Dinamik Programming 1

8/17/2019 Dinamik Programming 1

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Electrical Power

System OperationUnit Commitment (part 1)Week#5


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Load Demand Cycles Human activity follows cycles systems supplying services will also experience usage cycles

transportation, communication, an electric power systemselectric power consumption follows a aily, weekly, anseasonal cycles

!ig! power usage uring t!e ay an evening !ours in ustrial an commercial operations an lig!ting loa s

lower usage on t!e weeken s !ig!er usage uring t!e summer an winter

greater temperature extremes

"oa cycles create economic pro lems for powergeneration

it is $uite expensive to continuously run all generation, w!ic!is nee e to meet t!e peak power eman s


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Load Demand Cycles %e&nition

commitment means to turn'on a givengeneration unit!ave t!e prime mover operating t!e unit atsync!ronous speesync!roni e an connect t!e unit to t!enetwork gri

conomicssavings are gaine y decommitting some oft!e generation units w!en t!ey are not nee tomeet t!e current loa emant!e engineering pro lem is committing enoug!units to meet current an future loa eman sw!ile minimi ing starting an operating costs


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Load Demand Cycles xample

consi er t!e cost for operating t!ree generation unitsUnit 1 * +1( 1)-5.1/0 23 1/4 4415.3 13 154 1 .44Unit 3 * +3( 3)-614/0 75 3/4 44128 33 144 3 844Unit 6 * +6( 6)-26 ./2 5. 6/4 445078 63 54 6 344

w!at com ination of units is est to supply a 554 9W loa :

Unit 1 Unit2

Unit 3 MaxGen

MinGen

P 1 P 2 P 3 F 1 F 2 F 3 F total

Off Off Off 0 0 Infeasible

Off Off On 200 50 Infeasible

Off On Off 400 100 Infeasible

Off On On 600 150 0 400 150 0 3760 1658 5418

On Off Off 600 150 550 0 0 5389 0 0 5389

On Off On 800 200 500 0 50 4911 0 586 5497

On On Off 1000 250 295 255 0 3030 2440 0 5471

On On On 1200 300 267 233 50 2787 2244 586 5617


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Load Demand Cyclesxample notes*

t!e least expensive way to supply t!e generation isnot wit! all t!ree units running or wit! anycom ination involving two unitst!e optimal commitment is to only run unit #1, t!emost economic unit

y only running t!e most economic unit, t!e loa can

e supplie y t!at unit operating closer to its este;ciencyif anot!er unit is committe , ot! unit #1 an t!eot!er unit will e loa e furt!er from t!eir este;ciency points, resulting in a !ig!er net cost


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Load Demand Cycles %aily loa patterns

consi er t!e loa eman wit! a simple peak-valleypatternin or er to optimi e t!e operation of t!e system

units must e s!ut own as loa goes ownt!en t!e units must e recommitte as loa goes ack upsimple approac! to t!e solution is a simple priority listsc!eme


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Load Demand Cycles xample

use a rute forcetec!ni$ue to o tain a


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Constraints in Unit

Commitment rimary constraints

enoug! units are committe to supply t!e loaeconomically

?pinning reserve constraints spinning reserve e&nition t!e total amount of on'line, sync!roni e generation powercommitte less t!e current loa ing an power losses supplie

protects t!e network from an unexpecte loss of one or moregeneration units

typical spinning reserve rules t!e reserve is a given percentage of t!e forecaste eman must e capa le of making up t!e loss of t!e most !eavilyloa e generation unit

reserves must e sprea aroun t!e system to avoi transmissionlimitations ( ottling) an permit parts of t!e system to run as


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Constraints in UnitCommitment

xampleconsi er a power system consisting of twoisolate regions

transmission tie'lines @oin t!e regions an maytransfer power up to a maximum of 554 9W ineit!er irection

&ve units !ave een committe to supply 64249W of loa ing

Region Unit Unit Capacity(MW)

Unit Output(MW)

RegionalGenerati

on

(MW)

SpinningReserve

(MW)

RegionalLoad

(MW)

Interchange

(MW)

Western 1 1 ! 1"# 1 1! 1$ (in)

% & #% '&

' & #% '&

astern # 1% 1 # 1' 1$ 11! 1$ (out)

$ '1 %!

*otal ## ' ! ' ! 1'1 ' !


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Constraints in Unit

Commitment xample

verify t!e allocation of spinning reserves in t!e system western region

generation of largest unit* 244 9W availa le spinning reserve

A local* 0.4 9WB tie'line capacity* 624 9WB eastern region* 8549WA total* 1154 9W ' loa can e supplie

eastern region generation of largest unit* 1484 9W availa le spinning reserve

A local* 854 9WB tie'line capacity* 554 9WB western region* 0449WA total* 1444 9W ' loa can not e completely supplie

lack 84 9W of spinning reserve in t!e eastern region commit 84 9W of new generation wit!in t!e eastern region


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Constraints in Unit

Commitment !ermal unit constraints

a t!ermal unit can un ergo only gra ual temperaturec!anges

results in a time perio of several !ours to ring a unit on'lineminimum up time* it s!oul not e turne oD imme iatelyminimum own time* once ecommitte , t!e minimum time

efore a unit can e recommittecrew constraint* at a multiple unit plant, t!ere is usually onlyenoug! personnel to start one unit at at time

a certain amount of energy is expen e to ring a uniton'line

to slowly ring up t!e temperature an pressuret!is energy oes not result in any power elivere from t!eunitt!e energy cost is roug!t into t!e unit commitment pro lemas a start'up cost


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Constraints in Unit

Commitment ?tart'up costs

t!e start'up cost can vary from a maximumcol 'start value to a muc! smaller warm'startvalue

warm unit* a recently turne 'oD unit wit! latent !eatt!at is near t!e normal operating temperature

two approac!es availa le to treating a t!ermal

unit uring its own timeallow t!e oiler to cool own an t!en !eat it ack upto operating temperature in time for a sc!e ule turn'onprovi e enoug! fuel to supply su;cient energy to t!e

oiler to @ust maintain t!e operating temperature


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Constraints in UnitCommitment

?tart'up cost comparison cooling

allowing t!e unit to cool own start'up cost function*

ankinginput su;cient energy intot!e oiler to @ust maintaint!e operating temperature

anking cost function*

( )/1 shutdownt cold cold fuel fixed C H e F C α −= − +

bank bank fuel shutdown fixed C H F kt C = +


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Unit Commitment Solution

Methods ypical utility situation involving t!ecommitment pro lem

must esta lis! a loa ing pattern for M perio s !ave N generation units availa le to commit an

ispatc! t!e M loa levels an operating limits on t!e N unitsare suc! t!at any one unit can supply t!e loa emanan any com ination of units can also supply t!e loa s

Commitment y enumeration a rute force met!o

total com inations to investigate* 3E'1 for t!e total perio of M intervals, t!e maximumnum er of possi le com inations is(3E'1)9

example* for a 38'!our perio ma e up of 1'!r intervals, a

5 unit network ecome . 3 F1465com inations


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Methods riority'"ist 9et!o s

consist of a simple s!ut' own ruleo taine y an ex!austive enumeration of all unitcom inations at eac! loa levelor o taine y noting t!e full'loa averagepro uction cost of eac! unit

t!e full'loa average pro uction cost is t!e net !eatrate at full loa multiplie y t!e fuel cost

various en!ancements can e ma e to t!epriority'list sc!eme y t!e grouping of units toensure t!at various constraints are met


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Methods ypical s!ut' own rules

at eac! !our w!en loa is ropping, eterminew!et!er ropping t!e next unit on t!e list leaves su;cientgeneration to supply t!e loa plus t!e spinning'reservere$uirements

if t!e supply is not su;cient, keep t!e unit committeetermine t!e num er of !ours efore t!e unit is nee e

again if t!e time is less t!an t!e minimum s!ut' own time for t!e

unit, keep it committeperform a cost comparison

t!e sum of t!e !ourly pro uction costs for t!e next num er of!ours wit! t!e next unit to e roppe eing committean t!e sum of t!e restart costs for t!e next unit ase ont!e minimum cost of cooling t!e unit or anking t!e unit


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Unit Commitment SolutionMethods

xamplet!e commitment sc!eme

ignoring minimum upG own times an start'up costsnotes

t!is sc!eme oes not completely parallel t!e s!ut'own se$uence escri e in t!e &rst example t!ere unit 3 was s!ut own at .44 9W leaving unit 1 !ere unit 1 is s!ut own at 844 9W leaving unit 3 w!y t!e iDerences: w!ere is t!e pro lem:

Combination Min M Max M

1 ! 2 ! 3 300 1200

1 ! 2 250 1000

2 100 400

Dinamik Programming 1

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