Chapter2 091411w Notes

8/4/2019 Chapter2 091411w Notes

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CHAPTER 2 THREE PHASE SYSTEMS

SINGLE PHASE POWER

v t( ) 2 Vrmscos t( )VrmsVrms

i t( ) 2 Irms cos t( )Irms

p t( ) v t( ) i t( )v

p t( ) 2Vrms Irms cos t( ) cos t( )Vrms

cos A( ) cos B( )1

2cos A B( )

1

2cos A B( )cos A( ) cos B( )

p t( )

1

2 2Vrms Irms cos 2 t( )

1

2 2Vrms Irms cos ( )cos

over a period, the first term averages to zero

p t( ) Vrms Irms cos ( )cos

CIRCUIT BELOW:


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AVERAGE SINGLE PHASE POWER FOR A REAL LOAD; Z = R +j0 = 0

V_60hz t( ) 160sin 2 60t( )

I_60hz t( ) 40sin 2 60t( )( )

P t( ) V_60hz t( ) I_60hz t( )

0 0.02 0.04200

100

0

100

200

5 103

0

5 103

V_60hz t( )

I_60hz t( )P t( )

t

v t( ) 2 V_rms sin t( )V_rms i t( ) 2 I_rms sin t( )I_rms

p t( ) v t( ) i t( )v

p t( ) V_rms I_rms cos 2 t( ) V_rms I_rmsV_rms


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AVERAGE SINGLE PHASE POWER FOR A REACTIVE LOAD; Z = 0 +jXc = 90

1 v(1) 2 i(c1) 4 p

-8.00

-4.00

0

4.00

8.00

i ( c

1 ) i n a m p e r e s

-200

-100

0

100

200

v ( 1 ) i n v o

l t s

P l o t 1

1

2

10.0m 30.0m 50.0m 70.0m 90.0mtime in seconds

-800

-400

0

400

800

p i n w a

t t s

P l o t 2

4

AVERAGE POWER

VOLTAGECURRENT

1

V1

C1

100u

REAL POWER 0 AS THE IMPEDANCE ANGLE MAG > 0


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AVERAGE SINGLE PHASE POWER AS A FUNCTION OF ANGLE (3 CASES)

RESISTIVE / INDUCTIVE

REAL

+j -AXIS

-j -AXIS

1


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RESISTIVE / CAPACITIVE

REAL

+j -AXIS

-j -AXIS

2


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RESISTIVE

REAL

+j -AXIS

-j -AXIS


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Power Triangle method to represent APPARENT, REAL, REACTIVE

VA WORK = REAL PWR = WATTS

HEAT LOSS = REAL PWR = WATTS


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Power Triangle method to represent APPARENT, REAL, REACTIVE

Real Power = V rms Irms cos( )Reactive Power = V rms Irms sin( )

Apparent Power = V rms Irms

Real Power = I 2Z cos( ) = V 2 / Z cos( )

Reactive Power = I2

Z sin( ) = V2

/ Z sin( )Apparent Power = I 2Z

Where Z = R + jX (XL is j L or X C = 1 / j C)

or Z complex number: Z = R + jX = Z cos( ) + j Z sin( )

The REAL power is represented by P = I 2R

The REACTIVE power is represented by Q = I 2X

The impedance is also represented as Z

Magnitude of Z

REAL

+j -AXIS

-j -AXIS

1

2

1

2


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Power system Grid

1. Consider having a power (grid tie) system nationwide

a. How to generate power efficiently at the required voltages?b. How to distribute power across US over long distances and at what voltages?c. How to transform from higher to lower or lower to higher voltage?d. Safely measure system parameters (voltage, current, etc.) for monitoring

2. DC system ??3. AC single phase system nationwide??4. Poly-phase power system


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LOW VOLTAGE DC SYSTEM ORIGINAL EDISON APPROACH

Start with DC system design operating such that the maximum voltage (Edisons/JP Morgan idea wasbased on a 100 VDC transmission system). Current for 1 Megawatt of power?

P = I 2 R = V I

Resistivity of Copper: 1.7 X 10 -8

Resistivity of Alum is twice that of Cu: 3.4 X 10 -8 Outer Diameter of Alum overhead transmission line = 1 inch

Determine resistance of 1-mile length and corresponding voltage drop:

EXAMPLE

1. 100 volt system limitations2. Efficiency will be poor must increase the voltage drastically to reduce power losses3. Increase voltage to 1,000,000 volts4. Discuss how to step down large voltages and measure currents at 1 Mvolt


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CHAPTER 2 MAIN POINTS:

1. ELECTRICAL POWER INFRASTRUCTURE

a. DIRECTION FINALLY TAKEN TO FULLY TAKE ADVANTAGE OF FARADAYS LAWb. MAXIMIZE THE POWER EFFICIENCY ACROSS LONG DISTANCES MINIMIZE LOSS

BY TRANSMITTING POWER AT VERY HIGH VOLTAGES

2. STANDARDIZED A GRID SYSTEM TO ALLOW BUSS INTEGRATION OVER DISTANCES

a. GENERATE AT 25KVb. TRANSMIT AT 115, 230, 500 KVc. STEP DOWN TO 120/240 -RESIDENTIAL

3. USE A POLYPHASE APPROACH TO OPTIMIZE POWER TRANSMISSION AS OPPOSED TOA SINGLE PHASE WITH RETURN APPROACH

a. SMOOTH POWER FLOWb. CONSTANT POWER WITH MINIMIZED POWER RIPPLE WHEN COMPARED TO

SINGLE PHASE POWER TRANSMISSION

4. DELTA AND WYE CONFIGURATIONS ADVANTAGES & DISADVANTAGES

5. VECTOR REPRESENATIONS OF 3 PHASE CIRCUITS

6. PER PHASE EQUIVALENT CIRCUIT

7. DELTA TO WYE (VICE VERSA) LOAD CONVERSIONS


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PRESENT DAY ELECTRICAL GRID

1. CONSISTS OF POLYPHASE (3 PHASE) 60 HERTZ POWER GRID ACROSS THE US

2. MAP OF US ELECTRICAL GRID

http://www.npr.org/templates/story/story.php?storyId=110997398

3. MAP OF ELECTRICAL GRID SOUTHEASTERN PART OF US SOUTHERN CO.

http://www.southerncompany.com/corporateresponsibility/overview/map.html

4. SOUTHERN COMPANY

Southern Company is a public utility holding company of primarily electric utilities in the southernUnited States . It is headquartered in Atlanta, Georgia and is currently the 16th largest utilitycompany in the world and the fourth largest in the U.S. Through its subsidiaries it owns andoperates more than 42,000 megawatts of generation capacity and serves 4.3 million customersin Alabama , Georgia , Florida and Mississippi . Southern Companys regulated regional electricutilities serve a territory with of distribution lines.


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GENERATION OF AC VOLTAGES USING ROTATING MAGNETIC FIELD

Single phase allows you to easily step up and step down as well as safely measure system voltage andcurrents

V_induced = - N(velocity X B) length

So the "flux rule" that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both).... Yet in our explanation of the rule we have used two completely distinct laws for the two cases V = v X B for "circuit moves" and X E = - B/ t for "field changes". We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena. Richard P. Feynman , The Feynman Lectures on Physics

http://www.animations.physics.unsw.edu.au/jw/electricmotors.html

Rotating Ma gnet

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Chapter2 091411w Notes