Sizing curve for design of isolated power systems

Sizing curve for design ofisolated power systemsArun P., Rangan Banerjee, and Santanu Bandyopadhyay

Energy Systems Engineering, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, IndiaE-mail (Bandyopadhyay): [email protected]

Isolated power systems meet electricity demand by generating power close to its point of utilisation.They are an option to electrify communities located in remote areas where extending the grid couldbe uneconomic. Diesel generators, photovoltaic panels and energy storage using battery banks havebeen used for meeting the electrification needs of remote areas. The design objective for suchsystems is the estimation of the ratings of the generators and the storage capacity requirements formeeting specified reliability and economic constraints. A review of different methods for sizingphotovoltaic-battery systems indicates that they fall into mainly two categories, analytical methodsand simulation-based schemes. A generalised methodology for generating a “sizing curve” relatingthe generator rating and storage capacity, based on a time series simulation approach, is presentedin this paper. It helps in the identification of a “design space” which enables the exploration ofall the feasible system configurations meeting a given demand for a site. It further serves as a toolfor system optimisation. Two specific options for isolated power generation, diesel generator-batterysystem and photovoltaic-battery system, are illustrated for a typical Indian site. Sizing curve anddesign space are plotted on normalised generator rating vs. storage capacity coordinates for theseoptions.

1. IntroductionIsolated power systems meet electricity demand at a lo-cation by generating power close to its point of utilisation.They are an option to electrify communities whose re-moteness from the main grid could make extension of thegrid to them uneconomic. In India, of the 119,570 villageswhich are unelectrified, 18,000 are located in remote areaswhere extending the grid is not feasible [MNRE, 2005;MoP, 2006]. The installed capacities of isolated generationsystems useful in such locations are generally in the rangeof 10 to 250 kW [Willis and Scott, 2000]. Decentralisedpower generation may be based on diesel generator (DG)sets, renewable energy-based units like solar photovoltaic(PV) panels, wind turbines, small hydro power or througha combination of these systems (hybrid energy systems).

DG sets, being modular and having a high power-to-weight ratio, are the preferred option for isolated systems.Typical remote location load curves exhibit a varying loadprofile. DG-alone systems sized on the basis of expectedpeak demand result in generator operation at part-loadconditions for large durations of time. One of the optionswould be the integration of battery banks into the systemfor improving the system efficiency. PV systems whichenable the direct conversion of solar energy to electricpower are also preferred for remote electrification. Thespecific advantages of photovoltaics are the reasonableconversion efficiencies obtained for both direct and dif-fuse solar radiation, modularity of the system and its staticcharacter. They have been successfully used for meetingpower requirements of small loads in remote areas. Many

hybrid systems also becoming popular incorporate renew-able energy systems like PV panels and wind generatorsintegrated with conventional diesel generators and energystorage systems. In India, steps have already been takentowards renewable energy-based distributed generation atthe rural level. A typical example is the Sagar island re-gion of West Bengal, where several renewable energy-based isolated systems have been installed. These includestand-alone PV power plants and hybrid systems integrat-ing wind and diesel generators.

Isolated power systems have to be designed to meet thepower demand of a location subject to the techno-eco-nomic constraints and expected reliability requirements.PV-battery system design has to cater for the variabilityof the solar energy resource. Simple sizing methods pro-pose the methodology of designing the battery size on thebasis of the number of autonomy days. But the estimationof “no sun” days would be purely subjective, depending onthe designer. PV systems may be sized on the basis of a“worst-case” approach, designing for the lowest insolationperiod. In general such methods offer an incomplete evalu-ation of options and the systems are thus sub-optimally de-signed. The “design space” approach maps all the feasibleconfigurations of a system and is a useful tool in systemdesign. Kulkarni et al. [2006] have introduced a method foridentifying a design space for solar hot water systems.

2. Review of PV-battery system sizingSizing of a PV-battery system involves choosing the PVarray size (in terms of array area) and the storage (battery

Energy for Sustainable Development • Volume XI No. 4 • December 2007

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capacity). The array size and battery capacity may be ex-pressed in terms of the load. On a daily basis, the PV-arraycapacity, CA, may be defined as the ratio between themean PV-array energy production and the average powerconsumption (L, Wh/day).

CA = η0 IDT A / L (1)Here η0 is the photovoltaic system efficiency, IDT (Wh/m2)is the total insolation incident on the PV array over theday per unit area, and A is the total array area (m2). Thestorage capacity, CS, may be expressed in terms of theperiod of autonomy (obtained by dividing the battery ca-pacity (Br) by the average power consumption).

CS = Br / L (2)The sizing methods can be grouped under three cate-

gories [Egido and Lorenzo, 1992] which include thefollowing.1. Sizing rules based on the designer’s experience (intui-

tive or empirical)Here the relationship between the normalised array ca-pacity (CA), normalised battery capacity (CS) and thesystem reliability is decided on the basis of the de-signer’s experience. It is very easy to implement butis limited to obtaining the preliminary system design.For example, typical values of normalised array capac-ity and normalised battery capacity for systems cater-ing for telecommunications applications in Spain aretaken as 1.3 and 7 respectively [Egido and Lorenzo,1992]. It may be noted that such an approach wouldalways tend to oversize the system.

2. Analytical methods3. Simulation-based methodsSeveral analytical and simulation-based procedures havebeen reported for PV-based isolated system design. Someof these are discussed briefly in the following sections.2.1. Analytical methodsIn this approach the objective is to obtain a closed formrelation between the system capacities and the requiredreliability for the PV system. They include a probability-based approach, methods based on empirical coefficientsand those which apply novel methods like artificial neuralnetworks (ANN)[1].

Bucciarelli [1984] has described an approximatemethod to study the performance of stand-alone PV sys-tems following an approach that treats energy capture,storage and disbursement processes as a random walk inthe storage domain. The probability density for daily in-crement or decrement of storage level is approximated bya two-event probability distribution. A rule for calculatingthe storage size (required to achieve predefined systemreliability) for a given array size is developed. Plots of“average array output relative to the load” against “daysof autonomy” for different values of loss of load prob-ability (LOLP) are presented. The method was extendedto account for the effect of correlation between day-to-dayinsolation values [Bucciarelli, 1986]. Gordon [1987] hadused a method similar to that proposed in [Bucciarelli,1986] but extended it considering the level of the storagetaking up three states. Bucciarelli’s method had consid-ered only two events, either an increase in battery energy

or a decrease. The additional state in the “three-event”approach corresponds to the condition when the batterystate remains constant over the days considered. Barra etal. [1984] had developed an analytical procedure for de-termining the optimal size of a stand-alone PV plant. Theprocedure relies on coefficients obtained through long-term simulation data. An analytical function relating arrayarea and storage capacity for a given covered fraction ofthe load is given. The coefficients are validated only forcertain typical locations in Italy. Bartoli et al. [1984] hadproposed an analytical procedure similar to that given in[Barra et al., 1984]. Monthly average solar insolation anddaily loads were considered, with examples given for Ital-ian sites. Analysis of the system cost with different valuesof fraction of the load covered and types of PV cells aregiven. Egido and Lorenzo [1992] proposed a correlationconnecting the normalised array capacity, storage size andLOLP and have illustrated the results for different loca-tions in Spain. The corresponding equations are given asan example for the correlations typically used in the sys-tem sizing:

CA = mCS –n (3)

m = m1 + m2 log(LOLP) (4)

n = exp(n1 – n2LOLP) (5)

Here m1, m2, n1, n2 are coefficients evaluated for the dif-ferent sites. The comparison of this method with certainother previously developed models is also presented[Egido and Lorenzo, 1992]. Hontoria et al. [2005] havefollowed an ANN-based methodology to obtain the systemsizing curve for stand-alone PV systems. Markvart et al.[2006] had presented the system sizing curve as a super-position of contributions from individual climatic cyclesof low daily solar radiation for a location in the south-eastof England.2.2. Simulation-based methodsIn the category of simulation-based methods for design,Tsalides and Thanailakis [1986] have used an hourly time-step-based model, for optimum “simulation-based design”of stand-alone PV systems for a remote village in northernGreece. The input solar radiation data were generated us-ing a stochastic model developed by the authors. For agiven array orientation, the optimum array tilt angle(which minimizes the size of the PV system) was foundto be independent of the chosen values of LOLP. As anexample of a simulation-based approach the methodologyproposed in [Tsalides and Thanailakis, 1986] is brieflydescribed. The system is simulated with an hourly timestep to obtain the battery energy balance. The battery en-ergy state B(t) has to lie between the maximum value BMand the minimum value Bm. Depending on the system op-eration, whenever overcharging occurs, the control systemintervenes and the charging process is stopped. This mayhappen when the solar radiation level is high or the de-mand is low. Similarly, when over-discharging occurs, thecontrol system intervenes and disconnects the load. Thismay happen for low solar radiation levels or high demand.


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LOLP is evaluated as follows:LOLP = Probability (available power < demand) (6)

At any given hour j, available power is defined byAvailable power = Ej + BPAj (7)

In the above relation Ej is the total power generated fromthe installed PV arrays at hour j, BPAj is the availablepower from the battery at hour j, taken to be zero or posi-tive depending on whether the state of charge B(t) is equalto or greater than Bm respectively. A is the array area. Thebehaviour of the batteries has been approximated by using

constant efficiency for both the charging and dischargingphases. The above definition of available power showsthat power delivered to the load is supplied either by thebatteries or by the PV arrays directly or by both. Thesystem reliability (expressed as LOLP, which equals zerofor a totally reliable system) is evaluated by simulatingthe system with various assumed system configurations.The flow chart representation of the algorithm is given inFigure 1. Sidrach de Cardona and Lopez [1998] have useda simulation model for PV systems taking a daily time

Figure 1. Simulation-based method proposed in [Tsalides and Thanailakis, 1986]


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step. The analysis had been carried out for 2 to 9 days ofsystem autonomy. The simulations were carried out on thebasis of meteorological data for different locations ofSpain. The method also included a linear regression analy-sis to determine the independent variables affecting theestimation of the array size. A time-series approach forsystem sizing has also been followed for hybrid systemslike PV-diesel-battery systems, PV-wind systems, andwind-diesel systems, where multiple sources of energyand storage are integrated.

It is observed that each group of sizing methods has itsmerits and demerits. In the case of PV-battery systems,the relation between CA, CS and LOLP depends on theexperience of the PV designer when the design is basedon rules of thumb. Such intuitive designs are simple andare useful to have an initial rough idea of the PV systemdimensions, but they do not allow quantification of thereliability. Empirical coefficients available for system siz-ing are mostly site-specific. In analytical methods, theshape of the iso-reliability curve (relating CA and CS forconstant LOLP) has prompted the designers to describe itin an analytic form. A study on probability-based methodsby Bucciarelli and the “three-event approach” shows thatfor normalised array size (CA) greater than about 1.2, botharray and battery size tend to increase for the same LOLP,which restricts its usability to a specific range. A similarobservation was made by Egido and Lorenzo [1992]. Insimulation-based methods, the LOLP for a given pair ofCA and CS values is calculated by means of a detailedsimulation of the PV-system behaviour after formulatingmathematical models for the individual components.Though data-intensive, simulation models allow detailedmodelling of the system and help in capturing the dailyand seasonal variations in the load and resource.

3. Sizing curve and design spaceA generalised method is proposed to relate the isolatedpower plant generator rating and storage capacity require-ments for a given electricity demand pattern and systemcharacteristics. The approach is used to generate a sizingcurve which identifies the generator ratings and corre-sponding minimum battery capacities meeting a specifiedload pattern on a generator rating vs. battery capacityplane. The curve indicates the minimum and maximumgenerator ratings and corresponding energy storage re-quirements. The method is illustrated for DG-battery andPV-battery systems.

The mathematical model for the analysis considers thenet power flow into the storage accounting for the powerconversion efficiencies in the charging and dischargingprocesses. It is based on the system energy balance andthe model is represented by the following equation:

dQB / dt = (P – D)f (8)where

f = ηc for P ≥ D (9)f = 1/ηd for P < D (10)

Here QB represents the storage energy, P the input powerfrom any source (DG or PV), D the demand, ηc the charg-

ing efficiency and ηd the discharging efficiency at anypoint in time. The energy stored in the battery QB at anyinstant t would be:

QB(t) = QB(t – Δt) + ∫ t − Δ t

t

(P (t) – D (t)) fdt (11)

Considering a discrete time interval Δt, the energystored in the battery is given by:

QB(t) = QB(t – Δt) + (P(t) – D(t)) fΔt (12)During the system operation over a period Δt, when theenergy supplied by the generator is greater than the de-mand (P(t) > D(t)), the energy surplus is used for chargingthe battery. If the energy supplied by the generator islower than the load, then the battery makes up the energygap. It is assumed that the charging and discharging takeplace with a constant efficiency and the variation in thebattery energy with time is assumed to take place withoutany self-discharge losses. The basic inputs required forthe method are the expected load time series for the lo-cation (sampled at certain fixed time intervals, for t = 1,2, ... T), and the charging and discharging efficiencies.The resource data in the form of global solar insolationat the specified time steps are required for PV-based sys-tems. It is possible from the above formulation to deter-mine the minimum capacity of the generator and thecorresponding battery bank rating for meeting the speci-fied load. Given the load curve for the site, knowing D(t)for the given time period, and values of ηc and ηd, batteryenergy at each time step (QB(t)) may be computed usingEquation (12) for all the time periods. For obtaining theminimum generator requirement, a numerical search isperformed to obtain that constant minimum value of Psatisfying the following conditions:

QB(t) ≥ 0 (13)QB(t=0) = QB(t=T) (14)

The above conditions ensure that the battery energy takespositive values at all times and also enforces the repeat-ability of battery state of energy for the time series con-sidered. The repeatability condition maintains that thereis no net energy drawn from the battery for the time periodconsidered. It is assumed that the load is recurring in thesame pattern after time T. The required battery bank ca-pacity (Br) is obtained as

Br = max{QB(t)} / DOD (15)Here DOD is the allowable depth-of-discharge of the bat-tery, suitably assumed. This provides the value of theminimum possible generator capacity (P = Pmin) and thecorresponding sizing of the battery bank (Br). It is of in-terest from a design perspective to identify the variousfeasible combinations for the generator and the storagewhich forms the design space for the system. Thus, amethodology is proposed extending the system sizingprinciples outlined above, to generate a sizing curve. Toidentify the points of the sizing curve, the generator isconsidered to be operating at power levels greater thanthe minimum identified rating (which is obtained from thenumerical search). When the generator rating is increasedfrom Pmin, over certain time steps it would be operatingat part-load conditions. The simulations are carried out


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for different assumed values of P (> Pmin) in steps. Foreach P considered, the corresponding minimum batterybank size is obtained by minimising the battery size Br(Equation (15)), the variables being the initial battery en-ergy QB(t=0) and the generator power at each time step(P(t)). This gives pairs of P and Br, which are plotted onthe (generator size, battery capacity) coordinates to obtainthe sizing curve. An example of a typical sizing curve isshown in Figure 2. The sizing curve demarcates the fea-sible region of system sizing in the generator rating vs.battery capacity space and indicates all the minimum stor-age points. Considering the design space formed by thegenerator rating-battery capacity axes, the sizing curvethus identifies the feasible design space. Following thesame approach the system sizing curve may be generatedfor a PV-battery system. Here the input power term is:

P = η0ITA (17)where η0 is the PV system efficiency, IT is the total ra-diation incident on the array (W/m2) at the time step con-sidered (hourly in this case) and A is the array area (m2).

4. Isolated power system sizing: case-studyThe concept of sizing curve and design space based onthe proposed method is illustrated for DG-battery and PV-battery systems for a remote site. The daily load curve ofthe remote location is shown in Figure 3 and is used forthe case-study (based on data provided by the West Ben-gal Renewable Energy Development Agency). For the PV-battery system, it is assumed that the array tilt is equalto the latitude of the location (22.56º N). The data inputin the form of monthly-average hourly solar insolation

values is required for the method, available in the hand-book of solar radiation data for India [Mani and Rangara-jan, 1982]. The solar radiation on the array plane iscalculated using the relations given in [Sukhatme, 1997].The other parameters assumed for the system sizing (PV-battery and DG-battery) are given in Table 1. The basicsteps followed in the approach are presented in Figure 4.For the site considered, the method yields the sizing curvefor the PV-battery system as shown in Figure 5. For il-lustration, the curve is generated taking December as thedesign month. The minimum array area required is 347.2m2 and the corresponding storage capacity is 249 kWh.In the sizing curve, the array capacity and battery capacityis normalised with the average power consumption. Fromthe sizing curve it may be observed that for normalisedarray ratings above 1.7, the corresponding minimum bat-tery capacity remains almost constant.

The sizing curve for a DG-battery system is given inFigure 6. The minimum generator and storage capacityrequirements are 10.5 kW and 154 kWh respectively. Themaximum generator rating is 24.2 kW, which is the peakdemand, and there is no storage requirement in this case.In the sizing curve, the generator capacity is normalisedusing the maximum load and the battery capacity is nor-malised with the average power consumption. Thus thesizing curve identifies the design space distinguishing thefeasible combinations of the generator and storage capaci-ties. The designer may select the appropriate combinationof generator and storage from this plot. It serves as a toolfor obtaining an optimum system based on an appropri-ately chosen objective function. For existing systems, if

Figure 2. Typical sizing curve and design space


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the optimum is identified on basis of the design space,economic evaluations for possible retrofit options may beconsidered. Thus, it serves as a useful tool in the overalldesign process.

5. ConclusionA methodology for sizing isolated power systems is pro-posed which enables the generation of a sizing curve for theidentification of a design space. The concept is illustrated

Figure 3. Daily load curve for the site

Figure 4. Design space approach

Table 1. Isolated power system parameters

Array tilt 22.56º

PV system efficiency 13 %

Charging/discharging efficiency 86 %

Battery bank depth of discharge 50 %


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for the options of diesel generator-battery systems andPV-battery systems. The design space is mapped ongenerator rating vs. storage capacity coordinates for agiven load pattern. The method offers a simplified ap-proach for system sizing and helps in identifying all the

feasible configurations for meeting a given load. The siz-ing method can be generalised to incorporate multiplesources (hybrid systems). The design space approach canbe a useful tool in identifying an optimum system whenapplied to the design of isolated power systems.

Figure 5. Sizing curve for PV-battery system

Figure 6. Sizing curve for diesel generator-battery system


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Note

1. Da Silva et al. [2007] say, “According to the free internet encyclopedia Wikipedia, whereseveral links for additional information and complete references are also available, an‘artificial neural network (ANN), often just called a “neural network” (NN), is an inter-connected group of artificial neurons that uses a mathematical model or computationalmodel for information processing based on a connectionist approach to computation.In most cases an ANN is an adaptive system that changes its structure based onexternal or internal information that flows through the network’ (extracted from http://en.wikipedia.org/wiki/Artificial_neural_networks in June 14, 2007).”

References

Barra, L., Catalanotti, S., Fontana, F., and Lavorante, F., 1984. “An analytical method todetermine the optimal size of a photovoltaic plant”, Solar Energy, 33(6), pp. 509-514.

Bartoli, B., Cuomo, V., Fontana, F., Serio, C., and Silvestrini, V., 1984. “The design ofphotovoltaic plants: an optimisation procedure”, Applied Energy, 18(1), pp. 37-47.

Bucciarelli, L.L., Jr., 1984. “Estimating loss-of-power probabilities of stand-alone photovoltaicsolar energy systems”, Solar Energy, 32(2), pp. 205-209.

Bucciarelli, L.L., Jr., 1986. “The effect of day-to-day correlation in solar radiation on theprobability of loss-of-power in a stand-alone photovoltaic energy system”, Solar Energy,36(1), pp. 11-14.

Da Silva, A.N.R., Costa, G.C.F., and Brondino, N.C.R., 2007. “Urban sprawl and energyuse for transportation in the largest Brazilian cities”, Energy for Sustainable Development,XI(3), pp. 44-50, September.

Egido, M., and Lorenzo, E., 1992. “The sizing of stand alone PV-systems: a review and aproposed new method”, Solar Energy Materials and Solar Cells, 26, pp. 51-69.

Gordon, J.M., 1987. “Optimal sizing of stand-alone photovoltaic solar power systems”, SolarCells, 20(4), pp. 295-313.

Hontoria, L., Aguilera, J., and Zufiria, P., 2005. “A new approach for sizing stand alonephotovoltaic systems based in neural networks”, Solar Energy, 78(2), pp. 313-319.

Kulkarni, G.N., Kedare, S.B., and Bandyopadhyay, S., 2006. “The concept of design spacefor sizing solar hot water systems”, Proceedings of International Congress on RenewableEnergy 2006, Hyderabad, India, pp. 302-305.

Mani, A., and Rangarajan, S., 1982. Solar Radiation over India, Allied Publishers, NewDelhi.

Markvart, T., Fragaki, A., and Ross, J.N., 2006. “PV system sizing using observed timeseries of solar radiation”, Solar Energy, 80(1), pp. 46-50.

MNRE (Ministry of New and Renewable Energy, Government of India), 2005. Annual Report2004-05, http://www.mnes.nic.in, August 1.

MoP (Ministry of Power, Government of India), 2006. http://www.powermin.nic.in, August 1,2006.

Sidrach de Cardona, M., and Lopez, L.M., 1998. “A simple model for sizing stand alonephotovoltaic systems”, Solar Energy Materials and Solar Cells, 55(3), pp. 199-214.

Sukhatme, S.P., 1997. Solar Energy – Principles of Thermal Collections and Storage (2nded.), Tata McGraw-Hill, New Delhi.

Tsalides, P.H., and Thanailakis, A., 1986. “Loss-of-load probability and related parametersin optimum computer-aided design of stand-alone photovoltaic systems”, Solar Cells, 18(2),pp. 15-127.

Willis, H.L., and Scott, W.G., 2000. Distributed Power Generation Planning and Evaluation,Marcel Dekker Inc., New York, USA.

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Sizing curve for design of isolated power systems