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ECE 476 POWER SYSTEM ANALYSIS. Lecture 2 Complex Power, Reactive Compensation, Three Phase Professor Tom Overbye Department of Electrical and Computer Engineering. Reading and Homework. For lectures 2 through 3 please be reading Chapters 1 and 2 HW 1 is 2.7, 12, 21, 26; due Thursday 9/4.

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ece 476 power system analysis

ECE 476POWER SYSTEM ANALYSIS

Lecture 2

Complex Power, Reactive Compensation, Three Phase

Professor Tom Overbye

Department of Electrical andComputer Engineering

reading and homework
Reading and Homework
  • For lectures 2 through 3 please be reading Chapters 1 and 2
  • HW 1 is 2.7, 12, 21, 26; due Thursday 9/4
vertical monopolies

Generation

Transmission

Distribution

Customer Service

Vertical Monopolies
  • Within a particular geographic market, the electric utility had an exclusive franchise

In return for this exclusive

franchise, the utility had the

obligation to serve all

existing and future customers

at rates determined jointly

by utility and regulators

It was a “cost plus” business

vertical monopolies1
Vertical Monopolies
  • Within its service territory each utility was the only game in town
  • Neighboring utilities functioned more as colleagues than competitors
  • Utilities gradually interconnected their systems so by 1970 transmission lines crisscrossed North America, with voltages up to 765 kV
  • Economies of scale keep resulted in decreasing rates, so most every one was happy
history cont d 1970 s
History, cont’d -- 1970’s
  • 1970’s brought inflation, increased fossil-fuel prices, calls for conservation and growing environmental concerns
  • Increasing rates replaced decreasing ones
  • As a result, U.S. Congress passed Public Utilities Regulator Policies Act (PURPA) in 1978, which mandated utilities must purchase power from independent generators located in their service territory (modified 2005)
  • PURPA introduced some competition
history cont d 1990 s 2000 s
History, cont’d – 1990’s & 2000’s
  • Major opening of industry to competition occurred as a result of National Energy Policy Act of 1992
  • This act mandated that utilities provide “nondiscriminatory” access to the high voltage transmission
  • Goal was to set up true competition in generation
  • Result over the last few years has been a dramatic restructuring of electric utility industry (for better or worse!)
  • Energy Bill 2005 repealed PUHCA; modified PURPA
the california enron effect

WA

ME

MT

VT

ND

MN

OR

NH

ID

SD

WI

NY

MA

WY

MI

RI

PA

CT

IA

NV

NE

NJ

OH

IN

DE

IL

UT

DC

W

VA

MD

CO

VA

KS

CA

MO

KY

NC

AZ

TN

OK

NM

AR

SC

GA

MS

AL

TX

LA

AK

FL

HI

electricity

restructuring

suspended

restructuring

delayed

restructuring

no activity

Source : http://www.eia.doe.gov/cneaf/electricity/chg_str/regmap.html

The California-Enron Effect
2007 illinois electricity crisis
2007 Illinois Electricity Crisis
  • Two main electric utilities in Illinois are ComEd and Ameren
  • Restructuring law had frozen electricity prices for ten years, with rate decreases for many.
  • Prices rose on January 1, 2007 as price freeze ended; price increases were especially high for electric heating customers who had previously enjoyed rates as low as 2.5 cents/kWh
  • Current average residential rate (in cents/kWh) is 10.4 in IL, 8.74 IN, 11.1 WI, 7.94 MO, 9.96 IA, 19.56 CT, 6.09 ID, 14.03 in CA, 10.76 US average
review of phasors
Review of Phasors

Goal of phasor analysis is to simplify the analysis of constant frequency ac systems

v(t) = Vmax cos(wt + qv)

i(t) = Imax cos(wt + qI)

Root Mean Square (RMS) voltage of sinusoid

phasor representation cont d
Phasor Representation, cont’d

(Note: Some texts use “boldface” type for complex numbers, or “bars on the top”)

advantages of phasor analysis
Advantages of Phasor Analysis

(Note: Z is a complex number but not a phasor)

complex power1
Complex Power

(Note: S is a complex number but not a phasor)

conservation of power
Conservation of Power
  • At every node (bus) in the system
    • Sum of real power into node must equal zero
    • Sum of reactive power into node must equal zero
  • This is a direct consequence of Kirchhoff’s current law, which states that the total current into each node must equal zero.
    • Conservation of power follows since S = VI*
conversation of power example
Conversation of Power Example

Earlier we found

I = 20-6.9 amps

example
Example

First solve

basic circuit

example cont d
Example, cont’d

Now add additional

reactive power load

and resolve

power system notation
Power System Notation

Power system components are usually shown as

“one-line diagrams.” Previous circuit redrawn

Arrows are

used to

show loads

Transmission lines are shown as a single line

Generators are

shown as circles

reactive compensation
Reactive Compensation

Key idea of reactive compensation is to supply reactive

power locally. In the previous example this can

be done by adding a 16 Mvar capacitor at the load

Compensated circuit is identical to first example with

just real power load

reactive compensation cont d
Reactive Compensation, cont’d
  • Reactive compensation decreased the line flow from 564 Amps to 400 Amps. This has advantages
    • Lines losses, which are equal to I2 R decrease
    • Lower current allows utility to use small wires, or alternatively, supply more load over the same wires
    • Voltage drop on the line is less
  • Reactive compensation is used extensively by utilities
  • Capacitors can be used to “correct” a load’s power factor to an arbitrary value.
balanced 3 phase systems
Balanced 3 Phase () Systems
  • A balanced 3 phase () system has
    • three voltage sources with equal magnitude, but with an angle shift of 120
    • equal loads on each phase
    • equal impedance on the lines connecting the generators to the loads
  • Bulk power systems are almost exclusively 3
  • Single phase is used primarily only in low voltage, low power settings, such as residential and some commercial
advantages of 3 power
Advantages of 3 Power
  • Can transmit more power for same amount of wire (twice as much as single phase)
  • Torque produced by 3 machines is constrant
  • Three phase machines use less material for same power rating
  • Three phase machines start more easily than single phase machines
three phase wye connection
Three Phase - Wye Connection
  • There are two ways to connect 3 systems
    • Wye (Y)
    • Delta ()
wye connection line voltages

Vcn

Vab

Vca

Van

Vbn

Vbc

Wye Connection Line Voltages

-Vbn

(α = 0 in this case)

Line to line

voltages are

also balanced

wye connection cont d
Wye Connection, cont’d
  • Define voltage/current across/through device to be phase voltage/current
  • Define voltage/current across/through lines to be line voltage/current
delta connection

Ic

Ica

Ib

Iab

Ibc

Ia

Delta Connection
three phase example
Three Phase Example

Assume a -connected load is supplied from a 3 13.8 kV (L-L) source with Z = 10020W