James Madison University Department of Engineering

Eric J. Leaman

Jack R. Cochran

Faculty Advisor: Dr. Jacquelyn Nagel

Overview Background

Problem Statement

Broader Impact

Literature Review

Design Approach

Energy Storage Concepts

Models and Calculations

Model Validation and Experimental Results

Conclusions Future Work

2

Background 22% of total energy consumed in the United States is

used in residences Electricity accounts for 41%

Only 10.6% of energy generation is from renewable resources

Residential solar energy systems help to reduce dependency on fossil fuels for electrical energy If 15% of Shenandoah Valley households utilized PV

systems, carbon emission would be reduced by the equivalent of removing 5,000 passenger vehicles from the road [1]

3

Problem Statement Typical small-scale solar systems

use chemical batteries for energy storage Lead acid batteries account for

more than 2 million tons of total waste each year Comprised of regulated toxins

(sulfuric acid and lead) More than 200,000 tons is non-

recyclable

Off-gassing is another danger They are expensive – averaging

$115 to $160 per amp-hour capacity at 12V

Lifespans are short and discharge to below about 80% capacity damages battery

4

[2]

[3]

Broader Impact

5

Tec

hn

ical

So

cial

En

viro

nm

enta

l

Eco

no

mic

Advancement of renewable energy systems and greater incentive for skeptical adopters

Inexpensive, safe, and low-maintenance system for remote and poor locations

Reduction in waste, toxins, and emissions

Improvement of cost-feasibility for residential PV system

Pumped hydroelectric energy storage (PHES) Accounts for over 99% of

worldwide bulk energy storage

Up to 85% efficient

Advantages Good reliability

Low maintenance

Low environmental impact

Disadvantages High start-up costs

Typically used in large-scale systems such as power plants

6

PHES Reservoir in Rönkhausen, Germany

[8]

[8]

Compressed Air Energy Storage (CAES) Published overall

efficiencies typically around 50%

Highly reliable

Greater complexity than comparable storage methods

Typically used on very large scales

7

[10]

Design Approach

8

System Architecture

9

Functional Model

10

Concept Generation

11

PHES Architecture

12 (Not to scale)

House

Concept Selection – High-level Analysis Published efficiency values

for water turbines range from 60% to 90%

Published efficiencies for generators range from 80% to 95%

At minimum efficiency, this translates to a reservoir of about 5.6% the volume of an Olympic swimming pool at 62 m to meet power and energy requirements

13

System Parameters to Provide 1 kW Power for 11.4 h Using an 11 mm Nozzle

Results of High-level Analysis Stored energy is a

function of both reservoir height and volume

𝐸 = 𝑚𝑔ℎ = 𝜌𝑉𝑔ℎ

Power is a function of height:

𝑃 =𝑑𝐸

𝑑𝑡= 𝑚 𝑔ℎ

14

Needed Volume vs Height for 1 kW Power and 11.4 kWh Energy for No Loss, Max. Expected Efficiency, and Min.

Expected Efficiency

Compressed Air

𝑤𝑜𝑣 =𝑛

𝑛 − 1𝑃𝑖𝑛 1 −

𝑃𝑜𝑢𝑡𝑃𝑖𝑛

𝑛−1𝑛

𝑤𝑜𝑣 = Specific work that can be stored

n = value related to the conditions of the system

𝑃𝑜𝑢𝑡 = the pressure outside of the tank

𝑃𝑖𝑛 =denotes the pressure inside of the tank.

Compressed Air

𝑤𝑜𝑢𝑣 =𝑛

𝑛 − 1𝑃𝑚 1 −

𝑃𝑜𝑢𝑡𝑃𝑚

𝑛−1𝑛

𝑃𝑚= working pneumatic pressure

Replacing 𝑃𝑖𝑛 with 𝑃𝑚

𝑤𝑜𝑢𝑣 = wasted energy density

Tank Storage Needed

𝑤𝑜𝑒𝑣 = 𝑤𝑜𝑣 −𝑤𝑜𝑢𝑣

𝑉𝑖𝑛𝑡 =𝐸𝑠𝑡𝑤𝑜𝑒𝑣

Compressed Air System Efficiency

𝜂𝑠𝑡𝑜𝑟 =𝐸2𝐸1

= 43% 𝜂𝑥,𝑡 =𝑊𝑡

𝐸2= 36%

𝜂𝑠𝑡𝑜𝑟 = 𝐸𝑓𝑓𝑖𝑐𝑖𝑐𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑇𝑎𝑛𝑘

𝜂𝑥,𝑡 = 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑇𝑢𝑟𝑏𝑖𝑛𝑒 𝐸1 = 𝐸𝑛𝑒𝑟𝑔𝑦 𝑓𝑟𝑜𝑚 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝐼𝑛𝑙𝑒𝑡

𝐸2 = 𝐸𝑛𝑒𝑟𝑔𝑦 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑂𝑢𝑡𝑙𝑒𝑡 𝑊𝑡 = 𝑇𝑢𝑟𝑏𝑖𝑛𝑒 𝑊𝑜𝑟𝑘

Energy Conversion Turgo and Pelton turbines

operate in air

Francis and propeller turbines operate submerged

All shown practical at a small-scale

19

(From Williamson, et al. [11])

[12]

Dynamic System-level Model

20

𝑐 𝐼𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝐼𝑡𝑢𝑟𝑏𝑖𝑛𝑒

𝑇,𝜔

𝑇𝐿

𝑅𝑎 𝐿 𝑅𝐿 𝑉𝑏

𝑖𝑎

𝑉𝑎 𝑘𝑏𝜔 − 𝑖𝑎(𝑅𝐿 + 𝑅𝑎) = 0

𝐼𝑒𝜔 = 𝑇 − 𝑇𝐿 − 𝑐𝜔

𝑇𝐿 = 𝑘𝑇𝑖𝑎 =𝑘𝑏𝑘𝑇

𝑅𝐿 + 𝑅𝑎𝜔

The force on a vane of the turbine is: 𝐹 = 𝑚 𝑏 𝑣𝑗 − 𝑣𝑏 𝛽

Where: 𝑚 𝑏 = mass flow rate into turbine bucket 𝑣𝑗 = velocity of jet

𝑣𝑏 = tangential velocity of turbine 𝛽 = 1 + cos(𝛾) 𝛾 = 60° (angle between center of bucket and bucket wall) 𝜌 = density of water 𝐴𝑛 = cross-sectional area of nozzle outlet 𝑟 = radius of turbine 𝑣𝑏 = 𝑟𝜔

And: 𝑚 𝑏 = 𝜌𝐴𝑛(𝑣𝑗 − 𝑣𝑏)

Then the torque on the turbine is:

𝑇 = 𝐹𝑟 = 𝑚 𝑏𝑟 𝑣𝑗 − 𝑣𝑏 𝛽 = 𝑟𝜌𝐴𝑛𝛽 𝑣𝑗 − 𝑟𝜔2

21

(From Thake [15])

𝐼𝑒𝜔 = 𝑟𝜌𝐴𝑛𝑜𝑧𝑧𝑙𝑒𝛽𝑣𝑗2 − 2𝑣𝑗𝑟

2𝜌𝐴𝑛𝑜𝑧𝑧𝑙𝑒𝛽 +𝑘𝑏𝑘𝑇

𝑅𝐿 + 𝑅𝑎+ 𝑐 𝜔 + 𝑟3𝜌𝐴𝑛𝑜𝑧𝑧𝑙𝑒𝛽𝜔

2 Leading to:

Experimental Set-up The model was validated

by simulating a raised reservoir using a fluid bench and pump

22

Model Validation 6, 8, 10, 12, and 16 mm

nozzles tested Model accurate within 7%

of results on average for 10 and 12 mm nozzles

Accounting for loss due to air resistance and the support bearing brings model within 6% of results 1.2 × 10−3 Ns/m added

to damping coefficient

Smaller and larger nozzles less accurate: 27% average for 6 and 8

mm 14% average for 16 mm

23

Experimental Results Measured efficiency up

to about 40%

(power output

total kinetic jet power)

10 mm nozzle

Flow rate of 15.8 GPM

Total hydraulic head of 10.4 m

Max. Overall efficiency of about 32%

(power output

power potential)

24

Design of Experiments – What factors most significantly impact efficiency?

25

Level Nozzle Size Motor Speed

Load

1 8 mm 40 Hz 35 Ω

2 10 mm 45 Hz 50 Ω

3 12 mm 50 Hz 65 Ω

Parameter Effect

Gross head Flow rate

Pipe diameter Frictional losses at pipe walls

Pipe components

Frictional losses due changes in flow direction

Number of nozzles

Total power input to turbine

Nozzle geometry

Flow rate, jet velocity

Water jet position

Total power input to turbine

Load on generator

Induced torque on turbine

26

Modeled efficiency for 250 W target with optimized load and nozzle diameter at 20, 30, and 40 m

Conclusions and Future Work Target of 1 kW power output may be difficult to

achieve with great efficiency

Expectation is that residence is grid-connected

System is most cost effective by providing little power for a long time

System could be implemented in poor or remote locations, especially where local topography permits low-cost installation of raised reservoir

Further analysis and concurrent optimization of generator and turbine efficiency

27

References

28

1. Zimmerman, D. L., 2011. Residential Solar Energy in the Valley: A Feasibility Assessment and Carbon Mitigation (Master’s Thesis). Retrieved from James Madison University files database.

2. http://www.jadoopower.com/storage.php?Energy-Storage-Solar-VRLA-Batteries-4 3. http://www.solarenergy.gen.in/ 4. Nagel, J. K., (2012). Two-phase Energy System (Project proposal to Valley 25x’25). Source provided by Dr. Nagel. 5. October 25, 2012. Basic Tutorials: Storage Batteries. http://www.freesunpower.com/batteries.php. Free Sun Power. 6. October 25, 2012. Packing some power. http://www.economist.com/node/21548495?frsc=dg|a. The Economist. 7. Levine, J. G., 2003. Pumped Hydroelectric Energy Storage and Spatial Diversity of Wind Resources as Methods of

Improving Utilization of Renewable Energy Sources (Master’s Thesis). Retrieved from University of Colorado Boulder files database.

8. http://large.stanford.edu/courses/2012/ph240/doshay1/ 9. Young-Min K., Jange-Hee L., Seok-Jeon K., Favrat, D., 2012. Potential and Evolution of Compressed Air Energy

Storage: Energy and Exergy Analyses. Entropy 14 (8), 1501-1521. 10. http://www.pge.com/web/includes/images/about/environment/pge/cleanenergy/caes.jpg 11. Williamson, S., Stark, B., Booker, J., 2014. Low head pico hydro turbine selection using a multi-criteria analysis.

Renewable Energy 61, 43-50. 12. http://images.cpbay.com/uploadfile/comimg/big/Runner-of-Francis-Turbine-200KW-271584.jpg 13. Proczka, J., Muralidharan, K., Villela, D., Simmons, J., & Frantziskonis, G. (2013). Guidelines for the pressure and

efficient sizing of pressure vessels for compressed air energy storage. Energy Conversion and Management, 65, 597-605. Retrieved October 30, 2013, from the Science Direct database.

14. Elmegaard, B., Brix, W. Efficiency of Compressed Air Energy Storage. Retrieved from http://orbit.dtu.dk/fedora/objects/orbit:72193/datastreams/file_6324034/content

15. Thake, J., 2000. The Micro-hydro Pelton Turbine Manual. ITDG Publishing, London.