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Stand-Alone Flat-Plat PhotovoltaicPower Systems: System Sizing andLife-Cycle Costing Methodology forFederal Agencies

C.S. BordenK. VolkmerE.H. CochraneA.C. Lawson

May 1984

Prepared for

U.S. Department of Energy

Throu!^~ -.,) Agreement withNation.) j.(,ronautics and Space Administration

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Jet Propulsion LaboratoryP California Institute of Technology

Pasadena, California

JP^ Publication 84.37 9. -dif'(ll"n. -do -W.Vam.

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DOE/ET-20356-16Federal Photovoltaic Utilization Program

Distribution Category UC•63b

Stand-Alone Flat-Plate PhotovoltaicPower Systems: System Sizing andLife-Cycle Costing Methodology forFederal AgenciesC. S. BordenK. VolkmerE.H. CochraneA.C. Lawson

May 1984

Prepared forU.S. Department of EnergyThrough an Agreement withNational Aeronautics and Space AdministrationbyJet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California

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JPL Publication 84-37

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Prepared by the Jet Propulsion Laboratory, California Institute of Technology,for the U,S. Departrent of Energy through an agreement with the NationalAeronautics and Space Administration,

The JPL Flat-Plate Solar Array Project is sponsored by the U.S. Department ofEnergy and is part of the Photovoltaic Energy Systems Program to initiate amajor effort toward the development of cost-competitive solar arrays,

This report was prepared as an account of work sponsored by an agency of theUnited States Government, Neither the United States Government nor anyagency thereof, nor any of their employees, makes any warranty, express orimplied, or assumes any legal liability or responsibility for the accuracy, com-pleteness, or usefulness of any information, apparatus, product, or process

disclosed, or represents that its use would not infringe privately owned rights,

Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United StatesGovernment or any agency thereof, The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or any agency thereof,

This publication reports on work done under NASA Task RE-152, Amendment200, DOE/NASA IAA No, DE-A101-76ET20356,

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ABSTRACT

A simple methodology to estimate photovoltaic system size and life-cyclecosts in stand-alone applications is presented in this document. It isdesigned to assist engineers at Government agencies in determining thefeasibility of using small stand-alone photovoltaic systems to supply ac or dopower to the load. Photovoltaic system design considerations are presented at"well as the equations for sizing the flat-plate array and the battery storageto meet the required load. Cost effectiveness of a candidate photovoltaicsystem is based on comparison with the life-cycle cost of alternativesystems. Examples of alternative systems addressed herein are batteries,diesel generators, the utility grid, and other renewable energy systems. Acompanion document, Flat-Plate Photovoltaic Power Systems Handbook for FederalAgencies (Reference 10), is recommended for discussion of issues forevaluating the viability of potential photovoltaic applications; descriptionsof present photovoltaic system applications; synthesis of lessons learned fromphotovoltaic system design, installation, and operation; and identification ofprocurement strategies for Federal agencies.

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FOREWORD

This system sizing and life-cycle costing methodology povides a toolfor Federal agencies to use in estimating photovoltaic system size andlife-cycle costs for non-utility grid-interactive applications. It isspecifically intenaed for use by the Federal Government since use bynon-Government entities would require additional considerations such as theeffect of taxes. It is not intended for detailed system design, but ratherprovides a Government engineer, having limited background in photovoltaictechnology, with the concepts required to estimate the photovoltaic systemsize and corresponding life-cycle cost. The methodology is appropriate forsizing remote photovoltaic systems that use fixed flat-plate photovoltaiccollector technology with or without battery storage. In addition, theprocedures Lor determining initial capital costs and life-cycle costs can beused to estimate funding requirements for system procurement.

To evaluate the life-cycle costs for a photovoltaic system, a comparisonmust be made with those of any alternative system. The methodology permitscalculations of the life-cycle cost of both a photovoltaic power system andthat of any alternative system.

Should questions arise from the use of this methodology, contact theFederal Photovoltaic Utilization Program Office at the Jet PropulsionLaboratory, 4800 Oak Grove Drive, Pasadena, California, 91109, telephone (818)577-9523 or FTS 961-9523.

ACKNOWLEDGMENT

The U.S. Department of Energy Federal Photovoltaic Utilization Program,under the direction of Mr. Michael Pulscak, Program Manager, provides for theacquisition and installation of photovoltaic systems within various Federalagencies. Thin methodology has been prepared as part of this program.

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vii

4CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

A. ABOUT THIS DOCUMENT . . . . . . . . . . . . . . . . . . . . 1-1

1. Purpose . . . . . . . . . . . . . . . . . . . . . . . 1-1

2. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

3. Organization of the Document . . . . . . . . . . . . . . 1-1

B. POTENTIAL APP'+4ICATIONS FOR PHOTOVOLTAIC POWER SYSTEMS . . . . 1-2

C. PHOTOVOLTAIC POWER SYSTEM DESCRIPTION . . . . . . . . . . 1-2

1. The Solar Cell, Module, and Array . . . . . . . . . . . . 1-2

2. The Photovoltaic System . . . . . . . . . . . . . . . 1-3

3. Insolation Characteristics and Their Effecton System Sizing . . . . . . . . . . . . . . . . . . . . 1-5

II. SYSTEM SIZING . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

A. RATIONALE . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

B. SUMMARY OF THE PHOTOVOLTAIC SYSTEM SIZING METHODOLOGY . . . . 2-1

C. PHOTOVOLTAIC SYSTEM SIZING PROCEDURE . . . . . . . . . . . . . 2-5

1. Calculate the Load . . . . . . . . . . . . . . . . . . . 2-5

2. Determine Local Insolation . . . . . . . . . . . . . . . 2-6

3. Calculate "Worst-Month" Insolation and Load . . . . . . . 2-6

4. Determine Array and Battery Storage Sizing Factors . . . 2-8

5. Calculate Array Power and Area . . . . . . . . . . . . . 2-11

6. Calculate Battery Storage Size . . . . . . . . . . . 2-13

7. Determine Voltage Regulator Size . . . . . . . . . . . . 2-14

8. Determine Inverter or Converter Size . . . . . . . . . . 2-14

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III. SYSTEM COST ANALYSIS . . . . . . . . . . . . . . . . . . . . . 3-1

A. SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

B. COST ANALYSIS METHODOLOGY . . . . . . . . . . . . . . . . . 3-1

1. Photovoltaic System Life-Cycle Cost . . . . . .. . . . 3-1

2. Alternative Power System Life-Cycle Cost . . . . . . . 3-6

C. PHOTOVOLTAIC VERSUS ALTERNATIVE POWER SYSTEMCOST COMPARISON . . . . . . . . . . . . . . . . . . . . . . 3-7

IV. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

APPENDIXES

A. PHOTOVOLTAIC SYSTEM SIZING AND COSTING EXAMPLE . . . . . . A-1

B. ESTIMATION OF LOAD FRACTIONS SUPPLIED BY PHOTOVOLTAICARRAY AND BATTERY STORAGE . . . . . . . . . . . . . . . . . . B-1

xi

C. COMPARISON OF SIZING METHODOLOGY WITH ALTERNATIVES' k

APPROACHES. . . . . . . . . . . . . . . . . . . . . . . . . . C-1 i

D. AVERAGE DAILY INSOLAT"I.ON TABLES FOR UNITED STATES SITES . . . D-1,^

31

Figures

1-1. Typical Solar Cell . . . . . . . . . . . . . . . . . . . . . . 1-3

1-2. The Output of a Solar Cell Varies with Changes in theEnvironment: (a) Temperature and Solar Cell Voltage areInversely Related, (b) Izradiance and Solar Cell Currentare Directly Related . . . . . . . . . . . . . . . . . . . . . 1-4

1-3. Photovoltaic Module and Array: (a) Solar Cells Packaged intoi

a Photovoltaic Module, (b) Modules are Grouped into an Arrayto Increase Power Output . . . . . . . . . . . . . . . . 1-5

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1-4. Stand-Alone Photovoltaic System Configuration to Serve a doLoad . . . . . . . . . . . . . . . . L . . . . . . . . . . 1-5

1-5. Stand-Alone Photovoltaic System Configuration to Servean ac Load . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

1-6. Clear Sky Array Power Output Profile . . . . . . . . . . . . . 1-6

1-7. Effect of Season and Region on Insolation Level(a) Winter, (b) Summer . . . . . . . . . . . . . . . . . . . 1-7

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1-8. Insolation Available to the Array Under Clear Sky and CloudyConditions . . . . . . . . . . . . . . . . . . . . . l-8

1-9. Relative Energy Output at Various Array Tilt Angles . . . 1-9

2-1. Sequence of Steps in Sizing a Remote, Stand-AlonePhotovoltaic System . . . . . . . . . . . . . . . . . . 2-2

2-2. Photovoltaic System Model Showing Key System SizingParameters . . . . . . . . . . . . . . . . 2-3

2-3. Determining Array and Battery Storage Sizing Factors(at LOEP = 0.1) for Various Worst-Month Insolation Values 2-9

3-1. Approach for Determining Photovoltaic Power SystemCost Effectiveness . . . . . . . . . . . . . . . . , . . . 3-2

3-2. Life-Cycle Cost Comparison of Photovoltaic System(LCCpV ) and Non-Photovoltaic System (LCCALT ) • • • • • . . • • 3-8

A-1. Photovoltaic System Sizing Procedure . . . . . . . . . . . . . A-2

A-2. Determining Array and Battery Storage Sizing Factors(at LOEP = 0.1) for Various Worst-Month Insolation Values. . . A-6

A-3. Approach for Determining Photovoltaic System CostEffectiveness . . . . . . . . . . . . . . . . . . . . . A-8

.... B-1. Idealized Energy Usage by Time-of-Day for a Given Month . . . B-1

Tables

2-1. Example of Method for Determining the Appropriate Insolationand Load Combinations for Sizing the Array and BatteryStorage . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

A-1. Photovoltaic System Sizing Parameters: Relevant Ranges andDefault Values . . . . . . . . . . . . . . . . . . . . . . A-3

A-2. Monthly Insolation and Example Energy Load Values forThree Array Tilt Angles for China Lake, California . . . . . . A-4

A-3. Photovoltaic System Cost Parameters: Relevant Ranges andDefault Values . . . . . . . . . . . . . . . . . . . . . . . . A-9

A-4. Cost Elements . . . . . . . . . . . . . . . . . . . . . . . A-10

C-1. Array and Battery Storage Sizing Comparison C-2

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SECTION I ti

INTRODUCTION

A. ABOUT THIS DOCUMENT

1. Purpose

Photovoltaic (PV) power systems are potentially a cost-effectivealternative to conventional power sources (e.g., diesel generators, batteries)in a variety of remote applications where the operation, maintenance, and fuelcosts of the conventional sources are high. This document describes aphotovoltaic system sizing and life-cycle costing methodology that has beenprepared to assist Federal Government agencies in determining the feasibilityof using stand-alone photovoltaic systems that can supply either ac or dopower to a specified load. In addition, the procedure for determining initialcapital costs and life-cycle costs can be used to estimate funding require-ments for system procurement.

2. Scope

The methodology in this report applies to stand-alone fixedflat-plate photovoltaic systems (which include the array, voltage regulator,battery storage, and do-ac inverter or do-dc converter) as well as variouspossible alternatives such as battery storage, diesel generators, otherrenewable energy technologies, and extension of the utility grid to the remotesite. The methodology, therefore, permits a comparison of the economicviability of photovoltaics with that of the possible alternatives, thereby Ir

facilitating final selection of the preferred generating option.

This document considers only the relative cost effectiveness as a?selection factor in comparing photovoltaic and its alternatives. Additionalnon-cost-related factors in selecting a power system such as land limitations,limitations on noise generation, physical accessibility for maintenance, etc., salthough critical in some applications, are beyond the scope of this document.

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Finally, this methodology applies to flat-plate photovoltaic-onlysystems. It does not address hybrid arrangements that combine photovoltaicswith another conventional generation mode into a single power system. Sizingthe various generating elements of a hybrid system can be accomplished onlyafter a preliminary trade study to determine the most cost-effective

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3. Organization of the Document

The remainder of Section I presents a description of photovoltaictechnology and its application to typical remote loads. In addition, thevarious characteristics of solar irradiation (i.e., insolation) are described.Special attention is paid to insolation characteristics that may affect themanner in which the photovoltaic system is sized for an intended load.

' 1-1

Section II covers photovoltaic array and battery storage system sizing.Required inverter/converter and voltage regulator sizes are also addressed.Once the size calculations have been made, Section III is used to determine thelife cycle cost of both the photovoltaic power system and any alternativesbeing considered. A comparison of these life-cycle costs will provide thebasis for selecting the power ge Pration technology most appropriate for agiven application.

B. POTENTIAL APPLICATIONS FOR PHOTOVOLTAIC POWER SYSTEMS

Photovoltaic power systems may be considered potentially viable for anumber of remote applications. Typical loads that represent current andpotential near-term photovoltaic applications are listed below:

(1) Telecommunications.Example: radio repeater.

(2) Navigational aids.Examples: beacon, buoy, lighthouse.

(3) Aviation aids.Examples: radar beacon, anemometer.

(4) Environmental sensors.Examples: radiation sampler, noise monitor.

(5) Intrusion detectors.Examples: entry monitor, electric fence.

(6) Battery charging.

(7) Lighting.

(8) Refrigeration.Example: medical supplies refrigerator.

(9) Space conditioning.Examples: small cooler, ventilator.

(10) Water pumping.

(11) Water purification/desalination.

(12) Cathodic protection (corrosion protection).Examples: transmission tower, bridge, well, pipeline.

C. PHOTOVOLTAIC POWER SYSTEM DESCRIPTION

1. The Solar Cell, Module, and Array

Photovoltaic systems are electrical generating systems based onphotovoltaic, or solar, cells (Figure 1-1). The cells convert photons fromincident sunlight directly into do electricity. The solar cell typically

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consists of two different types of semiconductor material, called n-type andp-type. Energy carried by the photons frees positive and negative chargeswithin the cell material. The junction between the n- and p-type materialscreates an electric field, causing ths.freed charges to separate across thejunction and resulting in a voltage across the cell. Electrical contactsplaced on the p-side and on the n-side of the solar cell allow the currentgenerated within the cell to be applied to an external load.

The amount of electric current generated by a solar cell is primarilydependent on the intensity of solar radiation striking its exposed area. Theopen-circuit voltage produced, however, is primarily dependent on thetemperature of the cell. Voltage and cell temperature are inversely related[i.e., an increase in temperature lowers both the output voltage and theoutput power, thereby reducing the cell's efficiency (Figure 1-2)].

Because the power output of a single solar cell is small [approximately1 watt for a typical cell (100 cm 2 , 10% efficient)], a number of cells areinterconnected in series and parallel and sold as a package called aphotovoltaic module (Figure 1-3a). These, in turn, can be wired together intoan array (Figure 1-3b) to generate the amount of power required by theapplication.

2. The Photovoltaic System

A practical stand-alone photovoltaic power system typicallyrequires several elements in addition to the array in order to satisfy theintended load. A typical configuration for a do load is shown in Figure 1-4.

Battery storage, most commonly involving a lead-acid battery in presentapplications, stores electrical energy produced by the solar array in daytimefor use during the night or under cloudy conditions. To be consideredpractical for remote applications, a storage battery should have a long life,require low maintenance, and be able to survive a number of deep dischargecycles with subsequent recharge by the array.

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Another important component of a photovoltaic power system using storageis a voltage regulator that controls the output voltage from the array whenused to charge the battery. The regulator also limits the loss of water thatwould occur from gassing of the battery if it were permitted to becomeovercharged. At night or on cloudy days, a blocking diode ( see Figure 1-4)prevents the electrical energy stored• within the battery from dischargingthrough the voltage regulator or the array.

A system serving a do load may require a do-dc converter to match thesystem output voltage to the rated voltage of the load.

Some photovoltaic ap^:tlications do not necessarily require batterystorage. An example of this is water pumping, which needs only a photovoltaicarray, a water pump, a water storage tank, and minimum power regulation. Inthis case, water is pumped into the storage tank during sunlight hours. Thestorage tank then acts as a reservoir, providing water during non-sunnyperiods.

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Other applications may require power conditioning to provide thej

required power characteristics to an ac load. In this case, an inverter isused to convert the do voltage from the array into an ac voltage (Figure 1-5).

3. Insolation Characteristics and Their Effect on System Sizing

Array and battery storage size requirements to adequately servethe load energy requirement ultimately depend on the amount of insolation atthe location of the site. Since the amount of energy received from the sunwill depend on location, season, weather, and array orientation, it isessential to account for these factors in sizing the system. Furthermore,

G since the intended load may also vary seasonally, sizing will normally rewirea systematic accounting approach to ensure that sufficient solar energy willbe captured by the array to achieve acceptable system reliability througho,•tthe year.

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Insolation characteristics important for sizing photovoltaic systemcomponents include the following: diurnal variation, regional and seasonalvariability, weather, and array orientation relative to the direction of thesun. 'These characteristics are described below:

(1) Diurnal Variation. The most important characteristic ofinsulation is its diurnal pattern. The expected power availableto a fixed flat-plate array over a 24-hour period under clear skyconditions will follow a curve similar to that in Figure 1-6. Anyload that does not closely approximate this power output profiie,or accommodate deviations from it, will necessitate batterystorage or other backup to the photovoltaic system.

(2) Regional and Seasonal Variability. A second major factor in sizingthe system is the regional and seasonal variability in insolation.Figure 1-7a shows the total insolation on a fixed collector tiltedat latitude during the winter in the contiguous United States.Note that the insolation in kWh/m 2-day varies by up to a factorof 2.5, depending on region. Also, note in Figure 1-7b the mannerin which the total insolation differs between winter and summerfor a given location. The summer-to-winter difference ininsolation in prime locations such as the northern portions ofCalifornia and Nevada, for example, is seen to be a factor of

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between 1.5:1 and 2:1. These dFferences must be identified andallowed for in order to correctly size a system for a given loadand location.

As noted previously, these variations will require that the sizingmethod accounts for these differences to ensure that the solarenergy incident on the array is sufficient to serve the plannedload during all months of the year.

(3) Weather. cloudy weather will considerably reduce the amount ofinsolation and, thus, the output from the photovoltaic system (seeFigure 1-8). (The output typically will not drop to zero sinceflat-plate systems generate power roughly in proportion to theamount of light falling on the surface of the photovoltaiccells.) Since cloudy weather can occasionally persist for severaldays in any location, photovoltaic systems serving most loads willrequire storage or other electrical backup to ensure reliablepower. In sizing a photovoltaic system, the amount of storage isprimarily determined by the probable amount of cloudy weather at agiven site during the worst month of the year. The method forsizing the battery storage in Section TI.C.o is based on estimatesof this probability derived from historical weather records.Although previous weather history is not a perfect predictor offuture weather patterns, it does serve as a useful guideline forestimating photovoltaic system_ requirements.

(4) Orientation of the !gray. Since there are seasonal differences intbi daily path of the sun across the sky, the amount of solarenergy striking a fixed array will vary seasonally according toits orientation. Note that these effects are due only to annualchanges in sun angle and are distinct from typical seasonal

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Under typical weather conditions, the maximum annual energy outputfrom a fixed array occurs when the array is tilted at an angleequal to the latitude where it is sited. However, if the loadvaries seasonally, latitude tilt may not be the most cost-effectiveangle for the array; i.e., the smallest array size that satisfiesthe load. The method for selecting the correct tilt angle forsizing purposes will be described under II.C.3, Calculate"Worst-Month" Insolation and Load.

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b SECTION II

SYSTEM SIZING

A. RATIONALE

The term "sizing," as it is used in this document, means estimating therequired size or capacity of all major photovoltaic system elements so thatthe system will be able to satisfactorily serve the intended load. 2 Thesizing methodology described in this section is based on a target level ofphotovoltaic system reliability that is equivalent to conventional diesel orbattery alternatives. The size estimates obtained by this methodology areused to cost the system according to the method described in Section III. Thecost estimates, in turn, are compared with estimates for other possible powergenerating options in order to determine whether selection of a photovoltaicpower system is justified on a comparative life-cycle cost basis.

The sizing methodology is restricted to stand-alone systems servingeither ac or do loads. If the application involves both ac and do loads, themethod may be applied by sizing the system for the ac and do loads separatelyand then combining the results. This methodology is intended primarily totreat photovoltaic systems with storage since the majority of remote loadapplications will require at least part of their total energy needs at nightor during cloudy day periods of reduced system output. Some applications,however, do not require regular power availability and may be servedadequately by photovoltaic systems without battery storage capabilities. Theprimary example of this kind of application is a water pumping system in whichwater to serve periods of low pump output is stored io a reservoir or storage t

tank. The methodology will also address applications of Lhis kind. a

The required sequence of steps in the sizing methodology to be describedis summarized in Figure 2-1.

B. SUMMARY OF THE PHOTOVOLTAIC SYSTEM SIZING METHODOLOGY

Figure 2-2 schematically depicts a photovoltaic system serving a load.This simple representation illustrates the key factors involved in systemsizing. Radiant energy from the sun, or insolation (I) is converted to doelectrical energy by the array at a conversion efficiency ea. A fraction ofthe load energy, f a , may be received from the do array output through aninverter if the load is ac, or directly if the load is dc. A do-dc converteris used if the load operates at a do voltage above that produced by the arrayconfiguration. The remaining load fraction, fb, is received from thestorage batteries that are periodically recharged by the array during periodswhen array output exceeds the load requirements. Conversion efficiencies forthe voltage regulator, battery, and inverter or converter are evr, eb, and

{ 2Major system elements include the array, voltage regulator, battery storage,f and do-ac inverter or do-dc converter.

1►

2-1

o^

r;

W

CALCULATELOAD ENERGY

REQUIREMENT

DETERMINELOCAL

INSOLATION

CALCULATEWORST-MONTH

INSOLATIONAND ENERGY LOAD

DETERMINE ARRAYAND STORAGE

SIZING FACTORS j

CALCULATE ARRAYPOWER AND AREA

f^

CALCULATE BATTERYSTORAGE CAPACITY

I

CALCULATE VOLTAGEREGULATOR SIZE

m

}

I

CALCULATE INVERTER/CONVERTER SIZE

l PERFORMLIFE-CYCLE

COST .ANALYSIS

Figure 2-1. Sequence of Steps in Sizing a Remote, Stand-AlonePhotovoltaic System

2-2

4

INSOLAT IONI

ARRAY

F

OF pour:

f

I NVERTER/fib CONVERTER* LOAD

r eVc

VOLTAGE

BATTERYREGULATOR

STORAGc*AS REQUIRED

yr

e BY LOAD

Figure 2-2. Photovoltaic System Model Showing Key System Sizing Parameters

e i/c, respectively. 3 As appropriate, these terms should be used in systemsizing to account for losses occurring in these system elements during systemoperation.

The steps in the sizing methodology shown in Figure 2-1 are summarizedbelow (complete details of the sizing procedure are presented inSection II.C.):

(1) Calculate the Load. The average daily energy load inkilowatt-hours is calculated for each month of the year. In thesimplest case, a single load element draws constant power at alltimes. If several load elements are present, the individualelements must be summed. If the load totals vary from day to day,an average daily load over each month of the year will be required.

(2) Determine the Local Insolation. The appropriate amount of inputenergy (i.e., insolation, I) to the photovoltaic system at theapplication site may be obtained from tables in Appendix D forvarious array tilt angles. As insolation values will vary frommonth to month, average daily values for all months are includedin the tables.

3 In cases where neither an inverter or converter is required by the system,the ei /c term in the sizing calculations is equal to 1.0 (i.e., no conversionlosses). Similarly, if no storage is required, both ev r and eb are setequal to 1.0.

2-3

r

O

(3) Calculate "Worst-Month" Insolation and Load Values. The sizingapproach requires identification of the load and insolation valuesexpected during the "worst month" of the year. This is done byconstructing a "able of average insolation and load values foreach month of the year and then determining the month with thelowest ratio of insolation to load. The insolation and loadvalues for the selected worst month are used in subsequent stepsto calculate required array size and battery storage capacity.

(4) Determine Array and Battery Storage Sizing Factors. The approachused in the methodology to size the array and storage is to applypreviously determined "sizing factors" in the array and storagecalculations in order to scale the system to achieve a desiredlevel of autonomy (i.e., availability). These factors aredisplayed in a nomograph to facilitate selection of theappropriate sizing factor values for use in subsequent array andbattery size calculations.4

(a) In some sizing applications, the user may specify the levelof system autonomy by placing a requirement on the number ofsunless days during which the system must be able to satisfythe intended load. The sizing method in this document mayalso be applied in that case.

(b) Estimate the load fractions supplied by the array andbattery storage. Since energy supplied by the arraydirectly to the load suffers less power loss than thatpassing through the battery storage, the fraction flowing tothe load by each pathway should be estimated. In caseswhere these estimates are especially difficult to make, theuser may follow a conservative sizing approach by lettingthe fraction from the array equal zero and the fraction fromthe battery equal one.

(5) Calculate Array Power and Area. Calculating array size meanscalculating both its required peak power output in watts and itscorresponding area in square meters. The array sizingcalculations incorporate the worst-month load, array sizing factorbased on the worst-month insolation, efficiencies of all majorsystem elements, and a term to account for long-term arraydegradation.

A modification of the sizing methodology may be applied to certainspecialized applications that require no battery storage to backup the photovoltaic array, such as the case of pumping water to astorage reservoir.

(6) Calculate Battery Storage Size. Calculating battery storage sizerequires scaling the storage to supply the daily energy load for asufficient period of time to assure that the photovoltaic systemmeets the load requirements at least 96 to 98% of the time (or

W

4This approach has been adapted from Reference 3.

2-4

f c

tWA

A

^k

equivalently! a 0.1 "loss of energy probability" (LOEP) during theworst month of the year). Alternatively, the storage can be sizedto supply the load for a specified number of sunless days. Ineither case, the actual rated capacity is adjusted to ensurebattery operation within acceptable depth of discharge limits.

(7) Calculate the Voltage Regulator Size. The battery chargingvoltage regulator is sized to handle the maximum amount of arrayoutput power (dc) that is not being used to supply the load. Forconservatism, this will be considered to be the full rated peakarray output power to account for situations in which the load hasbeen disconnected.

(8) Calculate the Inverter/Converter Size. The inverter or converter,if either is required, is rated according to its output capacityin watts or kilowatts ac or dc, respectively. These units aresized to match or exceed the maximum steady state load powerrequirement (or maximum surge current for inductive loads)occurring at any time during the expected system life.

The remainder of Section II describes the sizing procedure in detail.

C. PHOTOVOLTAIC SYSTEM SIZING PROCEDURE

This section describes the procedure for sizing the photovoltaic systemusing the steps identified in Figure 2-1. An example implementation of this

.-- procedure, along with sample data, is shown in Appendix A. The associatedlife-cycle cost analysis procedure is described in Section III.

1. Calculate the Load Y

Sizing the photovoltaic system first requires a calculation of theaverage daily energy load for each month of the year. The daily energy loadfor a single device or element is calculated as the power it draws in rfkilowatts times the number of hours that it is in service during every 24-hourperiod. If more than one load element is to be served, the total daily energyload is obtained by summing the individual loads as shown in Equation (1).

f

Iv,Ltd PiDi/1000 (1)

3. = 1

/. where

:.Ltd = total daily energy load in kilowatt-hours per day

Pi = power drawn by load element i while it is in service, in watts

Di = amount of time per day in hours that load element i is in service

t ^

n = number of separate load elements

2-S ^^ l

K

For loads that vary from day to day, an average daily load is calculatedfor each month of the year. An average daily load for a given month is the

' sum of all daily loads divided by the number of days in the month- 5 If theload consists of both ac and do elements, the load calculations and subsequentsystem sizing procedures should be applied separately to the ac and do loads.The final array and battery sizes are then obtained by summing the separatearray and battery sizes calculated for the ac and do elements.

Note that this assumes that system and load are co-located. If thedistance from a power source to do load is increased beyond a few meters,resistive wiring losses will begin to become apparent. These losses willnecessitate a compensating increase in the required system size. If deemedsignificant, the user of this methodology may allow for do wiring losses byincreasing the calculated load size served by the photovoltaic system toinclude the 12R power losses calculated for the do run.

2. Determine Local Insolation

Average daily insolation values for each month of the year must bedetermined for the application site. Appendix D contains insolation valuesfor three possible array tilt angles for a variety of United States sites.Insolation for United States sites not listed may be estimated byinterpolation between nearest tabulated values. Other sources may beconsulted for non-United States locations. Insolation values determined forthe site will be used in the next step of the sizing methodology.

3. Calculate "Worst-Month" Insolation and Load

This methodology requires the remote, stand-alone photovoltaicsystem to be sized to meet the load during the "worst month" of the year. Theworst month is the one with the smallest ratio of energy falling on the array(insolation) to the energy required by the load. If the system is sized tomeet the load during the worst month, it will automatically be sizedadequately for all other months. 6 The worst-month insolation and loadvalues (i.e., values for which the insolation-load ratio is the smallest) aremost conveniently identified by setting up a table that lists daily averageinsolation for each month along with daily average load.

5If the daily load variation is sufficiently large, or if load peaksappear on consecutive days, it may be necessary to use the peak loadlevels in place of monthly averages. Otherwise, the system may beinadequately sized to accommodate cloudy periods'coinciding with these highload periods.

6System designers will often reduce the required array size and system costby relying on "long term storage" in which energy stored during months ofhigh insolation will be held for use during months of low insolation. Inthe present sizing method, the worst-month approach has been adopted toprovide a somewhat more conservative size estimate.

N

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In Table.2-1, the insolation data (in kWh/m 2-day) are those listed inAppendix D for China Lake, California; the load data (in kWh/day) were chosenarbitrarily to illustrate the procedure. Note that in the table, the loaddata are listed next to insolation data corresponding to three different arraytilt angles. The sizing procedure uses these insolation-load ratios in orderto accommodate non-constant insolation and loads over the year. The threetilt angles, tilt equal to latitude, latitude +15 deg, and latitude -15 deg,will typically bound the range of array orientations required to best matchthe load whether the load is constant year round, winter peaking, or summerpeaking. Using the tabular approach described below will assure a goodestimate of the minimum array size necessary to serve the load regardless ofthe annual load pattern.

Table 2-1. Example of Method for Determining the Appropriate Insolation andLoad Combinations for Sizing the Array and Battery Storage.(Sample Insolation Data are for China Lake, California.) Notethat the example load is month-dependent, i.e., not constant(see text for details).

Month I

Tilt Angle =Latitude -15 deg

Tilt AngleLatitude

Tilt Angle =Latitude +15 deg

Insolation(I) + Insolation ( I) + Insolation (1)Loa:"

-(Ltd ) = Load (Ltd) - Load (Ltd)

January 3.88 + 2.8 = 1.39 4.38 + 2.8 = 1.56 4.63 ; 2.8 = 1.6

February 4.77 + 2.8 = 1.70 5.13 + 2.8 = 1.83 5.70 + 2.8 = 1.86

March 6.19 + 2.5 = 2.48 6.34 + 2.5 = 2.54 6.13 + 2.5 = 2.45

April 7.33 + 2.5 = 2.93 7.07 + 2.5 = 2.83 6.46 + 2.5 = 2.58

May 7.88 2.5 = 3.15 7.26 - 2.5 = 2.90 6.32 + 2.5 = 2.53

June 8.30 + 2.5 = 3.32 7.50 + 2.5 = 3.00 6.38 + 2.5 = 2.55

July 8.07 + 2.5 = 3.23 7.43 + 2.5 = 2.97 6.45 + 2.5 = 2.58

August 8.63 + 2.5 = 3.45 8.34 + 2.5 = 3.34 7.61: 2.5 = 3.04

September 7.16 + 2.0 = 3.58 7.36 + 2.0 = 3.68 7.14 + 2.0 = 3.57

October 5.88 + 2.0 = 2.94 6.41 + 2.0 = 3.21 6.57 _ 2.0 = 3.29

November 4.53 + 2.0 = 2.27 5.17 + 2.0 = 2.59 5.51 + 2.0 = 2.76

December 3.82 + 2.8 = 1.36 4.43 + 2.8 = 1.58 4.78 + 2.8 = 1.71

t

2-7 ; e;

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f

To determine the worst-month insolation and load values, Table 2-1 isapplied as follows. In the columns below each tilt an-1e, enter theinsulation value for each month as it appears in Appendix A for theappropriate application site, To the right of each insolation value, enterthe calculated daily average load value for each month (see Step 1). The sameload values should appear in each of the three tilt angle columns. Note thatin the case of a constant, year-round load, all load values in the table willbe identical. For each pair or"' insolation ind load values, calculate theratio of insolation to load, as shown. For each tilt angle column, select andcircle the smallest resulting ratio. There may be duplicate values in one ormore columns. Next, select the largest of the circled values. This value isindicated by "*." This value is a best estimate of the worst-month insolation/load ratio for the example application. Insolation and load values obteinedin this manner are used in the following sizing steps. In Table 2-1, thesevalues appear in boxes. Note that ^,n this example, the array tilt angleselected is latitude +15 deg, denoting the choice that the array is orientedto serve a winter peaking load.

4. Determine Array and Bettery Storage Sizing Factors

The next step in the sizing procedure is to determine the factorsfor array and battery sizing to be used in subsequent calculations of theactual array size and battery storage capacity. ? These factors have beenderived from prior analyses of how the photovoltaic system loss of energyprobability (LOEP) depends on array and battery size for a range of possibleworst-month insolation levels (Reference 0. 8 By determining the requiredsize of array and battery storage per unit of load, dependent on theworst-month insolation, the proper array and battery sizes can then becalculated using insolation and load values determined in Step 3, above.

This probability value is the "worst-month LOEP;" i.e., the probabilitythat the system will be unable to meet load requirements during the monthhaving the smallest insolation/load ratio. The methodology in this documentis based on a worst-month LOEP value of 0.1. This LOEP value for the worstinsolation month corresponds to a monthly average LOEP of approximately0.02-0.04. This value will provide a service availability roughly equivalentto that of conventional competitor power systems such as diesel, etc. If =}comparing photovoltaic to other renewable energy systems, an equivalentavailability analysis is required for the other technologies. Reference 3also presents results for LOEP values of 0.01 and 0.001; i.e., higher systemavailabilities. (Generalized approaches are described in References 4 and 5which allow sizing the system to any LOEP value that may be required by thespecific application.) It should be noted that the LOEP is based on thecharacteristics of insolation only and does not take into account photovoltaicequipment reliability.

?Adapted from Reference 3. f'

8The loss of energy probability is an estimate of the probability thatduring a given time period, the energy output of the power system will beinsufficient to meet the energy load demand.

t

2-8

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1

Y

1 2 3 4 5 6 7 3 9 10 11 12

Il

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= 2.4A

4

3

ro

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1

T,_.

I (kWh/m2-DAY)

7.0

6.5

6,0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

LOWEST SYSTEM CAPITALCOST CURVE (SEE STEP 4)

7

6

5

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7

j 6Q0

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s 53

VPN

°GO 4u

C7Z 3NN

cc 2Q

1 2 3 4 5 6 7 8 9 10 11 12

BATTERY STORAGE SIZING FACTOR, S b (DAYS)

Figure 2-3. Determining Array and Battery Storage Sizing Factors(at LOEP 0.1) for Various Worst-Month InsolationValues. (Adapted from Reference 3)

` The sizing factors for the array and battery storage appear in:.. rr Figure 2-3 in the form of a nomograph. In the nomograph, the solid curves

each correspond to an insolation value s narked. Each solid curve shows therelationship between the array sizing f aL:jr, S a , and the battery storagesizing factor, Sb , for that insolation value. Sa and Sb values to beused in subsequent array sizing calculations are selected by first choosingthe solid curve whose worst-month insolation value equals that found by themethod in Step 3. Interpolation may be used to obtain more precise results.A trial point on the selected solid curve is chosen ner.•t: the point of

2-9

t

n

t

O j

e

0

intersection of the dashed line with the solid curve is the best initialchoice. (The significance of the dashed line will be discussed below.) Thearray sizing factor, S a , is found by extending a horizontal line from thatpoint on the curve to the scale on the left of the nomograph. Similarly, thebattery sizing factor, S b , is found by extending a vertical line down fromthe same point on the solid curve to the scale at the bottom of the nomograph.

An example is shown in Figure 2-3 for the case in which the worst-monthinsolation - 4.6 (see Table 2-1)• Any point on a given insolation curve willresult in a worst-month LOEP exactly equal. to 0.1. Different points on theinsolation curve, however, will result in different combinations of array andbattery sizes. For example, selecting a point on the solid curve farther tothe left will result in a system with larger array and smaller batterystorage, although it will still provide the same level of power availability(i.e, the same LOEP).

System capital cost will vary for different battery and array sizecombinations. For this reason, a dashed line intersecting the solid curvesalso appears in the nomograph. The intersection of the dashed line with therelevant insolation level defines the sizing factors that lead to lowestphotovoltaic system capital costs for each insolation curve as derived fromearlier photovoltaic component cost experience in remote, stand-alone systemapplications (Reference 3). The dashed line may thus be used as a guide forthe initial selection of sizing factor values.

It should be recognized, however, that use of this dashed curve will notnecessarily result in a lowest life-cycle cost estimate since it is based onlyon initial system capital costs. Other life-cycle cost factors such asoperation, maintenance, and various financial parameters, have not beenincorporated into the nomograph. Furthermore, since photovoltaic array costsare expected to decline in the future more rapidly than battery costs, thelowest capital cost system configuration is likely to be determined frompoints on the curves to the left of the present dashed line. The recommendedapproach in using this methodology is to initially select the point ofintersection of the dashed line and the so] I line nearest the worst-monthinsolation for the site. After determining the corresponding Sa and Sbvalues and calculating the array and battery storage sizes, the life-cyclecost should be computed according to the procedure in Section III. If it isfound in this initial cost estimate that the photovoltaic system appears lesseconomical than its competitors, additional array/battery size combinationsshould be examined. In this case, points on the solid curve to the left andright of the original point are chosen, corresponding array and storage sizesare calculated, and new life-cycle costs estimated. This process may berepeated until an approximate lowest (i.e., local optimum) life-cycle cost isobtained

as Determine. Sizing Factors for a Specified Number of Sunless Days.A photovoltaic system will frequently have to be sized under the conditionthat the system must be able to serve the load for a specified number ofconsecutive sunless days (or days of autonomy). The nomograph in Figur y 2-3may also be applied in these circumstances, but its use is somewhat different.

1 1k,

•- 2-10

sl

In this cases the specified number of sunless days is simply used as thebattery sizing factor, Sb. The user is cautioned that the chosen Sb mustbe at least as large as the Sb displayed in Figure 2-3 to ensure adequatepower to serve the load and recharge batteries at the stated level ofreliability (i.e., LOEP = 0.0. From the point on the scale in Figure 2-3where Sb is equal to the number of sunless days, a vertical line is drawn tointersect the solid curve whose value is closest to the appropriateworst-month insolation. From this intersection point, a line drawn left tothe Sa scale determines the proper value of Sa. Sizing the systemaccording to a specified number of sunless days generally will not yield thelowest capital -cost system having a given LOEP. However, specializedrequirements of the application (e.g,, very high reliability requirements asin %the case of microwave repeaters) will sometimes dictate this approach.

b. Estimate Load Fractions Supplied by the Array and Storage. Theenergy load fraction supplied by the array, fa, is that portion of the loadenerg*, that flows directly from the array, via an inverter or converter if oneis used. The fraction fb is thi portion of the load supplied from batterystorage. By definition, fa + fb = 1. Energy that flows from the arraythrough battery storage is subjected to greater losses than that flowingdirectly from array to load. Therefore, the relative sizes of fa and fbwill affect the required size of the array.

The equation to be used to calculate the array size in this methodology 1I

(Equation (2)) contains the load fractions fa and f b . However, precisecalculation of the load fractions is difficult due to varying photovoltaicoutput by time of day and can be additionally complicated for complex orirregular load profiles. A means of estimating these fractions is describedin Appendix B. The user may prefer to use the simplifying assumption that allof the array energy passes through the battery storage before passing to theload; i.e., letting fa = 0 and fb = 1. This is a conservative approachthat tends to overestimate the system size since in most applications the loadin part is supplied directly from the array, thus avoiding storage losses.For today ' s component efficiencies, the degree of oversizing will range from0 to 25%, respectively, for the case of a nighttime -only load and the case inwhich load and array output are perfectly matched. The degree of oversizing jfor a constant, 24-hours /day load is typically less than 10%.

5. Calculate Array Power and Area

Calculating the array size means calculating both i ts peak, poweroutput in watts and its area in square meters. Both results are required forsystem costing.

The array size calculation requires the worst-month load value, Ltd(determined in step 3), the array sizing factor, S a (found from Figure 2-3),and the load fractions f a and fb . Also, the efficiencies of the storagebatteries, voltage regulator, and inverter or converter are required. Typicalvalues of these efficiencies appearing in Appendix A may be used in case theyare not otherwise available. Finally, a factor, F, will be included in the

t ^

2-11 {

A

^^

T array calculation to account for array degradation over the lifetime of thesystem. This factor initially oversizes the array slightly to ensure that thesystem will meet load requirements until the end of its design life despitegradual array power output degradation.

xThe required array power is now calculated from Equation (2).

Ltd x 1000

Pa S a x F x e i /c [f b (evr x e

b ) + f a^(2)

where

Pa = array power in watts

Ltd = energy load value in kilowatt -hours/day

Sa = array sizing factor in kilowatt -hours per squaremeter per day

ei/c = inverter or converter efficiency at maximum steady state load, ifused; otherwise, e i /c = 1

f

F = factor to account for array degradation over the system lifetime

evr = efficiency of voltage regulator if used; otherwise, evr 1

eb = battery efficiency ,E

f a = fraction of load energy supplied directly by the array'

fb = fraction of the load energy supplied from battery storage

1000 = 1000 watts /m 2 ; a term to convert S into an equivalent numberof hours per day that 1000 watts

/

m^ insolation would be y.received by the array f

tThis equation may also be applied to systems without storage. As in the

case with storage, the array output energy on an average daily basis mustmatch the average daily load energy requirements. Equation ( 2) can be appliedby setting f b = 0, fa = 1, eb = 1, and Sa = the worst-month insolationvalue. Note that in this case the LOEP of the photovoltaic system has notbeen estimated; thus, this case departs from the comparable -reliability sizing

!;` approach that underlies the ba^ , ince of the document.

4►

{ Array area is based on the array power level determined in Equation (2)and is shown in Equation (3) below:

PA = a o (3)

em [1 + PTC (Top - 28 C)] x 1000

where

Aa = array area in square metersP

Pa = array power in watts obtained from Equation (2)

em = module efficiency at standard test conditions (STC)

PTC = module temperature coefficient; typically = -0.005/Co

Top = actual module operating temperature in degrees Celsius. Fortemperate climates, use the nominal operating cell temperature(800 mW/cm 2 , 200C ambient, 1 m/s wind speed, 1.5 air mass) Y

(NOCT). For hot climates (peak summer temperature ovier 110 to1150F), use NOCT +100C

1000 = 1000 W/m 2 at standard test conditionsF

6. Calculate Battery Storage Sizek

The next step in sizing the system is to calculate the required.size of the battery storage in kilowatt-hours. Battery storage size is based r

on S b from Figure 2-3 (or on a prior specification of the number of sunlessdays) and an allowance for the "depth of discharge" limit on the batteries.Operating within this limit prolongs battery life and protects the batteriesin applications subject to freezing temperatures. Caleulating the requiredbattery capacity also requires the worst-month load value previously used inthe array sizing equations. Finally, the inverter or converter efficiencyused to calculate storage size is the same value used for the array icalculation.

The required battery storage size is calculated using Equation (4).

Ltd x S Eb d x ei/c

(4)

where

Eb = rated battery energy storage in kWh

t:

2-13

Ltd = worst-month average daily load value in kWh/day(see Step 3)

Sb = battery sizing factor in days

d = maximum allowable depth of discharge

ei/c = efficiency of the inverter or converter. If neither isused, ei/c = 1

7. Determine Voltage Regulator Size

The battery charging voltage regulator is sized to handle themaximum amount of array output power likely to be available for charging thebatteries. For conservatism, the regulator [or batter,, protector as it isknown for small systems (<3 kW)1 must be able to handle the array output atnoon on a cold, clear day with the load disconnected. The voltage regulatoris therefore sized to match array output at standard test conditions(1 kW/m 2 , 280C cell temperature).

8. Determine Inverter or Converter Size

The inverter or converter typically is sized according to themaximum steady-state load power requirement in watts, ac or dc, respectively.However, if the photovoltaic system is to be used to power an inductive load,the inverter must be able to supply the full surge current required by theload. In the case of an induction motor, the starting current can be as largeas 4 to 5 times the rated motor requirements.

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SECTION III

r- SYSTEM COST ANALYSIS

A. SCOPE

Cost effectiveness is the primary criterion for evaluation of candidatephotovoltaic system applications. This section presents the life-cyclecosting methodology to be used for determining photovoltaic system costeffectiveness. The methodology is intended primarily for estimating theviability of a photovoltaic power system compared to a non-photovoltaic poweralternative, rather than precise energy cost estimation. Furthermore, it issolely intended for use by Government agencies since use by private entitieswould involve additional considerations such as the effect of taxes.

B. COST ANALYSIS METHODOLOGY

To determine whether a photovoltaic system is cost effective in a givenapplication, the life-cycle cost of the photovoltaic system should be comparedto the life-cycle cost of the alternative power system such as dieselgenerator, batteries, utility grid connection, or renewable energy technologies(see Figure 3-1). For the purpose of this comparison, the capabilities ofsatisfying load (i.e., availability) of all power systems being evaluated areassumed to be identical. The sizing analysis in Section II has been designedto ensure that photovoltaic system performance is adequate to satisfy thespecified load.

1. Photovoltaic System Life-Cycle Cost

Photovoltaic power system life-cycle cost is estimated from theinitial cost of the system installed at the site and the present value of allrecurrent costs associated with system operation. Photovoltaic systems aretypically capital intensive (i.e., they require a large initial capitalexpenditure), but have low operating costs (i.e., zero fuel cost and smallexpenditures for replacement, operation, and maintenance). The sum of capitaland recurrent expenditures represents the equivalent amount of money requiredat the time of system installation to completely cover all costs associatedwith the photovoltaic system, including a return on the investment, over itsoperating lifetime. 9 Life-cycle cost of the alternative to a photovoltaicsystem similarly combines the associated first cost and operating cost forcomparison with the photovoltaic option.

9The "lifetime" of a photovoltaic, or any other power system, may beinterpreted as the "financial lifetime" for the purposes of a life-cycle costanalysis. As such, the photovoltaic system operating lifetime provides aguideline, but not a constraint, on the lifetime chosen for the life-cyclecost analysis. Equal lifetimes must be chosen between competing technologiesin the cost analysis described in this document.

•

F

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3-1

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(a)

LIFE—CYCLECOST OF

PV SYSTEM

INITIALCOST OF

PV SYSTEM

OPERATINGCOST OF

PV SY STEM

LIFE—CYCLECOST OF

ALTERNATIVETO PV

OPERATINGCOST OF

ALTERNATIVETO PV

LIFE—CYCLECOST OF

ALTERNATIVETO PV

PREF=ERENCEFOR PV OR

ALTERNATIVE

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INITIAL ICOST OF

ALTERNATIVETO PV

LIFE—CYCLECOST OF

PV SY STEM

Figure 3-1. Approach for Determining Photovoltaic Power SystemCost Effectiveness

The initial cost of a photovoltaic system can be determined from the costof the array (in $/W); power-related balance-of-system cost [i.e., batterystorage in $/kWh; voltage regulator in $/W regulator input power, and inverter(or converter) costs in $/W ac (or dc)]; area-related balance-of-system costs(i.e., structures and wiring costs in $/m 2 of array); system installation andtesting cost in percent of equipment cost, and any indirect costs (i.e.,engineering and management fees, delivery, and contingency) in percent ofequipment cost.. Equation (3a) describes the analytical relationships andEquation (5b) displays the detailed procedure for estimating initial installedphotovoltaic system cost (IC).

3-2

(b)

(c)

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9 f

1, -^

i

q

Initial cost = [1 + indirect M + installation (%)]

.

x [delivered equipment, cost ($)] (5a)

IC = (1 + IND + INST) [(MOD x Pa) + (ABOS x Ad + (CONY x WDC)

+ (INV x WAC) + (REG x W*) + (BAT x BWh)] (5b)

where

IND = fractional indirect costs on equipment including engineering,management, and contingency fees

INST = fractional cost on equipment for installation, site preparation,testing, and checkout cost of the system

MOD = module cost in dollars per peak watt of array

Pa = peak watts of solar array (dc)

ABOS = area-related balance-of-system cost per square meter of arrayincluding cost of array structure, land, wiring, connectors, etc.

Aa = array area in square meters

CONV = converter cost per peak watt (dc)

WDC = rated size of converter in peak watts (dc)

INV = inverter cost per peak watt (ac)

WAC = rated size of the inverter in peak watts (ac). If more than oneinverter is used, sum the peak watts of each. If commerciallyavailable inverters do not match the load requirement exactly,select the smallest unit sufficiently large to satisfy the load

REG = voltage regulator cost per peak watt (dc) of maximum regulatorinput power. (Note that cost may vary as a function of inputvoltage level)

W* = maximum voltage regulator input power

BAT = battery cost per kilowatt-hour of energy storage

^. BWh = battery storage size in kilowatt-hours

Equipment cost estimates are assumed to include delivery to the site.All dollar amounts should be expressed in the same "base year" (e.g., 1984) for

i

t

3-3

(1)

3-4

'

i

consistency. Current dollar cost estimates based on prior year information" will need to be escalated to the appropriate "base-year" level.

In addition to the initial installed system cost described above,recurrent costs associated with photovoltaic system operations are to beincluded in the estimation of life-cycle cost. Estimates of operation,maintenance, and replacement costs are based on hardware performancecharacteristics and system operating strategy. Expenditures are primarily forbattery replacement (if battery storage is included in the system design) andarray, inverter or converter, and battery operation and maintenance. Thephotovoltaic system operating strategy (e.g., the system may or may not berequired to operate autonomously for a prolonged period of time) will affectboth the initial system cost and the recurrent costs.

Battery lifetimes are typically between 5 to 10 years depending onmanufacturer-specific battery characteristics, number of discharge cycles,design depth of discharge, and operating temperature. In contrast, theanticipated life of a photovoltaic array is estimated to be about 30 years.Battery replacement at regular intervals are, therefore, required throughoutthe operating lifetime of the photovoltaic array. The cost for eachreplacement of storage batteries (BR) is shown in Equation (6):

r

BR = (BAT x BWh) (1 - SV) + LREP (6)

where

3BAT X BWh = delivered cost of batteries from Equation (5b)

SV = fractional salvage value of batteries at time of &replacement r.'

LREP = labor cost of battery replacement (in base-year dollars)

Salvage value of the batteries is typically based on prices in the scrapmetal market (e.g., for lead or nickel) at the time of replacement. Thepresent value of the sum of all battery replacements (RPV) over thephotovoltaic system lifetime, escalated and discounted to account for thetiming of the expenditure, is estimated using Equation (7) as follows: j

nrep(11++e

j x k

RPVBR x

ach

dr (7)j.1

where

j = counter for number of battery replacements (1, nrep)

k = battery lifetime (years)

j x k - constrained to be strictly less than photovoltaic system

^rlifetime or lifetime used in life-cycle cost analysis (years)

BR - single-time battery replacement cost from Equation (6)in base-year dollars

escb - real (above inflation) annual escalation rate for storagebatteries (fraction)

dr - discount rate (cost of money to system owner, typically definedas 10% (real) for Government applications)

Expei:ditures for replacement of capital equipment (other than batteries)with lifetimes shorter than the assumed photovoltaic system lifetime can alsobe determined using Equation (7), appropriately modified to reflect their costand timing. For the purpose of this document, such replacements areconsidered minimal and are incorporated in the annual operation andmaintenance cost equation described below.

Regular operation and maintenance costs can be estimated on an annualcost basis. These costs include expenditures for activities such as array,battery, and inverter maintenance; component replacements (other thanbatteries); and grounds, structural and electrical upkeep. Annual operationand maintenance costs (OM) can be estimated on the basis of the number ofrequired visits to the site per year times the cost per trip in base-yeardollars. A heuristic frequently used to estimate annual operation andmaintenance expenditures is to assume that annual expenses are a fixedpercentage of the initial cost of equipment. The present value of the cost ofoperation and maintenance procedures is the derived annual amount summed overthe system lifetime, including any real escalation and discounting ofexpenditures over time. Annual expenditures are, therefore, growing in dollaramount at the constant rate of real escalation, if any. Present value ofoperation and maintenance cost (OMPV) is presented in Equation (8) as follows:

1 + escom1 + esc Nif dr esc (8)OMPV = OM x C dr - esc / x 1 - 1 + dr^momom

i

i

orr

where^s

f

OMPV = OM x N, if dr = escom

OM = annual operation and maintenance cost in base year dollars

escom = real (above inflation) annual escalation rate for operationand maintenance activities (fraction), typically 0%

k

3-5

iO

A {

'fk

4 4

tpdr = real discount rate (fraction); typically 10%

N = system lifetime (years)

Photovoltaic system life-cycle cost MCC) can now be determined from itsconstituent parts described above. Life-cycle cost is displayed in Equation (9)as the sum of the initial installed system cost, Equation (5) and the presentvalue of recurrent costs, Equation (7) plus Equation (8).

LCC = IC + RPV + OMPV

(9)

All costs are in base year dollars. Typical values for parameters inEquation (5b) are presented in an example in Appendix A. As a guide forphotovoltaic system cost analysis, initial installed system costs (IC)presently range from approximately $17 to $25/watt.

2. Alternative Power System Life-Cycle Cost

Photovoltaic system cost effectiveness is determined by comparisonof the photovoltaic system life-cycle cost with the life-cycle cost of thecompeting energy technology. For a given application, photovoltaics may becompeting with fossil fuel, battery, utility grid, or other renewable energyalternatives. In this section of the report, the cost of alternativetechnologies to photovoltaics are characterized. Section III.B.3 selects theleast-cost non-photovoltaic alternative as the basis for the cost-competitiveness assessment. {

Small stand-alone photovoltaic systems are potentially competitive with• number of alternatives including diesel generators, batteries, extension of• distant utility grid, and other current solar technologies. The life-cyclecost estimated for each alternative is consistent with the photovoltaic costapproach shown in Equation (9). Initial installed costs (IC), present valueof capital replacements over the system lifetime (RPV), and present value ofoperation and maintenance costs (OMPV) are summed to their respectivelife-cycle cost. For the purpose of this analysis, the capability of allpower systems to satisfy load (i.e., their availability) is assumed to beidentical.

Diesel power generation systems require initial capital expenditureis for` diesel generators, a fuel storage system, and installation (IC). Diesel

generators will require periodic repair, overhaul, and replacement within thetime frame of the analysis (approximately 20 to 30 years). Recurrentmaintenance and fuel costs for these types of systems are also of greatimportance. In many remote, stand-alone applications, the cost of fuel,labor, transportation and materials can be significant. Estimation of annualdiesel generator operation and maintenance costs (OM) should be based onactual cost data.

d

w

3-6

.r

Initial capital costs for battery systems are estimated in a mannersimilar to the battery cost term in Equation (51)), Bat x BWh, plus the cost ofassociated control equipment, indirect costs, and installation. However, thebattery system in this case must be sized to satisfy the entire load,accounting for system inefficiencies and assumed interval between recharges.Battery lifetimes are less than that of photovoltaic systems and thus willrequire replacement at regular time intervals within the assumed 20 to 30 yearphotovoltaic system lifetime. Battery electrical characteristics, cyclingrequirements, depth of discharge, and operating temperature contribute to theestimate of battery life. The present value of the cost of replacement iscalculated as described in Equations (6) and (7). Remaining salvage value ofused batteries is explicitly taken into account. Operation and maintenancecosts, Equation (8), include battery inspections, recharge, and equalizationat regular intervals depending on battery capacity, load being served, anddepth of discharge.

Extension of an existing utility grid line can be very expensive for aremote application with a relatively small load. The costs for extending gridpower to a remote site and for the kilowatt-hour meter are treated as initialcapital costs (IC). Cost estimates for this equipment can be obtained fromthe local utility company. Once the utility line is installed, the primaryrecurrent cost is the cost of energy to serve the load. Current utility ratestructures provide the basis for this cost over the photovoltaic systemlifetime (OMPV). Note that in some locations, utility reliability may also bea factor in the comparison between photovoltaics and utility-supplied power.

Life-cycle cost estimates for other renewable energy alternatives(non-photovoltaic) require cost information as described in Equation (9).Specific system design and associated cost inputs will need to he developed bythe organization performing the system comparison.

In addition to competing with the capital and operating costs associated r.with installing capacity to satisfy a new load is the potential forphotovoltaics to operate in a fuel-displacement mode for an already existingapplication. Energy cost-intensive technologies in remote areas may provide a R

potentially cost effective use for photovoltaic technology. Though therewould be no savings for initial capital expenditure on the alternativetechnology, the photovoltaic system would provide savings on operation andmaintenance cost (OMPV) and, potentially, on delaying capital replacement(RPV) of the non-photovoltaic alternative. In this fuel-displacement mode,daytime photovoltaic system output can h^e used to satisfy coincident load.Battery storage can be added if it is found to be cost effective in tkisapplication. Either with or without battery storage, reliability of thealternative technology combined with the photovoltaic system would be enhanced.

C. PHOTOVOLTAIC VERSUS ALTERNATIVE POWER SYSTEM COST COMPARISON

Photovoltaic system cost competitiveness can be determined by comparisonwith the least-cost non-photovoltaic power system that satisfies all performanceand reliability requirements. Using the approach displayed in Figure 3-1(c),and repeated in Figure 3-2 1 the life-cycle cost of the non-photovoltaic system

.,

k

3-7

p

LIFE-CYCLE

LIFE-CYCLE

PREFERENCECOST OF

COST OF

FOR PV ORPV SY STEM

ALTEPNATIVE

ALTERNATIVE(LCCPV)

(LCCALT)

TO PV

Figure 3-2. Life-Cycle Cost Comparison of Photovoltaic System (LCCpV)and the Non-Photovoltaic System (LCCALT)

(LCCALT) is subtracted from the life-cycle cost of the photovoltaic system(LCCpV). Three outcomes are possible:

(1) LCCppV— LCCCALT < $0. The photovoltaic system is cost effectivecompared the alternative system. The absolute value of thedifference is a first-order measure of the preference forphotovoltaics.

(2) LCC - LCCALT >$O. The photovoltaic system is more expensivethan the alternative; thus, it is not cost effective.

(3) LCCp - LCLCCALT = $0. The photovoltaic and alternative systemsare— of equal cost in present value terms.

This differential cost (or net present value) measure of cost competitivenessprovides the basis for deciding to pursue or terminate photovoltaic system Fanalysis and design activities. If in the initial estimate of photovoltaic °-system life-cycle cost the system is determined not to be cost effective, the t:sizing procedure should be repeated from the estimation of array and batterysizing factors (see discussion, Section II-4). c

If the photovoltaic system is determined to be cost effective (orreasonably close to cost effective) for a specific application, it is usefulto perform a sensitivity Analysis on important cost parameters over anappropriate range of values. This sensitivity analysis is useful to thedecision maker since small variations in cost drivers, such as escalation in jdiesel fuel or electricity prices over the system lifetime and the price ofphotovoltaic modules, can significantly alter the relative preference forcompeting power systems. The result of this analysis is an understanding ofthe effect of uncertainty in parameter values on photovoltaic system costeffectiveness.

l

3-8

u i

SECTION IV

REFERENCES

1. Solar Photovoltaic Applications Seminar: Design, Installation and Opera- r

tion of Smallp Stand-Alone Photovoltaic Power Systems, U.S. Departmentof Energy, DOE/CS/32522-Ti, July 1980.

2. Designing Small Photovoltaic Power Systems, Monegon, Ltd; Gaithersburg,Maryland, May 1981.

3. Rosenblum, L., Practical Aspects of Photovoltaic Technology,Applications, and Cost, NASA CR-168025, December 1982.

4. Macomber, H.L., Ruzek, J . B., Photovoltaic Stand-Alone Systems,DOE/NASA /0195-1, NASA CR-165352 M206, August 1981.

5. Bucciarelli, L.L., Jr., "Estimating Loss of Power Probabilities ofStand-Alone Photovoltaic Solar Energy Systems," Solar Energy, Vol. 32,

lNo. 2, pp. 205-209, 1984.

6. Photovoltaic Product Directory and Buyers Guide, Pacific NorthwestLaboratories, Battelle Memorial Institute, prepared for U.S. Departmentof Energy, PNL-5052, April 1984.

7. Simon, F., "Conceptual Design of Photovoltaic Medical Systems for RuralHealth Applications," NASA LeRC Report No. 4210- 055, March 1981.

8. Smith, J.H., Handbook of Solar Energy Data for South-Facing Surfaces inthe United States, Vol. I t UOE JPL-1.012-25, January, 1980.

r. 9. Cartwright, K., Carmichael, H.E., Kamien, J.H., and Siegel, B.,Comparison of Photovoltaic and Diesel Engine Systems for Village PowerApplications_, aerospace Corporation for NASA Lewis Research Center,May 1980.

10. Cochrane, E.H., Lawson, A.C., acid Savage, C.H., Flat-Plate PhotovoltaicPower Systems Handbook for Federal Agencies, JPL Publication 84-35,DOE ET 20356-14, April 1984.

4

i^

4--1 j^ o

e

APPENDIX APHOTOVOLTAIC SYSTEM SIZING

AND COSTING EXAMPLE

O l

' r

f

Yi

APPENDIX A

PHOTOVOLTAIC SYSTEM SIZING AND COSTING EXAMPLE

This appendix presents an example of sizing and costing a hypotheticalphotovoltaic system using the methodology described in this report. Estimatesof currently relevant photovoltaic system parameter values are shown as aguide for users of the methodology: A sample comparison of photovoltaicsystem cost effe n tiveness compared tG competing technologies is then presented.

To illustrate the system sizing procedure, an example is presented basedon the sample case described in Section Il of this report, The application isa small, seasonally variable load located near China Lake, California.Determination of photovoltaic system size follows the step-by-step proceduredescribed in Section II of this document and repeated in Figure A-1. Typical:values (and ranges) for several. o ` the photovoltaic system sizing parametersare displayed in Table A-1. The Cable should be consulted frequently in usingthis appendix for a description of each parameter name.

Step 1: Calculate Load

Total daily energy load (Ltd ) is determined from Equation (1) asfollows

Ltd _ Pi Di/1000 (1))

i = 1

It is assumed that each season has a separate, single (n = 1) ac load (P) for8 hours/day (D) during daytime hours. The power drawn by the single load ifor each month is:

r

350 watts: Decei::ber, January, February312.5 watts: March, April, May, .tune, July, August250 watts: September, October, November

° The corresponding daily energy load (Ltd ) is 2.8 kilowatt-hours,2.5 kilowatt-hours, and 2.0 kilowatt-hours, respectively.

Step 2: Determine Local Insolation

Appendix D contains the daily average insolation values for each monthof the -year and for three array tilt angles for a number of United Statessites. Locate the site insolation values for China Lake, California, on

W_ page D-2. These values will be used in the following step of the methodology.

r

A-1i

CALCULATELOAD ENERGYREQUIREMENT

DETERMINELOCAL

INSOLATION

CALCULATEWORST-MONTH

INSOLATIONAND ENERGY LOAD

^ tDETERMINE ARMYAND STORAGE

Si ZING FACTORSi

I•^I

CALCULATE ARRAYiPOWER AND AREA I l

I

CALCULATE BATTERYSTORAGE CAPACITY

x

CALCULATE VOLTAGEREGULATOR SIZE

i

CALCULATE INVERTER/CONVERTER SIZE I I

I PERFORM® LIFE-CYCLE

COST ANALYSIS

Figure I,. Photovoltaic System Sizing Procedure

A- 2

4/

T

Table A-1. Photovoltaic System Sizing Parameters: RelevantRanges and Default Values

141"r

ParameeerParameter Name Units Range Value

.Array area A m2 a

Battery depthof discharge d fraction 0.05-0.80 0.60

Load i duration Di hours/day --b

Battery efficiency e fraction 0.80-0.90 0.88

Inverter/converterefficiency ei/c fraction 0.85-0.97 0.93

Module efficiency em fraction 0.06-0.11 0.10

Voltage regulatorefficiency evr fraction 0.85-0.93 0.91

Degradation factor F fraction 0.75-0.95 0.85

Load fraction: array f a

fraction -- ci^

Load fraction:

F batteries f fraction -- c

Worst-monthinsolation I kWh/m2-day -- d,e

Worst-month load Ltd kWh/day --b,e

Load i power brequirement Pi watts --

Array power frequirement Pa watts --

Module temperaturecoefficient PTC fraction/C° -0.005 -0.005

i

Array sizing factor S kWh/m2-day -- g

-- i

Battery sizing factor S gb days --

Module operating 48 or

temperature Top oC 45-55 55he

aSee Equation (3).„ bSee Equation (1).

cSee Appendix B.dSee Appendix D.eSee Table 2-1.f See Equation (2).

. gSee Figure 2-3.hTemperate climate = 480C and hot climate = 550C.

A-3

As

.0

Sten 3: Calculate Worst-Month Insolation and Load

Construct a table of monthly insolation and load values using theinformation generated from steps 1 and 2. Display them as shoran in Table A-2,below. (This example is the same as shown in Table 2-1). For each month andtilt angle, divide i s le insolation value by the load and enter the ratio intothe table.

For each tilt angle column shown in Table A-2, identify the month with thesmallest ratio of insolation-to-load. Next, select the largest one of thesevalues (identified by "*"). The insolation (I = 4.6) and load (L td = 2.8)values corresponding to this particular value are the ones to be used in latersizing steps. This allows the system (array and battery) to be sizedsufficiently large to supply the load for the worst month (i.e., month oflowest insolation relative to load) and allows some optimization of array and

f

Table A-2. Monthly Insolation and Example Energy Load Values forThree Array Tilt Angles for China Lake, California

Month

Tilt Angle =Latitude -15 deg

Tilt Angle -Latitude

Tilt Angle =Latitude +15 deg

Insolation (I)-- !- Insolation (I) Insolation (I)Load (Ltd ) = Load (Ltd) = Load ( Ltd) -

January 3.88 : 2.8 - 1.39 4.38 _ 2.8 - 1.5 4.63 2.8 - .6

February 4.77 2.8 - 1.70 5.13 _ 2.8 = 1.83 5.20 2.8 . 1.86

March 6.19 2.5 = 2.48 6.34 - 2.5 - 2.54 6.13 2.5 - 2.45

April 7.33 2.5 - 2.93 7.07 = 2.5 = 2.83 6.46 2.5 = 2.58

May 7.88: 2.5 = 3.15 7.26 =2.5-2.90 6.32: 2.5-2.53

June 8.30 : 2.5 = 3.32 7.50 - 2.5 - 3.00 6.38 2.5 - 2.55

July 8.07 : 2.5 = 3.23 7.43 _ 2.5 - 2.97 6.45 2.5 - 2.58

August 8.63 : 2.5 - 3.45 I 8.34 _ 2.5 - 3.34 7.61 2.5 - 3.04

September 7.16 : 2.0 - 3.58 7.36 : 2.0 - 3.68 7.14: 2.0 = 3.57

October 5.88 : 2.0 - 2.94 6.41 _ 2.0 - 3.21 6.57 2.0 - 3.29

November 4.53 : 2.0 - 2.27 5.17 2.0 = 2.59 5.51 2.0 - 2.76

December 3.82 : 2.8 -G

4.43 _ 2.8 - 1.58 4.78 2.8 - 1.71

A-4 t

^J

sr

battery size as influenced by the potential benefit of varying array tiltangle. In this example, the array tilt angle of latitude +15 deg is preferredbased on January insolation and load conditions.

Step 4: Determine Array and Storage Sizing Factors

Using the results from Table A-2, insert the relevant insolationvalue (4.6 kWh/m 2-day) into Figure 2-3 (repeated as Figure A-2). For aninitial estimate of array and battery sizing factors (Sa) and (Sb),respectively, locate the intersection of insolation (I) equal to 4.6 and thedashed line. The resulting array sizing factor S a is 3.7 and battery sizingfactor Sb is 2.4.

Based on the monthly load and insolation levels, the fraction of the.load supplied directly by the array (f a) can be estimated. For thisexample, 50% of the load served directly by the array is predicted (see step 1for the assumptions on loads). Therefore, array fraction f a = 0.5 andbattery fraction f b = 0.5.

Step 5: Calculate Array Power and Area

Array size (Pa ) is now calculated using Equation (2) as follows:

Ltd x 1000

Pa Sa x F x ei/c [fb

( evr x eb ) + f a ] )w.

2.8 x 10003.7 x 0.85 x 0.93 [0.5(0.91 x 0.88) + 0.5]

t

= 1063 watts

Array area (Aa) associated with this array size is determined usingEquation (3) below:

PA = a (3)a em [1 + PTC (Top 280C)] x 1000

10630.10 [1 - 0.005(55 - 28)] x 1000

8665 = 12.3 m2

^it

A-5

l•

0

I (kW h /m2 -DAY)

7.0

6.5

6.0

5.5

` 5.0

4.5

S = 3.7 ^1^4.6p 4.0

3.5

3.0

2.5

2.0

LOWEST SYSTEM CAPITAL

S b = 2.4 COST CURVE (SEE STEP 4)

r

77

Q 606

N

-^ 5

0N

O 4U

OZ_ 3

N_N}

cc 2Q

5

4

3

2

Y

1

1 2 3 4 5 6 7 8 9 10 11 12

BATTERY STORAGE SIZING FACTOR, S (DAYS)

Figure A-2. Determining Array and Battery Storage Sizing Factors(at LOEP = 0.1) for Various Worst-Month lnsolation Values.(Adapted from Reference 3)

For the purpose of this example, China Lake, California, is considered ahot climatic area. Therefore, module operating temperature (Top) reflectsthe high point of the temperature range (5500 rather than the typical valueof 480C (which reflects nominal operating cell temperature (NOCT) at800 W/m2 , 200C ambient air temperature, and air mass 1.5).

d

ORIGINAL: PAGE 1OF POOR QUALITY

1 2 3 4 5 6 7 8 9 10 11 12

Aes =t

fGt

ti

A-6

+T

-14

pt

Step 6: Calculate Battery Storage Capacity

Battery storage (Eb) required for this application is based on theaverage daily load for the worst month of the year (L td, from step 3), thebattery sizing factor (Sb) based on the system reliability chart(Figure A-2), battery depth of discharge limit (d), and inverter efficiency(ei/c). These factors are combined in Equation (4) as follows:

Ltd x S

Eb - d x ei/c

(4)

= 2.8 x 2.4 _ 12.0 kWh0.6 x 0.93

Step 7: Calculate Voltage Regulator Size

The voltage regulator is sized at the peak array output at standard testconditions (1 kW/m2 and 280C cell temperature) and assumes no load. Voltageregulator size is, therefore, 1063 watts.

Step 8: Calculate Inverter/Converter Size

In order to satisfy the peak power requirements of the load, 350 wattsduring the winter months, an inverter size of 350 W ac is required, assumingthat the load is not inductive.

4

S

F

"r

Having completed the sample photovoltaic system sizing analysis, theestimation of system life-cycle cost follows. As necessary, array and batterysize refinements may be made so that life-cycle cost is reduced whileretaining equivalent reliability (see the life-cycle costing iteration step inFigure A-1).

The cost analysis is composed of three parts. First, photovoltaicsystem life-cycle costs ere estimated. Second, the cost of alternative energysystems in competition with photovoltaics are determined. Finally, thealternative energy generation systems are compared on the basis of leastcost. Figure A-3 displays the procedure.

Typical values and ranges for the current cost of photovoltaic equipment(in 1984 dollars, delivered to the site) and operational attributes (e.g.,battery lifetime) are presented in Table A-3. Data is based on availableinformation for small stand-alone systems, current cost estimates, and cataloginformation (e.g., see Reference 6). The table should also be consultedthroughout this appendix for a description of each parameter name.

i

A-7

t

k j

O

^x 7

e(a)

INITIALCOST OF

PV SYSTEM

LIFE—CYCLECOST OF

PV SY STEM

OPERATINGCOST OF

PV SYSTEM

.4(b)INITIAL

COST OFALTERNATIVE

TO PV

OPERATINGCOST OF

ALTERNATIVETO PV

LIFE—CYCLECOST OF

ALTERNATIVETO PV

(c)

rA++1j

Figure A-3. Approach for Determining Photovoltaic System Cost Effectiveness

i

Photovoltaic system life -cycle cost is determined in three steps:estimation of initial cost, estimation of operating costs, and summation to ilife-cycle cost. These steps are illustrated below:

Step 1. Estimate Initial Cost of Photovoltaic System

The initial cost of a photovoltaic system ( IC) includes expenditures forcapital equipment, installation, testing, and any indirect costs as shown inEquation ( 5a) below:

Initial cost = [ 1 + indirect (%) + installation (%)](5a)

x [delivered equipment cost ($)]

t

A-8r,

„

Table A-3. Photovoltaic System Cost Parameters: i

Relevant Ranges and Default Values

ParameterParameter Name Units Range Value

Array-related BOS cost ABOS $/M2 20-300a 150

A M2-- b

Array area

Battery cost BAT $/kWh 50-250 80

Battery storage size BWh kWh --c

Converter cost CONV $/Wdc 0.70-200 0.80

Discount rate (real) dr fraction 0.10d 0.10

Battery cost escalationrate (real) escb fraction 0-0.03 0

OM cost escalationrate (real) escom fraction 0-0.1 0

Indirect cost IND fraction 0.10-0.25 0.16

Installation andtesting cost INST fraction 0.20-0.50 0.30

Inverter cost INV $/Wac 0.30-0.80 0.40

Battery lifetime k years 5-10 10

Labor cost for batteryreplacement LREP $ Oe Oe

Module cost MOD $/Pa 7-10 10

Photovoltaic systemlifetime N years 20-30 30

Number of batteryreplacements nrep number 2-5 2

Annual OM cost OM $ or fraction 0.005-0.03ff

Voltage regulator cost REG $/W* 0.20-0.50 0.45

Battery salvage value SV fraction 0-0.2 0.1

Peak watts ac Wac watts -- g

gSystem peak watts do Wdc watts --

hArray peak watts do Pa watts --

Voltage regulatorinput power W* watts -- i

aLow-end value reflects very low cost structures and zero land cost.bSee Equation (3).cSee Equation (4).dFor Government applications, a 10% real discount rate is used.e lncluded in annual OM cost.(Relevant for fraction of delivered equipment cost; see Equation (5a).Range is based on photovoltaic systems without batteries.gSee Section II.C.8.bSee Equation (2).iSee Section II.C.7.

R

8

. 0#

'tom' k

4y*' S • ^:

t.

r

€e

40

Mt.^^yA

A-9

1

j

Indirect costs (IND) include engineering, management, and contingencyfees and are assumed to be a fractional multiple of delivered equipment cost.Similarly, the cost of installation, site preparation, and test of thephotovoltaic system (INST) is assumed to be a fractional multiple of deliveredequipment cost. All costs associated with the initial installation of thephotovoltaic system, excluding the cost of equipment itself, are to beincluded in the multipliers described above.

Delivered equipment cost represents the initial capital expenditures forall photovoltaic power-related equipment, structures, inverter or converter,protection equipment (e.g., voltage regulator), and battery-relatedequipment. Each cost element is described in terms of its "natural units" forcosting purposes as shown in Table A-4.

The initial installed cost (IC) of the photovoltaic system can now bepresented as in Equation (5b):

IC = (1 + IND + INST) [(MOD x P a ) + (ABOS x A a ) + (CONV x WDC)(5b)

+ (INV x WAC ) + (REG x W*) + (BAT x BWh)]

Table A-4. Cost Elements

Cost Element Cost Basis Engineering Units

Module Dollars per peak Peak watts of array powerwatt of array (MOD) output (Pa)

Area-related Dollars per square

Array area in square metersbalance of system meter of array (ABOS)

(Aa)

Inverter or converter Dollars per rated

Rated size of inverter, wattspeak watt ac (INV) or ac (WAC ) or converter,do (CONV), respectively watts do (WDC)

Regulator Dollars per watt of

Maximum regulator inputmaximum regulator power, watts (W*)input power (REG)

Battery-related Dollars per kilowatt- Battery storage sizeequipment hour of storage (BAT) in kilowatt-hours (BWh)

A-10

49

1

^F

44

d' Using the assumed values from Table A-3 and from the sizing analysis, initialinstalled cost is calculated to be:

IC = (1 + 0.16 + 0.34) [(10 x 1063) + (150 x 12.3) + (0)

+ (0.40 x 350) + (0.45 x 1063) + (80 x 12.0)]

(1.46) [$14,053] = ;20,517

The initial installed system cost (IC) per peak watt of array (Pa) for thisexample is:

4

$20,517= $19.30/watt +

1063 watts

This falls within the present-day range of $17 to $25/watt initial system cost.

Step 2: Estimate Photovoltaic System Operating Costs

1In addition to the initial installed system cost described above,

recurrent costs associated with photovoltaic system operations are to beincluded in the estimation of life-cycle cost. Estimates of operation, 1maintenance and replacement costs are based on hardware performancecharacteristics and system operating strategy. Expenditures are primarily for Ibattery replacement (if battery storage is included in the system design) andarray, power conditioning unit, and battery operation and maintenance.

The cost of each battery replacement (BR) in base year dollars isestimated from the initial cost of batteries shown in Equation (5b),BAT x BWh, less an allowance for salvage value (SV), plus the labor cost forreplacement (LREP). This is displayed in Equation (6):

BR = (BAT x BWh) (1 - SV) + LREP (6)

i

Using the financial inputs from Table A-3, battery replacement cost is:

BR = (80 x 12.0)(1-0.1) + 0

_ $864

0Vs

,-

Over the photovoltaic system operating lifetime, a number of batteryreplacements (nrep) will need to be made. The present value of these

r A-11

0 r I OV A, r

4replacements (RPV), escalated (at the real rate, escb) and discounted (at areal rate, dr) to account for the timing of the expendi ure, is estimatedusing Equation (7) as follows:

Wrapj x k

1 ++e sc

bRPV

BR xldr

(7)

j = 1

where k is the battery lifetime. Using the baseline inputs, assuming tworeplacements during the system lifetimes the present value of batteryreplacements is

2

1.0RPV ( 864) x - $462

l . l

^ - 1

Y

The present value of expenditures for replacement of capital equipment(other than batteries) with lifetimes shorter than the assumed photovoltaicsystem lifetime can also be determined using Equation (7) 7 appropriatelymodified to reflect their cost and timing. For the purpose of this example,such replacements are considered minimal and are incorporated in the annualoperation and maintenance cost equation described below.

Regular operation and maintenance costs can be estimated on an annualcost basis. These costs include expenditures for activities such as array,battery, and inverter maintenance; component replacements (other thanbatteries); and grounds, structural, and electrical upkeep. Annual operationand maintenance costs (OM) can be estimated on the basis of the number ofrequired visits to the site per year times the cost per trip in base yeardollars. A heuristic frequently used to estimate operations and maintenanceexpenditures is to assume that annual expenses are a fixed percentage of theinitial cost of equipment. The present value of the cost of operation andmaintenance procedures is the derived annual amount summed over the systemlifetime, including any real escalation (esco m ) and discounting (dr) ofexpenditures over the photovoltaic system lifetime (N). Annual expenditures i

are, therefore, growing in dollar amount at the constant rate of real jescalation, if any. Present value of operation and maintenance cost (OMPV) is !

r presented in Equation (8) as follows:

1 + esc 1 + esc N

OMPV = OM x x 1dr - escm 1 + drom

if dr escom (8)It

.M1^^ om .

war'° or

;.^•=y OMPV = OM x N, if dr = esc om

w A-12

f- ^

it

f

For this example, annual operation and maintenance cost is assumed to includesite visits once every 2 months for 4 hours per visit at a cost of $25 perhour. Annual operation and maintenance cost (OM) is therefore $600. The

. present value (OMPV) of these expenditures is:

0 30OMPV 600 x (0.10

.0 0 ) x 1 - (1.1)

= $5656

St_ ep 3: Sum to Life-cycle Cost

Photovoltaic system life-cycle cost (LCC) can now be determined from itsconstituent parts described above. Life-cycle cost is displayed inEquation (9) as the sum of the initial installed system cost, Equation (5),and the present value of recurrent costs, Equation (7) plus Equation (8).

LCC = IC + RPV + OMPV

T $20,517 + $462 + $5656 (9)

$26,635

The life cycle cost in this example is expressed in 1984 dollars.

Cost estimates for alternative power systems in competition withphotovoltaics are now required. For illustrative purposes, life-cycle costestimates are prepared for batteries and diesel generators. Load energy andpower requirements are identical to the assumptions used in the photovoltaicsystem sizing and life-cycle cost assessment.

1. Battery Cost Example

Battery storage size in kWh is based on the energy load, days ofstorage required between recharging, battery depth of discharge, and inverteror converter efficiency. The sizing algorithm is shown below:

Battery size = Energy load x days of storageMaximum depth of discharge x inverter/converter efficiency

where the maximum daily energy load battery depth of discharge andinverter/converter efficiency are the same as in the photovoltaic example; andrequired days of storage is based on a first order trade-off between theinitial cost of storage and the required recharging and maintenance costs (atthe assumed labor rates and maintenance frequency).

4

t

A-13

s Therefore,

Battery size - 2.8 x days of storage0.6 x 0.93

Since the operating costs associated with service personnel used torecharge and maintain batteries can be extremely high, sufficient batterystorage to supply one month's energy load is assumed in this example. Asmaller battery size would require more frequent visits and, thus, be moreexpensive from a life-cycle cost perspective. It is further assumed thatonce-a -month site visits for maintenance are required to ensure adequatesystem performance to satisfy the load. Battery size i s thus:

Battery size = 2.8 x 30

0.6 x 0.93

= 150 kWh

Using battery cost estimates from Table A-3, including indirecc andinstallation costs, initial battery system capital cost (IC) is%

IC = (1 + 0.16 + 0.30) (150 kWh x $80/kWh) = $179520

The cost of battery replacement (BR) every Y years is based onEquation (6) and the battery assumptions in Table A-3.

BR = (Battery size x battery cost per kWh) x (1-salvage fraction)+ labor cost

= (150 x 80) (1-0.1) + 0 = $10,800

For this example, labor cost is assumed to be included in the regularoperation and maintenance expenditure. In present value terms, batteryreplacement present value (RPV) per Equation (7) is:

prep1 + escb J x k

RPV = E BR x 1 + drj = 1

Using the values from the previous tables,

2j x 10

RPV = $10,800 x (1.00\- 1 1.1

= $10,800 (0.39 + 0.15) = $5830

6

1

i

A-14w

` ^ fa,

_ _ _ ,., ,_ - --•.^------ r k tee,

Annual cost for operation and maintenance includes battery rechargingand maintenance on the batteries and balance of system. For this example,monthly site visits are assumed, consistent with the sizing and cost trade-offdescribed above. Each visit requires one maintenance person for 8 hours at$25 per hour. Annual operation and maintenance cost (OM) for 12 site visitsis therefore:

OM = 8 hours/visit x $25/hour x 12 visits/year = $2400

The cost of equipment used for recharging and maintenance is typicallyincluded in the estimate of the labor rate. Over the assumed 30 yearlifetime, the present value of operation and maintenance cost (OMPV) is:

1 + escb1 + escb NOMPV = $2400 x dr - each x 1 1 + dr

1.0 30

_ $2400 x (0.10 - 0 t x 1- ( 1.0

1.1)

_ $22,625

The life-cycle cost (LCC) of the battery system alternative is the sum*^f the initial installed capital cost (IC), present value of batteryreplacement cost (RPV), and the present value of operation and maintenancecosts (OMPV) as shown below: f

LCC = IC + RPV + OMPV

_ $17,520 + $5830 + $22,625I

_ $45,975t

This life-cycle cost value will be used in the subsequent costcomparison of energy generation system alternatives.

2. Diesel Generator Cost Example

Though the ,,peak power required by the load is 350 W, a standard, ysmall size production diesel generator is typically 3 to 4 W. In thisexample, a single 4 kW Kohler diesel generator has been ahosen. All unit

A-15

r

:RT^Y

o

1

^

G

xs

capital costs and maintenance requirements are identified in Reference 9.Installed costs in 1980 dollars are shown below:

Diesel generator $ 4566

4 Fuel tank, 500 gallons 400Valves/piping 125Mounting frame 50Engine shelter 750

$5891

For consistency with the cost estimates for competing technolrO.es,diesel generating installed costs can be inflated from 1980 to 1984 dollarsusing the Gross National Product Implicit Price Deflator (which results in amultiplier equal to 1.30). Installed cost is therefore (1.30)($5891) =0658. This value is assumed to include the cost of system installation.Therefore, diesel generator system initial capital cost (IC) increments thisamount only by the indirect cost fraction (16%) as shown below:

IC = (1.16)($7658) = $8883

The Kohler diesel is a long-life unit that is assumed co requirereplacement costs equal to the cost of one unit after 15 years. Present valueof replacements (RPV) is, therefore, the initial generator: cost in 1980dollars inflated to 1984 dollars by the 1.30 multiplier and discounted for 15years as:

(1 + escomRPV = $4566 (s.30) ` 1

15

+ dr

15$4566 (1.30) (Y

.^01 = $1421

Annual expenditures for ongoing operation and maintenance azeestimated based on: (1) the operating strategies described and costed in thereferenced report, and (2) consistent labor hours and costs for thephotovoltaic and battery examples in this appendix. Maintenance schedule andcosts in 1984 dollars are shown below:

200 hours $29 parts + 4 hours labor = $ 129 = $0.65/hour

500 hours 2 days labor (16 hours) = $ 400 = $0.80/hour

10,000 hours $1000 for parts and labor = $1000 = $ 0.10/hour

$1.55/hour

A-16

E

The asssumed load operates 8 hours/day, 365 days/year, ort2920 hours/year. Annual maintenance expense is, therefore:

$1.55 x 2920 = $4526/year

Annual fuel costs are estimated from the yearly hours of energy load,diesel engine fuel consumption, and fuel price. Kohler engine fuelconsumption for the assumed load is 0.19 gallons/hour. Fuel price is assumed r

to be $1/gallon. Annual fuel cost is:

2920 hours/year x 0.19 gallons/hour x $1/gallon = $555/year

The present value of operation and maintenance costs (OMPV) over the 30year lifetime is:

1 + esc 1 + esc N r

OMPV - ($4526 + $555) (dr - escom) x 1 - 1 + drm)om

1 1.0 30

$5081 (0.1016.U)

x [1

r

- $47,914 I

11

^»- Diesel generator system life-cycle cost (LCC) is the sum of the initialcost (IC), present value of replacements (RPV), and operation and maintenance(OMPV) costs as shown below: r.,

LCC = IC = RPV + OMPV rj.

= $8883 + $1421 + $47,914

= $58,218

t

The life -cycle cost comparison between photovoltaic and the batteryand diesel alternatives can now be finalized. Life-cycle costs are summarizedbelow:

Photovoltaics $269635Batteries only $45,975Diesel generator $58,218

By inspection, the photovoltaic system is shown to be the least-cost

s^ alternative. On this basis, a decision to pj-,,sue photovoltaic system analysisand design activities is warranted. As stated in the text, however, it may be

F7additionally useful to perform sensitivity analyses on important costparameters to understand the effect of uncertainty in parameter values onphotovoltaic system cost effectiveness.

.- A-17

' f

t

we

3P

9

i

1

APPENDIX BESTIMATION OF LOAD FRACTIONS

SUPPLIED BY PHOTOVOLTAIC ARRAYAND BATTERY STORAGE

4

LLA PV TO STORAGE

STORAGE TO LOAD

PV TO LOAD

NHaOJY

- LOAD

R

*t.

Y-

r

'

bb

APPENDIX B

ESTIMATION OF LOAD FRACTIONS SUPPLIEDBY PHOTOVOLTAIC ARRAY AND BATTERY STORAGE

An operating photovoltaic system is typically required to satisfycoincident load as well as to recharge battery storage. By using thephotovoltaic array to satisfy load directly, rather than going through batterystorage, power losses due to round-trip battery inefficiencies are avoided.Therefore, for the purpose of sizing a photovoltaic system, it may beimportant to explicitly consider this to avoid unintended oversizing and thusincreased life-cycle cost.

Load can be served by either the photovoltaic array or battery storageas shown in Figure B-1.

Relating Figure B-1 to the discussion in Section II.C.4.b and toEquation (2) in Section II.C.5, the fraction of load supplied directly by thephotovoltaic array is the cross-hatched area, denoted as fa. The remainingfraction of the load is supplied by batteries, fb.

Quantifying array output supplied directly to the load, f a , is anon-trivial exercise due to the highly stochastic nature of array output andpotentially variable loads. As part of a system design optimization effort,but not as part of the present methodology, the most precise way of estimatingarray output sent directly to the load is by means of a computer simulation ofsite-specific weather conditions, array output, and user load over a typicalyear calculated on an hourly basis. Using this information, array size can becalculated using Equation (2). Since this approach is inappropriate for use

12am NOON 12am(MID) (MID)

TIME OF DAY

Figure B-1. Idealized Energy Usage by Time-of-Day for a Given Month

Ar,.

B-1

_

r

`In

to

in combination with the sizing and costing methodology described earlier, twoalternative approaches are described below:

(1) Bound and Estimate Load Fraction Supplied by Photovoltaic Array.In this case, the fraction of energy supplied directly to the loadby the photovoltaic array can vary between 0% (for nighttime onlydemand) and 100% ( for demand perfectly matched to photovoltaicoutput). For the 0% array-to-load assumption, all array outputmust pass through the battery and all battery-resultant efficiencylosses incurred. Conversely, if all array output supplies theload directly, no battery efficiency penalties apply. In general,most photovoltaic systems operate between these two extremes.

The assumption that all array output goes through the battery inthose applications where the array could supply the load directlyis a simplifying assumption that would cause the photovoltaicsystem to be somewhat oversized relative to the requirements ofthe load.. Conservative approaches have already been incorporatedin the methodology to ensure adequate system size. The usershould be careful not to unintentionally bias system size largerthan required due to this photovoltaic array-to-load factor.

At one boundary condition, the array is sized correctly for 0%(nighttime only demand) array-to-load case: compared to the requiredsize, assuming all energy goes through the battery. Conversely,with a perfect match between array and load, the array would beoversized approximately 25% based on the current baseline valuesfor voltage regulation and round-trip battery storage efficiencies(see Appendix A). A more realistic estimate of array oversizingis between these two values. For example, the degree of oversizingfor a constant, 24 hours/day load is typically less than 10%.

(2) Calculate Load Fraction Supplied by Photovoltaic Array Using aSimplified Procedure. A simple algorithm can be constructed tohelp estimate the load fraction supplied directly by thephotovoltaic array under some rather limiting constraints.Assuming clear-sky conditions, an idealized time-of-day profile ofarray output can be constructed, as shown in Figure B-1, for eachmonth of the year. Then, a representation of the deterministictime-of-day load for each month is incorporated. The load neednot be constant by time-of-day or between months. For the "worst"month (see Section II.B.3), estimate the fraction of the loadsupplied by the array, f a . This is the cross-hatched areadivided by the total load. Insert this fraction into Equation(2). Battery sizing is not affected by this procedure. Repeatthis procedure for each month of the year to ensure thatarray-to-load differences are adequately incorporated. Select themaximum array size, Pa , from Equation (2) to adequately covereach month of the year for the selected array tilt angle.

B-2

k.

>. -s. ^ .,r► F.^ew/yyi 'f'o'r Lam!--^ ^!. ..^ — _ ,

P

O

x4

1^

3

r

Use of this procedure requires acceptance of certain limitations.} Most importantly, to the extent that there is any variability in

time-of-day photovoltaic output (or load) such that the loadcannot be served according to the idealized pattern displayed inFigure B-1, this algorithm will overestimate the amount of arraypower sent directly to the load. Based on the degree ofvariability, this overestimate will result in the array andbattery to be sized smaller than required to meet the load by somevarying amount.

}

K

B-3

f

P

,* , .,9001 .

4

a

w

APPENDIX CCOMPARISON OF SIZING METHODOLOGY

WITH ALTERNATIVE APPROACHES

kF

l

Tw- 1 --^ter----`

^ ` e

L t }

tx

APPENDIX C

COMPARISON OF SIZING METHODOLOGY WITHALTERNATIVE APPROACHES

This section compares the results of applying the sizing methodology inthis document with the results of several other sizing approaches. Eachmethodology has been applied to the same application load example. Theexample is derived from Reference 3, and was discussed along with thealternative sizing methods.

The application load for this comparison is a constant power load of4.2 kWh /day. The site has a worst-month insolation value of 2.3 kWh/m2-day.Additional data used for the initial sizing are as follows:

fb = 0.6 (i.e., the fraction of the load met by thebattery. Therefore, f a = 1 - fb = 0.4)

evr . eb = 0.80

ei/c = 0.93

-

Application of the sizing methodology as described in Section II issimplified by the constant load and the prior stipulation of the worst-monthinsolation. Therefore, L td = 4.2 kWh /day and I = 2.3 kWh/M 2/day. The t

array sizing factor, S a , corresponding to I = 2 . 3 in Figure 2-3, is 1.7.No array degradation factor appears in the other sizing approaches. Forcomparison of the present method, therefore, F = 1.0.

The array power from Equation (2) is therefore:

ti

Ltd x 1000 i

Pa S x F x ei/c [f b (evr x eb) + fa]

t

4.2 x 10001.7 x 1.0 x 0.93 [0.6 (0.8) + 0.4]

4200 _ 4200

1.7 x 1.0 x 0.93 x 0.88 1.39

Therefore,

Pa = 3020 W (peak) ac

t

C-1 r: f,

0

Note that if an array degradation factor, F, equal to 0.85 is included,

the result becomes:

Pa = 3550 W (peak) ac

The battery storage sizing factor, S b , from Figure 2-3 is 7.5. Therequired battery storage capacity, assuming an 80% depth of discharge (d), is

therefore:

Ltd x S

Eb d x ei/c

_ 4.2x7.50.8 x 0.93

=42 kWh

These results are compared with three other approaches in the table below:

Table C-1. Array and Battery Storage Sizing Comparisoni

Battery Storage

Method Reference Array Size, Wp Size, kWh

NASA 7 3000 42r'

ROSSA 3 3140 42

Solarexa7 3150 30

FPUP -- 3020 42

(present

document)

aSolarex designed and built a system with this array and storage size forthe site in question. This system was designed for a load of 4.0 kWh/dayrather than for 4.2, as in the other examples.

This comparison shows that the present sizing method yields resultssimilar to those of three other approaches when applied to this load and

•

9

-^-'' c-2

d location. It should be recognized, however, that different sizing approacheswill frequently yield different results due to the built-in design margin orloss-of-energy probability (LOEP) selected as the basis of the sizingapproach. These differences argue for the use of an LOEP-based sizingapproach in order to ensure that power system alternatives being sized forcomparison purposes are all sized to the same level of estimated performance.

fwl+.

C-3

Y # E0

^e

44

APPENDIX DAVERAGE DAILY INSOLATION TABLES

FOR UNITED STATES SITES(ADAPTED FROM REFERENCE 8)

i

t^

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14

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O 0) m 00 to W In kD w W 1`- t- W t`+ t- koE-H I .^ rr rr r • rr .-rr r.--r rrr rw- .-

v

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t1 m to t U1 0) O U) t kD N ON a' d m t-- co 01 N N U1 Ol O

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to W .^1 co

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11

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