Lecture 26
October 25, 2013
Monthly Variations for Energy Production in Boulder
with Angle
Normalized Energy Production in US
Single Axis Tracker and Fixed Plate
Design Considerations
• 1. How much power per year do you need?
• 2. How much area is available to work with?
• 3. What type of solar cells , inverters and how many
modules do you want to use ?
4. How much budget is available?
• 5. What are your current costs for electricity and what
fraction can you get from a solar energy system?
• 5. Can you use the grid for backup or do you need
storage?
• 6. Will the utility pay for excess power?
Costs $/watt
Sensitivity to Module Price and
Efficiency
Theoretical Maximum Efficiency
Lecture 27
Capital Recovery Factor
i(1  i)
CRF (i, n) 
n
(
1

i
)

1
2. Example
• 1
n
Cost $4942 kWh/yr with i = 4.5% on 30 year loan
With costs $0.057/WDC then CRF=.06139
Annual payment $1177.8/yr
Cost = $0.238/kWh . This is high compared to
utility rates most places.
Capital Recovery Factor
Taxes Reductions Can Help
Tax Reduction Example
• Cost $19,186 for 4942 kWh/yr
• 30% tax credit Price goes to $13,430
• Annual Payment A=$824/yr, Interest $604 first
year. Tax saving 25% = $151.09
• Cost $673.40
• Cost $0.136 /kwh
First Year Net System Costs After
Rebates
Cash Flow Analysis
• Build Spread Sheet with initial cost, loan
amount, interest, taxes, derating, rebates, CRF,
discount rate, utility rate. See page 345
• Note present worth or present value
calculations. P =dollars today is worth more
than the same value in the future by what you
𝐹
can get by investing it. F = (1+d)n or P= 1+𝑑
𝑛
• d is the discount rate or interest rate.
Residential Rate Structures
•
•
•
•
•
•
1. Flat rate
2. Decreasing with use.
3. Increasing with use.
4. Time of Use ,TOU , use for shifting load.
5. Real time pricing, RTP. Bid into market.
6. Critical Peak Pricing CPP, Get low rates for
letting one be cut of a limited number of
unscheduled times.
California Residential Rate Structure
Summer
Time of Use Example
Critical Peak Pricing Rates
Commercial Pricing
• 1. Basic rates plus demand charges.
• 2. The basic rate may be time of use based.
• 3. Demand charges are high and based on
peak 15 minute period in a given month.
• Example base at peak $0.13/kWh
• Demand Charge to $14.59/kWh and is
charged on top of the regular rate.
Commercial Rates Charges
Demand Charges
• Demand charges can add 50% or more to the
total bill.
• This give an incentive to use PV if it can reduce
the peak load particularly if it is near peak
load on the system.
Modified Accelerated Cost Recovery
System ( MACRS)
• 1. Businesses allowed to Depreciate Capital
costs before taxes.
• 2. Can also get a tax credit
• 3. Example 30% tax credit and the amount
that can be depreciated can be reduced by
half of the 30%
• Net cost can be less than half the name plate
cost.
MACRS Example
Power Purchase Agreements
• 1. Used when can not get tax advantage
• 2. Third party buys and installs and operates
the PV system.
• 3. Can start a little higher or lower than the
utility rate but is fixed so as to save money
over time. The third party may make its
money on taxes or selling power to the utility.
Power Purchase Agreement
Utility Scale PV
• 1. Must compete at whole sale rates. Time of
Delivery rates (TOD)
Power Purchase
• Need to have a good estimate of how much
power you are going to generate to be able to
set the price.
• RPSs may drive the need by the utility to buy
the power.
Stand Alone PV
Battery
Battery Equivalent Circuits
Battery Charge Discharge
Household Loads
Household Loads.
Electronic Loads
Battery Types Energy Density.
Temperature Dependence of Lead
Acid Battery