YBus building algorithm of Power System using MATLAB

Nodal admittance matrix or Ybus matrix is a matrix that contains admittances of the power system. This matrix can be used to find voltages of buses.

This Ybus matrix can be found easily and then inverted and multiplied with currents to find voltages of buses. Although taking inverse of a large system is computationally not efficient and there are ways to find Zbus directly instead of taking inverse of Ybus.

Ybus is sparse matrix with a lot of zeroes in it. So its a large matrix with a lot of zeroes.

Algorithm used in our code is  of 3 steps.

1.     Circuit is converted into matrix from called data. First column of data contains from and second contains to means nodes to which a admittance is connected. Third and forth contains value of resistance and reactance respectively.

2.     Off-diagonal entries are just net admittances connected to node i and j.

3.     Diagonal entries contains sum of all entries connected to that node. For example Y 3,3 is net of all the entries connected to bus 3.

Code:

%Author: Muhammad Awais

%Electrical Engineering, UET Lahore

%Bus admittance matrix

%Write buss impedence in Z matrix and it will solve rest of the thing

%data matrix

   data=[0   1   0   1j

   0   2   0 0.8j

   1   2   0 0.4j

   1   3   0 0.2j

   2   3   0 0.2j

   3   4   0 0.08j];

 % from  to R   X

%Z=[0   1   0   1j

 %  0   2   0 0.8j

 %  1   2   0 0.4j

  % 1   3   0 0.2j

   %2   3   0 0.2j

   %3   4   0 0.08j];

%finding order of matrix in C language way

%o1=max(Z(:,1));

%o2=max(Z(:,2));

%order=(max(o1,o2))

%find number of rows of Z= Toatl number of nodes

%row=length(Z(:,1))

[row,col]=size(data);

order=col

%Change last column into admittance, now last column also inculdes R

for m=1:row

    data(m,4)=1/(data(m,3)+data(m,4));

end

Z2adm=data;

%Yadmittance as a matrixo of zeros first

Y=zeros(order,order);

%finding ybus matrix

%1-for off-digonal vlaues

for i=1:row

    for j=1:order

        %discard source node

        if data(i,1)==0||data(i,2)==0    

           a=0;

         %for off digonal entries

        elseif data(i,1)~=0||data(i,2)~=0

            Y(data(i,1),data(i,2))=-data(i,4);

            Y(data(i,2),data(i,1))=-data(i,4);

        end

        

    end

end

%2-digonal values 

for a=1:order     %for k

    for b=1:row

        if data(b,1)==a ||data(b,2)==a

           

            Y(a,a)=(Y(a,a)+data(b,4));

        end

    end

   

end

Ybus=Y

%To find Z bus

Zbus=inv(Y)

%As Ibus=Ybus*Vbus so we can find too if we know Ibus. As here two currnet

%sources so suppose

Ibus=[1;1;0;0];

Vbus=Ybus\Ibus

Examples:

Example 1: To solve following system using this method

Impedance Matrix:

data=[0   1   0   1j

   0   2   0 0.8j

   1   2   0 0.4j

   1   3   0 0.2j

   2   3   0 0.2j

   3   4   0 0.08j];

Results:

Ybus =

        0 - 8.5000i        0 + 2.5000i        0 + 5.0000i        0         

        0 + 2.5000i        0 - 8.7500i        0 + 5.0000i        0         

        0 + 5.0000i        0 + 5.0000i        0 -22.5000i        0 +12.5000i

        0                  0                  0 +12.5000i        0 -12.5000i

Zbus =

        0 + 0.5000i        0 + 0.4000i        0 + 0.4500i        0 + 0.4500i

        0 + 0.4000i        0 + 0.4800i        0 + 0.4400i        0 + 0.4400i

        0 + 0.4500i        0 + 0.4400i        0 + 0.5450i        0 + 0.5450i

        0 + 0.4500i        0 + 0.4400i        0 + 0.5450i        0 + 0.6250i

Vbus =

        0 + 0.9000i

        0 + 0.8800i

        0 + 0.8900i

        0 + 0.8900i

Example 2:

Impedance Matrix:

data=[0   1   0  0.25j

   0   1   0  -4j

   1   4   0   0.4j

   1   3   0   .1j

   0   2   0    .2j

   0   2   0    -4j

   0   3   0    -4j

   0   3   0.9412  .2353j

   3   4   0      0.2j

   0   4   0     -4j

   0   4   .4706  0.11765j

    ];

Results:

Ybus =

        0 -20.2500i        0 + 4.0000i        0 +10.0000i        0 + 2.5000i

        0 + 4.0000i        0 -15.0000i        0                  0 + 6.2500i

        0 +10.0000i        0             1.0000 -15.0000i        0 + 5.0000i

        0 + 2.5000i        0 + 6.2500i        0 + 5.0000i   2.0000 -13.9998i

Zbus =

   0.0359 + 0.1305i   0.0303 + 0.0718i   0.0481 + 0.1134i   0.0498 + 0.0887i

   0.0303 + 0.0718i   0.0264 + 0.1224i   0.0398 + 0.0744i   0.0439 + 0.0878i

   0.0481 + 0.1134i   0.0398 + 0.0744i   0.0652 + 0.1733i   0.0648 + 0.1061i

   0.0498 + 0.0887i   0.0439 + 0.0878i   0.0648 + 0.1061i   0.0736 + 0.1538i

Vbus =

   0.0662 + 0.2023i

   0.0567 + 0.1941i

   0.0879 + 0.1878i

   0.0937 + 0.1765i

Reference:

Examples were taken from Power System Analysis - Hadi Saadat