Power Engineering - University of Iceland · Transformer stations ... all over Iceland by means of microwave radio and optical ... Lecture 1 Instantaneous Sinusoidal Current/Voltage

23 September 2011

1Power Engineering - Egill Benedikt HreinssonLecture 1

Power Engineering

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The 3 facets of power engineering

Power Systems

Electric DrivesPower Electronics

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3Power Engineering - Egill Benedikt Hreinsson 3Lecture 1

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Electric power systems 101 for the absolute beginner!

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Key concepts and devices

Power Stations

Transmission lines

Transformer stations

Distribution stations

Loads

Loads

Loads

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Centralization or decentralization

Fuel cells

Solar energy

Micro generation

Centralized generation

Source: Networking assets, Sweet, W. IEEE Spectrum, Jan 2001, page(s): 84-86, 88

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What is an Electric Power System• One of the most complicated technical

systems in modern society• It is composed of different units, such as:

– Generation (power stations)– Transmission system (high voltage lines,

transformer stations)– electricity distribution (cables distribution

stations)– customers – “loads”

– Trading of electricity .....!!• Individual unit behavior – System behavior

Generation

Transmission

Distribution

Electricity Sales

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Power System Basics

• All power systems have three major components: (1) Generation, (2) Transmission/distribution and (3) Load

• Generation: Creates electric power.• Load: Consumes electric power.• Transmission/distribution: Transmits and delivers electric

power from generation to the load.• Power systems are 3-phase AC (Alternating current) systems

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What is a power system?

One of the most complex technological system of modern society.....

Source: W. Sweet: “Restructuring the thin stretched grid”, IEEE Spectrum, June 2000

The photos are from the California ISO, Folsom,CA

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10Power Engineering - Egill Benedikt HreinssonLecture 1 A major disturbance, August 14, 2003

The following plot illustrates the frequency excursion experienced by the power grid in Knoxville, Tennessee due to the sequence of events leading to the blackout in the northeast on Thursday, August 14, 2003 at 4:10:57.250 PM. Due to the interconnected nature of the nations electric power system, major disturbances to the grid can be measured hundreds of miles away.

http://www.enernex.com/special/blackout.htm

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The first event was GPS time stamped at 4:10:57.250 PM EDT and the event recovery swell shown above ended at 4:13:09.770 PM EDT. Over the course of those two minutes and twelve seconds, millions of people lost power over several states and in Canada. The final figure that follows shows the voltage profile for the entire day of August 14, 2003 - the day to be remembered for years to come as the day the New York Blackout of 2003 occurred.


A major disturbance, August 14, 2003 (2)

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A major disturbance, August 14, 2003 (3)


The location where the following measurements were taken near Newark, New Jersey is fed from a portion of the bulk transmission system that was not physically disconnected from the national grid during the sequence of events that blacked out the majority of the Northeastern United States. This bit of luck permitted the measurement equipment to have a front row seat view of the disturbance as it unfolded. The next figure shows the same frequency disturbance shown above but as measured at the New Jersey location. The tightly coupled nature of the power system can be observed by how closely the power system frequency traces are to each other even though they are 700 miles apart.

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For Consideration...

• George Santayana : "When experience is not retained ... infancy is perpetual”.

• “Those who cannot remember the past are condemned to repeat it."

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0 50 100 km

Mýrará 0.06 MWFossar 1.2 MW

Mjólká 8.1 MW

Reiðhjalli 0.5 MW

Blævardalsá 0.2 MW

Sængurfoss 0.7 MW

Þverá 1.7 MWLaxárvatn 0.5 MW

Blanda 150 MW

Skeiðsfoss 4.9 MW

Gönguskarðsá 1.1 MW

Garðsá 0.2 MW

Krafla 60 MW

Bjarnarflag 3.2 MW

Laxá 28 MW

Lagarfoss 7.5 MW

Fjarðará 0.2 MW

Grímsá 2.8 MW

Búðará 0.2 MW

Smyrlabjargaá 1.0 MW

Rjúkandi 0.8 MW

Andakílsá 7.9 MW

Elliðaár 3.2 MW

Straumsvík 35 MW

Svartsengi 46.4 MW

Sog 89 MW

Búrfell 270 MW

Hrauneyjafoss 210 MW

Sigalda 150 MW Raforkuver

Aðveitustöðvar

Flutningslínur > 30 kV:MeginflutningskerfiTenging virkjana > 3,5 MWAðrar flutningslínurFlutningslínur dreifiveitna

RAFORKUKERFI ÍSLANDS 2002

Nesjavellir 90 MWSultartangi 120 MW

Húsavík 2 MW

Vatnsfell 90 MW

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What is Electricity Deregulation?

• The transmission system is a kind of highway network transportingelectricity.

• Generating companies should sell to retail consumers, businesses or brokers by using trading forums/systems

• Competition between sales companies when selling to consumers. • Consumer choice. the consumer can choose where he buys.• Unbundling of activities into competitive and monopoly factors. • This is analogous to distinguishing between the road infrastructure

and the service vehicles travelling on the road network.

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Unbundling of Major Components

Raforkusala

Raforkudreifing

Raforkuflutningur

RaforkuframleiðslaRaforkuframleiðsla

Raforkuflutningur

Raforkudreifing

Raforkusala

• Unbundling of generation and transmission where electricity from many suppliers is transported in a common transportation (transmission) system

• Unbundling of distribution and retail sales and distinguish between the energy that is transported through the wires and the wires themselves

Generation

Transmission

Distribution

Electricity Sales

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The Goal: Customer Choice

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19Power Engineering - Egill Benedikt HreinssonLecture 1 Major Deregulation Concepts in the USA

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Supply and Demand in an Electricity Market

• The market price where supply and demand meet

• This is the amount or quantity of electricity traded in the markets

Demand

Price

Supply

Quantity

Final price

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Supply and Demand curves at night in the Electricity Market in New Zealand

• The supply and demand curves intersect when prices are low at night

• Energy prices are changing when we have

– 24 hour variation– Seasonal variation– Long term trends

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Energy prices in the UK and Norwegian electricity market

Kraftpriser Desember 2002

0,00

200,00

400,00

600,00

800,00

1000,00

NO

K/M

W

NorgeUK

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Actual Electricity Prices in Midwest ISO (MISO)September 5, 2006, 14:30 (US$/MWh)

Raunverulegt verð á markaði íBandaríkjunum er mismunandi íhnútapunktum kerfisins (LMP=LocationalMarginal prices)

http://www.pserc.org/cgi-pserc/getbig/generalinf/presentati/psercsemin1/4psercsemin/tesfatsion_pserc_tele-seminar_feb08.pdf

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Landsvirkjun’s Dispatch CentreLandsvirkjun‘s Dispatch Centre in Reykjavík was commissioned in 1989. Its role is coordinating operation of the electricity system. Its chief task is to ensure conditions that allow the system to handle variable loads at all times, thereby safeguarding operational security and efficiency. It monitors the entire power system and controls both production of electricity and its transmission nation-wide. In order to fullfill its role, the Dispatch Centre must have comprehensive hands-on data about the electricity system and therefore needs to be in constant, reliable contact with all its units. The Dispatch Centre is linked to power plants all over Iceland by means of microwave radio and optical fibre cables. These carry an average of 600 status point indications per minute from 35 remote terminals to its control computer, which gives real-time information about each and every part of the system. It sends warnings of any deviations to the two dispatchers who are on duty at any time, and with a complete overview of the electricity system they are able to respond accordingly and prescribe the correct action to be taken, via the remote control system. Source: http://www.lv.is

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The Electricity Industry - USA

More than 2,000 community-owned electric utilities, serve over 40 million people or about 15 percent of the nation's electricity consumers

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The Nordel Electricity System

• AC is the medium in all large power systems (AC) and connects Norway, Sweden, Denmark and Finland

• High Voltage Direct Current (HVDC) connects Jylland, Germany, Poland and Russia

• A nordpool electricity market• Power exchange in Nord Pool

Sour

ce: s

vk.se

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The Nordel power system capacity (MW) and energy capability (TWh/year)

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Power and Energy concepts

•Mechanical Energy•Rotational Energy•Electrical Energy•Power•Electrical Power

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29Power Engineering - Egill Benedikt HreinssonLecture 1 The basis for reactive power: - LC oscillation

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Instantaneous Sinusoidal Current/Voltage in Power Systems

Frequency: 50Hz in Europe (60 Hz in North America)

0

510

15

2025

30

3540

45

5055

60

49,86-49,90

49,90-49,94

49,94-49,98

49,98-50,02

Frequency Range (Hz)

50,02-50,06

50,06-50,10

50,10-50,14

[%]

tími

Spenna

Straumur

1/50 sek

max( ) sinv t v tω=

maxvmaxi max( ) sin( )i t i tω φ= −

φ

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The Definition of a Voltage RMS Value and rotating phasors

If we have a sinusoidal voltage form the RMS will be equal to the maximum value divided by the square root of 2

Re

Im

A Projection on theRe axis

Voltage orcurrent phasor

RMS values Rotating Phasors1

1

1

1

2

2

1 ( )

1 ( )

t t T

RMSt t

t t T

RMSt t

v v t dtT

i i t dtT

= +

=

= +

=

=

=

∫

∫

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Phasors in Power Systems

max( ) cos( )v t V tω δ= +Consider the sinusoidal voltage:

V V= max

2

Define the RMS value:

cos sinje jφ φ φ= +and using

( )( ) Re 2 Re 2 Re 2j t j j t j tv t V e V e e Veω δ δ ω ω+⎡ ⎤ ⎡ ⎤ ⎡ ⎤= = =⎣ ⎦ ⎣ ⎦ ⎣ ⎦

..we get:

Where a phasor is defined as a complex number:

jV V e δ=

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Power in AC Circuits

tvtv ωsin)( max=

)sin()( max φω −= titi

Consider a simple AC circuit with voltage and current:

max

max

( ) sin( ) sin( )

v t v ti t i t

ωω φ

== −

max max( ) ( ) ( ) sin sin( )p t v t i t v i t tω ω φ= = −

Instantaneous power will be current times voltage:

[ ]1sin sin cos( ) cos( )2

x y x y x y= − − +

Use the trigonometric identity:

( )max max( ) cos cos 22

v ip t tφ ω φ⎡ ⎤= − −⎣ ⎦

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Current, Voltage and Power

Voltage v(t)Current i(t)

Instantaneouspower p(t)

Realaveragepowerφ

time

Voltage, current or power

( )max max( ) cos cos 22

v ip t tφ ω φ⎡ ⎤= − −⎣ ⎦

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Phasors and Instantaneous Power

max

max

2

2

vV

iI

=

=

Define: Then from the previous eq.:

( ) cos cos(2 )p t V I V I tφ ω φ= − −

cos( ) cos cos sin sinx y x y x y− = +

Using a trigonometric identity:

we get: ( )( ) cos 1 cos 2 sin sin 2p t V I t V I tφ ω φ ω⎡ ⎤= − −⎣ ⎦

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Real Power - Reactive Power

cosP V I φ=Defining the following quantities

sinQ V I φ=We get:

( )( ) 1 cos 2 sin 2p t P t Q tω ω= − −

(P is called Real Power)

(Q is called Reactive Power)

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Real Power - Reactive Power

• From the last equation ⇒ the instantaneous power is made up of 2 components:– The first component is always positive with an average

value P.⇒ Power is always transferred in the same direction and can do useful work

– The second component swings back and forth. The average = 0, while the amplitude is Q ⇒ power swings back and forth and does NOT do useful work

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Real and Reactive Power

Instantaneous power, p(t)

Qsin(2 ω t))

Average power or real power, P

P(1-cos(2ω t))

currentvoltage

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Instantaneous power and in-phase and out of phase current

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Apparent Power

S V I= ⋅

Apparent power is defined as the product of the RMS Voltage and RMS current:

The unit of measurement is watt. However the power industry tradition is to use the unit VA(= volt - amperes), or kVA or MVA

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Definition of Power Concepts

Power concept

Units Formula

Real power W, kW,MW

P V I= cosφ

Reactive power

Var, kVar,MVar

φsinIVQ= Apparent power

VA, kVA,MVA

S V I=

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The Power Triangle

cosP V I φ=

sinQ V I φ=

S V I=2 2S P Q= +

Q

P

φ

S

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The Power Factor

cos P PV I S

φ = =⋅

The power factor is defined as the ratio between real power and apparent power

• The power factor can either be “leading” or “lagging”

– Lagging means the current “lags”behind the voltage (in phase) (φ is positive)

– Leading means the current leads the voltage (φ is negative)

V

I

φ

V V e

I I e

j

j

=

= −

0

φ

V

Iφ

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Real Power

The instantaneous power in an AC circuit oscillates, with a frequency double that of the voltage and current, around a certain average value. (In a 50 Hz system the frequencey of the power oscillation is thus 100 Hz)

The real power is a measure of this average value

(~ is this average value)

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Reactive power

The instantaneous power in an AC circuit oscillates, with a frequency double that of the voltage and current, around a certain average value.

The reactive power is a measure of the amplitude of this oscillation (or a measure of

the deviation of the instantaneous power from this average value)

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The Apparent Power

In an AC circuit of a specified voltage the apparent power is a measure of the magnitude (amplitude) of the

alternating current (AC)

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Current/voltage Phasors and Power

V

IIr

Ix

φ

Ix

Ir

V V e

I I e

j

j

=

= −

0

φ

cosr

r

I I

P V I

φ=

= ⋅

sinx

x

I I

Q V I

φ=

= ⋅

…This leads to a new characterization (definition) of real and reactive power...

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Real/reactive power characteristics

• Real power in an AC circuit is the product of the RMS voltage and the part of the RMS current that is parallel (in-phase) with the voltage. (determined by the power factor)

• Reactive power in an AC circuit is the product of the RMS voltage and the part of the RMS current that is perpendicular to the voltage (out of phase) .

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Real/Reactive power characteristics(2)

• Real power in an AC circuit is determined by the part of the current that “works with” the voltage. (determined by the power factor)

• Reactive power in an AC circuit is determined be the part of the current that “works against” the voltage.

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Integrated Software Laboratory

• Matlab / Simulink– General analysis of technical systems, including power

systems

• PSCAD/EMTPDC– Simulation of transient phenomena in power systems

• POWERWORLD– Simulation and power flow

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References

• J.D. Glover, M.S. Sarma: Power System Analysis and Design, Thomson Learning. 2002

• J. J. Grainger, W.D. Stevenson, Power Systems Analysis. McGraw Hill, 1994 • T. Gönen, Modern Power Systems Analysis, John Wiley & Sons, 1988 • V.D. Toro: Electric Power Systems, Prentice Hall 1992 • C.A. Gross: Power System Analysis, John Wiley & Sons, 1986 • O.I. Elgerd: Electric Energy Systems Theory, McGraw-Hill, 1983 • A.R. Bergen, V. Vittal: Power Systems Analysis, 2nd ed. Prentice Hall 2000 • E. Lakervi, E.J. Holmes: Electricity Distribution Network Design Peter

Peregrinus 1995, 2nd Ed

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References (2)

• El-Hawary, M. E., Electrical Power Systems Design and Analysis, Reston Publishing Company Inc., Reston, 1983.

• Rustebakke, H. M., Electric Utility Systems and Practices, Fourth Edition, John Wiley & Sons, New York, 1983.

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53Power Engineering - Egill Benedikt Hreinsson 53Lecture 1

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Power Engineering - University of Iceland · Transformer stations ... all over Iceland by means of microwave radio and optical ... Lecture 1 Instantaneous Sinusoidal Current/Voltage