1. Economic Load Dispatch
Optimum scheduling problem in power
system generally can be partitioned into two
sub problems namely optimum allocation of
units (generator) called unit commitment (U.C)
and optimum allocation of generation to each
unit called economic load dispatch (E.L.D) or
economic load scheduling (E.L.S).They both
combined together called optimal unit
commitment.Unit commitment should be
solved first before go for economic load
scheduling problem.
3. METHODS OF GEN
SCHEDULING
Base loading to capacity: -Loaded to capacity according to
their Efficiencies
Base loading to most efficient load:-Loaded to their
most efficient load according to their heat rates
Loading proportional to capacity:-Loaded
proportional to their capacities
Loading proportional to most efficient load: -
Loaded to their most efficient load.If loaded all units, additional load is
distributed proportional to the difference between the rated capacity and the
most efficient load
Incremental loading: -The load is divided to keep the units
operating at equal incremental cost.
4. Thermal plant modeling:
Heat rate curve:-Heat Energy needed to generate one unit
of Electrical Energy.
Input / output curve:-Input energy rate (Mcal/h) or cost
of fuel used per hour (Rs/h) as a function of generator output. It is a
concave curve.
Incremental cost:-It is the ratio of small change in input to
small change in output. Mathematically it is defined as below
&Expressed as (Rs/Kwh)
Incremental cost= Δ input / Δ output i.e.dCi / dPGi
5. Heat rate curve:- Heat rate curveHi(PGi) which is
the heat energy (Mkcal) needed to generate one unit
of electrical energy (MWh)
6. Input / output curve:-Input energy rate (Mcal/h) or
cost of fuel used per hour (Rs/h) as a function of generator
output. It is a concave curve.
7. Incremental cost:-It is the ratio of small change in
input to small change in output. Mathematically it is defined
as below &Expressed as (Rs/Kwh)
Incremental cost= Δ input / Δ output i.e.dCi / dPGi
9. Scheduling Without Tr
Losses
We assume that the inequality constraints is not
effective, and
k k
PGi = PD or ( PGi ) – PD = 0
i=1 i=1
Using this method we define an augmented cost
function (lagrangian) as
k
C = C - ( PGi – PD )
i=1
10. ( ∂C / ∂PGi ) = 0; For minimization purpose
Or dCi / dPGi = , i =1,2,3,……k
Where dCi / dPGi is the incremental cost of the
ith generator (Rs / Mwh )
dC1 / dPG1 = dC2 / dPG2 = ---- = dCn / dCGk =
This is called coordination Equation
This equation tells that optimum loading of units
are so happened when ever the units face equal
incremental cost
12. Scheduling with Tr. Losses
)
/
(
)
(
1
1
h
Rs
P
P
P
P
C
C
m
i
L
D
Gi
m
i
Gi
i
m
i
L
D
Gi P
P
P
1
0
m
i
n
i
L
Di
Gi P
P
P
1 1
0
13. ,
0
/
/
/
Gi
L
Gi
i
Gi P
P
dP
dC
P
C
(i=1, 2, . . ., m
Coordination Equation
,
i
i
Gi
L
Gi
i
L
IC
or
P
P
dP
dC
)
(
/
1
/
Gi
L
i P
P
L
/
1
/
1
is called the penalty factor of the ith plant
14. The Lagrangian multiplier has the units of rupees
per megawatt-hour.
Minimum fuel cost is obtained, when the incremental
fuel cost of each plant multiplied by its penalty factor
is the same for all the plants
The partial derivative PL/PGi is referred to as the
incremental transmission loss (ITL)i, associated with
the ith generating plant.
;
)
(
1
)
( i
i ITL
IC
This equation is referred to as the exact coordination
equation
15. SEQUENCE OF ADDING
UNITS
If there are four units A, B, C, and D
feeding the power system, each having
capacity 150 MW such that B has the
lowest heat rate, D has next higher heat
rate, A has still higher and C has the
highest heat rate. The loads at which the
units are to be added are given by the
points of intersection as shown in fig .
16. TOTAL STATION LOADS, (Mw)
0 100 200 300 400 500 600
ADD D ADD A ADD C
UNITS B, D, A & C
UNITS B, D & A
UNITS
B&D
UNIT B
HEAT
RATE
K-CAL/KWH
2600
2550
2500
2450
17. Constraints of Scheduling
Power balance constraints
Spinning reserve constraints
N
∑ ( U n PG max , n ) >= ( PD, t +R t ) .
n=1
N
∑ U n PG n , t =PD, t .
n=1
19. (down state)
(up state)
0
1
t1(up) t2(up) t3(up)
(up) time
t1(down) t2(down) t3(down)
Repair
Failure
Down
Time
Time
Fig: Random Unit performance record neglecting
scheduled outages
Security Constraints
20. PGi min< PGi < PGi max
1.Hydro constraints:Unit commitment cannot be
completely separated from the scheduling of hydro units
2. Must Run: Some units are given a must-run status
during certain times of the year for reason of voltage support
on the transmission network or for such purposes as supply of
steam for uses outside the steam plant itself.
Unit’s generation capacity constraints
Other Constraints
21. Fuel Constraints:A system in which some units
have limited fuel, or else have constraints that require
them to burn a specified amount of fuel in a given
