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
2 YAGTP3918
icfi.com
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.
3 YAGTP3918
icfi.com
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
4 YAGTP3918
icfi.com
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)
5 YAGTP3918
icfi.com
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
6 YAGTP3918
icfi.com
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
7 YAGTP3918
icfi.com
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
8 YAGTP3918
icfi.com
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
9 YAGTP3918
icfi.com
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
10 YAGTP3918
icfi.com
11. Basics of AC Circuits
• Power consuming components in the network include
– Resistors
– Inductors
– Capacitors
11 YAGTP3918
icfi.com
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
12 YAGTP3918
icfi.com
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
13 YAGTP3918
icfi.com
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
14 YAGTP3918
icfi.com
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
15 YAGTP3918
icfi.com
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
16 YAGTP3918
icfi.com
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
17 YAGTP3918
icfi.com
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
18 YAGTP3918
icfi.com
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)
19 YAGTP3918
icfi.com
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
20 YAGTP3918
icfi.com
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
21 YAGTP3918
icfi.com
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
22 YAGTP3918
icfi.com
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)
23 YAGTP3918
icfi.com
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
24 YAGTP3918
icfi.com
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)
25 YAGTP3918
icfi.com
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
26 YAGTP3918
icfi.com
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
27 YAGTP3918
icfi.com
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)
28 YAGTP3918
icfi.com
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
29 YAGTP3918
icfi.com
30. Power Transmission – Auto-transformers
• Shared coil, lighter, cheaper, but no isolation
30 YAGTP3918
icfi.com
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
31 YAGTP3918
icfi.com
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
32 YAGTP3918
icfi.com
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
33 YAGTP3918
icfi.com
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)
34 YAGTP3918
icfi.com
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)
35 YAGTP3918
icfi.com
36. Power Flow Analysis – PTDFs
Gen 1
~
A 60 MW
20 MW 40 MW
Gen 2
B
~ 20 MW
C (Reference Bus)
36 60 MW YAGTP3918
icfi.com
37. Power Flow Analysis – PTDFs
Gen 1
~
A 60 MW
10 MW 50 MW
Gen 2
B
~ 40 MW
C (Reference Bus)
30 MW
37 90 MW YAGTP3918
icfi.com
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
38 YAGTP3918
icfi.com
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
39 YAGTP3918
icfi.com
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
40 YAGTP3918
icfi.com
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
41 YAGTP3918
icfi.com
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)
42 YAGTP3918
icfi.com
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
43 YAGTP3918
icfi.com
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
44 YAGTP3918
icfi.com
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
45 YAGTP3918
icfi.com