๐ ๐=๐ ๐ m , m = masses k = universal gravitational...
TRANSCRIPT
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FIGURE 1-1 Gravitational attraction of two masses.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
Copyright ยฉ2005 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
๐ = ๐๐๐๐๐
๐๐โข f = the force attracting the two masses
โข r = radius between centers of mass
โข m1, m2 = masses
โข k = universal gravitational constants =
6.67 x 10-11 Nยทm2/kg2
1
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FIGURE 1-2 Gravitational attraction of the earth.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
Copyright ยฉ2005 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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โข Let m1 be the mass of earth, m2 is the mass at the surface of the earth.
โข The separation distance r is approximately the radius of the earth (if the
earth is considered to be a point mass.
โข f = m2g, where the gravitational constant of g = 9.81 N/kg = 9.81 m/sec2
โข f and g are Vectors โ magnitude and direction
2
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Energy
โข Potential Energy
โข Kinetic Energy
โข Energy Stored in Electric
and Magnetic Fields
โ Electric Field Energy
โ Magnetic Field Energy
โข Nuclear Energy
โข 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
3
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FIGURE 1-3 Potential energy of a mass at an elevation.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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โข Move the mass up the ramp to an altitude h, by
traveling a distance โโข Neglecting friction between the mass and the ramp
โข The energy required to move the mass
w = mโgโh = mโgโ(โ sinฮธ) = PE (potential energy)
4
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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)?
โข Solution
W = mโgโh
= 4000 kg โ 9.81N/kg โ300m
= 11,772,000 Nโm = 11.77 MJ
1 Nโm = 1 Joule
1 kwh = 3.6 MJ
Source: OTIS,http://www.otisworldwide.com/k2-elevators.html
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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.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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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:
โข Amount of water (mass) to be pumped:
mass = 5m * 1.0 km * 1.0 km = 5 (106) m3 = 5(109) kg
โข Energy needed:
W = massโgโh = 5(109)kg โ 9.81m/s2 โ400m
= 19.64 x 1012 J = 19.64 Tera Joule
โข Equivalent electric energy storage:1 kwh = 3.6 MJ
W = 19.64 x 1012 / 3.6 x106 = 5.46 x 106 kwh =5460 Mwh
7
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FIGURE 1-5 Example of storing energy to generate electricity by storing compressed air in an unused salt mine.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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Compressed Air Energy Storage Systems
โข Energy Storage System (EES) project โ Projects, Sandia
National Laboratories,
http://www.sandia.gov/ess/projects_home.html
โข 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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FIGURE 1-6 Translational and rotational motion.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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๐ธ =1
2๐๐ฃ2
๐ธ =1
2๐ผฯ2
โข Kinetic Energy: energy stored in moving mass
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US DOT Connect Vehicle Technology
Researchโข V2V Safety Applications: USDOT Connected Vehicle Technology, Safety
Pilot Project (V2V-SP)
โข USDOT โ 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
โข Communication Infrastructures: Vehicle-to-Vehicle (V2V), Vehicle to
Infrastructure, (V2I), Vehicle-to-Consumer Devices (V2D)
โข Collected and Exchanged Data: Vehicleโs 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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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
โข 600 RPM => 10 RPS => Angular velocity
= 2ฯ(10) rad/s = 62.83 rad/s
โข I (moment of inertia) = ยฝ m r2 = ยฝ(192,300kg)(1m2)
= 96,150 kgโm2
โข Mass = ฯV
V = ฯโr2โโ = ฯ โ1m2โ(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
โข Energy E = 1/2Iฯ2 = ยฝ(96,150 kgโm2)(62.83 rad/s)2 = 189.8 MJ12
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FIGURE 1-7 Parallel-plate capacitor and its electric field.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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โข Capacitance ๐ถ =๐๐ด
๐Farads
โข ๐ is the permittivity of the material
between the parallel plates
โข Stored energy Welec = ยฝ CV2
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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.
Timothy L. Skvarenina and William E.
DeWitt
Electrical Power and Controls, 2e
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โข Inductance L = ๐0 ๐
2๐ด
2๐๐
โข Energy stored in an inductor Wmag = ยฝ LโI2
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FIGURE 1-9 Components of the power system.
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Electrical Power and Controls, 2e
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FIGURE 1-13 Conceptual diagram of a coal-fired power plant.
Timothy L. Skvarenina and William E.
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Electrical Power and Controls, 2e
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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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Electrical Power and Controls, 2e
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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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Electrical Power and Controls, 2e
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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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Electrical Power and Controls, 2e
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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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