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Energy 33 (2008) 1155–1168
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Optimum sizing of battery-integrated diesel generator for remoteelectrification through design-space approach
P. Arun, Rangan Banerjee, Santanu Bandyopadhyay�
Energy Systems Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
Received 17 February 2007
Abstract
Battery integrated diesel generation is one of the options for decentralized power production. They are particularly suitable for loads
with significant variation in the daily demand. A methodology for the optimum sizing of integrated system involving diesel generator and
battery bank for an isolated electrical power generation is proposed in this paper. The proposed methodology is based on the design-
space approach involving a time series simulation of the entire system. Based on the proposed approach, for a given load demand,
characteristics of the diesel generator and battery bank, a sizing curve is identified on the diesel generator rating vs. storage capacity
diagram. The sizing curve helps in identifying all possible feasible system configurations or the design space. Based on the minimum
capital cost and the minimum operating cost of the system, the Pareto optimum curve is identified on the system-sizing curve. Optimum
system configuration is identified based on the minimum cost of energy through optimal dispatch strategy. Two operating strategies,
involving continuous and intermittent operation of the diesel generator are studied and compared. Effect of the load profile on the system
sizing is also presented in this paper.
r 2008 Elsevier Ltd. All rights reserved.
Keywords: Diesel–battery system; Optimum system sizing; Sizing curve; Design space
1. Introduction
Isolated power systems serve the electricity demand of alocation by generating power near its point of utilization.These isolated power systems form a subset of thedistributed generation system and include small generationunits typically in the capacity of about 10–250 kW [1]. Theyare viewed as a means to electrify remote areas which arelocated far from the centralized power stations, where gridextension could be uneconomic. In India, of the 119 570villages which are not electrified, about 18 000 villages arelocated in remote locations where extending the grid is notconsidered to be feasible [2,3]. Diesel engine coupled withelectrical generator is one of the possible solutions forelectrification. It is portable, modular, and has a highpower-to-weight ratio. Diesel generators may also beintegrated with other sources (e.g., photovoltaic, wind
e front matter r 2008 Elsevier Ltd. All rights reserved.
ergy.2008.02.008
ing author. Tel.: +9122 25767894; fax: +91 22 25726875.
ess: [email protected] (S. Bandyopadhyay).
turbine, etc.) and energy storage systems making it an idealchoice for isolated power generation.The key issue faced by power stations using diesel
generators is the variation in the load. Severe variation inthe load results in poor engine performance. The generatorperforms efficiently when it is operating close to its ratedcapacity. Continued operation at lower loads results in aninefficient plant performance and higher cost of energy.One of the methods suggested by manufacturers to preventpart load operation is the use of dummy loads, whereresistive load banks are used to absorb the excess power tokeep the engine loading high. However, such methods arenot energy efficient. Use of multiple generator sets that canrun in parallel is also suggested [4].Integration of battery banks with diesel generator
improves the system efficiency. In many diesel generatorpower plants located in remote areas of Australia, Alaskaand Kenya, battery integration has been proposed andimplemented, with some of the systems having supplemen-tary photovoltaic generation [4–6]. Peak load is met by thediesel generator together with the inverter operating in
ARTICLE IN PRESS
Nomenclature
a fuel curve coefficient, l/kWhb fuel curve coefficient, l/kWhB battery bank capacity, kWhBr maximum battery energy value, kWhBmin minimum battery energy value, kWhc fraction of the battery capacity that holds the
available chargeCf fuel cost, Rs./ld discount rateD demand, kWDmax maximum demand, kWDmin minimum demand, kWf net charging/discharging efficiencyFC daily fuel cost, Rs.k rate constant of the charge diffusion, h�1
l time fractionl* time fraction above which battery integration
becomes viablem fuel flow rate, l/hP power generated by the diesel generator, kWPmin minimum diesel generator power, kWPr rated diesel generator power, kWq0 total battery charge at the preceding time step,
coulombq1 available charge, coulombq2 bound charge, coulomb
qmax maximum charge, coulombQB battery energy, kWhQB0 total battery energy at the preceding time step,
kWhQB1 available energy, kWhQB2 bound energy, kWhr load ratiot period of low load, hT total time period, h
Greek symbols
DP difference between input power and demandpower, kW
Dt time step of simulation, hZc charging efficiencyZd discharging efficiencys hourly self discharge rate of battery
Abbreviations
ACC annualized capital cost, Rs./yearAFC annual fuel cost, Rs./lAOM annual operation and maintenance cost, Rs./yearCOE cost of energy, Rs./kWhCRF capital recovery factorDOD depth of discharge
P. Arun et al. / Energy 33 (2008) 1155–11681156
parallel. It allows operation of the diesel generator at thefull load conditions and thus, enabling efficient operationof the generator. In such integrated systems, the totalgenerator operating hours could be brought down and thenight time generator operation could be restricted, follow-ing an appropriate power dispatch strategy. It is importantto study the optimal generator dispatch and batterycharge–discharge scheduling from the system operationpoint of view. Optimal operation of such systems has beenstudied using methods such as simulated annealing [7].
In isolated power systems where the diesel generator andthe battery storage is considered as an option, the designobjective is to obtain the ratings of the generator and thebattery bank required to meet a given load pattern.Typically, diesel generator is sized based on the peakdemand and the storage capacity is decided depending onthe number of days of autonomy. However, such a sizingprocedure need not be optimal. There are specific softwaretools available for arriving at sizing of a battery-integrateddiesel generator system. RETScreen [8] developed byCANMET Energy Diversification Research Laboratory isuseful for preliminary system sizing of isolated powersystems. The Hybrid Optimization Model for ElectricRenewables (HOMER) [9] uses hourly simulations forarriving at optimal system sizing. Hybrid2 [10] developedby National Renewable Energy Laboratory, USA, is
capable of performing the detailed time series simulationof isolated power systems. However, a generalized sizingtool must not be restricted in simulating and exploring asingle design configuration and it should generate differentdesign options. It must also be robust to handle non-linearmodels. In this paper, a methodology is proposed tooptimally size a battery-integrated diesel generator system.It helps in constructing a sizing curve which connects thegenerator ratings and corresponding minimum batterycapacities meeting a specified load pattern plotted on agenerator rating vs. battery capacity diagram. In practice,it is also desirable from a design perspective to determinethe entire range of feasible system configurations formeeting a given load pattern. In this paper, the entirerange of feasible system configurations is identified througha novel concept, called the design space. Generation of thedesign space helps in optimizing and selecting an appro-priate system configuration. Originally, Kulkarni et al. [11]have introduced the concept of design space for optimumsizing of solar hot water systems. In this paper, selection ofthe optimum battery-integrated diesel generator system isillustrated based on the criterion of the minimum cost ofenergy. Minimization of the operating cost of the system ispresented in this paper based on two dispatch strategies:continuous generator operation and intermittent generatoroperation (where on/off control on the generator is
ARTICLE IN PRESSP. Arun et al. / Energy 33 (2008) 1155–1168 1157
imposed). It has been observed that with continuousgenerator operation, the optimum lies on the sizing curveand with on/off conditions of the generator it lies slightlyinside the design space.
2. Description of the battery-integrated diesel generator
system
Load curve for a typical remote location exhibits avarying demand profile. For diesel generator alone systems,generators are sized based on the expected peak demand.In such systems, generator operates at part load conditionfor a large duration of time. One of the options for the loadmanagement is to integrate battery banks with suchsystems to improve the overall system efficiency. Hybridsystems incorporating renewable energy based units suchas photovoltaic panels, wind generators, etc. may also beintegrated into the diesel grids with battery banks.
The schematic of a diesel generator–battery systemconfiguration is shown in Fig. 1. The components includediesel generator set, battery bank and bi-directionalconverter. A generic system may also have other renewableenergy based generators such as photovoltaic or windgenerators. During the system operation, the dieselgenerator and the converter can operate in parallel.The operational characteristic of this power system has amajor implication in the sizing of the diesel generator setand the battery bank. The load could be shared by thediesel generator and the inverter together. Thus, it ispossible to have the rating of the diesel generator lowerthan the expected peak demand. This improves thecapacity factor of the diesel generator as the generatoroperates at considerably higher load factors compared tothe diesel-only mode. The generator can go offline whenthe load goes below a preset value depending on theallowable minimum loading of the generator. The systemoperates in one of three modes based on the generatordispatch:
(i)
F
Converter only operation: At lower loads, the systemwould operate in the inverter mode (depending on the
Battery bank
AC load
Bi directionalconverter
Dieselgenerator
AC busDC bus
ig. 1. Schematic of a battery-integrated diesel generator system.
available state of charge of the battery, with thebattery discharging) when the generator is allowed tobe shut down.
(ii)
Diesel generator only operation: At certain periods, thesystem operation would be such that the generatorsimultaneously meets the load and charges the batterybank enabling it to attain its full capacity.(iii)
Parallel operation: This corresponds to the peak loadperiods when both DG and battery operate together toserve the load.Nayar [4] has discussed the following advantages of theparallel configuration over other system topologies:
�
System load can be met optimally, as whenever thegenerator is operating, it is operating at full load ornear full load conditions corresponding to higherefficiencies. � DG maintenance can be minimized by reducing the partload operation of the diesel engine.
� Reduction in the rated capacities of the diesel generatorand the battery bank while meeting the peak load can beachieved.
3. System modeling and generation of the design space
A methodology to obtain the system sizing for the dieselgenerator–battery system for a given load profile and togenerate feasible design space is discussed in this section.The proposed methodology employs a time series simula-tion approach based on the energy balance of the overallsystem. The net power flow across the storage is accountedconsidering the efficiencies for the power conversion duringcharging and discharging processes. The rate of change ofenergy stored (dQB/dt) in the battery bank is proportionalto the net power generated. The power generated isrepresented as the difference between the power generatedby the diesel generator set (P) and the power required bythe load (D).
dQB
dt¼ ðP�DÞf (1)
where f represents the efficiencies associated with thecharging and discharging processes.
f ¼ Zc whenever PXD
f ¼1
Zd
whenever PoD (2)
Above equations relate the rate of change of energy ofthe storage with the input power, demand power and thepower conversion efficiencies in charging/discharging. Thestored energy QB over a time period of Dt may be expressedas follows:
QBðtþ DtÞ ¼ QBðtÞ þ
Z tþDt
t
ðPðtÞ �DðtÞÞf dt (3)
ARTICLE IN PRESS
Generator rating (kW)
Bat
tery
cap
acity
(kW
h)
Infeasible design region
Minimum generator rating
Feasible design region(design space)
sizing curve
Maximum demand(Minimum diesel generator rating without battery storage)
Battery capacity corresponding to the minimum generator rating
Fig. 2. Typical sizing curve and design space for a diesel generator–
battery system.
P. Arun et al. / Energy 33 (2008) 1155–11681158
For a relatively small time period, Eq. (3) may beapproximated as
QBðtþ DtÞ ¼ QBðtÞ þ ðPðtÞ �DðtÞÞfDt (4)
During the system operation over the time period Dt,whenever the energy supplied by generator is greater thanthe demand (P(t)4D(t)), the energy surplus is used forcharging the battery. If the generator dispatch is such thatthe energy delivered by generator is lower than the load,then the battery meets the deficit. The load can be met ifthe battery has not reached its depth of discharge and inthat case, the stored chemical energy is converted intoelectrical energy. It is assumed that the charging anddischarging take place with an efficiency that remainsconstant over time. The self-discharge loss for the battery isassumed to be negligible. The minimum generator ratingrequired and the corresponding storage capacity formeeting the specified load may be obtained by solvingEq. (4) over the entire duration. To solve Eq. (4), requiredinputs are the expected load curve over a specific timeinterval (e.g., daily, seasonal or yearly load curve) and thenominal charging and discharging efficiencies of thebattery bank-converter system. The appropriate loadmodels which capture the real world load variations wouldserve as valuable input for the design-space approach andwould yield a robust system design. In the generalizedmethodology, to obtain the minimum generator rating, anumerical search is performed that satisfies the energybalance (4) and the following conditions:
QBðtÞX0; 8t (5)
QBðt ¼ 0Þ ¼ QBðt ¼ TÞ (6)
Eq. (5) ensures that the battery energy level is always non-negative, while Eq. (6) represents the repeatability of thebattery state of energy over the time horizon. Therepeatability condition implies that there is no net energysupplied to or drawn from the battery bank over the timehorizon. It is assumed that the load is recurring in the samepattern after time T. The required battery bank capacity(Br) is obtained as
Br ¼maxfQBðtÞg
DOD(7)
where DOD is the allowable depth of discharge of thebattery.
The proposed procedure provides the value of theminimum diesel generator capacity (P ¼ Pmin) and thecorresponding capacity of the battery bank (B). Any dieselgenerator rating higher than the minimum is capable ofsupplying the load. However, the capacity of the batterybank is expected to be lower. It is important fromdesigners’ perspective to identify all the feasible combina-tions for the generator rating and the correspondingstorage capacity. To identify the minimum storage capacityfor a given diesel generator rating, the energy balance
Eq. (1) may be modified as follows:
dQB
dt¼ ðP� Pdu �DÞf (8)
Here, P(t)�Pdu(t) represents the part load power of thegenerator. As the diesel generator rating is higher than theminimum possible, the system operation would be suchthat at certain periods there would be part load operationof the generator.The simulations to obtain the minimum storage capacity
are carried out for different values of the diesel generatorratings (P4Pmin). For each value of P considered, thecorresponding minimum battery bank capacity is obtainedby minimizing the required storage capacity Eq. (7). Theoptimization variables are the initial battery energy,QB(t ¼ 0) and Pdu(t). The combinations of the differentgenerator ratings and the corresponding minimum storagerequirements may be plotted on a generator rating vs.battery bank capacity diagram which may be called thesizing curve of the system. The sizing curve represents theminimum storage capacity required for a given dieselgenerator rating. The sizing curve divides the entire spaceinto regions, a feasible and an infeasible region. The regionabove the sizing curve represents the feasible region as anycombination of diesel generator rating and battery capacityrepresents a feasible design option. The entire feasibleregion including the sizing curve is the design space for agiven problem. A typical sizing curve and associated designspace are shown in Fig. 2. It may be noted that the pointwhere the sizing curve intersects the x-axis (axis represent-ing the diesel generator rating) represents the peak demandof the system and the corresponding storage capacity iszero.
3.1. Example 1
The methodology of system sizing is illustrated with anexample in this section. The representative daily load curveof a typical remote location is shown in Fig. 3 [7]. It showsa significant variation in the load over the day with an
ARTICLE IN PRESS
0
4
8
12
16
20
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
Load
(kW
)
Minimum load = 2.42 kW
Maximum load = 20 kW
Average load = 7.63 kW
Fig. 3. Load curve for Example 1.
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20 22Generator rating (kW)
Bat
tery
cap
acity
(kW
h)
Minimum generator rating without storage (20 kW)
Design Space
sizing curve
Minimum generator rating point(8.23 kW, 92 kWh)
Fig. 4. Sizing curve and design space for Example 1.
Table 1
Input parameters used in the system sizing and optimization
Net charging efficiency (%) 86
Net discharging efficiency (%) 86
Depth of discharge (%) 50
Kinetic battery model parameters
k (h�1) 0.5821
c 0.40168
Diesel generator fuel curve coefficients
a (l/kWh) 0.08415
b (l/kWh) 0.246
0
4
8
12
16
20
24
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
Load
(kW
)
0
20
40
60
80
100
120
Bat
tery
ene
rgy
(kW
h)
LoadBattery energy
Load energy not met
Bat
tery
ene
rgy
(kW
h)
0
4
8
12
16
20
24
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
Load
(kW
)
0
10
20
30
40
50
60
70
80
90
DG powerLoadBattery energy
Fig. 5. (a) Variations in load, generator power, and battery energy over
the day for a configuration from the infeasible region (Pr ¼ 7 kW,
Br ¼ 100 kWh, generator operating at rated condition over the entire
duration) for Example 1. (b) Variations in load, generator power, and
battery energy over the day for a configuration from the feasible region
(Pr ¼ 12 kW, Br ¼ 100 kWh) for Example 1.
P. Arun et al. / Energy 33 (2008) 1155–1168 1159
evening peak. Following the proposed procedure, thesystem-sizing curve for the site is obtained and is shownin Fig. 4. The charging/discharging efficiencies and depthof discharge considered in the analysis are given in Table 1.Following the procedure, the minimum generator rating of8.23 kW and corresponding battery bank capacity of92 kWh are obtained. The generator rating without anystorage requirement is 20 kW, which is the maximumdemand (Fig. 3). Any system configuration located on thesizing curve and design space will always meet the loadbalance conditions while any configuration in the infeasible
region will not satisfy the load requirement. To illustrate, aconfiguration from the infeasible region (P ¼ 7 kW andB ¼ 100 kWh) is considered first. Variations in load,generator power, and battery energy over the day for thesystem are shown in Fig. 5(a). It is observed that thebattery energy values at the evening peak duration are suchthat the load balance cannot be met by the overall system.As illustrated in Fig. 5(a), from 7 to 8 PM, 58% of the loadenergy requirement is not met by the system and from 8 to9 PM, 22% of the load energy is unmet. Even though theoverall load balance is satisfied beyond this, the battery isnot charged to the required capacity towards the end of theday. Considering one of the systems from the feasibleregion of the design space (P ¼ 12 kW and B ¼ 100 kWh),the system performance is presented in Fig. 5(b). In thiscase it is observed that the load balance is met all the timeand the battery reaches its initial conditions towards theend of the day.
ARTICLE IN PRESSP. Arun et al. / Energy 33 (2008) 1155–11681160
The user has the choice of selecting an appropriateconfiguration from the feasible design region (design space)according to the requirements of additional capacityreserve and autonomy. The design space which containsall the feasible configurations thus provides a frameworkfor system optimization based on an appropriately selectedobjective function. It may be noted that the design spaceencompasses all possible scenarios to satisfy the overallload requirement.
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1 1.2Normalised generator rating
Nor
mal
ised
sto
rage
cap
acity
(day
s)
simple battery model
kinetic battery model
Fig. 6. Sizing curves with simple and kinetic battery models for Example 1.
3.2. System sizing with kinetic battery model
The analysis performed for Example 1 to generate thedesign space has considered the charging–dischargingprocesses based on constant nominal efficiency values.However, the generation of the design space is not limitedto such assumption. To illustrate, the kinetic battery modelproposed by Manwell and McGowan [12] is considered inthe sub-section. In the kinetic battery model, the battery isexpressed as a system containing bound and availablecharges separated by a conductance. Available charge isimmediately available (q1) to be used by the load andbound charge (q2) is that which is chemically bound.Conductance corresponds to the chemical reaction bywhich the bound charge becomes available. The rate atwhich the bound charge becomes available is consideredproportional to the level difference of the charges [12].According to the kinetic battery model, the diffusionreaction is assumed to be of first order rate. It is alsoassumed that a current regulator is placed between thebattery and the load, which ensures that power drawn andhence current is constant over the time step [12]. The modelcharacterizes the battery with a set of three constants, therate constant of the charge diffusion (k), the fraction ofthe battery capacity that holds the available charge (c) andthe maximum battery capacity (qmax). These parameterscan be estimated from the battery test data [9]. Theconstitutive relations for the available and the boundcharges are as follows:
dq1
dt¼ �I � kð1� cÞq1 þ kcq2 (9)
dq2
dt¼ kð1� cÞq1 � kcq2 (10)
Amount of the available and the bound charges is obtainedby solving the above equations.
q1ðtþ DtÞ ¼ q1ðtÞ e�kt þ
ðq0ðtÞkc� IÞð1� e�ktÞ
k
�Icðkt� 1þ e�ktÞ
k(11)
q2ðtþ DtÞ ¼ q2ðtÞ e�kt þ q0ðtÞð1� cÞð1� e�ktÞ
�Ið1� cÞðkt� 1þ e�ktÞ
k(12)
q0ðtÞ ¼ q1ðtÞ þ q2ðtÞ (13)
Eqs. (11) and (12) are modified in a manner suitable tobe adopted in the proposed methodology by converting thebattery charge values in terms of energy. Denoting QB1(t)and QB2(t) as the battery energy values at the beginning ofthe time step and DP as difference between the powerdemand and the power supplied by the source, aboveequations may be modified as follows:
DP ¼ ðPðtþ DtÞ �Dðtþ DtÞÞ (14)
QB1ðtþ DtÞ ¼ QB1ðtÞ e�kt þ
ðQB0ðtÞkc� DPÞð1� e�ktÞ
k
�DPcðkt� 1þ e�ktÞ
k(15)
QB2ðtþ DtÞ ¼ QB2ðtÞ e�kt þQB0ðtÞð1� cÞð1� e�ktÞ
�DPð1� cÞðkt� 1þ e�ktÞ
k(16)
QB0ðtÞ ¼ QB1ðtÞ þQB2ðtÞ (17)
QBðtþ DtÞ ¼ QB1ðtþ DtÞ þQB2ðtþ DtÞ (18)
Following the proposed methodology, the sizing curvemay be generated adopting the kinetic battery model as theminimum battery capacity (qmax) can be determined for agiven diesel generator rating. The values of k and c used fornumerical calculations are given in Table 1 [12]. The sizingcurve obtained using the kinetic battery model for Example1 is shown in Fig. 6 and it is compared with the sizing curveobtained using simple charging/discharging model. For thepurpose of comparison, the diesel generator rating isnormalized with respect to the peak demand (20 kW) andthe battery capacity is normalized with respect to the dailyload energy (183 kWh). It may be observed that the simplemodel with constant charging/discharging efficiency givesslightly conservative design space.It may be noted that for both the battery models, the
variation in the battery energy with time is assumed to takeplace without any self-discharge losses in the above cases.Incorporating the self-discharge losses, Eq. (4) may be
ARTICLE IN PRESS
Table 2
Economic parameters considered for system optimization
Discount rate (d%) 10
Diesel generator life (years) 10
Battery bank life (years) 5
Converter life (years) 10
Charge controller life (years) 10
Cost of diesel generator (Rs./kW) 25 000
Cost of battery bank (Rs./kWh) 4000
Cost of converter (Rs./kW) 18 000
Cost of charge controller (Rs./kWh) 350
Fuel cost (Cf Rs./l) 38
Note: 1 US$ ¼ Rs. 45.
Inputs: Power demand, generator operating limits, Initial battery
energy, battery depth of discharge
Available power > Demand
power?
Generator ‘ON’, Decide operating power level
Battery charger ‘ON’
Final battery level based on allowable depth of
discharge
Paralleloperation?
Generator ‘ON’, Decide operating power level
Inverter ‘ON’, Decide operating power level
Generator ‘OFF’No No
YesYes
Fig. 7. System dispatch strategy.
P. Arun et al. / Energy 33 (2008) 1155–1168 1161
modified in the following form:
QBðtþ DtÞ ¼ QBðtÞð1� sÞ þ ðPðtÞ �DðtÞÞfDt (19)
Here s is the hourly self-discharge rate of the battery. Nosignificant deviation in the design space was observed whenthe self-discharge losses are added. As the sizing curvesobtained using these two models with and without self-discharge loss, are comparable, for brevity, the simplemodel of constant charging/discharging efficiency withoutany self-discharge loss is applied to illustrate the aspects ofsystem optimization.
4. System optimization
The sizing curve identifies the design space which helpsthe designer in choosing an optimum system configurationbased on the intended objective. In this section, theprocedure for selecting an optimum system configurationis discussed. The cost of energy (COE), which accounts thecapital as well as the operating costs associated with thesystem, is chosen as an appropriate economic parameter toevaluate and to optimize the system configuration. It iscalculated as
COE ¼ACC þ AOM þ AFC
Egen
(20)
The annualized capital cost (ACC) is calculated as
ACC ¼X
i
C0i � CRFi (21)
where
CRF ¼dð1þ dÞn
ð1þ dÞn � 1(22)
C0i is the capital cost of the ith system component(corresponding to the diesel generator, battery bank,converter and charge controller). CRFi is the capitalrecovery factor for the ith component and it is a functionof the discount rate (d) and life of the component (ni). Itmay be noted that different components have different lifetimes. For successful operation of the entire systemcomponents such as battery bank, may have to be replaced.The capital recovery factor calculated based on thedifferent life times of different components consider thisaspect appropriately [13]. The annual operating andmaintenance cost of the system (AOM) has been taken as2.5% of the capital cost. AFC is the annual fuel costestimated based on optimum dispatch of the generator andEgen is the total annual energy delivered. To demonstratenumerically Example 1 has been considered. The cost dataconsidered for the economic analysis are given in Table 2[14,15]. The system operating cost (the fuel cost for thegenerator operation) is determined for the optimal powerdispatch of the generator. Two different schemes for dieselgenerator operation are considered: (1) continuous gen-erator operation, where the generator is not shut down and(2) intermittent generator operation, where the generator is
allowed to shut down. Under both the operational modes,the optimum dispatch of the generator is considered. Thecontroller decisions are based on the energy balance andthe operating limits of the various components of thesystem. The flowchart illustrating the system dispatch isshown in Fig. 7.
4.1. Continuous generator operation
In this strategy, the generator is operational throughoutthe time period of analysis. The fuel cost (FC) is calculatedfor a day as
FC ¼ Cf
X24t¼1
mðtÞ (23)
where the hourly fuel consumption (l/h), m(t) is related tothe part load characteristic of the diesel generator.
mðtÞ ¼ aPr þ bPðtÞ (24)
In the above equation, a and b are constants (given inTable 1), Pr is the rated power of the generator and P(t)denotes the actual power generated by the diesel generator[16]. The relation has been validated with the actual fuel
ARTICLE IN PRESSP. Arun et al. / Energy 33 (2008) 1155–11681162
consumption data of generators obtained from manufac-turer’s test data. The total fuel consumption of thegenerators at 25%, 50%, 75%, 80% and 100% loads forgenerators in the capacity range of 150–1800 kW whereavailable. Based on these data, a linear model (24) wasfitted for the total fuel consumption as a function of thepower output. The model coefficients obtained for this dataare a ¼ 0.0184 l/kWh and b ¼ 0.2088 l/kWh with a coeffi-cient of determination (R2) of 0.99. The correspondinggenerator efficiency characteristics against the manufac-turer’s test data are shown in Fig. 8. For the examplesdiscussed in the paper, the generator ratings were less than20 kW and hence, the model coefficients reported bySkarstein and Uhlen [16] were used for the systemoptimization (Table 1). The diesel generator model relatingthe fuel consumption of the generator and the poweroutput indicates that the maximum efficiency of thegenerator corresponds to the rated power of the generator.But this may not be universally true for all types ofgenerators as the maximum efficiency point could alsocorrespond to near rated conditions of the generator.However, it may be noted that the proposed methodologyis not restricted to this assumption. In the proposedmethodology, the generator dispatch is optimized so thatthe system operates under the most energy efficientcondition. The objective is to minimize the total fuel costfor a given diesel generator sizing. The optimum dispatch,P(t) has been determined satisfying the load balanceconditions (4) and charge constraints (5)–(6). It is furtherassumed that the generator has to operate between therated and a specified minimum value. In Example 1, theminimum loading on the generator is taken as 30% ofthe rated power.
PminpPðtÞpPr (25)
The battery energy has to be between the rated andminimum values depending on the allowable depth ofdischarge.
BminpQBðtÞpBr (26)
0
0.5
1
1.5
2
2.5
3
3.5
4
1 2 3 4
1/ef
ficie
ncy
Rated power/Generator power
Fig. 8. Diesel generator efficiency characteristics.
The initial battery energy (at time t=0) is also taken as anoptimization variable. After evaluating the operating costsfor the various configurations in the design space, it is seenthat for Example 1, the minimum operating cost is obtainedfor the configuration, Pr=8.23 kW and Br=92kWh.It is observed that for a specific generator rating, there is
no change in the operating cost as the capacity of batterybank is increased from the corresponding minimum (asidentified from the sizing curve). The operating cost isgoverned by the amount of fuel consumed, which is directlyproportional to the power delivered by the generator. Forcontinuous generator operation, the optimized dieseldispatch is independent of the battery bank capacity andthus, the operating cost remains constant. Therefore, for agiven diesel generator rating, configuration which corre-sponds to the minimum operating cost lies on the sizingcurve. Configuration with the minimum possible generatorrating corresponds to the overall minimum operating cost.Therefore, for continuous generator operation, the mini-mum operating cost configuration is independent of thefuel price. It may be noted that the minimum operatingcost configuration depends on the load curve.Capital cost of the overall system linearly depends on the
diesel generator rating and the battery bank capacity. Asthe capital cost of the system is a linear function of thegenerator rating and battery capacity, configurations witha constant capital cost may be depicted on the design spaceas a straight line. Different iso-capital cost lines may beplotted on the design space. The point where the iso-capitalcost line is tangential to the sizing curve represents theconfiguration with the minimum capital cost.Configurations which correspond to the minimum oper-
ating cost as well as the minimum capital cost arerepresented on the sizing curve (Fig. 9). It may be notedthat the segment of the sizing curve, connecting theminimum operating cost and the minimum operating cost,represents a Pareto optimal curve. Any objective functionwhich combines the operating cost and the capital cost of
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25
Bat
tery
cap
acity
(kW
h)
Minimum operating cost designP = 8.23 kW, B = 92.04 kWh
Minimum capital cost designP = 10 kW, B = 53.22 kWh
Pareto optimal curve
sizing curveIso capital cost line
a
b
Generator rating (kW)
Fig. 9. Pareto optimal curve in the design space for Example 1.
ARTICLE IN PRESS
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
%
DG power
Battery energy
Load
Fig. 10. Variations in load, generator power, and battery energy over the
day for the minimum operating cost design (Pr ¼ 8.23 kW,
Br ¼ 92.04 kWh) for Example 1.
2200
2400
2600
2800
3000
3200
3400
3600
Ope
ratin
g co
st (R
s/da
y)
10 kW
16 kW
20 kW
P. Arun et al. / Energy 33 (2008) 1155–1168 1163
the system may be chosen for optimizing the overall system.The optimum configuration for such an objective functionhas to lie on the Pareto optimal curve. It may be noted thatfor continuous generator operation, any configuration, noton the Pareto optimal curve, cannot be optimum in thePareto sense. However, such systems are more reliable dueto uncertainties associated with the load curve.
Variations in load, generator power, and battery energyover the day for the minimum operating cost configurationare shown in Fig. 10. The above parameters have beendetermined by simultaneously solving the overall systemmodel based on the load balance (4) and equipmentconstraints (25), (26). The load and the generator powerare expressed as a percentage of the rated capacity of thegenerator and the battery energy is expressed as apercentage of the rated capacity of the battery bank. Thegenerator operates by meeting the load and simultaneouslycharging the battery bank and bringing it to fully chargedcondition by middle of the day. The peak load occurring inthe afternoon and the evening is met by the generator andthe inverter together by parallel operation. The batteryenergy state falls to its allowable minimum by the nighttime. The generator goes to the charging mode as the cyclerepeats. Based on the cost of energy calculated for differentconfigurations, the overall minimum cost of energy isobtained for the system with Pr=9.1 kW and Br=70kWh.It may be noted that the rate of charging and dischargingof the battery has not been considered explicitly in thepresent study. However, with out loss of generality, suchconstraints may be added in the proposed model. It may benoted that the proposed methodology is not restricted tosuch simplifying assumptions.
20000 20 40 60 80 100
Battery capacity (kWh)
Fig. 11. Variation in operating cost with intermittent generator operation
for Example 1.
4.2. Intermittent generator operation
It may be possible to run the diesel generator withintermittent operations. During periods of very low load,
the diesel generator may be shut down completely toreduce the operating cost of the generation system. The on/off condition of the generator is modeled using binaryvariables, s(t). In this model, s(t)=1 indicates that thegenerator is on and supplying power whereas s(t)=0denotes that the generator is off. These binary variablesmay be included in the objective function.
FC ¼ Cf
X24t¼1
ðmðtÞsðtÞÞ (27)
The constraint for the generator power is modified as
PðtÞ ¼ 0 whenever sðtÞ ¼ 0
PminpPðtÞpPr whenever sðtÞ ¼ 1 (28)
The remaining constraints are same as those considered forthe continuous generator operation case.Variation of the operating costs with intermittent
generator operations are shown in Fig. 11. It shows theeffect of increasing the battery capacity from the identifiedminimum battery bank capacity (as obtained from thesizing curve) for a particular generator rating. It may benoted that the operating cost reduces initially and there-after remains almost constant with addition of storagecapacity. As expected, with intermittent generator opera-tion, the dispatch strategy is such that at low load periodsthe generator remains offline. Whenever the generatordelivers power, it operates at or near its rated capacityenabling an efficient operation. Therefore, there is a furtherreduction in the operating cost compared to the continuousoperation of the diesel generator. Exploring the differentconfigurations in the design space, the minimum cost ofenergy corresponds to Pr ¼ 10 kW and Br ¼ 60 kWh.The optimum configurations are represented in the design
space (Fig. 12). The methodology has been presented basedon the load data for a site with an existing dieselgenerator–battery system [7], which is also represented inthe design space along with the optimum configurations.The optimum cost of energy with continuous generator
ARTICLE IN PRESS
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25Generator rating (kW)
Bat
tery
cap
acity
(kW
h)
P = 9.1 kW, B = 70 kWh Optimum with continuousgenerator operation
P = 10 kW, B = 60 kWh Optimum with intermittentgenerator operation
P = 16.3 kW, B = 52 kWh Existingsystem
Fig. 12. Optimum configurations in the design space for Example 1.
0
50
100
150
200
250
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
%
DG power
Battery energy
Load
Fig. 13. Variations in load, generator power, and battery energy over the
day for the optimum configuration (Pr ¼ 10 kW, Br ¼ 60 kWh) with
intermittent operation for Example 1.
Input: load time series, generator and battery characteristics
System simulation with assumed values of generator rating
.. energy balance
. non negativity of battery energy
. repeatability of battery energy
Selection of minimum generator rating (Pmin) satisfying:
Obtain corresponding battery capacity
Determination of minimum battery capacities corresponding to various
generator ratings (>Pmin)
Generation of sizing curve and identification of design space
Operating cost evaluation of the various configurations subject to
generator economic dispatch(following continuous or intermittent
generation)
Selection of optimum configuration from the design space based on minimum cost
of energy
Fig. 14. Steps involved in generating the design space and system
optimization of battery-integrated diesel generator systems.
P. Arun et al. / Energy 33 (2008) 1155–11681164
operation is Rs. 15.97/kWh and with the intermittentgenerator operation, it reduces to 15.66/kWh. For the basecase with diesel-only system (rated at 20kW), the cost ofenergy is Rs. 20.40/kWh. It is observed that, withcontinuous generator operation, the optimal configurationlies on the sizing curve and for the intermittent generatoroperation, the optimal configuration is located slightlyinside the design space. It may also be noted that theoptimum configuration with intermittent generation movestowards a slightly higher generator capacity side comparedto continuous generation. The generator offline mode ispossible only at comparatively higher generator capacities,thus there is a slight shift towards the higher generator side.
Considering the cost data, the capital cost of theequipment in the system is not expected to changesignificantly over time, while the fuel cost may vary. Theoptimum dispatch evaluation is dependent on the uncer-tainties in the fuel price. The optimum system based on theintermittent generator operation is located very close to theconfiguration with the minimum capital cost. A slight overdesign in the storage from the minimum capital cost pointwould make the design close to the optimum configurationwith intermittent generation and this would furtherimprove the system reliability.
The variations in load, generator power, and batteryenergy over the day under the intermittent operationscheme are shown in Fig. 13. The inverter handles theperiods of low load in the early morning period when thegenerator is offline. In both the schemes it may be notedthat once the generator is online, it is maintained at nearrated power conditions. The different steps involved ingenerating the design space and system optimization issummarized in Fig. 14.
5. Example 2: case study on battery integration into an
existing isolated power system
This section illustrates the generation of sizing curve forone of the existing isolated power systems located in Sagar
island, West Bengal, India. The isolated power systemcomprises of two 150 kW DG units and three 50 kW windturbines. During the winter months (October–February)which are nonwindy periods, the system operates in dieselonly mode. The daily load curve for the site is shown inFig. 15. The load is met by two diesel generators, with one
ARTICLE IN PRESS
020406080
100120140160180200
0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour of the day)
Load
(kW
)
Fig. 15. Load curve for Sagar island isolated power system.
0
200
400
600
800
1000
1200
1400
1600
1800
0 100 200 300 400Generator rating (kW)
Bat
tery
cap
acity
(kW
h)
Proposed system P = 150 kW, B = 326 kWh
Existing system P = 300 kW
Fig. 16. Sizing curve for Sagar island isolated power system.
Table 3
Details of emission for Example 2
Emission factor for CO2 (kg/kWh) 0.699
Emission factor for NOx (kg/kWh) 0.019
CO2 emission for existing system (tonnes/year) 286.5
CO2 emission for battery integrated system (tonnes/year) 277.4
NOx emission for existing system (tonnes/year) 7.7
NOx emission for battery integrated system (tonnes/year) 7.5
Time (hour of the day)
Dem
and(
kW)
Dmin
Dmax
t T
r = Dmin / Dmaxl = t / T
Fig. 17. Load profile for parametric study.
P. Arun et al. / Energy 33 (2008) 1155–1168 1165
of them operating at part load conditions. The sizing curvefor the diesel generator–battery system for the site is givenin Fig. 16. From the design space it may be noted that byintegrating a battery bank into the existing system, the loadmay be met by a combination of the existing 150 kW DGunit and 326 kWh of battery. With this option, comparedto the existing system, an estimated annual savings in fuelcost of Rs. 5.26 lakhs is possible. Considering theadditional hardware requirements, the simple paybackperiod is 7.8 years. It may be noted that the savings in thefuel cost is more significant for projects like this as theoperating cost needs to be raised from the rural commu-nities while the capital cost mostly comes as aid/grant fromthe Government agencies. Further, based on the proposedsystem configuration, one of the 150 kW generators wouldact as a standby unit. This would enhance the systemreliability by providing reserve capacity for generation. Acomparison of emissions from the diesel generation unitbased on the existing system and with battery integrationhas also been made. The details of the emission coefficients[17] and the total CO2 and NOx emissions from the systemshave been reported in Table 3. It is observed that the CO2
and NOx emissions have been lowered by 3.2% withbattery integration when compared with the existing
system operating in diesel only mode. This exampleillustrates the usefulness of the design-space approach inexploring alternate retrofit options for existing plants.The emission limits, imposed by various governing bodies
and regulations, should be considered for deciding theoptimal dispatch of electrical power for various generators.Different environmental norms may be incorporated in theproposed model as constraints to determine the optimaldispatch of electrical energy. This is especially important forintegrating different electric power generating sources. In thepresent study, however, system based on a single dieselgenerator has been studied. It is assumed that the dieselgenerator meets different environmental regulations im-posed on. It may be noted that the methodology may beextended to include different environmental concerns.
6. Parametric studies on effect of load profile
Effects of load profile on the design space and theoptimum cost of energy are studied in this sectionconsidering a simple step load profile. For brevity, a two-level load as shown in Fig. 17 is adopted. The load curve ischaracterized by two factors. The time fraction l capturesthe effect of the periods of low load. It is defined as the timefraction for which the low load prevails over the total timeload is prevailed.
l ¼ t=T (29)
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where t denotes the period of low load (Dmin) and T
indicates the total time load is prevailed. The load ratio, r,is defined as the ratio of the minimum load (Dmin) to themaximum load (Dmax).
r ¼ Dmin=Dmax (30)
A class of load profiles is parameterized based on thetime fraction (l) and the load ratio (r). The sizing curvesgenerated in each case are plotted on the normalizedcoordinates. Generator rating is normalized with respect tothe peak demand (Dmax) and the battery capacity isnormalized with reference to the load energy. It is seenthat for a specified value of r as the value of l is increased,the sizing curve shifts towards lower values of generatorrating (away from the generator rating corresponding tothe maximum demand) as shown in Fig. 18(a). Consideringthe variation of r for specified values of l, it is seen thatthere is a steady decrease in the requirement of storage as r
increases and the curve shifts towards the generator ratingwhich is close to the peak demand (Fig. 18(b)). This showsthat as the period of low load increases the demand can bemet by a generator of considerable lower rating compared
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2Normalised generator rating
Nor
mal
ised
bat
tery
cap
acity
(day
s) 3/24
12/24
16/24
20/24
23/24
0
0.2
0.4
0.6
0.8
1
1.2
0.5 0.7 0.9 1.1Normalised generator rating
Nor
mal
ised
bat
tery
cap
acity
(day
s)
r = 0.25
r = 0.75
Fig. 18. (a) Sizing curves for different values of time fraction l for load
ratio r ¼ 0.1 and (b) sizing curves for load ratio of r ¼ 0.25 and 0.75 and
time fraction l ¼ 12/24.
to a generator only system rated at the peak load. On theother hand, as the load profile becomes more and more flat(increasing r) the load can be met by generator coupledwith lower capacities of storage.The parameters l and r can be used to arrive at some
generic conclusions regarding the viability of optingbattery integration with diesel generator for a site withgiven load curve. This may be done by comparing the costof generation for the optimum configuration (for a specificload profile) with the diesel generator only system. Forsimplicity continuous generator operation is considered.The optimum cost of energy for the diesel generator–bat-tery system for different time fractions and specified loadratio are plotted in Fig. 19(a). Similarly, cost of energy forthe diesel generator only system for different values of l andr are shown in Fig. 19(b). In case of diesel generator onlysystem, cost of energy monotonically increases withincreasing time fraction (Fig. 19b). On the other hand,the cost of energy goes through a maximum for battery-integrated diesel generator system. It has been observedthat beyond a particular time fraction, the size of the dieselgenerator gets reduced significantly. This results in areduction in the cost of energy.
12
13
14
15
16
17
18
0 0.2 0.4 0.6 0.8 1time fraction
Cos
t of e
nerg
y (R
s/kW
h)
r = 0.25
r = 0.5
r = 0.7
12
13
14
15
16
17
18
19
20
21
0 0.2 0.4 0.6 0.8 1time fraction
Cos
t of e
nerg
y (R
s/kW
h)
r = 0.25
r = 0.5
r = 0.7
Fig. 19. Variation of cost of energy (a) for diesel generator–battery system
and (b) for diesel generator-only system for different values of load ratio.
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12
14
16
18
20
22
24
26
28
30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9time fraction
Cos
t of e
nerg
y (R
s/kW
h)
DG-batteryDG-only
l*
12
13
14
15
16
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9time fraction
Cos
t of e
nerg
y (R
s/kW
h)
DG-batteryDG-only
l*
Fig. 20. Cost of energy comparison with diesel generator only system for
load ratio (a) r ¼ 0.1 and (b) r ¼ 0.5.
00.10.20.30.40.50.60.70.80.9
1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1load ratio
time
fract
ion
DG-only
DG-battery
Fig. 21. Optimum time fraction as a function of load ratio for selecting
optimum configuration.
P. Arun et al. / Energy 33 (2008) 1155–1168 1167
It is seen that for different values of load ratio, a dieselgenerator–battery system can be cost effective when thevalue of time fraction is greater than a specific value (sayl*). Such a comparison is shown in Fig. 20 to obtain thevalue of l*. But it is seen that with increase in r, the costdifference between the diesel generator–battery system andthe diesel generator-only system is relatively less. This isshown for the case of r ¼ 0.1 and 0.5 (Fig. 20). A plot ofthe minimum values of l above which the diesel gener-ator–battery system becomes viable (l*) against the loadratio (r) is shown in Fig. 21. It is seen that for lower valuesof load ratios, integration of battery is viable for a widerrange of time fractions. For high values of load ratio, as theload curve is almost flat it is seen that storage may not beincluded under such conditions.
This analysis, using the design-space approach andsystem optimization, links the parameterized load and thesystem selection. For a given load profile, with theknowledge of the load ratio and the time fraction, thesystem selection chart (Fig. 20) gives preliminary informa-tion about the suitability of battery integration. It alsoindicates the limiting value of the load conditions abovewhich it is cost effective to have only a diesel generator tomeet the load.
7. Conclusions
The concept of design-space approach for the optimumsystem sizing of diesel generator–battery bank systems ispresented in this paper. Based on the proposed approach,for a given load demand and system characteristics, a sizingcurve may be plotted on the diesel generator rating vs.storage capacity diagram. Such a sizing curve also helps inidentifying the design space. The methodology offersflexibility in the overall design process as it identifies allthe feasible configurations for meeting a given load. Themethod can be adopted incorporating alternate models forbattery energy calculation without loss of generality.Through examples, identification of an optimum systemwith continuous and intermittent diesel generation ispresented. A Pareto optimal region is identified on thedesign space based on the minimum capital cost andminimum operating cost of the system. It is observed that ifcontinuous generator operation strategy is followed, theoptimum system is independent of the fuel price. Withintermittent generator operation, the optimal configurationis seen to lie close to the minimum capital cost configura-tion in the design space.Based on a case study of an existing system, it is shown
that retrofit options may also be analyzed using theproposed methodology. By considering alternate designoptions, the savings in fuel cost and effect on the emissionsfrom the diesel system can be explored with this approach.By suitable characterization of the load, the influence of theload profile on system sizing is also studied. The loadparameters enables to establish the conditions under whichthe battery integration may be adopted for a given loadprofile.It may be noted that the primary objective of this paper
is to present an appropriate methodology for sizingbattery-integrated diesel generation systems. The aim isnot to justify the operations of diesel based powergeneration. Environmental concerns due to emission ofdifferent pollutants are significant in the case of dieselbased power generation systems. However, diesel generator
ARTICLE IN PRESSP. Arun et al. / Energy 33 (2008) 1155–11681168
systems represent a significant part of isolated powersystems in many developing countries, including India. Theworld wide installed capacity of stationary reciprocatingengines for power generation is about 146GW [18]. It maybe noted that through appropriate design of the overallsystem, it is possible to reduce CO2 and NOx emissions, asillustrated through an example.
Diesel generation system is one out of the several optionsfor electrifying remote communities. But as diesel systemsare associated with the limitations of emissions and dieselspillage which adversely affect the environment, whereverfeasible, integration of renewable energy systems or‘renewable-only’ system has to be considered during thesystem planning stage. The design-space methodology canbe suitably generalized incorporating other sources alongwith the diesel generator like biomass gasifier, photovoltaicor wind energy systems which will be considered as a partof our on going research work. The design-space approachcan be a useful tool in the design of isolated power systems.
Acknowledgements
The authors wish to thank Mr. S.P. Gon Chaudhuri,Director, West Bengal Renewable Energy DevelopmentAgency, for permitting to use of data collected from theSagar island isolated power system. The first author isgrateful to the Ministry of New and Renewable Energy,Government of India, for providing the financial supportfor the research work.
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