POWER SYSTEM ANALYSIS
MISSAN UNI.\ COLLEGE OF ENGINEERING\ELECTICAL DEP.
Chapter Three
Economic Dispatch
A power system has several power plants. Each power plant has several
generating units. At any point of time, the total load in the system is met
by the generating units in different power plants. Economic dispatch
control determines the power output of each power plant, and power
output of each generating unit within a power plant , which will minimize
the overall cost of fuel needed to serve the system load.
•
We study first the most economical distribution of the output of a
power plant between the generating units in that plant. The method
we develop also applies to economic scheduling of plant outputs
for a given system load without considering the transmission loss.
•
Next, we express the transmission loss as a function of output of
the various plants.
Then, we determine how the output of each of the plants of a system is
scheduled to achieve the total cost of generation minimum,
simultaneously meeting the system load plus transmission loss.
*This section describes how the real power output of each controlled
generating unit in an area is selected to meet a given load to minimize the
total operating cost in the area.
*The input to the thermal plant is generally measured in BTU/h and the
output is measure by MW.
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- the BTu/h is the British temperature unit and it is the unit of measure the
amount of heat in order to generate the electrical power in thermal plant.
*Fig. (1) show a simplified input- output cure of a thermal unit known as
a heat- rate .
cost
Fuel input
BTu
P input
P input
- AHeat-rate curve
- bfuel- cost curve
*There are two type of cost
1-Fixed cost :.
Such as the capital cost of the installing the unit wages and
salaries ….. etc.
2- Running cost :.
Such as fuel cost, maintenance and repair ….. etc.
* only those cost ( Running cost ) that deals with fuel are function of unit
power output- that is, those cost that can be controlled by operating
strategy- enter into the economic dispatch formulation.
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*It is often convenient to express C interims of BTu which is relatively
constant over the life time of the unit rate than
which can change
monthly or daily due to the price of fuel .
*
can be converted to
by multiplying the fuel input in BTU/ h by
the cost of fuel in
Converting the ordinate of heat- rate carve from
to
result in
the fuel – cost curve as shown in fig.
*The fuel cost of generator can be represented as quadratic function of
real power generation
(1)
Where
*An important characteristics is obtained by plotting the derivative of
fuel- cost curve versus the real power this known as the incremental fuelcost curve as shown in the fig. (2) below
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Pi (MW)
=
2
Pi+
……..(2)
*The ratio of output energy to the input energy gives a measure of fuel
efficiency of the unit.
As example if
The efficiency =
= 37.92 %
Where
(3)
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*For the area of an interconnected power system consisting of N units
operating on economic dispatch
The total variable cost CT of operating these units is
Where
expressed in
includes the fuel cost as well as any other
variable costs of unit .
Let
equal to the total load demand in the area Neglecting the
transmission line losses
The economic dispatch is find the values of
That minimize the total cost
A criterion for the solution to this problem is
All units on economic dispatch should operate at equal incremental
operating cost :.
=
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Ex1) An area of an interconnected power system has two fuel unit
operating on economic dispatch.
The variable cost of these unit are given by
Where
and
are in MW. Determine the limit of economic dispatch
and find the power output of each unit, the incremental operating cost and
varies from 500 to
the total operating cost, If the total load demand
1500 Mw.
Not- that The transmission line losses are neglected.
Sol)
increment
fuel cost
For economic dispatch
At
(
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at
economic
dispatch
The total cost of these units
500
600
700
800
900
1000
1100
1200
1300
1400
1500
206
259
312
365
418
471
524
576
629
682
735
244
341
388
435
482
529
576
624
671
718
765
The limit of economic dispatch is from
13.29
14.14
14.99
15.84
16.68
17.53
18.38
19.22
20.07
20.92
21.76
5529
6901
8358
9899
11525
13235
15030
16910
18875
20924
23058
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MISSAN UNI.\ COLLEGE OF ENGINEERING\ELECTICAL DEP.
Ex2) An area of an interconnected power system has two fuel units. The
variable cost of these units are given by :.
Where
. Determine the limit of economic dispatch
and find the power output of each unit, the incremental operating cost of
fuel and the total operating cost
if the load demand is varies from 500
to 1500 Mw. The transmissions line losses are neglected
So1)
at economic dispatch
In order to check the limit of economic dispatch we take at first the lower
limit of unit 2 which is 400 MW where its incremental operating fuel cost
At
Additional load comes from unit 1 unit
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which is in the limit
If you need to take the other value of
100
and this value is out of range where
The first limit of economic dispatch is at
Now we take the other unit
Cheek the limit
And this value of
where
is in the limit where
If we want to check the other limit of p which is p = 100 Mw
We must make the same proceedings above
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And this value of is out of range where 400
*The second limit of economic dispatch is at
The limit of economic dispatch is from (725
Or
NOW for economic dispatch
For economic dispatch (
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For
The power, the incremental operating fuel cost
in the following table :-
500
600
700
725
800
900
1000
1100
1200
1244
1300
1400
1500
100
200
300
325
365
418
471
524
576
600
600
600
600
As example take
400
400
400
400
435
482
529
576
624
644
700
800
900
11.6
13.2
14.8
15.2
15.84
16.68
17.53
18.38
19.22
19.6
19.6
19.6
19.6
and the cost of each unit is
15.2
15.2
15.2
15.2
15.84
16.68
17.53
18.38
19.22
19.6
20.6
22.4
24.2
5720
6960
8360
8735
9899
11525
13235
15030
16910
17765
18890
21040
23370
which is in the limit of economic dispatch
*For
less than 725 Mw where is less than 325 Mw
The incremental operating cost of the area is determined by unit 1 alone.
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Also for
greater than 1244 Mw where
is greater than 644 Mw. The
incremental operating fuel cost of the area is determine by unit 2 alone.
At a heavy loads, unit 1 operate at its upper limit of 600 Mw. Where its incremental
operating fuel cost is
*Additional load comes from unit 2 for all values of
greater than 19.6 $/MWh
Ex3) An area of an inter connected power system has two fuel units operating on
economic dispatch. The variable operating cost of these units are
The system load vary from (500
Determine which unit placed at first at economic dispatch
So1) At first mean
At economic dispatch (
Range of power
Where 200
where
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Ex4) An area of an interconnected power system has two fuel units. The variable
cost these units are given by
Where
and
.determine :.
1-Find the limit of economic dispatch of these units and find the power and the
incremental operating fuel cost of each unit.
2-Which unit placed at first at economic dispatch. Note that the load vary from 5001500 Mw
So1) at
Out of range
*At
Out of range
There is no first limit of economic dispatch
· At
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Out of range
*At
Out of range
there is no second limit of economic dispatch
there is no limit of economic dispatch and so that these units will be operate
at normal condition and there is no economic dispatch in the system.
Therefore the power and the incremental fuel cost of the two unit at normal
condition will be as follow :-
500
800
1000
1300
1500
Where
100
300
400
500
600
400
500
600
800
900
6.6
7.8
8.4
9
9.6
12
13
14
16
17
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2) at economic dispatch
6
At first
In the range 100
The second unit is out of range and therefore the first unit is placed at first of
economic dispatch condition because it is in the limit where 100