Stanford Summer Energy School
Fundamentals of the Electric Grid
!
Kevin Tomsovic
CTI Professor and EECS Department Head
tomsovic@tennessee.edu
Overview – Part 1
•
Broad overview of power grid fundamentals
• DC vs. AC
• Edison and Westinghouse (Edison may yet win)
• Three phase systems
• Power concepts
• Traditional generation technologies
• Synchronism as the foundation of operation
• Load – Frequency control
• Load following – frequency control
• The power system in the steady-state
• Transmission system and power flows
• Reactive power/voltage and real power/phase
• Power system reliability
• Security vs. adequacy
Components of the Grid
• Generation
• Transmission
– 115 kVolts 765 kVolts
– Networked
• Distribution
– 4 kVolts to 69 kVolts
– Radial
• Load
http://www.nerc.com/page.php?cid=1|15
DC vs. AC
• Direct current (DC)
– DC machines
– Batteries
– Fuel cells
– Photovoltaic
!
i (t ) = I
!
• Alternating current (AC)
– AC machines
– Power electronic converters
– 60 Hertz in the US
i(t ) = I sin(2πft )
Edison vs. Tesla/Westinghouse
• DC
– Pushed by Thomas Edison (GE)
– Could not change voltage levels (no transformer) so cannot
transmit over long distances
– DC generator (high maintenance)
– Difficult to interrupt high currents (no zero crossing)
• AC
– Nikola Tesla (moved from Edison to Westinghouse)
– Can efficiently change voltage levels (transformer) and so
transmit over long distances (high voltage)
– Induction and synchronous machines
– Easier to interrupt high currents
!
➔
DC actually has many advantages
Frequency and Phase
• The number of “cycles” per second (Hertz)
– Zero for DC
– Many options for AC
– Grid - 60 in the US, 50 in Europe, both in Japan
– Aircraft – 400, Some trains in Europe – 16.67
• Phase – relative relationship between two signals
– Usually measured in degrees (easy to translate to time)
!
!
!
!
– 30 degrees or 1.4 msec
i1 (t ) = I sin(2πft )
i2 (t ) = I sin(2πft − π / 6)
Phasors
• Need a simpler notation and all that matters is
magnitude and relative phase if single
frequency
• Define
δ
i(t ) => I∠δ
!
• We properly do this using Euler’s identity
!
e j 2πft + jδ = cos(2πft + δ ) + j sin(2πft +Oδ )
• with j an imaginary number or 90
Three phase power
an extremely useful trick
• All large scale power applications
i!a (t ) = I sin(2πft )
i!b (t ) = I sin(2πft − 2π / 3)
i!c (t ) = I sin(2πft − 4π / 3)
!
!
i!a (t ) + ib (t ) + ic (t ) = 0
• No need for return line to carry current
Electric power
• By definition
!
!
!
p(t ) = v(t )i(t )
i(t ) = I sin(2πft )
v(t ) = V sin(2πft + π / 6)
• Average power is what does useful work
!
!
• P
1T
P = ∫ p(t )dt
oftenT called
real
0
power
Three phase electric power
another major benefit
• Assume balanced in all three phases
!
p ( t ) = p a ( t ) + pb ( t ) + p c ( t )
!
!
!
!
• Constant power output – far more efficient
Apparent Power S
calculation using phasors
• By definition
!
S = VI * = P + jQ
P – real part of S
Q – imaginary part of S, reactive power
S
Q
V
I
P
What is reactive power?
And why should we worry about it?
• The part of p(t) which does no work on average (but it may
be needed to get work done)
• Analogies
– Pressure in a water hose
•
– Foam on the beer (just takes
up room in glass)
• Physically
– Primarily line charging (magnetic fields) associated with
transmission lines and motor windings
• Practically
– Needed to maintain voltage for long distance transmission and to
supply induction machines
P (Watts – you pay for this)
Energy Conversion
Three phase synchronous Machines
• DC supplied to rotor which is driven at some constant speed of
rotation (say 3600 RPM for two pole machine resulting in 60
Hz)
• Three phase windings spaced by 120 degrees
• Power is produced only at this frequency (else p(t)=0)
• Relative angle between fields determines real power output
STATOR
b'
c
ROTOR
a
N
c'
S
b
a'
Generator mix
80% Thermal (nuclear, coal, gas, etc.)
20% Hydro
Essentially all synchronous
Steam Turbine/Generator
Coulee
Hydro Units at
Synchronism
Since most generation is from synchronous machines, the
interconnected power system swings together.
Frequency
• To maintain frequency, load and generation (minus losses) must balance
• An increase in load decreases frequency so generators respond to frequency dip by
increasing output
• Coordination from control centers results in a simple but very effective means of
load following
!
• Load frequency control
• Inputs – scheduled and actual tie line flows (difference is area control errors), frequency
deviation (also frequency response characteristic)
• Output – generator set point adjustments around once every 4 seconds
North American Control Areas
Frequency Monitoring
(FNET – Yilu Liu, UT)
Frequency Monitoring
(FNET – Yilu Liu, UT)
Frequency Event
Nigeria – Shows system dependence
Summary Comments and Opinions
• Electricity grid is central to solving energy problems
• Wind has perhaps the greatest potential – difficulty of
variability may have been overstated by media and
utilities
• Appropriate control methods need to be developed
with greater demand side response and new storage
• Shifting of greater load to grid has benefits both for
reduced emissions and for easier control
References
• A few useful websites
http://tcip.mste.uiuc.edu/applet1.html
http://tcip.mste.uiuc.edu/applet2.html
http://www.eia.doe.gov/
!
• Some general introductory power texts
Bergen and Vittal, Power Systems Analysis, Prentice Hall, 2000.
El-Sharkawi, Electric Energy: An Introduction, CRC Press, 2005.
Reference List
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System,” CIGRE Meeting, Paper 14-107, Paris, 1998.
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Proceedings of the 2000 IEEE PES Winter Power Meeting, Vol. 2, pp. 1020-1025, July 2000.
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Reference List
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•X. Wei, J. H. Chow, B. Fardanesh, and A.-A. Edris, “A Common Modeling Framework of Voltage-Sourced Converters for Loadflow, Sensitivity, and Dispatch
Analysis,” IEEE Transactions on Power Systems, vol. 19, pp. 934-941, May 2004.
•X. Jiang, X. Fang, J. H. Chow, A.-A. Edris, E. Uzunovic, M. Parisi, and L. Hopkins, “A Novel Approach for Modeling Voltage-Sourced Converter Based FACTS
Controllers,” IEEE Transactions on Power Delivery, vol. 23, no. 4, pp. 2591-2598, Oct. 2008.
•W. D. Jones, “Blackout a Turn-on for Long Island Cable,” IEEE Spectrum, Oct. 2003.
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Troy, NY, March 2008.
•X. Jiang, J. H. Chow, A-A. Edris, B. Fardanesh, and E. Uzunovic, “Transfer Path Stability Enhancement by Voltage-Sourced Converter-Based FACTS Controllers,”
submitted to IEEE Trans. on Power Delivery.
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