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Analysis & Detection of Fault Location in Transmission Line of a Power System Network

 

Presentation on Analysis & Detection of Fault Location in Transmission Line of a Power System Network

OBJECTIVE

Our main objective is-
  1. Analysis & detection of fault location in transmission line of a power system network with steel ground and ACSR ground wire.
  2. Finally, we varies relative fault distance of simulated fault and detect relative distance to the faulted tower.
Methodology

Analysis & Detection of Fault Location in Transmission Line of a Power System Network
Program Flowchart
Program Flowchart
MATLAB PROGRAM FOR FAULT LOCATION

CASE-1: Short Line with Steel Ground Wire (Line Length=5km)
L=5; % line length in km
R=10; %tower footing resistance in ohm
ds=0.25; %relative distance in km
Zd=[(0.1199+j0.4086)*L]; %positive-sequence impedance for total line length
Z0=[(0.3242+j1.2614)*L]; %zero- sequence impedance for total line length
I0=5; %input current in amp.
Ia=25; %ground fault current flowing left from fault place
r=(0.963-j0.065); %reduction factor
γ=(1.4204+j0.0120); %phase angle of coefficient
Zf =((1.4105+j0.2711)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((1.4804+j0.2514)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.1283); %phase angle of coefficient
Zf =((1.4105+j0.2711)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=20; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((1.8568+j0.4044)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0282); %phase angle of coefficient
Zf =((2.0589+j0.3848)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.01283); %phase angle of coefficient
Zf =((1.8568+j1.4044)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=40; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((2.2996+j0.5716)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7365-j0.0290); %phase angle of coefficient
Zf =((2.7182+j0.5942)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.1283); %phase angle of coefficient
Zf =((2.2996+j0.5716)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=80; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((2.6732+j0.7489)/ds); %ground fault impedance
Z(R)=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((3.3241+j0.8574)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.1283); %phase angle of coefficient
Zf =((2.6732+j0.7489)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)* tgфf)])

CASE-2: Long Line with Steel Ground Wire(Line Length=50km)
L=50; % line length in km
R=10; %tower footing resistance in ohm
ds=0.025; %relative distance in km
Zd=[(0.1199+j0.4086)*L]; %positive-sequence impedance for total line length
Z0=[(0.3242+j1.2614)*L]; %zero- sequence impedance for total line length
I0=5; %input current in amp.
Ia=25; %ground fault current flowing left from fault place
r=(0.963-j0.065); %reduction factor
γ=(1.0545-j0.0070); %phase angle of coefficient
Zf =((1.6354+j0.3671)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/[imag(Z)
(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.9492-j0.0116); %phase angle of coefficient
Zf =((1.7348+j0.3387)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(13.2861-j2.2623); %phase angle of coefficient
Zf =((1.6354+j0.3671)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=20; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0485-j0.0084); %phase angle of coefficient
Zf =((2.0385+j0.4888)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((2.3519+j0.4415)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9949); %phase angle of coefficient
Zf =((2.0385+j0.4888)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=40; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0494-j0.0070); %phase angle of coefficient
Zf =((2.4516+j0.6337)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((3.2278+j0.5886)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9948); %phase angle of coefficient
Zf =((2.4516+j0.6337)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=80; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((0.3627+j0.6434)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((0.4941+j0.8405)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2490-j0.1292); %phase angle of coefficient
Zf =((0.3627+j0.6434)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)*tgфf)])
CASE-3: Short Line with ACSR Ground Wire (Line Length=5km)

L=5; % line length in km
R=10; %tower footing resistance in ohm
ds=0.25; %relative distance in km
Zd=[(0.1199+j0.4086)*L]; %positive-sequence impedance for total line length
Z0=[(0.3242+j1.2614)*L]; %zero- sequence impedance for total line length
I0=5; %input current in amp.
Ia=25; %ground fault current flowing left from fault place
r=(0.963-j0.065); %reduction factor
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((0.3929+j0.4270)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7382-J0.0311); %phase angle of coefficient
Zf =((0.5237+j0.4689)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.1283); %phase angle of coefficient
Zf =((0.3929+j0.4270)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=20; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((0.3970+j0.5339)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((0.5469+j0.6480)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2328-j0.1281); %phase angle of coefficient
Zf =((0.3970+j0.5339)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=40; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((0.3802+j0.6047)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((0.5231+j0.7720)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2341-j0.1283); %phase angle of coefficient
Zf =((0.3802+j0.6047)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=80; %tower footing resistance in ohm
ds=0.25; %relative distance in km
γ=(1.4195+j0.0120); %phase angle of coefficient
Zf =((0.3627+j0.6434)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.50; %relative distance in km
γ=(1.7378-j0.0297); %phase angle of coefficient
Zf =((0.4941+j0.8405)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.75; %relative distance in km
γ=(2.2490-j0.1292); %phase angle of coefficient
Zf =((0.3627+j0.6434)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)* tgфf)])
CASE-4: Long Line with ACSR Ground Wire (Line Length=5km)

L=50; % line length in km
R=10; %tower footing resistance in ohm
ds=0.025; %relative distance in km
Zd=[(0.1199+j0.4086)*L]; %positive-sequence impedance for total line length
Z0=[(0.3242+j1.2614)*L]; %zero- sequence impedance for total line length
I0=5; %input current in amp.
Ia=25; %ground fault current flowing left from fault place
r=(0.963-j0.065); %reduction factor
γ=(1.0482+j0.0200); %phase angle of coefficient
Zf =((0.3944+j0.4499)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/ [imag(Z)
(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((0.6276+j0.4232)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5482-j1.9949); %phase angle of coefficient
Zf =((0.3944+j0.4499)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=20; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0494+j0.0070); %phase angle of coefficient
Zf =((4232+j0.5429)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9320-j0.0110); %phase angle of coefficient
Zf =((0.8783+j0.5784)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9949); %phase angle of coefficient
Zf =((0.4232+j0.5429)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=40; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0494+j0.0070); %phase angle of coefficient
Zf =((0.4407+j0.6258)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9320-j0.0110); %phase angle of coefficient
Zf =((1.2328+j0.7982)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9949); %phase angle of coefficient
Zf =((0.4407+j0.6258)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=80; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0288+j0.0040); %phase angle of coefficient
Zf =((0.4499+j0.6951)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((1.7343+j1.1085)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5474-j1.9942); %phase angle of coefficient
Zf =((0.4499+j0.6951)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)*tgфf)])
CASE-4: Long Line with ACSR Ground Wire (Line Length=5km)

L=50; % line length in km
R=10; %tower footing resistance in ohm
ds=0.025; %relative distance in km
Zd=[(0.1199+j0.4086)*L]; %positive-sequence impedance for total line length
Z0=[(0.3242+j1.2614)*L]; %zero- sequence impedance for total line length
I0=5; %input current in amp.
Ia=25; %ground fault current flowing left from fault place
r=(0.963-j0.065); %reduction factor
γ=(1.0482+j0.0200); %phase angle of coefficient
Zf =((0.3944+j0.4499)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/[imag(Z)
(real(Z)*tgфf)])
ds=0.500; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((0.6276+j0.4232)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5482-j1.9949); %phase angle of coefficient
Zf =((0.3944+j0.4499)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=20; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0494+j0.0070); %phase angle of coefficient
Zf =((4232+j0.5429)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9320-j0.0110); %phase angle of coefficient
Zf =((0.8783+j0.5784)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)*tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9949); %phase angle of coefficient
Zf =((0.4232+j0.5429)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=40; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0494+j0.0070); %phase angle of coefficient
Zf =((0.4407+j0.6258)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9320-j0.0110); %phase angle of coefficient
Zf =((1.2328+j0.7982)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5483-j1.9949); %phase angle of coefficient
Zf =((0.4407+j0.6258)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
R=80; %tower footing resistance in ohm
ds=0.025; %relative distance in km
γ=(1.0288+j0.0040); %phase angle of coefficient
Zf =((0.4499+j0.6951)/ds); %ground fault impedance
Z=[Zd+(Z0-Zd)*(I0/Ia)-(1/R)]; %line impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.500; %relative distance in km
γ=(1.9319-j0.0110); %phase angle of coefficient
Zf =((1.7343+j1.1085)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)]/
[imag(Z)-(real(Z)* tgфf)])
ds=0.975; %relative distance in km
γ=(12.5474-j1.9942); %phase angle of coefficient
Zf =((0.4499+j0.6951)/ds); %ground fault impedance
tgфf=imag (r* γ*Zf)/real (r* γ*Zf);
syms Za df
[Za , df]= solve (Za-[df*Z+r* γ*Zf], real(Za)-[df*real(Z)+real(r* γ*Zf)])
Syms di dr
[di , dr]= solve (di-[df+(imag(r* γ*Zf)/imag(Z))], df-[(imag(Z)*di)-(real(Z)*dr* tgфf)] / [imag(Z)
(real(Z)* tgфf)])
The Result of Calculations are Presented in Table – 1

For Short Line with Steel Ground Wire

Table – 1
R(Ω) ds Zf(Ω) γ di df
10 0.25 1.4105+j0.2711 1.4204+j0.0120 0.3242 0.2678
10 0.50 1.4804+j0.2514 1.7378-j0.0297 0.5608 0.5000
10 0.75 1.4104+j0.2711 2.2341-j0.1283 0.7643 0.6730
20 0.25 1.8568+j0.4044 1.4195+j0.0120 0.3679 0.2814
20 0.50 2.0589+j0.3848 1.7378-j0.0282 0.6119 0.4926
20 0.75 1.8568+j1.4044 2.2341-j0.1283 0.8561 0.7159
40 0.25 2.2996+j0.5716 1.4195+j0.1020 0.4221 0.2864
40 0.50 2.7182+j0.5942 1.7365-j0.0290 0.6749 0.4725
40 0.75 2.2996+j0.5716 2.2341-j0.1283 0.9252 0.7050
80 0.25 2.6732+j0.7489 1.4195+j0.0120 0.4834 0.2884
80 0.50 3.3241+j0.8574 1.7378-j0.0297 0.7834 0.4753
80 0.75 2.6732+j0.7489 2.2341-j0.1283 1.0059 0.6820
The Result of Calculations are Presented in Table – 2
For Long Line with Steel Ground Wire

Table – 2
R(Ω) ds Zf(Ω) γ di df
10 0.025 1.6354+j0.3671 1.0545-j0.0070 0.0322 0.0252
10 0.500 1.7348+j0.3387 1.9492-j0.0116 0.5145 0.4994
10 0.975 1.6354+j0.3671 13.2861-j2.2623 0.9653 0.8830
20 0.025 2.0385+j0.4888 1.0485-j0.0084 0.0348 0.0276
20 0.500 2.3519+j0.4415 1.9119-j0.0110 0.5146 0.4992
20 0.975 2.0385+j0.4888 12.5483-j1.9949 1.0347 0.8912
40 0.025 2.4516+j0.6337 1.0494-j0.0070 0.0382 0.0301
40 0.500 3.2278+j0.5886 1.9319-j0.0110 0.5189 0.4990
40 0.975 2.4516+j0.6337 12.5483-j1.9948 0.9999 0.8958
80 0.025 2.8413+j0.7868 1.0494-j0.0070 0.4180 0.0327
80 0.500 4.4688+j0.7978 1.9319-j0.0110 0.5253 0.4986
80 0.975 2.8413+j0.7868 12.5483-j1.9948 1.0219 0.9055
The Result of Calculations are Presented in Table – 3
For short line with ACSR ground wire

Table – 3
R(Ω) ds Zf(Ω) γ di df
10 0.25 0.3929+j0.4270 1.4195+j0.0120 0.3534 0.2749
10 0.50 0.5237+j0.4689 1.7382-j0.0311 0.6300 0.4937
10 0.75 0.3929+j0.4270 2.2341-j0.1283 0.9000 0.7647
20 0.25 0.3970+j0.5339 1.4195+j0.0120 0.3826 0.2730
20 0.50 0.3802+j0.6047 1.7378-j0.0297 0.6889 0.4913
20 0.75 0.5231+j0.7720 2.2328-j0.1281 0.9459 0.7582
40 0.25 0.3802+j0.6047 1.4195+j0.1020 0.4026 0.2681
40 0.50 0.3627+j0.6434 1.7378-j0.0297 0.7316 0.4884
40 0.75 0.4941+j0.8405 2.2324-j0.1283 0.9770 0.7345
80 0.25 0.3627+j0.6434 1.4195+j0.0120 0.4139 0.2634
80 0.50 0.4941+j0.8405 1.7378-j0.0297 0.7560 0.4865
80 0.75 0.3627+j0.6434 2.2490-j0.1292 0.9967 0.7186
The Result of Calculations are Presented in Table – 4
For Long line with ASCR ground wire

Table – 4
R(Ω) ds Zf(Ω) γ di df
10 0.25 0.3944+j0.4499 1.0482+j0.0200 0.0332 0.0293
10 0.50 0.6276+j0.4232 1.9319-j0.0110 0.5124 0.4998
10 0.75 0.3944+j0.4499 12.5482-j1.9949 1.0535 0.9941
20 0.25 0.4232+j0.5429 1.0494+j0.0070 0.0349 0.0309
20 0.50 0.8783+j0.5784 1.9320-j0.0110 0.5169 0.4997
20 0.75 0.4232+j0.5429 12.5482-j1.9949 1.0735 1.0115
40 0.25 0.4407+j0.6258 1.0494+j0.0070 0.0365 0.0325
40 0.50 1.2328+j0.7982 1.9320-j0.0110 0.5232 0.4996
40 0.75 0.4407+j0.6258 12.5483-j1.9949 0.0919 1.0286
80 0.25 0.4499+j0.6951 1.0288+j0.0040 0.0376 0.0337
80 0.50 1.7343+j1.1085 1.9319-j0.0110 0.5322 0.4995
80 0.75 0.4499+j0.6951 12.5474-j1.9949 1.1076 1.0439
Scope of future work
In future the system can be developed for three phase –to- ground fault detection which achieved by taking into account the imaginary part of the ground fault impedance at the fault place.
Conclusion
We are successfully completed in our thesis on ‘Analysis & detection of Fault location in transmission line of a power system network’. Our simulated results are presented in tables which see that fault distance length (df) increases with increases in relative distance of the simulated fault (ds) .When the faulted tower is most often one of the two nearest then simulated result is high accuracy obtained for the faults at the sections satisfying the condition |Ia|>|Ib|. We try as possible as more accurate result of the detection of fault location. As a result, more smoothly operate in transmission line of a power system network. In our thesis paper presents highly accurate fault location algorithm for the single phase –to- ground faults on a transmission line, connecting the transmission and the distribution networks. With a somewhat lower accuracy, the algorithm can be used for the lines connecting a strong and a weak network. The algorithm is based on MATLAB program. The main advantages of the algorithm in comparison to the previous presentation algorithm methods are achieved by taking in to account the imaginary part of the ground fault impedance at the fault place. Our supervisor sir helps us for successfully completed our thesis.
Submitted By Mohammad Ohiduzzaman and Pranabesh Dutta
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