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
[2]
more than 2 million tons of
total waste each year


Comprised of regulated toxins
(sulfuric acid and lead)
More than 200,000 tons is nonrecyclable
 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
[3]
4
Advancement of renewable
energy systems and greater
incentive for skeptical adopters
Inexpensive, safe, and lowmaintenance system for
remote and poor locations
Economic
Environmental
Social
Technical
Broader Impact
Reduction in
waste, toxins,
and emissions
Improvement of costfeasibility for
residential PV system
5
Pumped hydroelectric energy
storage (PHES)
 Accounts for over 99% of
worldwide bulk energy
storage
 Up to 85% efficient
 Advantages
 Good reliability
[8]
 Low maintenance
 Low environmental impact
 Disadvantages
 High start-up costs
 Typically used in large-scale
systems such as power plants
PHES Reservoir in Rönkhausen, Germany [8]
6
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
[10]
7
Design Approach
8
System Architecture
9
Functional Model
10
Concept Generation
11
PHES Architecture
House
(Not to scale)
12
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
System Parameters to Provide 1 kW Power for
11.4 h Using an 11 mm Nozzle
13
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
= 𝑚𝑔ℎ
Needed Volume vs Height for 1 kW Power and 11.4 kWh
Energy for No Loss, Max. Expected Efficiency, and Min.
Expected Efficiency
14
Compressed Air
𝑛−1
𝑛
𝑛
𝑃𝑜𝑢𝑡
𝑤𝑜𝑣 =
𝑃𝑖𝑛 1 −
𝑛−1
𝑃𝑖𝑛
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
𝑃𝑜𝑢𝑡
=
𝑃𝑚 1 −
𝑛−1
𝑃𝑚
𝑛−1
𝑛
𝑃𝑚 = working pneumatic pressure
Replacing 𝑃𝑖𝑛 with 𝑃𝑚
𝑤𝑜𝑢𝑣 = wasted energy density
Tank Storage Needed
𝑤𝑜𝑒𝑣 = 𝑤𝑜𝑣 − 𝑤𝑜𝑢𝑣
𝐸𝑠𝑡
𝑉𝑖𝑛𝑡 =
𝑤𝑜𝑒𝑣
Compressed Air System Efficiency
𝜂𝑠𝑡𝑜𝑟
𝐸2
𝑊𝑡
=
= 43% 𝜂𝑥,𝑡 =
= 36%
𝐸1
𝐸2
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
(From Williamson, et al. [11])
[12]
 All shown practical at a small-
scale
19
Dynamic System-level Model
𝐼𝑒 𝜔 = 𝑇 − 𝑇𝐿 − 𝑐𝜔
𝑇𝐿
𝑐
𝐼𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒
𝐼𝑡𝑢𝑟𝑏𝑖𝑛𝑒
𝑇, 𝜔
𝑘𝑏 𝜔 − 𝑖𝑎 (𝑅𝐿 + 𝑅𝑎 ) = 0
𝑇𝐿 = 𝑘 𝑇 𝑖𝑎 =
𝑘𝑏 𝑘 𝑇
𝜔
𝑅𝐿 + 𝑅𝑎
𝑉𝑎
𝑅𝐿
𝐿
𝑅𝑎
𝑉𝑏
𝑖𝑎
20
The force on a vane of the turbine is:
𝐹 = 𝑚𝑏 𝑣𝑗 − 𝑣𝑏 𝛽
𝑚𝑏 = 𝜌𝐴𝑛 (𝑣𝑗 − 𝑣𝑏 )
And:
Then the torque on the turbine
is:
𝑇 = 𝐹𝑟 = 𝑚𝑏 𝑟 𝑣𝑗 − 𝑣𝑏 𝛽 = 𝑟𝜌𝐴𝑛 𝛽 𝑣𝑗 − 𝑟𝜔
Where:
𝑚𝑏 = 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
Leading to:
𝐼𝑒 𝜔 =
𝑟𝜌𝐴𝑛𝑜𝑧𝑧𝑙𝑒 𝛽𝑣𝑗2
− 2𝑣𝑗
𝑟 2 𝜌𝐴
2
(From Thake [15])
𝑘𝑏 𝑘 𝑇
+ 𝑐 𝜔 + 𝑟 3 𝜌𝐴𝑛𝑜𝑧𝑧𝑙𝑒 𝛽𝜔2
𝑛𝑜𝑧𝑧𝑙𝑒 𝛽 +
𝑅𝐿 + 𝑅𝑎
21
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?
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
Level
Nozzle Size
Motor
Speed
Load
Water jet
position
Total power input to
turbine
1
8 mm
40 Hz
35 Ω
2
10 mm
45 Hz
50 Ω
Load on
generator
Induced torque on
turbine
3
12 mm
50 Hz
65 Ω
25
Modeled efficiency for 250 W target with optimized load and nozzle diameter
at 20, 30, and 40 m
26
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
1.
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3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
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.
http://www.jadoopower.com/storage.php?Energy-Storage-Solar-VRLA-Batteries-4
http://www.solarenergy.gen.in/
Nagel, J. K., (2012). Two-phase Energy System (Project proposal to Valley 25x’25). Source provided by Dr. Nagel.
October 25, 2012. Basic Tutorials: Storage Batteries. http://www.freesunpower.com/batteries.php. Free Sun Power.
October 25, 2012. Packing some power. http://www.economist.com/node/21548495?frsc=dg|a. The Economist.
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.
http://large.stanford.edu/courses/2012/ph240/doshay1/
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.
http://www.pge.com/web/includes/images/about/environment/pge/cleanenergy/caes.jpg
Williamson, S., Stark, B., Booker, J., 2014. Low head pico hydro turbine selection using a multi-criteria analysis.
Renewable Energy 61, 43-50.
http://images.cpbay.com/uploadfile/comimg/big/Runner-of-Francis-Turbine-200KW-271584.jpg
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, 597605. Retrieved October 30, 2013, from the Science Direct database.
Elmegaard, B., Brix, W. Efficiency of Compressed Air Energy Storage. Retrieved from
http://orbit.dtu.dk/fedora/objects/orbit:72193/datastreams/file_6324034/content
Thake, J., 2000. The Micro-hydro Pelton Turbine Manual. ITDG Publishing, London.
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