal model realized with a 3 Resistance 1 Capacitance (3R1C) thermal network based on the solution of the lumped capacitance method. The simplified model evaluates the energy efficiency ratio (EER) of a heat pump through the determination of the hourly second law efficiency of a reversed Carnot cycle. The results of the simplified method were finally compared with those provided by EnergyPlus, a dynamic building energy simulation program, and those collected from an outdoor test cell in real working conditions. The results are presented in temperatures and energy consumptions profiles and are validated using the Bland-Altman test.


Introduction
The increasing demand for building services has persuaded the EU to take decisive measures for energy efficiency.The building sector represents 40% of the European Union's energy consumption [1].Through the so called Europe 2020 Strategy, the European Commission set the ambitious goal to improve the energy efficiency of each state by increasing the energy production by renewable sources aimed at the reduction of greenhouse gases, confirmed by the recent Europe 2030 Strategy.In this context, the improvement of the performance of buildings plays a key role, both by reducing the energy losses and by using high-performance systems and renewable energy sources [2].The new paradigm requires a new concept of building energy simulation (BES) software by integrating the real and the predicted performance [3][4][5][6], by considering the real working conditions of buildings [7][8][9][10] and the real external data [11].
According to the EN ISO 15603 [12], the methods used for the assessment of the overall energy consumption of the building can be divided into two main categories, measured and calculated.The former is based on the monitoring of energy consumption and other physical parameters of buildings during the operational phase.The latter is based on more or less complex algorithms of the heat balance equations of buildings as a function of the level of detail of the analysis.This approach can be itself divided into two sub-categories: steady-state or quasi-steady-state methods, calculating the heat balance over a sufficient time period, during which the dynamic effects are taken into account by an empirically gain/loss utilization factor; and dynamic methods, calculating the heat balance with short time steps taking into account the heat stored and released from the mass of the building.The performance of these methods has been assessed [13][14][15][16] with different degree orders as a function of the building's characteristics [17].
The hourly calculation methods based on the lumped capacitance-resistance (RC) network model take place between these approaches.Several studies demonstrate how the results of the RC models are close to the real energy behavior of buildings [18][19][20][21].The RC models are applied to the building envelope, with different degree orders, as a function of the number of the considered capacitances [22].Equivalent RC schemes are broadly used to represent thermal systems.This method of representation arises from the lumped capacitance solution of transient heat transfer equations, a well-known consequence of the thermal-electric analogy.This is clearly not the case of the building envelope, where sparse temperature distributions come along with heat sinks (thermal bridges, air gaps, etc.) and gains (solar radiation, etc.).Although this approach cannot represent a fine temperature distribution, it is a good candidate to represent the overall thermal behavior of a building.The lumped parameter models take place in the so-called grey box approach, i.e., a tool for identifying system characteristics from physical and measured data, different from the white-box and black-box approaches, where the physical behavior is completely known and stochastically estimated, respectively [23].The evaluation of the plant performance can be carried out following the different approaches [24].Next to the well-established white-and black-box approaches in recent years, the scientific community has focused attention on the next level by incorporating the lumped parameter model with systems and controls [25], with a focus on the heat pump system [26,27], also combined with other approaches [28].In the present article, the lumped RC model is combined with a simplified hourly method for the calculation of the thermal and energy performance of a heat pump.The envelope was represented by a 3 Resistance 1 Capacitance (3R1C) network in which the components are connected each other through the internal air temperature node.The overall behavior of the building envelope is completed described by the differential equations of transient heat conduction.The heat pump behavior is completely described by the equations governing the thermodynamic cycle, according to the white box approaches.The basis of the developed model is the second law efficiency through the reversed Carnot cycle, which has been adapted to an hourly method.
The calculation of the hourly consumption of the heat pump is based on the evaluation of the coefficient of performance in winter (COP) and the energy efficiency ratio in summer (EER), which is calculated through the values of the hourly average temperature of the refrigerant fluid in the condenser and in the evaporator of the heat pump.These temperatures are calculated using some complex relations starting from the energy needs of an envelope [29].The so-defined calculation method is tested in real working conditions through a seasonal experimentation in real test cell equipped with a heat pump with pre-defined use profiles and control setup.The test was conducted starting from the co-heating test methodology [30], properly applied to evaluate the performance of the air condition system.Finally, to evaluate the suitability of the model, a comparison with the results obtain with EnergyPlus [31] are presented, which is one of the widespread building energy simulation (BES) programs, an expression of the black-box approach.

Heat Pumps
Heat pumps have become increasingly widespread in European countries [32] thanks to several factors (policies, infrastructural facilities, research and development) [33].The recent international directives regarding the energy performance of buildings have greatly contributed to the establishment of such devices.
In general, a heat pump follows the principle of the reversed Carnot cycle, consisting of two isotherms and two adiabatic transformations.
The difficulties that are encountered while practically performing the reversed Carnot cycle can be overcome by performing the ideal reverse steam compression cycle [34].In this case, as shown on the plan entropy-temperature (ST) in Figure 1, the heat absorption continues until reaching the condition of dry saturated steam (point 2), so that subsequent isentropic compression occurs in the superheated steams zone (segment 1-2).
Buildings 2016, 6, 16 3 of 15 the plan entropy-temperature (ST) in Figure 1, the heat absorption continues until reaching the condition of dry saturated steam (point 2), so that subsequent isentropic compression occurs in the superheated steams zone (segment 1-2).After being compressed, the fluid is desuperheated and condensed to become a saturated liquid, passing in the condenser (segment 2-3) and releasing heat to the external environment.Following segment 3-4, the fluid is expanded through an expansion valve.Finally, entering the evaporator (segment 4-1), the fluid absorbs heat and is transformed again into saturated steam.In this regard, the compression refrigeration cycle is better suited for the purposes of a heat pump.
The performances of a heat pump are determined by considering the COP and the EER in the heating and the cooling seasons, respectively.
COP and EER are given by the relation between the useful effect (Qh, in winter or Qc, in summer) and the energy supplied (W), according to the following formulas: In the ideal case, by adopting the reversed Carnot cycle, knowing that: The ideal COP and EER are given by: where: Tc is the absolute temperature of the cold reservoir (K), Th is the absolute temperature of the hot reservoir (K).With a few simple steps, a direct relation between COPid and EERid is obtained as follows: After being compressed, the fluid is desuperheated and condensed to become a saturated liquid, passing in the condenser (segment 2-3) and releasing heat to the external environment.Following segment 3-4, the fluid is expanded through an expansion valve.Finally, entering the evaporator (segment 4-1), the fluid absorbs heat and is transformed again into saturated steam.In this regard, the compression refrigeration cycle is better suited for the purposes of a heat pump.
The performances of a heat pump are determined by considering the COP and the EER in the heating and the cooling seasons, respectively.
COP and EER are given by the relation between the useful effect (Q h , in winter or Q c , in summer) and the energy supplied (W), according to the following formulas: In the ideal case, by adopting the reversed Carnot cycle, knowing that: The ideal COP and EER are given by: Buildings 2016, 6, 16 where: T c is the absolute temperature of the cold reservoir (K), T h is the absolute temperature of the hot reservoir (K).With a few simple steps, a direct relation between COP id and EER id is obtained as follows:

Calculation Model
The work carried out aims at identifying a methodology for the hourly calculation of the performances of a heat pump and the associated consumption.The model is developed on the basis of the international standard EN 15316-4-2:2008 [35], where monthly weather data are sorted into discrete groups (bin method), adapted to an hourly calculation.
In particular, the following relation takes place: EER " η II ¨EER id (7) where η II is the second law efficiency.
To determine the value of the second law efficiency, with the known temperature values of the heat sink and the cold source, respectively, it is necessary to perform a double interpolation starting from two known values of temperature for the heat sink, T h,1 and T h,2 , and two known values of temperature for the cold source, T c,1 and T c,2 , generally supplied by the manufacturer.
Hence, the following equation: where: Th,2 ´Th,1 ˘¨`T h ´Th,1 ˘( 9) The temperatures T h and T c are calculated to perform the hourly calculation of the EER.The calculation of these temperatures requires knowing the thermodynamic properties of the refrigerant used by the heat pump, in this case R410A.
The procedure used to determine the temperatures T h and T c is rather complex and is based on a number of assumptions.However, the adoption of an iterative process makes it possible to reduce to acceptable levels the errors due to the initial approximations.
According to the manufacturer information, the superheating of the refrigerant is set at 7 K beyond the saturated steam curve (segment 1-1' in Figure 2) in order to prevent the refrigerant from entering the compressor in the liquid state, because the real cycle is less predictable than the ideal cycle.In the case, instead, of the expansion process the design practice recommends to subcool a refrigerant by 5 K beyond the saturated liquid curve (segment 3-3' in Figure 2) in order to improve the overall efficiency of the system.
According to the manufacturer information, the superheating of the refrigerant is set at 7 K beyond the saturated steam curve (segment 1-1' in Figure 2) in order to prevent the refrigerant from entering the compressor in the liquid state, because the real cycle is less predictable than the ideal cycle.In the case, instead, of the expansion process the design practice recommends to subcool a refrigerant by 5 K beyond the saturated liquid curve (segment 3-3' in Figure 2) in order to improve the overall efficiency of the system.First, the temperature of the refrigerant at the saturation points is obtained by knowing the thermodynamic properties of the refrigerant along the curve formed by the points of the saturated First, the temperature of the refrigerant at the saturation points is obtained by knowing the thermodynamic properties of the refrigerant along the curve formed by the points of the saturated liquid and steam, by intersecting it with the enthalpy of saturation or the corresponding pressure.At this time, the procedure of calculation has been implemented, referring to which general refrigeration cycle is taken on (Figure 2), which should be representative of the generic cycle of a refrigerating machine, illustrated in the enthalpy-pressure plan (p-H).
Contrary to the refrigerant cycle, it is necessary to proceed in reverse order starting from point 1 to determine the position of the real cycle in the diagram.
It is necessary to know the energy needs, i.e., the quantity of heat to be removed from the environment, for each hour and for a set-point temperature.
where: Q H,nd is the energy need of the building envelope, q is the mass flow rate of the cooling fluid.Once ∆h 41 is known, starting from the superheated steam at point 1 and at unknown pressure, the enthalpy at point 4 is determined.
Considering that the expansion process, which is based on the conservation of energy principle, takes place in an isenthalpic manner, disregarding the error given by the irreversibility of the process, the following equation is defined: It is possible to graphically plot point 3 intersecting the isenthalpic passing through point 4 with an isobar whose segment 3-3' is equal to 5 K, that corresponds to the difference between the subcooled liquid temperature (point 4) and the temperature of the saturated liquid in 3', defined by the manufacturer.
In order to determine ∆h 23 , which corresponds exactly to an enthalpy of desuperheating (segment 2-2') of condensation (segment 2'-3') and of subcooling (segment 3'-3), the enthalpy generated by the compression of the fluid in the process 1-2 must first be calculated.
The compression phase follows an isentropic curve in an ideal cycle (segment 1-2").In the real case, there is a dissipation of energy due to the compressor efficiency, η c , provided by the manufacturer and equal to 0.8.When the enthalpy and the pressure corresponding to point 1 are known, the enthalpy at point 2" can be calculated intersecting the isentropic at point 1 and the isobar at point 3. Consequently, point 2 can be obtained by inverting the following formula: where: W id is the ideal work of compression process; W r is the real work of compression process; h 2" is the specific enthalpy of refrigerant obtained at the end of ideal compression process; h 1 is the specific enthalpy of refrigerant obtained at the beginning of compression process; h 2 is the specific enthalpy of refrigerant obtained at the end of real compression process.Point 2 and then ∆h 23 can be calculated by knowing the enthalpy and the pressure corresponding to points 2 and 3, respectively.
Then, by once again applying the obtained relations through the thermodynamic properties, the real pressure values, p h and p c , and the actual refrigerant temperatures, T h and T c , are calculated.At this point the EER can be determined according to Equation (7).

Test Case
The described calculation model has been validated by comparing the calculated data with those monitored in an external test cell located at the ITC-CNR headquarters near Milan.
The test cell, with internal dimensions equal to 2.8 m ˆ5 m ˆ2.5 m (W ˆL ˆH) with a south-facing shorter side, is built with concrete loadbearing walls insulated with expanded polystyrene.Moreover, the south-facing wall is equipped with a glazed surface with an area of 3 m 2 .The heating/cooling system is an inverter heat pump which may work in different configurations: cooling, dehumidification, ventilation and heating.The nominal cooling power is equal to 2.60 kW with an electrical power consumption of 0.65 kW.The internal airflow can be adjusted to three different values: 250, 300 and 500 m 3 /h.The refrigerant fluid is R410A.Table 1 contains the manufacturer's information.The fluid flow rate is continuously regulated by the inverter that varies the compressor speed as a function of the thermal load.Several sensors to detect the indoor environmental parameters (air temperature, radiant temperature, air speed and relative humidity) are installed in the test cell, as shown in Figure 3.
The monitoring of the environmental and energy variables of the test cell was conducted from April to October 2014.The following analyses are referred to a typical summer week, for 13-19 August, allowing for a better comprehension of the results (Figure 4).DB = Dry bulb.
The fluid flow rate is continuously regulated by the inverter that varies the compressor speed as a function of the thermal load.Several sensors to detect the indoor environmental parameters (air temperature, radiant temperature, air speed and relative humidity) are installed in the test cell, as shown in Figure 3.The monitoring of the environmental and energy variables of the test cell was conducted from April to October 2014.The following analyses are referred to a typical summer week, for 13-19 August, allowing for a better comprehension of the results (Figure 4).
The thermal model of the envelope focuses on the idea of using the lumped solution's uttermost important features to build a 3R1C module (Figure 5) suitable for the representation of heat gains, losses and dynamic response of a single element of the building envelope.A whole system RC scheme is then assembled, connecting these modules according to the structure of the building envelope, through the internal air temperature node.
The thermal mass of the system stores and releases heat according to instantaneous boundary conditions, both defined from the internal space (Ti,s node) and external environment (Te,s node).The external air temperature node, Te, is a boundary condition.This node is connected to the Te,s with an overall heat transfer coefficient Ho,e (W/K), representing the convective and radiative surface heat exchange altogether.The internal temperature is determined by means of surface temperature values, Ti,s, as for the operative temperature, which describes internal conditions according to surfaces radiative and convective heat exchange, Ho,i (EN ISO 13790).The obtained results are previously validated with the hourly measured data.

Model Results
The first evaluation concerns the calculation of the EER.The calculation procedure is based on the second law efficiency, adapted to an hourly assessment.The method provides hourly values of EER, one for each time at which the heat pump is running.The results are shown in Figure 6.The thermal model of the envelope focuses on the idea of using the lumped solution's uttermost important features to build a 3R1C module (Figure 5) suitable for the representation of heat gains, losses and dynamic response of a single element of the building envelope.A whole system RC scheme is then assembled, connecting these modules according to the structure of the building envelope, through the internal air temperature node.

Model Results
The first evaluation concerns the calculation of the EER.The calculation procedure is based on the second law efficiency, adapted to an hourly assessment.The method provides hourly values of The thermal mass of the system stores and releases heat according to instantaneous boundary conditions, both defined from the internal space (T i,s node) and external environment (T e,s node).The external air temperature node, T e , is a boundary condition.This node is connected to the T e,s with an overall heat transfer coefficient H o,e (W/K), representing the convective and radiative surface heat exchange altogether.The internal temperature is determined by means of surface temperature values, T i,s , as for the operative temperature, which describes internal conditions according to surfaces radiative and convective heat exchange, H o,i (EN ISO 13790).The obtained results are previously validated with the hourly measured data.

Model Results
The first evaluation concerns the calculation of the The calculation procedure is based on the second law efficiency, adapted to an hourly assessment.The method provides hourly values of EER, one for each time at which the heat pump is running.The results are shown in Figure 6.

Model Results
The first evaluation concerns the calculation of the EER.The calculation procedure is based on the second law efficiency, adapted to an hourly assessment.The method provides hourly values of EER, one for each time at which the heat pump is running.The results are shown in Figure 6.The EER values in the different running hours of the system are not constant but vary between 2.59 and 4.63.These results are in compliance with those expected, but 7% of the calculated values are lower than 3.2, which differ from what expected.The causes of this inconsistency may be found in the analysis of the refrigerant temperatures in the condenser and in the evaporator: the temperature of the cool reservoir, i.e., in the evaporator, is much higher than the expected value.There is a correlation between these values and the cooling power; indeed, the EER outliers correspond to a cooling power lower than 350 W. The model shows an insufficiency in the modeling of the refrigerant flow rate modulation made by the inverter that causes an incorrect calculation of the refrigerant temperature in the evaporator.
The second step of the validation consists in the evaluation of the calculated energy consumption and in the relation with the outdoor temperature and the cooling power of the heat pump.
Figure 7 shows the trend of three cumulated energy consumptions over the experimental period: RC model, monitored and EnergyPlus v.8.4 cumulated consumptions.The test case was implemented in EnergyPlus using a direct expansion (DX) cooling coil and condensing unit, that includes an electric compressor and a condenser fan.The difference between the calculated (simplified model) and monitored consumption is equal to 2.1 kWh, and the final cumulated deviation is lower than 3%.The simplified model follows the real energy consumption well, always remaining below.and in the relation with the outdoor temperature and the cooling power of the heat pump.
Figure 7 shows the trend of three cumulated energy consumptions over the experimental period: RC model, monitored and EnergyPlus v.8.4 cumulated consumptions.The test case was implemented in EnergyPlus using a direct expansion (DX) cooling coil and condensing unit, that includes an electric compressor and a condenser fan.The difference between the calculated (simplified model) and monitored consumption is equal to 2.1 kWh, and the final cumulated deviation is lower than 3%.The simplified model follows the real energy consumption well, always remaining below.The difference between the simplified model and EnergyPlus is equal to 9 kWh and lower than 9%.The EnergyPlus model is a black box that does allows to input physical numbers.In fact, the calculation of consumption is obtained through the determination of biquadratic and quadratic performance curves that parameterizes the variation of the energy input to cooling output ratio (EER), i.e., as a function of the indoor wet-bulb temperature.The graph shows, however, that EnergyPlus overestimates the real consumption (11.9%).
Figure 8 shows the trend of the indoor temperature related to the calculated values with the simplified model (blue line), with the EnergyPlus v.The difference between the simplified model and EnergyPlus is equal to 9 kWh and lower than 9%.The EnergyPlus model is a black box that does allows to input physical numbers.In fact, the calculation of consumption is obtained through the determination of biquadratic and quadratic performance curves that parameterizes the variation of the energy input to cooling output ratio (EER), i.e., as a function of the indoor wet-bulb temperature.The graph shows, however, that EnergyPlus overestimates the real consumption (11.9%).
Figure 8 shows the trend of the indoor temperature related to the calculated values with the simplified model (blue line), with the EnergyPlus v. Different considerations can be carried out comparing the real data with the calculated data (simplified model).When the system is switched off, mainly in the nighttime, the indoor temperature is strongly dependent on the external temperature.The same correlation determines the trend of the energy consumption, directly proportional to the external temperature.A 3R1C (3 Resistance and 1 Capacitance) lumped model makes it possible to take into consideration the heat exchanges between Different considerations can be carried out comparing the real data with the calculated data (simplified model).When the system is switched off, mainly in the nighttime, the indoor temperature is strongly dependent on the external temperature.The same correlation determines the trend of the energy consumption, directly proportional to the external temperature.A 3R1C (3 Resistance and 1 Capacitance) lumped model makes it possible to take into consideration the heat exchanges between the envelope components and the internal air mass.
During the running phase of the system, the model simulates the heat pump modulation of the refrigerant flow linked to the compressor speed variation.
Another aspect to be considered is the good behavior of the model toward the solar gain through the south-facing window.At noon, when the solar radiation comes into the cell and radiates a variable surface of the floor, peak temperature occurs indoors.
Introducing the EnergyPlus simulation it is possible to consider some differences.When the external temperature decreases, the internal temperature decreases very quickly.Furthermore, the solar gains behavior are not highlighted in the model.The last consideration refers to the operating hours of the heat pump that are shifted to a few hours.
Finally, in order to evaluate the sensitivity of the model to the environmental variables, the energy signature method has been applied, allowing to correlate the cooling energy consumption to the external temperature trend [36,37] between calculated and measured powers.

Validation
In order to reflect data consistency accurately (internal temperature and energy consumption) between the simulation and experimental data, the Bland-Altman test [38] is used in this paper.
In particular, when the graph points are within 95% confidence interval (Equation ( 14)), it can be affirmed that the two methods give consistent results. where: x is average differences, s is standard deviations.
As regards the points that fall outside the confidence interval considered, it can be said that, in general, most of them are points scattered or spurious if they fall within the 99% confidence interval

Validation
In order to reflect data consistency accurately (internal temperature and energy consumption) between the simulation and experimental data, the Bland-Altman test [38] is used in this paper.
In particular, when the graph points are within 95% confidence interval (Equation ( 14)), it can be affirmed that the two methods give consistent results.
I " x ˘1.96¨s (14) where: x is average differences, s is standard deviations.
As regards the points that fall outside the confidence interval considered, it can be said that, in general, most of them are points scattered or spurious if they fall within the 99% confidence interval calculated as follows: I " x ˘3¨s In any case, the points that fall outside the range of confidence are accepted as random or systematic errors.
Results reported in Table 2 show that the model give a better prediction of the internal temperature and the energy consumption.Results in terms of bias values referred to the considered time show that the model overestimates the plant power output for 0.8 W on average, while it underestimates the internal temperature for ´0.22 K. Further characteristics can be deduced from plot visual analysis in terms of the internal temperature.
After careful analysis of the data, 93.4% of the points is placed within the confidence interval 95% (Figure 10).In order to define the nature of the points that fall outside the range considered, it has been expanded in the above range, as previously described.In this way, it is found that more than 98.1% of the points arise within a confidence interval of 99%, with a 4.7% difference that represents the number of spurious or scattered points.After careful analysis of the data, 93.4% of the points is placed within the confidence interval 95% (Figure 10).In order to define the nature of the points that fall outside the range considered, it has been expanded in the above range, as previously described.In this way, it is found that more than 98.1% of the points arise within a confidence interval of 99%, with a 4.7% difference that represents the number of spurious or scattered points.It is possible to draw the same consideration in energy consumption (Figure 11).Starting from a confidence interval at 95%, 92% of the points fall inside.By extending the confidence interval at 99%, it is found that 98.7% fall within it.It is possible to draw the same consideration in energy consumption (Figure 11).Starting from a confidence interval at 95%, 92% of the points fall inside.By extending the confidence interval at 99%, it is found that 98.7% fall within it.It is possible to draw the same consideration in energy consumption (Figure 11).Starting from a confidence interval at 95%, 92% of the points fall inside.By extending the confidence interval at 99%, it is found that 98.7% fall within it.Some values and outliers draw a line, which indicates that the ratio of the difference on the mean is constant for all these values.This particular correlation can be explained according to model results.The modelled heat pump supplies more inrush power than the real one.

Conclusions
This work aims at formulating a calculation model of the energy performance of a heat pump in cooling mode, which is able to provide results as close as possible to the real behavior of buildings in Some values and outliers draw a line, which indicates that the ratio of the difference on the mean constant for all these values.This particular correlation can be explained according to model results.The modelled heat pump supplies more inrush power than the real one.

Conclusions
This work aims at formulating a calculation model of the energy performance of a heat pump in cooling mode, which is able to provide results as close as possible to the real behavior of buildings in terms of indoor air temperature and energy consumption.Attention is focused on different configurations of the heat pump.
The updated model is based on the international standard EN 15316-4-2, providing for the application of the second law efficiency to a reversed Carnot cycle.The hourly consumption of the heat pump is based on the assessment of the COP or EER, calculated through the average hourly temperatures of the refrigerant fluid in the condenser and in the evaporator, determined through the reversed Carnot cycle.
An experimental campaign was conducted on an external test cell, aimed at validating the proposed calculation model; during the tests, the indoor temperatures and the energy consumption were monitored from April to October 2014.The simplified model was also compared with a dynamic simulation in order to investigate different approaches.On the one hand, the energy consumptions are close; on the other hand, the internal temperatures are very different.EnergyPlus is a black box that does not make it possible to understand the physical approaches used, and is studied in order to carry out an energy diagnosis of a building or parts of it.The calculated data with the suggested hourly calculation method demonstrate a high degree of accuracy in terms of energy consumption, indoor air temperature and energy signature with respect to the monitored data in order to correctly size a plant or maintain optimal indoor thermal comfort.
Most values are located within the confidence interval and good consistency was verified between values calculated by model and experimental results.
It should be noted that this model has been applied to a heat pump operating in the cooling mode.Possible future developments will provide for its generalization even in winter and for the assessment of the efficiency under different airflow rates that can be set by the user.L.B. has performed the assessment of the energy consumption.L.D. has performed the hourly calculation method.M.M. has performed the dynamic simulation.

Conflicts of Interest:
The authors declare no conflict of interest.
8.4 model (orange line) and measured (red line).The green line represents the detected external temperature over the considered period.All the environmental parameters have hourly step representations.The trends of the calculated and measured data are almost equal except for the first hours of 13 August due the initialization of the simulation.

Figure 9
shows two rising fitting lines: the red one represents the measured average daily consumption and the blue one the calculated average daily consumption.The slopes of the line give information about the energy performance of the test cell.Both slopes and the intercepts are almost identical and equal to 15 W/K, showing a substantial parallelism of the lines.The results of the calculation model are very close to matching those monitored in the test cell.Buildings 2016, 6, 16 10 of 15

Figure 9 .
Figure 9.Comparison of the measured and calculated average daily powers through the energy signature method.

Figure 9 .
Figure 9.Comparison of the measured and calculated average daily powers through the energy signature method.

Table 2 .
Consistency verifications of model values and experimental results.