chapter three economic dispatch

ANALS 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 severalgenerating units. At any point of time, the total load in the system is metby the generating units in different power plants. Economic dispatchcontrol determines the power output of each power plant, and poweroutput of each generating unit within a power plant , which will minimizethe overall cost of fuel needed to serve the system load.

• We study first the most economical distribution of the output of apower plant between the generating units in that plant. The methodwe develop also applies to economic scheduling of plant outputsfor a given system load without considering the transmission loss.

• Next, we express the transmission loss as a function of output ofthe various plants.

Then, we determine how the output of each of the plants of a system isscheduled 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 controlledgenerating unit in an area is selected to meet a given load to minimize thetotal operating cost in the area.*The input to the thermal plant is generally measured in BTU/h and theoutput is measure by MW.


- the BTu/h is the British temperature unit and it is the unit of measure theamount 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 asa heat- rate .

- A- - b- Heat-rate curve fuel- cost curve

*There are two type of cost1-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 unitpower output- that is, those cost that can be controlled by operatingstrategy- enter into the economic dispatch formulation.

Fuel input

P input P input

cost

BTu


*It is often convenient to express C interims of BTu which is relativelyconstant over the life time of the unit rate than which can changemonthly or daily due to the price of fuel .* can be converted to by multiplying the fuel input in BTU/ h bythe cost of fuel in

Converting the ordinate of heat- rate carve from to result inthe fuel – cost curve as shown in fig.*The fuel cost of generator can be represented as quadratic function ofreal power generation

(1)

Where

*An important characteristics is obtained by plotting the derivative offuel- cost curve versus the real power this known as the incremental fuel-cost curve as shown in the fig. (2) below


= 2 Pi+ ……..(2)

*The ratio of output energy to the input energy gives a measure of fuelefficiency of the unit.As example if

The efficiency =

= 37.92 %

Where

(3)

Pi (MW)


*For the area of an interconnected power system consisting of N unitsoperating on economic dispatchThe total variable cost CT of operating these units is

Where expressed in includes the fuel cost as well as any othervariable costs of unit .Let equal to the total load demand in the area Neglecting thetransmission line losses

The economic dispatch is find the values ofThat minimize the total costA criterion for the solution to this problem is

All units on economic dispatch should operate at equal incrementaloperating cost :.

=


Ex1) An area of an interconnected power system has two fuel unitoperating on economic dispatch.The variable cost of these unit are given by

Where and are in MW. Determine the limit of economic dispatchand find the power output of each unit, the incremental operating cost andthe total operating cost, If the total load demand varies from 500 to1500 Mw.Not- that The transmission line losses are neglected.

Sol)

increment

fuel cost

For economic dispatch (

At


at economic dispatchThe total cost of these units

500 206 244 13.29 5529600 259 341 14.14 6901700 312 388 14.99 8358800 365 435 15.84 9899900 418 482 16.68 115251000 471 529 17.53 132351100 524 576 18.38 150301200 576 624 19.22 169101300 629 671 20.07 188751400 682 718 20.92 209241500 735 765 21.76 23058

The limit of economic dispatch is from


Ex2) An area of an interconnected power system has two fuel units. Thevariable cost of these units are given by :.

Where . Determine the limit of economic dispatchand find the power output of each unit, the incremental operating cost offuel and the total operating cost if the load demand is varies from 500to 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 lowerlimit of unit 2 which is 400 MW where its incremental operating fuel cost

At

Additional load comes from unit 1 unit


which is in the limit 100If you need to take the other value of

and this value is out of range where

The first limit of economic dispatch is at

Now we take the other unitCheek the limit where

And this value of is in the limit where

If we want to check the other limit of p which is p = 100 MwWe must make the same proceedings above


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 (


For

The power, the incremental operating fuel cost and the cost of each unit isin the following table :-

500 100 400 11.6 15.2 5720600 200 400 13.2 15.2 6960700 300 400 14.8 15.2 8360725 325 400 15.2 15.2 8735800 365 435 15.84 15.84 9899900 418 482 16.68 16.68 115251000 471 529 17.53 17.53 132351100 524 576 18.38 18.38 150301200 576 624 19.22 19.22 169101244 600 644 19.6 19.6 177651300 600 700 19.6 20.6 188901400 600 800 19.6 22.4 210401500 600 900 19.6 24.2 23370

As example take which is in the limit of economic dispatch

*For less than 725 Mw where is less than 325 MwThe incremental operating cost of the area is determined by unit 1 alone.


Also for greater than 1244 Mw where is greater than 644 Mw. Theincremental 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 incrementaloperating 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 oneconomic dispatch. The variable operating cost of these units are

The system load vary from (500Determine which unit placed at first at economic dispatch

So1) At first mean where

At economic dispatch (

Range of power

Where 200


Ex4) An area of an interconnected power system has two fuel units. The variablecost these units are given by

Where and .determine :.

1-Find the limit of economic dispatch of these units and find the power and theincremental operating fuel cost of each unit.2-Which unit placed at first at economic dispatch. Note that the load vary from 500-1500 Mw

So1) at

Out of range*At

Out of range

There is no first limit of economic dispatch

· At


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 operateat normal condition and there is no economic dispatch in the system.Therefore the power and the incremental fuel cost of the two unit at normalcondition will be as follow :-

500 100 400 6.6 12800 300 500 7.8 131000 400 600 8.4 141300 500 800 9 161500 600 900 9.6 17

Where


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 ofeconomic dispatch condition because it is in the limit where 100

chapter three economic dispatch

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