ECE 333 Renewable Energy Systems

Lecture 5: Transformers, Harmonics, Power Industry History

Prof. Tom Overbye

Dept. of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

overbye@illinois.edu

Announcements

• Be reading Chapter 3 from the book• Homework 2 is 2.16, 3.5, 3.8, 3.12, 3.13 It will be

covered by an in-class quiz on Thursday Feb 5• Talk by Jana Sebestik, "Sparking Interest in Smart Grid

Stuff", Friday Feb 6 at 1pm in NCSA Auditorium

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Internships: San Diego Gas & Electric

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In the News

• In a report released on Jan 29, 2015, the World Resources Institute released a report stating that Western governments made a mistake supporting large-scale conversion of plants into fuel

• Key point is biofuels are so inefficient they are unlikely to ever supply a substantial portion of global energy demand– Biofuel claims have been vastly exaggerated– Inherent competition between using plants and land for

biofuels versus their use for food and carbon storage; 30 to 40% of US corn crop is currently converted to fuel

4Source: NYTimes, "New Report Urges Western Governments to Reconsider Reliance on Biofuels," Jan 28, 2015

US Corn Prices, Last Five Years

5http://spendmatters.com/wp/wp-content/uploads/2014/05/Corn-CBOT.jpg (CBOT is Chicago Board of Trade)

Transformers Overview

• Power systems are characterized by many different voltage levels, ranging from 765 kV down to 240/120 volts.

• Transformers are used to transfer power between different voltage levels.

• The ability to inexpensively change voltage levels is a key advantage of ac systems over dc systems.

• In 333 we just introduce the ideal transformer, with more details covered in 330 and 476.

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Distribution Transformer Picture

115 – 35 kV distribution transformer

Radiators W/Fans

LTC

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Transmission Level Transformer

230 kV surge arrestors

115 kV surge arrestors

Oil Cooler

Radiators W/Fans

Oil pump

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Ideal Transformer

• We’ll develop the voltage/current relationships for an ideal transformer– no real power losses– magnetic core has infinite permeability– no leakage flux

• We’ll define the “primary” side of the transformer as the side that usually takes power, and the secondary as the side that usually delivers power.– primary is usually the side with the higher voltage, but

may be the low voltage side on a generator step-up transformer.

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Ideal Transformer Relationships

1 1 2 2

1 21 1 2 2

1 2 1 1

1 2 2 2

Assume we have flux in magnetic material. Then

= turns ratio

m

m m

m m

m

N N

d d d dv N v N

dt dt dt dtd v v v N

adt N N v N

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Current Relationships

'1 1 2 2

'1 1 2 2

'1 1 2 2

'1 1 2 2

To get the current relationships use ampere's law

mmf

length

length

Assuming uniform flux density in the core

lengtharea

d N i N i

H N i N i

BN i N i

N i N i

H L

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Current/Voltage Relationships

'1 1 2 2

1 2 1 2'

1 2 12

1 2

1 2

If is infinite then 0 . Hence

1or

Then

0

10

N i N i

i N i NN i N ai

av v

i ia

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Impedance Transformation Example

Example: Calculate the primary voltage and current for an impedance load on the secondary

21

21

0

10

a vvviZa

21 2 1

21

1

1 vv av i

a Zv

a Zi

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Real Transformers

• Real transformers– have losses– have leakage flux– have finite permeability of magnetic core

• Also issues about how three phase transformers are connected

• Details are covered in ECE 330 and 476

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Residential Distribution Transformers

Single phase transformers are commonly used in residential distribution systems. Most distributionsystems are 4 wire, with a multi-grounded, common neutral.

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Power System Harmonics

• So far class has talked about fundamental frequency analysis. Many traditional loads only consume power at the fundamental frequency. However, some loads, mostly electronic-based, tend to draw current in non-linear pulses, which gives rise to harmonics.– If current has half-wave-symmetry (values are equal and

opposite when separated by T/2) then there are no even harmonics

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Quick Review of Fourier Analysis

01 2 3

1 2 3

n0

n0

f(t) cos cos2 cos32

sin sin 2 sin3

2where 2 ,

2a ( )cos , 0,1,2,

2( )sin , 1,2,

T

T

aa t a t a t

b t b t b t

f T

f t n t dt nT

b f t n t dt nT

.

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Quick Review of Fourier Analysis

01 2 3

1 2 3

n0

n0

f(t) cos cos2 cos32

sin sin 2 sin3

2where 2 ,

2a ( )cos , 0,1,2,

2( )sin , 1,2,

T

T

aa t a t a t

b t b t b t

f T

f t n t dt nT

b f t n t dt nT

.

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Switched-Mode Power Supply Current

Source: www.utterpower.com/commercial_grid.htm19

Harmonic Current Spectrum

The below figure shows the harmonic current components for an 18-W, electronic-ballast compact fluorescent lamp.

Source: Fig 2.34 of “Renewable and Efficient Electric Power Systems” by Masters, 1st edition 20

Current Waveform for CFL

( ) 2 0.145cos 0.140cos3 0.132cos5 0.155cos7i A t t t t

Figure 2.35

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Total Harmonic Distortion (THD)

2

21 2 3

2 2 2 2

( ) 2 cos cos2 cos3

But the square term is simplied by recognizing

( ) ( 2 2 2

and noting that the average value of the product of two sinusoids

of d

rms avgavg

I i I t I t I t

a b c a b c ab ac bc

22 22 2 231 21 2 3

2 2 22 3 4

1

iffering frequency is zero. This leaves

22 2 2

A common metric for distortion is total harmonic distortion (THD)

THD

rms

II II I I I

I I I

I

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Key Problems with Harmonics

• A key problem with the third harmonic is neutral current since the fundamental 120 degree phase shift becomes 360 degrees for the third harmonic so the third harmonic values do not cancel (also true for other triplen harmonics)– Delta-grounded wye transformers prevent triplen harmonic

currents from flowing into the power grid

• Harmonics cause transformer overheating since core losses are proportional to frequency

• Harmonic resonance, particularly with shunt capacitors (can be around 5th or 7th harmonic values)

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Power Supplies for AC to DC

• Two main types of power supplies: linear (simpler) and switched-mode (more efficient)

Linear Switched-mode24

A Little Background on the Electric Utility Industry

• First real practical uses of electricity began with the telegraph (around the civil war) and then arc lighting in the 1870’s (Broadway, the “Great White Way”).

• Central stations for lighting began with Edison in 1882, using a dc system (safety was key), but transitioned to ac within several years. Chicago World’s fair in 1893 was key demonstration of electricity

• High voltage ac started being used in the 1890’s with the Niagara power plant transferring electricity to Buffalo; also 30kV line in Germany

• Frequency standardized in the 1930’s 25

Regulation and Large Utilities

• Electric usage spread rapidly, particularly in urban areas. Samuel Insull (originally Edison’s secretary, but later from Chicago) played a major role in the development of large electric utilities and their holding companies– Insull was also instrumental in start of state regulation in 1890’s

• Public Utilities Holding Company Act (PUHCA) of 1935 essentially broke up inter-state holding companies– This gave rise to electric utilities that only operated in one state– PUHCA was repealed in 2005

• For most of the last century electric utilities operated as vertical monopolies

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Vertical Monopolies

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

Generation

Transmission

Distribution

Customer Service

In return for this exclusivefranchise, the utility had theobligation to serve all existing and future customersat rates determined jointlyby utility and regulators

It was a “cost plus” business

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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

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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, but its implementation varied greatly by state

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PURPA and Renewables

• PURPA, through favorable contracts, caused the growth of a large amount of renewable energy in the 1980’s (about 12,000 MW of wind, geothermal, small scale hydro, biomass, and solar thermal)– These were known as “qualifying facilities” (QFs)– California added about 6000 MW of QF capacity during the

1980’s, including 1600 MW of wind, 2700 MW of geothermal, and 1200 MW of biomass

– By the 1990’s the ten-year QFs contracts written at rates of $60/MWh in 1980’s, and they were no longer profitable at the $30/MWh 1990 values so many sites were retired or abandoned

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Abandoned Wind Farm Need South Point in Hawaii

Source: Prof. Sanders31

Electricity Prices, 1960-2010

Source: EIA, Annual Energy Review, 2010, Figure 8.10 32

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

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Historic State Variation in Electric Rates

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The Goal: Customer Choice

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The Result for California in 2000/1

OFF

OFF

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The California-Enron Effect

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

RI

AK

electricityrestructuring

delayedrestructuring

no activitysuspended

restructuring

WA

OR

NV

CA

ID

MT

WY

UT

AZ

CO

NM

TX

OK

KS

NE

SD

NDMN

IA

WI

MO

IL IN OH

KY

TN

MS

LA

AL GA

FL

SC

NC

WVA VA

PA

NY

VT ME

MI

NH

MA

CTNJ

DEMD

AR

HI

DC

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August 14th, 2003 Blackout

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My Favorite 8/14/2003 Blackout Cartoon!

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