Rough estimate of cost of panels and inverters

1

Price of electricity• Regional variations: $0.16/kWh in New England, $0.11/kWh in east south

central, $0.37/kWh in Hawaii.

• Naperville: $0.09/kWh (I paid $57.72 in December, plus $20 wind power surcharge).

2

The role of interest rates• If you could invest $1M to save $2M in energy costs over 30 years, your

decision would be affected by interest rates.

3

Amount borrowed $1,000,000 B1 (pv)Annual interest

rate4.0% B2 (rate - per year)

Years 30 B3 (nper - years)Monthly payment $4,774.15 B4: =-PMT(B2/12,B3*12,B1)Annual payment $57,290 B5: =12*B4

Total paid $1,718,695 B6: =B3*B5

Excel: =pmt(rate,nper,pv)

0 5 10 15Annual interest rate (%; compounded monthly)

$0

$50,000

$100,000

$150,000

Annu

al p

aym

ent Cost of borrowing $1,000,000

Your midterm paper assignment• Will be due on Tuesday, February 5, and submitted through SafeAssign/

Blackboard.

• The assignment will be this: write a 6 page (minimum) paper on a solar parking lot project anywhere in the US. Include graphs and photos if relevant. You should identify a parking lot, estimate the cost of construction, estimate the energy produced and its market value, and discuss strategies to achieve economic breakeven.• This is a complex project!

• You can work in teams of 2-3 people on the calculations, but each person must write their own paper.

• You must attach, or hand-in, an appendix showing the detail of all your calculations. This can be handwritten if you wish; the appendix will not be graded based on neatness! I just want to see how you have arrived at your numbers.

4

Electrical load profile by year

5

Jan-020.0

0.2

0.4

0.6

0.8

1.0

Rela

tive

load

Feb-01Mar-03Apr-02 May-02Jun-01Jul-02 Aug-01Aug-31Sep-30Oct-31 Nov-30Dec-30

Daily maximum

Daily minimum

www.nationalgridus.com (Northeast USA)

Electrical load profile by week

6

0 1 2 3 4 5 6 7Day of week (Aug. 8, 2011)

0.0

0.2

0.4

0.6

0.8

1.0R

elat

ive

load

SunMon Tue Wed Thu Fri Sat

www.nationalgridus.com (Northeast USA)

Electrical power flows

7http://www.eia.gov/todayinenergy/detail.cfm?id=4270

Electricity storage

8http://www.electricitystorage.org/images/uploads/static_content/technology/technology_resources/ratings_large.gif

Pumped Hydro: Bad Creek, South Carolina

• 1,065 MW peak power output.

• Large power plants in the US are typically 1,000-3,000 MW capacity

9http://www.duke-energy.com/power-plants/pumped-storage-hydro/bad-creek.asp

Pumped Hydro: Bath County, Virginia

• Largest in the world: 3,000 MW peak power capacity.

• Cost: $1.6 billion. Enough concrete was poured during construction to build 200 miles (322 kilometers) of interstate highway.

• The station consists of two large reservoirs — one 1,262 feet (385 meters) higher than the other, a massive power house and the huge tunnels that connect them. When demand is low, water is pumped from the lower reservoir to the upper one.

• When demand is high, valves permit water to run through the tunnels to the lower reservoir at a rate as high as 13.5 million gallons (852 cubic meters/second) per minute, turning six turbine generators. The water level in the 265-acre upper reservoir can fluctuate as much as 106 feet (32.3 meters) when the unit is operated.

10

https://www.dom.com/about/stations/hydro/bath-county-pumped-storage-station.jsp

11

Bath County pumped hydro

Upper reservoir has area of 1.07 km2 and height fluctuation of 32meters⇤:

(1.07 km2) ·✓

1000 m1 km

◆2

· (32 m) ·✓

1000 kgm3

◆= 3.42 ⇥ 1010 kg.

Height difference between the two reservoirs is 380 meters, so totalpotential energy is (all in SI units)

mgh = (3.4 ⇥ 1010 kg) · (9.8 m/sec2) · (380 m) = 1.28 ⇥ 1014 Joules

or(1.3 ⇥ 1014 J) · ( 1 MWh

106 J/s · 3600 sec) = 35, 400 MWh

or 11.8 hours of running time if 100% efficient (actual efficiency is75–78%†, so actual running time is ⇠ 9 hours).

⇤https://www.dom.com/about/stations/hydro/bath-county-pumped-storage-station.jsp

†http://www.cleanenergyactionproject.com/CleanEnergyActionProject/CS.Bath_County_Pumped_

Storage_Station___Pumped_Storage_Hydropower_Case_Studies.html

Homework due Jan. 29• Can be written on a sheet of paper handed in, or can be emailed.

• Consider an average water storage tower used by a water utility. How much water mass does it hold, and how high up? How much potential energy?

• How many such water towers are there in the US? How much total energy might they store?

•

12

Compressed air energy storage

13http://www.sandia.gov/ess/publications/ESHB%201001834%20reduced%20size.pdf

Compressed air energy storage

14http://www.sandia.gov/ess/publications/ESHB%201001834%20reduced%20size.pdf

Beacon Power: flywheels• Flywheels: ~85% efficient energy recovery.

• Each flywheel: 25 kWh energy storage, 100 kW max power (i.e., minimum 15 minute “charge”/”discharge” time)

• Plant in Stephenstown, NY has 200 flywheels for 20 MW max power, 5 MWh storage. Small compared to 1,000-2,000 MW power plants; mainly used for AC phase regulation with wind power.

15

• Plant cost $69 to build, and financing include a US DoE loan guarantee of $40M in July 2009.

• Company went bankrupt in Oct. 2011; bought by Rockland Capital for $30M in Feb. 2012; will repay 70% of DoE loan.

Sodium-sulphur batteries used for load leveling

16http://www.sandia.gov/ess/publications/ESHB%201001834%20reduced%20size.pdf

Sodium-sulfur battery lifetime

17http://www.sandia.gov/ess/publications/ESHB%201001834%20reduced%20size.pdf