Matlab Coding for the demonstration of Ferranti Effect in Transmission lines

"When a long transmission line is without electrical load or very lightly loaded, the voltage at the receiving end (V_r) is greater than the voltage at the sending end (V_s). This effect seen in transmission lines is called Ferranti effect."

"Ferranti effect" is because of the substantial amount of charging current drawn by the distributed shunt capacitance of the transmission line. This charging current is greater than the current drawn by the load at the receiving end (in case of light loads). This over-voltage at the receiving end can be nicely demonstrated with the help of MATLAB. The "Ferranti effect" can be well shown in a Lab using tube-light chokes and fan capacitors.

The typical values of series inductance and shunt capacitance of a 400 kV transmission line are:

Inductance, L = 1.044 mH per km of line length, and

Shunt capacitance, C = 12 nF per km of line length.   

Assuming a system frequency of 50 Hz and a line length of 800 km, the coding is as given below.

>> C = 12*10^-9;

% Length of the line (len) is taken as 800 km with an equal spacing of 25 km.

>> len = 0:25:800;

% Total capacitance of the 800 km long line,

>> C_tot = len*C;

% Series inductance, L = 1.044 mH per km of line length

>> L = 1.044*10^-3;  

>> L_tot = len*L;

>> f = 50;

% For a sending end voltage of 400 kV,

>> Vs = 400;
% phase shift,

>> beta = len.*(2*pi*f*sqrt(L*C));

% Characteristic Impedance is Zc,

>> Zc = sqrt(L/C);

% Sending end Voltage is Vr,

>> Vr = Vs./cos(beta);

>> plot(len, Vr);

>> axis([0 800 0 700]);

>> xlabel(‘line length in km’);

>> ylabel(‘Receiving end Voltage in kV’);

>> grid;

As can be seen from the MATLAB results and plot, the receiving end voltage of a 400 kV line of length 800 km at no-load may reach 635 kV which is quite harmful. 

This dangerously high over-voltage at the receiving end can be controlled by using shunt reactor. The lagging reactive current drawn by the shunt reactor compensates for the charging current of the line and hence the increase in voltage at the receiving end is controlled.