Branch Modeling

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

2. R + j X BSH BSH • 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:)

3. Node specification may include a fixed reactor or shunt capacitor. R + j X BSH BSH • BSH may be specified in: • per unit (PU). • MVAR = QSH=V2BSH, BSH>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. 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. 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 Type Col. 19 • 0 → Transmission Line • Branch Impedance Cols. 20-39 • R, X in 2F10.6 • Line Charging Cols. 41-49 • 2*BSH

7. Tap Side Impedance Side I1 I2 R + j X=Z=Y-1 1:a + V1 - + V2 - I1 I2 Ya + V2 - + V1 - Yb Yc • Transformer Modeling: • We want to find an equivalent circuit in the form:

8. I1 I2 Ya + V2 - + V1 - Yb Yc • We want to find an equivalent circuit in the form: • Calculate the short-circuit admittance parameters for this two-port circuit.

9. Tap Bus Impedance Bus I1 I2 R + j X=Z=Y-1 1:a + V1 - + V2 - • Calculate the short-circuit admittance parameters for the xfmr as a two port. • For the ideal transformer: • By power balance:

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

11. I1 I2 + V2 - + V1 - Impedance Bus Tap Bus

12. I1 I2 Y 1:a + V1 - + V2 - I1 I2 + V2 - + V1 - • Teams: For the following circuit show the equivalent model is. • This model cannot be used simply with IEEE format. • No division by ‘a’ is somewhat of an advantage.

13. IEEE Format • Transformer (Branch) Data • Terminal Identifier - 4 digit right justified bus numbers • Tap Bus Cols. 1-4 • Impedance Bus Cols. 6-9 • Circuit Number Cols. 17 • Integer 1-9 used to identify parallel transformers

14. IEEE Format • Transformer (Branch) Data cont’d • Branch Type Col. 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. IEEE Format • Transformer (Branch) Data cont’d • Branch Impedance Cols. 20-39 • R, X in per-unit • Line Charging Cols. 41-49 • 2*BSH • Control Bus Cols. 69-72 • Specifies where the quantity being controlled is measured. • Side Col. 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. Tap Bus Impedance Bus I1 I2 R + j X=Z=Y-1 1:a + V1 - + V2 - • ↑Increase ‘a’ to ↑ increase voltage of bus located on ‘tap side’ of xfmr. • ↓Decrease ‘a’ to ↑ increase voltage of bus on impedance side of the xfmr.

18. 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