Dynamic Modelling and Simulation of Power Systems · sequence), the detailed machine model can be reduced to phasor models useful for stability and steady state analysis. • Phasor

Dynamic Modelling and Simulation of Power

SystemsClaudio CanizaresDept. Electrical and Computer Engineeringwww.power.uwaterloo.cawww.wise.uwaterloo.ca

Grid Science Winter School, Santa Fe, NM, Jan. 7, 2019

http://www.power.uwaterloo.ca/http://www.wise.uwaterloo.ca/

The University of Waterloo

2

Waterloo Quick Facts• 6 Faculties: Applied Health

Sciences, Arts, Environmental Studies, Science, Math, Engineering.

• 29000 undergraduate students, 4800 graduate students (4500 international), 1100 faculty members, 2184 staff.

• Largest co-operative education program in the world:– 18,500/yr students enrolled– 5200 employers– Students earned $225M (2014)

3

Waterloo Quick Facts• $190 M annual research• World’s largest centre for education in math

& computer sciences (Waterloo and Stanford = largest source of computer science talent recruitment in North America)

• World’s largest concentration of quantum information research

• Canada’s largest Engineering faculty• WatCar – largest auto research centre in

Canada (125 researchers)• Waterloo Institute for Nanotechnology (70+

researchers)• Water Institute (125 researchers)• Waterloo Institute for Sustainable Energy

(100+ researchers)• Top research university six years in a row

(Comprehensive category) Research Infosource

4

Waterloo Quick Facts• Canada’s largest engineering

university• Eight departments:

– Chemical Engineering– Civil and Environmental

Engineering– Electrical and Computer

Engineering– Management Sciences– Mechanical and Mechatronics

Engineering– Systems Design Engineering– School of Architecture– Conrad Business and

Entrepreneurship• 100% co-operative study

6554 Undergraduate Students700 International Students

1829 Graduate Students286 Faculty202 Staff

5

Overview• Power systems:

– Structure– Supply technologies

• Basic elements:– Generators– Transmission system:

• Transformers• Transmission lines

– Loads:• Inductions motors• Aggregate loads

– Flexible AC Transmission Systems (FACTS)– Solar Photo-Voltaic Generation (SPVG)– Wind Generation (WG)

• Application example

6

Power System• Operated by independent system operators (e.g.

IESO):

Generator(station)

Transmission Lines

Connecting Buses or Nodes

Load

Transformer

683 GW Cogeneration Gas Plant Halton Hills

Transformer PowerStream

(Alectra)

500kV Milton

7

Power System• Ontario’s grid:

8

Power System• Generator station:

– Synchronous machine, exciter, primary voltage regulator and stabilizer.

– Turbine (e.g. thermal, gas, hydro) and primary frequency controls (governor).

– Fuelling system and controls (e.g. boiler, reservoir, valves)

– Owned and run by generation companies or GENCOS (e.g. OPG).

9

Power System• Transmission system:

– High voltage transmission lines: overhead wires and towers, underground cables.

– Transformers: step-up or step-down voltage levels to reduce transmission losses.

– Switching stations (buses/nodes): connections, breakers, protections, etc.

– Owned and maintained by transmission companies or TRANSCOS (e.g. Hydro One).

10

Power System• Loads:

– Large industrial customers and distribution networks.

– Represent aggregate models of the distribution grid, including motors, lighting, heating, feeders, etc.

– Owned by large customers and/or local distribution companies or LDCs (e.g. Toronto Hydro)

11

Power System• Renewable Energy (RE) generation:

– Mostly wind and SPV generation:• Wind mostly at the transmission system level as wind farms.• Solar mostly at the distribution system level as rooftop and ground-mounted.

– Wind generation more significant than SPVG at most jurisdictions, with a few exceptions where solar resources are high (e.g. Hawaii, Arizona, Australia).

– Mostly interfaced to the system through power electronic converters.– Generation technologies are relatively mature but new installations,

connection standards, and controls are still under development, with system impacts not yet fully understood and thus being still studied.

– Mostly privately owned by GENCOS (wind farms) and consumers (SPVG rooftop/ground-mounted).

12

Peak demand (Dec.):411.0 GW

• Europe’s electrical energy supply and demand [UCTE/ENTSO-E]:

Supply Technologies

13

Supply Technologies• US electricity supply and demand [US gov.]:

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

TWh

year

Others

G/S/W/B

Nuclear

Thermal

Hydro

0

100

200

300

400

500

600

700

800

900

1000

200520042003200220012000199919981997199619951994

year

GW

DemandReserves

14

Chart2

19901990199019901990

19911991199119911991

19921992199219921992

19931993199319931993

19941994199419941994

19951995199519951995

19961996199619961996

19971997199719971997

19981998199819981998

19991999199919991999

20002000200020002000

20012001200120012001

20022002200220022002

20032003200320032003

20042004200420042004

2005P2005P2005P2005P2005P

Hydro

Thermal

Nuclear

G/S/W/B

Others

year

TWh

292865846

2103780605

576861678

357238072

3615663

288994189

2103262931

612565087

357773453

4738849

253088003

2138704811

618776263

326857825

3719887

280494008

2230741008

610291214

356707290

3487156

260125733

2270132580

640439832

336660876

3666925

310832748

2293908429

673402123

384798133

4103808

347162063

2346018207

674728546

422957667

3571279

356453295

2430319913

628644171

433636114

3611990

323335661

2547065197

673702104

400424067

3571410

319536029

2569669781

728254124

398959031

4023773

275572597

2692478478

753892940

356478571

4793914

216961044

2677004758

768826308

294946101

4689931

264328832

2730166178

780064087

351250924

5713991

275806328

2758649951

763732695

363216797

6120827

268417308

2825010758

788528387

358825769

6678560

265077680

2903275650

780464675

357165661

3650896

US Generation

Table 8.2a Electricity Net Generation: Total (All Sectors), 1949-2005

(Sum of Tables 8.2b and 8.2d; Thousand Kilowatthours)

YearFossil FuelsRenewable EnergyOther 9Total

Hydro-

Nuclearelectric

Coal 1Petroleum 2TotalElectricPumpedConventionalBiomassSolar 8WindTotal

NaturalOtherPowerStorage 5HydroelectricGeo-

Gas 3Gases 4Power Wood 6Waste 7thermalDemand in MWh

1949135,451,32028,547,23236,966,709NA200,965,2610[10]94,772,992386,036NANANANA95,159,028NA296,124,289

1950154,519,99433,734,28844,559,159NA232,813,4410[10]100,884,575389,585NANANANA101,274,160NA334,087,601

1951185,203,65728,712,11656,615,678NA270,531,4510[10]104,376,120390,784NANANANA104,766,904NA375,298,355

1952195,436,66629,749,76168,453,088NA293,639,5150[10]109,708,251481,647NANANANA110,189,898NA403,829,413

1953218,846,32538,404,44979,790,975NA337,041,7490[10]109,617,396389,418NANANANA110,006,814NA447,048,563

1954239,145,96631,520,17593,688,271NA364,354,4120[10]111,639,772263,434NANANANA111,903,206NA476,257,618

1955301,362,69837,138,30895,285,441NA433,786,4470[10]116,235,946276,469NANANANA116,512,415NA550,298,862

1956338,503,48435,946,772104,037,208NA478,487,4640[10]125,236,621151,678NANANANA125,388,299NA603,875,763

1957346,386,20740,499,357114,212,525NA501,098,0899,670[10]133,357,930176,678NANANANA133,534,608NA634,642,367

1958344,365,78140,371,540119,759,302NA504,496,623164,691[10]143,614,545175,003NANANANA143,789,548NA648,450,862

1959378,424,21046,839,719146,619,391NA571,883,320188,101[10]141,154,533152,877NANANANA141,307,410NA713,378,831

1960403,067,35747,986,893157,969,787NA609,024,037518,182[10]149,440,035140,166NA33,368NANA149,613,569NA759,155,788

1961421,870,66948,519,376169,285,998NA639,676,0431,692,149[10]155,536,444125,734NA94,021NANA155,756,199NA797,124,391

1962450,249,23848,879,536184,301,293NA683,430,0672,269,685[10]172,015,646127,796NA100,462NANA172,243,904NA857,943,656

1963493,926,71952,001,610201,602,073NA747,530,4023,211,836[10]168,990,140127,940NA167,953NANA169,286,033NA920,028,271

1964526,230,01956,953,712220,038,479NA803,222,2103,342,743[10]180,301,506148,076NA203,791NANA180,653,373NA987,218,326

1965570,925,95164,801,224221,559,434NA857,286,6093,656,699[10]196,984,345268,804NA189,214NANA197,442,363NA1058385671

1966613,474,80078,926,172251,151,562NA943,552,5345,519,909[10]197,937,538333,926NA187,988NANA198,459,452NA1147531895

1967630,483,36389,270,724264,805,785NA984,559,8727,655,214[10]224,948,605315,688NA316,309NANA225,580,602NA1217795688

1968684,904,580104,275,833304,432,723NA109361313612,528,419[10]225,873,158375,062NA435,826NANA226,684,046NA1332825601

1969706,001,240137,847,152333,278,945NA117712733713,927,839[10]253,468,237319,933NA614,710NANA254,402,880NA1445458056

1970704,394,479184,183,402372,890,063NA126146794421,804,448[10]250,957,442136,000220,450525,183NANA251,839,075NA1535111467

1971713,102,454220,225,423374,030,784NA130735866138,104,545[10]269,531,459111,330199,869547,752NANA270,390,410NA1615853616

1972771,131,265274,295,961375,747,796NA142117502254,091,135[10]275,928,828130,859199,7741,452,795NANA277,712,256NA1752978413

1973847,651,470314,342,926340,858,192NA150285258883,479,463[10]275,430,574130,403197,8901,965,713NANA277,724,580NA1864056631

1974828,432,921300,930,538320,065,088NA1449428547113,975,740[10]304,211,80568,523182,1542,452,636NANA306,915,118NA1870319405

1975852,786,222289,094,900299,778,408NA1441659530172,505,075[10]303,152,67317,551173,5683,246,172NANA306,589,964NA1920754569

1976944,390,993319,988,137294,623,911NA1559003041191,103,531[10]286,924,23884,386182,0783,616,407NANA290,807,109NA2040913681

1977985,218,596358,178,822305,504,859NA1648902277250,883,283[10]223,598,687307,634173,2713,582,335NANA227,661,927NA2127447487

1978975,742,083365,060,441305,390,836NA1646193360276,403,070[10]283,465,224197,193140,4342,977,630NANA286,780,481NA2209376911

19791075037091303,525,209329,485,107NA1708047407255,154,623[10]283,075,976299,859198,1923,888,968NANA287,462,995NA2250665025

19801161562368245,994,189346,239,900NA1753796457251,115,575[10]279,182,090275,366157,7975,073,079NANA284,688,332NA2289600364

19811203203232206,420,775345,777,173NA1755401180272,673,503[10]263,844,664245,201122,6285,686,163NANA269,898,656NA2297973339

19821192004204146,797,490305,259,749NA1644061443282,773,248[10]312,374,013195,940124,9794,842,865NANA317,537,797NA2244372488

19831259424279144,498,593274,098,458NA1678021330293,677,119[10]335,290,855215,867162,7456,075,101NA2,668341,747,236NA2313445685

19841341680752119,807,913297,393,596NA1758882261327,633,549[10]324,311,365461,411424,5407,740,5045,2486,490332,949,558NA2419465368

19851402128125100,202,273291,945,965NA1794276363383,690,727[10]284,310,538743,294639,5789,325,23010,6305,762295,035,032NA2473002122

19861385831452136,584,867248,508,433NA1770924752414,038,063[10]294,005,219491,509685,23410,307,95414,0324,189305,508,137NA2490470952

19871463781289118,492,571272,620,803NA1854894663455,270,382[10]252,856,093783,088693,94110,775,46110,4973,541265,122,621NA2575287666

19881540652774148,899,561252,800,704NA1942353039526,973,047[10]226,100,803935,986738,25810,300,0799,094871238,085,091NA2707411177

1989111583779139164,517,957352,628,8667,862,4182108788380529,354,717[10]271,976,93627,236,6689,162,88714,593,443250,6012,112,043325,332,5783,829,8492967305524

19901594011479126,621,142372,765,15410,382,8302103780605576,861,678-3,507,741292,865,84632,521,88913,260,37915,434,271367,0872,788,600357,238,0723,615,6633037988277

19911590622748119,751,573381,553,01711,335,5932103262931612,565,087-4,541,435288,994,18933,725,35815,664,74615,966,444471,7652,950,951357,773,4534,738,8493073798885

19921621206039100,154,163404,074,37213,270,2372138704811618,776,263-4,176,582253,088,00336,528,66217,816,03516,137,962399,6402,887,523326,857,8253,719,8873083882204

19931690070232112,788,180414,926,79812,955,7982230741008610,291,214-4,035,572280,494,00837,623,40718,333,03116,788,565462,4523,005,827356,707,2903,487,1563197191096

19941690693864105,900,983460,218,68213,319,0512270132580640,439,832-3,377,825260,125,73337,937,36419,128,59515,535,453486,6223,447,109336,660,8763,666,92532475223885068886400

1995170942646874,554,065496,057,94513,869,9512293908429673,402,123-2,725,131310,832,74836,521,08220,404,97113,378,258496,8213,164,253384,798,1334,103,80833534873625167173600

1996179519559381,411,225455,055,57614,355,8132346018207674,728,546-3,088,078347,162,06336,800,31020,911,33614,328,684521,2053,234,069422,957,6673,571,27934441876215277356880

1997184501573692,554,873479,398,67013,350,6342430319913628,644,171-4,039,905356,453,29536,948,44121,709,07314,726,102511,1683,288,035433,636,1143,611,99034921722835417087640

19981873515690128,800,173531,257,10413,492,2302547065197673,702,104-4,467,280323,335,66136,338,38422,447,93514,773,918502,4733,025,696400,424,0673,571,41036202954985589633360

19991881087224118,060,838556,396,12714,125,5922569669781728,254,124-6,096,899319,536,02937,040,73422,572,17514,827,013495,0824,487,998398,959,0314,023,77336948098105727787320

20001966264596111,220,965601,038,15913,954,7582692478478753,892,940-5,538,860275,572,59737,594,86623,131,31414,093,158493,3755,593,261356,478,5714,793,91438021050435965043160

20011903955943124,880,222639,129,1209,039,4732677004758768,826,308-8,823,445216,961,04435,199,90521,764,56413,740,501542,7556,737,332294,946,1014,689,93137366436535911537080

2002193313035394,567,394691,005,74611,462,6852730166178780,064,087-8,742,928264,328,83238,665,04022,856,63214,491,310554,83110,354,279351,250,9245,713,99138584522526100253760

20031973736750119,405,640649,907,54115,600,0202758649951763,732,695-8,535,065275,806,32837,529,09823,735,67214,424,231534,00111,187,467363,216,7976,120,82738831852056103547520

20041978620218120,645,844[R]708978606[R]16,766,0902825010758788528387[R]-8,488,210268,417,308[R]37,576,418[R]23,302,172[R]14,810,975[R]575,15514,143,741[R]358,825,7696,678,560[R]39705552646069874080

2005P2014172634121,910,223751,549,11115,643,6822903275650780,464,675-6,568,160265,077,68037,828,37923,996,55615,124,491541,39214,597,163357,165,6613,650,89640379887226539077200

1Anthracite, bituminous coal, subbituminous coal, lignite, waste coal, and coal synfuel.9Batteries, chemicals, hydrogen, pitch, purchased steam, sulfur, and miscellaneous technologies.

2Distillate fuel oil, residual fuel oil, petroleum coke, jet fuel, kerosene, other petroleum, and waste oil.10Included in "Conventional Hydroelectric Power."

3Natural gas, plus a small amount of supplemental gaseous fuels that cannot be identified separately.11Through 1988, all data except hydroelectric are for electric utilities only; hydroelectric data through 1988

include industrial plants as well as electric utilities. Beginning in 1989, data are for electric utilities, independent

power producers, commercial plants, and industrial plants.

4Blast furnace gas, propane gas, and other manufactured and waste gases derived from fossil fuels.R=Revised. P=Preliminary. NA=Not available. (s)=Less than 0.05 billion killowatthours.

5Pumped storage facility production minus energy used for pumping.Notes: · See Note 1, "Coverage of Electricity Statistics," at end of section. · Totals may not equal sum of

components due to independent rounding.

6Wood, black liquor, and other wood waste.Web Page: For related information, see http://www.eia.doe.gov/fuelelectric.html.

7Municipal solid waste, landfill gas, sludge waste, tires, agricultural byproducts, and other biomass.Sources: · 1949-1988Table 8.2b for electric power sector, and Table 8.1 for industrial sector. · 1989

forwardTables 8.2b and 8.2d.

8Solar thermal and photovoltaic energy.

US Generation

Hydro

Thermal

Nuclear

G/S/W/B

Others

year

TWh

US Demand

Table 3.2. Net Internal Demand, Capacity Resources, and Capacity Margins by North American Electric Reliability Council Region, Summer, 1994 through 2005

(Megawatts)

Region and Item200520042003200220012000199919981997199619951994

ECAR[1]

Net Internal Demand[2]NA953009848710125110023598651940729235991103885738564384967

Capacity Resources[3]NA127919123755119736113136115379107451105545105106104953103003101605

Capacity Margin (percent)[4]NA25.520.415.411.414.512.512.513.315.616.916.4

ERCOT

Net Internal Demand[2]590605853159282558335510653649516975025447746456364499043630

Capacity Resources[3]667247385074764768497079769622654235978855771552305507454219

Capacity Margin (percent)[4]11.520.720.727.322.222.92115.914.417.418.319.5

FRCC



Capacity Margin (percent)[4]8.51313.712.47.917.214.3131716.717.318.7

MAAC[1]




MAIN[1]



Capacity Margin (percent)[4]NA23.120.520.519.619.215.813.613.415.91716.4

MRO (U.S.)[5]



Capacity Margin (percent)[4]18.218.813.615.915.918.213.514.417.117.615.916.8

NPCC (U.S.)




ReliabilityFirst[6]

Net Internal Demand[2]190200NANANANANANANANANANANA

Capacity Resources[3]220000NANANANANANANANANANANA

Capacity Margin (percent)[4]13.5NANANANANANANANANANANA

SERC




SPP




WECC (U.S.)



Capacity Margin (percent)[4]19.72219.617.913.617.517.717.52324.723.521.8

Contiguous U.S.




[1] ECAR, MAAC, and MAIN dissolved at the end-of-2005. Utility membership joined other reliability regional councils. Also, see Footnote 6.

[2] Net Internal Demand represents the system demand that is planned for, which is set to equal Internal Demand less Direct Control Load Management and Interruptible Demand by the electric power industry`s reliability authority. See Technical Notes for d

[3] Capacity Resources: Utility- and IPP-owned generating capacity that is existing or in various stages of planning or construction, less inoperable capacity, plus planned capacity purchases from other resources, less planned capacity sales.

[4] Capacity Margin is the amount of unused available capability of an electric power system at peak load as a percentage of capacity resources.

[5] Regional name has changed from Mid-Continent Area Power Pool to Midwest Reliability Organization.

[6] ReliabilityFirst Corporation (RFC) came into existence on January 1, 2006, and submitted a consolidated filing covering the historical NERC regions of ECAR, MAAC, and MAIN. Many of the former utility members joined RFC.

NA = Not available.

Notes: • NERC Regional Council names may be found in the Glossary reference. • Represents an hour of a day during the associated peak period. • The summer peak period begins on June 1 and extends through September 30. • The MRO, SERC, and SPP regional b

Sources: Energy Information Administration, Form EIA-411, "Coordinated Bulk Power Supply Program."

US Demand

Demand

Capacity

year

GW

Canada

Electricity Generation and Consumption in Canada (in billions of kilowatt-hours)

19931994199519961997199819992000200120022003

Net Generation518.1539.7544.1557.2556.9545562.2587.9570.9582.2566.3

hydroelectric320.3326.4332.6352.1347.2328.6342.1354.7329.7346.8322.5

nuclear90.1102.49388.177.967.769.869.272.971.870.8

geo/solar/wind/biomass4.55.45.35.55.96.37.57.588.58.5

conventional thermal103.2105.5113.3111.5126142.4142.8156.5160.3155.2154.5

Net Consumption455.1458.1467.9477.9482.4479.1492.9510.6508.6518.3520.9

Imports2.70.92.51.97.511.71312.716.11323.6

Exports29.444.840.642.24339.542.948.838.436.129.3

Canada

Hydro

Thermal

Nuclear

G/S/W/B

Consumption

year

TWh

Chart2

20052005

20042004

20032003

20022002

20012001

20002000

19991999

19981998

19971997

19961996

19951995

19941994

Demand

Reserves

year

GW

746470

882125

692908

875870

696752

856131

696376

833380

674833

788990

680941

808054

653857

765744

638086

744670

618389

737855

602438

730376

589860

727481

578640

711583

Sheet1


(Megawatts)

Region and Item200520042003200220012000199919981997199619951994

ECAR[1]




ERCOT




FRCC




MAAC[1]




MAIN[1]




MRO (U.S.)[5]




NPCC (U.S.)




ReliabilityFirst[6]




SERC




SPP




WECC (U.S.)




Contiguous U.S.










NA = Not available.



Sheet1

Demand

Capacity

year

GW

Sheet2

Sheet3

Supply Technologies• Canada’s electricity supply and demand [NRC]:

0

100

200

300

400

500

600

700

1993 19941995 19961997 1998 19992000 20012002 2003

year

TWh

0

10

20

30

40

50

60

70

80

GW

G/S/W/BNuclearThermalHydroGW Consumption

15

Chart6

199319931993199352.6736111111

199419941994199453.0208333333

199519951995199554.1550925926

199619961996199655.3125

199719971997199755.8333333333

199819981998199855.4513888889

199919991999199957.0486111111

200020002000200059.0972222222

200120012001200158.8657407407

200220022002200259.9884259259

200320032003200360.2893518519

Hydro

Thermal

Nuclear

G/S/W/B

GW Consumption

year

TWh

GW

320.3

103.2

90.1

4.5

326.4

105.5

102.4

5.4

332.6

113.3

93

5.3

352.1

111.5

88.1

5.5

347.2

126

77.9

5.9

328.6

142.4

67.7

6.3

342.1

142.8

69.8

7.5

354.7

156.5

69.2

7.5

329.7

160.3

72.9

8

346.8

155.2

71.8

8.5

322.5

154.5

70.8

8.5

US Generation

Table 8.2a Electricity Net Generation: Total (All Sectors), 1949-2005

(Sum of Tables 8.2b and 8.2d; Thousand Kilowatthours)

YearFossil FuelsRenewable EnergyOther 9Total

Hydro-

Nuclearelectric

Coal 1Petroleum 2TotalElectricPumpedConventionalBiomassSolar 8WindTotal

NaturalOtherPowerStorage 5HydroelectricGeo-

Gas 3Gases 4Power Wood 6Waste 7thermal

1949135,451,32028,547,23236,966,709NA200,965,2610[10]94,772,992386,036NANANANA95,159,028NA296,124,289

1950154,519,99433,734,28844,559,159NA232,813,4410[10]100,884,575389,585NANANANA101,274,160NA334,087,601

1951185,203,65728,712,11656,615,678NA270,531,4510[10]104,376,120390,784NANANANA104,766,904NA375,298,355

1952195,436,66629,749,76168,453,088NA293,639,5150[10]109,708,251481,647NANANANA110,189,898NA403,829,413

1953218,846,32538,404,44979,790,975NA337,041,7490[10]109,617,396389,418NANANANA110,006,814NA447,048,563

1954239,145,96631,520,17593,688,271NA364,354,4120[10]111,639,772263,434NANANANA111,903,206NA476,257,618

1955301,362,69837,138,30895,285,441NA433,786,4470[10]116,235,946276,469NANANANA116,512,415NA550,298,862

1956338,503,48435,946,772104,037,208NA478,487,4640[10]125,236,621151,678NANANANA125,388,299NA603,875,763

1957346,386,20740,499,357114,212,525NA501,098,0899,670[10]133,357,930176,678NANANANA133,534,608NA634,642,367

1958344,365,78140,371,540119,759,302NA504,496,623164,691[10]143,614,545175,003NANANANA143,789,548NA648,450,862

1959378,424,21046,839,719146,619,391NA571,883,320188,101[10]141,154,533152,877NANANANA141,307,410NA713,378,831

1960403,067,35747,986,893157,969,787NA609,024,037518,182[10]149,440,035140,166NA33,368NANA149,613,569NA759,155,788

1961421,870,66948,519,376169,285,998NA639,676,0431,692,149[10]155,536,444125,734NA94,021NANA155,756,199NA797,124,391

1962450,249,23848,879,536184,301,293NA683,430,0672,269,685[10]172,015,646127,796NA100,462NANA172,243,904NA857,943,656

1963493,926,71952,001,610201,602,073NA747,530,4023,211,836[10]168,990,140127,940NA167,953NANA169,286,033NA920,028,271

1964526,230,01956,953,712220,038,479NA803,222,2103,342,743[10]180,301,506148,076NA203,791NANA180,653,373NA987,218,326

1965570,925,95164,801,224221,559,434NA857,286,6093,656,699[10]196,984,345268,804NA189,214NANA197,442,363NA1058385671

1966613,474,80078,926,172251,151,562NA943,552,5345,519,909[10]197,937,538333,926NA187,988NANA198,459,452NA1147531895

1967630,483,36389,270,724264,805,785NA984,559,8727,655,214[10]224,948,605315,688NA316,309NANA225,580,602NA1217795688

1968684,904,580104,275,833304,432,723NA109361313612,528,419[10]225,873,158375,062NA435,826NANA226,684,046NA1332825601

1969706,001,240137,847,152333,278,945NA117712733713,927,839[10]253,468,237319,933NA614,710NANA254,402,880NA1445458056

1970704,394,479184,183,402372,890,063NA126146794421,804,448[10]250,957,442136,000220,450525,183NANA251,839,075NA1535111467

1971713,102,454220,225,423374,030,784NA130735866138,104,545[10]269,531,459111,330199,869547,752NANA270,390,410NA1615853616

1972771,131,265274,295,961375,747,796NA142117502254,091,135[10]275,928,828130,859199,7741,452,795NANA277,712,256NA1752978413

1973847,651,470314,342,926340,858,192NA150285258883,479,463[10]275,430,574130,403197,8901,965,713NANA277,724,580NA1864056631

1974828,432,921300,930,538320,065,088NA1449428547113,975,740[10]304,211,80568,523182,1542,452,636NANA306,915,118NA1870319405

1975852,786,222289,094,900299,778,408NA1441659530172,505,075[10]303,152,67317,551173,5683,246,172NANA306,589,964NA1920754569

1976944,390,993319,988,137294,623,911NA1559003041191,103,531[10]286,924,23884,386182,0783,616,407NANA290,807,109NA2040913681

1977985,218,596358,178,822305,504,859NA1648902277250,883,283[10]223,598,687307,634173,2713,582,335NANA227,661,927NA2127447487

1978975,742,083365,060,441305,390,836NA1646193360276,403,070[10]283,465,224197,193140,4342,977,630NANA286,780,481NA2209376911

19791075037091303,525,209329,485,107NA1708047407255,154,623[10]283,075,976299,859198,1923,888,968NANA287,462,995NA2250665025

19801161562368245,994,189346,239,900NA1753796457251,115,575[10]279,182,090275,366157,7975,073,079NANA284,688,332NA2289600364

19811203203232206,420,775345,777,173NA1755401180272,673,503[10]263,844,664245,201122,6285,686,163NANA269,898,656NA2297973339

19821192004204146,797,490305,259,749NA1644061443282,773,248[10]312,374,013195,940124,9794,842,865NANA317,537,797NA2244372488

19831259424279144,498,593274,098,458NA1678021330293,677,119[10]335,290,855215,867162,7456,075,101NA2,668341,747,236NA2313445685

19841341680752119,807,913297,393,596NA1758882261327,633,549[10]324,311,365461,411424,5407,740,5045,2486,490332,949,558NA2419465368

19851402128125100,202,273291,945,965NA1794276363383,690,727[10]284,310,538743,294639,5789,325,23010,6305,762295,035,032NA2473002122

19861385831452136,584,867248,508,433NA1770924752414,038,063[10]294,005,219491,509685,23410,307,95414,0324,189305,508,137NA2490470952

19871463781289118,492,571272,620,803NA1854894663455,270,382[10]252,856,093783,088693,94110,775,46110,4973,541265,122,621NA2575287666

19881540652774148,899,561252,800,704NA1942353039526,973,047[10]226,100,803935,986738,25810,300,0799,094871238,085,091NA2707411177

1989111583779139164,517,957352,628,8667,862,4182108788380529,354,717[10]271,976,93627,236,6689,162,88714,593,443250,6012,112,043325,332,5783,829,8492967305524

19901594011479126,621,142372,765,15410,382,8302103780605576,861,678-3,507,741292,865,84632,521,88913,260,37915,434,271367,0872,788,600357,238,0723,615,6633037988277

19911590622748119,751,573381,553,01711,335,5932103262931612,565,087-4,541,435288,994,18933,725,35815,664,74615,966,444471,7652,950,951357,773,4534,738,8493073798885

19921621206039100,154,163404,074,37213,270,2372138704811618,776,263-4,176,582253,088,00336,528,66217,816,03516,137,962399,6402,887,523326,857,8253,719,8873083882204

19931690070232112,788,180414,926,79812,955,7982230741008610,291,214-4,035,572280,494,00837,623,40718,333,03116,788,565462,4523,005,827356,707,2903,487,1563197191096

19941690693864105,900,983460,218,68213,319,0512270132580640,439,832-3,377,825260,125,73337,937,36419,128,59515,535,453486,6223,447,109336,660,8763,666,9253247522388

1995170942646874,554,065496,057,94513,869,9512293908429673,402,123-2,725,131310,832,74836,521,08220,404,97113,378,258496,8213,164,253384,798,1334,103,8083353487362

1996179519559381,411,225455,055,57614,355,8132346018207674,728,546-3,088,078347,162,06336,800,31020,911,33614,328,684521,2053,234,069422,957,6673,571,2793444187621

1997184501573692,554,873479,398,67013,350,6342430319913628,644,171-4,039,905356,453,29536,948,44121,709,07314,726,102511,1683,288,035433,636,1143,611,9903492172283

19981873515690128,800,173531,257,10413,492,2302547065197673,702,104-4,467,280323,335,66136,338,38422,447,93514,773,918502,4733,025,696400,424,0673,571,4103620295498

19991881087224118,060,838556,396,12714,125,5922569669781728,254,124-6,096,899319,536,02937,040,73422,572,17514,827,013495,0824,487,998398,959,0314,023,7733694809810

20001966264596111,220,965601,038,15913,954,7582692478478753,892,940-5,538,860275,572,59737,594,86623,131,31414,093,158493,3755,593,261356,478,5714,793,9143802105043

20011903955943124,880,222639,129,1209,039,4732677004758768,826,308-8,823,445216,961,04435,199,90521,764,56413,740,501542,7556,737,332294,946,1014,689,9313736643653

2002193313035394,567,394691,005,74611,462,6852730166178780,064,087-8,742,928264,328,83238,665,04022,856,63214,491,310554,83110,354,279351,250,9245,713,9913858452252

20031973736750119,405,640649,907,54115,600,0202758649951763,732,695-8,535,065275,806,32837,529,09823,735,67214,424,231534,00111,187,467363,216,7976,120,8273883185205

20041978620218120,645,844[R]708978606[R]16,766,0902825010758788528387[R]-8,488,210268,417,308[R]37,576,418[R]23,302,172[R]14,810,975[R]575,15514,143,741[R]358,825,7696,678,560[R]3970555264

2005P2014172634121,910,223751,549,11115,643,6822903275650780,464,675-6,568,160265,077,68037,828,37923,996,55615,124,491541,39214,597,163357,165,6613,650,8964037988722

1Anthracite, bituminous coal, subbituminous coal, lignite, waste coal, and coal synfuel.9Batteries, chemicals, hydrogen, pitch, purchased steam, sulfur, and miscellaneous technologies.

2Distillate fuel oil, residual fuel oil, petroleum coke, jet fuel, kerosene, other petroleum, and waste oil.10Included in "Conventional Hydroelectric Power."

3Natural gas, plus a small amount of supplemental gaseous fuels that cannot be identified separately.11Through 1988, all data except hydroelectric are for electric utilities only; hydroelectric data through 1988

include industrial plants as well as electric utilities. Beginning in 1989, data are for electric utilities, independent

power producers, commercial plants, and industrial plants.

4Blast furnace gas, propane gas, and other manufactured and waste gases derived from fossil fuels.R=Revised. P=Preliminary. NA=Not available. (s)=Less than 0.05 billion killowatthours.

5Pumped storage facility production minus energy used for pumping.Notes: · See Note 1, "Coverage of Electricity Statistics," at end of section. · Totals may not equal sum of

components due to independent rounding.

6Wood, black liquor, and other wood waste.Web Page: For related information, see http://www.eia.doe.gov/fuelelectric.html.

7Municipal solid waste, landfill gas, sludge waste, tires, agricultural byproducts, and other biomass.Sources: · 1949-1988Table 8.2b for electric power sector, and Table 8.1 for industrial sector. · 1989

forwardTables 8.2b and 8.2d.

8Solar thermal and photovoltaic energy.

US Generation

Hydro

Thermal

Nuclear

G/S/W/B

Others

year

TWh

US Demand


(Megawatts)

Region and Item200520042003200220012000199919981997199619951994

ECAR[1]




ERCOT




FRCC




MAAC[1]




MAIN[1]




MRO (U.S.)[5]




NPCC (U.S.)




ReliabilityFirst[6]




SERC




SPP




WECC (U.S.)




Contiguous U.S.










NA = Not available.



US Demand

Demand

Capacity

year

GW

Canada

Electricity Generation and Consumption in Canada (in billions of kilowatt-hours)

19931994199519961997199819992000200120022003

Net Generation518.1539.7544.1557.2556.9545562.2587.9570.9582.2566.3

hydroelectric320.3326.4332.6352.1347.2328.6342.1354.7329.7346.8322.5

nuclear90.1102.49388.177.967.769.869.272.971.870.8

geo/solar/wind/biomass4.55.45.35.55.96.37.57.588.58.5

conventional thermal103.2105.5113.3111.5126142.4142.8156.5160.3155.2154.5

Net Consumption455.1458.1467.9477.9482.4479.1492.9510.6508.6518.3520.9

Net Consumption (GW)52.673611111153.020833333354.155092592655.312555.833333333355.451388888957.048611111159.097222222258.865740740759.988425925960.2893518519

Imports2.70.92.51.97.511.71312.716.11323.6

Exports29.444.840.642.24339.542.948.838.436.129.3

Canada

Hydro

Thermal

Nuclear

G/S/W/B

Consumption GW

year

TWh

GW

Supply Technologies• Supply and demand in Ontario-Canada [IESO, ON gov.]:

16

2009

Supply Technologies• Nuclear power

generation [European Nuclear Society]: – Clean from green

house gases emissions point of view.

– To supply base load since does not control f.

17

Supply Technologies• Coal plant (thermal) [TVA]:

– “Dirty” from GHG point of view. – Mainly to supply base load given slow response.

18

Supply Technologies• Combined-cycle plant

(thermal) [power-technology.com]: – Gas + steam turbine.– Cleaner that coal

plants.– To supply base

(steam) and peak load (gas).

19

Supply Technologies• Hydro plant [US DOE]:

– Large and small (run of the river).

– Supplies base and peak load (fast response)

20

wind turbine

gears

generator

substation

• Wind power [EON]: Clean, but not yet dispatchable.

Supply Technologies

21

Supply Technologies– Types of wind power

units [PSAT]:

22

Supply Technologies• Solar power:

– PV [an-energy-efficient-home.com] and thermal [acciona-energia.com]

– Dispatchable with energy storage systems.

23

Supply Technologies• Load supply in Ontario by generator type [MEI]:

24

Generator• Generator components:

– Generator:– Synchronous machine: AC stator and DC rotor.– Excitation system: DC generator or static converter plus voltage

regulator and stabilizer.

25

Generator• Generator with DC exciter and associated controls:

26

Generator• Generator with static exciter and associated controls:

27

Synchronous Machine

28

Synchronous Machine• Electrical (inductor) equations:

where [v] = [vas vbs vcs vF vD vQ1 vQ2]T and similarly for [i] and [λ].• Mechanical (Newton’s) equations:

29

Synchronous Machine• Park’s transformation equations:

30

Synchronous Machine• Detailed dqo equations:

– Stator equations:

– Rotor equations:

31

Synchronous Machine– Magnetic flux equations:

32

Synchronous Machine– Mechanical equations:

33

Synchronous Machine• 3-phase short circuit at generator terminals:

Ea(0) is the open-circuit RMS phase voltage

34

Simplified Models • Assuming balanced operation (null zero

sequence), the detailed machine model can be reduced to phasor models useful for stability and steady state analysis.

• Phasor models are based on the following assumptions:– The rotor speed does not deviate “much” from the

synchronous speed, i.e. ωr ≈ ωs = (2/P) 2 π fo, i.e.θr = ωs t + π/2 + δ

– The rate of change in rotor speed is “small”, i.e. |dωr/d t | ≈ 0.

35

Simplified Models• Subtransient models capture the full machine

electrical dynamics, including the “few” initial cycles (ms) associated with the damper windings.

• Transient models capture the machine electrical dynamics starting with the field and induced rotor core current transient response. Damper windings transients are neglected.

• Steady sate models capture the machine electrical response when all transients have disappeared after “a few” seconds.

36

Subtransient Model

37

Subtransient Model

38

Subtransient Model• The subtransient reactances (Xq", Xd") and open circuit time

constants (Tqo", Tdo"), as well as the transient reactances (Xq', Xd') and open circuit time constants (Tqo', Tdo') are directly associated with the machine internal resistances and inductances.

• In practice, most of these constants are determined from short circuit tests.

• All the E voltages are “internal” machine voltages directly associated with the “internal” phase angle δ.

• The internal field voltage Ef is directly proportional to the actual field dc voltage, and is typically controlled by the voltage regulator.

• The mechanical power Pm is controlled through the governor.

39

Subtransient Model• Typical machine parameters:

H = π fo M = J ωo/SBXo = 0.1 to 0.7 of Xd"

rs = Ra

40

Subtransient Model

41

Transient Model• Obtained by eliminating the damper

winding dynamic equations as follows:

42

Transient Model

43

Transient Model• The damping D in the mechanical

equations, which is typically a small value, is assumed to be large to indirectly model the significant damping effect of these windings on ωr.

• It’s the typical model used in stability studies.

44

Transient Model• Neglecting the induced currents in the rotor (winding

Q2):

leads to the transient equations:

45

Transient Model• The phasor diagram in this case is:

46

Transient Model• For faults near the generator terminals, the q axis has

little effect on the system response, i.e. Iqs ≈ 0.• This results in the classical voltage source and transient

reactance generator model used in most theoretical stability studies:

47

Transient Model

where:

48

Transient Model• A further approximation in some cases is used by

neglecting the field dynamics, i.e. Tdo' = 0. • In this case, Ea' is a “fixed “ variable controlled

directly through the voltage regulator via Ef, i.e. Ea' = Ef.

• The limits in the voltage regulator are used to represent limits in the field and armature currents.

• These limits can be “soft”, i.e. allowed to temporarily exceed the hard steady state limits, to represent under- and over-excitation.

49

Controls• A simple voltage regulator model (IEEE

type 1):

50

Controls• A static voltage regulator model:

51

Controls• A simple governor model (hydraulic valve

plus turbine):

52

Controls• A governor-steam turbine model:

53

Steady State Model• When all transients are neglected, the generator model

becomes:

which, for a round rotor machine (Xd = Xq), leads to the classical steady state generator model:

54

Steady State Model• Based on this simple

model, the field and armature current limits can be used to define the generator capability curves (for a given terminal voltage Vas = Vt):

55

Steady State Model• Considering the voltage regulator effect, the generator can be

modeled as a constant terminal voltage within the generator reactive power capability, delivering constant power (Pm).

• This yields the PV generator model for power flow studies:

where P = Pm = constant, and V = Vt = constant for Qmin ≤ Q ≤ Qmax; otherwise, Q = Qmax/min and V is allowed to change.

56

Single-phase Transformers

• The basic characteristics of this device are:– Flux leakage around the transformer windings is represented by a leakage inductance

Ll.– The core is made of magnetic material and is represented by a magnetization

inductance (Lm>>Ll), but saturates.– Losses in the windings (Cu wires) and core (hysteresis and induced currents) are

represented with lumped resistances (r and Gm).– Steps up or down the voltage/current depending on the turn ratio

a = N1/N2 = V1/V2

57

Single-phase Transformers• The phasor equivalent circuit is, assuming

Zm >> Zl1:

58

Single-phase Transformers• Or Π form:

59

Single-phase Transformers• Neglecting Zm (Ym is small given the core

magnetic properties):

60

Single-phase Transformers• Some programs/data formats (e.g. PSAT and IEEE

common format) model the transformer as follows:

• This is equivalent to the previous model but seen from the secondary side.

61

Load Tap Changers (LTCs)• Certain transformer have built-in Under-Load Tap Changers (ULTCs) or

LTCs.• This are either operated manually (locally or remote controlled) or

automatically with a voltage regulator; the voltage control range is limited (approximately ± 10%) and on discrete steps (about ± 1%).

• The time response is in the order of minutes, with 1-2 min. delays, due to ULTCs being implemented using electromechanical systems.

• These are typically used to control the load voltage side, and hence are used at subtransmission substations.

• Nowadays, power electronic switches are used, leading to Thyristor Controller Voltage Regulators (TCVR), which are faster voltage controllers and are considered Flexible AC Transmission Systems (FACTS).

• These types of transformers are modeled using the same transformer models, but a may be assumed to be a discrete controlled variable through a voltage regulator with a dead-band.

62

Phase Shifters• Transformers with special

connections and under-load tap changers can also be used for phase shift control and are known as Phase Shifters:

63

Phase Shifters• These control the phase shift difference between the two terminal voltages

within approximately ± 30o, thus increasing the power capacity of a transmission line.

• It is also used to eliminate “loop” currents, i.e. “normalize” a system (e.g. interconnection between Ontario and Michigan/NY).

• Phase shifters are modeled using a similar model but the tap is a phasor as opposed to a scalar:

• A Π equivalent circuit cannot be used in this case.

64

Three-phase Transformers

65

Three-phase Transformers• The 3 single-phase transformers form a

3-phase bank that induces a phase shift, depending on the connection:

66

Three-phase Transformers

67

Three-phase Transformers• In balanced, “normal” systems, the net phase shift between

the generation and load sides is zero, and hence is neglected during system analyses:

• In these systems, the p.u. per-phase models of the transformers are identical to the equivalent single-phase transformer models.

68

Saturation• The magnetization inductance Lm changes with

the magnetization current due to saturation of the magnetic core.

• Saturation occurs due to a reduction on the number of “free” magnetic dipoles in the enriched core.

• This results in the core behaving more like air than a magnet, i.e. magnetic “conductivity” decreases.

• It’s typically represented using a piece-wise linear model.

69

Transmission Lines (and Cables)

70

Transmission Lines• In transmission systems, most lines are overhead lines,

like for example the 500 kV near the 401 in Milton:

71

Transmission Lines• If a line is transposed to balance the phases, the length

of the barrel B must be much less than the wavelength (s/f ≈ 5,000 km @ 60 Hz ) B ≈ 50 km), thus leading to:

72

Transmission Lines• Sequence transformation: Vopn = Ts-1 Vabc

Iopn = Ts-1 Iabc

• Similarly for [yopn] = Ts-1 [yabc] Ts.

73

Transmission Lines• Positive sequence (per-phase) phasor model:

74

Transmission Lines

Dm is the GMD of the 3 phases:

Rb' is the GMR of the bundled (Nb) and wires:

Rb is the GMR of the bundled:

75

Transmission Lines• This can be converted into the Π

equivalent circuit:

76

Loads• Load classification by demand level:

– Residential: lighting and heating (RL + controls); AC (motor + controls); appliances (small motors + controls)

– Commercial: similar types of devices as residential.– Industrial: motor drives (induction and dc motor-based mostly); arc

furnaces; lighting; heating; others (e.g. special motor drives).• By type:

– RLC + controls– Drives: ac/dc motors + electronic controls– Special (e.g. arc furnaces).

• Most controls are implemented using a variety of power electronic converters.

• Aggregate load models are necessary at the transmission system modeling level; only large loads are represented with their actual models.

77

Induction Motor

78

Induction Motor• Assuming a balanced, fundamental frequency (ω =ωo) system, the

model can be reduced to a p.u. “transient” model (3rd order model):

79

Induction Motor

80

Induction Motor• If the electromagnetic transients are neglected,

the system can be reduced to the following quasi-steady state equivalent circuit model:

81

Induction Motor• Or equivalently:

• Plus the mechanical equations.

82

Induction Motor• This simplification can be justified from the point

of view of the Torque-speed characteristic:

83

Induction Motor• If the mechanical dynamics are ignored, the slip S becomes a

fixed value, and hence the equivalent circuit can be reduced to a simple equivalent reactive impedance, i.e. a Z load.

• For loads with multiple IMs, an equivalent motor model can be used to represent these motors.

• Neglecting the motor dynamic equations in large or equivalent aggregate motors can lead to significant modeling errors, as the transient model and mechanical time constants can be on the same range as the generator time constants.

• Double-cage IMs can be modeled by introducing an additional inductance on the rotor side, which leads to a “subtransient” model.

84

Impedance Load Models• Ignoring “fast” and “slow” transients, certain loads can

be represented using an equivalent impedance.• A Z load model is typically used for a variety of

dynamic analysis of power systems.• Using these load models, an equivalent impedance

can be readily obtained for all loads connected at a particular bus at the transmission system level.

• ULTCs are used to connect distribution systems (subtransmission and LV systems and the loads connected to these) to the transmission system to control the steady state voltage on the load side.

85

Power Load Models• Hence, for “slow” dynamic analysis of balanced, fundamental

frequency system models:

• This is typically referred as a constant PQ model.

86

Power Load Models• Load recovery of certain loads (e.g thermostatic) with

respect to voltage changes can be modeled as:

87

Power Load Models• This results in the following time response:

88

Power Load Models• Certain loads have been shown to behave in steady

state as follows:

89

Power Load Models• ZIP model:

90

Power Load Models• Mixed dynamic model:

91

FACTS

92

• SVC and TCSC controllers are based on the following basic circuit topology:

TCR-FC

FC

TCR

+ v(t) -

93

TCR-FC• Each thyristor is “fired” every half cycle.• The firing angle α is “synchronized” with

respect to the zero-crossing of the voltage (or current).

• Hence, 90o ≤ α ≤ 180o for the TCR, since:

94

TCR-FC• For α = 90o ⇒ full XL (inductive)

LL

95

TCR-FC• For α = 120o ⇒ less inductive, more capacitive

LL

96

TCR-FC• For α = 160o ⇒ mostly capacitive, since iL(t) ≈ 0

LL

97

SVC

98

SVC• Assuming a sinusoidal bus voltage under

balanced, fundamental frequency operation, the controller can be modeled as:

99

SVC• This yields the following steady state

control characteristic:

100

TCSC

101

TCSC• The controller has a resonant point that must to

be avoided, as the controller becomes an open circuit:

102

TCSC• Thus, the controller limits on α have two regions

to avoid the resonant point (harmonics are high near this point).

• Assuming a sinusoidal line current, the balanced, fundamental frequency model for this controllers is:

103

TCSC• Most stability programs use a variable

impedance model to represent the TCSC, with limits defined by the corresponding α limits.

• The typical control for this type of model is:

104

TCSC• The power flow or “slow” control is designed to

maintain a constant controller impedance.• The stability or “fast” control is usually designed to

reduced system oscillations after contingencies.• The typical use of this type of controller in practice

is for the control of inter-area oscillations (e.g. North-South ac interconnection in Brazil).

• For simple series compensation, MSC are a much cheaper option; however, these can lead to Sub-synchronous Resonance (SSR) problems.

105

TCVR & TCPAR• TCVR and TCPAR are basically ULTC and

phase-shifters, respectively, with thyristor switching as opposed to electromechanical switching.

• Thus, these controllers have better dynamic response, i.e. smaller time constants, than the corresponding electromechanical-based devices.

• Controls are typically discrete, but with certain designs these can be continuous.

106

TCVR & TCPAR• The typical topology is:

107

TCVR & TCPAR– Valves 1 and 7 (positive cycle), and 2 and 8

(negative cycle) add Vc to Vo.– Valves 3 and 5 (positive cycle), and 4 and 6

(negative cycle) add -Vc to Vo.– Valves 1 and 5 (positive cycle), and 2 and 6

(negative cycle) cancel Vc; similarly for 3-4 and 7-8.

• These devices are typically modeled as ULTC and phase-shifters in dynamic and steady state studies.

108

VSC• Typical six pulse VSC with IGBT/GTO switches:

109

VSC• Switching scheme:

110

VSC• Modeling full commutation:

111

VSC

• Observe the high content of harmonics in the ac voltages and currents.

112

VSC• Pulse-width modulation (PWM) control

techniques may also be used (“popular” in low voltage level applications).

• Beside the control advantages, this technique eliminates certain lower harmonics, although it creates high level harmonics.

• For example, for a 6-pulse VSC:

113

VSCFire valves when carrier and

modulation signals crossCARRIER:

MODULATION:

114

VSC• This results on:

• Changing the modulation ratio, i.e. the magnitude of the modulation signal, results in changes of the ac voltage magnitudes.

• Shifting the modulation signal leads to phase shifts on the ac voltages.

115

STATCOM

116

STATCOM• It is basically a VSC controlling the bus

voltage.• The phase-locked loop (PLL) is needed to

reduce problems with spurious zero voltage crossings associated with the high harmonic content of the signals for this controller, especially with PWM controls.

117

STATCOM• Two types of controls can be implemented:

– Phase control in a multi-pulse VSC: By controlling the phase angle of the voltage, the capacitor can be charged (α < δ ⇒ controller absorbs P) or discharged (α > δ ⇒ controller delivers P), thus controlling the voltage output Vi.

118

STATCOM• PWM control in a 6-pulse VSC: the voltage

output Vi can be controlled through the modulation ratio m independently of its phase angle α, which in turn controls Vdc.

119

STATCOM• The typical steady state control strategy is:

• The current limits are due to the valve current limitations.

120

STATCOM• Assuming balanced,

fundamental frequency operation, the controller can be modeled as:

121

SSSC

122

SSSC• Similar to the STATCOM but connected in

series and synchronized with respect to the line current.

• A phase angle β control charges and discharges of the capacitor, thus controlling the output voltage Vi.

• PWM controls can be decoupled or coupled:

123

SSSC– Decoupled PWM controls:

124

SSSC– Coupled PWM controls (better overall performance):

125

SSSC• Assuming balanced,

fundamental frequency operation, the controller can be modeled as:

126

UPFC

127

UPFC• This controller is basically the STATCOM and

SSSC combined, with independent controls, especially for PWM:– The STATCOM controls the sending-end voltage

Vk and dc voltage Vdc.– The SSSC controls the power on the line Pl and

Ql.• There is a “demo” UPFC controller in Ohio

(AEP-EPRI venture).

128

IPFC• A combination of 2 SSSCs connected independently to 2 lines is referred to

as an Interline Power Flow Controller (IPFC):

• In this case the power on both lines can be controlled independently.

129

CSC• A combination of 2 SSSC and 2 STATCOMS

connected to 2 independent lines is referred to as a Convertible Static Compensator (CSC).

• In this case the control possibilities are many, as it can work as a STATCOM, SSSC, UPFC and IPFC.

• The CSC has been implemented in NY to relief congestion (NYPA-EPRI venture) [E. Uzunovic et al, “NYPA convertible static compensator (CSC) application phase I: STATCOM,” Proc. Trans. & Dist. Conf. and Expo., vol. 2, 2001, pp. 1139-1143]:

130

CSC

131

HVDC Light• Based on VSCs as opposed to the current sourced converters (CSCs) used

in classical HVDC:

• IGBTs (Insulated-gate bipolar transistors have a FET gate and a BJT switch) instead of GTOs are used as switches; have lower losses, higher frequency switching capacity, are cheaper, but have less reverse voltage blocking capacity.

• These switches allow using PWM controls, which yield greater control flexibility.

132

HVDC Light• The reduced reverse voltage blocking capacity of IGBTs

versus GTOs reduces the overall power capacity of the link; this is the reason for the “light” label.

• The overall costs of the link are lower, allowing for wider applications of this technology.

• Classical HVDC is most cost effective at power ranges above ~250 MW, whereas HVDC Light ratings are typically in the order of a few tens of MW (the technology current upper limits are 1,200 MW and ±320 kV).

• Visit http://www.abb.com/industries/us/9AAC30300394.aspxfor more details and actual projects.

133

http://www.abb.com/industries/us/9AAC30300394.aspx

SPVG~100 MWpeak solar farm connected to Bluewater Powerdistribution system

134

SPVG Controls• Original PQ controls:

– P output kept at maximum using an MPPT control of the dc-dc converter VI output:

– Q = 0 (unity power factor) with Q/V control of PWM VSC, so it is not a Q load for the system with negative impact on voltage.

135

SPVG Controls• RE generators were required

to disconnect under faults, which created low voltage and frequency problems with loss of power.

• Now they are required to provide reactive power during fault conditions via Low-Voltage Ride-Through (LVRT)/ or Fault Ride-Through (FTR) control, i.e. converter Q injection.

• More jurisdictions are now requiring full V output control like standard generators.

LVRT/FTR converteroutput characteristics

136

SPVG Controls• Some jurisdictions are

also requiring nowadays some frequency control:– MPPT control is

deactivated to allow some limited P control, thus de-rating the generator.

– Some manufactures are providing controls so that generator provide also virtual inertia, such as the Synchronous Power Controller (SPC):

137

WG• Ripley-Kincardine WG plant: 76 MW with 38x2

MW Enercon Tyep 4/D SGPM generators connected at 230kV.

138

WG• Type 1/A: Fixed speed with pitch control.

Generator

P controls

Pitch

Gear Box

vw

ωm

β

PmTm

139

WG• Type 2/B: Doubly Fed Induction Generator (DFIG) with variable

speed through variable rotor resistance, plus pitch control.

Generator

P controls

Pitch

Gear Box

vw

ωm

β

PmTm

140

WG• Type 3/C: DFIG with rotor converters plus pitch controls.

Generator

DC Link

P and V/Q controls

Pitch

DC link controls

VSC VSC

Gear Box

ωm

β

Pm

VtItPtQt

VdcIdc

VRIR

vw

Tm

141

WG• Type 4/D: Permanent Magnet Synchronous Generator (PMSG) or IG

with ac-dc-ac full converter interface, similar to SPCG.

Generator

DC Link

P controls

Pitch

Q/V controls

VSC VSC

vw

ωm

β

PmVtItPtQt

VdcIdc

VGIG

Tm

142

WG Controls• Depend on technology:

– Type 1/A: Only slow pitch controls to keep torque and/or turbine speed at rated values and/or within limits to avoid turbine problems.

– Type 2/B: Slow pitch control plus some fast P control through variable resistors.

– Type 3/C: Slow pitch control plus fast P and Q/V control through rotor ac-dc-ac converter.

– Type 4/D: Slow pitch control plus fast P and Q/V control through full ac-dc-ac converter interface.

143

WG Controls• Type 3/C and 4/D P control:

– MPPT based on:

– MPPT deactivated for some frequency control, de-rating the WG.

144

SPVG and WG Simplified Models

• Simplified model, based on WECC wind generator phasor (average) model:

• V and f droop controls for this model:

145

Dynamic Grid Studies• Time domains of dynamic studies (IEEE PES PSDPC TF on

“Stability Definitions and Characterization of Dynamic Behavior in Systems With High Penetration Of Power Electronic Interfaced Technologies”):

146

Dynamic Grid Studies• Tools:

– Wave and electromagnetic phenomena: PSCAD/EMTDC, EMTP, ATP, and others.

– Electromechanical phenomena: DSATools, PSS/E, PSAT, DIgSILENT PowerFactory, and many others (e.g. ETAP).

– Thermodynamic phenomena: partially DSATools, PSS/E, and others.

147

Dynamic Grid Studies• Techniques:

– Steady and quasi-steady state:• Power flows.• PV curves.• Eigenvalues and eigenvectors.

– Transients:• Detailed time-domain simulations for unbalanced and

converter systems.• Transient stability simulations of phasor-based,

balanced system models.

148

Dynamic Grid Studies• Grid stability studies (IEEE/CIGRE Joint Task Force on Stability Terms and

Definitions, “Definition and Classification of Power System Stability”, IEEE Trans. Power Systems and CIGRE Technical Brochure 231, 2003):

• These definitions and classification are being updated in the context of faster dynamics (e.g. converter-based systems).

149

Dynamic Grid Study Example• For the IEEE 145-bus, 50-machine test system:

150

Dynamic Grid Study Example– For an impedance load model, the PV curves yield:

151

Dynamic Grid Study Example– Hence, a line 90-92 outage yields:

152

Dynamic Grid Study Example– This has been typically solved by adding Power

System Stabilizers (PSS) to the voltage controllers in “certain” generators, so that the equilibrium point is made stable, i.e. the Hopf is removed (FACTS may also be used to address this problem):

153

AVR

Vref

Vt

+

+_

Dynamic Grid Study Example– A participation factor analysis in this case yields:

154

Dynamic Grid Study Example– The line 90-92 outage with PSS at generators 93 and

104 yields:

155

Dynamic Grid Study Example• More details regarding this example can

be found in: N. Mithulananthan, C. A. Cañizares, J. Reeve, and G. J. Rogers, “Comparison of PSS, SVC and STATCOM Controllers for Damping Power System Oscillations,” IEEE Transactions on Power Systems, Vol. 18, No. 2, May 2003, pp. 786-792.

156

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Dynamic Modelling and Simulation of Power Systems · sequence), the detailed machine model can be reduced to phasor models useful for stability and steady state analysis. • Phasor