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 water that is subsequently fed into the local heating network of 90/70 OC 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]:

=

= Nt 1

NPV + tt Jr 0

max)

CF1(

(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) strDS QQN && ++ )1(DGd NNWP& =+ Then particular elements of the equation 1 can be decomposed as follows:

(3) =

+ Pn

kPjSG NNN

1)1(

QQQ strn

jKjCHPi

K &&& ++ =1

=

+= CHPn

iCHPiD NN

1

(4) QQn

iD

CHP && = =1

= =

=+= CHP Kn

i

n

jKjdCHPidd WPWPWP

1 1)()( &&& (5)

= =+CHP K

n

i

n

j Ekj

Kj

CHPiE

CHPi QN1 1_

&

Ratio of electricity and heat for CHP plant is expressed by the cogeneration index : (6)

CHPi

CHPii Q

N&=

The minimum value of the cogeneration index is limited by the maximal possible heat output of the particular gas engine.

Particular parameters of the machinery characteristics (E_CHP, ) 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)

= 23,485 N0,0691R2 = 0,7203

3000 4000 5000 6000 7000c elektryczna, kW

20

25

30

35

40

45

0 1000 2000mo

spra

wno

, %

0

0,2

0,4

0,6

0,8

1

1,2

0 1000 2000 30moc

wsk

ani

k sk

ojar

zeni

a

= 0.3605 N0.1137R2 = 0.5821

00 4000 5000 6000 7000elektryczna, 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: ( ) 2431.00025.0

)(3

_

_ = elnomCHPE

CHPE ( ) ( ) 6537.0587.02 ++ elel (7)

( ) 9848.18147.0 3 = elelnom

( ) ( ) 3968.07756.12 ++ el (8)

where: - dimensionless load, = 0.2 1. nomel

elel N

N_

=el

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

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:

( ) 9556.01165.02 + xx1096.01693.01318.0 34 += xxnomEkEk

(9)

where: - dimensionless load. nomQQx &&=

Q&DQQ && =

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: (10)

The 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: ( )CHPiN min (11) ( )nomCHPiCHPi NN ( KjQ& (12) ) ( )nomKjKj QQ && min

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: (13) ( )+++

tdRopLPSK )

==+== N

tEn

N

tt KSJCF

00

0(CF

In order to estimate investment costs J0 the typical curves of unitary cost i were used: a) for gas boilers (boiler purchase cost, z/kW): (14) 13.0250 = nomQi &

nomwhere Q& 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) 2857.0)(9.2594 = nomNi

= R dNS Sn

0

rpMOen KKK

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:

(16)

Total exploitation cost can be expressed as follows:

E KK = & (17) +++The most important is the cost of energy:

dkNkQ

elGfkEkjk

Kj

+ )(

&

LHVk

LHVNdKK

R KCHPR n

j

n

ifCHP

CHPiECHP

CHPienen

+====0 11 _0

& (18)

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:

(19) =

=R CHP

dNkn

iCHPiMO

0 1&

( ) ] dkGdk R WWPik +0

_&

BPCHPPi GG __ , &&

= kEK MOelMO &&Environmental costs are given by equation:

(20) [ GGdKK RR ni

PiCHPPienvenv +===1 0

_0

&&&

Typically 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 z = 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 Number of variant Nominal

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 kW 350 350 350 350 350 350 350 350 330 300 300 kW 350 350 300 300 300 285 275 260 260 260 250 kW 160 140 170 155 140 140 140 140 140 150 150

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

60 70 80 90 100 110 120tric power of the CHP module

ET modeHT mode FL modeid in HT modeid in FL mode

0100200300400500600700800900

100011001200130014001500

1 2Nominal elec

Hea

t los

s, G

J/a

Heat loss in ET mode

Heat loss in FL mode

0

100

200

300

400

500

600

700

800

900

1000

20 30 40 50

MW

h

Nominal elec

Gross electricity production -Gross electricity production -Gross electricity production -Electricty sold to the utility grElectricty sold to the utility gr

3 4 5 6 7 8 9 10 11tric power of the CHP module

Figure 4. On-site electricity production and heat loss in particular variants of the plant configuration

0,75

0,80

0,85

0,90

0,95

20 30 40 50Nomina

Tota

l effi

cien

cy o

f the

CHP

mod

ule

60 70 80 90 100 110 120l electric power of the CHP module

ET modeHT modeFL mode

0,75

0,80

0,85

0,90

0,95

20 30 40 50Nominal ele

Net t

otal

effi

cien

cy o

f the

pla

nt

n

60 70 80 90 100 110 120ctric power of the CHP module

ET modeHT modeFL mode

Figure 5. Total efficiency (EUF) of the cogeneration module and the whole pla t

1KQ&CHPQ&

2KQ&

3KQ&

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 refe f d e Crence case. It was oun that the b st mode of operation of the HP 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

0

50000

100000

150000

200000

250000

300000

350000

400000

20 30 40 50 60 70 80

Electric power of the CHP m

Diff

eren

ce in

NPV

in c

ompa

rison

to re

fere

nce

case

, PLN

Mode: Electricity trackingMode: Heat trackingMode: Full power

90 100 110 120

odule, kW Figure 6. Results of the optimization procedure

he procedure of optimal s tion plants on the example of

dem

CONCLUSIONS

T izing of a cogeneraonstration 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.

NOMENCLATURE CFt Cash Flow in year t, N

Q&PG&WG&

electric power or lifetime of the project

heat flux mass flow of pollutant mass flow of water

r discounted cash flow rate Sn incomes KE costs of exploitation Ken cost of energy; Kop operational costs J0 investment capital Pd income tax, L salvage value

KO&dWP&

Q&

M operation and maintenance cost stream chemical energy of fuel

momentary heat shortage; LHV lower heating values of fuels SR economic loses resulted from heat

shortages Kp labour cost; Kenv environmental cost. kfCHP, kfk cost of fuels; kel() cost of electricity, variable in time according to tariffs. kPi unitary emission fees, kW unitary cost of water

Greek symbols E energy production efficiency binary variable index of allowable heat shortage,

time. R an annual time of the operation

Subscripts CHP

D related to demand site G related to utility grid P plant self use of electricty S sale str losses min minimal nom nominal i,j,k related to i-th, j-th, k-th module

related CHP module K related to boiler

1,0

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. Materiay konferencji ASME Cogen-Turbo Conference. Wiede, 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. Stycze 1995.

This work has been supported by the Polish Committee for Scientific Research under the research grant No. 4 T10B 02225