A homeowner in Atlanta, GA designed a PV array with 5-kw (DC, STC) capacity for

Question

A homeowner in Atlanta, GA designed a PV array with 5-kw (DC, STC) capacity for which the estimated annual insolation 5.12kWh/m^2/d. The PV array is made up with modules with NOCT=45 C and a temperature coefficient for rated power of -0.38%/ C above the STC cell temperature of 25 C

a. Estimate the array's DC output under PTC conditions (with ambient temperature 20 C and insolation=1 sun), and the array's AC output under PTC conditions with overall DC-AC conversion efficiency 85%.

b. Using the peak hours approach to estimate the annual energy that will be delivered from the Pv array and the system capacity factor.

c. Suppose the current system cost is $5.71/W (without incentives). If the homeowner finances the net cost of the system after receiving a 30% federal tax credit using the 5%, 30-year loan, what would be its cost of electricity?

d. If the SunShot goal of $ 1.5/W is achieved, what would the electricity cost be using the same financing?

Explanation / Answer

a)

Under PTC the DC rating of the system is

P PTC,DC  = PSTC,DC + (Power Coefficient) (TC - Ta ) *PSTC,DC

= 5000 - 0.0038*(45-20)*5000

= 4525 W or 4.525 kW

Given DC-AC ratio 85%

AC output of the installed system is PAC = 4.525 * 0.85 = 3846.25 W or 3.846 kW

b)

Annual energy delivered from PV system is E = PAC * 365 *24 = 3.84625*365*24 = 33693.15 kWh/year theoritical

Actual energy delivered from the PV system is Ea  = PAC * 5.12 *365 = 3.84625 * 5.12 * 365 = 7187.872 kWh/year

Capacity factor = Ea / E = 7187.872 / 33693.15 = 0.2133 or 21.33 %

c)

Given system cost is $ 5.71 / W

Total cost of system C = 5000 * 5.71 = $ 28550

Finance of owner after 30% federal tax credit is Cf = $ 28550 - $ 0.3*28550 = $ 19985

Interest is 5 % for 30 years

Cost of Electricity = (Total Cost of PV system for 30 years) / Total energy generated in 30 years

Cosidering no degredation of energy output

Cost of Electricity = (19985 * (1 + 0.05)^30) / (7187.872 * 30) = 86374.01837 / 215636.16 = $ 0.4

d)

If cost of system is C = 1.5 * 5000 = $ 7500

Final cost of system is Cf = $7500 - $ (0.3*7500) = $ 5250

Cost of Electricity is = (5250 * (1+0.05)^30) / (215636.16) = 22690.19747 / 215636.16 = $ 0.105

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