1. Lecture #16 EEE 574 Dr. Dan Tylavsky Branch Modeling

2. © Copyright 1999 Daniel Tylavsky –There are two types of branches we wish to model: Transmission Lines Transformers –Let’s first look at transmission line modeling. (Assuming nominal or equivalent pi model:) R + j X B SH

3. Branch Modeling © Copyright 1999 Daniel Tylavsky R + j X B SH Node specification may include a fixed reactor or shunt capacitor. –B SH may be specified in: per unit (PU). MVAR = Q SH =V 2 B SH, B SH >0 (where V is the nominal system voltage.) –Branch/node may also include a switched reactor or capacitor. Data format may not allow enough info to tell if shunt branch is lost when T-line is lost.

4. Branch Modeling © Copyright 1999 Daniel Tylavsky 4 Power flow data formats: (Many!) IEEE Common Format for Exchange of Solved Load Flow Data. –We’ll use and discuss this format. PECO (Philadelphia Electric Co.) Format. WSCC (Western Systems Coordination Council) Format. Etc.

5. Branch Modeling © Copyright 1999 Daniel Tylavsky –IEEE Format T-Line (Branch) Data –Terminal Identifier- 4 digit right justified bus numbers »Node From Cols. 1-4 »Node To Cols. 6-9 –Circuit Number Cols. 17 »Integer 1-9 used to identify parallel lines –Branch TypeCol. 19 »0 → Transmission Line –Branch ImpedanceCols. 20-39 »R, X in 2F10.6 –Line ChargingCols. 41-49 »2*B SH

6. Branch Modeling © Copyright 1999 Daniel Tylavsky

7. Branch Modeling © Copyright 1999 Daniel Tylavsky –Transformer Modeling: –We want to find an equivalent circuit in the form: Ya YcYb I2I2 +V2-+V2- +V1-+V1- I1I1 R + j X=Z=Y -1 1:a +V2-+V2- +V1-+V1- I1I1 I2I2 Tap Side Impedance Side

8. Branch Modeling © Copyright 1999 Daniel Tylavsky –Calculate the short-circuit admittance parameters for this two-port circuit. –We want to find an equivalent circuit in the form: Ya YcYb I2I2 +V2-+V2- +V1-+V1- I1I1

9. Branch Modeling © Copyright 1999 Daniel Tylavsky –Calculate the short-circuit admittance parameters for the xfmr as a two port. –For the ideal transformer: R + j X=Z=Y -1 1:a +V2-+V2- +V1-+V1- I1I1 I2I2 Tap Bus Impedance Bus –By power balance:

10. Branch Modeling © Copyright 1999 Daniel Tylavsky –Equating like coefficients. –With 4 equations & 3 unknowns, the system is over-determined. –Can be solved if one constraint is redundant. –This is the case if a=a*. Turns ratio is real (no phase shift.)

11. Branch Modeling © Copyright 1999 Daniel Tylavsky I2I2 +V2-+V2- +V1-+V1- I1I1 Tap Bus Impedance Bus

12. Branch Modeling © Copyright 1999 Daniel Tylavsky Y 1:a +V2-+V2- +V1-+V1- I1I1 I2I2 –Teams: For the following circuit show the equivalent model is. I2I2 +V2-+V2- +V1-+V1- I1I1 –This model cannot be used simply with IEEE format. –No division by ‘a’ is somewhat of an advantage.

13. Branch Modeling © Copyright 1999 Daniel Tylavsky –IEEE Format Transformer (Branch) Data –Terminal Identifier- 4 digit right justified bus numbers »Tap Bus Cols. 1-4 »Impedance BusCols. 6-9 –Circuit Number Cols. 17 »Integer 1-9 used to identify parallel transformers

14. Branch Modeling © Copyright 1999 Daniel Tylavsky –IEEE Format Transformer (Branch) Data cont’d –Branch TypeCol. 19 »0 → transmission line »1 → fixed voltage ratio and/or fixed phase angle. »2 → fixed phase angle and variable voltage ratio with voltage control (ULTC). »3 → fixed phase angle and variable voltage ratio w/ MVAR control. (rare) »4 → fixed voltage ratio and variable phase angle w/ MW control.

15. Branch Modeling © Copyright 1999 Daniel Tylavsky –IEEE Format Transformer (Branch) Data cont’d –Branch ImpedanceCols. 20-39 »R, X in per-unit –Line ChargingCols. 41-49 »2*B SH –Control BusCols. 69-72 »Specifies where the quantity being controlled is measured. –SideCol. 74 »0 - controlled bus is at the transformers terminals »1 - the remote controlled bus is near the tap side »2 - the remote controlled bus is near the impedance side.

16. Branch Modeling © Copyright 1999 Daniel Tylavsky R + j X=Z=Y -1 1:a +V2-+V2- +V1-+V1- I1I1 I2I2 Tap Bus Impedance Bus 4 ↑Increase ‘a’ to ↑ increase voltage of bus located on ‘tap side’ of xfmr. 4 ↓Decrease ‘a’ to ↑ increase voltage of bus on impedance side of the xfmr.

17. Branch Modeling © Copyright 1999 Daniel Tylavsky

18. Branch Modeling © Copyright 1999 Daniel Tylavsky Transformer Types 0 → transmission line 1 → fixed voltage ratio and/or fixed phase angle. 2 → fixed phase angle and variable voltage ratio with voltage control (ULTC). 3 → fixed phase angle and variable voltage ratio w/ MVAR control. (rare) 4 → fixed voltage ratio and variable phase angle w/ MW control.

19. The End