fast decoupled load flow

1. Load Flow Study
Fast Decoupled Load Flow(FDLF)
Presented by-
fs

2. Overview
 Fast decoupled load flow
 Why FDLF?
 Flowchart
 Program
 Output
 Conclusion
 Reference

3. Fast decoupled load flow
 Algorithm is based on Newton-Raphson method.
 When transmission lines has a high X/R ratio, the newton Raphson could be
further simplified.
 Consider the Newton-Raphson load flow equation:
 ∆𝑃 are less sensitive to ∆|𝑉| and more sensitive to ∆𝛿.
 ∆𝑄 are less sensitive to ∆𝛿 and more sensitive to ∆|𝑉| .
 So, N and J elements can be eliminated.
∆𝑃
∆𝑄
=
𝐻 𝑁
𝐽 𝐿
∆𝛿
∆|𝑉|
............(1)

4. cos𝛿𝑖𝑘 ≅ 1, sin𝛿𝑖𝑘 ≅0
G𝑖𝑗 sin𝛿𝑖𝑘<<B𝑖𝑘, and Q𝑖<<B𝑖𝑖|V𝑖|2
With these assumptions H and L are square submatrices of dimension (n-
1) and (m-1) respectively are:
For i = k, H𝑖𝑖=L 𝑖𝑖 ≈
- B𝑖𝑖|V𝑖|2
For i≠ 𝑘, H𝑖𝑘=L 𝑖𝑘 ≈- |V𝑖| |V 𝑘| B𝑖𝑘
With further simplification,the matrix equation for the solution of load
flow by FDLF method are:
∆𝑃/|𝑉| = 𝐵′ ∆𝛿 ………..(2)
∆𝑄/|𝑉| = 𝐵′′ ∆|𝑉| … … … . (3)
Where, B’ and B” are matrices of elements -B𝑖𝑘(i=2,…..n and k=2,….n)
and -B𝑖𝑘(i=2,…..,m and k=2,….,m).

5. Why FDLF?
 For practical accuracies, only 2-5 iterations are required.
 More reliable than NR method
 Speed is 5 times that of NR method
 Storage requirement is 60 percent of NR
 Constant jacobian
 Physically justifiable assumptions

6. FLOWCHART:
calculate ∆𝑷𝒊𝒓 for i=(2,3,4 … . … … 𝐧)(𝐏𝐕 𝐚𝐧𝐝 𝐏𝐐 𝐛𝐮𝐬𝐞𝐬)
solve for ∆ 𝜹𝒊 𝒇𝒐𝒓 𝒊 = 𝟐, 𝟑 … … 𝒏
calculate ∆𝑸𝒊 𝒓 for i=(2,3,4 … . … … 𝐦)(𝐏𝐐 𝐛𝐮𝐬𝐞𝐬)

7. Solve for ∆|Vi| for i=2,3 … . … . m.

8. PROGRAM-
fdlf.txt
OUTPUT-

9. Conclusion
 Due to constant jacobian, defining functions are not sensitive to any humps.
 It can be employed in optimization studies.
 Used for obtaining information of both real and reactive power for multiple
load flow studies.

10. References
 M. A.PAI , Computer Techniques in Power System Analysis.
 D.P. Kothari, Modern Power System Analysis .

11. THANK YOU!!!