Economic Dispatch Of thermal generating units Using Equal Incremental Cost Criteria Neglecting Generation Limits & Transmission Losses

Objective

                            In Power Systems Generation Allocation (Economic Dispatch) is Major Problem, Therefore we will try to Allocate Generation to Committed Units so as to Satisfy Demand With Minimum Expenses(Minimum $/h) . We will Use Lagrange Multiplier Techniques in this Session.i.e;

a)      Incremental Cost Criteria

b)      Lambda(LaGrange Multiplier) Iteration Technique

Explanation

                              Incremental Cost Criteria is stated as

“Allocate Generation so that total Demand is Satisfied & All Incremental Costs are equal in Economic Dispatch Problem”

It is Most Widely Used Technique for Solution of Economic Dispatch Problems.

However it is Constrained Continuous Problem Therefore it is Difficult to Solve system keeping in mind the Inequality constraints. Transmission losses are also to be neglected for simplicity. Therefore Neglecting

         b)    Calculation Using Lambda Iteration Method

Lambda Iteration method Uses an Initial Assumption of Lagrange Multiplier and uses Continuous iterations to find correct value of Lambda. This correct value is found at Satisfaction of Demand.

Steps of Calculation Include

Ø  1^st Step to Solve a Dispatch Problem is to write cost characteristic equations of committed units for Meeting Demand Using equation (1).

Ø  Assume a Value of Lagrange Multiplier and Calculate Generation Sharing (Generation Allocation) at that value of Lambda using equation (3).

Ø  Calculate Difference in Value of Power demand and Total Generation.(Error)

Matlab Program & Results

Equal Incremental Cost Criteria

Code

function [Lambda,P,Total_Cost]=IncrementalCC(Pd,A)

Pd=input('Total Power Demand = ');

n=input('Number of Generating Stations = ');

x=Pd*0.10:10:Pd;

for i=1:n;

    a=input('No Load Speed Cost of Unit($/h) = ');

    b=input('Slope of linear line of unit ($/MWh) = ');

    c=input('Coefficient of 2nd order term of Unit(($/h)/MW^2) = ');

    A(i,:)=[a b c];

    y=[2*c*x+b];

    plot(x,y)

    hold on

end

xlabel('Power(MW)');

ylabel('Incremental Cost ($/MWh)');

Title('Incremental Cost(Economic Dispatch Problem Solution)');

hold off

a=A(:,1);

b=A(:,2);

c=A(:,3);

Lambda=(Pd+sum(b./(2*c)))/sum(1./(2*c))

P=(Lambda-b)./(2*c)

Total_Cost=[sum(a)+sum(b.*P)+sum(c.*(P.^2))]

Results

Conclusion

                                Economic Dispatch is Online Function Carried on real Time (Minimum Cost of Production meeting Constraints). Economic Dispatch is an Important for Power System Operation because Economy is a Major factor which Influence Structure and Complexity of System. Even Unit Commitment Involve Economic Dispatch Solution as 1^st step. In this Session we Solved Problem Neglecting T/L Losses and Generation Limits. However When we take into Account T/L Losses.
Equal-Incremental Criteria is most widely used technique for Solution of ED Problem;