Stevenson J. Power system analysis
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536
CHAPTER 13 ECONOMIC OPERATION OF POWER SYSTEMS
A cue of A versus plant load establishes the value of A at which each unit
should operate for a given total plant load.
For a plant with two units operating under economic load distribution the
A of the plant equals Ai of each unit, and so
Solving for P
g
l and P
g
2
, we obtain
-
b
,
Pg l =
a,
and
-
b
2
P
2
=
a
2
Adding these results together and then solving for give
or
where
and
( 2 1 )-1
a
T
=
L
.
a
·
1
=
1
I
b
T
=
a
T
E-I
(
2
b. )
i= 1
a
i
( 13.3)
(
1
3
.
4
)
(13.5
)
(13 .6)
is the total plant output. Equation (13.6) is a closed-form solution fo r which
applies to a plant with more than two units on economic dispatch when the
ap
propriate number of terms is added to the summations of Eq. (13.5). For
instance, if the plant has K units operating on economic dispatch, then the
coecients of Eq. (13.6) are given by
( 13.7
)
(
1
3
.8
)
and the total plant output P
g
T
is (P
g
1
+ Pg 2 + .
..
+ Pg K). The indivipual
output
of each of the K units is then calculated from the common value of A
1
3
.1
DI
STRIBUTION OF LOAD BEEEN UNITS WITHIN A PNT
537
given by Eq. (13.6). If maximum and minimum loads are specied for each unit,
some
units will be unable to operate at the same incremental fuel cost as the
other
units and still remain within the limits specied for light and heavy loads.
Suppose that this occurs for K =
4
and that the calculated value of Pg
4
violates
a specied limit of Unit 4. We then discard the calculated
outputs of all four
units and set the operating value of Pg4 equal to the violated limit of Unit 4.
Returning to Eq. (13.6), we recalculate the coecients aT and bT for the other
three units and set the e
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