A MATHEMATICAL MODEL OF A MICRO-COGENERATION SYSTEM COUPLED TO A HEAT PUMP FOR RESIDENTIAL APPLICATIONS: AN ENERGETIC PERFORMANCE ASSESSMENT M.Badamia, I. Bertinib, F. Ceravolob, B. Di Pietrab*, F. Margiottab, A. Portoraroa, and G. Puglisib a DENERG - Politecnico di Torino - Corso Duca degli Abruzzi, 24 - 10129 Torino Italy b ENEA UTEE-GED - Via Anguillarese, 301 - 00123 Roma (Italy) *corresponding author:
[email protected]
ABSTRACT This paper describes a mathematical steadystate model of a micro-cogeneration system made up of an internal combustion engine, mechanically coupled to a reversible heat pump (GHP unit). The small-scale cogenerator model is based on the experimental performance maps of the engine, that have been normalized, in order to allow the model to be scaled for the simulation of a large range of plant in the very small sizes (1-10 kWel). The electricity produced by the cogenerator feeds the heat pump, which is able to provide both heating and cooling power. The natural gas fired heat pump model is integrated in a novel software platform for dynamic simulation of the whole building-HVAC system called ODESSE (Optimal DEsign Smart Energy System). ODESSE platform has been developed by the Italian National Agency for New Technologies, Energy and Environment (ENEA) using MATLAB/Simulink software, and is aimed at assessing the technical-economic feasibility of interventions for the energy improvement of existing buildings. This platform is supposed to be an interesting tool also for the analysis of performances of CHP systems in polygeneration and district-heating configuration. The GHP model, within the ODESSE platform, is employed for the simulation of the energetic performance of micro-cogeneration systems, when applied in residential air conditioning applications, such as the household energy demands of small block of family users. This research is carried out by Politecnico di Torino and ENEA (Italy) in the framework of “R&D activities of general interest for the National Electric System” funded by Ministry of Economic Development (MSE). The main results of the study are thoroughly presented in the paper. Keywords: GHP, micro-cogeneration systems, natural gas heat pump, polygeneration, ODESSE, simulation model.
INTRODUCTION In this work is presented a steady-state model to simulate the real work condition of a unit consisting of an internal combustion engine with natural gas coupled to a heat pump (GHP unit). The internal combustion engine drives the compressor of the refrigeration circuit by means of a belt transmission, while a heat exchanger allows to transfer the heat from the exhaust gases to the cooling circuit and / or production of sanitary hot water . The GHP model has been integrated in a novel software platform for dynamic simulation of the whole building-HVAC system and energy demands of small block of buildings called ODESSE (Optimal DEsign Smart Energy System) developed by the Italian National Agency for New Technologies, Energy and Environment (ENEA) using MATLAB/Simulink software. (Bertini et all, 2009). The aim of this work was to evaluate by means ODESSE platform, the effective economical and energy convenience of different available heat pump technologies, on the effective economical and energy convenience in air conditioning plants for single family house in Italy. For this reason we considered two kind of available technology , a reversible air-water GHP unit and a air-water EHP unit.
METHOD Description of the GHP model The GHP model has been developed on the Matlab/Simulink platform. Aim of the model is to simulate a natural gas fed heat pump, made up of a small-scale internal combustion engine cogenerator, mechanically coupled to a reversible heat pump. The software allows the GHP unit to follow the thermal or the cooling load of the building, to which the plant is connected. A picture of the main blocks of the model is reported in Figure 1.
Pm_CHP
feedback
Tamb
2 Pm_CHP
Pfuel
1
Goto
Pfuel
Tamb
1 Tamb
Tf
Tf ,c
Tf ,c
Tf
Tamb -C-
Power Lost
Tamb
m_dot_hm m_dot_f
m_dot _hm [kg/s]
m_dot_f
From
m_dot_f
m_dot_f
4 flue
Thm,u,saa
Thm,i,saa
Thm,i,saa
Thu,i,saf
Thu,i,saf
Pth,hu,saf
m_dot_hu
Internal Combustion Engine
m_dot_hm
m_dot_hu
Thu,u,saf
Pth,hu,saa
2 m_dot _hu
m_dot_hu
3 Thu ,i,saa
Thu,i,saa
Pradiatore
heat exchanger water / water / exhaust gases 5 Pradiatore
Thm,u,saa
heat exchanger water / water
-K cp_h
Product
3 Pth,CHP
4 Building Thermal load Tamb
Pth,tot
outside temperature
T_Tank
Pth,HP
Thermal storage Pm_CHP
Heat Pump
Pth _HP
Pth,HP
6 Pth,HP
Figure 1: Simulink mathematical modelof the GHP unit The ICE cogenerator model gas been derived, by means of several changes and optimizations, from a previous model which was set-up for the simulation of CHP plant in the 100-500 kWel range [10]. The GHP unit is made up of the following components: − an internal combustion engine; − a water / water heat exchanger; − a gas / water heat exchanger; − a reversible heat pump. Moreover, a thermal tank between the user side (the building) and the thermal production side (the cogenerator and the heat pump) has been provided, in order to decouple the load side from the production side; a thermal / cooling load following control has been implemented in order to maintain a chosen setpoint temperature inside the tank, both during the heating, and the cooling period. In the winter season, both the thermal recovery of the ICE, and the thermal power delivered by the heat pump, are employed for heating purposes. In the summer season, only the cooling production of the heat pump is considered for the building air conditioning. The model works by means of the experimental maps of the modelled cogenerator. The electrical power map and the temperature of the exhaust gases map as a function of the fuel power have to be inserted in the model. A detailed study was conducted on the experimental data of several microcogeneration systems available on the market, in order to find out the experimental performances of these power systems. Moreover, both maps are then made dimensionless in order to be suited to work properly with different cogenerators in the small-scale range (1-10 kWel). The
experimental electrical efficiencies at nominal and at partial load, for the different analysed units, are reported in Figure 2. The fitting blue curve, has then expressed as a function of the input fuel power (Figure 3), and inserted in the Simulink software (Figure 4).
Figure 2: Experimental electrical efficiencies of the analyzed micro-CHP systems at nominal and partial load condition
Figure 3: Experimental electrical power of the analyzed micro-CHP systems as a function of the fuel input power
The functional scheme of the integration between the ICE and the HP, is depicted in Figure 7.
Figure 4: Simulink block with the experimental electrical power map The heat pump was modelled by simulating the refrigeration cycle. Pressure-Enthalpy Diagram for HFC-134a coolant has been inserted in the heat pump Simulink block. The external air temperature and the one of the space to be heated/cooledhave to be provided, together with the temperature drops at the condenser and at the evaporator. The model calculates the condensing and the evaporating temperatures, and all the thermodynamic figures of the refrigeration cycle, under the hypothesis that no subcoolingor superheating are realized. The COP and the EER of the cycle are also evaluated. The Simulink code which provides the full refrigeration cycle calculation is reported in Figure 6, while an example of the cycle simulated by the software is reported in Figure 6.
Figure 7: Functional scheme of the ICE-HP integration The governing equationson the basis of the GHP unit operation, are the following: P =η P m,HP
m
m,CHP
P
=η
P
= COP P
P
= EER P
P
=P
el,HP th,HP c,HP th,tot
P
P
el,HP
m,HP el,HP
el,HP
th,CHP
+P
th,HP
th,CHP
=P *η f
th
GUEwinter = P
th,HP
GUEsummer = P
/P
c,HP
Figure 5: Simulink code employed in the refrigeration cycle calculation
Figure 6: Example of the simulated refrigeration cycle
f
/P
f
Where COP, EER and GUE are the Coefficient of Performance, the Energy Efficiency Ratio and the Gas Utilization Efficiency of the GHP unit, respectively. Description of the input and outputs The GHP model requires the following data in input: − ambient temperature; − hot water mass flow to the thermal user; − hot water temperature from thermal user. The main outputs of the model are the thermal power recovered from the water/water and the gas/water heat exchangers, respectively, and the thermal power to the ICE radiator and to the stack. Natural gas consumption and temperatures of the hot water to the user are also calculated. All the thermodynamic figures of the refrigeration cycle, together with the heat pump COP and EER, are finally evaluated.
Model validation The GHP model has been validated by means of the experimental data provided by the unit manufacturer, listed in Table 1. Two simulations have been carried out, based on the nominal data of the 8HP and 10HP models, as their size was the closer to the one of the small-scale systems here analyzed. Only the heating configuration was considered in the calculations. Table 1: Nominal data of the two GHP units considered for the model validation NOMINAL DATA MODEL
Pm,HP [kW]
Pf [kW]
8HP
5.0
15.5
10HP
6.5
20.1
Figure 8: Position of nominal and simulated total thermal recovery on the GHP performance map
The following setup data were assumed, for both simulations and case study:
DISCUSSION AND RESULT ANALYSIS
ηel,HP = 0.85 ηm,HP= 0.85 ηm= 0.87 ηis,c= 0.70 Tair = 7°C (cold source) Twater = 35°C (hot sink) ∆Tc= 2°C ∆Te = 2°C The simulation was aimed at calculating the total thermal recovery Pth,tot, given by the sum of the thermal recovery from the internal combustion engine, and the thermal production of the heat pump.The results are shown in Table 2, where the data provided by the manufacturer are compared to the output of the simulation model, and the discrepancy between the two values is also reported.
Case study The study concerns the analysis and energy simulation of two systems, a microcogeneration system made up of an internal combustion engine, mechanically coupled to a reversible heat pump (GHP unit with nominal data showed in table 3) and an electric heat pump (EHP unit with nominal data showed in table 3) for the air conditioning of a typical residential building (figure 9) in four italian cities Palermo, Naples, Rome and Milan respectively for B, C, D and E climatic zones. Table 3: Nominal data of GHP air-water units considered for the case study
SIMULATED DATA
∆%
8HP
23.5
23.7
+0,9%
10HP
30.0
30.7
+2,3%
The total thermal recovery in the two cases is also reported in the performance map of the GHP unit (Figure 8), provided by the manufacturer, where is plotted as a function of the fuel power input into the unit.
21 kW
Rated heating capacity
33 kW
Rated mechanical output
Table 2: Results of the simulation (Pth,tot [kW]) MANUFATURER DATA
Rated cooling capacity
6 kW
Table 4: Nominal data of EHP air - water units considered for the case study Rated cooling capacity
18.4 kW
Rated heating capacity
21 kW
Rated mechanical output .
6 kW
that are the same for the four orientation. The Tables 8 and 9 refers the structural characteristics of the horizontal external walls, respectively of the roof and of the ground floor. Table 7: thermophysical characteristics of the vertical external walls Structural characteristics of the vertical external walls
t
l
R
U
(m)
(W/mK)
(m²K/W)
(W/m²K)
Rsi Plaster
0.13 0.025
1.4
0.02
0.08
0.90
0.09
0.12
0.67
0.180
Insulating Perforated brick
0.08
0.17
0.47
0.12
0.90
0.13
Table 5: dimensional elements of the building
Plaster
0.025
1.4
0.02
Height
m
3
Rse
Length
m
10
Depth
m
10
Volume Form factor S/V
m3
300
Figure 9: plan of a typical residential building As reported in the following table consists of a plan whose area is of 100 square meters and volume is of 300 cubic meters.
1,07
The distribution of the outer opaque and transparent surfaces for the four types of orientation of the external wall as shown in the following table: Table 6: Opaque and transparent surfaces
NORTH SOUTH EAST WEST Ground floor Roff
Total
Opaque
Transparent
(m2) 30 30 30 30 100 100
(m2) 27,9 24,82 25,8 25,8 100 100
(m2) 2,1 5,18 4,2 4,2
The structure of the building has been designed with reinforced concrete and with double glass windows. In the three following tables are reported the thermophysical characteristics of the external surfaces of the building. In particular the Table 7 refers the structural characteristics of the vertical external walls,
Perforated brick Air layer
TOTAL
0.04 0.45
1.079
0.927
Table 8: thermophysical characteristics of the roof t
l
R
U
(m)
(W/mK)
(m²K/W)
(W/m²K)
Rsi Plaster
0.03
0.7
0.1 0.043
Attic
0.18
0.60
0.300
Insulating
0.03
0.046
0.652
Screed
0.03
1.4
0.021
Concrete lining
0.03
1.4
0.021
Rse TOTAL
0.040 0.30
1.178
0.849
In particular the tables 10a and 10b refer the thermophysical and dimensional characteristics of the windows of the two types of windows, respectively “A” and “B” type. In the building there are two types of windows, Type “A” and Type “B”.
Table 9: thermophysical characteristics of the ground floor
Table 10b: dimensional characteristics of the windows Dimensional Characteristics
t
l
R
U
(m)
(W/mK)
(m²K/W)
(W/m²K)
Rsi
0.17
Shingle
0.18
0.7
0.257
Attic
0.22
0.67
0.330
Insulating
0.05
0.046
1.087
Screed
0.03
0.9
0.033
Tiles
0.02
1
0.020
Rse TOTAL
0.50
1.900
0.52
Table 10a: thermophysical characteristics of the windows Thermophysical Characteristics Glass Thermal Transmittance (W/m²K) Frame Thermal Transmittance (W/m²K) Linear Thermal Transmittance (W/mK) TOTAL TRANSMITTANCE WINDOW (W/m²K)
Ug
3
3
Uf
2.4
2.4
ψl
0.08
0.08
Uw
3.12
3.17
Type "B"
Total Surface (m2)
Aw
2.1
3.08
2
Glass Surface (m )
Ag
1.54
2.51
Frame Surface (m2)
Af
0.56
0.57
l
7.48
10.68
Perimeter joint glass-frame (m)
-
Type "A"
Results In order to make an economic analysis of the two system configurations, an analysis of the prices (inclusive of all taxes) of natural gas and electricity was performed. As in Italy there is the free market, the price changes are such that they determine the advantage of one of the two configurations. In the tables 12 and 13 have been reported energy consumption, separated by heating seasons; in particular for the GHP configuration are shown gas consumption (gas), the heat supplied by the heat pump after recovery of the thermal energy from the exhausted gases and from the engine (Et_HP), the total heat energy supplied by GHP (Et_GHP) and the percentage of heat energy recovered from the exhausted gases and from the engine (% rec). The simulation has been completed considering the using profile of building as shown in the following table:
Table 11: Using profile of the building
Heating
Working days Saturday Holidays
h
Using profile of the building Number of Infiltration Activity Occupants m3/h Type n. 0.3 Sedentary 5
6-8
16 - 23
24
6-8 17-23
6-8
16 - 23 0 - 23
24 24
6-8 17-23 24
Installed Power W/m2 3 6-8
Illuminated Area m2 50 16 - 23 17 - 23 17 - 23
Table 12: GHP energy consumption GHP PA
NA
RM
MI
gas_w (m3)
626.79
787.55
883.39
1589.40
Et_HP_w (kWh) Et_GHP_w (kWh) % rec
3262.48
4542.28
5893.80
8797.60
4963.70
6880.38
8763.70
13646.43
34.3%
34.0%
32.7%
35.5%
gas_s (m3)
182.01
128.30
111.68
42.89
2250.46
1728.96
1538.90
652.74
Et_HP_s (kWh)
convenient the GHP configuration, while in the northern areas (Milan), convenience is more strongly influenced by the price. In all cases examined, the difference in absolute value between the two configurations is limited so that it can be concluded affirming that the two technologies are substantially equivalent.
for HP configuration are shown the heat (Et) and electrical (Ee) consumption: Table 13: HP energy consumption HP PA
NA
RM
MI
Et_w (kWh)
4827.56
6665.41
8589.59
13277.04
Ee_w (kWh)
1578.00
2233.50
2908.50
4878.00
Et_s (kWh)
2250.46
1728.96
1538.90
652.74
Ee_s (kWh)
706.50
498.00
433.50
166.50
It can highlight how the GHP allows to recover from the flue gases from the engine and a percentage of thermal energy always greater than 30%, in each of the 4 cases simulated. In order to make an economic analysis that shows how the convenience of one of the two solutions is strongly influenced by the cost of primary energy carrier, were considered two values of prices, a minimum and maximum:
Figure 10: winter costs for case 1 prices
Figure 11: summer costs for case 1 prices
Table 14: unit costs UNIT COSTS Min electric energy [€/kWh] methane [€/Sm3]
Max
(Case 1)
(Case 2)
0.8
1
0.27
0.31
Figure 12: total costs for case 1 prices The analysis shows that, in essence, the two technologies, in the case of the building under consideration, are equivalent. Following are shown the diagrams for each price case and for each city. It can observe how the GHP configuration is always convenient for cooling for each of the 4 cities, regardless of price. For heating, instead, the convenience is not unique. The configuration HP is cheaper in the south of Italy (Palermo and Naples) for both prices, in the central areas (Rome), it is always
Figure 13: winter costs for case 2 prices
[3] Bertini I., Ceravolo F., Citterio M., De Felice M., Di Pietra B., Margiotta F., Pizzuti S., Puglisi G. 2010. Ambient Temperature Modeling with Soft Computing Techniques Solar Energy Journal, Volume 84, Issue 7, 1264-1272
Figure 14: summer costs for case 2 prices
[4] Erbs, D.G., S.A. Kein e J.A. Duffie, 1982. , 28, 293 (1982). Estimation of the Diffuse Solar Radiation Fraction for Hourly, Daily and Monthly-Average Global Radiation, Solar Energy, Vol. 28, 293-302. [5] Erbs D.G., Klein S.A., Beckman W.A. 1983. Estimation of degree-days and ambient temperature bin data from monthly-average temperatures, Ashrae Journal, 60-65.
Figure 15: toral costs for case 2 prices
CONCLUSION The paper analyzes a mathematical model of a GHP unit, made up of a micro-cogeneration system with an internal combustion engine, coupled to a reversible heat pump mechanically. The model was developed in Matlab Simulink platform, and was validated by data provided by the main manufacturers. The discrepancies have been calculated and they result below 2.5% by nominal data. Further the paper analyzes the energy and economical performances of two configuration plants: a GHP unit; an electric heat pump (EHP) for the air conditioning of a typical italian residential building. The simulations show that basically the two configurations, in the case of the building examined, are economically equivalent. This work is dedicated to our dear friend Francesco.
REFERENCES [1] I. Bertini, F. Ceravolo, M. De Felice, B. Di Pietra, F. Margiotta, S. Pizzuti, G. Puglisi 2009. Sviluppo dell'ambiente di progettazione Optimal DESign for Smart Energy – ODESSE, RICERCA SISTEMA ELETTRICO, [2] Ceravolo F., Di Pietra B., Pizzuti S., Puglisi G. 2008. Neural Models for Ambient Temperature Modelling, IEEE - CIMSA08, Istanbul Turkey.
[6] Ceravolo F., Di Pietra B., Margiotta F., Puglisi G. 2010. ODESSE: simulazione dinamica del sistema edificio-impianti per la climatizzazione estiva, ODESSE, RICERCA SISTEMA ELETTRICO, Report RSE/2010/, Italy. [7] G. Ruscica, M. Badami, A. Portoraro. Micro - cogenerazione nel settore residenziale con l’utilizzo di motori a combustione interna: Sviluppo di un modello matematico per la simulazione oraria e analisi di un caso reale RICERCA SISTEMA ELETTRICO, Report RSE/2010/, Italy. [8] Dorer V., Weber A. (2007). Methodology for the Performance Assessment of Residential Cogeneration Systems. IEA/ECBCS Annex 42 Report [9] Di Pietra B. (ed). (2008). Performance Assessment of Residential Cogeneration Systems in different Italian climatic zones. IEA/ECBCS Annex 42 Report. [10] Badami M., Bertini I., Ceravolo F., Di Pietra B., Portoraro A. , Puglisi.G. (2011) A New Tool For Simulation And Design Of SmallScale Internal Combustion Engine Cogenerator In Energy Efficient Buildings.
% rec
NOMENCLATURE CHP COP EER GUEwinter
HP EHP GHP ICE P
combined heat and power coefficient of performance energy efficiency ratio Gas Utilization Efficiency (heating) Gas Utilization Efficiency (cooling) heat pump Electrical heat pump Gas heat pump internal combustion engine mechanical power provided by
P
the ICE mechanical power input to the
P
HP electric power input to the HP
P
thermal power provided by the
HP P
thermal power recovered from
P
the ICE total useful
P
(HP+ICE) cooling power provided by the
P
HP fuel input power to the GHP
GUEsummer
m,CHP
m,HP
el,HP th,HP
th,CHP
th,tot
c,HP
f
thermal
power
η
unit temperature drop on the condenser temperature drop on the evaporator ICE HP mechanical
η
transmission efficiency electric efficiency of the HP
η
thermal efficiency of the CHP
η
system electric efficiency of the CHP
∆Tc ∆Te m
el,HP th
el
t
system isentropic efficiency of the compressor thickness
l
conductivity
R U gas_w Et_HP_w
resistance transmittance gas consumption in winter thermal energy from the exhausted gases and from the engine in winter total heat energy supplied in winter
ηis,c
Et_GHP_w
gas_s Et_HP_w
Et_w Ee_w Et_s Ee_s PA NA RM MI Rsi Rse
percentage of heat energy recovered from the exhausted gases and from the engine gas consumption in summer thermal energy from the exhausted gases and from the engine in summer heat consumption in winter electrical consumption in winter heat consumption in summer electrical consumption in summer Palermo Naples Rome Milan internal liminal thermal resistance exsternal liminal thermal resistance
