Three Phase pi-section model of power system transmission lines

In summary: What I should have done is to multiply R10, L10, C10 with (Distance*Fo). I corrected the code and the results are better.
  • #1
krishkr
2
0
I am using the "Three-Phase PI Section Line" Matlab-Simulink block from Simpowersystems blockset for modelling an electric power system transmission line.

I had obtained the data from a research paper regarding the transmission line specifications (provided as sequence values).

Since I am trying to do actual impedance calculations of each phase for distance protection & fault location purposes, I tried to compute the variation of per phase impedance using a Matlab program (given below).

Code:
 clear all; clc;close all;
    a=exp(deg2rad(120)*1j);  %% a = -0.5000 + 0.8660j
    A = [1 1 1; 1 a^2 a; 1 a a^2]; %% Matrix for Symmetrical component transformation
    Fo = 60;
    
    %% Line Specification using sequence values (taken from paper)
    R10 = [0.0317   0.3192];   L10 = [0.3204   1.0083]./(2*pi*60) ;   C10 = [10.838e-9  7.6493e-9];
    Distance = 1:150; %% in km
    
    for k = 1:length(Distance)
        R10 = R10*Distance(k); L10 = L10*Distance(k); C10 = C10*Distance(k);
        XL10 = (2*pi*Fo)*L10;  XC10 = 1./((2*pi*Fo)*C10);    
        Z10 = R10 + 1j*( XL10 - XC10 );
        
        Z0(k) = Z10(2);     Z1(k) = Z10(1);     Z2(k) = Z1(k);
        Z012 = [Z0(k) 0 0; 0 Z1(k) 0; 0 0 Z2(k)];
        Zabc = A*Z012*((1/3)*(A'));
        
        Zs(k) = Zabc(1); Zm(k) = Zabc(2);
            
    end
    
    figure(1);subplot(2,1,1);plot(Distance,real(Z0));subplot(2,1,2);plot(Distance,imag(Z0));
    figure(2);subplot(2,1,1);plot(Distance,real(Z1));subplot(2,1,2);plot(Distance,imag(Z1));
    figure(3);subplot(2,1,1);plot(Distance,real(Zs));subplot(2,1,2);plot(Distance,imag(Zs));
    figure(4);subplot(2,1,1);plot(Distance,real(Zm));subplot(2,1,2);plot(Distance,imag(Zm));
The program takes the system data of the transmission line (which are given in unit/km), which can be used as parameters for the Simulink 3 phase pi-section block.
The distance is multiplied to the data to get the actual values.
The impedances are computed, the sequence impedances and the per phase impedances are found out. The values of resistance and reactance are computed from the real part and imaginary part respectively. This operation is done for various distances and the plot shows that.

I find that the values plot rise to very high values (order of 1e200). How can current flow if impedance is so high ? If the system data is inappropriate, please tell me why.
Please suggest the reason for such a problem and how can I overcome it?
Thanks in advance :)
 
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  • #2
Why are you adding the capacitances to Z10? In the PI model, you should also have an admittance part, where you would have G and C (where G is usually neglected)... Check for instance "Power System Analysis and Design" from Glover.

M.
 
  • #3
Thank you Mbert. It was stupid of me to add the capacitance as if it was in series with the R and L. Also, I did a programming mistake; the above code repetitively multiplies R10, L10, C10 with Distance. I unintentionally end up with a geometric progression.
 

1. What is a Three Phase pi-section model of power system transmission lines?

The Three Phase pi-section model of power system transmission lines is a simplified representation of a three-phase transmission line used in power system analysis. It consists of three series impedances, representing the resistance and inductance of each phase, and two shunt admittances, representing the capacitance between the conductors and to ground.

2. What are the advantages of using a Three Phase pi-section model?

One advantage of using a Three Phase pi-section model is that it simplifies the analysis of a three-phase transmission line, making it easier to calculate parameters such as voltage and current. It also allows for a more efficient representation of the line, as it only requires five parameters compared to the nine parameters needed in a full ABCD matrix model.

3. How is the Three Phase pi-section model different from the ABCD matrix model?

The Three Phase pi-section model is a simplified version of the ABCD matrix model, with fewer parameters and assumptions made for ease of analysis. The ABCD matrix model takes into account the distributed nature of a transmission line, while the pi-section model treats the line as lumped elements. Additionally, the ABCD matrix model can account for line length and frequency, while the pi-section model assumes a single frequency and short line length.

4. What are the limitations of the Three Phase pi-section model?

The Three Phase pi-section model has some limitations, as it is a simplified representation of a transmission line. It assumes a balanced three-phase system and does not take into account line length or frequency variations. It also does not consider the effects of skin and proximity effects, which can be significant at higher frequencies.

5. How is the Three Phase pi-section model used in power system analysis?

The Three Phase pi-section model is commonly used in power system analysis to calculate parameters such as voltage, current, and power flow in a transmission line. It can also be used to study the effects of faults and disturbances on the line. However, for more accurate and detailed analysis, the ABCD matrix model or other more complex models may be used.

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