112947101 Sreeraj Chatterjee Bandyopadhyay 2010 Design of Isolated Renewable Hybrid Power Systems

8/13/2019 112947101 Sreeraj Chatterjee Bandyopadhyay 2010 Design of Isolated Renewable Hybrid Power Systems

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Design of isolated renewable hybrid power systems

E.S. Sreeraj a, Kishore Chatterjee a, Santanu Bandyopadhyay b,*

a Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, Indiab Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, India

Received 7 January 2010; received in revised form 15 March 2010; accepted 17 March 2010Available online 10 April 2010

Communicated by: Associate Editor Mukund Patel

Abstract

Isolated electrical power generating units can be used as an economically viable alternative to electrify remote villages where gridextension is not feasible. One of the options for building isolated power systems is by hybridizing renewable power sources like wind,solar, micro-hydro, etc. along with appropriate energy storage. A method to optimally size and to evaluate the cost of energy producedby a renewable hybrid system is proposed in this paper. The proposed method, which is based on the design space approach, can be usedto determine the conditions for which hybridization of the system is cost effective. The simple and novel methodology, proposed in thispaper, is based on the principles of process integration. It finds the minimum battery capacity when the availability and ratings of variousrenewable resources as well as load demand are known. The battery sizing methodology is used to determine the sizing curve and therebythe feasible design space for the entire system. Chance constrained programming approach is used to account for the stochastic nature ofthe renewable energy resources and to arrive at the design space. The optimal system configuration in the entire design space is selectedbased on the lowest cost of energy, subject to a specified reliability criterion. The effects of variation of the specified system reliability andthe coefficient of correlation between renewable sources on the design space, as well as the optimum configuration are also studied in thispaper. The proposed method is demonstrated by designing an isolated power system for an Indian village utilizing windsolar photo-voltaic-battery system. 2010 Elsevier Ltd. All rights reserved.

Keywords: Design space; Renewable hybrid system; Chance constrained method; Process integration; Battery sizing

1. Introduction

Isolated power systems using renewable energy sourceslike wind, solar, biomass, micro-hydro, etc. can be utilizedto provide electricity for remote locations where grid exten-

sion is not feasible and/or economical. It was estimatedthat more than 1500 million people around the world hadno access to electricity in 2005 (International EnergyAgency, 2006). A vast majority of them are from Sub-Sah-aran Africa and South Asia, where electrification rates areonly 25.8% and 51.8%, respectively (International EnergyAgency, 2006). In 2001, about 44% of the households in

India do not have access to electricity ( Govt. of India,2001). As electricity is important for rapid economicgrowth and poverty alleviation, Indian government hasdecided to provide electricity access to all households.Along with rapid expansion in conventional power genera-

tion, Indian government has also decided to go for powergeneration from new and renewable sources. For manyremote non-electrified rural areas, power generation fromstand-alone systems is cheaper than grid extension.

The National Electricity policy of India states that wher-ever it is neither cost effective nor optimal to provide gridconnectivity, decentralized distributed generation facilitiestogether with local distribution network would be providedso that every household gets access to electricity (Govt. ofIndia, 2005). Non-conventional sources of energy could be

0038-092X/$ - see front matter 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2010.03.017

* Corresponding author. Tel.: +91 22 25767894; fax: +91 22 25726875.E-mail address:[email protected] (S. Bandyopadhyay).

www.elsevier.com/locate/solener

Available online at www.sciencedirect.com

Solar Energy 84 (2010) 11241136
http://dx.doi.org/10.1016/j.solener.2010.03.017mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.solener.2010.03.017


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utilized even where grid connectivity exists, provided it isfound to be cost effective (Govt. of India, 2003).

Isolated systems using renewables can be powered by asingle or a combination of renewable power sources. Thepower available from the renewable sources is stochasticin nature. However, some of the renewable resources likesolar and wind are complementary in nature. This meansthat during seasons of low insolation, the wind speed is

typically higher and the wind speed is generally low for sea-sons of high insolation. InFig. 1, monthly average value ofwind speed, monthly average total rainfall, and monthlyaverage daily global insolation for an Indian town, Rat-nagiri during each month is plotted (Mani and Rangarajan,1982). FromFig. 1, it can be observed that the amount ofrainfall and wind speed is negatively correlated to solarinsolation. During monsoon months, when the rainfall ishigh, the wind speed is also high and solar insolation islow. The wind speed and rainfall are low for summermonths when the insolation is high. Thus, it is apparentfromFig. 1 that it may be advantageous to make a wind

solar or a micro-hydro-solar hybrid power system. Due

to complimentary nature of wind and solar power andthe cost effectiveness of hybridizing these two systems, avast literature deals with windsolar hybrid systems andis recently reviewed byDeshmukh and Deshmukh (2008).

The performance of a hybrid system depends uponproper sizing of the system. Design and simulation fol-lowed by optimization are main steps involved in sizingan isolated hybrid system. The size of a system, that can

supply the required power demand, can be determined bysimulating the entire system using the resource and thedemand data. Optimization of the entire system may beperformed to arrive at a sizing which satisfies certain costand reliability criteria. This is typically achieved by mini-mizing the net present cost of the system or the levelizedcost of generated energy. The reliability of the power pro-duced by the hybrid system is also generally included in theoptimization process either in the form of constrains or asanother variable to be maximized. In the latter case, amulti-objective optimization routine has to be revokedand the solution set generally consists of a set of Pareto-

optimal configurations, out of which a suitable one has

Nomenclature

AP total array area (m2)

ACC annualised capital cost (Rs)AOM annualised operation and maintenance cost (Rs)

B battery capacity (kW h)a confidence levelC0 capital cost of the component (Rs)COE cost of energy (Rs/kW h)CRF capital recovery factorD load demand (W)d discount rateDactual the deterministic demand to be met taken in the

chance constrain (W)Dt time step for the simulation (h)f factor representing net charging/discharging

efficiencyfi factor that represents inverter efficiency

H wind turbine height (m)Hi specified meteorological mast height (m)IT total radiation incident on the array (W/m

2)lPjt

mean of power available fromith power source(W)

n life of the component (years)gc battery charging efficiencygd battery discharging efficiencygi inverter efficiencygP photovoltaic system efficiencyPnet net power available at the dc bus (W)Pdu dumped excess power (W)

Ppv power generated by the photovoltaic array (W)

Pr rated electrical power of the wind power gener-ating unit (W)

Pw power generated by the wind turbine (W)

Pj power generated by thejth power source (W)QB energy stored in the battery (kW h)Qmax1 maximum stored energy of the battery energy

before tref(W h)Qmax2 maximum stored energy of the battery energy

after tref(W h)Qmin minimum stored energy by the battery (W h)qj(t) multiplication factor for finding out power pro-

ducedqij coefficient of correlation between the power

available from ith and jth sourcesrPj t standard deviation of power available from ith

power source (W)

T time horizon for the simulation (h)t time (h)tmax1 time at which battery reaches maximum energy

before tref(h)tmax2 time at which battery reaches maximum energy

after tref(h)tref time at which battery reaches minimum energy

(h)vc cut-in wind speed (m/s)vf cut-off wind speed (m/s)vi wind speed at reference height Hi(m/s)vr rated wind speed (m/s)

X depth of discharge of batteryz power law exponent

E.S. Sreeraj et al./ Solar Energy 84 (2010) 11241136 1125


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to be selected (Gavanidou and Bakirtzis, 1992). The indicesthat are generally used to evaluate system reliability are: (a)number of days of autonomy (Natarajan and RajendraPrasada, 2006), (b) loss of load probability (Gavanidouand Bakirtzis, 1992; Beyer and Langer, 1996), (c) loss ofpower supply probability (Ai et al., 2003; Yang et al.,2003), and (d) unmet load (Chedid and Rahman, 1997).

There are primarily two different approaches to designand simulate a hybrid system: deterministic and probabilis-tic (Deshmukh and Deshmukh, 2008). In deterministicapproaches, the renewable energy resources and thedemand are considered as deterministic quantities and their

variation with respect to time is assumed to be known.Usually, time for which the system has to be analyzed (timehorizon), is divided into smaller time periods, during whichthe resources availability and load are assumed to be con-stant. In deterministic methods, the chronological sequenceof the data is extremely important. Sometimes the calcula-tion based on the worst case scenario, say worst month,can also be used in designing of the system (Beyer andLanger, 1996; Protogeropoulos et al., 1997; Celik, 2002a).Typical weather year for a particular location can also beused to design a renewable power system (Yang et al.,2003). However, the typical year data for more than onerenewable resource are difficult to obtain. Celik (2002b)has employed synthetically simulated weather data to sim-ulate a hybrid system. These approaches are either compu-tationally intensive (if it uses data for a long time period,say many years) or produce sub-optimal results (if it usesthe worst month scenario for calculation).

In probability-based approaches, energy generated bypower sources, and load demand in some cases, are consid-ered as random variables. Some methods may not considerthe chronological sequence of the data, which makes themless accurate.Karaki et al. (1999) proposed a probabilisticmodel for an autonomous photovoltaicwind system withseveral wind machines, accounting uncertainties related

to fluctuations in primary energy output, and outages of

the individual components due to hardware failures. Forstand-alone photovoltaicwind hybrid system, the stochas-tic nature of the resources is modelled as a three event Mar-kov process byBagul et al. (1996). This is an extension ofthe two state Markov process, proposed by Bucciarelli(1984). A transformation theorem based method for sizingof a stand-alone photovoltaicwind system has been pro-posed by Abousdar and Ramkumar (1990, 1991) wheresolar insolation, wind speed and load are considered asrandom variables.

The set of feasible configurations that can meet the givenload demand forms the design space. The concept of design

space is introduced for optimized sizing of solar hot watersystems byKulkarni et al. (2007, 2008, 2009). For isolatedpower systems, the representation of the design space isused for diesel generatorbattery systems (Arun et al.,2008), photovoltaic-battery systems (Arun et al., 2007),wind-battery systems (Roy et al., 2009) and windphoto-voltaic hybrid systems (Roy et al., 2007). The design spacerepresentation for a photovoltaic battery system incorpo-rating uncertainty through chance constrained program-ming has been presented by Arun et al. (2009). Chanceconstrained programming approach (Charnes and Cooper,1959), dealing with stochastic programming, has beenapplied in various fields of engineering to deal with uncer-tainty (Rao, 1980; Changchit and Terrell, 1993; Azaiezet al., 2005; Li et al., 2008).

As mentioned earlier, deterministic and probabilisticapproaches for system design and simulation have theirown merits and demerits. Design methodology utilizingdeterministic methods are either computationally intensiveor produce sub-optimal results depending upon the typeand amount of data used. Whereas, design methodologiesbased on stochastic methods are simple. However, deter-ministic methods take into account the chronologicalsequence of data, and hence, can produce accurate resultscompared to that of stochastic methods. In order to over-

come the limitation of inaccuracy in stochastic methods

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

900

1000

monthlyaverageofdailyglob

alinsolation(kWh/m2)

monthlyaveragewin

dspeed(km/h)

monthlyaveragerainfall(cm)

month

insolation

wind speed

rainfall

25

20

15

10

05

10

8

6

4

2

Fig. 1. Monthly average rainfall, wind speed and solar insolation at Ratnagiri, India.

1126 E.S. Sreeraj et al. / Solar Energy 84 (2010) 11241136


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reported in the literature (e.g.,Bucciarelli, 1984), a new sto-chastic method to optimally size a renewable hybrid systemwith more than one power source and to determine the costof energy produced is proposed in this paper. The methodcombines the advantages of both the deterministic andprobabilistic approaches while retaining inherent simplicity

of stochastic method. The system chosen is constrained tosupply power to the load satisfying certain reliability crite-rion. The probabilistic approach is used to incorporateuncertainty in available energy from each power source.The variability associated with power available from eachpower source along with coefficient of correlation betweenthem is used in the analysis as these quantities affect theperformance and reliability of the system. The emphasisis on the system design part and the optimum configurationthat is found by doing a search in the design space. Theproposed sizing method incorporates a simple and novelmethodology to find the battery capacity when renewableresource availability, ratings of renewable power sources

and load demand are known. This methodology also helpsto plan further load growth, as it gives the durations forwhich load can be increased without additional capacitygrowth. When the random nature of the resources is con-sidered, chance constrained programming is used to arriveat the design space. The effectiveness of the proposedmethod is demonstrated by designing an isolated powersystem for an Indian village with wind and solar poweras potential options.

2. Design space generation with deterministic approach

System sizing methodology for a renewable hybrid sys-tem following a deterministic approach is discussed in thissection. Renewable power sources can produce ac or dcelectric power depending on the type of generator andpower electronic interfaces connected to the system. Thehybrid system considered here has both ac and dc powersources. The average power available from each powersource during every time step is assumed to be known fromthe resource data and the capacity of the power source. Thetime series simulation, based on the energy balance of theoverall system is performed to arrive at the required batterycapacity. The schematic of an isolated renewable hybrid

system with power sources connected to either ac bus ordc bus and load connected to the ac bus is shown inFig. 2. During some instants the battery may be fullycharged and the net power produced by the sources isgreater than the demand. The excess power is dumpedusing the dump load and it is connected to the dc bus.

The system considered has n power sources, with thefirst m sources (1st to mth) connected to the ac bus andremaining n m sources (m+ 1st to nth) connected tothe dc bus. Let Pj(t) represents the power generated bythe jth source. The net power available at the dc bus thatcan be used to charge the battery (Pnet(t)) is the sum ofthe power generated by the sources connected to the dcbus and the power available from the ac bus.

Pnett Xn

jm1

Pjt Xmj1

Pjt Dt

!fit 1

The term inside the bracket is the net power generated atthe ac bus. D is the power required by the load and firep-resents the efficiency associated with the inverter (gi).Depending on the sign of the net power generated in theac bus, that is the difference of power generated by the var-ious power sources and the load demand, the power flowwill take place from ac bus to dc bus or vice versa. Thepower loss in inverter is accounted by the factor, fiwhichrepresents the inverter efficiency and is given as follows:

fit gi whenPm

j1

PjtP Dt

1gi

otherwise

2

During some time periods, the net energy that can beproduced by the system may be greater than the sum ofthe energy consumed in the load and that can be storedin the battery. This excess energy has to be dumped orlower amount of energy has to be produced by the powersources. The hybrid system considered in this paper has adump load connected to the dc bus and the excess energyis dumped using that load. The energy transfer across thebattery bankdQBt=dt is proportional to the net poweravailable at the dc bus (Pdc(t)) minus the dumped power(Pdu(t)).

Source-1

AC Load Battery bank

Converter

Source-m+1

AC Bus DC Bus

Dump load

Source-m

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Fig. 2. Schematic of renewable energy based isolated power system.



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dQBt

dt Pnett Pdutft 3

where f(t) represents the efficiencies associated with thecharging (gc) and discharging processes (gd) of the battery.

ft gc when PnetP 0

1gd when Pnet


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In terms of pinch analysis, the variation of stored energylevel is equivalent to the grand composite curve in heatexchange networks and the point of minimum stored energyis equivalent to the pinch point. Pinch analysis began as athermodynamic-based approach to energy conservation(Linnhoff et al., 1982), and later evolved over the years to

become a powerful tool for resource optimization (Linn-hoff, 1993; Shenoy, 1995; Smith, 1995). Pinch analysis hasbeen fruitfully used in analyzing heat exchanger networks(Shenoy, 1995), utility systems (Shenoy et al., 1998), massexchanger networks (El-Halwagi and Manousiouthakis,1989), water networks (Wang andSmith, 1994; Bandyopad-hyay et al., 2006; Pillai and Bandyopadhyay, 2007), distilla-tion column (Bandyopadhyay, 2002; Bandyopadhyay et al.,

2003, 2004), production planning (Singhvi and Shenoy,2002; Singhvi et al., 2004), etc. Pinch analysis recognizesthe importance of setting targets before design. This allowsdifferent process design objectives to be screened prior tothe detailed design of the process. Pinch analysis provides

graphical representation tools and full control to the pro-cess designer over decision making processes.

Along with finding the minimum battery capacityrequirement, the proposed methodology can be extendedto find the maximum possible amount of energy that canbe dumped at various instants. This helps to plan furtherload expansion. A load which consumes less power thanthe dumped power at that time can be added to the systemwithout any addition in system capacity. The time horizon(T) is divided into four parts, (AB, BC, CD and DE inFig. 3), using the points A (t= 0), B (t= tmax1), C (t= tref),D (t= tmax2) and E (t= T) as shown inFig. 3. The excess

energyQB(t= T) has to be dumped such that the differencebetween the maximum and the minimum of the storedenergy level should be minimum. The difference betweenQmax1 and Qmin cannot be reduced further because thereis no excess energy between tmax1 and tref. The peak ofthe stored energy curve that occurs after tref (Qmax2) canbe reduced by dumping the excess energy between trefand tmax2. A part of the excess energy, (min(-QB(t= T),Qmax2 Qmax1)), has to be dumped during timeinterval CD. Since the reduction of Qmax2 beneath Qmax1will not further reduce the battery capacity the remainingexcess energy can be dumped during other time intervals.The minimum amount of excess energy that has to bedumped during interval CD is QB(t=T), if Qmax2Qmax1 P QBt T and Qmax2 Qmax1, if Qmax2 Qmax1 QBt T Qmax1Qmax2QBt T AB, CD, DEQmax2Qmax1 CD

Qmax2 Qmax1 6 QBt T QBt T CD



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model the PV array. The power generated by the photovol-taic array (Ppv) is given as:

Ppv gpAPIT 14

where gPis the photovoltaic system efficiency,ITis the totalradiation incident on the array (W/m2) at that time step,and APis the total array area (m

2). The power generatedby the wind turbine (Pw) is obtained from the power curveof the wind turbine (Powell, 1981).

Pw

Prv2v2cv2rv

2c

for vc < v < vr

Pr for vr: 15

Pris the rated electrical power (W), vcis cut-in wind speed(m/s),vfis cut-off wind speed, (m/s) and vris the rated wind

speed (m/s). The wind speed data is generally available at a

specified meteorological mast height, Hi. The wind speed atturbine height His calculated by the following correlation(Justus, 1978):

v viH

Hi

z16

where v is wind speed at turbine hub height H, viis windspeed at reference height Hi, and z is the power law expo-nent.Figs. 5 and 6 show the power produced by a 1 kWpsolar PV array and the power produced by a 1 kW ratedwind turbine respectively kept in the location of case study.

2.3.1. PVbattery system

The solar array rating is varied from zero to 1000 kWpand the minimum battery capacity required to meet theload is determined to generate the sizing curve of the

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (hour of the day)

Load(kW)

Minimum load = 0.6 kW

Maximum load = 3.8 kW

Average load = 1.8 kW

Fig. 4. Load variations on a typical day at Sukhalai in Hoshangabad.

Table 2Input parameters used in the system sizing and optimization.

Photovoltaic system efficiency, gP(%) 10Mast height, Hi(m) 10

Turbine hub height, H(m) 20Power law index, z 0.14Cut-in wind speed, vc (m/s) 3Rated wind speed, vr(m/s) 8Cut-off wind speed,vf(m/s) 15Net charging efficiency, gc (%) 90Net discharging efficiency, gd(%) 90Depth of discharge, gD (%) 60Inverter efficiency, gi(%) 90

Table 3Economic parameters considered for system optimization.

Discount rate (d%) 10Wind generator life (years) 20Photovoltaic system life (years) 20Battery bank life (years) 5Converter life (years) 10Cost of photovoltaic system ($/kWp) 3213Cost of wind generator ($/kW) 3427Cost of battery bank ($/kW h) 86Cost of converter ($/kW) 386Operation and maintenance cost as a % of total capital cost 1

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time (hour of the day)

Outputpowerfrom1kWpPVarray(kW)

Fig. 5. Hourly average power available from a 1 kWp PV array atSukhalai in Hoshangabad.

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

time(hour of the day)

outputpowerfroma1kW

windturbine(kW)

Fig. 6. Hourly average power produced by 1 kW rated wind turbine at

Sukhalai in Hoshangabad.



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system. The design space for the solar alone system is theportion above the sizing curve and is shown inFig. 7. Asthe rating of photovoltaic array is increased, the minimumbattery capacity required to meet the load decreases till acertain point, beyond which the battery capacity remainsthe same. This is because of the non-availability of solar

insolation during night time and a minimum amount ofstorage is required for any amount of PV array to supplythe load at night. The optimum configuration correspondsto a system with PV array of 10.2 kWp, battery capacity of57.5 kW h, and the cost of energy is $0.38/kW h. It is seenfromFig. 7that the optimum configuration corresponds tothe one with the maximum amount of storage, with theminimum PV array rating.

2.3.2. Windbattery system

The wind turbine rating is varied from 0 to 80 kW todetermine the sizing curve and the design space for the sys-

tem (Fig. 8). Optimum system configuration calls for awind turbine capacity of 8 kW and battery capacity of19.7 kW h. The minimum cost of energy is determined tobe $0.24/kW h.

Comparing the sizing curves (Figs. 7 and8), it is seen thatthere is always a requirement of storage for any large solararray capacity. This is primarily due to non-availability ofpower during night. As wind is always available, for largevalues of wind turbine capacity, the storage capacity fallsto zero and the system can be designed with no storage(Fig. 8). However, the optimum configuration based on low-est cost of energy contains a large amount of storage for boththe cases. The amount of storage required for the minimum

PV array is larger than the amount of storage required forthe minimum wind turbine capacity and this is also due tothe non-availability of insolation for the entire night.

2.3.3. Windsolar hybrid system

The wind turbine rating is varied from 0 to 20 kW andPV array peak rating from 0 to 100 kWp to obtain the min-

imum battery size required to meet the load. The sizing-curve, shown in Fig. 9, is a surface in three-dimensionalspace formed by the PV array rating, wind turbine ratingand the minimum battery storage capacity required to meetthe load. Every point above the sizing curve in the figure isa feasible design point and collection of all of them consti-tutes the design space. The sizing curve is also shown on thebattery capacity vs. total generator rating diagram for var-ious values of solar PV and wind turbine ratings inFig. 10.For a typical configuration with solar and wind turbine rat-ing of 5 kWp and 4 kW, respectively, the minimum batterycapacity required is determined to be 36.6 kW h and the

corresponding cost of energy is $0.31/kW h. From storagecapacity vs. total generation graph for various fixed valuesof wind turbine/PV array rating, it is seen that all optimumpoints lie towards the maximum storage side. As the cost ofgenerators is comparatively more than storage cost and theconfiguration with largest battery storage is the optimumone. The overall optimum configuration corresponds to

0 100 200 300 400 500 600 700 800 900 100038

40

42

44

46

48

50

52

54

56

58

Solar array rating (kWp)

Batteryrating(kWp)

Feasible

region

Infeasible region

Optimum configuration

Designspace

Sizing curve

Fig. 7. Design space for solar-battery system.

0 10 20 30 40 50 60 70 800

5

10

15

20

25

Wind trbine rating(kW)

Batteryratin

g(kWp)

Feasibleregion

Infeasible region

Optimum configuration

Designspace

Sizing curve

Fig. 8. Design space for wind-battery system.

020

4060

80100

0

5

10

15

200

20

40

60

PV array rating(kWp)Wind rating(kW)

Batterycapacity(k

Wh)

Feasible region

Infeasible region

Designspace

Sizing curve

Fig. 9. Three dimensional plot showing the sizing surface and the design

space.



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the wind-battery system with no photovoltaic array. It iseconomical to go for a stand-alone wind-battery systemthan the hybrid system for this location.

Variation of cost of generators and battery bank affectthe optimum system configuration and the COE. Fig. 11shows the type of hybrid system which is cost effective asthe cost of solar PV array and wind turbine varies. It showsthat for most small variations around the price considered,the optimum configuration is a wind alone system. Hencefor these cases the optimum cost is not dependent on thecost of PV array. But as both cost of PV array decreasesby a large amount and cost of wind turbine increases bya large amount, the system moves from wind alone towindsolar. Solar alone system is not cost effective, evenif the solar cost decreases by 50% and wind turbine costincreases by 50% from their respective base cost.

3. Generation of design space and optimization with

probabilistic approach

The methodology used to arrive at the design space indeterministic approach is extended to incorporate theeffects of uncertainty in the power available from the

resources. The hourly values of power available from thepower sources are considered as random variables. The sys-tem is sized for a specified reliability level using chance con-strained programming approach. This approach is used byArun et al. (2008)for sizing a photovoltaic battery system.It is assumed that the power available from the ith powersource (Pi(t)) during each hour follows a normal distribu-tion with mean lPit and standard deviation rPit. qij isthe coefficient of correlation between the power availablefrom ith and jth power sources. The load is assumed tobe deterministic over the time step. The source uncertaintyis expressed as a probabilistic constraint. The system has tocater to the specified deterministic demand with probability

greater than a specified value. The chance constrain relat-ing the probability of the demand, D(t) being met by thesystem is:

P DtP Dactualt P a 17

where Dactual(t) is the deterministic demand to be met overthe time step and a is the specified reliability of complianceof the constraint or the confidence level. Combining (17)with the energy balance (7), the overall chance constraintcan be written as:

P Xnj1m

Pj

t QBtDt

ftDt

QBt

ftDt Xm

j1

Pj

t Dactual

t !fit PdutP0Pa 18

Separating stochastic and deterministic variables andmodifying the above equation, we get:

PXn

j1m

Pjt Xmj1

Pjtfit 6QBt Dt

ftDt

QBt

ftDt

Dactualtfit Pdut 6 1 a 19

Since the random variables (Pj(t)) are normally distrib-uted, the sum of the stochastic variables in the aboveexpression is a new random variable Pt(t) with mean lPjtand standard deviation rPjt such that

lPttXnj1

lPjtqj 20

r2

PttXnj1

Xnk1

qjkrPjtrPktqjtqkt 21

where

qjt fit if j 6 m

1 otherwise 22

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

actual cost of wind turbine/cost considered

actualcostofPVarray/cos

tconsidered

Wind only

Wind-solar

Fig. 11. Type of hybrid system which is cost effective as the cost of PV

array and wind turbine varies.

0 20 40 60 80 100 1200

10

20

30

40

50

60

total generation capacity(kW)

Batterycapacity(kWh)

No wind turbine

No PV array

Wind turbine=2 kW

Wind turbine=4 kW

Wind turbine=6 kW

optimumconfigurations

for each sizin curve

Fig. 10. Sizing curves for different options for isolated power generation.



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where qjkis the coefficient of correlation between the poweravailable fromjth andkth sources. The deterministic equiv-alent of(19)can now be expressed as:

QBt Dt

ftDt

QBt

ftDtDactualtfit Pdut

lPtt rPttZa 23wherez

ais the inverse of the cumulative normal probability

distribution corresponding to the required confidence levelawith zero mean and unity standard deviation. Expressingthe deterministic equivalent in terms of the battery energyvalues for any time step, we get:

QBt Dt QBt lPtt rPttza Dactualtfit

PdutftDt 24

It may be noted that the deterministic energy balance (7)and the probabilistic energy balance(24)are equivalent. Asthe random variable P

t(t) in the stochastic case is repre-

sented by its deterministic equivalent, the methodologydeveloped to find the design space for the deterministic casecan be applied directly.

Even though we have assumed that the power availablefrom the sources follows normal distribution, the powersources cannot produce negative power. Eq. (24) is cor-rected when the deterministic equivalent of the power pro-duced by any power source becomes negative. If thedeterministic equivalent of power produced by any sourceis negative, it is considered that particular source is notproducing any power. The mean and standard deviationof the power produced by such sources are zero. This can

be incorporated by modifying only the expression ofqj(t)in(22).

qjt

0; if lPjt rPjtza 6 0

fit; if j 6 m and lPjt rPjtza> 0

1; if j> m and lPjt rPjtza> 0

8>: 25

3.1. Illustrative example

Illustrative example, discussed in Section2.3, is extendedto incorporate the uncertainty associated with the powerproduced by different sources. For energy related applica-tions, wind speed is generally described using gamma distri-bution function, or its special cases like Weibull or Rayleighdistribution functions, or using bivariate normal distribu-tion function (Hennessey, 1977). The solar insolation gener-ally forms a bimodal distribution function and can beapproximated by the superposition of two distributionfunctions. Those two distribution functions can be fromnormal, beta or Weibull distributions (Khallat and Rah-man, 1986). However, if the number of days for which thedata taken is sufficiently large, using central limit theorem(Papoulis and Pillai, 2002), the power produced by the pho-tovoltaic array and the wind turbine tends to follow a bivar-

iate normal distribution with known mean and standard

deviation. The standard deviation of power produced byeach generator is assumed to be a fixed percentage of themean value of it. The PV array is considered to be a rela-tively less variant power source with standard deviationequal to 45% of the mean of the power available. The windis taken as a high variable source with standard deviation

equal to 80% of the mean power available from wind. Thereliability requirements for rural applications are consid-ered to be not very high and the specified reliability of com-pliance is varied from 50% to 90%. The coefficient ofcorrelation between the power sources is varied in full pos-sible range to study its effect.

The wind turbine rating is varied from 0 to 100 kW andPV array peak rating from 0 to 100 kWp, respectively andthe minimum battery size required to meet the load foreach case is determined. Similar to Fig. 10, sizing curvesfor a reliability of 80% are shown in Fig. 12, where thepower produced from the two sources are assumed to beindependent. Optimum configuration (shown in Fig. 12)

with 8 kWp of solar PV, 7 kW of wind turbine, and batterycapacity of 44.29 kW h, compliance with a reliability of80% and the corresponding COE is $0.47/kW h. It maybe noted that the COE almost doubled to enhance the reli-ability of the system from 50% to 80%. It may also be notedthat the optimum system is hybrid system, comprising ofboth the PV and wind generators unlike wind-battery sys-tem for deterministic case. Effect of reliability and coeffi-cient of correlation of sizing curve of the overall systemare shown inFigs. 13 and 14, respectively. From the sizingcurves shown in Fig. 13, the increase in storage capacityrequired with the increase in the system reliability require-

ment can be observed for a hybrid windsolar system with6 kW wind turbine. The power available from the twosources is considered as independent. It can be noted fromFig. 14 that as the coefficient of correlation between thepower sources varies from 1 to +1, the system sizeincreases. The variation of sizing curve for 80% reliable

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

Total generation capacity(kW)

Batterycapacity

No wind turbine

wind turbine=2.5kW

wind turbine=5kW

wind turbine=7.5kW

wind turbine=10kW

No solar array

Optimum configuration(8kWp,7kW,44.29kWh)

Fig. 12. Sizing curves for a reliability of 80%.



11/13

windsolar system with 6 kW wind turbine is shown inFig. 14. The optimum configuration corresponding to eachsizing curve is also shown.

The type of hybrid system which is cost effective for dif-ferent reliability of compliance and coefficient of correla-tion is given in Fig. 15. As the reliability of complianceincreases, a predominantly wind system shifts to a predom-inantly solar system. This can be attributed to the differ-ence in variability of the power available from the twosources. For low values of alpha (0.50.6), the optimal sys-tem is a wind-battery system (variability of power fromwind turbine is more than that of solar PV) while for a highreliable system with confidence level of 90%, its a solaralone system. Windsolar hybridisation is a cost effectivesolution for moderate values of alpha. The cost and size

of power sources and battery reduces for highly negatively

correlated power sources. So hybridisation is more effectivein such cases.

Hybridisation is most effective for

(a) Moderate values of reliability of compliance.(b) High negative values of coefficient of correlation.

Constant alpha curves are plotted between PV array rat-ing and wind turbine rating in Fig. 16 with coefficient ofcorrelation equal to zero. It can be observed that for awind-battery (y-axis) system, the increase in the wind tur-

bine rating is more than three times when the required reli-ability changes from 50% to 80%, while for a solar-batterysystem (x-axis), the increase in PV rating is only about 1.5times.

The effect on the type of hybrid system with change inthe cost of individual components is studied. The change

0 20 40 60 80 100 12015

20

25

30

35

40

45

50

55

60

Total generation (kW)

Batterycapac

ity(kWh)

alpha=.50,deterministic

alpha=0.60

alpha=0.70

alpha=0.80

alpha=0.90

Fig. 13. Variation of design space with the confidence level (wind turbinerating of 6 kW and zero coefficient of correlation).

0 20 40 60 80 100 12034

36

38

40

42

44

46

48

Total generation capacity (kW)

Batterycapacity(kWh)

Coefficient of correlationincreasing from-1 to 1steps of 0.333,6kW wind turbine,alpha=80%

Optimum configurationfor each sizing curve

Fig. 14. Variation of sizing curves with coefficient of correlation.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

alpha

coefficientofcorrelation

Wind solar

solaralone

wind

alone

Fig. 15. Type of hybrid system which is costeffective for differentreliability of compliance and coefficient of correlation.

0 2 4 6 8 10 12 14 16 180

5

10

15

20

25

30

Windturbineratin

g(kW)

alpha=0.8

alpha=0.7

alpha=0.6

alpha=0.5

0 2 4 6 8 10 12 14 16 180

5

10

15

20

25

30

solar array rating (kWp)

alpha=0.5

alpha=0.6

alpha=0.7

alpha=0.8

Fig. 16. PV array capacity vs. wind capacity for various values of

reliability of compliance.



12/13

in cost of power sources affects the type of system whichcan produce power at the lowest possible cost and hence,the effect of variation of cost of wind turbine and PV arrayis studied. The type of hybrid system which is cost effectiveas the cost of PV array and wind turbine varies is shown inFig. 17with alpha of 0.7 and coefficient of correlation of 0.For the base cost (considered in Table 3), the optimumconfiguration is a wind-battery system. The ratio of thevaried cost of the wind turbine and PV array to the basecost is plotted in x- and y-axis of the figure respectively.

It shows that the system varies from a wind only system(when solar cost is high and wind cost is low) to a solaralone system (when solar cost is low and wind cost is high).For small cost variations around the actual values of costof power sources considered, its a hybrid system.

4. Conclusions

Renewable energy based isolated hybrid systems arepotential alternatives to grid extension for remote electrifi-cation. The random nature of the renewable resources andthe non-linearities involved in the modeling of powersources makes the design and sizing of hybrid systems chal-lenging. Deterministic or probabilistic approach is gener-ally used to size the system and both have its own meritsand demerits. The method proposed in this paper combinesthe advantages of both these approaches and takes uncer-tainty of resources into account. Design space approachfor designing and optimizing stand alone windsolarhybrid power generating system has been demonstratedin this paper. A methodology is proposed to find the min-imum battery capacity required when the ratings of renew-able energy sources are known. This methodology is usedto derive the sizing curve and the design space. The meth-

odology also helps to plan further load growth as it can

find out the durations for which more load can be addedwithout any change in system sizing.

A case study from Sukhalai in Hoshangabad district ofMadhya Pradesh, India to illustrate the proposed method-ology for a windsolar hybrid system, is presented. Usingdeterministic procedure (as described in Section2), the cost

of energy from a PVbattery system is determined to be$0.38/kW h and the same for wind-battery system is$0.24/kW h. The wind power generating system is a cheapsource of electric power compared to solar PV, but the var-iability of the power available from the wind is greater thanthat of the solar PV. Hence, if the reliability requirement islow, wind-battery system is cost effective. On the otherhand, if the reliability requirement of the power producedis high, solar-battery system is cost effective. For moderatevalues of reliability requirement, the optimum choice is awindsolar hybrid system. Applying the chance constraintprogramming, the optimum configuration for 80% reliabil-ity consists of 8 kWp of solar PV, 7 kW of wind turbine, and

battery capacity of 44.29 kW h, and the correspondingCOE is $0.47/kW h.

Among the various available renewable options forhybridization at a location, a proper choice of combinationof power sources and their sizing depends upon various fac-tors. From the case study performed in this paper, it can beconcluded that the characteristics of the available resourcesat that location, the quality and reliability of the power sup-ply required and the cost of various components decide theoptimum configuration. The characteristics of the availableresources can be captured by two parameters, the variabilityassociated with the power available from each source and

the coefficient of correlation between the powers availablefrom various sources. Negatively correlated power sources,as shown inFig. 1, are good choices for hybridization. Ahighly variable power source with low cost can be a betterchoice compared to a low variable higher cost power sourceif the power supply reliability requirement is small and thereverse is true for high reliability requirement. For moder-ate values of reliability, hybridization of these sources willlead to cost effective solution.

References

Abousdar, I., Ramkumar, R., 1990. Loss of power supply probability ofstand alone wind electric conversion systems: a closed form approach.IEEE Trans. Energy Convers. 7 (3), 445452.

Abousdar, I., Ramkumar, R., 1991. Loss of power supply probability ofstand alone photovoltaic systems: a closed form approach. IEEETrans. Energy Convers. 6 (1), 445452.

Ai, B., Yang, H., Shen, H., Liao, X., 2003. Computer-aided design of PV/wind hybrid system. Renew. Energy 28 (10), 14911512.

Arun, P., Banerjee, R., Bandyopadhyay, S., 2007. Sizing curve for designof isolated power systems. Energy Sustain. Dev. 11 (4), 2128.

Arun, P., Banerjee, R., Bandyopadhyay, S., 2008. Optimum sizing ofbattery integrated diesel generator for remote electrification throughdesign-space approach. Energy 33, 11551168.

Arun, P., Banerjee, R., Bandyopadhyay, S., 2009. Optimum sizing ofphotovoltaic battery systems incorporating uncertainty through design

space approach. Sol. Energy 83 (7), 10131025.

0.6 0.8 1 1.2 1.4 1.60.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

actual cost of wind turbine/cost considered

actualcostofPVarray/costconsidered Wind only

Wind-solar

PV only

Fig. 17. Type of hybrid system which is cost effective as the cost of PVarray and wind turbine varies (alpha is 0.7 and zero coefficient of

correlation).



13/13

Azaiez, M.N., Hariga, M., Al-Harkan, I., 2005. A chance-constrainedmulti-period model for a special multi-reservoir system. Comput.Oper. Res. 32, 13371351.

Bagul, A.D., Salameh, Z.M., Borowy, B., 1996. Sizing of stand-alonehybrid windphotovoltaic system using a three-event probabilitydensity approximation. Sol. Energy 56 (4), 323335.

Bandyopadhyay, S., 2002. Effect of feed on optimal thermodynamicperformance of a distillation column. Chem. Eng. J. 88 (13), 175186.

Bandyopadhyay, S., Malik, R.K., Shenoy, U.V., 2003. Feed precondi-tioning targets for distillation through invariant rectifyingstrippingcurves. Ind. Eng. Chem. Res. 42 (26), 68516861.

Bandyopadhyay, S., Mishra, M., Shenoy,U.V., 2004. Energy-based targetsfor multiple-feed distillation columns. AIChE J. 50 (8), 18371853.

Bandyopadhyay, S., Ghanekar, M.D., Pillai, H.K., 2006. Process watermanagement. Ind. Eng. Chem. Res. 45, 52875297.

Beyer, H.G., Langer, C., 1996. A method for the identification ofconfigurations of PV/wind hybrid systems for the reliable supply ofsmall loads. Sol. Energy 57 (5), 381391.

Bucciarelli Jr., L.L., 1984. Estimating loss-of-power probabilities ofstandalone photovoltaic solar energy systems. Sol. Energy 32 (2), 205209.

Celik, A.N., 2002a. Optimization and techno-economic analysis ofautonomous photovoltaic wind hybrid energy systems in comparisonto single photovoltaic and wind systems. Energy Convers. Manage. 43(18), 24532468.

Celik, A.N., 2002b. The system performance of autonomous photovol-taicwind hybrid energy systems using synthetically generated weatherdata. Renew. Energy 27 (1), 107121.

Changchit, C., Terrell, M.P., 1993. A multiobjective reservoir operationmodel with stochastic inflows. Comput. Ind. Eng. 24 (2), 303313.

Charnes, A., Cooper, W.W., 1959. Chance-constrained programming.Manage. Sci. 6, 7379.

Chedid, R., Rahman, S., 1997. Unit sizing and control of hybrid windsolar power systems. IEEE Trans. Energy Convers. 12 (1), 7985.

Deshmukh, M., Deshmukh, S., 2008. Modeling of hybrid renewableenergy systems. Renew. Sustain. Energy Rev. 12 (1), 235249.

El-Halwagi, M.M., Manousiouthakis, V., 1989. Synthesis of massexchange networks. AIChE J. 8, 12331244.

Gavanidou, E.S., Bakirtzis, A.G., 1992. Design of stand-alone system withrenewable energy sources using trade off methods. IEEE Trans. EnergyConvers. 7 (1), 4248.

Government of India, 2001. Tables on Houses, Household Amenities andAssets (H Series Tables). Census of India, New Delhi.

Government of India, 2003. The Electricity Act, 2003, The Gazette ofIndia, Extraordinary, 2003, Part II Section 3 Sub-section (ii). Ministryof Power, New Delhi.

Government of India, 2005. National Electricity Policy, The Gazette ofIndia, Extraordinary, Part I Section 1. Ministry of Power, New Delhi..

Hennessey Jr., J., 1977. Some aspects of wind power statistics. J. Appl.Meteorol. 16 (2), 119128.

International Energy Agency, 2006. World Energy Outlook, second ed.IEA Publications.Justus, C.G., 1978. Wind energy statistics for large arrays of wind turbines

(New England and central US regions). Sol. Energy 20, 379386.Karaki, S.H., Chedid, R.B., Ramadan, R., 1999. Probabilistic perfor-

mance assessment of autonomous solarwind energy conversionsystems. IEEE Trans. Energy Convers. 14 (3), 766772.

Khallat, M.A., Rahman, S., 1986. A probabilistic approach to photovol-taic generator performance prediction. IEEE Trans. Energy Convers. 1(3), 3440.

Kolhe, M., Kolhe, S., Joshi, J.C., 2002. Economic viability of stand-alonesolar photovoltaic system in comparison with diesel-powered systemfor India. Energy Econ. 24 (2), 155165.

Kulkarni, G.N., Kedare, S.B., Bandyopadhyay, S., 2007. Determinationof design space and optimization of solar water heating systems. Sol.Energy 81 (8), 958968.

Kulkarni, G.N., Kedare, S.B., Bandyopadhyay, S., 2008. Design of solarthermal systems utilizing pressurized hot water storage for industrialapplications. Sol. Energy 82, 686699.

Kulkarni, G.N., Kedare, S.B., Bandyopadhyay, S., 2009. Optimization ofsolar water heating systems through water replenishment. EnergyConvers. Manage. 50 (3), 837846.

Li, P., Arellano-Garcia, H., Wozny, G., 2008. Chance constrainedprogramming approach to process optimization under uncertainty.Comput. Chem. Eng. 32 (12), 2545.

Linnhoff, B., 1993. Pinch analysis: a state-of-the-art overview. Chem. Eng.Res. Des. 71, 503522.

Linnhoff, B., Townsend, D.W., Boland, D., Hewitt, G.F., Thomas,B.E.A., Guy, A.R., Marsland, R.H., 1982. User Guide on ProcessIntegration for the Efficient Use of Energy. The Institution ofChemical Engineers, Rugby, UK.

Mani, A., Rangarajan, S., 1982. Solar Radiation Over India. Allied Pub.,New Delhi.

Natarajan, E., Rajendra Prasada, A., 2006. Optimization of integratedphotovoltaicwind power generation systems with battery storage.Energy 31 (12), 19431954.

Papoulis, A., Pillai, S.U., 2002. Probability, Random Variables andStochastic Processes, fourth ed. Tata McGraw-Hill.

Pillai, H.K., Bandyopadhyay, S., 2007. A rigorous targeting algorithm forresource allocation networks. Chem. Eng. Sci. 62, 62126221.

Powell, W.R., 1981. An analytical expression for the average poweroutput of a wind machine. Sol. Energy 26 (1), 7780.

Protogeropoulos, C., Brinkworth, B.J., Marshall, R.H., 1997. Sizing andtechno-economical optimization for hybrid solar photovoltaic/wind power systems with battery storage. Int. J. Energy Res. 21,465479.

Rao, S.S., 1980. Structural optimisation by chance constrained program-

ming techniques. Comput. Struct. 12 (6), 777781.Roy, A., Arun, P., Bandyopadhyay, S., 2007. Design and optimization ofrenewable energy based isolated power systems. SESI J. 17, 5469.

Roy, A., Kedare, S.B., Bandyopadhyay, S., 2009. Application of designspace methodology for optimum sizing of wind-battery systems. Appl.Energy 86 (12), 26902703.

Shenoy, U.V., 1995. Heat Exchanger Network Synthesis: ProcessesOptimization by Energy and Resource Analysis. Gulf PublishingCompany, Houston.

Shenoy, U.V., Sinha, A., Bandyopadhyay, S., 1998. Multiple utilitiestargeting for heat exchanger networks. Chem. Eng. Res. Des. A 76,259272.

Singhvi, A., Shenoy, U.V., 2002. Aggregate planning in supply chains bypinch analysis. Chem. Eng. Res. Des. 80 (6), 597605.

Singhvi, A., Madhavan, K.P., Shenoy, U.V., 2004. Pinch analysis for

aggregate production planning in supply chains. Comput. Chem. Eng.28 (67), 993999.Smith, R., 1995. Chemical Process Design. McGraw-Hill, New York.Wang, Y.P., Smith, R., 1994. Wastewater minimization. Chem. Eng. Sci.

49 (7), 9811006.Yang, H.X., Lu, L., Burnett, J., 2003. Weather data and probability

analysis of hybrid photovoltaicwind power generation systems inHong Kong. Renew. Energy 28 (11), 18131824.

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112947101 Sreeraj Chatterjee Bandyopadhyay 2010 Design of Isolated Renewable Hybrid Power Systems