𝒎 𝒇=𝒌 𝒓 m , m = masses k = universal gravitational...

FIGURE 1-1 Gravitational attraction of two masses.

Timothy L. Skvarenina and William E.

DeWitt

Electrical Power and Controls, 2e

Copyright ©2005 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

All rights reserved.

𝒇 = 𝒌𝒎𝟏𝒎𝟐

𝒓𝟐• f = the force attracting the two masses

• r = radius between centers of mass

• m1, m2 = masses

• k = universal gravitational constants =

6.67 x 10-11 N·m2/kg2

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FIGURE 1-2 Gravitational attraction of the earth.


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• Let m1 be the mass of earth, m2 is the mass at the surface of the earth.

• The separation distance r is approximately the radius of the earth (if the

earth is considered to be a point mass.

• f = m2g, where the gravitational constant of g = 9.81 N/kg = 9.81 m/sec2

• f and g are Vectors – magnitude and direction

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Energy

• Potential Energy

• Kinetic Energy

• Energy Stored in Electric

and Magnetic Fields

– Electric Field Energy

– Magnetic Field Energy

• Nuclear Energy

• Table 1-1 Some Energy Equivalents

Energy Unit Equivalent

1 Btu * 1 match tip

1 million Btu * 90 lb of coal

* 8 gallons of gasoline

* 11 gallons of propane

1 quad (1015 Btu) * 45 million tons of coal

* 109 ft3 of natural gas

* 170 million barrel of oil

1000 kwh (1 Mwh)

of electricity * 0.588 barrels of crude oil

* 310 lb of coal

* 3300 cu ft of natural gas

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FIGURE 1-3 Potential energy of a mass at an elevation.


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• Move the mass up the ramp to an altitude h, by

traveling a distance ℓ• Neglecting friction between the mass and the ramp

• The energy required to move the mass

w = m∙g∙h = m∙g∙(ℓ sinθ) = PE (potential energy)

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Example 1-1

An elevator in the Sears Tower

in Chicago is required to lift a

load of 4000 kg to an altitude of

300 m. How much energy must

the motor provide (neglecting

any losses in the hoist

mechanism)?

• Solution

W = m∙g∙h

= 4000 kg ∙ 9.81N/kg ∙300m

= 11,772,000 N∙m = 11.77 MJ

1 N∙m = 1 Joule

1 kwh = 3.6 MJ

Source: OTIS,http://www.otisworldwide.com/k2-elevators.html

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http://www.otisworldwide.com/k2-elevators.html

FIGURE 1-4 Pumped storage of energy to generate electricity. a. Water drives the generator during the day. b. Electricity is used to

pump the water to a higher elevation during the night.


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Example 1-2

How much energy could be stored in a pumped-storage facility if

the reservoirs are separated by 400 m in altitude and each is 1.0

km square and 5.0 m deep? (Note: 1.0 cc of water has a mass of

1.0 g and 1.0 m3 of water has a mass of 1000 kg)?

Solution:

• Amount of water (mass) to be pumped:

mass = 5m * 1.0 km * 1.0 km = 5 (106) m3 = 5(109) kg

• Energy needed:

W = mass∙g∙h = 5(109)kg ∙ 9.81m/s2 ∙400m

= 19.64 x 1012 J = 19.64 Tera Joule

• Equivalent electric energy storage:1 kwh = 3.6 MJ

W = 19.64 x 1012 / 3.6 x106 = 5.46 x 106 kwh =5460 Mwh

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FIGURE 1-5 Example of storing energy to generate electricity by storing compressed air in an unused salt mine.


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Compressed Air Energy Storage Systems

• Energy Storage System (EES) project – Projects, Sandia

National Laboratories,

http://www.sandia.gov/ess/projects_home.html

• Lessons from Iowa: Development of a 270 Megawatt

Compressed Air Energy Storage Project in Midwest

Independent System Operator, January 2012, by Robert H.

Schulte, Nicholas Critelli, Jr., Kent Holst amd Georgianne

Huff, Sandia Report SAND2012-0388,

http://www.sandia.gov/ess/publications/120388.pdf

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http://www.sandia.gov/ess/projects_home.html

http://www.sandia.gov/ess/publications/120388.pdf

FIGURE 1-6 Translational and rotational motion.


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𝐸 =1

2𝑚𝑣2

𝐸 =1

2𝐼ω2

• Kinetic Energy: energy stored in moving mass

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US DOT Connect Vehicle Technology

Research• V2V Safety Applications: USDOT Connected Vehicle Technology, Safety

Pilot Project (V2V-SP)

• USDOT – National Highway Traffic Safety Administration (NHTSA), DOT

HS 811 373, October 2011,

www.nhtsa.gov/DOT/NHTSA/NVS/Crash%2520Avoidance/Technical%252

0Publications/2011/811373.pdf

• Communication Infrastructures: Vehicle-to-Vehicle (V2V), Vehicle to

Infrastructure, (V2I), Vehicle-to-Consumer Devices (V2D)

• Collected and Exchanged Data: Vehicle’s latitude, longitude, time,

heading angle, speed, lateral acceleration, longitudinal, acceleration, yaw

rate, throttle position, brake status, steering angle, headlight status, turn

signal, status, vehicle length, vehicle width, vehicle mass, bumper height,

and the number of occupants in the vehicle

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http://www.nhtsa.gov/DOT/NHTSA/NVS/Crash Avoidance/Technical Publications/2011/811373.pdf

Example 1-3A 345,000 kVA (345 MVA) synchronous machine is used for power factor

correction and has a rotor that is 2m in diameter and 8 meter long. Assume the

rotor is solid steel, with a density of 7.65 g/cm3, and calculate the kinetic energy

of the rotor is the machine runs at 600 RPM.

Solution

• 600 RPM => 10 RPS => Angular velocity

= 2π(10) rad/s = 62.83 rad/s

• I (moment of inertia) = ½ m r2 = ½(192,300kg)(1m2)

= 96,150 kg∙m2

• Mass = ρV

V = π∙r2∙ℓ = π ∙1m2∙(8m) = 25.13 m3 = 25.13 (106) cm3

Mass = m = 25.13 (106) cm3 x (7.65 g/cm3) = 192.3 (106)g =

192,300 kg

• Energy E = 1/2Iω2 = ½(96,150 kg∙m2)(62.83 rad/s)2 = 189.8 MJ12

FIGURE 1-7 Parallel-plate capacitor and its electric field.


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• Capacitance 𝐶 =𝜖𝐴

𝑑Farads

• 𝜖 is the permittivity of the material

between the parallel plates

• Stored energy Welec = ½ CV2

FIGURE 1-8 a. A loosely wound coil and the magnetic field resulting from the coil current. b. A tightly wound, toroidal coil in which the

magnetic field is confined to the interior of the coil.


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• Inductance L = 𝜇0 𝑁

2𝐴

2𝜋𝑟

• Energy stored in an inductor Wmag = ½ L∙I2

FIGURE 1-9 Components of the power system.


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FIGURE 1-13 Conceptual diagram of a coal-fired power plant.


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FIGURE 1-14 U.S. generation capacity during the twentieth century.


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FIGURE 1-16 Simple power system.


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FIGURE 1-17 Simplified one-line diagram of a power system.


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FIGURE 1-18 Typical variation of electrical load during a week.


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FIGURE 1-19 Graph of typical electrical frequency fluctuations.


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FIGURE 1-20 Map showing the North American Electric Reliability Council regions.


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FIGURE 1-21 Number of utility nuclear generating plants over time.


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FIGURE 1-22 Status of electric utility restructuring in the United States. (Source: U.S. Dept. of Energy.)


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FIGURE 1-23 Electrical generation by utilities and nonutilities. (Source: U.S. Dept. of Energy, March 2003, Monthly Energy Update.)


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FIGURE 1-24 Annual, per-capita greenhouse gas emissions for a number of industrialized nations.


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FIGURE 1-25 Change of population, per-capita emissions, GDP, and emissions per dollar of GDP from 1990 to 2000.


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FIGURE 1-26 Monthly average cost per MWhr in California.


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FIGURE 1-27 Price of Enron stock from 1992 to 2002.


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FIGURE 1-28 System for Problem 1-9.


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𝒎 𝒇=𝒌 𝒓 m , m = masses k = universal gravitational...

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