Hydroelectric System Design

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HYDROELECTRIC SYSTEM DESIGN

A Thesis

presented to

the Faculty of California Polytechnic State University,

San Luis Obispo

In Partial Fulfillment

of the Requirements for the Degree

Master of Science in Electrical Engineering

byTimothy McDonnell Brown

December 2010



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© 2010

Timothy McDonnell Brown

ALL RIGHTS RESERVED



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COMMITTEE MEMBERSHIP

TITLE: Hydroelectric System Design

AUTHOR: Timothy McDonnell Brown

DATE SUBMITTED: December 2010

COMMITTEE CHAIR: Dr. Ahmad Nafisi, Professor

COMMITTEE MEMBER: Dr. Taufik, Professor

COMMITTEE MEMBER: Dr. Ali Shaban, Professor



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ABSTRACT

Hydroelectric System Design

Timothy McDonnell Brown

Hydroelectric power generation is not a viable option as a prime

source of electrical energy for the Pico Blanco Boy Scout Camp, as

determined by this thesis. The hydroelectric power system can only

provide a maximum power capacity of 17kW as limited by the available

mechanical energy of the water source. This power capacity is

inadequate to reliably supply power to the electrical loads at the camp

during peak demand periods. The purpose of this thesis was to study the

feasibility of supplying the Boy Scout Camp with a renewable source of

electrical energy through an exploration of various hydroelectric system

design concepts.



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ACKNOWLEDGMENTS

I would like to thank Dr. Stanley Crane for providing me with the

opportunity to develop this study for the Pico Blanco Boy Scout Camp. Dr.

Crane not only created the concept for the thesis, but was also a key

factor in its development. He coordinated the site visit of the Camp, led

the effort to obtain site data, and identified many of the resources used to

develop this thesis. Without him, this thesis would not have been

possible.

I would also like to thank Dr. Nafisi, Dr. Taufik, and Dr. Shaban for

providing me with the technical background in power systems engineering

at California Polytechnic State University, San Luis Obispo.

I would finally like to thank Bill Thoma, for providing me with the

industry experience used to supplement the development of this thesis. It

was during my employment at Thoma Electric, Inc., with the help of Bill

Thoma and many others, that I was able to learn about and perform the

electrical design of commercial distribution systems.



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TABLE OF CONTENTS

Page

LIST OF TABLES ………………………………………………………………….. viii

LIST OF FIGURES ………………………………………………..……………….ix

CHAPTERS

I. Introduction ………………………………………………..………………………1

A. Development of Hydroelectric Power………………………………………2

B. Advantages and Disadvantages of Hydroelectric Power Generation…..3

C. Site History ……………………………………………………………………7

D. Site Topography ……………………………………………………………..12

II. Design Requirements…………………………………………………………….15

III. Site Visit and Survey……………………………………………………………...22

A. Existing Distribution System……………………………………………….22

B. Head Measurements………………………………………………………..28

C. Flow Rate Measurements………………………………………………….31

IV. Civil Design………………………………………………………………………..39

A. Exploitation Scheme Types………………………………………………....39

i. Dam Scheme……………………………………………………….......39

ii. Diversion Scheme………………………………………………….......40

iii. Pumped Storage…………………………………………………….….41

B. Exploitation Scheme Selection…………………………………………..…42

V. Mechanical Design……………………………………………………………......46

A. Hydraulic System Considerations…………………………………………..46i. Water Flow in Pipes……………………………………………………46

ii. Head Losses…………………………………………………..………..53

B. Turbine Types…………………………………………………………………57

i. Reaction Turbine…………………………………………………….…59



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a. Francis Turbine……………………………………………………..59

b. Kaplan and Propeller Turbine……………………………….…….60

ii. Impulse Turbine…………………………………………………………60

a. Pelton Turbine………………………………………………………60

b. Turgo Turbine……………………………………………….………64

c. Crossflow Turbine…………………………………………………..65

C. Turbine Selection……………………………………………………………..66

i. Selection Criteria…………………………………………………….….66

a. Cavitation Problems…………………………………………….….67

b. Net Head…………………………………………………………….68

c. Range of Discharges Through the Turbine……………………..69

VI. Electrical Design…………………………………………………………….…….73

A. Generator Types…………………………………………………………..….73

i. Synchronous Generator………………………………….……………74

ii. Asynchronous Generator…………………………………………...…76

iii. Generator Selection………………………………………………..…..77

B. System Design…………………………………………………………….….81

i. Conductor Sizing and Selection………………………………….…..81

ii. Overcurrent Protection Device Sizing and Selection…………..…..88

iii. Overall System Design………………………………………………..89

iv. Motor Starting Considerations…………………………………….….94

v. Turbine & Generator Control……………………………………….…97

VII. Development and Construction…………………………………………………101

VIII. Economic Analysis……………………………………………………………….105

IX. Conclusion…………………………………………………….……………….….109

BIBLIOGRAPHY ……………………………………………………………………..112



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LIST OF TABLES

Table Page

1. U.S. Energy-Related Carbon Dioxide Emissions by Fossil Fuel………..52. Hydroelectric System Design Requirements……………………………..21

3. Existing Diesel Generator Specifications…………………………………254. Existing Manual Transfer Switch Specifications………………………....265. Existing Main Panel Specifications………………………………………..266. Existing Panel ‘KA’ Specifications……………………………………...….26 7. Existing Refrigerator Compressor Specifications………………………...278. Existing Freezer Compressor Specifications……………………………..279. Gross Head Measurements………………………………………………...3010. Time to Fill Bucket…………………………………………………………...3111. Site 1 Depth and Width Measurements…………………………………...34 12. Site 1 Velocity Measurements…………………………………………...…34 13. Site 2 Depth and Width Measurements……………………………….......35

14. Site 2 Velocity Measurements……………………………………………...35 15. Site 3 Depth and Width Measurements……………………………….......35

16. Site 3 Velocity Measurements…………………………………………...…36 17. Site 4 Depth and Width Measurements…………………………………...36

18. Site 4 Velocity Measurements…………………………………………...…36

19. Site 5 Depth and Width Measurements………………………………...…37

20. Site 5 Velocity Measurements……………………………………………...37 21. Float Method Average Velocity and Volumetric Flow Rate for 5 Sites....3822. Dynamic and Kinematic Viscosity of Water………………………………..5223. Turbine Type and Typical Net Head Range…………………………..…..6824. Acceptable Variations of Flow and Head for Various Turbine Types......71

25. New Hydro Generator Specifications…………………………………...…8026. NEC Ampacity Table……………………………………………………...…8427. NEC Ch.9 Table 9 AC Resistance Table………………………………….8528. Approximate Project Costs………………………………………………....106



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LIST OF FIGURES

Figure Page

1. Aftermath of Lightning Fires at Pico Blanco, CA…………………………...82. Camp Ranger’s Home after the Fires…………………………………….…93. Existing Dam at the Top of the Creek Run………………………………...104. Topographic Overview of Surrounding Areas ………………………….....125. Enlarged Topograph of Boy Scout Camp………………………………….13 6. Waterfall at the Base of the River Run……………………………………..14 7. Boy Scout Camp Mess Hall………………………………………………….168. Freezer Compressor Nameplate………………………………………….....17 9. Refrigerator Compressor Nameplate……………………………………….18 10. Locations of the Compressors…………………………………………….…18 11. Compressor Disconnect Switches………………………………………….19 12. Existing Synchronous Generator Nameplate………………………………22 13. Generator Nameplate & Operator Interface………………………………..22 14. Existing Boy Scout Camp Electrical Distribution System…………………24 15. Manual Transfer Switch………………………………………………………2516. The Head of the River Flow……………………………………………….….2817. Surveyor’s Method…………………………………………………………….2918. Folsom River Dam………………………………………………………….….40 19. Diversion Scheme……………………………………………………………..4120. Racoon Mountain Pumped-Storage Plant……………………………...…..4221. Downhill View of River Run………………………………………………......4322. Pipe Emerging From Dam……………………………………………….……44 23. (a) Laminar Flow and (b) Turbulent Flow in a Closed Pipe ……………....4924. Laminar vs. Turbulent Flow #1…………………………………………….…50

25. Laminar vs. Turbulent Flow #2……………………………………………….5526. Reaction Turbine……………………………………………………………....5827. Impulse Turbine………………………………………………………………..5828. Francis Turbine……………………………………………………………...…59 29. Horizontal Axis Francis Turbine…………………………………………..….5930. Kaplan Runner…………………………………………………………………6031. Cross Section of a Nozzle with Deflector……………………………….…..61 32. View of a Two Nozzle Horizontal Pelton…………………………….……...6233. View of a Two Nozzle Vertical Pelton………………………………….……63 34. Pelton Runner…………………………………………………………………6335. Principle of a Turgo Turbine…………………………………………….……65

36. Principle of a Crossflow Turbine……………………………………….…….6637. Typical Flow Ranges for Various Turbines…………………………………7038. Canyon Hydro Pelton 751-2 Turbine………………………………………..72 39. Graph of Flux Versus Field Current for Synchronous Generator ………..75



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I. Introduction

Boy Scouts of America is a program that aims to develop the

character of our youth through team-building and educational activities.

This large national program not only teaches lifelong values but also helps

to create a future leadership in the United States of America through local

councils and dedicated outdoor camping reserves. In the campsite

setting, the Boy Scouts are able to learn how to live a sustainable life in

which a symbiotic relationship with nature exists. It is only natural then to

exhibit sustainability in as many facets of these campsites as possible.

Camp Pico Blanco, located in Los Padres National Forest along the

central coast of California, is just one of the many outdoor camping

reserves that host the Boy Scouts of America program. A map of the

Camp and the surrounding terrain is illustrated in the figure below.



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Figure 1 Topographic Overview of Surrounding Areas [8]



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Forest fires caused by lightning strikes in this area have damaged

much of the infrastructure and associated systems at the Camp.

Examples of this damage are shown in the photographs below.

Figure 2 Aftermath of Lightning Fires at Pico Blanco, CA

Figure 3 Camp Ranger’s Home after the Fires

One of the systems in need of replacement due to the fires is the

existing diesel generator which serves as the primary electrical power

source for the Boy Scout Camp. Diesel generators emit greenhouse

gases which pollute the atmosphere and thus do not provide a sustainable

solution for the Pico Blanco Boy Scout Camp. The Camp has the



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opportunity to exhibit greater levels of sustainability by replacing the

existing diesel generator with a cleaner source of electrical energy.

A. Development of Hydroelectric Power

The concept of harnessing the energy available in moving water to

perform work has been around for thousands of years. Ancient societies

captured the energy in moving water through various devices in order to

drive pumps, crankshafts, and other various loads. For example, over

2000 years ago, the Greeks were using water wheels to grind wheat into

flour. Many cities also used running water to drive water wheels and to

pump water throughout the city. Hydropower was even used in the 1700’s

in the milling lumber and grain industries to pump irrigation water.

The invention of the DC generator led to the development of

hydroelectric power stations. It wasn’t until the discovery of AC power in

the late 19th

century that hydroelectric power stations began to be widely

employed. Previously, hydroelectric power stations generating DC power

were limited by the short distances the DC power could be transmitted.

AC power can be transmitted much longer distances paving the way for

large, centralized generation plants such as hydroelectric power stations.

The first hydroelectric power station was installed on the Fox River in

Wisconsin in 1882 which delivered approximately 12.5 kW [1]. By 1907

and 1920, hydroelectric power accounted for 15% and 25%, respectively,

of the total electricity generated for the United States [2].



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B. Advantages and Disadvantages of Hydroelectric Power Generation

In 2008, renewable energy electricity production represented 9% of

the total electrical energy generation in the United States [3]. Of this 67%

came from hydropower, 15% from biomass, 14% from wind, 4% from

geothermal, and 0.2% from solar [4]. Hydropower is the largest and the

oldest renewable energy source of electricity generation for utilities in the

United States.

Hydroelectric power generation provides many advantages. If

needed, hydropower can produce electricity at a constant rate given a

steady stream flow and head. The energy can also be stored in reservoirs

through the control of gate valves. The ability that hydropower systems

can control the amount of water flowing through the water turbines makes

hydropower a valuable asset of the spinning reserve. This is especially

true for systems employing a pumped storage exploitation scheme. The

spinning reserve supports the local power grid during power quality

disturbances such as in the events that large step-loads are started across

the line or large generators are taken off-line. The spinning reserve uses

generation units that are already connected to the grid, such as

hydropower stations, to maintain system voltage and frequency during

these power quality disturbances. Hydropower plants also have lower

operating costs compared to other generation sources such as nuclear

power plants that depend upon high cost fuel contracts for their operation.

Another advantage of hydropower plants is that the upstream reservoirs



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created through dams can be used for recreational purposes such as

boating, skiing, fishing, and swimming. One of the most important

advantages of hydropower is that it is an emission free source of

electricity. The major contributor to carbon dioxide emissions are

petroleum, coal, and natural gas based prime movers. However,

hydroelectric power does not produce any carbon dioxide. This classifies

hydro power as a clean source of energy helping to reduce our carbon

footprint on the world. The table below outlines the quantity, in million

metric tons, of carbon dioxide produced by each of these fossil fuels

between the years 1995 and 2002.

Table 1 U.S. Energy-Related Carbon Dioxide Emissions

by Fossil Fuel [5]

For example, coal, with a carbon content of 78%, emits about 205

pounds of carbon dioxide per million Btu when completely burned [4].



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Large amounts of greenhouse gas emissions destroy the Earth’s natural

ozone layer leading to global warming.

Though hydroelectric power does not directly produce any carbon

dioxide, the overall system still has negative environmental impacts

outlined by the following excerpts.

Although electricity generated from water plants is relatively

emissions free, significant amounts of methane are produced from

the decomposition of plants in the flood areas. In addition to

methane, hydropower can have significant environmental effects

such as fish injury and impact on downstream water quality. By

diverting water out of the water bodies for power, dams remove

water needed for healthy in-stream ecosystems thereby disrupting

the natural river flows. Dams also slow down the flow of the river.

Many fish species, such as salmon, depend on steady flows to

flush them down river early in their life and guide them upstream

years later to spawn. Slow reservoir pools disorient migrating fish

and significantly increase the duration of their migration. [6]

To be completely environmentally conscious, it is also necessary to

focus on the negative impacts of hydroelectric systems such as the ones

listed above.

In addition, bacteria present in decaying vegetation can

also change mercury, present in rocks underlying a reservoir, into a



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form that is soluble in water. The mercury accumulates in the

bodies of fish and poses a health hazard to those who depend on

these fish for food. [7]

Another disadvantage of hydropower plants are the high capital

costs associated with system installation. High initial costs result in longer

payback periods and thus reduce the economic feasibility of hydroelectric

power systems. As mentioned earlier, the construction of large reservoirs

results in upstream flooding. Although providing the advantages of

increased recreational use, this also has the negative effect on the

environment as explained above and can cause people living in towns and

villages near the flooded areas to relocate.

II. System Design Requirements

The feasibility of the hydroelectric system proposed will be

determined by comparing the proposed design against the following

conceptual basic design requirements. The hydroelectric power station

source must be able to supply reliable power to the Boy Scout Camp

throughout the year despite varying water levels and other associated

environmental conditions. The rated maximum power capacity must be

greater than the Camp’s current peak energy demands in order to not only

meet existing demands but to also allow for possible future load

expansion. The design will also require that the installation and continual

operation of the power plant exhibit minimal to negligible environmental

impact. Finally, the total project cost to design and build the system must



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be economical and within the Camp’s allotted budget for the diesel

generator replacement. The table below highlights each of these

requirements.

Table 2 Hydroelectric System Design Requirements

Generation Classification RenewableEnvironmental Impact MinimalMinimum Real Power Capacity 23.9kW*Minimum Reactive Power Capacity 7.87kVAR*Maximum Project Cost $50,000**Reliability Must be capable of supplying full

power demand at the Boy Scout Camp

while minimizing power interruptions tothe camp*For calculation of the minimum required real and reactive power capacities refer to Section VI(B)(iii) “OverallSystem Design”

**The maximum project cost was an estimate derived from the insurance money allocated for the generatorreplacement including anticipated donations from patrons of the Pico Blanco Boy Scout Camp

III. Site Visit and Survey

A. Site Description

The Boy Scout Camp is located deep in a valley that is densely

populated with trees. The Little Sur River flows through the Camp with

many smaller creeks feeding into it. There are vast amounts of fish and

other wildlife species that inhabit the Little Sur River. The installation of a

hydroelectric power station on the Little Sur River would disrupt the natural

ecosystem and thus would violate this design requirement. The small

creeks that feed into the Little Sur River, on the other hand, do not harbor

fish or other wildlife. The biggest of these creeks results in a small,

approximately 15’ high waterfall that feeds into the Little Sur River. This

waterfall is displayed in the photograph below.



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Figure 4 Waterfall Feeding Little Sur River

This creek will be the proposed location to install a hydroelectric

power station. The creek first appears aboveground at an existing dam a

few hundred feet upstream of the waterfall. The dam is displayed in the

photograph below.

Figure 5 Existing Creek Dam



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Figure 6 Enlarged Topography of Boy Scout Camp

In the figure above, the proposed creek that will power the hydro

turbine-generator unit is labeled “A”. The location of the existing diesel

generator and main service panel is labeled “B”. The proposed location of

the hydroelectric power station is the point at which the small creek feeds

into the Little Sur River. The distance between this point and the location

of the existing main service panel is approximately 630 feet. This distance

is used in later sections to determine the minimum required conductor

size.



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B. Existing Distribution System and Electrical Loads

An evaluation of the Boy Scout Camp’s existing distribution system

and electrical loads provides insight into and a rough characterization of the

Camp’s electrical loads. The majority of the static loads at the Boy Scout

Camp consist of various plug loads for appliances, computer stations, and

incandescent and fluorescent lighting. The majority of the lighting loads were

resistive, incandescent light sources located in the Mess Hall shown in the

figure below. The remainder of the lighting load consisted of various

fluorescent and incandescent light bulbs located in various offices and

buildings.

Figure 7 Boy Scout Camp Mess Hall

The majority of the rotating loads consisted of two 208V, 3ø, 3 wire

compressors. The compressors are located on small skids in an outdoor

utility room and serve the refrigerator and freezer in the Main Mess Hall. Both

compressors are continually connected to the distribution system and are



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cycled on and off as determined by the system’s temperature controls.

According to the device nameplates, the rated locked rotor amps (LRA) for

the refrigerator and freezer compressors were 31A and 82A, respectively. A

compressor’s LRA is defined as the current drawn by the motor when the

rotor “locks” or completely stops. The rotor windings of a motor produce an

electrical magnetic force (EMF) that is 180° out of phase with the EMF

produced by the stator windings. The “back” EMF produced by the rotor

windings reduce the amount of current that is drawn by the motor. If the rotor

is stopped or “locked”, then there is no back EMF produced and thus the

motor will draw its maximum current.

Photographs of the compressors and their associated disconnects are

displayed in the figures below.

Figure 8 Freezer Compressor Nameplate



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Figure 9 Refrigerator Compressor Nameplate

Figure 10 Locations of the Compressors



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Figure 11 Compressor Disconnect Switches

The existing diesel generator supplying power to the Boy Scout

Camp is rated 75kVA, 208/120V, 3ø, 4 wire. The photographs below

display the generator nameplate and its associated operator interface.

Figure 12 Existing Synchronous Generator Nameplate



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Figure 13 Generator Nameplate & Operator Interface

Contrary to common energy saving practices, the facility managers

at the Boy Scout Camp require the light fixtures remain on at all times.

This rule is imposed on all of the Camp residents to prevent the damage

of the diesel generator. It is common for diesel generators that are lightly

loaded to experience “wet-stacking”. If diesel generators are not loaded to

a minimum level as specified by the manufacturer, then the engine prime

movers will not be able to reach their designed operating temperature

potentially resulting in unburned fuel. If operated under this condition for

extended periods of time, the unburned fuel will begin to deposit on

exhausts, turbo blades, and exhaust valves. These effects cause the

efficiency of the diesel generators to drop and can eventually cause

significant equipment damage if left unattended for long periods of time.

The existing diesel generator is oversized compared to the total electrical

load at the Camp with a maximum power demand utilizing about 25% of

its nominal capacity.



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The following single line diagram represents the Camp’s existing

distribution system as determined through the site survey.

Figure 14 Existing Boy Scout Camp Electrical Distribution System

A photograph of the existing manual transfer switch is shown in the

figure below.



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Figure 15 Manual Transfer Switch

The switch positions are labeled “Backup Gen”, “Off”, and “Main

Gen”. There is currently no backup generator but the intention to

eventually install one is apparent through the switch labels.

The specifications for the existing electrical equipment depicted in

the single line diagram above are listed in the following tables.



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Table 3 Existing Diesel Generator Specifications

Manufacturer Elliot Magnetek PowerSystems

Model Number 70 QLSerial Number BU05J265Apparent Power Rating at3ø

75kVA

Real Power Rating at 3ø 60kWReal Power Rating at 1ø 46kWPower Factor at 3ø 0.8Power Factor at 1ø 1Rated Speed 1800 RPM

Table 4 Existing Manual Transfer Switch Specifications

Manufacturer Square DModel Number E-1Serial Number 82354Voltage Configuration 240V, 3ø, 4WNumber of Poles 3PBus Rating 200ABus Bracing 10kAICNEMA Enclosure 3R

Table 5 Existing Main Panel Specifications

Manufacturer Square DModel Number NQOD442L225Serial Number -Voltage Configuration 240/120V, 3ø, 4WBus Rating 225ABus Bracing 10kAICMain Circuit Breaker

Rating

200A/3P

NEMA Enclosure 3R



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Table 6 Existing Panel ‘KA’ Specifications

Manufacturer Square DModel Number NQOD442M150CUSerial Number -Voltage Configuration 240/120V, 3ø, 4WBus Rating 150ABus Bracing 10kAICMain Circuit BreakerRating

150A/3P

NEMA Enclosure 3R

Table 7 Existing Refrigerator Compressor Specifications

Manufacturer CopelandModel Number REK3-0125-TFC-212Serial Number 98B14819Voltage 208V, 3øRated Horsepower 1.5 HPLocked Rotor Amps 31 APower Factor 0.85

Table 8 Existing Freezer Compressor Specifications

Manufacturer CopelandModel Number CS27K6E-TF5-970Serial Number 04J12761BVoltage 208V, 3øRated Horsepower 3 HPLocked Rotor Amps 82 APower Factor 0.85

The generator operator interface displays the real-time phase

current drawn by each of the phases. The operator interface displays the

current drawn by phase 3 to be 62A at 206.3V. The load currents for

phases 1 and 2 were noted as 48A and 56A at 207V and 210V,



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respectively. The phase currents are unequal and thus the system is

unbalanced resulting in a neutral current. The design will assume a

balanced system with a maximum phase current demand of 70A at the

nominal 208V. These assumptions are necessary to ensure the design of

a reliable system that meets the current peak demand requirements as

well as allows for the future load expansion at the Camp. The apparent

power demand at the Boy Scout Camp is calculated below:

ø √ 3 √ 370208 25.2 (3-1)

This apparent power demand will be used in later sections to

determine if the creek can deliver enough power to the Boy Scout Camp.

C. Head Measurements

Figure 16 The Head of a River Flow [9]

The gross head of a water resource is defined as the absolute

vertical distance between the points of entry of the intake system to the

point at which the water imparts onto the turbine. It is illustratively



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depicted in the figure above. The net head is defined as the gross head

minus all pipe losses due to friction and turbulence and is used to

calculate the available power capacity of the water resource. To

determine the net head, the river’s gross head must be measured and

pipe losses calculated. The pipe losses are calculated using the

dimensions and characteristics of the penstock.

Figure 17 Surveyor’s Method

The gross head was measured at the Boy Scout Camp using the

surveyor’s method. This method is illustratively depicted in the figure

above. At the Boy Scout Camp, the proposed location of the pipeline

intake and the water turbine is at the existing dam and at the top of the

waterfall, respectively. The data collected for the horizontal and vertical

distances measured are recorded in the table below.



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Table 9 Gross Head Measurements (measured in feet)

*THD: Total Horizontal Distance*VD: Vertical Distance



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The total vertical distance measured is the sum of the values in the

vertical distance (VD) columns and is 235.9 feet. With a horizontal

distance of 936 feet and a vertical distance of 235.9 feet, the length of the

associated penstock is calculated as:

√ 936 235.9 965.3 (3-2)

D. Flow Rate Measurements

The flow rate of the creek was first measured using the bucket fill

method. The bucket fill method measures the time it takes to fill a

container of known volume. A 5 gallon plastic bucket was used at the Boy

Scout Camp. The flow rate data measured using this method is recorded

in the table below.

Table 10 Time to Fill Bucket

Trial Bucket Volume(gallons) Time to Fill (s)

1 5 13.22 5 15.13 5 14.34 5 13.7Average 5 14.1



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From this data the average volumetric flow rate of the creek can be

calculated:

. 0.355 (3-3)

or

0.355 1

7.481

0.0474 0.0474

An alternative method to measure flow rate is the float method. In

this method, the time it takes a buoyant object to float along a section of

the creek of known length and depth is measured. The cross sectional

area in this particular section of the creek is calculated using the

measured width and average depth. Five locations along the creek were

used to take these measurements. The data collected from these

measurements is recorded in the tables below. For reference, the first

measurement was taken immediately downstream of the existing dam

(Site 1) and last measurement was taken immediately upstream of the

waterfall (Site 5).



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Table 11 Site 1 Depth and Width Measurements

Width [ft] 3

Depth Measurements [ft] 0.083

0.250.3750.330.160.16

Average Depth [ft] 0.226333

Average Cross SectionalArea [ft2] 0.679

Table 12 Site 1 Velocity Measurements

Time [s] Distance [ft] Velocity [ft/s]8.89 4 0.449944

12.56 4 0.3184719.51 4 0.42061

13.53 4 0.295639Average 0.371166

• Site 1 Average Volumetric Flow Rate: 0.252022 ft3/s


Width [ft] 2

Depth Measurements [ft] 0.0830.1450.2080.2080.083





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Time [s] Distance [ft] Velocity [ft/s]3.47 3 0.8645533.78 3 0.793651

3.78 3 0.793651Average 0.817285



Width [ft] 6.66


0.250.479

0.50.25

0.229




Time [s] Distance [ft] Velocity [ft/s]3.98 2.5 0.6281413.98 2.5 0.6281413.72 2.5 0.6720433.99 2.5 0.626566

Average 0.638723




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Width [ft] 2.5


0.1660.1660.1250.250.250.250.25

0.333




Time [s] Distance [ft] Velocity [ft/s]15.92 9 0.56532712.4 9 0.725806

10.07 9 0.893744

11.22 9 0.8021397.61 1.182654

Average 0.833934




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Width [ft] 3


0.250.25

0.3330.3330.2080.125




Time [s] Distance [ft] Velocity [ft/s]12.93 8 0.61871613.58 8 0.58910211.42 8 0.70052512.9 8 0.620155

Average 0.632125


The table below compiles all of the average fluid velocities and

volumetric flow rates for the five different sites.



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Table 21 Float Method Average Velocity and Volumetric Flow Rate

for 5 Sites

Location Fluid Velocity[ft2/s]

CrossSectionalArea [ft2]

Volumetric FlowRate [ft3/s]

Site 1 Average 0.371166 0.679 0.252022Site 2 Average 0.817285 0.2908 0.237666Site 3 Average 0.638723 2.08014 1.328633Site 4 Average 0.833934 0.502778 0.419Site 5 Average 0.632125 0.713571 0.451

Total Average 0.6586466 0.853 0.538

The gross head and flow rate data will be used later to calculate the

maximum power rating of the generator. To summarize, the site offers a

gross head of 235.9 feet and an average volumetric flow rate of Q = 0.538

ft3 /s or 0.01523 m3 /s.

The discrepancies between the data obtained by the bucket

method and the float method can be mainly attributed to the inaccuracies

in performing the bucket method at the Boy Scout Camp. Ideally, when

performing the bucket fill method, a temporary dam is built with a single

outlet pipe that directs the water into a bucket just below the pipe. This

ensures all of the water enters the bucket and minimizes splashes which

can lead to inaccurate results. It was not possible to build this dam

because of the rigid bedrock in the waterfall. Inevitably, portions of the

waterfall managed to miss the bucket leading to inaccurate

measurements. It was also difficult to determine when the bucket was





32

IV. Civil Design

A. Exploitation Scheme

One of the first steps in the development of a hydroelectric system

design is to determine the desired water control scheme. The two most

important parameters that influence this decision are the head and flow

rate of the water source. The following are descriptions of common hydro

system water control schemes.

i. Dam Scheme

Dams are hydraulic structures used in many water control

schemes. A dam stores the potential energy of water by concentrating the

hydraulic head in a reservoir. This subsequently increases the water level

of the river upstream of the dam. Upstream flooding could potentially

pose a problem if significant flooding occurs. Flooding can lead to the

destruction of existing wildlife and their habitat.

Figure 18 Folsom River Dam [10]



33

ii. Diversion Scheme

A diversion scheme, sometimes called “run-of-the-river” scheme,

employs the use of hydraulic structures to divert a portion of the stream

flow to a remote hydro powerhouse. In this water control scheme, the

potential and kinetic energy of the water are harnessed through the

natural flow and elevation drop of the river. In a typical diversion scheme,

the water resource is diverted through a penstock, a low pressure water

pipe, into the powerhouse which houses the turbine-generator set.

Following the powerhouse, the diverted water is then discharged through

a tailrace downstream of the original water resource. Common hydraulic

structures used in these schemes include but are not limited to weirs,

penstocks, dams, and spillways. Diversion schemes are optimal when

used at a site with a steady, constant flow of water throughout the year.

These schemes do not perform well during the dry months with low water

levels and so it is necessary to evaluate the range of water level

fluctuations throughout the year. It is possible to mitigate this problem

through the installation of a large reservoir. The reservoir can store water

to avoid the impacts of dry seasons and provide energy during peak

demand periods with high energy prices increasing the overall efficiency of

the plant.



34

Figure 19 Diversion Scheme [11]

iii. Pumped Storage

A pumped storage facility uses water for potential energy storage

and requires the use of unique bi-directional hydro turbines. The rotating

machines coupled to these bi-directional turbines can be operated as

generators or motors. When reversed, the turbines are used to pump

water from the downstream reservoir at the power station to upstream

reservoir. This water is stored as potential energy and can be dispatched

and used to generate electricity during peak demand periods when energy

prices are the highest. This allows the plant to take advantage of price

arbitrage and increase the entire operating efficiency of the plant.



35

Figure 20 Racoon Mountain Pumped-Storage Plant [13]

B. Exploitation Scheme Selection

The water source at the Pico Blanco Boy Scout Camp developed a

gross head of 235.9 feet over 936 feet of horizontal terrain. The average

volumetric flow rate was measured to be 0.538 ft3 /s. Compared to other

systems, this flow rate is low given the head capacity developed over 936

feet. The following photograph depicts a downhill view where the creek

flows toward the waterfall.







38

V. Mechanical Design

A. Hydraulic System Considerations

Hydroelectric power systems capture the kinetic and potential

energy of water through the use of hydraulic structures, turbines, and

generators. Hydraulic engineering estimates and calculates the effects of

various hydraulic structures on fluid flow. This knowledge allows the

designer to not only estimate or calculate the total available system

energy, accounting for inherent system losses, but to also optimize the

performance of the hydroelectric system.

i. Water Flow in Closed Pipes

One of the major hydraulic structures used in a diversion scheme is

low pressure penstock used to divert the water resource to the hydro

power station. The penstock plays an important role in developing and

capturing the available potential and kinetic energy of the fluid. It

effectively translates the potential energy of the water at the intake into the

kinetic energy of the flowing fluid. The kinetic energy is then imparted

onto the turbine blades rotating the machine generating electrical energy.

An increase in the velocity or kinetic energy of a fluid occurs

simultaneously with a decrease in the fluid’s pressure or potential energy.

This fundamental principle was developed and published in various

hydrodynamic books in 1738 by Daniel Bernoulli, a Dutch-Swiss

mathematician [14]. Bernoulli’s principle assumes that the fluid is nearly

inviscid and incompressible experiencing a steady flow while exhibiting



39

negligible heat transfer. A nearly inviscid fluid is one that is characterized

by low viscosity as is the case with hydropower. In mathematical form his

principle states [15]:

(5-1)

Where:

H 1: the total potential energy head [m]

h 1: the elevation of the point above a reference plane (in the

positive z-direction) [m]

P 1: the pressure at that point [kg/m-s2]

ρ: the density of the fluid at all points throughout the fluid [kg/m3]

g : the gravitational acceleration [m/s2]

ρg : the specific weight of water [kg/m2-s2]

V 1 : the fluid flow rate at a point on the streamline [m/s]

The total energy head H 1 of a fluid is the sum of the fluid’s elevation

h 1, pressure head or potential energy, and velocity head or kinetic

energy . As mentioned earlier, this relationship is only true for closed

pipe systems where the fluid is nearly inviscid and incompressible.

Solving explicitly for the pressure P 1 yields:



40

· · (5-2)

According to the equation above, the pressure P 1 approaches zero

as the fluidic velocity V 1 increases. This implies that at some high velocity

the fluid exhibits a pressure P 1 that is negative although the majority of

fluids cannot attain a zero pressure let alone a negative absolute

pressure. This realization highlights the boundaries and limitations of

Bernoulli’s equation. Cavitation, a natural phenomenon, is one of the

reasons that Bernoulli’s equation exhibits these limitations.

The manner in which a fluid flows through a pipe depends on

characteristics of the fluid such as viscosity and velocity as well as

characteristics of the pipe such as internal diameter and the roughness of

the interior surface. Laminar and turbulent flow compose the two main

types of fluid flow. Laminar flow, commonly called streamline flow,

describes fluid flows that are smoother and more predictable. On the

other hand, turbulent flow describes fluid flows that are mainly

unpredictable and chaotic. Illustrations of both types of fluid flows are

depicted in the figure below.



41

Figure 23 Laminar vs.Turbulent Flow [17]

Laminar flow is described as parallel flowing fluid “sheets”. The

velocity of each of these “sheets” is different from the adjacent “sheet”. It

is possible to plot the velocity of each of the “sheets” on the same graph to

obtain the velocity distribution profile of the fluid. Laminar fluid flows in

closed pipes exhibit a parabolic velocity distribution profile as illustrated in

the figure below.

Figure 24 (a) Laminar Flow and (b) Turbulent Flow in a Closed Pipe [14]



42

Referring to the velocity distribution profile for laminar flow in the

figure above, the maximum velocity occurs at the centerline of the pipe.

The portion of the fluid that is in direct contact with the pipe’s interior

surface will exhibit zero velocity. The velocity distribution profile for

turbulent flow is also illustrated in the figure above. The velocity profile of

the fluid in turbulent flow is illustrated to be approximately constant across

the entire diameter of the pipe. In contrast to laminar flow, the portion of

the fluid that is in direct contact with the pipe’s interior surface exhibits

non-zero velocity.

Fluids characterized by either laminar or turbulent flow will exhibit

different system parameters and associated system performance. Thus it

is necessary for the designer to understand the type of flow the water in

the penstock will be characterized by. The type of fluid flow can be

generally predicted and estimated by calculating a parameter called the

Reynold’s number. Reynold’s number is a ratio that defines the

relationship between inertial forces to viscous forces of a fluid. This

number not only helps predict the type of fluid flow exhibited but will

determine at what point the fluid might change between laminar and

turbulent flow. Generalized for fluid flow in a closed circular pipe, the

equation for Reynold’s number is defined as [14]:

(5-3)



43

Where:

ρ: the density of the fluid [kg/m3]

V : the average (mean) fluid velocity [m/s]

D : the inner diameter of the penstock [m]

µ : the dynamic viscosity of the fluid [kg/m-s]

: the kinematic viscosity of the fluid [m2 /s]

This equation can be derived by dividing the fluid’s inertial or drag

forces (

) by the viscous forces (). Inertial or drag forces tend to

produce turbulent, chaotic flow instabilities such as eddy currents and

vortices in fluids. Viscous forces produce predictable, smooth, and

constant fluid motion leading to the parabolic velocity distribution profile of

laminar flow. Evaluating the ratio defining the Reynold’s number shows

that fluids characterized by dominant inertial forces will have a high

Reynold’s number and most likely will exhibit a turbulent flow. Fluids

characterized by dominant viscous forces have a low Reynold’s number

and most likely will exhibit a laminar flow.

The industry accepted transition point between laminar and

turbulent flows in closed circular pipes is identified by a Reynold’s number

R e of approximately 2300. Typically, fluids characterized by a Reynold’s

number above 2300 and below 2300, can be described by turbulent and

laminar flows, respectively. The transition point between the two flow



44

types are not precisely predictable and so a Reynold’s number of 2300 is

used as an approximate transition point. In reality, the transition occurs

over a range of Reynold’s numbers depending on fluid and system

parameters.

The average volumetric flow rate of the creek at the Boy Scout

Camp was measured to be Q = 0.538 ft3 /s (0.01523 m3 /s). Hydroelectric

systems with similar head and flow rates use penstocks with an internal

diameter of 6” (0.152 meters). The same internal penstock diameter will

be used in this design. Although it is proposed to couple a 6” penstock to

the existing 2” outlet pipe protruding from the dam, the calculations will be

performed using a 6” pipe as this will constitute over 99% of the entire

length of the penstock. The average fluid flow velocity is calculated as:

0.01523

0.1522 0.839 /

The kinematic and dynamic water viscosity coefficients used to

calculate the Reynold’s number are listed in the table below for varying

ambient temperatures.



45

Table 22 Dynamic and Kinematic Viscosity of Water [19]

Temperature

- t -

( o

C)

DynamicViscosity

- µ - (kg/(m∙s)) x 10-3

KinematicViscosity

-

-

(m2 /s) x 10-6

0 1.787 1.787

5 1.519 1.519

10 1.307 1.307

20 1.002 1.004

30 0.798 0.801

40 0.653 0.658

50 0.547 0.553

60 0.467 0.475

70 0.404 0.413

80 0.355 0.365

90 0.315 0.326

100 0.282 0.294

The site’s annual temperature cycles were evaluated using data

from the National Oceanic and Atmospheric Administration (NOAA).

According to this data, the annual average temperature is around 20°C.

Referring to the table above, the kinematic viscosity of water at this

ambient temperature is 1.004 x 10-6 m2 /s. This coefficient is used to

calculate the Reynold’s number:

0.839 0.152

1.004 10 / 1.2710

The high Reynold’s number indicates that our fluid will exhibit a

turbulent flow. This is a typical result as “most engineering air and water

pipe flows are turbulent, not laminar” [14].





47

· ·

(5-5)

Where:

f : friction factor [unit less]

L: length of the pipe [m]

D : internal pipe diameter [m]

V : average fluid velocity [m/s]

g: gravitational acceleration [m/s2]

The equation above applies for systems with incompressible fluids

exhibiting a steady flow rate through a closed circular pipe of any cross

section. It is valid for both turbulent and laminar flows.

For fluids exhibiting laminar flow, the friction factor f is calculated

using the following equation [14]:

(5-6)

The friction factor is independent of the penstock’s material

properties, as implied by the equation above. In laminar flows, according

to the above equation, the friction factor is inversely proportional to

viscous energy losses. Thus the system’s head losses can be calculated

by inserting the friction factor f into the Darcy-Weisbach equation defined

above [14]:



48

, · ·

·

·

(5-7)

The system’s head losses are proportional to the fluid’s average

velocity V . This is in accordance with Newton’s fundamental kinematic

principles, which as applied here, state that an increase in the fluid’s

impending velocity on the penstock’s interior surface will result in an

increase in friction losses.

For fluids exhibiting turbulent flow, the friction factor f can be

approximated applying the following equation for system’s employing

penstock’s with a smooth interior surface [14]:

2.0log · 0.8 (5-8)

It is interesting to note from the equation above, that the friction

factor f is independent of the penstock’s material properties, specifically

the roughness of the interior surface. The friction factor f can also be

approximated explicitly using the alternative equation defined below [14]:

0.316 4000 10 (5-9)

1.8 log .

The Reynold’s number R e for this particular system at the Boy

Scout Camp was calculated to be 1.27x105. Thus observing the defined



49

boundaries for the equations above, the latter equation can be applied to

approximate the friction factor f for this system where the fluid is in

turbulent flow. The friction factor f is calculated below.

1.8 log 1.27106.9 0.01696

The Darcy-Weisbach equation is then evaluated by inserting the

friction factor calculated above applying a pipe diameter D of 0.152

meters, a total penstock length L of 936 ft (285 meters), and an average

velocity V of 0.839 m/s: ,

2 0.01696 285

0.152 0.839/29.81 1.14

The head loss inherent in this system is 1.14 m (3.74 feet). The

head losses are used to calculate the system’s net head:

235.9 3.74 232.2

B. Hydraulic Turbines

A turbine is a mechanical device that converts the kinetic energy in

a moving fluid into the rotational energy of the turbine rotor. The two

major turbine types are the reaction and impulse turbines. A reaction

turbine creates power by directly reacting to the fluid's pressure over its

runner blades. Common reaction turbines include Francis and Kaplan

turbines.



50

Figure 25 Reaction Turbine

On the other hand, an impulse turbine first converts the potential energy of

water pressure into kinetic energy through the use of nozzles. It then

imparts this kinetic energy onto the runner blades of the turbine. Common

impulse turbines include Pelton, Turgo, and Cross Flow turbines.

Figure 26 Impulse Turbine

i. Turbine Selection Criteria

Selecting a specific hydraulic turbine type for the system

design is not always “black and white” as it is possible to use various

turbine types in multiple applications. It is important to not only

evaluate the site conditions affecting available output power

throughout the year, but to also consider the customer’s preferences





52

and the accompanying loud “bang” noise. If not addressed, over time,

the repetitive action can cause pitting of the runner blades or hub and

will eventually result in cracks and other mechanical failures.

Therefore, careful design measures must be taken to avoid

situations such as these and thus it is necessary to understand the

reasons these cavities form and how to solve these problems. The

system proposed at the Boy Scout Camp does not experience flow

rates and head pressures great enough to experience cavitation

problems but it is still important to be aware of these issues as they

arise in many other systems.

b. Net Head

The gross head of the site’s water resource is defined as the

vertical distance between the location of the upstream intake of the

penstock and the downstream outlet where the water imparts onto

turbine. The gross head alone does not provide an accurate

estimation of the amount of available power from the site’s water

resource as it assumes an ideal system model. In order to accurately

estimate the available power, the designer must take into account

inherent system losses. Thus the net head is defined as the gross

head minus head energy losses. Typical turbine types selected for

various net head ranges are outlined in the table below.



53

Table 23 Turbine Type and Typical Net Head Range [14]

Turbine Type Head Range [meters]Kaplan and Propeller 2 < Hn < 40Francis 25 < Hn < 350

Pelton 50< Hn < 1300Crossflow 5 < Hn < 200Turgo 50< Hn < 250

The net head at the Boy Scout Camp was previously calculated to

be 232.2 feet (70.8 meters). According to the table above, Francis,

Pelton, Crossflow, and Turgo turbines are all possible candidates for the

proposed system design given the site’s net head.

c. Range of Discharge Through Turbine

The range of flow rates and discharges of the water resource

throughout the year provide another important parameter helping the

designer to select an appropriate turbine type for the system application.

The varying flow rates affect the site’s net head as system losses may be

altered.

An evaluation of and research into the flow rates of the Boy Scout

Camp throughout the year reveal that the most applicable concern is

having too little flow during the summer and fall season. There is no

concern regarding flow rates that may be too high throughout the year.

The safety factors inherently built into the hydraulic structures and other

system components are more than adequate to handle any high flow rates

the site can experience, if any. Thus it is most important to evaluate the





55

Figure 27 Typical Flow Ranges for Various Turbines [15]

The minimum volumetric flow rate of 0.01523 m3 /s and net head of

70.8 meters at the Boy Scout Camp places the system below the lower

region of the Pelton turbine. The diagonal power capacity lines in the

figure above indicate that the lower boundary of the Pelton range is 50kW.

Thus the maximum power capacity at the Boy Scout Camp is below this.

The figure above is intended to be used as a reference guide. Although

the available power at the Camp does not fall directly into one of the





57

The use of various turbines for the application at the Boy Scout

Camp was also discussed with hydroelectric turbine manufacturers and

system designers. The general consensus and recommendation was that

a Pelton turbine would be optimal for the Camp which aligns with the

turbine selected above. The proposed turbine is a Canyon Model #751-2

Pelton turbine with a 7.5 inch pitch diameter and double nozzle. A

photograph of the turbine is inserted below.

Figure 28 Canyon Hydro Pelton 751-2 Turbine

ii. Pelton Turbine

As mentioned previously, Pelton turbines are a type of impulse

turbine. In this type of turbine, a circular disk is mounted on the rotating

shaft or rotor. Nozzles are arranged around the periphery of a wheel with

buckets.



58

Figure 29 Pelton Runner

The buckets are arranged to receive the water jets exiting the

nozzles and are positioned tangentially to the circumference of the turbine

to maximize the amount of energy translated in the process as illustrated

in the figure above. A needle valve will control the flow of water through

these jets as illustrated in the figure below.

Figure 31 Cross Section of a Nozzle with Deflector

The available water pressure, head, and other operating

requirements will determine the configuration of the nozzles placed around



59

the turbine. The nozzle axes are typically placed in the plane of the

turbine runner. Additional control may be added to the nozzles for

emergency stop situations such as a load rejection. Some units are built

with deflectors that can divert the jet of water exiting the nozzles. This

helps to ensure that the turbine will not reach its runaway speed if the

highly pressurized water imparts too much kinetic energy onto the runner

blades. The deflectors provide a second level of control in addition to the

flow rate control provided by the needle valves to the nozzles. If needle

valves close abruptly during transient high flow rate events or transient

load changes, it is possible for the upstream pipeline to experience

instantaneous overpressure surges which can damage the equipment.

Deflectors allow the needle valves to remain open during these types of

events preventing overpressure surges.

Pelton turbines are an optimal solution for sites with high net heads.

A high net head increases the water velocity in the pipe resulting in a high

speed jet stream exiting the nozzles and subsequently striking the turbine

runner blades. The water exiting the nozzles gain a significant increase of

kinetic energy as the fluid moves from the high pressure region of the

penstock to an area of low atmospheric pressure. The kinetic energy of

the water is reduced as it rotates the runner blades. The buckets

surrounding the periphery of the wheel are designed to help maximize the

energy translated from the kinetic energy of the flowing fluid to the



60

rotational energy of the turbine runner and minimize the energy lost in this

process.

Pelton turbines can be configured with an orientation in either the

horizontal or vertical axes. A vertical axis Pelton turbine will typically have

three or more nozzles directing the water onto the runner blades. The

maximum number of nozzles integrated into a Pelton turbine is typically

six. Pelton turbines with this many nozzles are usually installed in large

scale hydroelectric systems. The proposed Pelton turbine for the Boy

Scout Camp is configured with two nozzles and oriented in the horizontal

axis. Schematics of double nozzle Pelton turbines oriented in the

horizontal and vertical axes are depicted below.

Figure 31 Two Nozzle Horizontal Pelton Turbine





62

If the nozzles are supplied with a constant flow of water, then the

turbine speed will only vary according to changes of the load torque place

on the turbine output shaft. A constant system frequency is required thus

the turbine-generator unit must rotate at a constant speed. The water flow

through the nozzles can be controlled and kept constant in steady state

conditions through the use of the needle valves. The positions of the

needle valves are adjusted by servomotors which react to various load

changes on the rotor shaft.



63

VI. Electrical System Design

The Boy Scout Camp’s stand-alone, radial feed power distribution

system is currently supplied by a single 75kVA, 3ø diesel generator. The

Camp cannot be tied to the grid and must operate stand-alone due to long

distance between the site and the nearest electric utility power distribution

lines. An important step when evaluating the feasibility of using a

hydroelectric power plant as the Camp’s primary generator is comparing

the available power supplied by the water resource to the electrical load

demands of the site.

A. Generator Selection

The purpose of an electrical generator is to transform the

mechanical energy supplied by the prime mover into electrical energy. A

generator is simply an electric motor that is rotated via a mechanical input.

An AC generator induces an AC voltage on the stator coils as a result of

the rotating alternating magnetic fields of the rotor coils. The prime mover

can be derived from various mechanical sources such as steam power or

an internal combustion engine fueled by diesel, natural gas, or alternative

fuel types. In a hydroelectric power system the generator’s prime mover is

the hydraulic turbine. The two main types of AC generators are

synchronous and asynchronous generators. Asynchronous generators

are more commonly referred to as induction generators.



64

i. Synchronous Generator

In general, a synchronous machine maintains a speed, the

synchronous speed, which matches the frequency of the stator current in

the armature windings under steady state conditions. In voltage source

mode, the electrical frequency will be dictated by the speed of the

generator input shaft driven by the prime mover. The shaft speed, and

thus system frequency, is regulated by a governor which monitors this

shaft speed and compares it to the desired frequency set point. The

electrical frequency is defined as [16]:

(6-1)

Where:

f e : Electrical frequency in Hertz [Hz]

n m : Mechanical speed of the magnetic field in revolutions per

minute [rpm]

P : Number of poles

The equation above simultaneously defines the rotor speed as the

two are approximately equal in a synchronous machine.

The amplitude of the internal generated voltage is proportional to

the frequency and the field current and can be expressed by [16]:

(6-2)



65

Where:

K : Constant representing the construction of the machine

φ : Flux in the machine

ω: Speed of the machine

The magnetic flux of the machine increases linearly with increasing

field current until the iron saturates after which the flux characteristics are

non-linear. A graph comparing the flux to the field current for a

synchronous generator is illustrated below:

Figure 33 Graph of Flux Versus Field Current for Synchronous Generator [16]

The internal generated voltage E A is proportional to the flux and

thus will exhibit the same characteristics as illustrated in the graph above

assuming a constant synchronous speed ω. In order to optimally control

the system voltage, the machine must not be saturated. A significant





67

consumption and terminal voltage control. External sources supply the

reactive power that magnetizes the machines core. In a grid-tied

application, the external source of reactive power can be the connected

utility which is modeled as an infinite bus. If operating stand-alone, then

the induction generator will require local capacitor banks to supply the

magnetizing current to generate a terminal voltage. The generator

terminal voltage varies with the amount of magnetizing current flowing in

the rotor. Thus the size of the externally connected capacitor banks,

which supply this magnetizing current, will determine the terminal voltage

generated. The reactive current supplied by a capacitor is directly

proportional to voltage applied to it as defined in the equation below [16]:

2 (6-3)

The following equation defines the impedance of a capacitor and

illustrates the linear relationship between voltage and current.

(6-4)

At a constant frequency, the slope of the impedance line increases

with decreasing capacitance. The intersections between the capacitor V-I

graph and the terminal voltage versus no-load armature current graph of

the induction machine, when operated as a motor, will determine the

amount of the magnetizing current from the capacitor needed to generate

a specific terminal voltage.



68

Even with externally connected capacitor banks supplying steady

state reactive power to the induction machine, there needs to be some

intermittent source of reactive power in order to start the machine. Thus it

is common to connect and temporarily run a small synchronous generator

to produce the initial magnetizing current needed by the machine.

iii. Generator Selection

The major advantages of an induction generator are an increase in

reliability and a decrease in cost compared to that of a synchronous

machine. The major drawback of an induction generator is the lack of a

field winding which results in starting complications and a reduced ability

to control terminal voltage. The induction generator, operating stand-

alone, must rely upon an externally connected synchronous generator to

aid in initial start-up and externally connected capacitor banks to supply

steady state reactive power. The lack of voltage control is a greater

concern when there are additional reactive loads in the system, such as

the refrigerator and freezer compressors at the Boy Scout Camp. The

transient and steady state control complexities associated with induction

generators require an increased level of operations and maintenance and

also require a facility operator with intimate knowledge of the intricacies of

such a system. The Boy Scout Camp does not currently support this level

of operations and maintenance and thus an induction generator does not

prove to be a viable solution for the hydroelectric system design.



69

The proposed generator for this design is a four pole synchronous

generator. A permanent magnet will supply the field windings with a DC

current creating a source of reactive power that will be used to maintain

the generator terminal voltage. The synchronous generator will be

connected to the Pelton turbine output shaft through a flexible coupling.

The synchronous generator’s apparent power rating is calculated

from the creek’s mechanical power capacity. Conceptually, this is

performed by first determining the total kinetic energy available from the

creek and then translating it into electric energy while accounting for the

turbine’s rated efficiency. Inherent system losses are then applied to

determine the system’s actual power capacity. The equation below

defines the mechanical power output of the turbine [21]:

ρ (6-5)

Where:

P m : the mechanical power output of the turbine [W]

ρ: the density of the fluid at all points [kg/m3]

Q: volumetric flow rate of the fluid [m3 /s]

g: gravitational acceleration [m/s2]

H : the net head [m]

ηT : turbine efficiency



70

The net head and volumetric flow rate were previously determined

to be 232.2 feet (70.8 meters) and 0.538 ft3 /s (0.01523 m3 /s), respectively.

The turbine selected is rated for an efficiency of 80% and thus the

mechanical power applied to the turbine shaft is calculated as:

1000 9.81

70.8 0.01523 80%

8462.4 · 8.46

The torque applied to the generator rotor, neglecting rotational

losses in the flexible coupling, can be calculated from the mechanical

output determined above. The following equation defines the load torque

as a ratio of the applied mechanical power to the rotor speed [21]:

ω (6-6)

The governor isochronously controls the electrical frequency and

thus shaft speed to 60Hz. As stated previously, the electrical frequency

for a synchronous generator is defined as [16]:

(6-7)

Where n m is the speed of the rotor magnetic field and P is the

number of poles. This particular generator will be constructed with 4 poles

and will operate at a nominal 60Hz. The mechanical speed is calculated

as:



71

120 120604 1800

This corresponds to a mechanical speed of:

1800 2 60 188.5 /

The mechanical input torque and thus the minimum torque rating of

the generator shaft is calculated as:

ω

8.46 188.5 / 44.9 ·

The proposed generator power rating is 14kW. Hydro generator

units with this rating are readily available and generally recommended for

systems of this size according to hydroelectric system designers and

installers. This rating is much greater than the available power that can be

supplied by the water resource during the dry season which is about

8.5kW as calculated above. This is intended to ensure that hydroelectric

power system can deliver the full amount of power available throughout

the year. The specifications of the proposed hydro generator selected are

outlined in the table below.



72

Table 25 New Hydro Generator Specifications

Manufacturer Marathon ElectricModel Number 283PSL1707Apparent Power Rating at3ø

17.5Kva

Real Power Rating at 3ø 14kWVoltage Configuration 208V, 3ø, 4WPower Factor 0.8Rated Speed 1800 RPMField Winding Source Permanent Magnet

B. System Design

i. Conductor Sizing and Selection

The generator feeder cables must be rated to carry the generator

nominal output current continuously under normal operating conditions.

The generator output current is defined below:

ø, √ ø, (6-8)

As indicated in the specification above, the generator selected is a

MagnaPlus 283PSL1707 with an apparent power rating of 17.5kVA. The

output current supplied by the generator is calculated as:

ø, 17.5 √ 3 208 48.6

The rated minimum ampacity of the conductor selected must be

greater than or equal to the generator rated output current as calculated

above. The size of the conductor will also be selected to minimize voltage

drop during normal operating conditions. The amount of voltage drop



73

along a circuit depends on the size of the conductor and thus its

resistance. The resistance of a metal conductor is defined below [22]:

1 (6-9)

In the equation above, R0 is the conductor resistance at T0, α is the

percentage change in resistivity per unit temperature, T is the operating

temperature of the conductor, and T0 is the reference temperature which is

typically room temperature. The equation above mathematically illustrates

the linearly proportional relationship between operating temperature and

resistance. An increase in the conductor operating temperature is

accompanied by an increase in its resistance. Thus as operating

temperatures increase the circuit voltage drop and total system losses will

also increase. This concept is the basis for the cable ampacity derating

factors provided by the National Electric Code.

The hydroelectric generator is anticipated to supply current

continuously throughout the day. There will be additional thermal

contributions to the operating temperature of the conductor due to the fact

that it will carry this current continuously. In conditions where the

conductor continuously carries current for three hours or more, the

National Electric Code requires the designer to select a conductor

ampacity that is greater than or equal to 125% of the nominal current. The

generator maximum continuous output current is calculated to be:

1.25 ø, 1.25 48.6 60.75



74

Thus the minimum ampacity of the conductor selected must be

greater than or equal to 60.75A. The National Electric Code provides an

ampacity table that defines the ampacity of a cable with a given insulation,

conductor size, and environmental operating conditions. This table is

inserted below:



75

Table 26 NEC Ampacity Table

According to the table above, a #6 AWG THWN has a minimum

ampacity of 65A in an ambient operating temperature of 30°C which is

greater than the calculated current of 60.75A. THWN type insulation is a

commonly used cable insulation system that is rated for exposure to



76

moisture and contains flame retardant additives for additional fire

resistance. This cable insulation is not rated for direct burial and thus

must be protected by conduit underground.

The National Electric Code provides an AC resistance table for

various conductor sizes and their respective operating conditions and

application. This table is inserted below.



77

Table 27 NEC Ch.9 Table 9 AC Resistance Table

According to the table above, the impedance of a #6 AWG 3ø,

600V copper conductor, with 75°C insulation (THWN) operating at 60Hz

with three single conductors in PVC conduit is:



78

0.49 0.051 1000 || 0.492 1000

The total circuit voltage drop must be calculated to ensure minimal

system losses. The design goal is to maintain a total maximum line to line

voltage drop of 2%. A 2% voltage drop is selected as a design goal in

accordance with the recommendations of the National Electric Code for

feeder circuit voltage drops.

The line to neutral voltage drop for a single phase AC circuit is

calculated as follows:

|ø| 2 · · || · || (6-10)

Where L is the length of the circuit, Z is the impedance per unit

length of the conductor selected, and I is the continuous current flowing in

the conductor. The factor of 2 appears in the equation above accounts for

the current flowing in both the line and neutral conductor thus establishing

the total circuit voltage drop.

The output circuit configuration of the hydroelectric generator is 3ø,

4 wire. In this design, it is assumed that the Boy Scout Camp loads are

balanced resulting in negligible neutral current. For 3ø circuits, the

voltage drop between any two phase conductors is 0.866 times the

voltage drop calculated by the preceding formula.

ø, 0.866 · 2 · · || · || (6-11)



79

ø, 0.866 · 2 · 630 · 0.000492 ·60.75 32.6

The equations above assume a balanced 3ø load and thus there is

no current flowing in the neutral conductor and the voltage drop between

phases A-B, B-C, and C-A will be identical. According to the calculations

above, the service voltage at the main distribution panel in the proposed

design is:

ø, 208 32.6 175.4

The connected loads at the Camp cannot operate with a supply

voltage of 175.4V. The voltage drop expressed as a percentage of the

nominal circuit voltage is calculated:

ø, % 32.6 208 100 15.7%

This is greater than the design requirement of a maximum 2%

voltage drop. The conductor impedance Z is explicitly defined in order to

determine the maximum conductor resistance that will satisfy the 2%

voltage drop design requirement. The maximum allowable voltage drop

along a nominal 208V circuit is calculated:

2%· 208 4.16

An upper limit for the conductor impedance is defined using the

design voltage drop calculated above:



80

|| .··· (6-11)

|| 4.16

0.866 · 2 · 630 · 60.75· 1000 0.0628 1000

The maximum impedance is thus 0.0628 [ per 1000 feet]. Thus a

minimum #300kcmil THWN is required which has a corresponding

impedance of 0.059 [ per 1000 feet].

ii. Overcurrent Protection Device Sizing and Selection

Ungrounded system conductors require overcurrent protection in

order to prevent cable damage during overload and short-circuit events.

Overcurrent protective devices include fuses, circuit breakers, and shunt

circuit breakers. This requirement does not apply to grounded conductors

such as grounding electrode conductors, equipment ground conductors,

and neutral conductors in solidly grounded 4 wire systems.

In AC systems, circuit breaker ratings are selected to be the sum of

the non-continuous load current plus 125% of the continuous load current.

It is acceptable to select the rating as the non-continuous current plus the

continuous current if the overcurrent device and its assembly are listed for

100% duty operation. The circuit breaker protecting the generator feeder

cables will not be bear this listing and thus the rating will be selected as

125% of the generator nominal output current. This value, which was also

calculated previously, is determined to be:

1.25 ø, 1.25 48.6 60.75





82

During the site survey it was noted that the Camp electrical loads

were mainly resistive except for the two compressors which operated at

0.85 lagging power factor. The “resistive” component of the connected

loads is assumed to be operating at an aggregate 0.99 lagging power

factor. The ratio of the compressor loads to the total camp load can be

estimated from the circuit breaker ratings indicated in the Camp’s existing

single line diagram. The circuit breakers protecting the compressors are

each rated 30A while the main circuit breaker supplying the entire

distribution system is rated for 200A. Thus the rotating loads comprise

30% (60/200 = 0.3) of the total system load. The overall Camp operating

power factor is then 0.95 lagging (30% x 0.85pf + 70% x 0.99pf = 0.95pf).

The phase angle difference between the operating voltage and current is:

cos 0.95 18.2°

This translates to a maximum real power demand of:

, cos 25.2 0.95 23.9

The maximum reactive power demand is calculated as:

, ·sin 25.2 ·sin18.2° 7.87

If the apparent power rating of the hydroelectric generator is

17.5kVA and the load power factor is 0.95 lagging, then the maximum real

power supplied is:

, · cos · 17.5 · 0.95 16.6





84

supply the remainder of the electrical demand. This system operation

minimizes the supplemental generator operating time which reduces fuel

operating costs and greenhouse gas emissions.

The proposed supplemental generator is a diesel generator rated

for 30kVA, 208V, 3ø, 4 wire. Operating at a 0.95 lagging power factor the

real power capacity of the generator is calculated as:

, · cos · 30 · 0.95 28.5

The reactive power capacity is calculated as:

, · sin 30 · sin 18.2° 9.37

The diesel generator output is configured 3ø, 4 wire with a solidly

grounded neutral. The hydroelectric generator output is configured in an

identical fashion. Any line to neutral loads connected to the Boy Scout

Camp distribution system can be supplied by the derived neutral of either

generator. A 4 pole transfer switch is required to transfer between

generation sources. The fourth pole in the transfer switch is needed to

switch the system neutral from either generator. If the neutral pole was

not switched between the two systems and instead kept solidly tied, it

would then be possible for neutral current to flow along the ground circuit

and energize any metal enclosures connected to it. This poses a safety

hazard as these metal enclosures are exposed to the public. The single

line diagram below illustrates the proposed system:



85

Figure 35 Existing Distribution System with New Hydro

and Diesel Generator Sources

iv. Motor Starting Considerations

As mentioned previously, there are two compressors connected to

the distribution system at the Boy Scout Camp. The prime movers for the

compressors are 3ø induction motors. The construction of an induction

motor is identical to that of an induction generator. In an induction motor,

the rotor speed is less than the synchronous speed consuming real power.

In comparison, the rotor speed of an induction generator is greater than

the synchronous speed providing real power.







88

determined. This conservative approach was used to guarantee a reliable

and robust design. The reactive power supplied by the hydroelectric and

supplemental diesel generator is 5.47 kVAR and 9.37 kVAR, respectively.

This provides a total of 14.8 kVAR of reactive power that can be supplied

by all of the generation sources. This is adequate to supply the Boy Scout

Camp’s maximum reactive power demand of 7.87 kVAR.

v. Turbine & Generator Control for Stand Alone Operation

Grid-tied electrical distribution systems are supplied with a constant

frequency and voltage with a specified tolerance from the local utility grid.

The total amount of generation and load within the distribution system is

much smaller than that of utility source which makes the utility source

appear like an infinite bus to the distribution system. Transient step-loads

within the distribution system will have negligible effect on the system

voltage and frequency because of the inertia associated with the utility

grid. Thus there is no need for the distribution system to actively monitor

service voltage and frequency from the utility.

In a stand-alone system, the on-site generation sources will set the

system voltage and frequency. Stand-alone systems lack the inertia to

passively maintain system voltage and frequency. Large step-loads and

generators going on or off line will have an adverse affect on system

voltage and frequency thus requiring active frequency and voltage control.

The major control devices that maintain the system frequency and voltage

are the governor and automatic voltage regulator (AVR), respectively.



89

The system frequency in a stand-alone application is dictated by the rate

of rotation of the generator rotor shaft. Changes in the amount of

generation and load within the system will contribute to system frequency

changes. The role of the governor is to adjust the fuel input to the prime

mover in order to maintain the nominal shaft speed. The Boy Scout Camp

nominal shaft speed was calculated to be 1800 rpm corresponding to a

system frequency of 60Hz. For example, if the fuel supply to the prime

mover increases when a constant load is connected, the rotor will

experience a transient acceleration. This translates into an increased

system frequency. Depending on the governor control algorithm, this

frequency will either remain, as in droop control methods, or be returned

to nominal 60Hz, if isochronous methods are used. The opposite is true

for a decrease in fuel supply with a constant load connected, the system

frequency will drop. For example, if a large electric load is suddenly

connected across the line, then the speed or frequency of the system will

drop to unspecified level if uncontrolled and fuel supply left constant. And

vice versa, if a load is taken off-line then the system frequency will

increase.

The automatic voltage regulator (AVR) performs a similar role in

actively maintaining the system voltage at the generator terminals. The

AVR will increase the DC field current in order to boost the terminal

voltage and vice versa. The amplitude of the generator’s terminal voltage

determines whether the generator is consuming or supplying reactive



90

power and the amount of reactive power consumed or supplied. Thus a

synchronous machine is capable of controlling terminal voltage and

reactive power itself through the control of the DC field current.

The two main types of voltage and frequency control methods are

isochronous and droop control. A generator operating in isochronous

mode will maintain a constant nominal frequency and/or voltage

regardless of the real and reactive power demand of the system. The

range of the apparent power demand is finite but within these limits the

AVR and governor maintain a constant system voltage and frequency,

respectively. Generators operating in droop control mode allow the

voltage or frequency to droop or rise as defined by the specific control

algorithm implemented by the AVR and governor. The majority of

generators connected to the utility grid operate in droop control mode.

These generators share system load changes as determined by their

respective droop algorithms. Typical droop algorithms allow the system

voltage or frequency to deviate between 3% and 5% of the system

nominal set points. Droop control methods help to increase system

stability. If multiple parallel connected generators with long time delays

were controlled isochronously there could be large power swings within

the system when trying to maintain a nominal system voltage or

frequency. The long time delays associated with the voltage and

frequency correction of these machines cause the parallel connected

generators to “hunt” thus the system will never achieve stability. Droop



91

control allows generators to share the power load between each other as

specified by the droop algorithm and rated power capacity of the

generator.

Stand-alone systems with multiple parallel connected generation

sources will typically operate one generator in isochronous mode and the

other generators in droop mode. The generator operating in isochronous

control mode would be the “leader” between the generator sources

maintaining a nominal 60 Hz cycle speed. The other generator would

operate in droop control mode where it would be able to share load

changes by allowing its frequency to droop. Mutual voltage control by the

generators would be accomplished by cross current regulation. This

method uses current transformers to measure the current flowing in the

generator feeder conductors, compare the two, and adjust the associated

DC field currents of either generator to maintain a constant system voltage

at both of the generator terminals.

The governor proposed for this system design is an electronic load

control governor manufactured by Thomson and Howe Energy Systems.

These governors are widely used in stand-alone small scale hydroelectric

power system applications.



92

Figure 42 Thomson & Howe Electronic Load Control Governor

Stand-alone system applications require that the governor be

connected to a small excess of either generation or load at all times. The

governor uses this excess to maintain system frequency. Systems that

have greater generation capacity than load capacity require “waste” loads

to be directly connected to the generator through the governor. These

“waste” loads are resistive and turned on by the governor when generation

becomes excessive. It is optimal to select “waste” loads that can provide

a beneficial use to the site which will help contribute to the overall

efficiency of the system. The following are a list of recommended “waste”

loads [23]:

1. Swimming pool heaters

2. Concrete imbedded heating cables



93

3. Hot water heating (with high temperature relief valve

or pump).

4. Soil heating cables or greenhouse heating

5. Snow melting cables in driveways

6. Furnace heating elements (with a backup heat

source)

Currently, the Boy Scout Camp does not have any loads from the

above list or that would qualify as a “waste” load. Thus it will be

necessary to install a “waste” load such as a baseboard heating element

in order for the governor to function properly and perform its intended role.



94

VII. Development and Construction

A brief evaluation of what site development and construction is

necessary to construct the hydroelectric power system will provide an

insight into the rough capital costs associated with the proposed system.

The following list highlights the major scope of work items associated with

each subcontractor.

• Civil/Structural

o Preparation and grading of the hillside in order to

facilitate the penstock installation

o Demolition and drilling of waterfall bedrock in order to

facilitate hydro power station concrete pier installation

o Create and set forms and rebar cage for concrete piers

o Pour and cure concrete piers

o Create and set forms and rebar cage for hydropower

station foundation pad

o Pour and cure concrete foundation pad

• Mechanical

o Construct hydropower station enclosure

o Install penstock



95

o Install a trash rake on penstock intake

o Install hydro turbine-generator skid

o Install hydro turbine-generator unit

o Install various plumbing fittings and accessories for

complete system installation

• Electrical

o Install control equipment including governor,

communication modules, and current transformers

o Install low voltage electrical equipment including circuit

breakers, junction boxes, and other enclosures

o Install complete steel conduit system and accessories

within the hydrostation powerhouse

o Pull and terminate wire complete control and low voltage

cable system within the hydrostation powerhouse

o Trench between hydropower station and Camp main

electrical service panel

o Install complete PVC Schedule 40 conduit system and

accessories below grade in the trench



96

o Backfill trench with sand and native soil and install

warning tape 12” above top of conduit maintaining NEC

required distances (no compaction required)

o Pull and terminate control and low voltage feeder circuit

cables between the hydrostation power house and Camp

main service equipment

The figure below represents a high level system diagram depicting

the major system components.

G

Main Panel

New Manual

Transfer

Switch

New Diesel

Generator

G

New Hydro

Generator

New Pelton

Turbine

New Generator-Turbine

Coupling Shaft

New Penstock

Existing Water

Intake

New Conduit

and Feeders New AVR New Governor

New

Powerhouse

Figure 37 Overall System Diagram



97

VIII. Economic Analysis

A design requirement of the proposed system is that project

economics are feasible and aligned with the Camp’s allotted budget. In

order to understand rough material costs of the major system equipment,

vendor quotes were solicited from select hydroelectric system component

manufacturers. The total capital cost to develop and construct this project

not only includes construction material and labor costs, but also includes

licensed professional engineering designs, associated construction

documents, and various construction administration items including

construction permit applications. The table below summarizes the major

project costs.







100

The proposed supplemental diesel generator is rated 30kVA and

will also be continuously loaded below 25% of its rated capacity. Thus the

new operating costs are calculated:

1.3 24

365 $11,388

The new annual operating costs will also be dominated by costs

associated with the diesel fuel. The Camp’s fiscal budget must account

for an annual preventive maintenance plan and must also allocate a

budget to address additional maintenance costs associated with any

unforeseen system malfunctions or failures.



101

IX. Conclusion

A hydroelectric power plant alone cannot adequately supply

enough power to meet the maximum electrical demand at the Boy Scout

Camp. In order to preserve the installation of a renewable energy source,

it is necessary to install a supplemental diesel generator. The

supplemental diesel generator would supply the remainder of the Camp

energy demand as well as supply the entire Boy Scout Camp electrical

load in the event the hydroelectric system fails or is taken off-line for

maintenance. An additional supplemental generator increases the

proposed system’s capital costs. It also increases system control

requirements and thus increases system complexity which results in a

decrease in system reliability. The proposed project is not economically

feasible with a total estimated project cost of $154,000. The Boy Scout

Camp generator replacement budget does not cover this large of a capital

cost and thus the proposed system cannot be built.

Renewable energy systems are more expensive than systems

powered by fossil fuels. The economics associated with renewable

energy systems become more attractive as various governments begin to

establish tax incentive and rebate programs that help to subsidize high

project costs. The assistance of subsidized programs allows renewable

energy technologies to further improve system efficiencies and decrease

system costs. Continual improvements in the manufacturing process and

construction costs help make renewable energy systems more affordable



102

and economically feasible. It is the hope that one day, through these

continuing efforts to improve system designs and reduce project costs,

that there will be grid parity.





[16] Chapman, Stephen J BAE SYSTEMS Australia . “Electric Machinery

Fundamentals” Fourth Edition. McGraw Hill Higher Education, 2005.

[17] Avalanche Center. http://www.avalanche-

center.org/Education/glossary/laminar-flow.php

[18] “Turbulent Flow”. Wikipedia. http://en.wikipedia.org/wiki/Turbulent_flow

[19] Engineering Toolbox. http://www.engineeringtoolbox.com/water-dynamic-

kinematic-viscosity-d_596.html

[20] Hydro Power, INDAR. http://www.indar.ch/hydro%20power%202.htm

[21] Nazir, Refdinal. “Modeling and Simulation of an Induction Generator-Driven

Micro/Pyco Hydro Power Connected to the Grid System”. Proceedings of the

International Conference on Electrical Engineering and Infomatics Institut

Teknologi, Indonesia June 17-19, 2007.

[22] “Electrical Resistance”, Wikipedia,

http://en.wikipedia.org/wiki/Electrical_resistance

[23] Product “A2” Installation and Operation Manual. Version 0.3, January 2002.

Thomson and Howe Energy Systems.

[24] “Approximate Fuel Consumption Chart”. Diesel Services & Supply Inc.

http://www.dieselserviceandsupply.com/Diesel_Fuel_Consumption.aspx

[25] “Gasoline and Diesel Fuel Update”. U.S. Energy Information Administration,Independent Statistics and Analysis.

http://tonto.eia.doe.gov/oog/info/gdu/gasdiesel.asp

[26] Craig, Scott; Maher, S. Cody; Ross, Jesse; Vanstratum, Brian. “MicroHydro

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Hydroelectric System Design

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