Realistic generation cost of solar photovoltaic electricity

lable at ScienceDirect

Renewable Energy 35 (2010) 563–569

Contents lists avai

Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Realistic generation cost of solar photovoltaic electricity

Parm Pal Singh*, Sukhmeet SinghSchool of Energy Studies for Agriculture, Punjab Agricultural University, Ludhiana, Punjab – 141004, India

a r t i c l e i n f o

Article history:Received 2 March 2009Accepted 26 July 2009Available online 1 September 2009

Keywords:Solar photovoltaic economicsSolar electricity priceGraduated payment loanLevelized costVariable costSPV electricity generation cost

* Corresponding author. Tel.: þ91 1612401960–fax: þ91 1612402456/2404604.

E-mail address: [email protected] (P.P. Sin

0960-1481/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.renene.2009.07.020

a b s t r a c t

Solar photovoltaic (SPV) power plants have long working life with zero fuel cost and negligible main-tenance cost but requires huge initial investment. The generation cost of the solar electricity is mainly thecost of financing the initial investment. Therefore, the generation cost of solar electricity in differentyears depends on the method of returning the loan. Currently levelized cost based on equated paymentloan is being used. The static levelized generation cost of solar electricity is compared with the currentvalue of variable generation cost of grid electricity. This improper cost comparison is inhibiting thegrowth of SPV electricity by creating wrong perception that solar electricity is very expensive. In thispaper a new method of loan repayment has been developed resulting in generation cost of SPV electricitythat increases with time like that of grid electricity. A generalized capital recovery factor has beendeveloped for graduated payment loan in which capital and interest payment in each installment arecalculated by treating each loan installment as an independent loan for the relevant years. Generalizedresults have been calculated which can be used to determine the cost of SPV electricity for a given systemat different places. Results show that for SPV system with specific initial investment of 5.00 $/kWh/year,loan period of 30 years and loan interest rate of 4% the levelized generation cost of SPV electricity withequated payment loan turns out to be 28.92 ¢/kWh, while the corresponding generation cost withgraduated payment loan with escalation in annual installment of 8% varies from 9.51 ¢/kWh in base yearto 88.63 ¢/kWh in 30th year. So, in this case, the realistic current generation cost of SPV electricity is9.51 ¢/kWh and not 28.92 ¢/kWh. Further, with graduated payment loan, extension in loan period resultsin sharp decline in cost of SPV electricity in base year. Hence, a policy change is required regarding theloan repayment method. It is proposed that to arrive at realistic cost of SPV electricity long-termgraduated payment loans may be given for installing SPV power plants such that the escalation in annualloan installments be equal to the estimated inflation in the price of grid electricity with loan period closeto working life of SPV system.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Solar photovoltaic (SPV) electric power generation is a prom-ising clean technology with vast potential. The technical feasibilityof solar photovoltaic (SPV) electricity is well established but thereare questions about its economical competitiveness with gridelectricity. The SPV power plant requires very high initial invest-ment as compared to conventional thermal power plant. It istherefore necessary to determine whether such an investment iseconomically feasible. The economic feasibility of SPV electricityproject has been determined by performing economic analysisbased on several figures of merit such as payback period, net lifecycle savings, internal rate of return (IRR), net present value (NPV),

78x278, þ91 9464366722;

gh).

All rights reserved.

etc. [1–10]. The payback period for SPV electricity projects turns outto be quite long but payback period has important drawback that itignores the cash flows after the payback period [3,10]. The othereconomic indicators such as net life cycle savings, internal rate ofreturn and net present value do not suffer from the drawback ofpayback period. These economic indicators indicate that SPV elec-tricity projects are close to being economically feasible. However,economic feasibility is not enough to sell the product commercially.The price of a product at given time is more important consider-ation [11,12]. A consumer will not buy expensive SPV electricitynow though it may be cheaper or even free later on.

For SPV electricity the major portion of generation cost is thecost of financing the huge initial investment as the fuel cost is zerowhile operating and maintenance costs are quite small. The loantaken for initial investment can be returned by different methodse.g. equated payment loan, graduated payment loan, etc. Theamounts of installments in different years depend on the loan

Nomenclature

Cg(n) generation cost of SPV electricity for nth year withgraduated payment loan ($/kWh)

Crf capital recovery factor for equated payment loanCrfg generalized capital recovery factorCs specific initial investment ($/kWh/year)e escalation in annual loan installment (%)Es specific electric output of SPV panel at a given place

(kWh/kWp-year)Eu electric output per year at a given place (kWh/year)i interest rate (%)L loan repayment period (years)Pl(n) loan payment/installment for nth year ($)Pr price of SPV system per unit rated capacity ($/kWp)Rc rated capacity of the SPV system (kWp)r common ratio of geometric progression

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569564

repayment method. The generation cost of SPV electricity in a givenyear is equal to the installment of loan repayment in that yeardivided by the annual number of units (kWh) of electricity gener-ated. Most common method of loan repayment is the equatedpayment method. With this method the annual loan payment foreach year during long loan payment period of 20–30 years remainssame resulting in levelized generation cost for SPV electricity [1].

The levelized generation cost for SPV electricity for residential,commercial and industrial applications has been calculated basedon current prices of solar PV system [13]. The financing cost hasbeen assumed as 5% per annum and costs are amortized over 20years. For September 2008, for installed industrial system of500 kWp with initial investment of 4963.9 $/kWp, the cost of SPVelectricity turns out to be 21.39 ¢/kWh for sunny climate (5.5average sun-hours at standard intensity) and 47.06 ¢/kWh forcloudy climate (2.5 average sun-hours at standard intensity). Onthe other hand for small residential PV systems (2 kWp) the initialinvestment is higher at 9023.5 $/kWp and the cost of SPV electricityturns out to be 37.77 ¢/kWh for sunny climate and 83.09 ¢/kWh forcloudy climate. The cost of commercial systems is in between theindustrial and domestic systems. In this way the current price ofSPV electricity in USA is stated to be 4–5 times that of grid elec-tricity. However, It may be noted that the price of SPV electricitywill be same even in 20th years while the cost of grid electricity willincrease many folds by that time due to increased fuel costs. Furtherthese results show that the initial investment required for largeindustrial level plants is only 55% of the initial investment requiredfor small domestic systems, so it is better to install large industriallevel solar PV power plants. Obviously as far as possible the solar PVpower plants should be installed in regions with sunny climate.

The cost of electricity generated by solar PV system has beencalculated as a function of initial investment and specific output[14]. Results have been calculated by levelized cost method byassuming cost of financing as 10% and loan period of 20 years. Thecost of SPV electricity is given in tabular form for initial investmentranging from 200 to 5000 $/kWp and specific output from 800 to2400 kWh/kWp-year. It has been mentioned that normally PVmodules have 25-year warranty but they should be fully functionaleven after 30–40 years. This means that SPV electricity generatedafter the loan repayment period of 20 years will be free and this freeelectricity is not accounted for in the cost analysis resulting inunrealistic higher cost of SPV electricity.

Feed-in Tariff for SPV electricity introduced by Germany andfollowed by few other countries are also based on levelized costmethod [14]. Germany is offering 20-year flat rate contract at 51.8–

56.8 V-¢/kWh. Here also SPV electricity generated after 20 yearswill be free of cost and unaccounted for.

The generation cost of electricity from solar thermal powerplant named Andasol 1 has been calculated [15]. It is reported thatthe cost per unit capacity is not enough as solar systems havedifferent output at different places. It is suggested that the first stepin the calculation is to determine the investment for the productionof 1 kWh in a year. For this project total investment is V 310 millionand output is 179 GWh a year resulting in the investment of V 1.73per kWh output per year. Similar term named ‘specific initialinvestment’ has been used in the current paper also as it helps toobtain generalized results. Although the investment for one kWh/year production is suitable for comparing the price of different solarpower plants, it does not give the price per kWh yet. The way offinancing has a great influence on the final price. The capitalrecovery factor for loan period of 25 years and interest rate of 7%turns out to be 11.65 resulting in levelized generation cost of SPVelectricity of V 0.15 per kWh. If the operation and maintenance costof one-cent is added, then the levelized cost is V 0.16/kWh. It issuggested that effect of inflation on cost needs to be considered anddifferent ways of loan repayment should be explored. However, nosolution has been provided. In the current paper a different methodof loan repayment has been developed which takes into accountthe effect of inflation on electricity cost.

The above literature review indicates that basically there aretwo discrepancies in the calculation of generation cost of SPVelectricity. The first discrepancy is that due to use of levelized costmethod based on equated payment loan the cost of SPV electricityremains static during long loan repayment period of 20–30 years.However, during the same period the cost of grid electricity willincrease many folds due to increase in fuel cost. In other words, ascompared to grid electricity the levelized cost of SPV electricitytends to be high at the time of installation though it may be cheaperlater on. The second discrepancy is that loan is given for the guar-antee period and not working life of SPV system. So the SPV elec-tricity tends to be free of cost after the loan repayment period tillthe end of working life of SPV system and this fact is not accountedfor in the cost calculations. In this paper a method of long-termvariable installment loan has been developed to determine realisticgeneration cost of SPV electricity that increases with time like thatof grid electricity.

2. Theoretical basis

2.1. Specific initial investment

The rated capacity of solar photovoltaic (SPV) system for powergeneration in kWp is the electric output of SPV panels understandard conditions. Solar photovoltaic system of a given ratedcapacity installed at different places gives different amount ofannual electric output (kWh/year) due to variations in solar irra-diation on SPV panels, ambient temperature, dust, etc. The designfeatures such as adjustment in inclination of panels, use of suntrackers, use of concentrators, etc. also affect the electric output. Totake all these factors into account a term ‘‘specific electrical output’’of the system is defined [14]. The specific electric output is theannual electric output of SPV system at a given place per unit ratedcapacity of the system (Equation (1)).

Es ¼ Eu=Rc (1)

Where

Es¼ specific electric output of SPV panel at a given place (kWh/kWp-year)

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569 565

Eu¼ units of electricity generated per year at a given place(kWh/year)Rc¼ rated capacity of the SPV system (kWp)

A term called ‘‘specific initial investment (Cs)’’ has been definedas the ratio of price of SPV system per unit rated capacity (Pr) tospecific electric output (Es) at a given place (Equation (2)).

Cs ¼ Pr=Es (2)

Where

Cs¼ specific initial investment ($/kWh/year)Pr¼ price of SPV system per unit rated capacity ($/kWp)

In other words, the specific initial investment is the initialinvestment required to install a SPV system capable of generatingone unit of electricity (kWh) per year throughout the working life ofthe system at a given place. So specific initial investment is locationspecific.

2.2. Payment of loan

A series of annual loan payments or installments (Pl(n)) aremade to pay off the loan taken to install SPV power plant. Theannual loan payments escalate with time. Though any value can beused for rate of escalation of loan payment, however, for realisticcost comparison with grid electricity, it is better to take escalationin annual loan payments (e) equal to the projected average inflationrate of grid electricity. Assuming the annual loan payment is madeat end of each year, the value of nth loan payment (Pl(n)) is given byEquation (3).

PlðnÞ ¼ Plð1Þð1þ eÞn�1 for n ¼ 1 to L (3)

Where

e¼ escalation in annual loan installment (%)L¼ loan repayment period (years)

Each annual loan installment to pay off the loan may beconsidered as an independent loan for the relevant years i.e. theloan may be assumed to be split into series of independent loans. Inother words, the annual payment for nth year may be considered asone time payment of loan taken for n years. So the loan payment innth year, Pl(n), will consist of some principal (P(n)) and interest onthis principal for n years at specified interest rate (i). It has beenassumed that the annual loan payment is made at the end of eachyear because then one can earn money by selling SPV electricityand make payment from the earnings. The amount of principle(P(n)) and interest (I(n)) paid in the nth loan payment (Pl(n)) can bedetermined from Equations (4) and (5) respectively. If the loanamount is equal to the specific initial investment (Cs) then theannual installment for nth year (Pl(n)) will be the cost of SPVelectricity in nth year.

PðnÞ ¼ PlðnÞð1þ iÞn

(4)

IðnÞ ¼ PlðnÞ � PðnÞ (5)

The loan amount (Cs) is equal to the summation of the principlespaid back in each annual loan payment for L years (Equation (6)).

Cs ¼Plð1Þð1þ iÞ þ

Plð2Þð1þ iÞ2

þ Plð3Þð1þ iÞ3

þ/þ PlðLÞð1þ iÞL

(6)

Using Equation (3) in Equation (6), we obtain

Cs ¼ Plð1Þð1þiÞ

�1þ ð1þ eÞð1þ iÞ þ

ð1þ eÞ2

ð1þ iÞ2þ/þ ð1þ eÞL�1

ð1þ iÞL�1

!orCs ¼ Plð1Þ

ð1þiÞ�1þ r þ r2 þ/þ rL�1

� (7)

where

r ¼ 1þ e1þ i

(8)

It may be noted that Equation (7) is similar to that for determiningpresent worth factor for series of inflating fuel payments [9].Present worth factor is inverse of the generalized capital recoveryfactor.

Now, Equation (7) is a geometric progression and using therelation for summation of geometric progression [16], we obtain;

Cs ¼Plð1Þð1þ iÞ

�1� rL

1� r

�(9)

Equation (9) can be rewritten in terms of generalized capitalrecovery factor (Crfg).

Plð1Þ ¼ ðCsð1þ iÞÞ�

1� r1� rL

�¼ CsCrfg (10)

where

Crfg ¼ ð1þ iÞ�

1� r1� rL

�(11)

Knowing the value of loan payment in base year (Pl(1)) fromEquation (10), the value of loan payment for nth year for graduatedpayment loan can be determined from Equation (3). If the principalof the loan is equal to the specific capital investment (Cs) thengeneration cost of SPV electricity for nth year (Cg(n)) is equal to thenth loan payment and can be obtained from Equation (12).

CgðnÞ ¼ CsCrfgð1þ eÞn�1 (12)

It may be noted that the capital recovery factor (Crf) used forequated payment loan is a particular case of generalized capitalrecovery factor (Crfg). For equated payment loan new value of r isobtained from Equation (8) by putting escalation in annual loanpayment (e) equal to zero. Then capital recovery factor for equatedpayment loan (Crf) is obtained by substituting this new value of r inEquation (11).

Crf ¼i

1� ð1þ iÞ�L (13)

In other words, the value of capital recovery for equated paymentloan can be obtained from Equation (11) by putting ‘e’ equal to zeroor Equation (13).

The sale price of SPV electricity for a given year may be deter-mined by adding O&M cost, insurance, profit, etc. to the cost ofgeneration calculated above.

3. Results and discussion

The first step in the calculation of generation cost of solar PVelectricity is to calculate the specific initial investment (Cs) of solarphotovoltaic (SPV) power plant for different values of specificelectric output (Es) and price of SPV power plant per unit ratedcapacity (Pr) using Equation (2). The results are shown in Fig. 1. Thecurves of Fig. 1 can be used to determine the value of specific initialinvestment required to install SPV system capable of generating

0

2

4

6

8

10

12

14

16

18

20

0 1000 2000 3000 4000 5000Es (kWh/kWp-year)

Cs

($

/kW

h/y

ea

r)

Pr=6000 $/kWpPr=8000 $/kWpPr=10000 $/kWpPr=12000 $/kWpPr=14000 $/kWp

Fig. 1. Specific initial investment (Cs) vs specific electric output (Es) for different valuesof cost of SPV system/kWp (Pr).

L=30 years

0

0.02

0.04

0.06

0.08

0.1

0.12

0% 5% 10% 15%i (%)

Crfg

e=0%e=2%e=4%e=6%e=8%

L=40 years

0

0.02

0.04

0.06

0.08

0.1

0.12

0% 5% 10% 15%

i (%)

Crfg

e=0%e=2%e=4%e=6%e=8%

L=20 years

0

0.02

0.04

0.06

0.08

0.1

0.12

0% 5% 10% 15%i (%)

Crfg

e=0%e=2%e=4%e=6%e=8%

a

b

c

Fig. 2. Generalized capital recovery factor (Crfg) vs different interest rate (i) fordifferent values of escalation rate in annual loan installments (e) for three loan periods(a) 20 years (b) 30 years (c) 40 years.

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569566

one unit of electricity per year. The value of specific initial invest-ment varies from 1.5 to 17.5 $/kWh/year for different values ofspecific electric output (800–4000 kWh/kWp-year) and priceof SPV system (6000–14000 $/kWp). For example, the current priceof SPV system in India is about 8000 $/kWp and specific output is1200 kWh/kWp-year, so in this case the specific initial investmentturns out to be 6.67 $/kWh/year. This means with investment of$6.67 in SPV system one unit (kWh) of electricity will be generatedduring each year of working life of the system.

The value of specific initial investment helps to determine theinitial investment required to generate given amount of electricityat a given place. Also it can be used to compare the initial invest-ment required for SPV systems with different types of solar cells.The specific electrical output of SPV system per unit rated capacity(Es) may be enhanced by using sun tracker, concentrator, etc. Thiswill result in increased price of system per unit rated capacity (Pr)also. Then new value of specific initial investment (Cs) may becalculated from Fig. 1 to determine if the increase in output iseconomically beneficial or not. Hence, the specific initial invest-ment accounts for investment related expenses which depend onthe type of solar cell panels used, use of sun tracker, use ofconcentrator, solar radiation level at a given place, etc. It may benoted that specific initial investment can also be used to comparedifferent renewable energy systems e.g. hydro-power plant, windenergy system, SPV system, etc.

The second step is to determine the values of generalized capitalrecovery factor (Crfg) for different loan conditions using Equation(11). The generalized capital recovery factor accounts for factorsrelating to cost of financing i.e. loan interest rate (i), escalation inannual loan payments (e) and loan period (L). The results are shown

in Fig. 2 (a,b,c) for loan period of 20, 30 and 40 years respectively. Ineach of these figures, the generalized capital recovery factor hasbeen plotted for graduated payment loan for different values ofloan interest rate (0–10%) and escalation in annual loan payments(0–8%). For 20-year loan period the generalized capital recoveryfactor varies from 0.021852 to 0.11746 as the loan interest ratevaries from 0% to 10% and escalation in annual loan payments from0% to 8%. The corresponding range of generalized recovery factorfor 30 and 40 year loan period is 0.008827–0.106079 and 0.00386–0.102259 respectively. It may be noted that the curve for zeroescalation in annual loan payments (e¼ 0%) gives the value ofcapital recovery factor (Crf) for equated payment loan. The lowervalue of generalized capital recovery factor (Crfg) is better as itresults in lower generation cost of SPV electricity in the base year. It

Table 1Generation cost of SPV electricity during each year of loan period for loan repaymentperiod (L) of 20, 30, 40 and 50 years for specific initial investment of 5 $/kWh/year,loan interest rate of 4% and escalation in loan installments of 8%.

Year Generation cost of SPV electricity with graduated payment loan(¢/kWh)

L¼ 20 year L¼ 30 year L¼ 40 year L¼ 50 year

1 17.74 9.51 5.67 3.572 19.16 10.27 6.13 3.863 20.70 11.10 6.62 4.174 22.35 11.98 7.15 4.505 24.14 12.94 7.72 4.866 26.07 13.98 8.34 5.257 28.16 15.10 9.00 5.678 30.41 16.30 9.72 6.129 32.84 17.61 10.50 6.6110 35.47 19.02 11.34 7.1411 38.31 20.54 12.25 7.7112 41.37 22.18 13.23 8.3313 44.68 23.95 14.29 8.9914 48.25 25.87 15.43 9.7115 52.11 27.94 16.67 10.4916 56.28 30.18 18.00 11.3317 60.79 32.59 19.44 12.2418 65.65 35.20 20.99 13.2219 70.90 38.01 22.67 14.2720 76.57 41.05 24.49 15.4121 44.34 26.45 16.6522 47.88 28.56 17.9823 51.71 30.85 19.4224 55.85 33.31 20.9725 60.32 35.98 22.6526 65.15 38.86 24.4627 70.36 41.97 26.4228 75.99 45.32 28.5329 82.07 48.95 30.8130 88.63 52.86 33.2831 57.09 35.9432 61.66 38.8233 66.59 41.9234 71.92 45.2735 77.67 48.9036 83.89 52.8137 90.60 57.0338 97.85 61.6039 105.68 66.5240 114.13 71.8441 77.5942 83.8043 90.50

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569 567

may be noted that for any given value of interest rate and loanperiod the value of generalized capital recovery factor for equatedpayment loan payment is more than that for graduated paymentloan. This means that in the base year the levelized cost of SPVelectricity will always be higher.

Finally, the generation cost of SPV electricity in the base year(Cg(1)) is calculated for different values of generalized capitalrecovery factor (0.003–0.12) and specific initial investment of solarPV system (1.5–17.5 $/kWh-year). The results are shown in Fig. 3.Hence, the generation cost of solar PV electricity in base year can becalculated by using Figs. 1–3. It may be noted that the cost of solarPV electricity in base year can also be calculated directly fromEquations (1), (11) and (12) without going through Figs. 1–3.However, in that case the effect of parameters affecting the specificinitial investment and generalized capital recovery factor are notknown separately.

Knowing the generation cost of SPV electricity in the base yearfor given conditions, the generation cost of solar PV electricity insubsequent years is calculated from Equation (13). Results in Table 1show the effect of loan period on the cost of SPV electricity. Theseresults are for specific initial investment of 5 $/kWh/year, loaninterest rate of 4% and escalation in loan installments of 8%. The costof SPV electricity in the base year decreases from 17.74 to 3.57 ¢/kWh as the loan period increases from 20 to 50 years. So increasingthe loan period results in substantial reduction in cost of SPVelectricity in base year. Obviously, the SPV electricity becomes freeof cost after the loan period till the end of working life of thesystem. The longer the period of unaccounted free electricity higherwill be the cost of SPV electricity. Ideally the loan period needs to beequal to the working life of SPV system. Currently, the loan period isbeing taken equal to the guaranteed life period of 20–25 years.During the long guarantee period of 20–25 years the decrease inoutput of PV panel is less than 10%, so there is no reason for the PVpanel to stop working after the guarantee period. The working lifeof the system is expected to be 30–40 years or even more [14]. Thisshorter loan period based on the guarantee period tends to artifi-cially increase the cost of SPV electricity. So there is urgent need forthe scientists working on the development of solar photovoltaiccells to give an authentic figure for the working life of the SPVsystem. Then the loan period may be extended as close to theworking life as possible to arrive at the realistic cost of SPVelectricity.

0

0.5

1

1.5

2

2.5

0 5 10 15 20Cs ($/kWh/year)

Cg

(1

) ($

/k

Wh

)

Crfg=0.003Crfg=0.04Crfg=0.08Crfg=0.12

Fig. 3. Generation cost of SPV electricity in base year (Cg(1)) vs specific initialinvestment of SPV system (Cs) for different values of generalized capital recovery factor(Crfg).

44 97.7445 105.5646 114.0147 123.1348 132.9849 143.6250 155.11Levelized generation cost of SPV electricity (¢/kWh)– 36.79 28.92 25.26 23.28

The effect of loan period on levelized cost of SPV electricity withequated payment loan is also shown in Table 1. Again results are forspecific initial investment of 5 $/kWh/year, loan interest rate of 4%and different values of loan period. The results show that the lev-elized cost of SPV electricity decreases from 36.79 to 28.92 ¢/kWhas loan period increases from 20 to 30 years. Further it decreases to25.26 and 23.28 ¢/kWh for loan period of 40 and 50 years. Sodecrease in cost is too small as loan period increases from 30 to 50years. Hence in equated payment loan it is less advantageous toextend the loan period close to working life.

The effect of change in loan interest rate on the cost of SPVelectricity is shown in Table 2. These results are for specific initialinvestment of 5 $/kWh/year, loan period of 30 years and escalation

Table 3Generation cost of SPV electricity during each year of loan period for specific initialinvestment of 5 $/kWh/year, loan interest rate of 4%, loan period of 30 years anddifferent values of escalation in annual loan payments (e).

Year Generation cost of SPV electricity (¢/kWh)

e¼ 0% e¼ 2% e¼ 4% e¼ 6% e¼ 8%

1 28.92 22.65 17.33 12.97 9.512 28.92 23.10 18.03 13.75 10.273 28.92 23.56 18.75 14.58 11.104 28.92 24.04 19.50 15.45 11.985 28.92 24.52 20.28 16.38 12.946 28.92 25.01 21.09 17.36 13.987 28.92 25.51 21.93 18.40 15.108 28.92 26.02 22.81 19.51 16.309 28.92 26.54 23.72 20.68 17.6110 28.92 27.07 24.67 21.92 19.0211 28.92 27.61 25.66 23.23 20.5412 28.92 28.16 26.68 24.63 22.1813 28.92 28.72 27.75 26.10 23.9514 28.92 29.30 28.86 27.67 25.8715 28.92 29.88 30.02 29.33 27.9416 28.92 30.48 31.22 31.09 30.1817 28.92 31.09 32.47 32.96 32.5918 28.92 31.71 33.76 34.93 35.2019 28.92 32.35 35.11 37.03 38.0120 28.92 33.00 36.52 39.25 41.0521 28.92 33.66 37.98 41.61 44.3422 28.92 34.33 39.50 44.10 47.8823 28.92 35.01 41.08 46.75 51.7124 28.92 35.71 42.72 49.55 55.8525 28.92 36.43 44.43 52.53 60.3226 28.92 37.16 46.21 55.68 65.1527 28.92 37.90 48.06 59.02 70.3628 28.92 38.66 49.98 62.56 75.9929 28.92 39.43 51.98 66.31 82.0730 28.92 40.22 54.06 70.29 88.63

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569568

in loan installments of 8% for different values of loan interest rate.The cost of SPV electricity in base year increases from 6.59 to 18.00 ¢/kWh as the loan interest rate increases from 2% to 8%. The change inloan interest rate has profound effect on the generation cost of SPVelectricity because cost of SPV electricity is basically the cost offinancing the huge initial investment. Ideally, the loan interest rateshould be equal to the prevailing loan interest rates. However, it maybe noted that the leverage in loan interest may be used to providelevel playing field to SPV electricity vis-a-vis energy sources thatgenerate CO2 and cause pollution [17–19]. In that case interest ratesmay be lowered to create grid parity and financial burden of thisinterest subsidy be added to the cost of electricity generated fromenergy sources that generate CO2 and cause pollution.

The results for the case with specific initial investment of 5 $/kWh/year, loan interest rate of 4%, loan period of 30 years anddifferent values of escalation in annual loan payments (0–8%) areshown in Table 3. These results bring out the effect of graduatedpayment loan on the generation cost of solar PV electricity indifferent years. With equated payment loan, the levelized genera-tion cost of solar PV electricity in base year is 28.92 ¢/kWh and itremains same up to 30th year. However, for graduated paymentloan with 4% escalation in loan installments, the generation cost ofsolar PV electricity varies from 17.33 ¢/kWh in base year to 54.06 ¢/kWh in 30th year. Similarly for graduated payment loan with 8%escalation in loan installments, the generation cost of SPV elec-tricity varies from 9.51 ¢/kWh in base year to 88.63 ¢/kWh in 30thyear. Hence, the levelized cost of SPV electricity in base year is28.92 ¢/kWh while with graduated payment loan the cost of elec-tricity in base year is 17.33 and 9.51 ¢/kWh for 4% and 8% escalationin loan installments respectively. In other words, at the time ofinstallation of SPV system the levelized cost is much higher thoughit is lower after 14–16 years.

Table 2Generation cost of SPV electricity during each year of loan period for specific initialinvestment of 5 $/kWh/year, loan period of 30 years, escalation in loan installmentsof 8% and different values of interest rate (0–8%).

Year Generation cost of SPV electricity (¢/kWh)

i¼ 0% i¼ 2% i¼ 4% i¼ 6% i¼ 8%

1 4.41 6.59 9.51 13.30 18.002 4.77 7.11 10.27 14.36 19.443 5.15 7.68 11.10 15.51 21.004 5.56 8.30 11.98 16.75 22.685 6.00 8.96 12.94 18.09 24.496 6.49 9.68 13.98 19.54 26.457 7.00 10.45 15.10 21.10 28.578 7.56 11.29 16.30 22.79 30.859 8.17 12.19 17.61 24.61 33.3210 8.82 13.16 19.02 26.58 35.9911 9.53 14.22 20.54 28.71 38.8712 10.29 15.36 22.18 31.01 41.9813 11.11 16.58 23.95 33.49 45.3314 12.00 17.91 25.87 36.16 48.9615 12.96 19.34 27.94 39.06 52.8816 14.00 20.89 30.18 42.18 57.1117 15.12 22.56 32.59 45.56 61.6818 16.33 24.37 35.20 49.20 66.6119 17.64 26.32 38.01 53.14 71.9420 19.05 28.42 41.05 57.39 77.6921 20.57 30.70 44.34 61.98 83.9122 22.22 33.15 47.88 66.94 90.6223 24.00 35.80 51.71 72.29 97.8724 25.91 38.67 55.85 78.08 105.7025 27.99 41.76 60.32 84.32 114.1626 30.23 45.10 65.15 91.07 123.2927 32.65 48.71 70.36 98.35 133.1528 35.26 52.61 75.99 106.22 143.8129 38.08 56.82 82.07 114.72 155.3130 41.12 61.36 88.63 123.90 167.74

Now the prices of all products including grid electricity increasewith time due to inflation. At the same time the income ofconsumers also increases with time due to inflation and growth ofeconomy. So at any given time, there is near match between theprice of grid electricity and paying capacity of consumers. Similarmatch between the price of SPV electricity and paying capacity ofconsumers can be obtained with graduated payment loan in whichannual loan payments escalate at the projected inflation rate of gridelectricity at a given place and annual loan payments are calculatedby treating each payment as an independent loan. However, withequated payment loan, there is mismatch between the static priceof SPV electricity and increasing paying capacity of the consumerbecause in this case the price of SPV electricity in base year (i.e. atthe time of installation of solar PV plant) turns out to be too highthough it may be cheaper than grid electricity after 10–15 years.Obviously nobody agrees to pay higher price now with promise topay lower price after 10–15 years. The consumers will be willing topay higher price later on due to increase in their income with time.

Therefore, the equated payment loans for SPV power plantsresult in unrealistic high levelized price of SPV electricity at thetime of installation of the system. Since, the levelized price of SPVelectricity in base year is very high (up to 5 times) as compared tothe current price of grid electricity, wrong perception has beencreated that SPV electricity is prohibitively expensive. However, thefact is that the realistic price of SPV electricity obtained withgraduated payment loan is much closer to the price of grid elec-tricity. The grid parity of SPV electricity can be realized if levelplaying field is provided by giving incentives due to clean energysource. Also, it may be noted that with graduated payment loan, theamount of financial incentive required to be provided to SPVelectricity to create grid parity in base year will be lesser.

Hence, it can be concluded that to trigger the growth of solar PVelectricity, banks/financial institutions need to start giving long-

P.P. Singh, S. Singh / Renewable Energy 35 (2010) 563–569 569

term soft graduated payment loans rather than the equatedpayment loans. The escalation in loan installments may be keptequal to the estimated inflation rate of grid electricity. Also the loanperiod needs to be close to the working life of SPV system.

4. Conclusions

1. Generalized method to determine the generation cost of SPVelectricity under different conditions has been developed.

2. The levelized generation cost of SPV electricity with equatedpayment loans results in artificially high price of SPV electricityin base year as compared to the prevailing price of grid elec-tricity at that time. The levelized price also does not match withthe paying capacity of the consumers that increases with time.

3. A method of repayment of loan by graduated payment has beendeveloped in which each annual loan installment is treated asan independent loan for that many years.

4. Graduated payment loan with escalation in loan installmentsequal to the estimated long-term rate of inflation in price ofgrid electricity results in realistic price of SPV electricity thatvaries like that of grid electricity.

5. Graduated payment loans needs to be given for long periodpreferably equal to the working life of the system to avoidunaccounted free electricity after the loan period.

References

[1] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York:John Wiley & Sons; 1980.

[2] Goswami DY, Krieth F, Kreider JF. Principles of solar engineering. Philadelphia:Taylor and Francis; 2000.

[3] Govind, Tiwari GN. Economic analysis of some solar energy systems. EnergyConversion and Management 1984;24:131–5.

[4] Perez R, Burtis L, Hoff T, Swanson S, Herig C. Quantifying residential PVeconomics in US – payback vs cash flow determination of fair energy value.Solar Energy 2004;77:363–6.

[5] Bakos GC, Souros M. Techno-economic assessment of a stand-alone PV/hybridinstallation for low-cost electrification of a tourist resort in Greece. AppliedEnergy 2002;73:183–93.

[6] Tasdemiroglu E, Arinç F. A method for technical–economic analysis ofsolar heating systems. Energy Conversion and Management 1988;28:95–103.

[7] Sevilgen SH, Erdem HH, Cetin B, Akkaya AV, Dagdas A. Effect of economicparameters on power generation expansion planning. Energy Conversion andManagement 2005;46:1780–9.

[8] Odeh I, Yohanis YG, Norton B. Economic viability of photovoltaic waterpumping systems. Solar Energy 2006;80:850–60.

[9] Brandemuehl MJ, Beckman WA. Economic evaluation and optimization ofsolar heating systems. Solar Energy 1979;23:1–10.

[10] Brighem EF, Houstan JF. Fundamentals of financial management. Mason, Ohio:Thomson South-Western; 2004.

[11] Matthews H Scott, Cicas Gyorgyi, Aguirre Jose L. Economic and environmentalevaluation of residential fixed solar photovoltaic systems in the United States.Journal of Infrastructure Systems 2004;10:105–10.

[12] Zehra Yumurtaci, Huseyin Erdem. Economic analysis of build-operate-transfermodel in establishing alternative power plant. Energy Conversion andManagement 2007;48:234–41.

[13] <http://www.solarbuzz.com/solarindices.htm>.[14] <http://en.wikipedia.org/wiki/photovoltaics>.[15] <http://en.wikipedia.org/wiki/solar_thermal_energy#Levelized_cost>.[16] Beyer William H. CRC standard mathematical tables. Florida: CRC Press, Inc.;

1981.[17] Frangopoulos CA, Caralis YC. A method for taking into account environmental

impacts in the economic evaluation of energy systems. Energy Conversion andManagement 1997;38:1751–63.

[18] Sanden BA. The economic and institutional rationale of PV subsidies. SolarEnergy 2005;78:137–46.

[19] Chandrasekar B, Kandpal Tara C. Effect of financial and fiscal incentives on theeffective capital cost of solar energy technologies to the user. Solar Energy2005;78:147–56.