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A methodology for a thermal energy building audit
Available online at www.sciencedirect.com
Building and Environment 39 (2004) 195 – 199 www.elsevier.com/locate/buildenv
A methodology for a thermal energy building audit Pantelis N. Botsarisa;∗ , Spyridon Prebezanosb a Laboratory
of Mechanical Engineering, Department of Electrical and Computer Engineering, Faculty of Energy Systems, Democritus University Of Thrace, Xanthi, Greece b Buildings Energy Certi#cation Center, Xanthi, Greece Received 14 March 2003; received in revised form 6 August 2003; accepted 20 August 2003
Abstract The present paper introduces a new method for the certi/cation of the energy consumption of a building recording its “energy behavior”. The method utilizes energy indices such as Index of Thermal Charge or Index of Energy Disposition to simulate the heat losses of the building and the heat 6ow because of the temperature di7erence (8T ) from the inner to outer space. The present method and the algorithm that is implemented could be used as a part of a building energy audit or as a single audit method. Additionally it could be used for the inspection of the energy e9ciency in public or municipal buildings. The forenamed method is currently under investigation by the present research team. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Energy saving; Energy technology; Energy audit; Building construction
1. Introduction The consumption of energy for the heating of buildings in the European Community (EC) represents 40% of the energy produced [1]. In Greece, heating in the domestic sector represents 61% of total energy consumption [1]. Apart from consumption, the combustion of liquid and gas fuels for the heating of buildings, as well as the increasing use of small conditioning units, burden the environment by releasing combustion gases (CO2 , CO, SO2 , NOX , HC) and smoke [2]. Also, the increased mortality of adults reported in recent years in Europe is attributed to the continuous degrading of the environment. The energy consumption in 1995 –2010 is predicted to continue [1]. As a result, Europe will face ever-bigger environmental problems than those it faced in the 20th century. In reality, the overlooked decision of the EC made in Kioto for the reduction of transmission of greenhouse gases (GHG) by 8% between 1990 and 2010 will not be achieved and, on the contrary, there is an expected increase by 6% [1]. For the reduction of energy consumption, its rational, long-lasting use is fundamental, and it generally ∗
Corresponding author. E-mail addresses: [email protected] (P.N. Botsaris), [email protected] (S. Prebezanos). 0360-1323/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2003.08.016
requires the existence of analytical facts and tools for decision-making in all individual areas. The achievement of the above-mentioned goals regarding the heating of buildings, the production of hot water, steam and hot air, is currently under investigation by the present work and research team. This work is based on the interpretation of the behavior of the source of thermal energy, i.e. of the operation and cessation time of the source, a behavior during which the source deterministic follows those factors that in6uence it [3,4]. The “decoding” of the behavior of the source is the key point in saving energy and protecting the environment. This point supported by modern technology operates as a powerful, safe and economical calculating tool.
2. Theoretical approach of indices 2.1. Index of thermal charge (ITC) The most important part of this method is the index of thermal charge (ITC). The thermal charge of a building for the heating of its spaces when is in a thermal balance, for a given moment in time is given by QH = EB =tA(QF; QV; QE) :
(1)
196
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
Nomenclature QP
Variables QH ET EB EG
EP EGS tA Qv QE tE m n0 MPH mPH SQH QW QR QSW QZ QG
1 The
the thermal charge of the building for the room heating, when the building is in thermal balance at every moment (kW) the heat that develops in space (kWh) the amount of heat transmitted from the source of thermal energy to the space which is being heated (kWh) the heat produced in space which is the sum of the internal sources of energy of the building (human, electrical appliances, etc.) (kWh) the heat produced in space, which results from the sum of the energy systems (kWh) the heat produced in space, resulting from the solar radiation (greenhouse e7ect) (kWh) the period of time of the cycle1 of heat exchange when it is in thermal balance (h) the thermal charge due to losses from renewal of the air in space (kW) the thermal charge due to losses from the speed of air and humidity in space (kW) the time of the transmitted heat from the source of thermal energy to the space2 which is being heated (h) the supply of fuel (kg/h) the degree of e9ciency of the source of thermal energy the index of Energy Disposition of the building (kW) the index of Energy Disposition of the building (w=m2 ) the sum of thermal charges of the variables— satellite (kW) the thermal charge due to losses from wind (kW) the thermal charge due to losses from the rain (kW) the thermal charge from the absorbed heat by the external surfaces of the building. This heat originates from solar radiation (kW) the thermal charge from unknown, unforeseen, etc. losses (kW) the thermal charge from heat produced in space, which originates from the sum of the internal sources of energy of the building (human, electrical appliances, etc.), (kW)
cycle of heat exchange of the system when it is in thermal balance is de/ned by the time period between two consecutive operations of the burner. 2 The time from the start of functioning of the burner until its cessation.
QSG ZSQH Pr m pr m Ti TB TBE Ta nc
the thermal charge from the heat produced in space, which results from the sum of energy systems (kW) the thermal charge from the heat produced in space, which results from the solar radiation (greenhouse e7ect) (kW) satellite coe9cient which gives the contribution of satellites in energy saving or consumption the “Pr m Index” of the building (w=m2 ) the “pr m Index” of the building (w=m3 ) mean temperature of air in space/position of measurement mean temperature of building air potential mean temperature of building air temperature of environmental air cloudiness
Constants E0 QF
Hu EB tA QPH QPR QPF QPW ZQPR qPH Pr q pr q AF VH
the speci/c heat produced in space (kWh) the thermal e9ciency of space due to losses from the di7erence between the temperature of internal space and the environmental temperature. This is lost from the outer surface of the building (kW) the lower heat of combustion (kWh/Kg) the maximum amount of heat transmitted from the energy source to the space that is being heated, so that it remains in thermal balance the maximum period for the cycle (see footnote 1) of heat exchange over ◦ C (h) the index of thermal charge of the building (kW) the charge of heating the space for a determined time period (kW) the charge of heating for windows and other elements which do not store heat (kW) the charge of heating for walls (kW) coe9cient of program burden for the heating of a determined time period the index of thermal charge of the building (w=m2 ) the energy identity of the building, “Pr q index” (w=m2 ) the energy identity of the building, “pr q index” (w=m3 ) the 6oor surface of space that is being heated the volume of space that is being heated
The developed heat, of any moment in time, is supplied by the equation ET = EB + EG + EP + ESG :
(2)
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
The transmitted heat by the source of thermal energy: EB = tE [mHu n0 ]:
(3)
The developed heat (ET ) is either transmitted by sources of thermal energy and the internal sources of the building (electrical appliances, human, etc.) or by solar power (greenhouse e7ect). Also, (ET ) could have its highest point de/ned (controlled by a thermostat) or not. Respectively and in relation to these two cases, there is either energy saving or the temperature increases in space. In the case that room temperature is controlled, the developed heat is de/ned as ET = E0 and Eq. (2) becomes E0 = EB + EG + EP + ESG :
(4)
Assuming that EG + EP + ESG = 0, the amount of heat transmitted from the energy source to the space takes its maximum value. E0 = EB = EB ;
(5)
⇒ EB = EB + EG + EP + ESG
(5a)
with the presence of variables EG + EP + ESG there is energy saving and its value for every moment in time is de/ned by Eq. (5a). In the case that room temperature is not controlled, ET = EB + EG + EP + ESG . There is an increase in room temperature and the amount of heat transmitted from the energy source to the room is always maximum, so the latter remains in thermal balance. In a complete cycle of the process, for the system to remain in thermal balance, the amount of heat transmitted by the energy source equals the amount of heat moves from the heated space to the environment. From Eq. (5) it is known that the amount of heat, which in this case is the maximum transmitted by the source. Therefore: E0 = EB = tA (QF + QV + QE ):
(6)
Since EB is constant and QF per ◦ C is the minimum stable charge of the sum [QF + QV + QE ], it follows that tA is the corresponding maximum value per ◦ C, when the charges QV + QE = 0. EB = tA QF = tA QF :
(7)
It follows that when [ EG + EP +ESG ]=0 and [QV +QE ]=0 Eq. (1) becomes QPH = EB =tA(QF)
and
qPH = EB =tA(QF) AF :
(8)
The value of the variable ESG is zero between 18:00 and 07:00 or for 24 h when cloudiness nC = 8=8. The value of the variable EP can be zero any time if we wish, given that EP is controlled for 24 h. The value of the variable
197
EG 3 becomes minimum to zero many times during a 24-h period, when the space is used for living in. This is due to the fact that in space we do not always have heat produced by the internal energy sources and the presence of habitants. If, assuming the worst case, we cannot achieve a zero value for the sum [ EG + EP + ESG ], the installation of a thermostat in the heated space is the best solution so that ET = E0 . The thermal charge index for the heating of spaces at any moment is expressed according to Eq. (8) as: the ratio of energy consumption (availability) per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month and town. 2.2. Index of energy disposition (IED) With the exception of the ITC, the e9ciency of the thermal energy source must also be taken into account considering that the source constitutes a basic element of the building. Therefore, we have the IED, which is expressed as: the ratio of fuel 4 consumption per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month and town. M PH = mB =tA
and
mPH = mB =tA AF :
(9)
2.3. Thermal charge index in relation to multiple variables Towards the thermal charge of the building, when it is in thermal balance, at any moment, with the exception of the thermal charge index, contributes also other thermal charges in relation to their values, which follow passively (satellite-variables) the thermal charge index. QH = QPH + SQH ; SQH = QW + QR + QSW + QZ :
(10) (10a)
By the sense of passivity, the thermal charges QG , QP , QSG , QV , QE are also satellites. QQH = QW + QR + QSW + QZ + ( QG + QP + QSG + QV + QE ); 3
(10b)
In the case the heated space is used as o9ce space, the value of the variable is zero when o9ces are closed. This is also true in other cases when buildings are used as public services, schools, factories, libraries, shops, churches, restaurants, sport places, gyms, etc. 4 Fuel consumption has been multiplied by the lower heat of combustion.
198
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
QH = QPH + [QW + QR + QSW + QZ + ( QG + QP + QSG + QV + QE )]:
(10c)
Conclusion: The thermal charge of the building at any moment is de/ned as the ratio of energy consumption per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month, town in relation to multiple variables. So, every building at any one time has a thermal charge index and in/nite satellites. From the above, we get coe9cient ZS QH from the equation ZSQH = QH =QPH , which gives the energy picture of satellites as far as their contribution to energy consumption and saving at any moment is concerned. 2.4. Charge of heating spaces for a speci#c time period In the case where we have to heat for a determined time period a space which is surrounded by walls (that can absorb heat), the calculation cannot possibly be done according to the previous, since there is no smooth movement of heat due to heat absorption by the walls. Smooth movement of heat is achieved only in glass-houses. The calculation is given by the equation:
As “prototype residence” is recognized the residence with the smallest “Pr q index” between similar buildings in terms of 6oor surface of heated space, construction, use, etc. The same applies for the “Pr m index of prototype residence”. It is obvious from (13) and (14) that the Pr q , Pr m values are variables, due the deviation of the combustion source from each preset value during a time period. Therefore, the long lasting inspection of the Pr q and Pr m values of the building is necessary. 3.1. Methodology for the recognition of the energy identity of each building Preliminary experimental results show that the curves of the ITC and the IED respectively are linear so, if the values of at least two points of the indices are known, all their values per ◦ C are known. It is considered: qPH = Pr q (Ti − Ta );
(15)
mPH = Pr m (Ti − Ta ):
(16)
In determining QPW we should take into account the sum of surfaces, beams, pillars, etc., surfaces that have the ability to absorb heat. In winter, it is necessary to take into account the fact that, in conditions of irregular operation of the heating system, since the walls are cold, more time is required and a lot more heat to return to temperature conditions acceptable for comfort. The additional burden for heating spaces for a short period of time, is given by the equation:
Since the index qPH and mPH deterministic follow each other, the following refers to the qPH index. The same applies to the mPH index. The present methodology aims to specify the optimum qPH index of each building for which the mean air temperature of the building (TB ) is given to the equation Pr q =0. The heat 6ow from the space to the environment is zero when 8T = 0. The determination of the “possible expected mean air temperature of the building” (TBE ) and afterwards the de/nition of the optimum qPH index according the methodology’s algorithm specify the buildings identity. Since the recognition of the mean air temperature of the heated space (TB ) of a building is practically impossible, sample temperatures are recorded from three or more representative points in space (Ti ). These recorded temperatures are considered to be the “possible expected mean air temperature of the building” (TBE ).
ZQPR = QPR =QH :
TBE = Ti =N:
QPR = QH + QPF + QPW :
(11)
(12)
For a long time period coe9cient ZQPR will have a small value and for a short time period a big one.
As a reference point for the energy identi/cation of buildings (Energy Identity) the Pr q index is inducted. This index is expressed when the thermal charge index (ITC) corresponds to the unit temperature ◦ C (8T = 1). Also, the Pr qm index is used when the IED corresponds to the unit temperature ◦ C. Pr q = EB =tA AF Pr m = mB =tA AF
and and
pr q = EB =tA VH ; pr m = mB =tA VH :
Also, is assumed that the mean air temperature of the building (TB ) is within ±1◦ C of the possible expected mean air temperature. (TB ) = (TBE ) ± 1◦ C:
3. Energy identity of a building
(13) (14)
(17)
(18)
It is considered that all the values between TBE + 1 and TBE − 1 could be “possible expected mean air temperature of the building”. As an example it is considered the value QPH for • index QPH = 0 for TBE , • index QPH = 0 for TBE + 1, • index QPH = 0 for TBE − 1. The recorded “possible expected mean air temperature of the building” is taken TBE =21:3◦ C. From the above, as mean air
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
temperature of the building (TB ) is regarded, the temperature which lies between the following values of temperature: 20:3 ¡ TBE ¡ 22:3. From Eqs. (8), (9), (13) the ITC, IED and Pr q indices, are calculated. According to preliminary experimental results, when there are two or more values QPH ¿ 0 on the line of the ITC and this line has the value QPH = 0 at temperature 20:3 ¡ TBE ¡ 22:3, then the ITC of the building is the same with the calculated index and the corresponding chosen temperature is the mean temperature of the building TB . In the case where for QPH = 0 the temperature is TB = 22:6◦ C or 19:9◦ C, the tolerance range given in Eq. (18) is probably small. 4. Conclusions The present paper introduces a new method for the certi/cation of the energy consumption of a building recording its “energy behavior”. The method utilizes energy indices such as Index of Thermal Charge (ITC) or Index of Energy Disposition (IED) to simulate the heat losses of the building and the heat 6ow because of the temperature di7erence (8T ) from the inner to outer space.
199
This work is based on the interpretation of the energy source behavior, i.e. the operation and cessation time of the source, a behavior during which the source deterministic follows those factors that in6uence it [3,4]. The present method and the algorithm that is implemented could be used as a part of a buildings energy audit or as a single audit method. Additionally it could be used for the inspection of the energy e9ciency in public or municipal buildings. The forenamed method is currently under investigation by the present research team. References [1] Prevezanos S. Energy certi/cation of buildings. Technical Journal 1999;153:56–61. [2] University of Athens. Energy Conservation in Buildings, Central Institution Energy E9ciency Education, 1994. [3] Botsaris PN, Prevezanos S. A monitoring method of a heating energy source e9ciency. Energy and Buildings International Journal 2000;33(6):609–12. [4] Botsaris PN, Prebezanos S. A method for the prediction of a heating energy source deviation from a preset value. Protection and Restoration of the Environment, Fifth International Conference, vol. II, Thassos Island, 3– 6 July 2000. pp. 1257–8.
Building and Environment 39 (2004) 195 – 199 www.elsevier.com/locate/buildenv
A methodology for a thermal energy building audit Pantelis N. Botsarisa;∗ , Spyridon Prebezanosb a Laboratory
of Mechanical Engineering, Department of Electrical and Computer Engineering, Faculty of Energy Systems, Democritus University Of Thrace, Xanthi, Greece b Buildings Energy Certi#cation Center, Xanthi, Greece Received 14 March 2003; received in revised form 6 August 2003; accepted 20 August 2003
Abstract The present paper introduces a new method for the certi/cation of the energy consumption of a building recording its “energy behavior”. The method utilizes energy indices such as Index of Thermal Charge or Index of Energy Disposition to simulate the heat losses of the building and the heat 6ow because of the temperature di7erence (8T ) from the inner to outer space. The present method and the algorithm that is implemented could be used as a part of a building energy audit or as a single audit method. Additionally it could be used for the inspection of the energy e9ciency in public or municipal buildings. The forenamed method is currently under investigation by the present research team. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Energy saving; Energy technology; Energy audit; Building construction
1. Introduction The consumption of energy for the heating of buildings in the European Community (EC) represents 40% of the energy produced [1]. In Greece, heating in the domestic sector represents 61% of total energy consumption [1]. Apart from consumption, the combustion of liquid and gas fuels for the heating of buildings, as well as the increasing use of small conditioning units, burden the environment by releasing combustion gases (CO2 , CO, SO2 , NOX , HC) and smoke [2]. Also, the increased mortality of adults reported in recent years in Europe is attributed to the continuous degrading of the environment. The energy consumption in 1995 –2010 is predicted to continue [1]. As a result, Europe will face ever-bigger environmental problems than those it faced in the 20th century. In reality, the overlooked decision of the EC made in Kioto for the reduction of transmission of greenhouse gases (GHG) by 8% between 1990 and 2010 will not be achieved and, on the contrary, there is an expected increase by 6% [1]. For the reduction of energy consumption, its rational, long-lasting use is fundamental, and it generally ∗
Corresponding author. E-mail addresses: [email protected] (P.N. Botsaris), [email protected] (S. Prebezanos). 0360-1323/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2003.08.016
requires the existence of analytical facts and tools for decision-making in all individual areas. The achievement of the above-mentioned goals regarding the heating of buildings, the production of hot water, steam and hot air, is currently under investigation by the present work and research team. This work is based on the interpretation of the behavior of the source of thermal energy, i.e. of the operation and cessation time of the source, a behavior during which the source deterministic follows those factors that in6uence it [3,4]. The “decoding” of the behavior of the source is the key point in saving energy and protecting the environment. This point supported by modern technology operates as a powerful, safe and economical calculating tool.
2. Theoretical approach of indices 2.1. Index of thermal charge (ITC) The most important part of this method is the index of thermal charge (ITC). The thermal charge of a building for the heating of its spaces when is in a thermal balance, for a given moment in time is given by QH = EB =tA(QF; QV; QE) :
(1)
196
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
Nomenclature QP
Variables QH ET EB EG
EP EGS tA Qv QE tE m n0 MPH mPH SQH QW QR QSW QZ QG
1 The
the thermal charge of the building for the room heating, when the building is in thermal balance at every moment (kW) the heat that develops in space (kWh) the amount of heat transmitted from the source of thermal energy to the space which is being heated (kWh) the heat produced in space which is the sum of the internal sources of energy of the building (human, electrical appliances, etc.) (kWh) the heat produced in space, which results from the sum of the energy systems (kWh) the heat produced in space, resulting from the solar radiation (greenhouse e7ect) (kWh) the period of time of the cycle1 of heat exchange when it is in thermal balance (h) the thermal charge due to losses from renewal of the air in space (kW) the thermal charge due to losses from the speed of air and humidity in space (kW) the time of the transmitted heat from the source of thermal energy to the space2 which is being heated (h) the supply of fuel (kg/h) the degree of e9ciency of the source of thermal energy the index of Energy Disposition of the building (kW) the index of Energy Disposition of the building (w=m2 ) the sum of thermal charges of the variables— satellite (kW) the thermal charge due to losses from wind (kW) the thermal charge due to losses from the rain (kW) the thermal charge from the absorbed heat by the external surfaces of the building. This heat originates from solar radiation (kW) the thermal charge from unknown, unforeseen, etc. losses (kW) the thermal charge from heat produced in space, which originates from the sum of the internal sources of energy of the building (human, electrical appliances, etc.), (kW)
cycle of heat exchange of the system when it is in thermal balance is de/ned by the time period between two consecutive operations of the burner. 2 The time from the start of functioning of the burner until its cessation.
QSG ZSQH Pr m pr m Ti TB TBE Ta nc
the thermal charge from the heat produced in space, which results from the sum of energy systems (kW) the thermal charge from the heat produced in space, which results from the solar radiation (greenhouse e7ect) (kW) satellite coe9cient which gives the contribution of satellites in energy saving or consumption the “Pr m Index” of the building (w=m2 ) the “pr m Index” of the building (w=m3 ) mean temperature of air in space/position of measurement mean temperature of building air potential mean temperature of building air temperature of environmental air cloudiness
Constants E0 QF
Hu EB tA QPH QPR QPF QPW ZQPR qPH Pr q pr q AF VH
the speci/c heat produced in space (kWh) the thermal e9ciency of space due to losses from the di7erence between the temperature of internal space and the environmental temperature. This is lost from the outer surface of the building (kW) the lower heat of combustion (kWh/Kg) the maximum amount of heat transmitted from the energy source to the space that is being heated, so that it remains in thermal balance the maximum period for the cycle (see footnote 1) of heat exchange over ◦ C (h) the index of thermal charge of the building (kW) the charge of heating the space for a determined time period (kW) the charge of heating for windows and other elements which do not store heat (kW) the charge of heating for walls (kW) coe9cient of program burden for the heating of a determined time period the index of thermal charge of the building (w=m2 ) the energy identity of the building, “Pr q index” (w=m2 ) the energy identity of the building, “pr q index” (w=m3 ) the 6oor surface of space that is being heated the volume of space that is being heated
The developed heat, of any moment in time, is supplied by the equation ET = EB + EG + EP + ESG :
(2)
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
The transmitted heat by the source of thermal energy: EB = tE [mHu n0 ]:
(3)
The developed heat (ET ) is either transmitted by sources of thermal energy and the internal sources of the building (electrical appliances, human, etc.) or by solar power (greenhouse e7ect). Also, (ET ) could have its highest point de/ned (controlled by a thermostat) or not. Respectively and in relation to these two cases, there is either energy saving or the temperature increases in space. In the case that room temperature is controlled, the developed heat is de/ned as ET = E0 and Eq. (2) becomes E0 = EB + EG + EP + ESG :
(4)
Assuming that EG + EP + ESG = 0, the amount of heat transmitted from the energy source to the space takes its maximum value. E0 = EB = EB ;
(5)
⇒ EB = EB + EG + EP + ESG
(5a)
with the presence of variables EG + EP + ESG there is energy saving and its value for every moment in time is de/ned by Eq. (5a). In the case that room temperature is not controlled, ET = EB + EG + EP + ESG . There is an increase in room temperature and the amount of heat transmitted from the energy source to the room is always maximum, so the latter remains in thermal balance. In a complete cycle of the process, for the system to remain in thermal balance, the amount of heat transmitted by the energy source equals the amount of heat moves from the heated space to the environment. From Eq. (5) it is known that the amount of heat, which in this case is the maximum transmitted by the source. Therefore: E0 = EB = tA (QF + QV + QE ):
(6)
Since EB is constant and QF per ◦ C is the minimum stable charge of the sum [QF + QV + QE ], it follows that tA is the corresponding maximum value per ◦ C, when the charges QV + QE = 0. EB = tA QF = tA QF :
(7)
It follows that when [ EG + EP +ESG ]=0 and [QV +QE ]=0 Eq. (1) becomes QPH = EB =tA(QF)
and
qPH = EB =tA(QF) AF :
(8)
The value of the variable ESG is zero between 18:00 and 07:00 or for 24 h when cloudiness nC = 8=8. The value of the variable EP can be zero any time if we wish, given that EP is controlled for 24 h. The value of the variable
197
EG 3 becomes minimum to zero many times during a 24-h period, when the space is used for living in. This is due to the fact that in space we do not always have heat produced by the internal energy sources and the presence of habitants. If, assuming the worst case, we cannot achieve a zero value for the sum [ EG + EP + ESG ], the installation of a thermostat in the heated space is the best solution so that ET = E0 . The thermal charge index for the heating of spaces at any moment is expressed according to Eq. (8) as: the ratio of energy consumption (availability) per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month and town. 2.2. Index of energy disposition (IED) With the exception of the ITC, the e9ciency of the thermal energy source must also be taken into account considering that the source constitutes a basic element of the building. Therefore, we have the IED, which is expressed as: the ratio of fuel 4 consumption per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month and town. M PH = mB =tA
and
mPH = mB =tA AF :
(9)
2.3. Thermal charge index in relation to multiple variables Towards the thermal charge of the building, when it is in thermal balance, at any moment, with the exception of the thermal charge index, contributes also other thermal charges in relation to their values, which follow passively (satellite-variables) the thermal charge index. QH = QPH + SQH ; SQH = QW + QR + QSW + QZ :
(10) (10a)
By the sense of passivity, the thermal charges QG , QP , QSG , QV , QE are also satellites. QQH = QW + QR + QSW + QZ + ( QG + QP + QSG + QV + QE ); 3
(10b)
In the case the heated space is used as o9ce space, the value of the variable is zero when o9ces are closed. This is also true in other cases when buildings are used as public services, schools, factories, libraries, shops, churches, restaurants, sport places, gyms, etc. 4 Fuel consumption has been multiplied by the lower heat of combustion.
198
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
QH = QPH + [QW + QR + QSW + QZ + ( QG + QP + QSG + QV + QE )]:
(10c)
Conclusion: The thermal charge of the building at any moment is de/ned as the ratio of energy consumption per unit time when, under de/ned internal room temperature and in full cycle operation, the amount of heat transmitted to space by the thermal energy source has reached its maximum value and equals the amount of heat that moves from the space to the environment in the maximum period of time per ◦ C, month, town in relation to multiple variables. So, every building at any one time has a thermal charge index and in/nite satellites. From the above, we get coe9cient ZS QH from the equation ZSQH = QH =QPH , which gives the energy picture of satellites as far as their contribution to energy consumption and saving at any moment is concerned. 2.4. Charge of heating spaces for a speci#c time period In the case where we have to heat for a determined time period a space which is surrounded by walls (that can absorb heat), the calculation cannot possibly be done according to the previous, since there is no smooth movement of heat due to heat absorption by the walls. Smooth movement of heat is achieved only in glass-houses. The calculation is given by the equation:
As “prototype residence” is recognized the residence with the smallest “Pr q index” between similar buildings in terms of 6oor surface of heated space, construction, use, etc. The same applies for the “Pr m index of prototype residence”. It is obvious from (13) and (14) that the Pr q , Pr m values are variables, due the deviation of the combustion source from each preset value during a time period. Therefore, the long lasting inspection of the Pr q and Pr m values of the building is necessary. 3.1. Methodology for the recognition of the energy identity of each building Preliminary experimental results show that the curves of the ITC and the IED respectively are linear so, if the values of at least two points of the indices are known, all their values per ◦ C are known. It is considered: qPH = Pr q (Ti − Ta );
(15)
mPH = Pr m (Ti − Ta ):
(16)
In determining QPW we should take into account the sum of surfaces, beams, pillars, etc., surfaces that have the ability to absorb heat. In winter, it is necessary to take into account the fact that, in conditions of irregular operation of the heating system, since the walls are cold, more time is required and a lot more heat to return to temperature conditions acceptable for comfort. The additional burden for heating spaces for a short period of time, is given by the equation:
Since the index qPH and mPH deterministic follow each other, the following refers to the qPH index. The same applies to the mPH index. The present methodology aims to specify the optimum qPH index of each building for which the mean air temperature of the building (TB ) is given to the equation Pr q =0. The heat 6ow from the space to the environment is zero when 8T = 0. The determination of the “possible expected mean air temperature of the building” (TBE ) and afterwards the de/nition of the optimum qPH index according the methodology’s algorithm specify the buildings identity. Since the recognition of the mean air temperature of the heated space (TB ) of a building is practically impossible, sample temperatures are recorded from three or more representative points in space (Ti ). These recorded temperatures are considered to be the “possible expected mean air temperature of the building” (TBE ).
ZQPR = QPR =QH :
TBE = Ti =N:
QPR = QH + QPF + QPW :
(11)
(12)
For a long time period coe9cient ZQPR will have a small value and for a short time period a big one.
As a reference point for the energy identi/cation of buildings (Energy Identity) the Pr q index is inducted. This index is expressed when the thermal charge index (ITC) corresponds to the unit temperature ◦ C (8T = 1). Also, the Pr qm index is used when the IED corresponds to the unit temperature ◦ C. Pr q = EB =tA AF Pr m = mB =tA AF
and and
pr q = EB =tA VH ; pr m = mB =tA VH :
Also, is assumed that the mean air temperature of the building (TB ) is within ±1◦ C of the possible expected mean air temperature. (TB ) = (TBE ) ± 1◦ C:
3. Energy identity of a building
(13) (14)
(17)
(18)
It is considered that all the values between TBE + 1 and TBE − 1 could be “possible expected mean air temperature of the building”. As an example it is considered the value QPH for • index QPH = 0 for TBE , • index QPH = 0 for TBE + 1, • index QPH = 0 for TBE − 1. The recorded “possible expected mean air temperature of the building” is taken TBE =21:3◦ C. From the above, as mean air
P.N. Botsaris, S. Prebezanos / Building and Environment 39 (2004) 195 – 199
temperature of the building (TB ) is regarded, the temperature which lies between the following values of temperature: 20:3 ¡ TBE ¡ 22:3. From Eqs. (8), (9), (13) the ITC, IED and Pr q indices, are calculated. According to preliminary experimental results, when there are two or more values QPH ¿ 0 on the line of the ITC and this line has the value QPH = 0 at temperature 20:3 ¡ TBE ¡ 22:3, then the ITC of the building is the same with the calculated index and the corresponding chosen temperature is the mean temperature of the building TB . In the case where for QPH = 0 the temperature is TB = 22:6◦ C or 19:9◦ C, the tolerance range given in Eq. (18) is probably small. 4. Conclusions The present paper introduces a new method for the certi/cation of the energy consumption of a building recording its “energy behavior”. The method utilizes energy indices such as Index of Thermal Charge (ITC) or Index of Energy Disposition (IED) to simulate the heat losses of the building and the heat 6ow because of the temperature di7erence (8T ) from the inner to outer space.
199
This work is based on the interpretation of the energy source behavior, i.e. the operation and cessation time of the source, a behavior during which the source deterministic follows those factors that in6uence it [3,4]. The present method and the algorithm that is implemented could be used as a part of a buildings energy audit or as a single audit method. Additionally it could be used for the inspection of the energy e9ciency in public or municipal buildings. The forenamed method is currently under investigation by the present research team. References [1] Prevezanos S. Energy certi/cation of buildings. Technical Journal 1999;153:56–61. [2] University of Athens. Energy Conservation in Buildings, Central Institution Energy E9ciency Education, 1994. [3] Botsaris PN, Prevezanos S. A monitoring method of a heating energy source e9ciency. Energy and Buildings International Journal 2000;33(6):609–12. [4] Botsaris PN, Prebezanos S. A method for the prediction of a heating energy source deviation from a preset value. Protection and Restoration of the Environment, Fifth International Conference, vol. II, Thassos Island, 3– 6 July 2000. pp. 1257–8.