unit commitment notes

7/26/2019 Unit Commitment Notes

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Unit Commitment

5.1 INTRODUCTION

BecaUSe

human activity follows cycles,most systems supplying services to a

large

population will experience cycles. This includes transportation systems,

communication

systems, as well as electric power systems. In the case of an

electric

power system, the total load on the system will generallybe higher

during

the daytime and early evening when industrial loads are high, lights areon,

and so forth, and lower during the late evening and early morning when

most

of thepopulation is asleep. In addition, the use of electricpower has

aweekly

cycle, the load being lower over weekend days than weekdays. But why

isthisa

problemin the operation of an electricpower system?Why notjust

simply

commit enough units to cover the maximum system load and leave them

running?

Note that to "commit" a generating

unit is to "turn it on;" that is,

tobringthe unit up to speed, synchronizeit to the system,and

connect it so

itcandeliverpower to the network. Theproblem with "commit enough unitsand

leavethem on line" is one of economics.As willbe shown in Example 5A,

it isquite expensive to run too many generating units. A great deal

of money

can

be savedby turning units off (decommitting

them) when they are not

needed.

EXAMPLE 5A

Suppose

one had the three units given here:

Unit

l:

Unit 2:

Unit 3:

Min = 150MW

Max = 600MW

HI= 510.0

+ 7.2P1

+

Min 100MW

Max - 400

MBtu/h

H2 310.0+ 7.85P2+ 0.00194203

MBtu/h

Min = 50 MW

Max=000 MW

780+ 7.97P3+ 0.00482P; MBtu/h


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132 UNIT COMMITMENT

INTRODUCTION1200 133

with fuel costs:

Fuel costl = 1.1R/MBtu

Fuel cost2 = 1.0 R/MBtuTotal

Fuel cost3

- 12

. R/MBtu load

500

If weare to supply a load of 550MW,what unit or combination Ofunits should

be usedto supply this load most economically?To solve thisproblem, simply

try all combinations of the three units. Some combinations

willbe infeasibleifthe sum of all maximumMW for the units committed is less than the load

if the sum of all minimum MW for the units committed is greater than the

load. For each feasiblecombination, the units will be

dispatched using thetechniquesof Chapter 3. The results are presented in Table 5.1.

Note that the least expensive way to supply the generation is not withallthreeunits running,or even any combination involving two units. Rather, theoptimumcommitmentis to only run unit 1, the most economic unit. Byonlyrunning the most economic unit, the load can be supplied by that unit Operatingcloser to its best efficiency. If another unit is committed,both unit I and theother unit will be loaded further from their best efficiencypoints such that thenet cost is greater than unit 1 alone.

Suppose the load followsa simple "peak-valley" pattern as shown in Figure5.la. If the operation of the system is to be optimized, units must be shut downas the

load goes down and then recommitted as it goesback up. We wouldlike to know which units to drop and when. As we will show later, thisproblemis far from trivial when real generating units are considered. One approach tothis solution is demonstrated in Example 5B,where a simplepriority list scheme

is developed.

TABLE5.1 Unit Combinationsand Dispatch for 550-MW Load of Example 5A

4 PM 4 AM

1200

MW

Total

load

Time of dayFIG. 5.1a Simple "peak-valley" loadpattern.

Unit 3Unit

3

Unit2Unit 2

Unit I

4 AMTime of day4 PM

Off OffOff OffOff

Off OnOn OffOn Off

On OnOn On

Off

On

Off

On

Off

On

Off

On

Infeasible200

400

600

600

800

'1000'

1200

50

100

150

150

200

250

Infeasible

Infeasible

300 267

0

550

500295

400

o255

150

o

50o

05389

49113030

3760

o

o'2440

1658

o

5860

3418

5389

54975471

233 50 2787 2244 586 5617

FIG. 5.1b Unit commitment scheduleusingshut-down

rule.

EXAMPLE

5B

Suppose

we wish to know which units to drop as a functionof system

load.Let

theunits and fuel costs be the same as in Example 5A, with the load varyingfrom

apeakof 1200 MW to a valley of 500 MW. To obtain a "shut-downrule,"Simply

use a brute-force technique wherein all combinations of units willbetned

(asin Example 5A) for each load value taken in stepsof 50MWfrom1200

to 500. The results of

rule

applying

is quite

this

simple.

brute-force techniqueare givenin

Table

5.2.Our shut-down

When

load is above 1000 MW, run all three units;between

1000

MW

and

600MW, run units 1 and 2;below 600 MW, run onlyunit 1.


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INTRODUCTION135

134 UNITCOMMITMENT

and lossesbeing supplied. Spinning reserve mustbe carried so that

load

ofone ormore units does not cause too far a drop in systemfrequencyTABLE 2 "Shut-down

Rule" Derivation for

Optimum

Example

Combination

5B

Unit 2Unit I

Load

h

apter9).Quite simply, if one unit is lost, there mustbe amplereserve

c

Other

units to make up for the loss in a specified

timeperiod.Unit 3 reserve must be allocated to obey certain

rules, usuallysetbyOn

1200On

1150On

1100On

1050On

1000On

950 On

850 On

800 On

750 On

700 On

650 OnOn

550 OnOn

On

On

On

On

On

On

OnOnOn

On

On

On

Off

Off

Off

On

On

On

On

Off

Off

Off

Off

Off

Off

Off

Off

Off

Off

Off

Figure5.1bshows the unit commitment schedule derived from this shut-down

rule as applied to the load curve of Figure 5.1a.

So far, we have only obeyed one simple constraint: Enough units will be

committed

to supply the load. If this were all that was Involved in the unitcommitmentproblemthatis,just meeting the loadwe could stop here andstate that the problem was "solved." Unfortunately, other constraints and other

phenomena must be taken into account in order to claim an optimum solution.These constraints will be discussed in the next section, followed by a descriptionof some of thepresently used methods of solution.

51.1 Constraints in Unit Commitment

Many constraints canbeplaced on the unit commitment problem. The listpresented here isby no means exhaustive. Each individual power system, powerpool, reliabilitycouncil, and so forth, may impose different rules on thescheduling

of units, dependingon the generation makeup, load-curve charac-teristics, and such.

51.2 Spinning Reserve

Spinning

reserveis the term used to describethe total amount of generatiOnavailable

from all units synchronized(i.e.,spinning) on the system, minus the

sPinning

ven

percentageofforecasted peak demand, or that reservemustbe capable

of

making

up theloss of the most heavily baded unit in a givenperiod of time.

Others

calculatereserve requirements as a function of theprobabilityof not

having

sufficientgeneration to meet the

loadNot

only must the reserve be sufficient to make up for a generation-unit

failure,

but the reservesmust be-allocated among fast-respondingunits and

slow-responding

to

units.

restore

This

frequency

allows the

andautomatic

interchangegeneration

quicklyincontrolthe event

systemof aChapter

9)(see

generating-unit

Beyond

outage.

reserve, the unit commitment problem may involve various

spinning

classes

of "scheduled reserves" or "off-line" reserves. These include quick-start

diesel

or gas-turbine units as well as most hydro-unitsandpumped-storage

hydro-units

that can be brought on-line, synchronized,and brought up to full

capacity

quickly. As such, these units canbe "counted" in the overallreserve

assessment,

as long as their time to come up to full capacity is taken into

account.

Reserves,

finally, must be spread around the power system to avoid

transmission

system limitations (often called "bottling" of reserves)and to

allow

variousparts of the system to run as "islands," should theybecome

electrically

disconnected.

EXAMPLE 5C

Suppose

a power system consisted of two isolated regions:a westernregion

and

an eastern region. Five units, as shown in Figure5.2,havebeencommitted

tosupply3090 MW. The two regions are separatedby transmission tie lines

that

can together transfer a maximum of 550MWin eitherdirection

This is

also

shoun in Figure 5.2. What can we say aboutthe allocationof spinning

reserve

in this system?Thedata for the system UinFigure 5.2 are

given in Table 5.3.With the

exception

of unit 4, the loss of anythissystem canbe

coveredby the

spinning

reserve on the remaining units. Unit 4presentsaproblem,however.

Ifunit4 were to be lost and unit 5 wereto be run to its

maximum of 600 MW,

the

easternregion would still need 590 MW to coverthe

load in that region.

The

590MW would have tobe transmittedover the tie lines

from the western

region,

which can easily supply 590MW from its

reserves.However,the tie

capacity

of only 550 MW limits thetransfer. Therefore,

the loss of unit 4cannot


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136 UNITCOMMITMENT

Units550 raw 4 and 5

Units maximum1. 2, and 3

Eastern region

Western region

FIG. 5.2 Two-regionsystem.

TABLE Data forthe System in Figure

5.2

Regional

Unit

Capacity

Region Unit (MW)

Western 1 1000

2 800

3 800

Eastern 4 1200

5

UnitOutput

420

420

1040

310

Genera-

tion

1740

1350

3090

SpinningReserve

100

380

380

160

290

1310

Regional

Load

1900

1190

3090

Inter.

charw

160 in

160 out

Total4400 3090

be coveredeventhough the entire system has amplereserves. The only solution

to thisproblemis to commitmore units to operate in theeastern region.

5.1.j Thermal Unit Constraints

Thermal units usually

require a crew to operate them, especially when turned

on and turned off. A thermal unit can undergo only gradual temperature

changes,and this translatesinto a time period of some hours required tobring

the unit on-line.As a result of such restrictions in the operation of a thermal

plant, variousconstraints anse, such as:

Minimum

up time:once the unit is running, it should not be turned Off

immediately.

Minimum

downtime:once the unit is decommitted, there is a minimumtimebeforeit canbe recommitted.

INTRODUCTION137constraints: if a plant consists of two or moreunits,theycannot

turned

on at the same time since thereare not enough

crewmembers

to attend both units whilestartingup

because the temperature and pressure of the thermal unit must

ddltion,

and

ISstart-up cost

can vary from a maximum "cold-start" valueto a muchThe

value ifthe unit was only turned off recently and is still relativelyclose

tooperatingtemperature. There are two approaches to treating a thermal unit

during

Its downpenod. The first allows the unit's boiler to cool down and then

h

eat

backup tooperating temperature

In time for a scheduledturn on. Thesecond

(calledbanking)requires that sufficient energy be input to theboiler to

just

maintainoperating temperature. The costs for the two canbe compared

sothat,ifpossible,the best approach (cooling or banking) canbe chosen.

Start-up cost when cooling= Cc(l

where

Cc

= cold-start cost (MBtu)

F = fuel cost

Cf = fixed cost (includes crew expense, maintenance expenses)(in R)

= thermal time constant for the unit

t = time (h) the unit was cooled

Start-up cost whenbanking= Ct x t x F + Cfwhere

Ct= cost (MBtu/h) of maintaimng unit at operating

temperature

Up to a certain number of hours, the cost ofbanking willbeless than the cost

of

cooling,

as is illustrated in Figure 5.3.

Finally,

the capacity limits of thermal units may changefrequently,

due to

maintenance

or unscheduled outages of various equipmentin theplant; this

must

alsobe taken into account in unit commitment.

5.1.4 Other Constraints

5.1.4.1Hydro-Constraints

Unitcommitment cannot be completelyseparated from the

schedulingof

hydro-units.

In this text,' we will assume that the hydrothermal

scheduling

(or

COOrdination")problem can be separatedfrom the unit

commitmentproblem.

We,Of

course, cannot assert flatly that ourtreatment in this

fashion will always

result

in an optimal solution.


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138 UNIT COMMITMENT

Start-upcost Cooling

Banking

1 2 3 4 5 h

FIG. 5.3 ' Time-dependent

start-up costs.

5.1.4.2 Must Run

Some units are given a must-run status during certain times of theyearreason of

voltage support on the transmission network or for suchpurpoas supply of

steam for usesoutside the steam plant itself.

5.1.4.3 Fuel Constraints

We will treat the "fuel scheduling" problem briefly in Chapter 6. A system

whichsome units have limited fuel, or else have constraints that require

thto burn a specified

amount of fuel in a given time,presents a most challengunit commitment problem.

5.2 UNIT COMMITMENT SOLUTION METHODS

The commitmentproblem Canbe very difficult.As a theoretical exercis

e

,letpostulate the followingsituation.

We must establisha loadingpattern for Mperiods.We haveN units to commit and dispatch.The M load levelsand operating limits on theN units are suchthatone unit

can supply

the individual

loads and that any combinati0units can also supply the loads.

Next,assumewe are going to establishthe commitmentby)rute total

number of combinations we need to try each

hour

unit commitment notes

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