Lecture #16 EEE 574 Dr. Dan Tylavsky Branch Modeling

© 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

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.

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.

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 »R, X in 2F10.6 –Line ChargingCols »2*B SH

Branch Modeling © Copyright 1999 Daniel Tylavsky

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

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

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:

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.)

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

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.

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

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.

Branch Modeling © Copyright 1999 Daniel Tylavsky –IEEE Format Transformer (Branch) Data cont’d –Branch ImpedanceCols »R, X in per-unit –Line ChargingCols »2*B SH –Control BusCols »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.

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.

Branch Modeling © Copyright 1999 Daniel Tylavsky

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.

The End