1. School of Engineering & Technology
Introduction to Electrical Engineering
Rajneesh Budania
Jaipur National University
June 29, 2012

2. Outline
• Basics of Electric Circuits
• AC Power
• Power Generation and Transmission
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3. Basics of Electric Circuits
• Current is the flow of electrons; must be induced by
electromotive force or voltage.
• Opposition to flow of power in a material is measured by the
resistance (R) of the material.
I
• Ohm’s law
– Current (I) is proportional to Voltage (V), where the constant
of proportionality is 1/R. (1/R is the conductance)
V R
– I = V/R or V = IR
– Resistance of 1 Ohm will allow a current of 1 Ampere to flow
when a voltage of 1 Volt is applied across it.
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4. Basics of Electric Circuits
• Flow of current governed by conservation rules called
Kirchoff’s Laws
– Kirchhoff’s Current Law: Sum of currents entering a point must equal sum of
currents leaving that point.
– Kirchhoff’s Voltage Law: The algebraic sum of all voltages in a loop must equal
zero.
i1 i2
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5. Basics of Electric Circuits
• Voltage and current can be direct
or alternating DC
• Direct voltage or current (DC)
– From sources such as batteries
• Alternating voltage or current (AC)
– From sources such as generators
– Alternates between plus and minus (60
AC
times a second in the US)
– Current and voltage typically specified as
the root mean square (RMS)
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6. Basics of Electric Circuits
200 Peak = 163 V
150
100
RMS = 115 V
50
0
0 45 90 135 180 225 270 315 360 405 450 495 540 585
-50
-100
-150
-200
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7. Basics of Electric Circuits
• Faraday’s Law: Changing magnetic flux through a loop of wire induces a
voltage in the wire
• Simple AC generator
– Spinning loop of wire between magnets generates AC voltage
– Replacing wire loop with a coil of wire with N turns creates N times the voltage
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8. Choice of AC Power For Transmission System
• First U.S. generating station at Pearl Street in Manhattan produced DC power,
beginning in 1882.
• “Battle of the Currents” fought throughout the 1880s, with Thomas Edison
promoting DC and George Westinghouse promoting AC
• Backbone of AC power system theory formulated by Serbian-American scientist
Nikola Tesla, originally employed by Edison, and later by Westinghouse
Thomas Edison George Westinghouse Nikola Tesla
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9. Advantages of DC Power in the 1880s
• Less dangerous, due to lower voltages used, and relative effect
of DC vs AC on the human nervous system
• Lower losses than AC at same voltage level
• DC generators and motors readily available in the 1880s
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10. Advantages of AC Power
• AC systems allow use of transformers to easily convert
between different voltages
• Higher transmission voltages mean lower currents, and lower
losses
• Voltage drop is less significant at high voltage, removing limit
to system size
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11. Basics of AC Circuits
• Power consuming components in the network include
– Resistors
– Inductors
– Capacitors
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12. Basics of AC Circuits
• Behavior of voltage and current, and hence power, depends on
the characteristics of the device
– Resistors: current and voltage in phase (Phase angle is zero)
– Inductors: current lags voltage by 90⁰
– Capacitors: current leads voltage by 90⁰
• Combined effect of these components is called Impedance
– Effect of resistors depends on their resistance, while that of inductors and
capacitors depends on their reactance
– Resulting phase angle will not be zero or ± 90⁰, but will depend on relative
effect of the components
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13. Basics of AC Circuits
• Power in an electric circuit is derived as the product of voltage
and current
– P = VI
• When voltage and current are in phase, instantaneous power
is never less than zero
• This is the best case scenario
– No “non-useful” power
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14. Basics of AC Circuits
1.50 Voltage has zero Average value of power is greater
average value than zero; instantaneous value is
never less than zero
Current has zero
1.00
average value
0.50
0.00
0 45 90 135 180 225 270 315 360 405 450 495 540
-0.50
-1.00 Voltage and current
are in phase
-1.50
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15. Basics of AC Circuits
• When voltage and current are not in phase, instantaneous
power is sometimes less than zero
• “Useful” power is scaled by a function of the phase angle
– P = VI*Cos (α)
– P = Cos (α) is called the power factor
• It is possible to decompose the power into two components
– First component never less than zero
– Second component has a zero average
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16. Basics of AC Circuits
1.50 Average value of power
Current has zero
average value is greater than zero
1.00 Voltage has zero
average value
0.50
0.00
0 45 90 135 180 225 270 315 360 405 450 495 540
-0.50
-1.00
Phase angle
-1.50
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17. Basics of AC Circuits
1
Instantaneous Power Component 1:
Never less than zero.
0.8
Average = 0.28
0.6
0.4 0.4
0.28
0.2
0
0 45 90 135 180 225 270 315 360
-0.2
Component 2:
-0.4 Has zero average.
Peak = 0.4
-0.6
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18. Basics of AC Circuits
• Component that is never less than zero represents power
consumed by resistive elements
– Average value is greater than zero
– Can be transformed into useful work
– Specified using the average value, P (measured in MW)
• Component with zero average value represents power in
inductive and capacitive elements
– Always 90 degrees out of phase with first component
– Specified using peak value, Q (measured in MVAr)
– Average value is zero
– Not available for useful work; stored and returned to circuit as charge
accumulations (capacitive) or magnetic fields (inductive)
– Important for voltage support
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19. Basics of AC Circuits
• Complex Power S = P + jQ
– P is “active” or “real” power
– Q is “reactive” or “imaginary” power
• Apparent Power |S| = sqrt (P2 + Q2)
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20. Single Phase AC vs. Three Phase AC
• Single Phase
– Two wires
– Uneven torque on generator
– Varying power over the AC cycle
• Three Phase
– Triple the power transmission, but number of wires only increases to three
– Constant torque on generator or motor
– Constant power
– Sum of current on three phases equals zero
• Why not more phases?
– More expensive generators, more transformers, more complicated tower and
wiring structure
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21. Power Generation and Supply
• Utilities produce power using 3-Phase generation
– Three equal phases of electricity different only in timing
– Requires fewer conductors to deliver the power – 3 or 4 instead of 6 for three
single phase circuits
– Instantaneous power is fixed; motors can operate with no variation in torque
– Reduced line losses – higher line voltage relative to single phase for the same
power; additional reduction if flow on neutral is zero
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22. Three Phase Load Connection: Delta vs. Wye
• Delta
– Higher voltage: Voltage difference between phases is 1.732 times higher than
phase to ground voltage.
– No neutral connection; currents add to zero.
• Wye
– Lower voltage, lower power draw
– Optional neutral connection
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23. Power Transmission – Characteristics of
Transmission Lines
• A transmission line has characteristics of a resistor, inductor
and capacitor
• Resistor: The line has a resistance that depends on the
characteristics of the conductor material
– Results in 3% to 7% losses in transmission lines
• Inductor: The line acts like many small inductors connected in
series, yielding an inductive reactance
• Capacitor: The line acts like a perfect conductor with many
small capacitors in parallel between the line and the neutral or
the ground, resulting in a capacitive reactance
– Usually ignored for short lines (less than 50 to 75 miles)
– Correction factor required for long lines (greater than 200 miles)
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24. Power Transmission – Characteristics of
Transmission Lines
• The line has a resultant impedance that depends on the
relative effects of the resistance, inductance and capacitance
• It can be represented using the PI model
• In an AC circuit the inductive reactance is typically much larger
than the resistance
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25. Power Transmission – Operation of Transmission
Lines
• Inductive reactance creates a reactive power demand (and a
loss of reactive power) in the line that results in a drop in
voltage at the receiving end
• As line becomes more reactive, current must increase for a
given amount of Real Power
• Increase in current further increases reactive losses (recall that
reactance >> resistance)
• Increased reactive losses results in larger voltage drop at
receiving end
• Relatively higher inductive reactance implies that it is
inefficient to deliver reactive power over long distances; it is
better to compensate for reactive demand locally
– Reactive power compensation devices include static devices (capacitors,
inductors, etc) and dynamic (generators, synchronous condensers, etc)
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26. Power Transmission – Reactive Power Compensation
i
XL R Q = 60 MVAr
115 kV α
P = 100 MW
• No reactive compensation
• Real Power = 100 MW
• Reactive Power = 60 MVAr
• Power Factor = Cos (α) = 0.857
• Apparent Power = 117 MVA
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27. Power Transmission – Reactive Power Compensation
i
XC XL R Q = 10 MVAr
115 kV α
P = 100 MW
• Reactive power compensation provided by capacitor
• Real Power = 100 MW
• Reactive Power = 60 MVAr – 50 MVAr = 10 MVAr
• Power Factor = Cos (α) = 0.995
• Apparent Power = 101 MVA
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28. Power Transmission - Transformers
• Used to convert power between different voltages via
magnetic coupling between coils of wire
• Types of transformers include
– Isolation transformers
– Auto-transformers
– Variable tap transformers
– Phase Angle Regulators (PARs)
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29. Power Transmission – Isolation Transformers
• No electrical connection between primary and secondary
creates galvanic isolation
EP N P
=
ES N S
Ep Es
IP NS
=
IS NP
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30. Power Transmission – Auto-transformers
• Shared coil, lighter, cheaper, but no isolation
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31. Power Transmission – Adjustable Transformers
• Variable tap transformers allow voltage to be adjusted
• Phase Angle Regulators (PARs) are combinations of
series/parallel connected transformers that draw reactive
power and change the power system phase angle at their
location, allowing power flows to be regulated
Phase Angle Regulator
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32. Power Flow Analysis
• Determine bus voltages (magnitude and angles), generator
dispatch and real and reactive power flows
• At generator buses specify real power and bus voltage
magnitude (PV)
– These can be regulated by the generator control systems
• At load buses specify real and reactive power (PQ)
– Assume we have knowledge of expected demand
• Select slack bus
– Necessary because losses depend on actual flow and are not known a priori
– Makes up for line losses and any demand not served by other generators
– Voltage at slack bus is specified as 1 per unit and phase angle as 0
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33. Power Flow Analysis (continued)
• Fundamental quantities to be solved are voltage magnitude
and voltage phase angle at each bus
– With voltage known, all real and reactive power can be determined
• Electrical parameters of transmission equipment (transmission
lines, transformers, etc) are known
• Real and reactive power absorbed at any bus should equal that
delivered to the bus
• Solve the Load Flow problem iteratively
– Nonlinear with no closed form solution
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34. Power Flow Analysis – PTDFs
• The Load Flow solution shows generation dispatch and power
flow on transmission lines
• Line flows are compared to transmission line limits to ensure
no line is overloaded
• Line flows can be adjusted using their sensitivities to bus
injections
• These sensitivities are called Power Transfer Distribution
Factors (PTDF)
• PTDFs are important for Transmission Loading Relief (TLR)
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35. Power Flow Analysis – PTDFs
Gen 1
~
Bus
A
A B C
A-B 1/3 -1/3
Reference
Reference
Bus
Bus
Line A-C 2/3 1/3
B-C 1/3 2/3
Gen 2
B
~ C (Reference Bus)
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36. Power Flow Analysis – PTDFs
Gen 1
~
A 60 MW
20 MW 40 MW
Gen 2
B
~ 20 MW
C (Reference Bus)
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37. Power Flow Analysis – PTDFs
Gen 1
~
A 60 MW
10 MW 50 MW
Gen 2
B
~ 40 MW
C (Reference Bus)
30 MW
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38. Power Flow Analysis – PTDFs
• PTDF of transaction from Gen 1 on Line A-C is 2/3
• PTDF of transaction from Gen 2 on Line A-C is 1/3
• Gen 1 has a larger impact on flows on Line A-C than Gen 2
• To relieve congestion on Line A-C by 1 MW
– Reduce Gen 1 by 1.5 MW; or
– Reduce Gen 2 by 3 MW
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39. Power Transmission – Loop Flows
• Loop flows arise whenever there are multiple paths for power
to travel on between two points
• Power cannot be directed to flow on specific paths
• Flow on all lines is in inverse proportion to impedances,
according to Kirchhoff’s laws
• When one path becomes overloaded, it can prevent additional
power transmission on other paths, even when they have
spare capacity
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40. U.S. Transmission / Distribution System
Structure
• Generation at medium voltage (4,000 – 13,000 volts)
• Power transformed to high voltage (115kV to 765kV for transmission)
• Stepped down to medium voltage for distribution
• Stepped down to customer voltage for end usage
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41. Power Line Physical Characteristics
• Conductor Types
– Standard high voltage line type is Aluminum Conductor Steel Reinforced (ASCR);
aluminum has a low resistance, and is cheaper than copper
– Lower resistance copper wires often used for underground cabling where cooling is an
issue
• Line Sag
– Line heating from loading close to capacity causes lines to sag
– Sag limits the distance between transmission towers
Aluminum Conductor
Steel Core
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42. Stability
• System could operate at x or y for some power transfer P
• At x, system maintains stability after disturbance
• At y, system loses stability after disturbance
• System typically operated well below 90°
P
V1 sin(θ1) V2 sin(θ2)
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43. Power Quality
• Voltage
– U.S. standard is ±5% from nominal voltage
– Voltage drop along transmission lines determined by load
– Transformer taps and reactive compensation used to maintain voltage
– Out-of-range voltage can damage equipment
• Frequency
– U.S. standard on order of ±1% of nominal frequency (±0.6 Hz)
• Harmonics
– Components of voltage/current waveform not at 60Hz
– Cause additional losses in transformers and lines
– Can damage or cause malfunctioning of sensitive equipment
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44. Summary
• AC voltage is sinusoidal in nature; described by magnitude and
phase angle
• Power has two components – Real and Reactive
• Real power describes average power delivered; it is non-zero
• Reactive power describes magnitude of oscillatory portion of
power delivered; has zero average
• Starting with predictions of demand and generator setpoints,
and knowledge of system characteristics, Power Flow used to
solve for voltage magnitudes and voltage phase angles; all
other parameters can be derived from these
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45. Summary
• Decoupling in power system operation
– Voltage phase angles depend mainly on real power
– Voltage magnitudes depend mainly on reactive power
• Real power flow on lines depends on voltage angles
• Changes in real power flow on lines can be calculated using
linearized sensitivities known as PTDFs
• Voltage angle typically kept small to maintain system stability
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