IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 181

Optimal Planning for Utility Generation byPhotovoltaic Sources Spread Across Multiple Sites

S. Roy, Senior Member, IEEE

Abstract—A new multiunit optimization algorithm is formulatedto plan participation by photovoltaic sources with significant pen-etration in utility generation. The focus is on the minimization ofthe overall levelized cost of energy, with constraints on demand, ca-pacity as decided by penetration, efficiency levels, and various costcomponents. Collector areas, unit ratings, and required investmentevolve as part of the plan.

A case study involving a utility service area, inclusive of 12 poten-tial installation sites, is used to illustrate features of the algorithm.

Index Terms—Energy resources, photovoltaic power systems,power generation, power generation planning, solar energy.

I. INTRODUCTION

PARTICIPATION of photovoltaic sources in future utilitygeneration depends largely on their competitiveness in

terms of price against other generation technologies [1], [2].Popular ways to achieve better price for photovoltaic energyinclude:

a) “Market diffusion” strategies for increasing participationby photovoltaic generators in suitably sequenced phases[3]–[5].

b) Development of high-efficiency photovoltaic modules[6]–[8] for better energy conversion.

c) Reduction of failure rates and, hence, the maintenancecost for the power-conditioning systems (PCS) and thebalance of systems (BOS) that accompany a generatingunit [9].

With such progress in technology and economic viability [10],[11], an individual utility may plan for multiple installationsspread over its service area, within a short duration of time, andin the most cost-effective manner possible. The available rangeof photoelectric generating units in terms of energy output andcost, as well as the effects of penetration into the existingpower system [12], [13] become important determinants ofsuch a plan.

This paper presents an algorithm that can be used by theinterested utility to evolve an optimal plan for multiple pho-tovoltaic installations. The aim is to minimize the global costof energy generated, given i) the total energy demand that theutility wishes to meet through its generation resources, ii) theknown utility load factor, iii) the permissible range of voltage

Manuscript received June 16, 2003; revised May 5, 2004. Paper no. TEC-00150-2004.

The author is with the Electrical and Electronics Engineering Group, BirlaInstitute of Technology and Science, Pilani 333 031, India (e-mail: roys@staff.bits-pilani.ac.in).

Digital Object Identifier 10.1109/TEC.2005.845452

variation due to changes in power demand as well as variationof photovoltaic generation, and iv) a required level of capacityfactor [14] that the utility wants the photovoltaic units to meet.It is assumed that both point-focus concentrator modules [15],as well as flat-plate modules [16] are available to the utility; sothat the optimal plan should indicate the best choice out of thetwo for each participating installation site with the available an-nual insolation data at each site.

Section II describes various techno-economic aspects of pho-tovoltaic technology that are useful for the planning exercise.Section III discusses the essential features of participating in-stallation sites with reference to annual insolation. Section IVelaborates the optimization model that forms an essential toolto evolve an installation plan. Finally, a case study inclusive ofmultiple sites within an existing utility of India and the optimalplan for the resulting scenario are presented in Section V.

II. ASPECTS OF UTILITY GENERATION BY

PHOTOVOLTAIC SOURCES

Over the past decade, operational and technoeconomicstudies on several installations across the globe [11], [17] haveindicated two distinct trends by which large-scale photovoltaicpower generation may progressively gain economic viabilitywith time:

development of new photovoltaic materials, evolution ofnew production processes, and economies of volume pro-duction [18];mutually beneficial technoeconomic alliances betweenmanufacturers, customer utilities, and research organiza-tions [19].

However, in practice, several issues complicate the economicsof multiunit utility generation.

A. Siting Considerations

A significant variation of insolation due to cloud cover, am-bient temperature, and wind speed [20] may often reduce thepotential of installation sites that otherwise have acceptable ter-rain, environment, and relatively few alternatives with the useof the land (such as agriculture or mining) [21]. For multiple in-stallations that are expected to function over several years, it isrational to expect meteorological factors (such as wind, cloudcover, and snow) at a specific site to be similar during a partic-ular month of any year. Insolation at a site may thus be consid-ered in terms of “typical days” over a year, and this serves asan important hypothesis for the optimization model to be intro-duced in Section IV.

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182 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006

B. Demand for Energy versus Penetration Bottlenecks

If the fraction of system load unserved by conventional powersources happens to be significant at all times, then photovoltaicgenerators may be installed without apprehension of operationalproblems. However, optimal planning procedures that typicallytry to minimize the cost of energy may, in doing so, evolvehigh levels of photovoltaic generation as feasible options. Op-erational fallout of high penetration must therefore be suitablyconsidered at the planning stage.

High penetration is suited to networks where photovoltaicgeneration coincides with periods of heavy loading. In utilitieswith significant diversity between photovoltaic generation andactive power demand [12], operational problems attributed tohigh penetration include a) overvoltages in low- and medium-voltage networks, b) difficulty in network access, and c) signifi-cant Joule losses due to voltage variations. All three phenomenacan be reduced effectively by [12]:

use of separate reception networks for photovoltaic gen-erators;provision of power control features for all photovoltaicunits;adjustment of tap changer settings on medium-to-lowvoltage transformers, which typically interface the pho-tovoltaic units to the remaining network.

With the current state of technology, the first two optionsbecome prohibitively expensive particularly if the overvoltageconditions are not very frequent over a year. The third approachrequires interruption of photovoltaic supply about twice a year,and is associated with relatively low-cost overheads [12].

Photovoltaic generators served by tap-changing transformerstherefore appear to be the ones best suited for multiunit instal-lations; and the optimal planning algorithm to follow assumesthat all generating units employed by the utility are accordinglyconfigured. Photovoltaic generation is thus restricted bythe average power demand (both normalized by the max-imum peak power demand ) [12], [13] as

ifif

(1)

where is a minimumthreshold value of below which photovoltaic generation isnot permissible, and is an empirical proportionality constantthat decides the extent of permissible generation by photovoltaicsources [12], [13].

Apart from overvoltages and the consequent problem of net-work access, voltage variations across the network due to di-versity between demand peaks and photovoltaic generation leadto unavoidable power loss in the transmission system. If thevoltage variation is confined to a moderate per-unit range ,then an approximate expression for the Joule losses (normalizedby the maximum peak power demand ) is

(2)

Details of (2) are provided in [13] while, in this paper, Joulelosses are accommodated in the optimal multiunit plan as equiv-alent reductions in energy output.

With limits (1) imposed on photovoltaic generation capacityin view of overvoltages and network-access restrictions, andwith Joule losses accounted by (2), it becomes difficult to planthe generating units optimally according to the explicit pre-decided requirement of energy. Rather, the planning approachshould be provided with the total utility energy requirementas well as the peak demand , and the plan must evolvewith due consideration of (1) and (2)—thereby determining themost suitable level of photovoltaic generation capacity.

C. Photovoltaic Unit Ratings and Performance Factors

The nameplate rating of a photovoltaic unit is a quantitythat determines the design of not only the photovoltaic mod-ules, but also the power-conditioning unit (PCU) and theBOS, consisting of insulation, protection, cabling, and panelsupport structures. In practice, however, most utility-ownedphotovoltaic units are forced to operate at power levels thatare substantially lower than the respective nameplate ratings.This is attributed to the weather variations described undersubsection above [16]–[18], [22], [23]; and has led to thedefinition of capacity factor [18] as

Annual kWh obtained from a unitkW rating of the unit No. of hours in a year

(3)

As far as possible, the planning utility would aim to achievesome predecided minimum acceptable value of the capacityfactor for all potential installation sites, and the planning optimaare to be decided accordingly.

D. Range of Cost Components

The cost of photovoltaic generation is typically analyzed interms of several components, each of which assumes a value in-dependent of the others. These are the photovoltaic modules costper square meter , the area-related BOS costs per squaremeter , the power related costs per kilowatt , and oper-ation and maintenance costs per kilowatt-hour . For con-centrator as well as flat-plate units, each cost component as-sumes a value within a characteristic range, while all of themtogether decide the overall generation cost [15], [16]. Theseranges must be taken into account for multiunit planning, butan exact dependence between them is difficult to define.

III. INSOLATION AT POTENTIAL INSTALLATION SITES

In order to represent all participating sites in a manner com-patible with the planning objective, it is important to considersolar radiation variability in both spatial (across land area) andtemporal (across the year) dimensions [21]. At a particular site,and at any given time, the total solar radiation power (usuallyreferred to as global radiation, and measured in kW/m ) typi-cally consists of three components [20], [21]:

i) Direct normal radiation is the direct beam from the solardisk reaching a receiving surface.

ii) Diffuse radiation reaches a receiving surface from the sky,excluding the solar disk.

iii) Ground reflected radiation is the solar light reflected bythe ground, as the name suggests.

ROY: OPTIMAL PLANNING FOR UTILITY GENERATION BY PHOTOVOLTAIC SOURCES SPREAD ACROSS MULTIPLE SITES 183

Components ii) and iii) must be considered only to the extentreceived within the field of view of the collector surface. Forcomponent i, this is accounted for by the component of the directbeam that is normally incident on the receiving surface.

For planning purposes, point-focus concentrator units can beassumed to be adequately supported by tracking mechanisms, sothat they remain ideally focussed to the direct normal beam andreceive essentially this component [21]. The daily direct normalradiation received on a horizontal surface at the th site in the

th month is measurable as a quantity (kWh/m ). To esti-mate the corresponding figure for an ideally focussed concen-trator, the direct normal insolation power (kW/m ) received ona focussed plane and a horizontal plane should bemeasured at a known time of the day (say, the local noon) [20].The daily direct normal radiation on a focussed concentrator atthe th site and the th month, can then be approximately esti-mated as

(4)

By contrast, the radiation received by flat-plate units includeseach component i–iii in some proportion. It is customary to tiltthe flatplates at an angle to the horizontal for acceptable recep-tion of the direct normal beam [17], [21]. The annual energyproduction is not very sensitive to the plate tilt angle as longas it is within of the site latitude. To account for tem-poral variability with seasons, most utilities set the tilt angle to“ ” in winter and “ ” in summer.Further precision in setting of tilt angles, if attempted, gener-ally proves to be uneconomical [21].

Again, for planning considerations, a flat-plate unit can beadequately represented if the daily global radiation (kWh/m ),and the daily tilt-factor are available to the planner for eachmonth of a year at each site [20]. The daily global radiation

is defined as the total energy per-unit area available overany day of the th month on a horizontal surface installed at theth site. Corresponding to the same site and month, the daily

tilt-factor provides the ratio of the daily global radia-tion received on a tilted surface (tilt angle assumed to be set at

for winter months and for summermonths), to that received on a horizontal surface as . With

and specified, it is straightforward to compute the dailyglobal radiation in the th month on a unit installed at the thsite as

(5)

To allow the planner to classify the suitability of each partic-ipating site for concentrator and flat-plate installations, the an-nual insolation available for both types of units is computed foreach site as and

(6)

where is the number of days in the th month. With presenttechnology, a site would be suitable for the installation of point-focus concentrator units if ranges between 2000 and 2900kWh/m , while flat-plate units are an option if assumes a

value between 1486 and 3550 kWh/m [15], [16]. The specificnumerical values may change with time as technology improves,but the above ranges are adequate for illustrative purposes.

IV. OPTIMAL PLAN FOR PHOTOVOLTAIC INSTALLATION

The treatment to follow assumes a set of participating sites, a set of photovoltaic generation technologies

, and the index for the months in a year.For the present, the set consists of only two elements,

namely concentrator technology and flat-plate technology.Associated with each site , we have a set of possibleoptions with one or both technologies as elementssubject to the suitability assessed earlier [see the discussionfollowing (6)]. The annual insolation for the th technology atthe th site is defined as for

for concentrator technologyfor flat-plate technology

(7)

A range of values can be assumed at the outset for unit con-version efficiency , module cost ( in Rupees per squaremeter), area-related BOS costs ( in Rupees per square meter)and power-related BOS costs ( in Rupees per kilowatt) basedon data available with reference to current technology [15],[16]1:

concentrator

for flatplate (8)

Associated with each site and , a variableis included to indicate the optimal choice of technology at theend of the planning exercise. For the photovoltaic technologyoptimally suited for a site, this variable will assume a value ofunity (otherwise zero). This is ensured by inclusion of the fol-lowing constraints for each site and technology

(9)

The energy that can be converted at the th site by theth technology is obtained as

(10)

where is the receiver area required. The annual energyalso determines the unit power rating as

(11)

where is the capacity factor that the utility intends to plan forand the factor of 8760 accounts for the number of hours in ayear.

1A conversion factor of Rs. 48.50 to the US dollar has been used throughoutthis paper

184 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006

Fig. 1. Daily global insolation at the 12 participating installation sites across all 12 months of a year.

Since (1) applies to active power levels throughout the year,it can be assumed to approximately apply to the annual averageload and annual peak load for the utility. Equation (1) can thusbe redefined as the following constraint:

(12)

where is the energy demand to be met by the utility over ayear, is the annual utility load factor defined as

annual utility peak power load(13)

and is the minimum value of at which photovoltaic gen-eration is admissible [12], [13].

The total energy generated by photovoltaic sources, less theenergy equivalent of Joule losses across the utility, is limited bythe total annual energy demand as

(14)

where the quadratic term in (14) has been obtained as an exten-sion of (2) across the utility to account for Joule losses over ayear.

The total capital investment required for technologyat site is obtained as

(15)

where is the known fractional indirect costs, including engi-neering cost, interests due to construction, etc. [16]. For a pre-decided fixed charge rate (a fraction ) and operation and main-

tenance cost ( , in Rs/kWh), (15) gives an annual cost of gen-eration at each site

(16)

where the factor of 0.8 accounts for losses in the dc-side wiringof the photovoltaic modules and ac bus side transformers, lossesin the PCU, losses due to module mismatch, and heating [16].

Finally, the levelized cost of electricity to be minimized glob-ally is easily defined as

(17)

where is a small nonzero constant included to avoid divide-by-zero conditions as (17) is minimized subject to (7)–(16) toevolve the optimal multiunit installation plan.

V. CASE STUDY

In this section, the evolution of the optimal installation planis illustrated for the service area of a major power utility inIndia, which includes 12 potential photovoltaic installation sites

. Of these, , and are coastal sites; , and areinland sites but in sufficient proximity to the coastline to be in-fluenced by its meteorological conditions; and the rest are deepinland sites that are independent of coastal weather conditions.The daily global insolation figures for over a year aredisplayed in Fig. 1, [20]. All 12 sites are very much subjected tosuspended dust particles in the air and, accordingly, the daily di-rect normal insolation varies over 40%–80% of the daily globalinsolation figures depending on the month and the site.

The optimal installation plans are generated on a general al-gebraic modeling system platform [24] over a range of utilitypower demand . For each study, the annual utility load factor

is assumed at a particular value. Typical values are fur-ther assumed for the planning parameters, as

ROY: OPTIMAL PLANNING FOR UTILITY GENERATION BY PHOTOVOLTAIC SOURCES SPREAD ACROSS MULTIPLE SITES 185

Fig. 2. Optimal cost of energy for the case study corresponding to differentutility demand (annual utility load factor p is indicated along each plot).

Fig. 3. Photovoltaic output energy for the case study, corresponding to theoptima in Fig. 2 (annual utility load factor p is indicated along each plot).

per kilowatt-hour, ,and . Corresponding to each value of (indicatedagainst the plot) and range of , Figs. 2–4, respectively, showthe optimal cost of output energy, the total output energy, andthe fraction of output energy lost as Joule losses.

The plans are presented for two ranges of voltage variation,expected due to diversity between generation and load. Of these,the relatively loose range of p.u. allows optimal plans toevolve smoothly, indicating marginal improvement in the costof energy at high demand essentially due to economies of scale.The output energy has an approximately linear variation with

, as the optima are progressively realized by increasing thereceiver area at most sites. In doing so, the Joule losses reachan approximately steady level for each value of considered.These are as high as 38% of output energy for , reacha minimum of 31.7% for , thereafter increasing to34.7% as increases to 0.8. Consistent violation of the pene-tration constraint (12) makes plans infeasible for and

.With a more stringent range of permissible voltage varia-

tion ( p.u.), the optima are obtained for limited to asmaller range (0.4–0.7); while for the limiting value of 0.7, theplans are infeasible at several values of demand (note the dis-

Fig. 4. Joule losses at optima for the case study, corresponding to Fig. 2(annual utility load factory p is indicated along each plot).

continuities in the plots corresponding to this value). As moreof the constraints become active, the feasible optima are expect-edly found to have more variation as observed in Figs. 2–4. TheJoule losses, in particular, may consume between 10% to 70%of the generated photovoltaic energy (Fig. 4) depending on thevalues of and !

VI. CONCLUSION

The approach introduced in this paper can serve as a usefultool for utilities contemplating significant photovoltaic installa-tion as part of their generation resources. The optimized plansinvolve a minimum required number of installation sites, se-lect the desired technology, specify the required module receiverareas, and above all, offer an estimate of the investment. Pene-tration effects and bottlenecks are suitably accommodated in theplanning objective and constraints.

For limited availability of land area, the planning process canbe easily modified by the additional inclusion of area constraintswith a consequent effect on the cost of energy and investment.

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S. Roy (M’89–SM’97) received the B.Eng. degree in electrical engineeringfrom the University of Roorkee, Roorkee, India, in 1985; the M.Eng. degreein electrical engineering from the Indian Institute of Science, Bangalore, India,in 1987; and the Ph.D. degree in electrical engineering from the University ofCalgary, Calgary, AB, Canada, in 1991.

Currently, he is a Professor of the Electrical and Electronics EngineeringGroup and Coordinator of the Centre for Renewable Energy and EnvironmentDevelopment (CREED), Birla Institute of Technology and Science, Pilani,India. From 1992 to 2004, he worked in various faculty positions at the IndiraGandhi Institute of Development Research, Mumbai, India, and the IndianInstitutes of Technology, Mumbai and Delhi, India. His research interestsinclude energy systems planning and modeling.