unit commitment notes
TRANSCRIPT
-
7/26/2019 Unit Commitment Notes
1/5
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
-
7/26/2019 Unit Commitment Notes
2/5
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.
-
7/26/2019 Unit Commitment Notes
3/5
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
-
7/26/2019 Unit Commitment Notes
4/5
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.
-
7/26/2019 Unit Commitment Notes
5/5
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