**AIM:**

To understand the fundamentals of economic dispatch and solve the problem using

classical method with and without line losses.

SOFTWARE REQUIRED:

SOFTWARE REQUIRED:

MATLAB 5.3

**THEORY:**

Mathematical Model for Economic Dispatch of Thermal Units

Without Transmission Loss:

Statement of Economic Dispatch Problem

In a power system, with negligible transmission loss and with N number of spinning thermal

generating units the total system load PD at a particular interval can be

met by different sets of

generation schedules

{PG1^(k) , PG2^(k) , ………………PGN^(K) }; k = 1,2,……..NS

Out of these NS set of generation schedules, the system operator has to choose the set of schedules,

which minimize the system operating cost, which is essentially the sum of the production cost of

all the generating units. This economic dispatch problem is mathematically stated as an

optimization problem.

**The number of available generating units N, their production cost functions, their**

Given:

Given:

operating limits and the system load PD,

**To determine:**The set of generation schedules,

Necessary conditions for the existence of solution to ED problem

The ED problem given by the equations (1) to (4). By omitting the inequality constraints

(4) tentatively, the reduce ED problem (1),(2) and (3) may be restated as an unconstrained

optimization problem by augmenting the objective function (1) with the constraint "

**Phi**" multiplied by

LaGrange multiplier, "

**Lamda**" to obtained the LaGrange function, L as

The solution to ED problem can be obtained by solving simultaneously the necessary conditions

(7) and (8) which state that the economic generation schedules not only satisfy the system power

balance equation (8) but also demand that the incremental cost rates of all the units be equal be

equal to "

**Lamda**" which can be interpreted as “incremental cost of received power”.

When the inequality constraints(4) are included in the ED problem the necessary condition (7) gets

modified as

**PROCEDURE:**

1. Enter the command window of the MATLAB.

2. Create a new M – file by selecting File - New – M – File

3. Type and save the program.

4. Execute the program by either pressing Tools – Run.

5. View the results.

EXERCISE-1:

EXERCISE-1:

The fuel cost functions for three thermal plants in $/h are given by

C1 = 500 + 5.3 P1 + 0.004 P1^2 ; P1 in MW

C2 = 400 + 5.5 P2 + 0.006 P2^2 ; P2 in MW

C3 = 200 +5.8 P3 + 0.009 P3^2 ; P3 in MW

The total load , PD is 800MW.Neglecting line losses and generator limits, find the optimal

dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB

program.

PROGRAM:

PROGRAM:

alpha = [500; 400; 200];

beta = [5.3; 5.5; 5.8]; gamma = [0.004; 0.006; 0.009];

PD = 800;

DelP = 10;

lamda = input('Enter estimated value of Lamda = ');

fprintf(' ')

disp(['Lamda P1 P2 P3 DP'...

' grad Delamda'])

iter = 0;

while abs(DelP) >= 0.001

iter = iter + 1;

P = (lamda - beta)./(2*gamma);

DelP = PD - sum(P);

J = sum(ones(length(gamma),1)./(2*gamma));

Delamda = DelP/J;

disp([lamda,P(1),P(2),P(3),DelP,J,Delamda])

lamda = lamda + Delamda;

end

totalcost = sum(alpha + beta.*P + gamma.*P.^2)

**EXERCISE-2:**

The fuel cost functions for three thermal plants in $/h are given by

C1 = 500 + 5.3 P1 + 0.004 P1^2 ; P1 in MW

C2 = 400 + 5.5 P2 + 0.006 P2^2 ; P2 in MW

C3 = 200 +5.8 P3 + 0.009 P3^2 ; P3 in MW

The total load , PD is 975MW.

Generation limits:

200 £ P1 £ 450 MW

150 £ P2 £ 350 MW

100 £ P3 £ 225 MW

Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result

using MATLAB program.

**PROGRAM:**

cost = [500 5.3 0.004

400 5.5 0.006

200 5.8 0.009];

mwlimits = [200 450

150 350

100 225];

Pdt = 975;

dispatch

gencost

**RESULT:**

Thus the fundamentals of economic dispatch and solve the problem using

classical method with and without line losses understood.

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