- ABCD Parameters Definition: ABCD parameters are used to model transmission lines in a two-port network, linking input and output voltages and currents.
- Transmission Line Categories: Transmission lines are classified as short, medium, or long, each requiring different ABCD parameter calculations.
- Open Circuit Analysis: With the receiving end open, parameter A shows the voltage ratio, and C represents the conductance, crucial for system analysis.
- Short Circuit Analysis: When short-circuited, parameter B indicates the resistance, and D the current ratio, essential for safety and efficiency checks.
- Practical Application: Understanding ABCD parameters of medium transmission line is key for engineers to ensure efficient power transmission and system reliability.
What are ABCD Parameters?
ABCD parameters, also called chain or transmission parameters, relate sending-end voltage and current to receiving-end voltage and current. They represent transmission lines as a two port network. The sign of the current terms depends on the stated port-current convention.
Power-system studies use these constants to calculate the transmission of electrical power between a sending bus and receiving substations. The results support voltage, current, loss and load-flow calculations.
The two-port form gives one pair of linear equations for the terminal quantities. Engineers can also cascade network sections by multiplying their ABCD matrices in physical order.
The line model supplies the values of A, B, C and D. Common teaching models cover short transmission lines, medium transmission lines and long transmission lines.
The formulas differ because short and medium approximations lump line impedance and admittance, while the long-line model distributes them. The separate high-field phenomenon called corona discharge does not define those models. The Ferranti effect follows from line capacitance and is more evident on lightly loaded long AC lines.
ABCD Parameters of a Two Port Network
The diagram labels the sending port PQ and receiving port RS. For this linear two-port model, sending-end voltage and current are written in terms of the receiving-end quantities. Each port has two terminals, and the chosen current directions set the equation signs.
The first terminal pair belongs to input port PQ.
The second terminal pair belongs to output port RS.
The ABCD matrix therefore maps the receiving-end voltage and current to the sending-end voltage and current for the linear network.
The equations below state that terminal relationship for the current convention shown.
Open-circuit and short-circuit receiving-end tests isolate the four ratios used to identify A, B, C and D.
ABCD Parameters When Receiving End is Open Circuited
With the receiving end open, receiving-end current IR = 0.
Substitution in equation (1) isolates A.
Parameter A, the ratio of sending-end voltage to receiving-end voltage under this open-circuit condition, is dimensionless.
Applying IR = 0 to equation (2) isolates C.
Parameter C, sending-end current divided by receiving-end voltage under the open-circuit condition, is a transfer admittance measured in siemens. Mho is its historical unit name.
C can include susceptance as well as conductance, so transfer admittance is the more precise term.
C = IS ⁄ VR S under the stated open-circuit condition.
ABCD Parameters When Receiving End is Short Circuited
With the receiving end short-circuited, receiving-end voltage VR = 0.
Substitution in equation (1) isolates B.
Parameter B is sending-end voltage divided by short-circuit receiving-end current. Its unit is the ohm, but it is a complex transfer impedance rather than pure resistance.
B = VS ⁄ IR Ω.
Applying VR = 0 to equation (2) isolates D.
Parameter D, the ratio of sending-end current to short-circuit receiving-end current, is dimensionless.
The frozen table summarises the ABCD parameters of the transmission line for the displayed current convention:
| Parameter | Specification | Unit |
| A = VS / VR | Voltage ratio | Unit less |
| B = VS / IR | Short circuit resistance | Ω |
| C = IS / VR | Open circuit conductance | mho |
| D = IS / IR | Current ratio | Unit less |
