Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UF00027406/00001
## Material Information- Title:
- An assessment of the economic feasibility of powering citrus irrigatin systems in Florida with photovoltaic arrays
- Series Title:
- Economics report
- Creator:
- Taylor, Timothy G
- Place of Publication:
- Gainesville Fla
- Publisher:
- Food and Resource Economics Dept., Agricultural Experiment Station, Institute of Food and Agricultural Sciences, University of Florida
- Publication Date:
- 1981
- Language:
- English
- Physical Description:
- iii, 41 p. : ill. ; 28 cm.
## Subjects- Subjects / Keywords:
- Irrigation systems ( jstor )
Electricity ( jstor ) Fixed costs ( jstor ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Bibliography:
- Bibliography: p. 26.
- General Note:
- Cover title.
- General Note:
- "December 1981."
- Statement of Responsibility:
- Timothy G. Taylor, J. Walter Milon, Clyde F. Kiker.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 026024764 ( ALEPH )
08960548 ( OCLC ) ALD8903 ( NOTIS )
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Decthber 1981
An Assessment of Economics Report 105 the Economic Feasibility of Irrigation Powering Systems in Citrus Florida with Photovoltaic Arrays Food and Resourac Economic Department Agricultua Experiment Stations Institute of Food and Agricultural Sciences University of Florida, Gainesville 32611 Timothy G. Taylor J. Walter Milon Clyde F. Kiker I B ABSTRACT A simulation model is developed to assess the economic feasibility of utilizing photovoltaic arrays to power irrigation systems in Florida. The model can be applied to any type of irrigation system. Furthermore, a variety of economic and institutional scenarios can be specified by means of user input variables. Simulation results for permanent over- head systems irrigating citrus suggest that the use of photovoltaic arrays to power irrigation systems may be economically feasible as early as 1984. Key words: solar energy, photovoltaic array, present value, simulation. TABLE OF CONTENTS ABSTRACT . . . . . . . INTRODUCTION . . . . . . BASIC CONCEPTS AND ASSUMPTIONS . . . . Conventional System Costs . . . . Photovoltaic Powered Irrigation System Costs . . Economic Feasibility Criterion . . . SIMULATION MODEL FOR ASSESSING THE ECONOMIC FEASIBILITY OF PHOTOVOLTAIC POWERED IRRIGATION SYSTEMS. . . Energy Requirement and Array Design Component. . Annual Array Generation and Irrigation Energy Demand Cc Economic and Institutional Component ... . . Present Valuation Component. . . . . AN APPLICATION TO CITRUS IRRIGATION. . . . Economic and Technical Assumptions . .. Simulation Results . . . . . CONCLUSIONS . . . . . . REFERENCES . . . . . . APPENDIX A--PHOTOVOLTAIC SYSTEMS . . . . APPENDIX B--CALCULATION OF PHOTOVOLTAIC SYSTEM PRICES . . . . . APPENDIX C--SAMPLE SIMULATION PROGRAM. .. Page .... i ... 1 3 . 3 *0* 4 . 5 . 9 )mp . 10 11 olnent 13 * 14 * 15 . 17 . 18 . 18 . 25 . 26 . 27 COSTS AND ELECTRIC . . . . * LIST OF TABLES Table Page 1 Estimated cost per peak kilowatt of photovoltaic systems 1981-2000. . . . . ... ...... 16 2 Economic scenarios for the photovoltaic feasibility simulation model . . . . ... .19 3 Estimated first year in which photovoltaic irrigation systems are economically feasible. . . ... 20 LIST OF FIGURES Figure 1 Basic flow diagram of photovoltaic powered irrigation system feasibility simulation model. . . ... 12 2 Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for this optimistic scenario and selected by back ratios. . . . . ... 21 3 Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for the base scenario and selected by back ratios . . . . ... ... 23 4 Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for the pessimistic scenario and selected by back ratios. . . . . ... 24 A-i Simplified schematic or a photovoltaic powered irrigation system . .. . . . . .... 30 A-2 Mean, minimum and maximum hourly solar insolation levels for Orlando/Herndon airport. . . . ... ..31 AN ASSESSMENT OF THE ECONOMIC FEASIBILITY OF POWERING CITRUS IRRIGATION SYSTEMS IN FLORIDA WITH PHOTOVOLTAIC ARRAYS Timothy G..Taylor, J. Walter Milon and Clyde Kiker INTRODUCTION The use of supplemental irrigation has become an increasingly common practice in the production of citrus in Florida. With relatively inexpensive energy prices prior to the 1970s, and more intensive culti- vation practices, irrigation has been a profitable operation for most citrus producers. However, the rise in energy prices since 1970 has threatened to reduce the economic benefits to citrus producers resulting from irrigation. Anaman [1981,75] has estimated that the economic bene- fits from irrigation could be completely dissipated if the price of energy relative to citrus prices increases threefold from current [1980] levels. The spectre of further increases in energy prices coupled with shortages in the supplies of some fossil fuels has provided the impetus to investigate the potential for utilizing fossil fuels more efficiently and using alternative energy sources in agricultural production. One source which appears to have considerable promise as a power supply for 1 irrigation is solar energy. The use of photovoltaic (PV) arrays to produce electricity for powering irrigation pump motors is currently technologically feasible [Matlin and Katzman, 1978]. The mere fact that photovoltaic arrays can be used to power irrigation systems, however, is not sufficient to conclude that such systems provide a viable alternative to current conventional power sources. Economic feasibility must also be established. ISee Appendix A for a description of PV systems and their use in irrigation. TIMOTHY G. TAYLOR and J. WALTER MILON are assistant professor of food and resource economics. CLYDE KIKER is associate professor of food and resource economics. The purpose of this report is to describe the results of a study on the economic feasibility of using photovoltaic arrays to power irri- gation systems in Florida. For this analysis a photovoltaic system is assumed to be economically feasible if the discounted cost of such a system over a given period of time is less than the corresponding dis- counted cost of currently used conventional systems. Following Matlin and Katzman [1978], the initial year in which photovoltaic ,co" will be economically feasible is determined under a variety of economic and institutional assumptions. The use of photovoltaic arrays for powering irrigation systems represents a substantial change in the structure of irrigation energy costs. The cost structure of powering irrigation systems with currently used conventional fuels (e.g., electricity, diesel fuel, etc.) is one that entails a moderate fixed cost in the pump-power unit, but rather substantial variable fuel costs [Harrison, 1976]. Conversely, the cost structure of irrigation systems powered by photovoltaic arrays is characterized by a substantial fixed cost in the pump power-unit, but very low (possibly negative) variable energy costs. This difference in energy cost structure is significant in that farmers using photovoltaic arrays reduce the direct impact of rising conventional fuel prices on irrigation energy costs. While such a shift in the composition of irrigation energy costs may be desirable, the high fixed cost of photovoltaic systems is currently prohibitive. At present, photovoltaic system costs are approximately $10.75 per peak watt [Litka et al., 1981]. Thus, the fixed investment cost of an array of sufficient size to power an irrigation system would not be justified economically. System costs, however, are expected to decline substantially as commercial production of these systems proceeds [Smith, 1981]. The key factors in determining the economic feasibility of powering irrigation systems with photovoltaic arrays are the cost of these systems, the rate at which conventional energy prices increase and the rates 2 utilities pay for electricity purchased from dispersed energy systems. 2Dispersed energy systems denote systems which produce energy, in this case electricity, at the site of use. Under Federal Energy To analyze the effects of these factors on the economic feasibility of photovoltaic systems several scenarios describing future economic condi- tions are simulated. The scenarios differ in the degree to which future economic events are conductive to establishing the economic feasibility of photovoltaic powered irrigation systems. Thus, the optimistic scenario assumes a rapid decline in the cost of photovoltaic arrays and a rapid rise in conventional fuel prices. Conversely, the pessimistic scenario tsPumes a very slow decline in array cost and no real increase in conventional fuel prices. The base scenario assumes a moderate decline in array cost and a moderate increase in fuel prices. For all scenarios, the ratio of the price utilities pay for electricity relative to the prices at which they sell electricity ("buyback" ratio) is varied over a range of values. BASIC CONCEPTS AND ASSUMPTIONS Any irrigation system is composed of two basic components. The water dispersal system structure (e.g., pipes, sprinklers, support structures) and a pump-power unit. A variety of energy sources can be used to drive the pump-power unit. The two most common types of energy used in Florida are diesel fuel and electricity [Stanley et al, 1980]. From a technical standpoint, the type of energy used to drive the pump- power unit is, in most cases, independent of the type of system structure. Thus, for example, a permanent overhead system can be powered by an electric motor or a diesel engine [Stanley et al., 1980]. Given this independence between pump-power units and the corres- ponding energy source, and water dispersal system structure, an assess- ment of the economic feasibility of utilizing photovoltaic arrays to power irrigation systems is fairly straightforward. If the discounted cost of currently used conventional alternatives over the useful life of the photovoltaic system, economic feasibility can be established.3 Regulation Commission (FERC) regulations, electric utilities are required to purchase surplus electricity from dispersed producers. 3The discussion here, and that which follows, assumes that irrigation as a cultivation practice is economically justified. Give this assumption The estimation of discounted costs for conventionally powered and solar powered pump-power units over some period of time requires a number of assumptions regarding the behavior of energy prices and other economic variables over time. Give that photovoltaic arrays are also dispersed generators of electricity, issues involving the resale of electricity and utility pricing policies must also be considered. The following discussion outlines the basic manner in which the discounted pump-power unit and energy costs are utilized to evaluate the economic feasibility of photo- 4 voltaic powered irrigation systems. Conventional System Costs The calculation of the discounted cost of a conventionally powered irrigation system is straightforward. This discounted cost of an irri- gation system with an investment life of T years is composed of a fixed investment cost and a stream of variable energy costs. The fixed cost investment of a irrigation system purchased in year j can be represented by ICC = SC + PPU j 1,...,J (1) where ICC = Fixed cost investment in year j SC = cost of water dispersal system structures purchased in year j PPUk cost of pump-power unit using fuel type K, k = g (gasoline), e (electricity), d (diesel), 1 (1-p gas) purchased in year j Annual variable energy costs for a system using energy type k, k = g, e, d, 1 are given by and the fact that the use of photovoltaic arrays involves no change in the way irrigation is practiced, the economic feasibility of these systems can be assessed by only examining costs relating to the pump-power units and commensurate energy costs. A detailed discussion of the measurement and calculation of these costs are contained in Appendix B. k k k VCECt = P E (2) t t t where k VCECt = variable energy cost of a conventionally powered system in year t k P = unit price of fuel type k in year t t k E = amount of energy type k used for irrigation in year t t The discounted cost of an investment in an irrigation system powered by fuel k can be written as k T+j DCC. = SC + PPU. + E D (VCEC ) j = 1,...,J (3) S3 J t t t=j where DCC = discounted cost of a conventional irrigation system pruchased in year j D = discounting factor, D = (l+r)t and r denotes the real t t discount rate Equation (3) provides a means of computing the discounted total cost of irrigation over a period of T years assuming the initial investment is made in year j, j + 1, and so on. While the theoretical construction of equation (3) is relatively simple, obtaining values for the included variables is a more difficult matter. Consider for example an invest- ment life of 20 years (T = 20) and the investment can be undertaken in any of 20 succeeding years (J = 20) beginning in 1980. Fixed investment costs must be estimated for the next 20 years and energy prices and the annual amount of irrigation must be estimated for the next 40 years. Thus, the variables in equation (3) could have many different values depending on one's forecasts about future prices. Photovoltaic Powered Irrigation System Costs Although the fixed cost structure of a photovoltaic powered irri- gation system is similar to that of a conventionally powered system, the variable energy cost structure is considerably different. The difference is that a photovoltaic system can produce electricity. During periods of time when irrigation is not needed, the electricity produced by the system can be sold to the utility.5 The fixed cost investment for a photovoltaic powered irrigation system purchased in year j can be written as ICS = SC. + PPU3 + PC. j = 1,...,J (4) where ICS. = fixed investment cost of a photovoltaic irrigation system purchased in year j SC. = cost of water dispersal system structures purchased in year j 3 PPU. = cost of electric pump-power unit purchased in year j 3 PC. = cost of a photovoltaic system purchased in year j The similarity of fixed investment costs between conventional and photovoltaic powered systems can be seen by comparing equations (1) and (4). If the conventional system is electrically powered, the fixed cost structures are identical with respect to water dispersal system structures cost and pump-power unit cost, differing only in that equation (4) con- tains the additional fixed cost of the photovoltaic array. Even if the systems are powered by different types of energy, the water dispersal system structures cost will be identical. Therefore, the economic feasibility of photovoltaic systems depends on whether the decrease in variable energy costs and surplus electricity sold to the utility can offset the additional fixed cost of the photovoltaic system. The variable energy costs of a photovoltaic irrigation system can be expressed by VSECt Pe Ee RP SAG (5) t t t t t where VSECt = variable photovoltaic system energy costs in year t Electricity produced by the array can also be used for other on- farm activities. In this report it is assumed that all surplus electri- city produced by the photovoltaic system is sold to a utility grid. This assumes that comparisons are being made for similar types of irrigation systems (e.g., permanent overhead, etc.). No attempt is made in this analysis to compare different types of irrigation systems. P = unit price of electricity in year t t Ee = electricity purchased to supplement array production in t year t RPt = resale unit price of electricity paid to dispersed producers for electricity in year t SAGt = quantity of surplus electricity produced by the photovoltaic array and sold to the utility in year t The variable energy cost structure of a photovoltaic system differs con- siderably from that of a conventional system. The first term on the righthand side of equation (5) reflects the fact that a photovoltaic array cannot supply all of the electricity necessary to power the irrigation system at all times. This reflects the dependence of the output of a photovoltaic system on incoming solar insolation levels (see Appendix A) and the fact that irrigation may also occur during the night. In the absence of battery storage of electricity, power must be purchased from the utility to supplement the array power. The second term on the righthand side of equation (5) represents the revenue from sale of surplus electricity to the utility. This sur- plus electricity is generated during time periods when no irrigation occurs and, during irrigation, whenever the photovoltaic array produces an amount of electricity greater than that required to power the pump motor. If the value of this resale of surplus electricity is greater than the value of purchased supplemental electricity, the variable energy costs of a photovoltaic system will be negative. The discounted cost of a photovoltaic powered irrigation system purchased in year j and having an investment life of T years can be expressed as the sum of equations (4) and (5). T+j DCS. = SC. + PPU + PC. + D (VSECt) J = 1,...,J (6) 3 3 3 3 t=jt where 7The use of battery storage of electricity is not included in the simulation model. DCSj = discounted cost of a photovoltaic powered irrigation system purchased in year j D = a discounting factor, D = (1+r)t and r denoting the t t discount rate This expression provides a means of computing the discounted cost of purchasing and utilizing a photovoltaic powered irrigation system for T years assuming the initial investment year occurs in years j, J+1, and so on until year J. As in computing the similar discounted cost for conventionally powered systems, prices and costs must be estimated over a considerable length of time. Estimation of prices for equation (6) is further com- plicated by institutional factors affecting the price utilities will pay for electricity produced by dispersed systems. The price utilities are required to pay for electricity produced by dispersed systems must reflect the "avoided cost"8 of producing an equivalent amount of electricity. In addition, the Public Utilities Regulatory Policies Act (PURRA) has provided the incentive for utilities to move in the direction of pricing electricity according to the cost of production in the form of time-of-use (TOU) rates [Milon, 1981]. Under TOU rates, electricity consumed during peak demand periods is more expensive than that consumed during off-peak demand periods. Thus, the increased cost of producing electricity during peak periods is reflected in higher electric rates. The implication for photovoltaic powered irrigation systems is that if surplus electricity production occurs during peak electric demand periods, avoided cost would be much higher than if surplus electricity production occurred during off-peak periods. Thus, if the prices utili- ties pay for electricity produced by dispersed systems reflect these costs, the value of surplus electricity produced by photovoltaic arrays will depend on the time period in which the surplus is produced. The 8The precise meaning of avoided cost is still unclear and currently subject to litigation [Norman, 1981]. The notion of avoided cost is intended to reflect the fact that dispersed energy systems, by producing and selling electricity to electric utilities, enabled the utilities to avoid incurring the cost of producing an equivalent amount of electricity. exact rates utilities will pay for electricity from dispersed systems unfortunately is still unclear [Norman, 1981]. Economic Feasibility Criterion Equations (3) and (6) give expressions for obtaining the discounted cost of purchasing and operating a conventionally powered and a photo- voltaic powered irrigation system for T years assuming the initial investment occurs in year j, j=l,...,J. Photovoltaic systems would be an economically feasible investment in year j, if DCS. < DCC j = 1,...,J (7) The first year of economic feasibility will be that year in which the discounted cost of a photovoltaic system is less than or equal to that of a conventionally powered system. Substituting for DCS. and DCC in equation (7) yields T+j SC + PPU + PC. + E Dt(VSECt) < SC. + PPU. + t J J t t 3 3 t=j T+j E Dt(VCECt) (8) t=j where all terms retain their original definitions. Upon simplification and rearranging terms, equation (8) can be rewritten as k e T+j -PC. + (PPU PPU.) + E D (VCEC VSEC ) > 0 (9) 3 t=j t t t - t=j j = 1,...,J In this form, the importance of the revenue earned from the sale of surplus electricity can be seen. Given the intermittent nature of irrigation, the sign of VSECt (equation (5)) is almost surely negative. Thus, the effect of this term in equation (9) is to offset the additional fixed cost (-PC ) attributable to the photovoltaic system. Equation (8) also facilitates the discussion of several additional aspects involving photovoltaic system feasibility. First, the effects of declines in the cost of photovoltaic arrays can be seen. The only significant negative term in equation (9) is the PC. term. Given that the cost of photovoltaic systems in the future is expected to decline, equation (9) demonstrates that the rate of decline will be a significant factor in determining when photovoltaic irrigation systems will be eco- nomically feasible. In addition, VSEC and VCEC enter equation (9) with a positive sign (note VSEC < 0 which implies -VSEC > 0). Thus, increases in conventional fuel prices or the value of electricity sold to the utility also offset the fixed array cost. Examination of equation (9) also reveals that the fixed cost of water dispersal system structures (SC.) drops out of the equation when similar irrigation systems are being compared. This could also occur if different system types have similar structure costs. In addition, when the pump-power units being compared are both electric, ;he cost of these units (PPUe) also drop out of equation (9). The economic feasi- bility of photovoltaic systems then rests primarily on a comparison of the discounted energy costs of irrigation over a fixed time horizon. SIMULATION MODEL FOR ASSESSING THE ECONOMIC FEASIBILITY OF PHOTOVOLTAIC POWERED IRRIGATION SYSTEMS This section describes the computer simulation model used to deter- mine the first year in which photovoltaic powered irrigation systems will be economically feasible. Because the economic feasibility of these systems depends on a number of assumptions regarding energy price increases, photovoltaic system costs, irrigation levels, and other technical and economic factors, the simulation model is designed to facilitate a wide variety of assumptions via user specified input variables. The model can be used to simulate a number of different types of irrigation systems by appropriately specifying a set of technical input variables. However, the model can only compare photovoltaic powered systems with conventional electric powered systems. The simulation model is composed of four basic components (Figure 1),whose functions The term (PPUk PPUe) k = g,e,d,l is probably positive. However, even if it is negative, the -PC. term would dominate this term in equa- tion (8). are discussed in the following sections. In addition, the underlying economic and technical assumptions are discussed. Energy Requirement and Array Design Component The primary function of this component is to determine the pump motor power requirements for a specific type of irrigation system and then determine the size (m 2) of the photovoltaic array necessary to power the system. The input variables for this component include acre inches of water per application (gross), total acres irrigated, hours per day irrigating, days to complete one irrigation and total dynamic head. Values for these variables depend on the type of irrigation system, irrigation strategy and geographic locations which can be obtained from Harrison [1978] and Stanley et al. [1980]. Given values for these variables, simple engineering equations [Harrison and Choate, 1969] are utilized to calculate the necessary pumping rate (GPM) and the continuous brake horsepower (BHPC) required at the pump shaft. These calculations assume a pump efficiency of 75 percent and a motor efficiency of 88 percent [Pair et al., 1975]. The estimated BHPC is then converted to a continuous kilowatts (1KW) per hour electrical demand using standard conversion values. Because the electri- cal demand of the pump motor is uniform over time, this value provides an estimate of continuous kilowatt hours (KWH) per hour required to power the system. This estimate is utilized in obtaining the necessary size of the photovoltaic array. The present model does not provide for battery storage of electri- city produced by the photovoltaic system. Given the variation in solar insolation level during the course of each day (see Appendix A) it is not reasonable (in terms of cost) to design a system which could hypo- thetically provide full power to the system during all sunlight hours. Thus, the design rule used in the simulation model is that the average hourly output of this photovoltaic array equals the continuous KWH per hour demand of the pump motor. Using the Orlando/Herndon Solmet data [U.S. National Climatic Center, 1980], a mean hourly solar insolation profile was estimated.0 10The Solmet data contains hourly surfact meteorological readings on a r------ S Technical user Specified variables I# of irrigations Energy demand and Tot. dynamic head .array output SWater applied S Frequency - S Acres Irrigation system and Dynam Operating time --photovoltaic evalua L----- ------ j array design Economic/institutional user specified S variables IScenario key I ____ Economic I I .and t rate institutional Discount rate I Structure I Resale price s- SEscalation rate SBuy-book ratio L -J Figure l.--Basic flow diagram of photovoltaic powered irrigation system feasibility simulation model ic .tion Assuming a total photovoltaic system efficiency of .069 [Litka et al., 1981] the average hourly output of the photovoltaic array was estimated at .03418 KWH/m2. By setting this expression equal to the continuous 2 KWH demand of the pump motor and solving for m the size of the photo- voltaic array is obtained. The peak kilowatt (KWP) output rating of the 2 2 array is determined by dividing the size of the array (m ) by 12.5 m This calculation is based on the photovoltaic array in operation at the Florida Solar Energy Center [Litka et al., 1981]. The assumptions utilized in determining the size of the photovoltaic system imply that during a day in which the irrigation system is func- tioning, there will be a period when the photovoltaic system's electri- cal output must be supplemented by purchase electricity and a period of time when the system is generating a surplus of electricity which can be sold to the utility. In addition, if irrigation occurs at night, all of the electricity used to power the system must be purchased. During time periods when no irrigation is occurring, the entire output of electricity produced by the photovoltaic system can be sold to the utility. Given the intermittent nature of irrigation, it is expected that surplus gen- eration sold to the utility will exceed supplemental electric purchases during the year. Annual Array Generation and Irrigation Energy Demand Component The annual amount of electricity produced by the photovoltaic system 2 is obtained by multiplying the annual amount of solar insolation per m by the estimated system operating efficiency (.069). This results in an 2 average expected system output of 118.1949 KWH/m2 annually. To obtain total annual system output, the size of the photovoltaic system (m 2) is 2 multiplied by this value. For example, an 800 m array (64 KWP) would annually produce approximately 94,556 KWH of electricity. The amount of electricity needed for irrigation is estimated by first determining the total number of KWH necessary to complete one irrigation. This estimate is then multiplied by the number of number of variables from 1952 to 1974. Data pertaining to global solar radiation on a tilted surface were used in calculating the hourly solar insolation profile. irrigations per year to obtain the annual quantity of electricity used for irrigation. The annual number of irrigations per year is a user specified input variable to the program. Net generation of the photovoltaic system is calculated by sub- tracting the annual electrical demand for irrigation from the annual total electrical output of the system. It should be noted that measuring net generation in this manner differs somewhat from the theoretically "correct" measurement as implied by equation (5). The error resulting from this approximation in the calculation of net generation can, however, be shown to be very small. Economic and Institutional Component The function of this component is to estimate the change over time in the economic variables used in calculating and comparing the discounted energy cost of photovoltaic powered and conventional electric powered irrigation systems. The basic input variables to this component are the escalation rate of electricity KWH charges, the discount rate, the price utilities must pay for electricity purchased from dispersed systems, and the rate of decline in the cost ($/KWH) of photovoltaic arrays. All prices and costs are expressed in terms of 1980 dollars and all rates of change are in real terms. Furthermore, it is assumed that time-of-use (TOU) electricity rate structures are in effect. Electricity rates are assumed to escalate in an exponential fashion with the real annual escalation rate specified by the user. The 1980 base price of electricity is set at $0.03604 per KWH. This price repre- sents the off-peak price of purchased electricity. Under the assumption that all irrigation occurs off-peak, the annual cost of electricity for a conventional system is obtained by multiplying the annual quantity of electricity used for irrigation by the corresponding "forecast price". The rates utilities must pay for electricity purchased from dispersed systems is assumed to be proportional (via the buy-back ratio) to the price at which utilities sell electricity. The buy-back ratio is a user specified variable which reflects institutional decisions regarding the precise definition of avoided cost. Thus a buy-back ratio greater than one implies that avoided costs are realized during peak periods. Conversely, a buy-back ratio of less than one implies the institutional decision that avoided costs were realized during off-peak periods. Because the buyback price of electricity is tied to the price utilities charge, it is assumed that this price increases over time at the same rate as utility electricity prices. This component of the model also contains three different time paths along which the cost of photovoltaic systems may follow. Each path reflects a differing view as to the rate at which technological innovation and commercial production techniques will be reflected in lower system costs. Costs under each scenario have a 1980 base cost of $10,750 KWP [Litka et al., 1981] and are projected over a twenty year period beginning in 1980 (Table 1). Cost scenario I is obtained by splicing two exponential functions such that the 1986 system cost is $2026.50/KWP and the year 2000 system cost is $945.70/KWP (see Appendix B). Scenario II is also obtained by splicing two exponential functions. Under this regime total system cost declines to $8062.50/KWP 1986 and to $2026.50/KWP in the year 2000. The final scenario (III) assumes a simple exponential decline to a total system cost of $945.70/KWP. The 1986 system cost is $5184.50/KWP. Cost Scenario I is extremely optimistic in reference to the fact that photovoltaic system costs decline substantially by 1986. This scenario is very similar to Department of Energy (DOE) projections [Smith, 1981]. There is considerable uncertainty in the rate at which technological innovation and improved commercial production techniques will be realized in the form of lower system costs, however. Thus, scenarios II and III are included to admit several less optimistic array cost paths over time. The inclusion of such diverse time paths for photoltaic system costs enables an examination of the sensitivity of the economic feasibility of these systems to cost behavior over time to be analyzed. Present Valuation Component This component of the model assimilates all of the information con- tained in the program and evaluates an expression similar in form to equation (9). Thus, assuming the investment in a photovoltaic system Table 1.--Estimated 1981-2000 cost per peak kilowatt of photovoltaic systems Cost scenario Year I II III 1980 10,750.00 10,750.00 10,750.00 1981 8,140.13 10,246.73 9,519.75 1982 6,163.89 9,767.02 8,430.29 1983 4,667.43 9,309.77 7,465.52 1984 3,534.28 8,873.93 6,611.15 1985 2,676.24 8,458.49 5,854.55 1986 2,026.50 8,062.50 5,184.55 1987 1,552.03 4,972.36 4,591.22 1988 1,494.00 4,640.62 4,065.80 1989 1,438.14 4,331.01 3,600.50 1990 1,384.36 4,042.06 3,188.45 1991 1,332.60 3,772.38 2,823.56 1992 1,282.78 3,520.70 2,500.43 1993 1,234.81 3,285.81 2,214.27 1994 1,188.64 3,066.59 1,960.87 1995 1,144.20 2,861.99 1,736.46 1996 1,101.42 2,671.05 1,537.74 1997 1,060.24 2,492.85 1,361.76 1998 1,020.59 2,326.53 1,205.92 1999 982.43 2,171.31 1,067.91 2000 945.70 2,062.50 945.70 Costs are expressed in 1980 dollars. is made in succeeding years from 1980 to 2000, the discounted cost of photovoltaic systems are compared with the discounted energy cost of a conventional electric powered irrigation system. Economic feasibility is said to be established in the first year in which an investment in a photovoltaic system has a discounted cost less than the corresponding cost of a conventional electric powered system. From the above discussion it should be apparent that most of the technical variables entered into equation (9) such as the number of irrigations per year, and the overall irrigation strategy remain fixed over time. Given the variation in weather and other factors over time, it is highly unlikely that any of these technical variables are in fact constant. Similarly, escalation rates in electricity prices almost certainly vary from year to year rather than exhibiting some constant real rate of increase. However, when evaluating an investment over a considerable length of time, detailed information on the behavior of technical and economic variables can seldom be known with a high degree of certainty. In such circumstances, the decision maker must formulate expectations concernin g how factors affecting the investment decision will change over time. Within the present context, the fixed nature of the technical variables and rates of change in the economic variables can be construed as representing a given set of expectations. Thus, the economic feasibility criterion estimated in this component can be considered as based on various technical and economic expectations specified in terms of the simulation program's input variables. AN APPLICATION TO CITRUS IRRIGATION The simulation model was utilized to examine the economic feasibility of utilitizing photovoltaic arrays to power permanent overhead citrus irrigation systems in the Ridge area of central Florida.1 The initial investment year was varied from 1980 to 2000 assuming an investment life of 20 years. The choice of a permanent overhead type system rests mainly on the fact that about 90 percent of the acreage utilizing these systems 11Counties located in the Ridge area of Florida can be found in Stanley et al. [1980, p. 4]. use electricity to power the pump motor [Stanley et al., 1980]. A sample simulation program is presented in Appendix C. Economic and Technical Assumptions Utilizing data contained in Harrison [1978], a hypothetical per- manent overhead system irrigating 40 acres of citrus was modeled. Each irrigation application was defined as two acre inches (gross of water applied in a period of six days with the system operating 18 hours per day. A total of six applications per year was assumed (12 acre-inches per year) and held constant throughout the program. Assuming a total dynamic head of 250 feed [Stanley et al., 1980], the motor size necessary to power the system was estimated to be 32 HP. When in operation, the motor required a continuous electrical load of approximately 24 KWH/H. Based on the photovoltaic system design rules discussed previously, the array size necessary to power the irrigation system was calculated to be approximately 766 m2 (61KWP). Under average solar insolation con- ditions this system is estimated to produce about 89,865 KWH of electri- city annually. The estimated annual amount of electricity needed for' irrigation is approximately 15,510 KWH, yielding a net generation of electricity for resale to the utility of 74,355 KWH. Three basic economic scenarios were simulated for the irrigation system described above (Table 2). The scenarios (base, optimistic, and pessimistic) differ primarily on the basis of expectations regarding the rate at which the cost of photovoltaic systems declines over time and the real rate of increase in electricity KWH rates over time. The scenarios also differ in the degree to which economic and technical assumptions are amenable to establishing the economic feasibility of photovoltaic powered irrigation systems. For each of these scenarios the buy-back ratio linking the price of resale electricity to utility rates is varied from 0.25 to 1.5 in 0.25 increments. Simulation Results For each of the three economic scenarios presented in Table 2, a total of six simulations were run. This resulted in a total of 18 different model scenarios. In all but two cases, the discounted cost Table 2.--Economic model scenarios for the photovoltaic feasibility simulation Buy-back Discount Fuel escalation Scenario Target costs ratio rateb rateb ratio rate rate 1980: $10,750/KWP Base 1986; 4,740/KWP 0.25-1.50 .06 .06 2000: 945.79/KWP 1980: 10,750/KWP Optimistic 1986: 2,026.50/KWP 0.25-1.50 .06 .06 2000: 945.79/KWP 1980: 10,750/KWP Pessimistic 1986: 8,062.50/KWP 0.25-1.50 .06 .00 2000: 2,026.50/KWP aFor each scenario, the buy-back ratio is varied between these limits in increments of 0.25. The discount rate and annual rate of increase in electricity rates are expressed in real terms. of using photovoltaic arrays to power irrigation systems became less than the discounted cost of purchasing electricity for powering irriga- tion systems before the year 2000 (Table 3). Table 3.--Estimated first year in which photovoltaic irrigation systems are economically feasible Buy-back ratio Scenario 0.25 0.50 0.75 1.0 1.25 1.50 Optimistic 1990 1987 1986 1985 1985 1984 Base 1997 1985 1993 1992 1991 1990 Pessimistic 2000+ 2000+ 1998 1997 1995 1994 Simulation results for the optimistic scenario, which assumed a rapid decline in photovoltaic system costs and a significant increase in electricity rates, indicated the first year of economic feasibility could occur as early as 1984 if the buy-back ratio was 1.50. Generally, each increase of 0.25 in the buy-back ratio moved the initial year of economic feasibility toward the present by 1 to 2 years. Increasing the buy-back ratio from 0.25 to 0.50 changed the initial year of feasibility from 1990 to 1987 whereas increasing the buy-back ratio from 1.25 to 1.50 changed the initial year of economic feasibility from 1985 to 1984. The estimated differences in the discounted costs of photovoltaic powered and conventional electric powered systems assuming the investment is made in succeeding years from 1980 to 2000 are plotted in Figure 2 for several buy-back ratios. The base model scenario was characterized by a moderate decline in the cost of photovoltaic systems over time. Similarly, the annual increase in utility electric rates was also moderate, increasing at an annual real rate of 2 percent. As with the optimistic scenario, as the buy-back ratio increased, the first year of economic feasibility moved closer to the present. With the buy-back ratio at 0.25, the initial year of feasibility was 1997, whereas a buy-back ratio of 1.50 resulted in photovoltaic systems being economically feasible in 1990. In general, each 0.25 increase in the buy-back ratio moved the initial year of 1.25 $1,000 0 :------ *: l Year 84 8 92 96 2000 -100- -200- -300 -400- -500- -600- Figure 2.--Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for this optimistic scenario and selected by back ratios feasibility up to one to two years. Figure 3 plots the estimated differ- ence in the discounted cost of the two systems for each investment year beginning in 1980. A very slow decline in photovoltaic system costs characterized the pessimistic scenario. Furthermore, no real increase in utility electric rates was allowed. Under this scenario, the first year of economic feasibility for buy-back ratios of 0.25 and 0.50 does not occur until after year 2000. With a buy-back xatio of 0.75 the initial year of feasibility is 1998. The effect of increasing the buy-back ratio on the initial year of economic feasibility is similar to the preceding scenarios. Each 0.25 increase in the ratio moves the initial year of feasibility up by one to two years. For each investment year, the difference is dis- counted costs of the two systems under comparison is plotted in Figure 4. The importance of the cost behavior of photovoltaic systems over time can also be inferred from the results of the simulation. For given buy-back ratios, the base model cost projections result in initial feasibility occurring an average of five years sooner than if system costs follow the pessimistic cost projections. Similarly, optimistic cost projections result in the initial economic feasibility of photovoltaic systems occurring an average of six years sooner than if base cost pro- jections held. These results imply that the effects of commercializing the manufacture of photovoltaic arrays, and the ensuing cost declines, have a significant impact on when photovoltaic powered irrigation systems are economically viable. Overall, the results of the simulation model appear internally consistent. Changes in the buy-back ratio generally have the same effect on the initial year of economic feasibility for a wide range of changes in system costs over time. Furthermore, the effects of changing the cost projections for system cost generate similar responses in the initial year of feasibility for differing buy-back ratios. Because the analysis of these types of problems require considerable abstraction and assumptions in the absence of any statistical measures, such consistency is extremely significant in giving the above results considerable credence. 1.25 .75 S ; -1 Year 85 90 95 2000 Figure 3.--Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for the base scenario and selected by back ratios $1,000 400- -300' -400" $1,000 400 300 200 100' 01 -100. Figure 4.--Estimated differences in the discounted costs of photovoltaic powered and conventional electric powered irrigation systems for the pessimistic scenario and selected by back ratios 1.25 -.75 CONCLUSIONS Agricultural production in Florida is very energy intensive. Be- cause of this, the need to investigate means of countering the rising costs of energy are paramount. It appears that the solution to the problem rests in either altering production practices to utilize less energy with greater efficiency or finding alternative sources of energy which can be used in agricultural production activities. In .:egards to the latter possibility, the results of this analysis have shown photo- voltaic systems to have considerable promise as a means of providing electricity to power irrigation systems. The feasibility of utilizing photovoltaic systems for such purposes does not rest on the development of technology which can produce electri- city from sunlight. Adequate technology already exists. The results of the simulations have shown that the cost of producing these systems has a significant effect on when photovoltaic systems will be economically feasible. If commercial production of photovoltaic systems results in a rapid decline in cost, these systems will be economically feasible in the mid- to late 1980s. Tf however, commercial production is slow to develop or the cost of photovoltaic systems declines slowly, economic feasibility is not likely until the mid- to late 1980s. The cost of such systems is only one factor which will have an effect on when photovoltaic powered irrigation systems will be economi- cally viable. Institutional factors such as the buy-back ratio also have been shown to have a significant impact on when these systems will be economically viable. Decisions as to what rates utilities must pay for electricity generated and sold by small decentralized producers can change the first year of economic feasibility by as much as seven years. The analysis presented here i not to be construed as definitive in concluding that the use of Elhtovoltaic arrays to power irrigation systems is a future certaiti: The promise of these systems, based on the preceding results, is considerable. However, energy costs and technological impediments may prevent photovoltaic irrigation systems, or even irrigation as a cultivation practice, from being justified as a sound economic practice in agricultural production, REFERENCES Anaman, Jehu Asomanin. 1981. "Optimal Irrigation Strategies for 'Valencia' Citrus Crop in Florida." Unpublished MS. thesis, Food and Resource Economics Department, Univ. of Fla. Cheremisinoff, Paul N. and Thomas C. Regino. 1978. Principles & Appli- cations of Solar Energy. Ann Arbor: Ann Arbor Science Publishers, Inc. Harrison, Dalton S. 1976. Energy Management in Irrigation. Univ. of Fla. Coop. Ext. Svc. Energy Conservation Fact Sheet EC-12. 1978. Irrigation Systems for Crop Production in Florida. Univ. of Fla. Water Resource Council Bulletin WRC-8. and Rush E. Choate. 1969. Selection of Pumps and Power Units for Irrigation Systems in Florida. Univ. of Fla. Coop. Ext. Sve. Cir. 330. Katzman, Martin T. and Ronald W. Matlin. 1978. "The Economics of Adopt- ing Solar Energy Systems for Crop Irrigation," American Journal of Agricultural Economics 60(Nov.): 648-654. Litka, Arthur, Robert Walker, Mukesh Khattar and Craig Maytrott. 1981. "The FSEC Photovoltaic Residence: Initial Operational Performance." Paper presented at AS/ISES Meeting, May 26-30, 1981. Milon, J. Walter. 1981. "Alternative Energy Systems and Electric Rate Reform," Public Utilities Fortnightly (June 4): 15-20. Norman, Collin. 1981. "Renewable Power Sparks Financial Interest," Science 212(June 26): 1479-1481. Pair, ClaudeH., Walter W. Hinz, Crawford Reid, and Kenneth R. Frost. 1975. Sprinkler Irrigation. Silver Springs, The Irrigation Association. Smith, Jeffrey L. 1981. "Photovoltaics," Science 212(June 26): 1972- 1978. Stanley, James M., Clifton Taylor, William R. Summerhill, Jr. and Lionel J. Beaulieu. 1980. "Citrus Energy Survey-Use Estimates and Con- servation." Univ. of Fla. IFAS Energy Report No. 2. U.S. National Climatic Center. 1980. "Hourly Solar Radiation Surface Meteorological Observation." Solmet Users Manual, Vol. 1-~TD-9724). APPENDIX A PHOTOVOLTAIC SYSTEMS Photovoltaic systems convert the energy in sunlight to electrical energy. This conversion is accomplished by using "solar cells" which are semiconductors constructed of cadmium or silicon. While a single solar cell can produce only a small amount of electricity, these cells may be interconnected to form large photovoltaic arrays capable of producing a considerable amount of electrical energy [Cheremisnoff and Regino, 1978]. Figure A-1 presents a basic schematic diagram of a photovoltaic system which is being used to power an irrigation pump motor. When sunlight (solar insolation) is received on the photovoltaic array (solar cells) a direct current (DC) of electricity is produced. This DC electricity is fed into an inveter which transforms the electri- city from DC to alternating current (AC). The inverter also upgrades the waveform of electricity produced by the array to be compatible with the utility grid current and regulates current flows. During periods when the electricity demand of the pump motor is greater than array output, the inverter feeds supplemental power from the utility to the pump motor. During periods when array generation exceeds the pump motor demand, surplus electricity is routed into the utility grid. Becuase photovoltaic systems rely on solar insolation to produce electricity, the output of these systems will vary with the movement of the sun both hourly and seasonally. Figure A-2 presents the average hourly insolation for a solar day. The insolation profile shown in this figure was estimated using the Orlando/Herndon Solmet Data [National Climatic Center, 1980]. On average, a positive level of solar insolation (KWH/m2) occurs between solar hours 6 and 19. This however varies seasonally. As would be expected, the greatest insolation levels occur at solar noon. The shape of the insolation curve shown in Figure A-2 demonstrates why an array with no electricity storage capabilities must use supple- mental electricity purchased from the utility at certain times. Assume that operation of the pump motor requires an array output of electricity equivalent to .35 KWH/m2 of array. It can be seen that array output per m is below this level during several hours of the day. During per m is below this level during several hours of the day. During A.C. KWH D.C. ELECTRICITY METER TO/FROM AC A.C. TO PUMP INVERTER I UTILITY ELECTRICITY ELECTRICITY MOTOR Figure A-1.--Simplified schematic or a photovoltaic powered irrigation system 0.9 0.8 0.7 Maximum 0.6 0.5- 0.4 - Mean 0.3 0.2 0.1- Minimum 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Solar hour Figure A-2.--Mean, minimum and maximum hourly solar insolation levels for Orlando/Herndon airport 32 these time periods, electricity must be purchased to supplement the array output. During the remaining time periods the array output is greater than required to power the pump and the surplus power is sold to the utility grid. Furthermore, when no irrigation occurs, the entire output of the photovoltaic system can be sold to the utility grid. Given the intermittent nature of irrigation, a substantial amount of surplus electricity can be generated and sold to the utility grid. APPENDIX B CALCULATION OF PHOTOVOLTAIC SYSTEM COSTS AND ELECTRIC PRICES Photovoltaic system cost is calculated for a 20 year time period. Cost is expressed in terms of $1980 per peak Kilowatt (KWP). The pro- gram contains three distinct cost scenarios representing different rates and magnitudes of array cost declines. All scenarios have a 1980 base cost of $10,750/KWP. The "pessimistic" cost scenario assumes that cost decreases will come about very slowly, with costs declining less than 25 percent by 1986. Under this scenario, array cost is estimated by using a spliced exponential function CKWPT(t) = d* 10750*EXP(-0.0479*(t-1)) + (1-d)*8062.5*EXP(-0.069 *(t-1)) (Bl) where CKWP(t) = estimated photovoltaic systems cost ($/KWP) in year t and d is a Kronecker Delta equal to 1 for t < 7 and 0 for t > 7. Thus, the splice occurs in 1986 (t=7). The "optimistic" cost scenario is also estimated by using a spliced exponential function. This scenario assumes a rapid and significant de- cline in photovoltaic system costs. By 1986, system cost is assumed to decline by more than 75 percent. The estimated equation for this scenario is given by CKWP(t) = d*10750*EXP(-0.2781*(t-l)) + (1-d)*2026.5*EXP(-0.0381* (t-1)) (B2) where all terms are defined as above. The third cost scenario is characterized by a moderate decline in the cost of photovoltaic systems. This scenario is moderate in that it is approximately mid-way between the above two rather extreme cost pro- jections. The moderate photovoltaic system cost decline is approximated by the exponential function CKWP(t) = 10750*EXP(-0.1215(t-1)) (B3) where all terms retain their previous definitions. For all cost scenarios the total system cost is estimated by multiplying the estimated cost per PKW by peak kilowatt rating of the system. The cost of electricity purchased from the utility C$/KWH) was estimated over a 40 year time period (1980-2020). This was also true for the rates utilities are required to pay for electricity produced and sold by dispersed systems. Since this price is tied to utility rates via the buyback ratio, it is only necessary to discuss the estimation of the former prices. The 1980 base price used in estimating future utility KWH rates is $.03604/KWH. This rate is assumed to correspond to the off-peak KWH charge for electricity. Estimation of KWH rates was accomplished using the exponential function PB(t) = 0.03604*EXP(n(t-1)) t = 1,...,41 (B4) where PB(t) = Estimated price per KWH of electricity in year t n = Annual (real) rate of escalation in utility KWH rates. As with the system cost estimates, all future estimates of the utility KWH rates are expressed in term of $1980. This appendix has presented the basic equations used to estimate future photovoltaic system costs and electricity prices. The interface of these equations with the user specified input variables and other model components is depicted in the sample program contained in Appendix APPENDIX C SAMPLE SIMULATION PROGRAM C THIS PROGRAM CALCULATES THE NET PRESENT VALUE OF INVESTING IN A SCLAR C PHCTOVCLTAIC POWERED IRRIGATION SYSTEM IN YEAR J. THIS VERSION OF THE C PFOGRAA CONSID=ES MAKING TH;- INVESTMENT IN EACH YEAR FROM 1990 TO C YEAR 2000. THERE ARE TWO SETS OF VARIABLES WHICH MUST BF SPECIFIED BY C THE USER: I RRI';ATION SUBMO EL VARILLES AND ECONOMIC VALUATIfN C SUSMCDEL VAfIA.LES C THE IRRIGATION SJROODEL VARIABLES ARE: C AI=INCH=S OF VATER APPLIED PER IRRIGATION (GROSS) C A=TOTAL ACRES TO 9E IRRIGATLD C H=HCURS PER CAY IN NHICH IRRIGATION OCCURS C D=0AYS TO COMPLETE ONE IRRIGATION (THIS SHOULD NOT EXCEED 75 C PERCENT OF THE IRRIGATION FREQUENCY) C TOH=TCTAL DYNAMIC HEAD GF THE SYSTEM (FEET) C TIR=NUMqER OF IRRTATTIONS PER YEAR. C THE ECONOMIC SU3MODEL VARIABLES ARE: C PRB=9ASE OF PERIOD MARKET PRICE OF ELECTRICITY (DOLLARS PER KWH) C ASSUMING TIME OF DAY UTILITY RATES. IN THIS PRCGPAM. PRB IS A C WEIGHTED AVERAGE PRICE OF THE PEAK AND OFF PEAK RATES. C R=DISCOUNT FACTOR C BR=EJY BACK CONSTRAINT OF PRGP3OTIONALITY FOR ELECTRICITY RESCLD TO C THE UTILITY GRID C TU=EXPECTED LLNG TERM ESCALTION RATE (ANNJAL) OF KWH CHANGES. C Z=AERAY COST OUTLOOK. Z=I IMPLIES A PESSIMISTIC VIEW. Z=2 C IMPLIES AN OPTIMISTIC VIEW(D.O.Ee PROJECTIONS). Z=3 OEONOTES C A MCCERATE COST DECLINE. 1 INTEGER Z 2 DIMENSION PK'P(21).PR(41)*P3(41),VRS(41A)TPE(41I) I FV(21)TAC(21) C ENTER TME USER SPECIFIED VARIABLES AT THIS POINT 3 Z=2 4 AI=2 5 A=40 6 H=13 ? D=6 E TDH=250 TIR=6 10 PrSB=.006 11 R=.06 12 BR=I.5 13 TL=.06 14 DC 5 1=1.21 15 PV(I)=0.. 16 5 CONTINUE C THIS PCRTICN OF THE PROGRAM DEFINES THE PHYSICALL SYSTEM DESIGN CN THE C BASIS CF SIMPLE ENGINEERING EQUATIONS GIVEN IN HARRISON AND CHOATE C (196 ) AND UTILIZED THE ORLANOO/HERNOCN SOLMET DATA TAPE. C THE PUMPING RATE IN GALLONS PER MINUTE IS GIVEN HY 17 GFM=(453*(AI)*(A))/((ll)*(D)) C THE CCNTINUCUS 3RAKE HORSEPOWER REQUIRED IS CALCULATED BY 1S BHFC=((GPM)(TDH))/2613.6 C THIS CALCULATICE ASSUMES A PUMP EFFICIENCY CF .75 AND MOTOR C EFFICIENCY OF -55. C THE CCTINrUOUS Kd DEMAND OF THE MOTOR IS GIVEN BY A1 CKW=.7457*3H0C C THE FCLLC.ING EQUATIONS CALCULATE THE PV ARRAY SIZE AND KWP C RATING. THE CALCULATION IS: AZ(4**2)=(I/0.03143)-CKWe* C THIS IS EQUIVALENT TO AZ=31.7L(2e*CKW. C (NQTE:SYSTEM EFFICIENCY IS ASSUMED TO BE 0.069). 20 AZ=Z1.7662*CKW 21 PKW=AZ/12.5 C THE FCLLC#ING EQUATIONS CALCULATE TOTAL ARRAY OUT'UT (TAO) C (KWH). ELECTRICITY UTILIZED FOR INRIGATION(EDIR) AND NET ARRAY C GENERATION FOR RESALE TO THE UTILITY GRID (AQN) 22 TAO=113.194?*AZ C NOTE: ANNUAL ARRAY GENERATION IS 116.1949KWH/(M*m*.). 23 EDI= (CKdI*r()f(D)*(TIRj 24 ACN=TA3-EDIR 25 P 'IT 1OS5 26 105 FCFMAT(5X. 3HGPMF.5X.HHtHPC.9X3MHCKWg9X2HAZ.IOX,3HPKW,9Xs3TAQ) 27 WRITE(6, 1 04) O;nM HPC.CKW AZ.PKW.TAQ 2d 104 FCFuAT(FL3.2,2X.F10.2.2Xe.F 1.2.ZA.FIO.2.2X.rlo.22X.FIO.2e2XI 21 P ['RI1TI05 39 106 FCl'.AT (4X, HE IRGX, 3HAQNI 31 FRITE(6.1 7) EDIR.AON J2 IC7 FCRV4T(F103.2.2X.FL0.2.2X) C THE FCLLC'I:IG STATEMENTS GErNERATE THE ARRAYS UTILIZED IN THE C ECONOMIC VALUATION' PORTION iF THE POGCRAYM 33 GC TO(50.60.701.Z 34 50 DC 100 J=1.2t 35 IF(J.LE.7))=2 36 IF(J.GT*7ID=O 37 rpJ-1 38 PKI (J) a( D*10750EXP( -0. 047947*M I 9 (-0)8062.5*EXP(-0.069047M*4)) 100 TAC( JI=PKW*PKWP(J) CC TO 500 60 DC 200 J=t.21 IF(J.LE.7)0D= IF(J.GT.7 )0=0 s= J- PKP ( J )=(010750*EXP(-0.278099*M)) 1 *( -0D)(206.5XP(-O.028 107*M) ) 200 TAC( J)=lPKk*PKWP(J GC TO 500 70 DC 300 J=1.21 M=J-l PKPI( J )-L0750*EXP(-0.125 37*M) 300 TAC(J)=PK 'PKWP(J) 500 CCNTINU. DC 101 1=1.41 N=I-L PR(2)-PRB*9'R *EXP(TU*N) 101 V.SCZI)=AONPR(Z) 00 102 1=141 PB( I =0.03604*EXP(TU*N 102 TPE(I)=EDIqaoB([) C THE FCLLC'ING SECTION COMPUTES THE NET PRESENT VALUE CP AN INVESTMENT C IN YEAR J. CC 110 J=1.21 K=J+20 DC 120 I=1.K L=J-I Pi(J)=PV(J)+(((I+RI**L)*(VRS(I)+TPE(l))) 120 CONTINUE PV(J)=PV(J)-TAC(J) 110 CONTINUE PR INT 103 108 FCFMAT(2Xl1HJ 6X.4HPKWP.9Xe3HTAC.9X2MHPV) 00 109 J=1.21 109 tRITE(6,11)t J.PKWP(J).TAC(J);PV(J) 111 FC;MAT(2X. 12o IXFIO.22ZX.FOe.2.2XeFIO.2s2X) PRItNT 112 112 FCFMAT(2X. HI e7X2HPR O1Xe.2HPB DO 113 1=1.41 113 w;ITE(6.l14) I. PR(I).PB(I) 114 FCRMATI2Xo.l2.IX.FIt.62XeF10.6) STCP EhO SENTRY GPSM 335.36 EOIR 15509.71 J PKWiD I 13750.( S2 8140.1 3 6163. 4 4667 .4 5 3534.; 6 2670.2 7 2026.! 8 1552.( 9 1494. 10 143. 1 11 13a4.J 12 1332 ( IJ 1232.7 14 123J41 15 11893. 16 1144. , 17 1131 3 . Is8 104U0.2 19 1020. 20 932.4 21 945.7 i PR I 0.0*09C 2 0.0646t J 0.0686< 4 0.07291 t 0.07741 6 .3 1220 7 0.0372; 8 0.026t ) 0 .9134 e,-Pc 32.10 ACN 74355.69 TAC )0 653871.30 3 495125.80 19 374920.10 3 283897.60 2! 214973.60 !4 162782.70 i0 123262.60 )3 ;4402.38 >0 90872.69 4 e7474.94 16 84204.25 60 81035.81 '8 7eo25.13 :1 75107.81 .4 7229~.50 !0 695;6. 19 12 b6;94.00 t4 644-39.12 i9 62077. a .1 59756.77 *0 57522.47 Po 10 0 031040 6. 0.013269 .5 0.040635 0 0.0411413 9 0.0458S16 16 0.043649 >0 0.051657 17 0 054591 9 0*058243 CKW. 23.93 AZ 760.32 PKW TAQ 60.83 89865.44 PV -545163.30 -374333.10 -240 15.50 -135547.70 -51027.31 18108.38 76030 .3J 124364.03 1500C0.60 176951.60 205683.30 236415.10 2693J13.43 304559.70 342346 .0 332682.10 426387.50 473099.80 523274.40 577183.50 635119.40 41 1C 0.104505 0.061845 11 3.110S67 0.065669 12 0.1i1729 0.069730 13 0.125115 0.074042 14 0.132552 0.073620 15 C.141067 0.033432 lu 0.149790 0.0Sd644 17 0.159052 0.094126 Id 0.168687 0.099946 19 3.179331 0.136126 20 0.1,0420 0.112659 21 0.2J2195 0.11S657 22 0.214698 0.127056 23 0.227974 0.134913 24 0.242071 0.143255 ? 0.257040 0.152114 26 0.272;35 0.161520 27 0.23)812 0.171508 28 0.307733 0.132113 29 0.326762 0.1;3374 30 0.346968 0.205332 31 0.363423 0.213029 32 0..391205 0.231511 33 0.415356 0.245e27 34 0.4410 3 0.261028 35 0.463358 0.277169 36 0.497319 0.294309 37 0.528C72 0.212508 s3 0.560726 0.331832 39 0.595400 0.352351 40 0.632217 0.374139 41 0.671311 0.397275 STATEMENTS EXECUTED= 2527 CORE USAGE CBJECT COOE= 3680 BYTESeARRAY AREA= 908 BYTESTOTAL AREA DIAGNOSTICS bUM8ER OF ERRORS= O0 NUMBER OF WARNINGS= O NUMBER COMPILE TIME= 0.05 SEC.EXECUTION TIMEa 0.05 SEC. .1034.19 TUESDAY CsSTOP Copies of this program are available from the authors on request. |