SMALL-SCALE COGENERATION FOR BUILDING
APPLICATIONS
PART 2 - OPTIMAL SIZING OF THE CHP PLANT
Jacek Kalina, Janusz Skorek
Division of Thermodynamics and Gas Energy, Institute of Thermal Technology,
Silesian University of Technology, 44-100 Gliwice, Konarskiego 22, Poland
Summary In the paper the problems of optimal sizing of a small-scale
CHP plant for building energy supply system are presented and discussed.
Calculation procedures are shown together with the results of sample
analysis. The factors that influences the final configuration of the system
are indicated.
Keywords: cogeneration, buildings, gas engines, gas turbines, electricity and
heat load variations, optimization, gas boilers.
INTRODUCTION
In this paper the problem of optimal sizing of a small-scale CHP plant for
building energy supply system is being discussed on the example of
demonstration project. The project consist in design and installation of CHP plant
that would meet the heat and electricity demands of the group of three different
buildings. The energy demand analysis has been presented in the part 1 of this
paper. The sizing procedure of the plant is based on daily heat and electricity load
profiles.
Schematic diagram of the heat and power plant is shown in figure 1. It has
been assumed that the system is based on the natural gas fired reciprocating
engine. It was found from the energy demand analysis that only microturbines or
fuel cells can be an alternative solution in this case. However, both turbines and
fuel cells are much more expensive than engines, what makes an economic effect
of the project worse.
In order to meet heating demand of the consumers the plant produces hot
O
water that is subsequently fed into the local heating network of 90/70 C
temperature characteristics (at external temperature -20OC). In case of installation
of the CHP module, the electricity is transmitted via common bus to either the
consumers or to the external grid operated by the electricity company. In the case
of electricity shortages, the bus can be also supplied with power from the grid.
Figure 1. Cogeneration plant (CHP  cogeneration module, B  gas boiler; VC 
ventilator cooler, HA  heat accumulator, G - generator)
The objective function for the plant optimisation procedure is the Net Present
Value of the project for specific time of economic life (typically N = 15 years)
[1,1,3]:
N
CFt
(1)
NPV = - J0 max
"
(1+ r)t
t=1
The objective function is typically constrained by technical parameters of the
plant and the economic environment. Therefore the complete analysis consists of
two integral parts: technical analysis and economic analysis. Scheme of the
optimization algorithm is shown in figure 2.
Figure. 2. Block diagram of plant sizing optimisation procedure
Momentary energy balance for the entire CHP plant can be written as follows:
& & &
(2)
PWd + ´NG = ND - (´ -1)NS + QD + Qstr
Then particular elements of the equation 1 can be decomposed as follows:
nCHP nP
(3)
ND = +´NG + (´ -1)NS -
"NCHPi "NPj
i=1 k =1
nCHP nK
(4)
& & &
QD = + -Qstr + "Q
"Q "Q & &
CHPi Kj
i=1 j=1
nCHP nK nCHP &
NCHPi nK QKj
(5)
& & &
PWd =
"(PW )CHPi + "(PW )Kj = "· + "·
d d
i=1 j=1 i=1 j=1
E _ CHPi Ekj
Ratio of electricity and heat for CHP plant is expressed by the cogeneration
index Ã:
NCHPi
(6)
à =
i
&
QCHPi
The minimum value of the cogeneration index à is limited by the maximal
possible heat output of the particular gas engine.
Particular parameters of the machinery characteristics (·E_CHP, Ã) typically
depend on the nominal electric power and momentary load. Figure 3 presents
energy characteristics of cogeneration modules with gas engines worked out for
the purpose of preliminary machinery sizing procedure.
a) b)
45 1,2
1
40
0,8
35
0,6
30
0,4
à = 0.3605 N0.1137
25 · = 23,485 N0,0691
0,2
R2 = 0.5821
R2 = 0,7203
0
20
0 1000 2000 3000 4000 5000 6000 7000
0 1000 2000 3000 4000 5000 6000 7000
moc elektryczna, kW
moc elektryczna, kW
Figure 3. Efficiency (a) and cogeneration index (b) of gas engine based CHP
modules in the electric power range of 50  6000 kW (note: exhaust gases cooled
down to 120 OC)
In order to estimate heat output and fuel energy consumption at partial loads
the following dimensionless characteristics of the CHP module have been used:
·E CHP (7)
_ 3 2
= 0.0025(¾el ) - 0.2431(¾el ) + 0.587(¾el )+ 0.6537
(·E CHP )nom
_
à (8)
3 2
= 0.8147(¾el ) -1.9848(¾el ) +1.7756(¾el )+ 0.3968
Ã
nom
Nel
¾el =
where: - dimensionless load, = 0.2  1.
¾el
Nel nom
_
Efficiency of gas boilers is mainly a function of heat transfer area. Therefore
for each nominal heat output of the boiler the same value of efficiency can be
sprawność
·
,
%
wskaz
nik skojarzenia
Ã
reached. it was assumed that this values is fixed at the level ·Ek = 0.92 and it does
not vary with the nominal heating power of the boiler. In order to estimate the
behaviour of the boiler at partial loads the following dimensionless characteristics
has been used:
·Ek (9)
= -0.1318x4 + 0.1693x3 - 0.1096x2 + 0.1165x - 0.9556
(·Ek )
nom
&
Q
where: - dimensionless load.
x =
&
Qnom
In was found from the heat load duration curve that the maximum heat
demand occurs only during a very short period of time over the year. Therefore it
is needless to size the heating system for maximum load as it will mostly operate
at partial load (with lower efficiency). It is usually possible that the building
designer allows shortages of heat in some periods. This allowances must be
known at the stage of planning the heating system. The temporary heat shortages
&
can be included in energy balance of the plant:
"Q
& &
(10)
"Q = Ä…QD
The Ä… index must be controlled over all period of the simulation of plant
operation. If the value of the index or the time of its appearance exceed the set up
limits the system must be configured again.
Each machine or device can operate only within the defined range of
allowable load. It means that the following inequality constraints have to be taken
into account:
(11)
(NCHPi ) d" NCHPi d" (NCHPi )
min nom
& & &
(12)
(QKj ) d" QKj d" (QKj )
min nom
If the local cogeneration system has to meet simultaneous demands for heat
and electricity there can be defined 9 cases of relations between the heat and
electricity demands and the production capacities of the plant [1] It was found
that the priority of the system operation strongly influences the final economic
effect of the project [1]. There are several possible modes of CHP module
operation. In this paper the following modes are taken into account:
1) electricity tracking (ET)  in this mode the priority is electricity production.
The power of the cogeneration module is following the demand of the
consumer. There is no transfer of surplus electricity to the external utility
grid. Heat demand is balanced by the boiler or heat storage tank. If there is a
surplus heat it is dissipated into the atmosphere.
2) heat tracking (HT)  in this mode the priority is heat production. The heat
output of the cogeneration module is following the demand of the consumer.
CHP module usually operates in parallel with boilers. Electricity demand is
balanced by the grid.
3) full load operation (FL) cogeneration module is run at full load no matter
what the demand of the consumer is. The momentary energy balance of the
plant converges by the cooperation with grid, boilers, storage tanks,
ventilator coolers and other devices.
Almost each cogeneration module equipped with standard automatic control
system can run in the above defined modes.
Optimization of the plant was done by searching for the best solution within
the predefined range of trial variants. Energy balance calculations were
performed as an  hour by hour simulation of the plant operation [1,2]. The
analysis was carried out with using an Excel spreadsheet and Visual Basic
macros. Columns of the spreadsheet (matrix) represent particular positions of
equations (2)  (5), whereas the rows represent time. Once the annual energy
balance of the plant is done the economic analysis starts.
The economic analysis basis on the cash flow CF calculation for the whole
lifetime of the project:
N N
(13)
CF = = (- J0 + Sn - (KE + Kop + SR ) - Pd + L)
"CF "
t
t
t=0 t=0
In order to estimate investment costs J0 the typical curves of unitary cost i
were used:
a) for gas boilers (boiler purchase cost, zł/kW):
&
(14)
i = 250Qnom -0.13
&
where Qnom denotes nominal heat output in kW. Heat output range 50 kW to
10000 kW.
b) cogeneration module with gas engine (together with ventilator cooler) 
unitary cost in US$/kW within the electric power range 9 kW do 6000 kW:
(15)
i = 2594.9(Nnom )-0.2857
All additional costs were estimated either with using a typical cost breakdown
or the offers from vendors. It appeared that equipment purchase cost lays down
typically in the range of 40% to 60% of the total investment cost J0.
In our case real incomes appear only for HT or FL modes of cogeneration
module operation. The income results from the sale of the electricity surplus to
the grid and it is calculated as follows:
Ä
R
(16)
Sn = NS dÄ
+"
0
Total exploitation cost can be expressed as follows:
(17)
KE = Ken + KO&M + Kp + Kśr
The most important is the cost of energy:
Ä Ä
R R nCHP nK &
ëÅ‚ öÅ‚
QKj
NCHPi (18)
&
Ken = KendÄ = k + k + NGkel (Ä )÷Å‚dÄ
" "
+" +"ìÅ‚
ìÅ‚ ÷Å‚
LHVCHP·E CHPi fCHP LHVk·Ekj fk
i=1 j=1
0 0 _
íÅ‚ Å‚Å‚
Operating and maintenance costs were calculated with using the typical index
of unitary costs for gas engines kO&M = 0.007 do 0.02 US$/kWh (at annual
availability in the range of 92  97 %). Therefore the following equation can be
used:
Ä
R nCHP
(19)
KO&M = EelkO&M = kO&M dÄ
"NCHPi
+"
i=1
0
Environmental costs are given by equation:
Ä Ä Ä
R n R R
(20)
& & & &
Kenv = dÄ = [(GPi CHP + GPi k )kPi]dÄ + kW dÄ
env " _ _ W
+"K +" +"G
i=1
0 0 0
Typically & &
GPi CHP ,GP B are calculated with using emission indices for
_ _
particulate machinery type. Emission fees in Poland are regulated by the
government: SO2 - 0.38 PLN/kg; CO2 - 0.00020 PLN/kg; CH4 - 0.00020 PLN/kg;
NO2 - 0.38 PLN/kg; CO - 0.10 PLN/kg; NMHC - 0.10 PLN/kg; dust - 0,25
PLN/kg (Note: 4.7 zł = 1 EURO).
REFERENCE CASE ANALYSIS
In the reference case of calculations it has been assumed that no cogeneration
module will be installed on site. The existing coal fired boiler plant will be
replaced with gas boiler plant, electricity will be purchased from the utility grid
separately for each building. Proposed gas boiler plant would consist of three gas
boiler of respectively 350, 350 and 200 kW heat output. Fuel and energy prices,
that were used in the analysis, are as follows:
" Natural gas price depends on an annual consumption,
average value is: 0.796 PLN/Nm3.
" Electricity price: - sport centre (tariff C21): 328.67 PLN/MWh,
- school (tariff C11): 336,17 PLN/MWh.
Technical and economic results of the project are given in table 1.
Table 1. Results of technical and economic analysis for base case project
No. Quantity Unit Value
1 Amount of heat produced at boiler plant GJ/a 7272
2 Heat shortage GJ/a 54
3 Total amount of electricity from utility grid kWh/a 661 637
4 Total amount of natural gas burned Nm3/a 230 871
5 Average efficiency of the boiler plant % 90.7
6 Total cost of electricity PLN/a 218 600
7 Total cost of natural gas PLN/a 183 750
8 Investment cost PLN 466 540
9 Net Present Value after 15 years PLN -3 463 600
PLANT WITH COGENERATION MODULE
Table 2 presents the configurations of the cogeneration plant that were defined
as trial solutions for optimization procedure.
Table 2. Selected variants of the configuration of the plant
Nominal Number of variant
parameter
1 2 3 4 5 6 7 8 9 10 11
NCHP kW 20 30 40 50 60 70 80 90 100 110 120
&
kW 44 62 79 96 112 128 143 158 173 188 203
QCHP
&
kW 350 350 350 350 350 350 350 350 330 300 300
QK 1
&
kW 350 350 300 300 300 285 275 260 260 260 250
QK 2
&
kW 160 140 170 155 140 140 140 140 140 150 150
QK 3
It was assumed that there will be only one cogeneration module. The minimal
allowable electric load of the module was set in the value of 40% of nominal
power. Figures 4 and 5 show the results of technical analysis. In the electricity
tracking mode there is no sale of the electricity surplus electricity to the grid,
however if the installed electric power of the CHP module is higher, the
production is much lower than potentially possible (compare to FL mode). On the
other hand in the ET mode the loss of heat form CHP module is lower.
1100
1600
Gross electricity production - ET mode
1500
1000 Heat loss in ET mode
Gross electricity production -HT mode
1400
Gross electricity production - FL mode
900 Heat loss in FL mode
1300
Electricty sold to the utility grid in HT mode
1200
800
Electricty sold to the utility grid in FL mode
1100
700
1000
900
600
800
500
700
400 600
500
300
400
200 300
200
100
100
0 0
20 30 40 50 60 70 80 90 100 110 120 1 2 3 4 5 6 7 8 9 10 11
Nominal electric power of the CHP module Nominal electric power of the CHP module
Figure 4. On-site electricity production and heat loss in particular variants of the
plant configuration
0,95 0,95
ET mode ET mode
HT mode HT mode
FL mode FL mode
0,90 0,90
0,85 0,85
0,80 0,80
0,75 0,75
20 30 40 50 60 70 80 90 100 110 120 20 30 40 50 60 70 80 90 100 110 120
Nominal electric power of the CHP module Nominal electric power of the CHP module
Figure 5. Total efficiency (EUF) of the cogeneration module and the whole plant
MWh
Heat loss, GJ/a
Net total efficiency of the plant
Total efficiency of the CHP module
In the HT and FL modes of CHP module operation the electricity can be sold
to the mains. If so, the selling price of surplus electricity will be 140 PLN/MWh.
Figure 11 shows the results of the economic analysis in relation to the
reference case. It was found that the best mode of operation of the CHP module is
electricity tracking. It was also found that there is an optimal solution that
consists in installation of CHP module in 80  90 kW electric power range and
three gas boilers. The difference in NPV comparing to base case analysis is at the
level of investment cost.
450000
Mode: Electricity tracking
400000 Mode: Heat tracking
Mode: Full power
350000
300000
250000
200000
150000
100000
50000
0
20 30 40 50 60 70 80 90 100 110 120
Electric power of the CHP module, kW
Figure 6. Results of the optimization procedure
CONCLUSIONS
The procedure of optimal sizing of a cogeneration plants on the example of
demonstration project has been presented in the paper. It has been demonstrated
that the optimal solution exists and it can be initially identified by using a general
model of the plant and statistical parameters of machinery characteristics. The
presented model is also suitable for selecting the optimal mode of the
cogeneration module operation.
Although the procedure is not a complicated one and quite effective, it must
be emphasized that it is only the first step of the analysis. In the next stage
technical and economic data for specific engines and boilers have to taken from
vendors. General characteristics have to be replaced by the real ones and the
whole calculation has to be done again. In some cases the technical and economic
real effects can be even more attractive than that one obtained from pre-feasibility
study.
For the analyzed case the initial study has proved that that the cogeneration
makes better solution than the boiler plant only.
case, PLN
Difference in NPV in comparison to reference
NOMENCLATURE
CFt Cash Flow in year t, KO&M operation and maintenance cost
N electric power or lifetime of & stream chemical energy of fuel
PWd
the project
&
momentary heat shortage;
"Q
&
heat flux
Q
LHV lower heating values of fuels
&
mass flow of pollutant
GP
SR economic loses resulted from
&
mass flow of water
GW heat
shortages
r discounted cash flow rate
Kp labour cost;
Sn incomes
Kenv environmental cost.
KE costs of exploitation
kfCHP, kfk cost of fuels;
Ken cost of energy;
kel(Ä) cost of electricity, variable in
Kop operational costs
time according to tariffs.
J0 investment capital
kPi unitary emission fees,
Pd income tax,
kW unitary cost of water
L salvage value
Greek symbols Subscripts
CHP related CHP module
·E energy production efficiency
K related to boiler
´ binary variable
D related to demand site
Ä… index of allowable heat shortage,
G related to utility grid
Ä… " 0,1
P plant self use of electricty
Ä time.
S sale
ÄR an annual time of the operation
str losses
min minimal
nom nominal
i,j,k related to i-th, j-th, k-th module
REFERENCES
1. Kalina J. Initial Sizing of the Heat and Electricity Source Under Known Daily Load
Profiles  Simplified Equation Based Analysis. Proceedings of the Seminar
Cogeneration in Industrial and Municipal Energy Systems. Gliwice, Poland, 2003.
Skorek J. Analysis of technical and economic effectiveness small-scale cogeneration
plants fuelled with gaseous fuels. Silesian University of Technology Publishing,
Gliwice 2002. (in Polish) ISBN 83-7335-127-2
2. Witzani M., Pechtl P. Modelling of (cogeneration)-power plants on time dependent
power demands of the consumer. Materiały konferencji ASME Cogen-Turbo
Conference. Wiedeń, Austria, August 1995.
3. Yokoyama R., Ito K. Multi-objective Optimization in Unit Sizing of a Gas Turbine
Cogeneration Plant. Journal of Engineering for Gas Turbines an Power. Vol. 117.
Styczeń 1995.
This work has been supported by the Polish Committee for Scientific Research under the
research grant No. 4 T10B 02225