Economic Load Dispatch (ELD)
With and Without Transmission Losses | GATE Electrical Engineering Notes
1. Definition
Economic Load Dispatch is the process of distributing total load demand among generating units such that total fuel cost is minimum while meeting load demand.
Objective: Minimize Total Cost
Total Power Generated = Total Load Demand
2. Cost Function of Generator
Fuel cost function is expressed as:
Fi(Pi) = ai + biPi + ciPi²
Where:Fi = fuel cost
Pi = power generated
ai, bi, ci = cost coefficients
3. Incremental Cost
Incremental Cost = dFi/dPi
dFi/dPi = bi + 2ciPi
4. Economic Load Dispatch WITHOUT Transmission Loss
Condition:
P1 + P2 + P3 + ... + Pn = PD
Where PD = Load demand
Optimal condition:
dF1/dP1 = dF2/dP2 = dF3/dP3 = λ
λ = Incremental cost
This is called:
Equal Incremental Cost Criterion
5. Economic Load Dispatch WITH Transmission Loss
Now,
Total Power Generated = Load Demand + Transmission Loss
ΣPi = PD + PL
Transmission loss formula:
PL = Σ Σ Pi Bij Pj
Bij = loss coefficient matrix
6. Penalty Factor
Penalty factor:
Li = 1 / (1 − ∂PL/∂Pi)
Modified economic dispatch condition:
Li × (dFi/dPi) = λ
7. Lambda Iteration Method
Steps:- Assume λ value
- Calculate Pi from incremental cost equation
- Check power balance
- Adjust λ until balance satisfied
8. Economic Dispatch WITHOUT Loss Example Formula
For two generators:
b1 + 2c1P1 = b2 + 2c2P2
P1 + P2 = PD
Solve to find P1 and P2
9. Economic Dispatch WITH Loss Formula
Li(bi + 2ciPi) = λ
More complex than without loss case.
10. Comparison Table
| Parameter | Without Loss | With Loss |
|---|---|---|
| Transmission loss | Ignored | Considered |
| Condition | dFi/dPi = λ | Li dFi/dPi = λ |
| Complexity | Simple | Complex |
| Accuracy | Less accurate | More accurate |
11. Important GATE Exam Points
Equal incremental cost criterion
Penalty factor formula important
Loss coefficient matrix Bij important
Lambda iteration method important
Cost function quadratic form important
Penalty factor formula important
Loss coefficient matrix Bij important
Lambda iteration method important
Cost function quadratic form important
