1. Hao Zhu Dept. of Electrical & Computer Engineering University of Illinois, Urbana-Champaign haozhu@illinois.edu ECE 498HZ: Power Distribution System Analysis Chapter 6: Distribution Line Models February 16, 2016

2. Clean Power Plan 2

3. Line Parameters 3

4. Special cases 4

5. Line Model 5

6. Circuit Analysis  At node m  At node n  Voltage diff 6

7. Generalized Line Matrices 7

8. Matrix form 8

9. Additional Line Matrices 9

10. Same to transmission, but 10

11. Example 6.1 11 microSiemens (1e-6)

12. Example 6.1  Calculating generalized matrices 12 Because shunt is too small

13. Example 6.1  Since load voltage is rated and balanced  At node m  At node n 13 Very close to I m Again, because of tiny shunt effects ~ 1.047p.u.

14. Voltage Unbalance  ANSI/NEMA standards  Note that all values are magnitudes  For Example 6.1, 14

15. Modified Line Models 15

16. Three-wire Delta Lines 16 Primitive impedance values No neutral line

17. Neutral and Ground Currents  To recover the neutral line current, recall the neutral transformation  From flow conservation 17

18. Example 6.2  Change Ex 6.1 to that node n is balanced, not the load node m  To solve for node m, compute  Equivalently no shunt 18

19. Example 6.2  Line-to-line voltage  Voltage unbalance  Load complex power 19

20. Example 6.3  Neutral transformation matrix  Neutral current  Ground current 20

21. Approximation using Sequence Matrix  Assuming transposed lines with balanced loads  Corresponding phase impedance matrix  So the voltage diff 21

22. Approximate Line Model  For phase a of node n  In addition, 22

23. Example 6.3 23

24. Example 6.4 24

25. Distribution Network Power Flow 25 ……

26. Forward sweep 26 Node n Node m

27. Backward sweep 27 Node n Node m

28. Iterative Ladder 28

29. Example 6.5  So far we only consider a single line segmant  Given the unbalanced load and source voltage 12.47kV –Phase a: 2500 kVA and PF = 0.9 lagging –Phase b: 2000 kVA and PF = 0.85 lagging –Phase c: 1500 kVA and PF = 0.95 lagging 29