Estimation of the Heat Loss Coefficient of Two Occupied Residential Buildings through an Average Method

energies Article Estimation of the Heat Loss Coefficient of Two Occupied Residential Buildings through an Average Method Irati Uriarte 1,*, Aitor Erkoreka 1, Pablo Eguia 2, Enrique Granada 2 and Koldo Martin-Escudero 1 1 ENEDI Research Group, Department of Energy Engineering, University of the Basque Country (UPV/EHU), Plaza Torres Quevedo 1, 48013 Bilbao, Spain; aitor[email protected] (A.E.); [email protected] (K.M.-E.) 2Department of Mechanical Engineering, Heat Engines and Fluid Mechanics, School of Industrial Engineering, University of Vigo, 36310 Vigo, Spain; [email protected] (P.E.); [email protected] (E.G.) *Correspondence: [email protected]; Tel.: +34-946-017-322 Received: 14 September 2020; Accepted: 29 October 2020; Published: 2 November 2020   Abstract: The existing performance gap between the design and the real energy consumption of a building could have three main origins: the occupants’ behaviour, the performance of the energy systems and the performance of the building envelope. Through the estimation of the in-use Heat Loss Coefficient (HLC), it is possible to characterise the building’s envelope energy performance under occupied conditions. In this research, the estimation of the HLC of two individual residential buildings located in Gainsborough and Loughborough (UK) was carried out using an average method. This average method was developed and successfully tested in previous research for an occupied four-story office building with very different characteristics to individual residential buildings. Furthermore, one of the analysed residential buildings is a new, well-insulated building, while the other represents the old, poorly insulated semidetached residential building typology. Thus, the monitored data provided were filtered in order to apply the abovementioned average method. Even without fulfilling all the average method requirements for these two residential buildings, the method provides reliable HLC values for both residential buildings. For the house in Gainsborough, the best estimated HLC value was 60.2 W/K, while the best approach for Loughborough was 366.6 W/K. Thus, despite the uncertainty sources found during the analysis, the method seems promising for its application to residential buildings. Keywords: heat loss coefficient; average method; building envelope’s in-use energy performance 1. Introduction The majority of buildings constructed in the European Union in the past were built without considering any thermal regulations, since energy efficiency was not considered a major issue until the 1970s [ 1 ]. It is well known that buildings in the EU are responsible for a considerable percentage of the energy consumption and CO 2 emissions in accordance with H2020 Energy Efficient Buildings. Therefore, the building sector is currently in a decarbonisation process to reduce the problem [2]. However, achieving an energy efficient building is not a simple task. Several buildings designed to obtain a considerable reduction in energy consumption have failed during this process. This is because there is still an important difference between the real performance and the theoretical performance given by the designers [ 3 ]. A considerable number of studies have shown that the real energy consumption can be up to two to five times higher than the predicted energy consumption [4,5]. Energies 2020,13, 5724; doi:10.3390/en13215724 www.mdpi.com/journal/energies Energies 2020,13, 5724 2 of 17 The energy performance difference, commonly known as the performance gap, has numerous different causes. Some are due to such factors as the construction or operation [ 6 ]; others derive from such data uncertainties as the climate conditions affecting the building, or the behaviour of the occupants. Several analyses have been carried out to study how a specific climate and the behaviour of the occupants can affect the energy behaviour of the building [ 7 , 8 ]. Moreover, the shape of the building is also linked to its energy efficiency [ 9 ]. Hemsath and Bandhosseini [ 10 ] and Montazeri et al. [ 11 ] have done research into how the relation between the height and the width of a building can affect the heat transfer. However, one of the main reasons for this performance gap is the energy performance of the building’s envelope [12]. Several works of research have focused on the monitorisation of the indoor energy of a building in order to test different retrofit solutions under different climatic conditions [ 13 ]. Last but not least, the high cost of monitoring buildings forces researchers to develop methods that can obtain robust results with a limited number of variables [14]. Achieving an accurate estimate of the real energy consumption is a complex task. This is due to the numerous problems found when estimating each of the different causes that create uncertainties in the energy consumption calculation. These problems can directly affect the modelling and simulations in the estimation process of an accurate energy consumption value. In order to solve the current problems in the building sector, the International Energy Agency IEA-EBC Programme [ 15 ] has been developed. This programme involves energy research and innovation with collaboration from several countries. Therefore, the informal group formed by different organizations, named DYNASTEE [ 16 ], is taking part in the IEA-EBC Annex 71 [ 17 ] project called “Building Energy Performance Assessment Based on In-situ Measurements”. This Annex is the step that follows the previously developed IEA-EBC Annex 58 titled “Reliable building energy performance characterization based on full scale dynamic measurements”, where the characterization of buildings’ energy performance based on dynamic measurements was investigated. Therefore, the aim of the IEA-EBC Annex 71 is to improve even further the characterization methods for the real energy performance of building envelopes and to provide in-situ quality assurance methods. The aim is to develop steady-state and dynamic data analysis techniques, along with good quality in-situ measurements. Therefore, the aim of the Programme is to monitor in-use buildings to obtain reliable, quality data and thus be able to provide accurate and reliable Key Performance Indicators (KPIs) of the building’s envelope energy performance using different methods [17]. One of the most important analyses carried out within the previous Annex 58 was the Round Robin Box test [ 18 ], in which the participants tested the thermal behaviour of the box by shipping it to different countries. Then, the obtained data was analysed using four main methods. On the one hand, averaging methods and simple or multiple linear regression [ 19 – 21 ] were used to estimate the stationary thermal properties of the box envelope. In this case, the HLC (Heat Loss Coefficient) is the main KPI that was estimated. This parameter considers the building’s heat transmission through the envelope and the ventilation and/or infiltration losses per temperature degree difference between indoors and outdoors in [W/K]. On the other hand, the ARX (Auto-Regression models) (ARMAX) [ 22 ] and State Space models [ 23 ] were used to estimate the stationary and dynamic thermal properties of the box envelope [24]. The ongoing Annex 71 is now focused on the in-situ estimation of the thermal behaviour of in-use building envelopes. Therefore, the aim of this paper is to demonstrate the validity of the average method developed in [ 25 , 26 ] for an occupied office building into two residential buildings, as never done before. The behaviour of the heating system, the internal heat gains and the solar gains is very different in office buildings compared to residential buildings. However, due to the difference found in the weight of the heat gain sources within an office building, it is possible that some of the average method requirements that limit the valuable monitoring periods for accurate HLC estimation cannot be fulfilled for residential buildings. Thus, the limits the method found when working in a residential building are also analysed. Energies 2020,13, 5724 3 of 17 The method is applied to two case study individual residential buildings with different sizes, occupation, internal gains, use, monitoring period and envelope insulation characteristics. The data from the analysed residential buildings is provided by the Annex 71. The first building is in Gainsborough (UK) (see Figure 1a) and is a well-insulated, occupied building. It is one of the four social houses monitored in [ 27 ] and the HLC ‘theoretical value’ given by the Annex 71 is 49.9 W/K. The latter value is estimated based on the building design characteristics. The Gainsborough case represents a not very detailed monitoring system of a real in-use house, but with a very long monitoring period of three years. However, the second house, in Loughborough (UK) (see Figure 1b), is inhabited by synthetic occupants. Moreover, it is a traditional uninsulated semidetached residential building. This house has already been tested through the co-heating method in [ 28 ] and the HLC ‘theoretical value’ is 382 W/K. The dataset used for the house analysed in Loughborough can be found in [ 28 ], where the house 1 (HT1) files were studied. The Loughborough case represents a very detailed monitoring system of a synthetic occupants’ in-use house, but with a short monitoring period of one month. Energies 2020, 13, x FOR PEER REVIEW 3 of 17 social houses monitored in [27] and the HLC ‘theoretical value’ given by the Annex 71 is 49.9 W/K. The latter value is estimated based on the building design characteristics. The Gainsborough case represents a not very detailed monitoring system of a real in-use house, but with a very long monitoring period of three years. However, the second house, in Loughborough (UK) (see Figure 1b), is inhabited by synthetic occupants. Moreover, it is a traditional uninsulated semidetached residential building. This house has already been tested through the co-heating method in [28] and the HLC ‘theoretical value’ is 382 W/K. The dataset used for the house analysed in Loughborough can be found in [28], where the house 1 (HT1) files were studied. The Loughborough case represents a very detailed monitoring system of a synthetic occupants’ in-use house, but with a short monitoring period of one month. (a) (b) Figure 1. (a) North side of Gainsborough house; (b) front side of Loughborough house [28]. Both houses show two extreme building situations: The first showing occupied, well-insulated, residential building conditions with a not very detailed monitoring system, but monitored for a long period; while the second is a synthetic occupant controlled, uninsulated residential building with a very detailed monitoring system, but monitored for a short period. Thus, these two cases are considered suitable for this research work, since they represent the extreme opposite situations for testing the average method in the residential building level. 2. Materials and Methods 2.1. Average Method The average method can be used for the HLC estimation of in-use whole buildings. The formulas developed in [25,26], and used to estimate the HLC, are: HLC =∑()   ∑(,,)   = ∑()    ∑(,,)    =                  [W/K] (1) HLC = ∑(,)   ∑(,,)   = ∑(,)    ∑(,,)    =                             [W/K] (2) where Qk is the heating system heat input in [W], Kk is the total electricity consumption of the building in [W], Sa is a fixed equivalent solar aperture to obtain the solar gains of the building in [m2] regarding Vsol,k (that is, the south global vertical solar irradiance [W/m2]). Moreover, Tin,k [°C] and Tout,k [°C] are the indoor and outdoor air temperatures. There are N measurement points in the analysed period and k is the measurement correlative index. The average method should only be used for periods with very low solar radiation and high space heating demand. For such periods, it is possible to ensure that the solar heat gains compared to the rest of the heat gains within the building (space heating plus all other internal gains excluding Figure 1. (a) North side of Gainsborough house; (b) front side of Loughborough house [28]. Both houses show two extreme building situations: The first showing occupied, well-insulated, residential building conditions with a not very detailed monitoring system, but monitored for a long period; while the second is a synthetic occupant controlled, uninsulated residential building with a very detailed monitoring system, but monitored for a short period. Thus, these two cases are considered suitable for this research work, since they represent the extreme opposite situations for testing the average method in the residential building level. 2. Materials and Methods 2.1. Average Method The average method can be used for the HLC estimation of in-use whole buildings. The formulas developed in [25,26], and used to estimate the HLC, are: HLCsimple =PN k=1(Qk+Kk) PN k=1(Tin,k −Tout,k)= PN k=1(Qk+Kk) N PN k=1(Tin,k−Tout,k) N =Q+K Tin −Tout [W/K](1) HLC =PN k=1(Qk+Kk+SaVsol,k) PN k=1(Tin,k −Tout,k)= PN k=1(Qk+Kk+SaVsol,k) N PN k=1(Tin,k−Tout,k) N =Q+K+SaVsol Tin −Tout [W/K](2) where Q k is the heating system heat input in [W], K k is the total electricity consumption of the building in [W], S a is a fixed equivalent solar aperture to obtain the solar gains of the building in [m 2 ] regarding V sol,k (that is, the south global vertical solar irradiance [W/m 2 ]). Moreover, T in,k [ ◦ C] and T out,k [ ◦ C] Energies 2020,13, 5724 4 of 17 are the indoor and outdoor air temperatures. There are N measurement points in the analysed period and k is the measurement correlative index. The average method should only be used for periods with very low solar radiation and high space heating demand. For such periods, it is possible to ensure that the solar heat gains compared to the rest of the heat gains within the building (space heating plus all other internal gains excluding solar radiation) are less than 10%. By estimating HLC simple and HLC, the weight of the solar gains in the HLC estimate can be analysed. By comparing the HLC to the HLC simple of an analysed period, it is possible to check whether the solar gains represent a considerable part of the total heat gains within the building. Since the not directly measurable solar gains, together with the metabolic heat generation, are the main uncertainty sources of the method, while it is interesting to estimate the HLC simple , it has no physical meaning. The average temperature difference between the indoor and outdoor air during the testing period must be high (values close to or higher than 15 ◦ C are recommended). Thus, measuring errors in temperature difference calculations will be minimized and high heating demands will also permit the heating supply to be accurately measured. According to [ 25 , 26 ], in order to check the reliability of the HLC estimates for the whole building using the average method, it is interesting to test if the HLC accumulated average value is stabilised during the last 24 h of the selected periods through plotting the accumulated average of the HLC. If the estimate is stabilised within a ± 10% band over the last 24 testing hours (see accumulated HLC average plots in Appendix A), it can be assumed that the obtained HLC with the average method is valid. Finally, due to the complexity of accurately estimating the accumulated heat of the building, it is mandatory to have the same average building temperature at the beginning and end of the selected periods for estimating the HLC. This temperature will be the average temperature between the indoor and outdoor temperatures. If this is fulfilled, it can be assumed that there will be no accumulated heat in the building in the analysed periods, since the start and end points of the analysis will have the same thermal level. Then, similar conditions to stationary conditions could be assumed. This issue is fully demonstrated in Section 2.1 of [26]. 2.2. Input Data The monitoring systems of each given building measured different parameters. A combination of smart meters and dedicated sensors were used in both buildings to monitor each of the parameters in Table 1with at least a 5 min frequency. The monitoring system of Gainsborough is described in detail in [ 27 ], while the monitoring system of Loughborough is described in detail in [ 28 ]. However, the input data provided were filtered in order to obtain common input parameters for both houses, as shown in Table 1. The filtering procedures were not the same due to the different characteristics of the monitoring systems. For the Gainsborough house, only the total gas consumed by the boiler was provided. However, the mains water consumption of the house was also provided. The boiler was providing heat for both the space heating and the DHW (Domestic Hot Water). The Gainsborough boiler is a Potterton Promax combination boiler with an efficiency of 91% regarding the SAP procedure, according to the manufacturer [ 29 ]. Like most conventional boilers, it does not produce DHW in parallel with space heating. Thus, when DHW is required, the boiler stops the space heating supply and all the heat produced by the boiler is used for DHW production. In order to estimate the gas consumed by the space heating from the total gas consumption, the following assumption was considered: If there was gas consumption at the same time as there was mains water consumption, all this consumed gas was considered as gas consumption solely for DHW. In other words, only the gas consumption while no mains water was consumed was considered as space heating. This filter was applied on a five minute basis. Moreover, for the Gainsborough building, only the electricity consumption was considered when estimating the internal gains (K). The occupancy heat created by the occupants’ metabolic Energies 2020,13, 5724 5 of 17 generation was neglected (part of K), as not enough information was provided to make an estimation. Different occupants lived in this building over the three winters of the data provided. Due to this, achieving occupancy patterns of the inhabitants to estimate the metabolic heat gain they produced was very complicated. However, the Loughborough house is a traditional uninsulated building occupied by monitored synthetic occupants. This means that the house behaves as if real people were living inside. Thus, the metabolic heat gain produced by these synthetic users was also considered as a heat gain. All the internal heat gains, including the metabolic generation of the synthetic occupants, were measured by means of several watt meters that measured all the electrical consumptions occurring within the building. Moreover, for the Loughborough house, the heat output of the boiler to the space heating system was directly measured. In other words, it was not necessary to use the boiler efficiency or split the space heating and the DHW consumptions. Moreover, accurately measured synthetic profiles were added to simulate the occupants’ behaviour. Therefore, all heat gains (Q +K), as well as the thermostat settings, were accurately known. In order to estimate the solar gains, since only cloudy periods should be used for applying the average method, the radiation could be considered purely diffuse and thus similar on all façades. Therefore, a g-value of 0.5 could be applied to the total window area, as in [ 30 ]. Once this roughly estimated solar gain was obtained, it could then be compared to the averaged (Q +K) value of the selected periods to see whether the averaged period solar gains were below 10% as compared to the averaged period (Q +K). Then, the HLC estimate would mainly be dependent on the measured Q and K that can be accurately measured when compared to solar gains. Moreover, the propagation of the uncertainty of the sensors was also considered when estimating the HLC error bands. The provided sensor accuracy for the monitoring systems of the two houses can be seen in Table 2. Note that, as in the average method [ 25 , 26 ], other uncertainty sources related to the assumptions made by the method are not propagated to the HLC estimations carried out in this work. In the case of the solar gains uncertainty, apart from the accuracy of the pyranometer (considered 5% for this analysis), the solar aperture uncertainty was also considered. As done in [ 25 , 26 ], despite the solar aperture (S a ) being unknown, a 10% error was considered for the latter. Thus, the total uncertainty considered for the solar gains of both buildings was 15%. Table 1. List of input parameters for applying the average method. Sensors Measured Parameter Description Thermocouple/Thermistors Outdoor temperature (◦C) Tout,k On-site outdoor air temperature Indoor temperature (◦C) Tin,k Measured in different rooms of the house. In order to achieve a unique temperature for the building, a non-weighted average temperature was estimated using the following formula: Tin,k =Tin,1+Tin,2+... +Tin,n n Energy consumption devices Boiler heat output (kWh) Qk When required, the gas consumption was converted by boiler efficiencies to space heating system kWh supply. Hot water energy supply is not considered in this term. Total electricity consumption (kWh) Kk Measured for the whole building or in each of the rooms of the house. Pyranometer Solar radiation (global horizontal solar irradiance [W/m2]) Hsol Obtained from the Waddington weather station. In order to apply the average method, it was converted into south global vertical solar radiation (Vsol) [31]. Energies 2020,13, 5724 6 of 17 Table 2. List of measurements and provided accuracy for applying the average method. Measurement Gainsborough Accuracy Loughborough Accuracy Indoor temperature ±0.25 ◦C±0.2 ◦C Gas meter ±2% ±2% Electricity consumption ±2% Not provided (±2% assumed) Outdoor temperature ±0.5 ◦C±0.2 ◦C In Table 1, due to the high homogeneity of indoor temperatures during the analysed periods, the indoor temperature is considered as the non-weighted average of all the measured indoor temperatures. A full development of the properties of the HLC, regarding its estimation in buildings comprising different thermal zones with different indoor temperature set points, is mathematically developed and demonstrated in Section 2.2 from the reference [ 26 ]. There, the requirements to be able to estimate the whole building HLC by means of the sum of the zone HLCs are described. Such needs are basically to know individually each zone heat gain (Q +K+S a V sol ) and each zone T in . In both of the one family residential buildings analysed in this work, it was only possible to consider one thermal zone, as the internal heat gains (Q +K+S a V sol ) could not be accurately split between the different rooms that make up the dwelling. Most of the internal gains were measured only on the whole building level. Furthermore, for each individual temperature measurement, the period averaged value has been compared to the period average of the non-weighted average indoor temperature. For all the analysed periods, the indoor temperature homogeneity of the buildings has been so high that the difference between the period averaged values of individual indoor temperatures and the non-weighted indoor temperatures have been within the sensor error band. In order to see the behaviour of each of the monitored parameters, Figure 2a shows the evolution over one month of the indoor and outdoor air temperatures for the Loughborough building. There, the temperature difference between the interior and the exterior is also plotted. From Figure 2a, it can be concluded that the temperature difference between the exterior and interior is considerably high during the selected period. A zoom-in of Period 1, used later to apply the average method, is also presented in Figure 2b. Figure 3a shows the evolution of the solar gains (S a V sol ), the space heating systems’ heat input (Q) and the total electricity consumption, including the synthetic occupants’ generation (K) for the Loughborough building, again including a zoom-in on period 1 in Figure 3b. If Figure 3a is analysed, it can be seen that it is not possible to find a three-day period where the solar gains remain below 10% when compared to the rest of the measurable heat gains (Q +K). Finally, as an example, Figure 4shows the accumulated average plot of the HLC for period 1 in Loughborough. It can be seen how the HLC value stabilises along the duration of the period and remains within the 10% bands over the previous 24 h. Energies 2020, 13, x FOR PEER REVIEW 6 of 17 Table 2. List of measurements and provided accuracy for applying the average method. Measurement Gainsborough Accuracy Loughborough Accuracy Indoor temperature ±0.25 °C ±0.2 °C Gas meter ±2% ±2% Electricity consumption ±2% Not provided (±2% assumed) Outdoor temperature ±0.5 °C ±0.2 °C In Table 1, due to the high homogeneity of indoor temperatures during the analysed periods, the indoor temperature is considered as the non-weighted average of all the measured indoor temperatures. A full development of the properties of the HLC, regarding its estimation in buildings comprising different thermal zones with different indoor temperature set points, is mathematically developed and demonstrated in Section 2.2 from the reference [26]. There, the requirements to be able to estimate the whole building HLC by means of the sum of the zone HLCs are described. Such needs are basically to know individually each zone heat gain (Q + K + SaVsol) and each zone Tin. In both of the one family residential buildings analysed in this work, it was only possible to consider one thermal zone, as the internal heat gains (Q + K + SaVsol) could not be accurately split between the different rooms that make up the dwelling. Most of the internal gains were measured only on the whole building level. Furthermore, for each individual temperature measurement, the period averaged value has been compared to the period average of the non-weighted average indoor temperature. For all the analysed periods, the indoor temperature homogeneity of the buildings has been so high that the difference between the period averaged values of individual indoor temperatures and the non-weighted indoor temperatures have been within the sensor error band. In order to see the behaviour of each of the monitored parameters, Figure 2a shows the evolution over one month of the indoor and outdoor air temperatures for the Loughborough building. There, the temperature difference between the interior and the exterior is also plotted. From Figure 2a, it can be concluded that the temperature difference between the exterior and interior is considerably high during the selected period. A zoom-in of Period 1, used later to apply the average method, is also presented in Figure 2b. Figure 3a shows the evolution of the solar gains (SaVsol), the space heating systems’ heat input (Q) and the total electricity consumption, including the synthetic occupants’ generation (K) for the Loughborough building, again including a zoom-in on period 1 in Figure 3b. If Figure 3a is analysed, it can be seen that it is not possible to find a three-day period where the solar gains remain below 10% when compared to the rest of the measurable heat gains (Q + K). Finally, as an example, Figure 4 shows the accumulated average plot of the HLC for period 1 in Loughborough. It can be seen how the HLC value stabilises along the duration of the period and remains within the 10% bands over the previous 24 h. (a) 0 5 10 15 20 -5 0 5 10 15 20 25 2014-02-16 2014-02-20 2014-02-24 2014-02-28 2014-03-04 2014-03-08 2014-03-12 2014-03-16 Temperature difference [°C] Temperature [°C] Tout Tin Tout_P1 Tin_P1 Tin-Tout Tin_P1-Tout_P1 Figure 2. Cont. Energies 2020,13, 5724 7 of 17 Energies 2020, 13, x FOR PEER REVIEW 7 of 17 (b) Figure 2. Indoor temperature, outdoor temperature and temperature difference: (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. (a) (b) Figure 3. Solar gains (SaVsol), space-heating systems’ heat input (Q) and total electricity consumption, including synthetic occupants’ generation (K): (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. 0 5 10 15 20 -5 0 5 10 15 20 25 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Temperature difference [°C] Temperature [°C] Tout_P1 Tin_P1 Tin_P1-Tout_P1 0 4000 8000 2014-02-16 2014-02-20 2014-02-24 2014-02-28 2014-03-04 2014-03-08 2014-03-12 2014-03-16 Internal heat gains [W] SaVsol Q K SaVsol_P1 Q_P1 K_P1 0 4000 8000 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Internal heat gains [W] SaVsol_P1 Q_P1 K_P1 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 HLC [W/K] Time [h] The accumulated HLC Lower limit Upper limit The accumulated HLC during the last 24h Figure 2. Indoor temperature, outdoor temperature and temperature difference: ( a ) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. Energies 2020, 13, x FOR PEER REVIEW 7 of 17 (b) Figure 2. Indoor temperature, outdoor temperature and temperature difference: (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. (a) (b) Figure 3. Solar gains (SaVsol), space-heating systems’ heat input (Q) and total electricity consumption, including synthetic occupants’ generation (K): (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. 0 5 10 15 20 -5 0 5 10 15 20 25 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Temperature difference [°C] Temperature [°C] Tout_P1 Tin_P1 Tin_P1-Tout_P1 0 4000 8000 2014-02-16 2014-02-20 2014-02-24 2014-02-28 2014-03-04 2014-03-08 2014-03-12 2014-03-16 Internal heat gains [W] SaVsol Q K SaVsol_P1 Q_P1 K_P1 0 4000 8000 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Internal heat gains [W] SaVsol_P1 Q_P1 K_P1 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 HLC [W/K] Time [h] The accumulated HLC Lower limit Upper limit The accumulated HLC during the last 24h Figure 3. Solar gains (S a V sol ), space-heating systems’ heat input (Q) and total electricity consumption, including synthetic occupants’ generation (K): ( a ) for the whole dataset in Loughborough, ( b ) for period 1 in Loughborough. Energies 2020, 13, x FOR PEER REVIEW 7 of 17 (b) Figure 2. Indoor temperature, outdoor temperature and temperature difference: (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. (a) (b) Figure 3. Solar gains (SaVsol), space-heating systems’ heat input (Q) and total electricity consumption, including synthetic occupants’ generation (K): (a) for the whole dataset in Loughborough, (b) for period 1 in Loughborough. 0 5 10 15 20 -5 0 5 10 15 20 25 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Temperature difference [°C] Temperature [°C] Tout_P1 Tin_P1 Tin_P1-Tout_P1 0 4000 8000 2014-02-16 2014-02-20 2014-02-24 2014-02-28 2014-03-04 2014-03-08 2014-03-12 2014-03-16 Internal heat gains [W] SaVsol Q K SaVsol_P1 Q_P1 K_P1 0 4000 8000 2014-02-28 2014-03-01 2014-03-02 2014-03-03 Internal heat gains [W] SaVsol_P1 Q_P1 K_P1 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 HLC [W/K] Time [h] The accumulated HLC Lower limit Upper limit The accumulated HLC during the last 24h Figure 4. Evolution of the accumulated average of the heat loss coefficient for period 1 in Loughborough. Energies 2020,13, 5724 8 of 17 3. Results The two houses presented have not been monitored for the same data periods. The house in Loughborough [ 28 ] was only monitored from 16 February to 15 March 2014. Unfortunately, the electrical consumption data started to be collected on 25 February, which limits the opportunity to find a suitable period within the provided data. The house in Gainsborough was monitored from 1 November 2012 until 30 April 2015. Thus, since a longer monitoring period was provided, it was easier to find suitable periods to estimate the HLC that fulfil the average method requirements. As explained in Section 2, the average method is able to estimate the HLC of a building using short time periods (at least 72 h periods). However, due to all the requirements demanded by the average method from the periods for analysis, finding suitable periods when short data series are provided is not straightforward. In this case, it was necessary to ease some of the method requirements, taking more flexible limitations for the solar gains 10% weight requirement, and this relaxation effect on the HLC estimation was analysed. In the next two subsections, both building data series are analysed separately. In order to demonstrate the reliability of the method, several useful independent periods should be found during the study of each building’s data sets. Thus, the individual results obtained for each period will be independent from each other and can then be compared for the same building. Thus, an average HLC estimation value was calculated for each of the houses. Considering the characteristics of each house, the reliability of the results are now discussed. 3.1. Gainsborough HLC Estimation Since a large dataset was provided for the house in Gainsborough, three consecutive winters are available to find suitable cold and cloudy periods to apply the average method. Thus, six useful periods that fulfil most of the average method requirements were found, see Tables 3and 4. Table 3. Necessary period averaged variable values to estimate the HLC simple (simple Heat Loss Coefficient) and HLC (Heat Loss Coefficient) for Gainsborough. The variables included are the outdoor temperature (T out ), the indoor temperature (T in ), the temperature difference (T in − T out ), the space heating heat input (Q), the electrical heat gains (K), the internal heat gains (Q+K) and the solar gains (SaVsol). Winter Period Input Data Tout [◦C] Tin [◦C] Tin-Tout [◦C] Q [W] K [W] Q+K [W] SaVsol [W] 2012–2013 Period 1 2012-12-03 18:02 → 2012-12-07 19:02 2.6 21.2 18.6 1066.5 11.9 1078.4 491.7 Period 2 2012-12-11 16:02 → 2012-12-14 11:02 −0.4 16.9 17.3 767.9 22.6 790.5 380.9 Period 3 2012-12-18 23:02 → 2012-12-22 8:02 5.9 16.9 11.0 544.7 9.3 554.0 110.7 2013–2014 Period 4 2013-11-27 2:02 → 2013-11-30 8:02 7.0 21.7 14.7 326.8 459.2 786 336.9 Period 5 2013-12-13 21:02 → 2013-12-17 3:02 9.5 21.7 12.2 393.8 453.7 847.5 282.0 2014–2015 Period 6 2014-11-26 3:02 → 2014-11-30 8:02 8.7 21.9 13.2 322.7 353.8 676.5 139.4 Energies 2020,13, 5724 9 of 17 Table 4. The HLC simple (simple Heat Loss Coefficient) and HLC (Heat Loss Coefficient) estimated values for Gainsborough. Winter Period Output Data HLCsimple [W/K] HLC [W/K] 2012–2013 Period 1 57.9 ±3.5 84.4 ±8.5 Period 2 45.9 ±2.9 68.0 ±7.2 Period 3 50.2 ±4.4 60.2 ±6.6 2013–2014 Period 4 53.6 ±3.8 76.6 ±8.4 Period 5 69.6 ±5.7 92.7±10.6 2014–2015 Period 6 51.4 ±3.9 61.9 ±6.1 The average value of the six HLC simple estimations presented in Table 4is 54.8 ± 4.1 W/K, and 74 ± 8.1 W/K for the HLC. As a comparison reference, the Annex 71 has provided a “theoretical HLC value” of 49.9 W/K. Note that the Gainsborough theoretical value only considers the envelope design transmittance values and design infiltration/ventilation characteristics, so it is not the “true” HLC value. However, as proven by [ 12 ], when design HLC values are compared to co-heating experimental HLC values, the co-heating HLC values are usually considerably higher than the design HLC values. These differences have been proven to be up to 100% higher in the co-heating HLC when compared to the design HLC values. Thus, the obtained results follow this proven trend of having higher experimental HLC values when compared to the design HLC values. In order to analyse the spread and reliability of the estimated in-use HLC results for Gainsborough, it is indispensable to carry out a more detailed study of the data. As explained in Section 2.2, Gainsborough’s gas consumption is not only providing space heating, but also DHW. Then, although a filter is developed to estimate the gas consumption for space heating and DHW production (see Table 5), this issue introduces an important uncertainty. The order of magnitude of the estimated energy dedicated to DHW is of the order of the estimated space heating requirements. However, periods 2 and 3 had no main water consumption and give very interesting information. Table 5. Space heating (Q), Domestic Hot Water consumption (Q DHW ), total (Q Tot =Q+Q DHW ) and corresponding DHW percentage of the total (%QDHW) for the analysed periods in Gainsborough. 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