Copyright © 2004 W.O. (Bill) Kennedy

What do You Need to Know About Electrical Power?

Electric Power Systems for Non Power System Experts

By

William (Bill) O. Kennedy, P.Eng., FEICIEEE Canada President For the IEEE Ottawa SectionMay 27, 2004 on 60th Anniversary of the IEEE Ottawa Section

2

PurposeGive a basic understanding of how power systems are put together and how they workConcepts will be emphasizedMathematics will be kept to a minimumMathematics only when necessary

3

IntroductionFirst part covers power system componentsSecond part covers how the components fit together and work along with some measures of power system performance

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A little bit of PhysicsHans Christian Oerstead discovered the relationship between magnetism and electricityMichael Faraday discovered that a voltage is induced on a wire when it’s moved in or through a magnetic fieldJames Clerk Maxwell developed the mathematics of electromagnetics

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Real and Reactive PowerReal power does the workReactive power helps real power do the workPower systems need both or they won’t workWhat is reactive power?

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Reactive powerQuarterback can throw a bullet, but not very farFor long distances, throws in an arcReal power is the bulletReactive power is the height of the arc

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Reactive PowerCapacitors store energy equal to ½CV2

Capacitor banks are used to boost or raise voltage

Reactors use energy equal to ½LI2

Motors and fluorescent lights require reactive power

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Part 1 - Equipment

GeneratorsTransformersTransmission LinesLoads

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Generators

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GeneratorsFundamental Law

E = N dΦ/dtWhere Φ is the fluxMagnetic example

High school physicsFaraday's discovery – motionMaxwell – mathematical theory

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GeneratorsRotor turns inside of the generator –satisfying Faraday’s LawVoltage induced on the stator – follows a sine waveTake advantage of space and put three coils equally spaced, 120o apart

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GeneratorsThree Phase

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 45 90 135 180 225 270 315 360

Degrees

Mag

nitu

de Phase APhase BPhase C

Motion of rotor induces a voltage on the statorStator doesn’t move and waveform reflects effect of rotor field as it moves inside the machine

13

GeneratorsControl

Terminal voltageSpeed

Terminal voltage controlled by varying the voltage applied to the dc field of the rotorSpeed controlled by governor, as load increases, fuel supply increases

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GeneratorsSpeed and frequency (60 Hz)Frequency (f) = n/60 * p/2

Poles are in pairs, hence divide by 2Speed in revolutions per minute, whereas frequency in cycles per second, hence divide by 60

Steam sets – high speed, small rotorsHydro sets – low speed, big rotors

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GeneratorsTwo pole machine rotates at 3600 rpm – steam generatorTwelve pole machine rotates at 600 rpm – hydro set

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Generators

Generation by Fuel Type (Canada)

14%

53%

3%

10%2%

16%

2%

0%

coalnuclearhyd roo ilgasdual fuelpumped s to rageo ther

Prime mover drives the generatorEnergy sources in Canada

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GeneratorsCapability curveLimits

Stator heatingRotor heatingStability

What’s requiredWhat’s used

Generator Capability Curve

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.00 0.25 0.50 0.75 1.00Real PowerR

eact

ive

Pow

er

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Generator Capability Curve

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.00 0.25 0.50 0.75 1.00Real PowerR

eact

ive

Pow

er

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TransformersFollow Faraday’s LawE1=N1dΦ/dt & E2=N2dΦ/dt Flux (dΦ/dt) is constantVoltage change depends on number of turns, and basic equations can be equated with the result:

E1/N1 = E2/N2

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TransformersSince conservation of energy must be preserved and voltage varies inversely, current must vary directly

I1N1 = I2N2

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Transformers

Usual connection for the transmission system is WYE grounded at the high voltageGenerators connected DELTALoads can be both

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Transmission linesTransmission lines are the highways on which power travelsLosses are proportional to the current squared on the line times the resistanceWant highest practical voltage to minimize lossesAs we will see, SIL is an important property of transmission lines

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Surge Impedance Loading (SIL)

Transmission line consists of:

Shunt capacitanceSeries resistance and inductanceDistributed along length of line

Treat as distributed lumped elementsCan ignore resistance

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Surge Impedance Loading (SIL)

Close the breaker at sending endShunt capacitance charges to ½ CV2

Close the breaker at receiving end and feed the loadSeries inductance uses energy at ½ LI2

Load

Load

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Surge Impedance Loading (SIL)

Equating shunt and series energies½ CV2 = ½ LI2

Performing the math yields

SIL (power) = V2/SI

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Properties of Surge Impedance (SI)Remains fairly constant over a wide range of voltagesStarts around 400 Ω at lower voltages and decreases with bundling to around 225 Ω at 1500 kVCapacitance and inductance also remain constantUsing this we can construct the following table

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Properties of Transmission LinesVoltage (kV) SI (Ω) R (Ω/km) X (Ω/km) Charging

(kVAr/km)SIL

(MW) X/R

69/72 370 0.4 0.5 15 13/14 1.2

138/144 370 0.2 0.5 70 50/55 2.5

230/240 single

340 0.07 0.45 225 170 6

230/240 bundled

300 0.07 0.4 290 180/195 6

345 bundled 285 0.026 0.365 525 415 14

500 bundled 250 0.018 0.345 1340 990 20

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0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

100

200

300

400

500

600

700

800

900

1000

Length (km)

Line

Loa

ding

(SIL

)

St. Clair Curve

3.25

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Loads

Three types of load modelsConstant MVA – motorsConstant current – resistive loadsConstant impedance – reactor & capacitor banksFor power flow – use constant MVAFor transient studies need a combination and may require frequency

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Summary – Part 1Generators – make the productTransformers – raise and lower voltage to allow efficient transport of productTransmission lines are the highwaysLoads are the end user of the product

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Lunch BreakLunch Break

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Characteristics of power systemsGeneration is usually remote from loadsTransmission needed to connect generation to loadTransformers needed to raise/lower voltageWant as high a voltage as practical for transmission – minimizes lossesUse load size, generator size and line SIL to get line voltageIn Alberta, lines are typically 150 km longAt that distance – loading 2 times SIL

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Putting it all togetherGenerators produce real power (P)Generators produce/consume reactive power (Q)Generator Q for underexcited operation is around half overexcited ability

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Putting it all togetherTransmission lines consume P in form of losses, typically 5% to 7% of generationLines produce/consume Q depending on power flow on the line as a fraction of SIL

< SIL – VArs flow out of line> SIL – VArs flow into lineHalf from each end, if voltages are equal

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Putting it all togetherLoads consume P & Q

P required for resistive loadsQ required for reactive loads – induction motorsSynchronous motors can produce/consume Q

Switching and/or load stationsUse shunt reactor/capacitor banks to produce/absorb QPrimarily for voltage control

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Breakers

Breakers used to connect/disconnect equipmentBreakers must be capable of picking up and dropping loads

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Breakers

Breakers must be capable of switching unloaded transmission linesBreakers must be capable of interrupting the symmetrical fault plus any dc offset

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How the power system worksFundamental rules

Maintain reactive power balance and voltages will be in required range –typically +/- 5% of nominalMaintain load/generation balance and frequency or speed remains constant –typically 60 Hz +/- 0.02 Hz

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Power flowTo solve a power flow need to solve for four variables at each bus

Bus voltage – VBus angle – бReal power – PReactive power – Q

However, some variables already knownLoad P & QGenerator bus V

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Power flowNeed a model of the systemPer unit system is bestMust have consistent voltage ratiosBase impedances on voltage levelMost models involve some lumping, i.e. not practical to model every detailHowever, this depends on the type of study

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Solution methodsFour solution methods

Gauss-Siedel – solves phasor equationsNewton-Raphson – solve for P & Q by separation of variablesdc – solves circuit as a dc circuit by treating jX as a resistanceDecoupled load flow – variant of Newton-Raphson. Separates V & б

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Solution methodsSolution results

Balance generation with load and lossesKeep all bus voltages within tolerance +/-5%

Require a slack or swing bus. Can be a fictitious generator to supply/absorb P & QSolution achieved when swing bus P & Q equal zeroNot practical, therefore minimize swing bus P & Q

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Types of studiesSteady state studiesOperations – study effect today and tomorrow, usually short time, e.g. up to one monthPlanning – study effect of load and generation three or more years in futureFault – study what happened yesterday

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Types of studiesDynamic studiesAll of the above: Operations, Planning & FaultTransients – what happens as power system moves from one steady state to anotherAdditional studies determine equipment ratings, e.g. breaker duty

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ContingenciesContingencies test the system for robustness Contingency – loss of one or more components at a timeCosts escalate if system designed for more than two contingenciesExample loss of a generator and line or transformer – N-G-1

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Power system exampleGo to example …

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Power System PerformanceLosses – we’ve ignored losses up to this pointMeasuring outages

Lines & StationsDelivery Point measures

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Transmission Losses

Transmission Losses

0

100

200

300

400

500

4750 5000 5250 5500 5750 6000 6250 6500 6750 7000 7250 7500 7750

Net Generation to Supply Alberta Load (MW)

Loss

es (M

W)

Losses are stochasticSimple system –losses vary as a square of currentComplex system – losses display a linear variance

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Transmission LossesTransmission Losses Histogram

0

100

200

300

400

50019

7

210

223

236

249

262

275

288

301

314

327

340

353

366

379

392

405

418

431

Losses (MW)

Coun

t

Histogram demonstrates a normal distribution pattern for losses

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Transmission lossesTransmission Generation, Load and Losses by Day

4000

4500

5000

5500

6000

6500

7000

7500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Gee

nrat

ion

& Lo

ad (M

W)

0

100

200

300

400

500

600

700

800

900

1000

Loss

es (M

W)

Net GenNet LoadLosses+3-sigma-3-sigmaAve Losses

Losses on AIES are very linear

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Power system performanceNeed measure system performanceMeasure frequency and duration of outagesReason – outages occur infrequentlyMeasures of performance look at all components and causesUsually stated as an average of whole system

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PerformanceFor Alberta, AESO publishes data to its website on line and terminal outages as an overall average for the voltage classFor Delivery Points frequency and duration data also published as a system averageFor comparison, all Canada data is included for Delivery Points

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PerformanceTwo types of duration are measuredMomentary < 1 minuteSustained > 1 minuteFollowing are examples of charts published on the AESO websitehttp://www.aeso.ca/transmission/5548.html

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Transmission - line

1.721,7010.05%6.074,5980.7675798,997Total

5.96950.03%2.64370.88141,595500

0.943200.04%4.931,1590.6923533,968240

1.266850.05%7.062,2720.5932254,417138/144

6.676010.14%6.081,1302.061869,01769/72

Frequencyper 100 km.a

(faults/100km.a)

Number ofMomentary

Faults

Unavailabilityper 100 km.a

(%)

AverageOutageDuration(hrs/fault)

TotalOutageDuration(hours)

Frequencyper 100 km.a

(faults100km.a)

Number ofSustained

Faults

KilometerYears(km.a)

VoltageClass (kV)

For the Period From 1997 - 2001

Summary for Line Related Forced Outages

Transmission Outage Statistics

Alberta Interconnected Electric System

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System Average Interruption Frequency

SAIFI-MI

0.0

0.4

0.8

1.2

1.6

1997 1998 1999 2000 2001

Year

Freq

uenc

y

Alberta

Canada

Ice StormRemoved

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System Average Interruption Duration

SAIDI

0

100

200

300

400

1997 1998 1999 2000 2001

Year

Dura

tion

(min

utes

) Alberta

Canada

Ice StormRemoved

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Summary – Part 2Power flow studies model and test the system for robustness yesterday, today and tomorrowN-G-1 is used to test the system for operation today and into the future

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Summary – Part 2Losses are an important part of power system design and operationHigher voltage lines reduce lossesHowever, losses are fixed when the conductor is chosen

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Summary – Part 2Outages are measured using frequency and duration techniquesPresented as system average numbers

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That’s all folks!

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