# Influence of Thermal Retrofitting on Annual Energy Demand for Heating in Multi-Family Buildings

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## Abstract

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## 1. Introduction

_{2}emission constitutes one of the main topics, enabling us to achieve sustainable development [24]. The target technical parameters and the actual energy effects of thermal retrofitting are of great importance. Prior to making the decision on realization of investment, technical and economic analyses were conducted in order to indicate optimal solutions, simultaneously meeting the requirements stated and described in relevant legal acts. One of the documents usually prepared prior to thermal retrofitting, is the energy audit of a building [8,25,26]. It contains, the analysis of the current state, as well as assessment of a building and its technical equipment in relation to the energy issues, a list and description of the possible technical solutions reducing the energy consumption within a building and improving its energy efficiency and an analysis of the investment and operational costs. The energy analysis of a building is conducted assuming the standard indoor and outdoor environment conditions. The calculations are carried out according to the applicable methodology based on the standards and requirements of different countries [26]. This means that an audit contains the theoretical calculations of the energy balance of a building before and after thermal retrofitting. The predicted energy effects calculated as part of the audit are comparable with the actual effects obtained during the building operation following thermal retrofitting. The relations between the expected and obtained values obtained under operational conditions are diverse [8,25,27,28,29,30]. The predicted energy savings are often achieved; however, the results which are superior to those stated in an audit, are seldom obtained [8,27]. In the buildings in which the thermal comfort parameters are not maintained, the actual effects may be worse than predicted [8]. It can be assumed that it results from the attempts of bringing the indoor environment parameters in a building to meet the standard requirements. In many countries, audits constitute one of the elements of implementing the national programs towards achieving energy savings and improving the energy efficiency in buildings. The actions recommended for particular buildings are then indicated in audits. The scope of these actions is dependent on the thermal insulation state of wall barriers and the total efficiency of the heating system within a building. Favorable effects are usually achieved, since there are numerous types of operations that can be performed to achieve energy savings [28,29].

## 2. Materials and Methods

^{2}. The buildings were supplied with energy from different district heating systems. Prior to thermal retrofitting, energy audits were conducted for each building, according to the methodology used in Poland since 1998 [5]. Before thermal retrofitting, the objects were non-insulated and the building envelopes of the specific buildings were characterized by different heat transfer coefficients, which varied between 0.93–1.18 W/(m

^{2}∙K) in the case of the external walls and between 0.8 and 1.07 W/(m

^{2}∙K) in the case of the flat roofs. Those values fulfilled the local requirements that were valid at the time of construction. In contrast, after thermal retrofitting, the values of coefficients were similar or frequently the same. In order to designate the energy coefficients for the specific buildings, the following data were taken into account: heat meter readouts from the years before and after thermal retrofitting, the year of thermal retrofitting, the aspect ratio values, heated usable surface area, and the energy savings level for heating according to the audit (Table 1).

^{2}·K); for flat roofs U = 0.20 ÷ 0.22 W/(m

^{2}·K). Central heating systems are in technically sound condition, the radiators are equipped with thermostatic radiator valves, and the distributing pipes are thermally insulated, according to the national guidelines. After retrofitting, the heating systems were hydraulically balanced in all cases, which improved the distribution of heat to particular rooms.

#### 2.1. Method of Determining the Energy Coefficients

- (1)
- Acquisition of data from legalized heat meters operating under actual conditions, collected for each building over the period of several years, i.e., measurement of heat consumption for heating in main pipes, before dividers (Q
_{p}, GJ/year). - (2)
- Collection of the data from heating suppliers, pertaining to the length of the heating period and mean monthly outdoor air temperatures in a given location.
- (3)
- Calculation of the number of degree-days for each analyzed year, according to the following dependency:$$Sd={\displaystyle \sum (}{\theta}_{\mathrm{int},H}-{\theta}_{e,m})\cdot L{d}_{m}$$
- Sd is the number of degree-days calculated for a particular year, day·K/year;
- θ
_{e,m}is the mean monthly outdoor air temperature in a given year, °C; - θ
_{int,,H}is theindoor air temperature in the heated zone, assumed at 20 °C; - Ld
_{m}is thenumber of heating days in a given month of a given year, day.

- (4)
- Calculation of a correction coefficient resulting from the variability of the number of degree days according to the following dependency:$$\phi =\frac{S{d}_{0}}{Sd}$$
- φ is the correction coefficient;
- Sd
_{0}is the number of degree-days in the standard year, calculated on the basis of mean monthly outdoor air temperatures obtained from multiannual measurements and theoretical length of the heating season (222 days), which, in the case of the location of the analyzed buildings amounts to 3825.2 (day·K)/year.Table 2 contains the values of correction coefficient in a given group and a given year, as well as the years for which the heat consumption measurements were conducted.

- (5)
- Correction of the measured consumed heat values to the standard year conditions performed in line with the following dependency:$${Q}_{0}={Q}_{p}\cdot \phi $$
- Q
_{0}is the adjusted annual heat consumption, i.e., adjustment to standard conditions, GJ/year; - Q
_{p}is the measured annual heat consumption, GJ/year.

- (6)
- Collection of the data from energy audits conducted for the analyzed buildings, pertaining to the predicted level of energy savings obtained through thermal retrofitting.
- (7)
- Determining the final energy savings in accordance with the following dependencies:ΔQ
_{%}= (Q_{01,avg}− Q_{02,avg})/Q_{01,avg}·100- $\overline{\mathsf{\Delta}{Q}_{\%}}$, ΔQ
_{%,min}, and ΔQ_{%,max}are the mean, minimal, and maximal (respectively) obtained reduction in final energy consumption following thermal retrofitting related to the value of mean annual final energy consumption prior to thermal retrofitting of the building, %; - Q
_{01,avg}is the mean annual final energy consumption before thermal retrofitting under standard conditions, GJ/year; - Q
_{02,avg}is the mean annual final energy consumption after thermal retrofitting under standard conditions, GJ/year.

- (8)
- Comparison of the energy savings level obtained under the operational conditions with the level predicted in energy audits.
- (9)
- Calculation of the annual final energy factor for heating after thermal retrofitting under operational conditions, according to the following dependencies:$$FE{F}_{H}=\frac{{10}^{6}\xb7{Q}_{0}}{3600\xb7{A}_{f}}$$
- FEF
_{H}is the annual final energy factor for heating, kWh/(m^{2}·year); - A
_{f}is the heated usable surface area of the building, m^{2}; - 10
^{6}is the unit converter, kJ/GJ; - 3600 is the unit converter, s/h.

- (10)
- Determination of the annual non-renewable primary energy factor for heating after thermal retrofitting under operational conditions, in line with the following dependence:PEF
_{H}= w_{H}·FEF_{H} - (11)
- Calculation of the boundary value of the factor of annual non-renewable primary energy demand for heating as a function of building shape coefficient, according to the national regulations for new and modernized buildings, at a time of thermal retrofitting, in line with the following dependence:new buildings PEF
_{H,0}= 55 + 90 · (A/V)modernized buildings PEF_{H,0}= 1.15 · [55 + 90 · (A/V)]- PEF
_{H,0}is the maximum value of annual non-renewable primary energy factor for heating, kWh/(m^{2}·year)

- (12)
- Comparison of the factor of the annual non-renewable primary energy factor for heating after thermal retrofitting under operational conditions with the limit values established in Polish regulations [34] at the time of investment.

#### 2.2. Description of the Data Analysis Methods

_{H}and primary energy PEF

_{H}consumption, was performed by means of the Wilcoxon–Mann–Whitney test, which is a non-parametric counterpart of the Student’s t-test for dependent samples [35]. This test was employed, because the assumptions of normality of dependent variables distribution and lack of homogeneity of variance were not met. These assumptions were verified by means of the Shapiro–Wilk test [36,37] and Bartlett’s test [38], respectively. The comparative analysis of dependent variables was additionally supplemented with the effect size estimator $r=Z/\sqrt{n}$, where Z is the test statistic of the Wilcoxon–Mann–Whitney test and n is the number of compared observation pairs [39]. The comparisons of central tendency measures, in the case of a greater number of independent variable classes, were performed by means of the Kruskal–Wallis test, which is a non-parametric counterpart of the ANOVA test [40]. This test was selected, since the assumptions of the parametric ANOVA test were not met. However, in the cases where the assumptions pertaining to the normality of dependent variable distribution and homogeneity of variance in groups were met, the ANOVA test was used for comparisons. The size of effects of independent variables were evaluated using the ${\u03f5}^{2}$ coefficient [41]. If the global ANOVA or the Kruskal–Wallis test indicated significance of differences, the analysis was carried out by means of post-hoc Dunn’s test with the Holm’s method [42].

## 3. Results

## 4. Discussion

_{H}factor in particular groups of buildings after thermal retrofitting, calculated on the basis of operational measurements and usable surface area, are presented in Table 8. The best results were obtained in groups G1 and G2. In turn, in G4, although the values of the A/V coefficient and the heat transfer coefficient of wall barriers in the final state were similar to those in other groups, the indices were less favorable. The mean in G4 was approximately twice as high as that obtained in G1. Similarly, as it was mentioned above, it may result from the lack of rational management of energy in the building. The buildings were managed by different business entities. The obtained levels of energy savings may be different due to diversified heat transfer coefficients of wall barriers prior to thermal retrofitting. However, after thermal retrofitting, the buildings should be characterized by a similar FEF

_{H}factor, because they had very similar technical parameters affecting the heat demand for heating in a building.

_{H}) is presented in Figure 5.

_{H,0}factor for the buildings being modernized during the period of studies, calculated according to Dependence (8), varies in the range 95.34 ÷ 115.00 kWh/m

^{2}·year. This constitutes about 21% in relation to a higher value. The obtained minimal, maximal, and mean values of the PEF

_{H}factor in particular groups are presented in Table 9, together with the mean PEF

_{H,0}values for each group of buildings.

_{H}factor, which is lower than the minimal limit value, whereas, in groups G3 and G4, the values that are much higher than maximum limit were obtained for some buildings (Figure 6 and Figure 7). In addition to the reasons enumerated while describing the percent decrease in energy consumption and FEF

_{H}factor, the coefficient of non-renewable primary energy input (w

_{H}), assumed to be in line with the technical and construction guidelines, also significantly affected the PEF

_{H}factor. This coefficient was characteristic for the given method of heat supply in a building and the type of energy carried and used as the heat source. In groups G1 and G2, the w

_{H}coefficient amounted to 0.8, whereas in G3 and G4 it was much higher and reached 1.3, which significantly affected the PEF

_{H}factor (Figure 7).

_{H}) after retrofitting was compared with the aforementioned input coefficient. In Figure 7, PEF

_{H}was compared with the maximal boundary annual non-renewable primary energy demand factors for new and modernized buildings PEF

_{H,0}. It should be noted that, in the case of groups G1 and G2 with input coefficient w

_{H}= 0.8, the measured average value of PEF

_{H}factor (57 kWh/(m

^{2}·year)) was significantly smaller from the boundary values (104.9 and 101.5 kWh/(m

^{2}·year), respectively). In the case of groups G3 and G4 with w

_{H}= 1.3, the boundary values (110 and 104.8 kWh/(m

^{2}·year), respectively) were exceeded.

^{2}·year), on average. There is also a visible discrepancy in the variability of features in both groups. The buildings with higher non-renewable primary energy input coefficient were characterized by greater variance; thus, the Kruskal–Wallis test was used to compare the central tendencies.

_{H}coefficient was equal to 0.8.

_{H}coefficient and thus on the values of the FEF

_{H}and PEF

_{H}factors. Therefore, in some cases, even though higher final energy savings and lower FEF

_{H}factor values were obtained, the value of PEF

_{H}can be higher than for a building with a greater FEF

_{H}factor. This stems from the fact that the assessment energy efficiency of a building and comparison of the building quality, its elements, and technical systems, should be based on the final energy factor (FEF

_{H}) rather than on the primary energy factor (PEF

_{H}). The primary energy consumption factor should instead be used in the evaluation of the environmental impact of a building in ecological terms, especially pertaining to the emission of carbon dioxide and particulate matter into the atmosphere.

## 5. Conclusions

- The thermal retrofitting conducted in multi-family residential buildings result in reduced heat consumption for heating ranging from 14 to 43%. The level of achieved final energy savings depends on the improvement degree of the technical parameters of wall barriers and efficiency of the heating system in a building. The more comprehensive the thermal retrofitting is and the greater the improvement of these parameters, the higher the reduction in heat consumption.
- The analysis indicates that the predicted savings determined on the basis of the calculations performed in accordance to the applicable algorithms found in respective standards and national legal acts are usually higher than the actual values. On the basis of the conducted studies, the mean obtained from an audit amounts to 38.4%, whereas from measurements, the mean obtained amounts to 30.2%. It should be noted that the predicted effects can be achieved under the operational conditions, which happened most often in group G2. Varying energy effects are obtained in different years, even within the same building. It is likely that this is connected with the method of energy supply and usage in particular rooms of a building.
- Despite similar parameters of wall barriers, the building shape coefficient (A/V = 0.31 to 0.5), and total efficiency of heating installations in the final state, some buildings were characterized with much higher values of the FEF
_{H}factor. These were mainly the objects belonging to group G4. This means that these buildings varied in terms of use, operation, and energy management. It should also be assumed that the method of energy management in a building largely affects its energy quality under the operational conditions. Therefore, thermal retrofitting of a building can be conducted to the same extent, yielding different energy effects under the actual conditions. This is indicated by diversified FEF_{H}values both within a single group and between them. - The buildings from groups G1 and G2 with input coefficient w
_{H}= 0.8 met the requirements for the annual primary energy factor, with mean values equal 104.9 and 101.5 kWh/(m^{2}·year), respectively, with the measured average value of this factor equal to 57 kWh/(m^{2}·year). On the other hand, the objects from groups G3 and G4 (with w_{H}= 1.3) did not meet those requirements, reaching greater PEF_{H}values compared to the boundary PEF_{H,0}values (110 and 104.8 kWh/(m^{2}·year), respectively). - All buildings supplied from a district heating system with a co-generational heat source met the requirements of modernized buildings found in technical guidelines. However, not every building supplied from a district heating system equipped with coal heat plant met the requirements related to the PEF
_{H,0}factor value, despite a FEF_{H}factor that was comparable to other buildings. This is indicated through the comparison of the FEF_{H}and PEF_{H}factors in groups G1 and G2 to the values of these factors in G3. - The current requirements give a boundary value for the primary energy factor (PEF
_{H+W, 0}) for heating combined with hot water production, so it is not possible to say what the limit value for heating is. However, in the period in which the heat consumption of the modernized facilities was analyzed, it was possible to compare the consumption for heating purposes of the PEF_{H,0}limit value, but only for heating purposes.

_{H}), whereas the environmental impact of a building should be calculated using the non-renewable primary energy demand factor (PEF

_{H}). The buildings with similar FEF

_{H}values can differ in terms of the PEF

_{H}factor, which does not necessarily indicate a lower energy quality of the building or its heating installation.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Comparison of the actual decrease in corrected annual energy consumption with the reduction predicted based on the audit.

**Figure 6.**Comparison of the annual primary energy consumption for different non-renewable primary energy input coefficients.

**Figure 7.**Comparison of the actual annual primary energy consumption factor (PEF

_{H}) after modernization with the boundary conditions for the modernized (old) and new buildings, divided into groups depending on the non-renewable primary energy input coefficient.

No. | Number of Build. | Heated Usable Area [m ^{2}] | Heat Source | w_{H} | A/V [1/m] | Meas. Period [Years] | Year of Thermal Retrofitting [Years] | Level of Energy Savings According to the Energy Audit [%] |
---|---|---|---|---|---|---|---|---|

G 1 | 11 | 1036.4 ÷ 3834.5 | Combined heat and power plant (cogeneration) | 0.8 | 0.35 ÷ 0.50 | 2005 ÷ 2010 | 2006 | 29.3 ÷ 37.3 |

G 2 | 11 | 3700.0 ÷ 4125.8 | Combined heat and power plant (cogeneration) | 0.8 | 0.34 ÷ 0.37 | 2003 ÷ 2010 | Depending on the building: 2004, 2005, 2006 or 2007 | 27.0 ÷ 39.1 |

G 3 | 11 | 1539.0 ÷ 3142.0 | Heating plant | 1.3 | 0.42 ÷ 0.50 | 2003 ÷ 2009 | 2004 | 42.8 ÷ 56.5 |

G 4 | 10 | 1090.5 ÷ 4519.6 | Heating plant | 1.3 | 0.31 ÷ 0.49 | 1998 ÷ 2008 | Depending on the building: 2001, 2003, 2004, or 2005 | 36.6 ÷ 45.4 |

No. | Year | Value of the Correction Coefficient φ | |||
---|---|---|---|---|---|

G1 | G2 | G3 | G4 | ||

1 | 1998 | - | - | - | 1.044 |

2 | 1999 | - | - | - | 1.113 |

3 | 2000 | - | - | - | 1.155 |

4 | 2001 | - | - | - | 1.020 |

5 | 2002 | - | - | - | 1.092 |

6 | 2003 | - | 0.929 | 0.997 | 1.051 |

7 | 2004 | - | 0.980 | 1.147 | 1.098 |

8 | 2005 | 1.031 | 1.033 | 1.046 | 1.020 |

9 | 2006 | 0.997 | 0.924 | 1.096 | 1.057 |

10 | 2007 | 1.072 | 1.271 | 1.140 | 1.114 |

11 | 2008 | 1.126 | 1.038 | 1.159 | 1.081 |

12 | 2009 | 1.081 | 1.070 | 1.128 | - |

13 | 2010 | 0.968 | 0.984 | - | - |

Year | Q_{p}[GJ/year] | Q_{0}[GJ/year] | Φ [-] | FEF_{H}[kWh/(m ^{2}·year)] | PEF_{H}[kWh/(m ^{2}·year)] | Q_{01,śr}[GJ/year] | Q_{02,śr}[GJ/year] | Savings per Audit [%] | Savings per Meas. [%] |
---|---|---|---|---|---|---|---|---|---|

2005 | 709 | 731 | 1.031 | 106.50 | 85.20 | 730.2 | 504.6 | 32.6 | 30.9 |

2006 | 676 | 674 | 0.997 | 98.27 | 78.62 | ||||

2007 | 525 | 563 | 1.072 | 82.02 | 65.62 | ||||

2008 | 413 | 465 | 1.126 | 67.75 | 54.20 | ||||

2009 | 451 | 487 | 1.081 | 71.01 | 56.81 |

Year | Q_{p}[GJ/Year] | Q_{0}[GJ/year] | Φ [-] | FEF_{H}[kWh/(m ^{2}·year)] | PEF_{H}[kWh/(m ^{2}·year)] | Q_{01,śr}[GJ/year] | Q_{02,śr}[GJ/year] | Savings per Audit [%] | Savings per Meas. [%] |
---|---|---|---|---|---|---|---|---|---|

2003 | 1758 | 1634 | 0.929 | 118.49 | 94.79 | 1429.0 | 1052.0 | 28.7 | 26.4 |

2004 | 1456 | 1427 | 0.980 | 103.54 | 82.83 | ||||

2005 | 1304 | 1347 | 1.033 | 97.74 | 78.19 | ||||

2006 | 1417 | 1310 | 0.924 | 94.98 | 75.98 | ||||

2007 | 906 | 1152 | 1.271 | 83.52 | 66.81 | ||||

2008 | 969 | 1006 | 1.038 | 72.99 | 58.40 | ||||

2009 | 996 | 1066 | 1.070 | 77.35 | 61.88 | ||||

2010 | 1102 | 1085 | 0.984 | 78.65 | 62.92 |

Year | Q_{p}[GJ/year] | Q_{0}[GJ/year] | Φ [-] | FEF_{H}[kWh/(m ^{2}·year)] | PEF_{H}[kWh/(m ^{2}·year)] | Q_{01,śr}[GJ/year] | Q_{02,śr}[GJ/year] | Savings per Audit [%] | Savings per Meas. [%] |
---|---|---|---|---|---|---|---|---|---|

2003 | 813 | 811 | 0.997 | 142.96 | 185.84 | 810.6 | 503.9 | 56.2 | 37.8 |

2004 | 629 | 722 | 1.147 | 127.24 | 165.41 | ||||

2005 | 447 | 468 | 1.046 | 82.46 | 107.20 | ||||

2006 | 497 | 545 | 1.096 | 96.07 | 124.89 | ||||

2007 | 430 | 491 | 1.14 | 86.46 | 112.39 | ||||

2008 | 418 | 485 | 1.159 | 85.44 | 111.08 | ||||

2009 | 472 | 533 | 1.128 | 93.90 | 122.07 |

Year | Q_{p}[GJ/year] | Q_{0}[GJ/year] | Φ [-] | FEF_{H}[kWh/(m ^{2}·year)] | PEF_{H}[kWh/(m ^{2}·year)] | Q_{01,śr}[GJ/year] | Q_{02,śr}[GJ/year] | Savings per Audit [%] | Savings per Meas. [%] |
---|---|---|---|---|---|---|---|---|---|

2002 | 1481 | 1618 | 1.092 | 186.64 | 242.63 | 1589.2 | 1052.8 | 45.4 | 33.8 |

2003 | 1522 | 1600 | 1.051 | 184.59 | 239.97 | ||||

2004 | 1413 | 1551 | 1.098 | 178.98 | 232.68 | ||||

2005 | 1310 | 1336 | 1.02 | 154.18 | 200.43 | ||||

2006 | 975 | 1031 | 1.057 | 118.93 | 154.61 | ||||

2007 | 915 | 1019 | 1.114 | 117.59 | 152.87 | ||||

2008 | 1026 | 1109 | 1.081 | 127.96 | 166.35 |

Data Source | Number of Buildings | Heat Consumption Decrease [%] | |||
---|---|---|---|---|---|

Minimal | Maximal | Median | Mean | ||

audit | 43 | 29.1 | 57.0 | 36.7 | 38.4 |

readout | 43 | 14.0 | 43.9 | 30.4 | 30.2 |

Building Group | FEF_{H} Value [kWh/(m^{2}·year)] | |||
---|---|---|---|---|

Minimal | Maximal | Median | Mean | |

G1 | 58.9 | 98.6 | 68.1 | 69.5 |

G2 | 66.0 | 80.3 | 73.5 | 73.2 |

G3 | 70.4 | 80.9 | 92.8 | 81.6 |

G4 | 114.6 | 156.3 | 137.3 | 138.5 |

w_{H} | Building Group | PEF_{H} Value [kWh/(m^{2}·year)] | Mean PEF_{H,0} Value [kWh/(m^{2}·year)] | |||
---|---|---|---|---|---|---|

Minimal | Maximal | Median | Mean | |||

0.8 | G1 and G2 | 47.1 | 78.9 | 57.9 | 57.0 | 104.9 and 101.5 |

1.3 | G3 and G4 | 91.5 | 203.2 | 120.6 | 141.3 | 110.0 and 104.8 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Życzyńska, A.; Suchorab, Z.; Majerek, D.
Influence of Thermal Retrofitting on Annual Energy Demand for Heating in Multi-Family Buildings. *Energies* **2020**, *13*, 4625.
https://doi.org/10.3390/en13184625

**AMA Style**

Życzyńska A, Suchorab Z, Majerek D.
Influence of Thermal Retrofitting on Annual Energy Demand for Heating in Multi-Family Buildings. *Energies*. 2020; 13(18):4625.
https://doi.org/10.3390/en13184625

**Chicago/Turabian Style**

Życzyńska, Anna, Zbigniew Suchorab, and Dariusz Majerek.
2020. "Influence of Thermal Retrofitting on Annual Energy Demand for Heating in Multi-Family Buildings" *Energies* 13, no. 18: 4625.
https://doi.org/10.3390/en13184625