How to create a 3 - by - 3 vector for a PI Section Line

PI Section Line

3 - by - 3 Vector

[Rahul]

Hi @Eddie, can you specify about which kind of pi section line are you trying to implement, and what '3 - by - 3 Vector' signify here?

[Eddie]

Thank you for your reply.

The Simulink block is taggged as a PI Section Line (mask) (link) in Simulink Power Grid Elements.

PI section transmission line. RLC elements are computed using hyperbolic corrections at specified frequency.

Completed the PI Section Line Block Paramets for a 2 x 2 vector as shown below.

However I still recieve the following alarm:

Parameter 'Resistance' in block must be a 2-by-2 vector.

Answer 1

[Rahul]

Hi Eddie,

Assuming that you are trying to use a pi-section line block in your Simulink Model, while passing a (1, 2) vectors of inductance and resistance per unit length. The specified error is being generated due to the use of a (2, 1) matrices, equal to the number of phases N (=2, in this case) rather than a (2, 2) or (N, N) impedance matrix, which has been mentioned in the documentation:

https://in.mathworks.com/help/sps/powersys/ref/pisectionline.html#:~:text=length%20(Ohms/km)%20%5B-,NxN%20matrix,-%5D%20%E2%80%94%20Resistance

In a 2-phase transmission line, the electrical behavior is influenced by both the self-impedance of each individual phase and the mutual impedance between the phases. The 2×2 impedance matrix Z is used to account for these two aspects:

1. Self-Impedances: The self-impedance for each phase describes the impedance that a particular phase (such as phase 1) experiences due to its own resistance and inductance. This corresponds to the inductors and resistors associated with each line (seen between points labeled as A and α for phases 1, 2, and 3 in the given figure).

In the matrix representation, the diagonal terms Z11​, Z22​, and would represent the self-impedances for phases 1, 2 respectively.

Z=[Z11 Z12;
   Z21 Z22];

1. Mutual Impedances: accounts for the coupling between phases. This means that the impedance of phase 1 will also influence phase 2, and vice versa, due to electromagnetic coupling between the conductors of different phases.

In the matrix representation, the off-diagonal terms Z12​, Z21​, etc., represent the mutual impedance between the phases. For example:

Z12​ describes the impact of phase 1 on phase 2.

Z21​ describes the reverse (phase 2 affecting phase 1).

The image depicts a 3-phase Pi-section transmission line model. In this configuration, each phase (1, 2, 3) is represented by a series inductance and resistance (R and L) as well as shunt capacitances (Cg​ and Cp​).

For more information regarding the usage of Pi-Section Line in Simulink, refer to the following documentation link:

https://www.mathworks.com/help/sps/powersys/ref/pisectionline.html

[Eddie]

Hi Rahul.

EXCELLENT answer, thank you SO much for your time, I have learnt from you answer and solved the issue.

THANK YOU !