Zigzag Earthing Transformer - Unearthed Generator - SLG Fault 1

Attached is the single-line-diagram annotated with PTW Comprehensive short-circuit study results for a SLG fault at BUS-A.

Attached is the PTW Comprehensive text report for SLG fault at BUS-A.

Any good power systems analysis text or the Westinghouse T&D Handbook will give the procedures for laying out the sequence diagrams. You can probably also find it by Googling sequence diagrams zig-zag. Also see What are good references for a Power Engineer?

The attached sequence impedance diagrams and excel spreadsheet calculations validate SKM/PTW SLG fault currents.
Attached file 1 of 3

The attached sequence impedance diagrams and excel spreadsheet calculations validate SKM/PTW SLG fault currents.Attached file 2 of 3

The attached sequence impedance diagrams and excel spreadsheet calculations validate SKM/PTW SLG fault currents.Attached file 3 of 3

EddyWirbelstrom,
This is Matlab calculation- PART I

% Zigzag Earthing Transformer - Unearthed Generator - SLG Fault
% thread238-278589 EddyWirbelstrom (Electrical) Aug 10 22:12
% CLARIFY PTW Comprehensive text report for SLG fault at BUS-A.
% ronaldo de almeida PARTE I

%%% Sbase, Vbase
Ub=11; %kV
Sb=100; %MVA
Ib= Sb*1000/(1.732*Ub);
Zb = Ub/Ib;

%%%%%Generator – Star connected, unearthed
Sng = 1; % MVA
Un = 11.000; %kV
Rg = 0.01 ;
R1=Rg;
R2= Rg;
X1 = 0.10; % pu
X2 = 0.10; % pu
ro = 0.01; % pu
xo = 0.10; %1 pu

%Zg in pu , base 100MVA -11kV:
Z1g= (Sb/Sng) * (R1 + j*X1);
Z2g= (Sb/Sng) * (R2 + j*X2);
Z0g= (Sb/Sng) * (ro + j*xo);

%%%%Zigzag earthing transformer
Snz=1; %MVA
Ro = 1; % per cent
Xo = 10 ; % per cent
R1 = 9999; % per cent
X1 = 9999 ; % per cent

%Zz in pu Sb MVA:
Z1z =(Sb/Snz)*(R1 + j*X1)/100;
Z2z= (Sb/Snz)*(R2 + j*X2)/100;
Z0z= (Sb/Snz) *(Ro + j*Xo)/100;

%% Z1 => Z1g//Z2z
Z1= 1 / (1/Z1g + 1/Z1z);
%% Z2 => Z2g//Z2z
Z2= 1 / ( 1/Z1g + 1/Z1z);
%% Z0 => Z0z (generator unearthed)
Z0= Z0z;

format short
%% Ifault
Zth=Z1+Z2+Z0;
%%% THEVENIN EQUIVALENT IMPEDANCE: 3.000 +j 30.000 (PU) Sb=100MVA Vb=11kV
X_R= imag(Zth)/real(Zth);
% THEVENIN IMPEDANCE X/R RATIO: 10.000
If= Ib * 3/Zth;
magIf=abs(If); % ====>522.4659 A
angIf = angle(If) *180/pi;% ==> -84.2722 degree
%%% INI. SYM. RMS FAULT CURRENT: 522.3 / -84. ( AMPS/DEG )

%% fault current of each phase
I1=If/3;
I2=I1;
I0=I1;
a=cos(2*pi/3)+j*sin(2*pi/3); %%operator a
Ia= I1 + I2 + I0;
Ib= a^2*I1 + a* I2 + I0;
Ic= a*I1 + a^2*I2 + I0;

format bank
magIa=abs(Ia) ; %%% ====>522.4659 A
angIa = angle(Ia) *180/pi; %%% ====>-84.2722 degree
magIb=abs(Ib); % ===>0
angIb = angle(Ib) *180/pi;
magIc=abs(Ic); %% ===> 0
angIc = angle(Ic) *180/pi;
% INI. RMS FAULTED CURRENT ( AMPS / DEG )
% AT TIME = 0.5 CYCLES
% ---PHASE A--- ---PHASE B--- ---PHASE C---
% 522.3 / -84.3 0.0 / 0.0 0.0 / 0.0

Thank you Odlanor and Jghrist. The Matlab calcs are more descriptive than my excel sheet.

EddyWirbelstrom,
This is Matlab calculation- PART II
% Zigzag Earthing Transformer - Unearthed Generator - SLG Fault
% thread238-278589: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault EddyWirbelstrom (Electrical) Aug 10 22:12
% CLARIFY PTW Comprehensive text report for SLG fault at BUS-A.
% ronaldo de almeida PARTE II
c= 0.5; %ciclo % relay time + Circuit Breaker opening time (cycle)
t= c * (1000*1/50) ; % cycle to ms
f = 50 ; %Hz
w = 2 * pi * f;
Is = 522.3; % A
XR=10; %X/R
tau = 1000*XR/w; %constant time
a= exp(-t/tau)*100; % assymetry in %
q=sqrt(1 + 2 * (a/100) ^2); % Is/Ias in rms
Iass= q *Is ; % assymetrycal current ===> 750.91 for 1/2 cycle
% ASYM RMS INTERRUPTING AMPS
% 1/2 CYCLES 2 CYCLES 3 CYCLES 5 CYCLES 8 CYCLES
% 750.9 563.0 534.2 523.2 522.3

EddyWirbelstrom,
This is Matlab calculation- PART III
There are discrepancy mainly in angle for Term ET-A
(See end of calculations)
I guess because Term ET-A Bus is 11000/-60 instead of
11000/0.
I do not know how to revise.

% Zigzag Earthing Transformer - Unearthed Generator - SLG Fault
% thread238-278589: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault EddyWirbelstrom (Electrical) Aug 10 22:12
% CLARIFY PTW Comprehensive text report for SLG fault at BUS-A.
% ronaldo de almeida PARTE II

%% determine current distribution factors
%%Z1
df1Zg= Z1z/(Z1g+Z1z);
df1Zz= Z1g/(Z1g+Z1z);
%check
abs(df1Zg + df1Zz)==1
%% Z2
df2Zg= Z2z/(Z2g+Z2z);
df2Zz= Z2g/(Z2g+Z2z);
%check
abs(df2Zg + df2Zz)==1
%% Z0
df0Zg= 0; %Z0z/(Z0g+Z0z);
df0Zz= 1; %Z0g/(Z0g+Z0z);
%check
abs(df0Zg + df0Zz)==1


%%% contribution current

% generator
I1g = I1 * df1Zg;
I2g = I2 * df2Zg;
I0g = I0 * df0Zg;
IAg= I1g + I2g + I0g; % A
IBg = a^2 * I1g + a*I2g + I0g; % A
ICg = a*I1g + a^2*I2g + I0g; % A
magIAg= abs(IAg);
angIAg= angle(IAg)*180/pi;
magIBg= abs(IBg);
angIBg= angle(IBg)*180/pi;
magICg= abs(ICg);
angICg= angle(ICg)*180/pi;
disp('*************Gen-A')
disp ([magIAg angIAg magIBg angIBg magICg angICg]);
% 348.12 / -84.30 174.06/ 95.70 174.06/ 95.70%
% Gen A ( Y star BUS-A 11000. 348.2/ -84. 174.1/ 96. 174.1/ 96.

% zigzag
I1z = I1 * df1Zz;
I2z = I2 * df2Zz;
I0z = I0 * df0Zz;
IAz= I1z + I2z + I0z;
IBz= a^2*I1z + a*I2z + I0z;
ICz= a*I1z + a^2*I2z + I0z;
magIAz= abs(IAz);
angIAz= angle(IAz) *180/pi;
magIBz= abs(IBz);
angIBz= angle(IBz) *180/pi;
magICAz= abs(ICz);
angICz= angle(ICz) *180/pi;
disp('*************Term ET-A')
disp([magIAz angIAz magIBz angIBz magIC angICz]);
% 174.35/-84.22 174.06/-84.30 0.00/-84.30
% Term ET-A 11000. 174.1/ 96. 174.1/ 96. 174.1/ 96.

EddyWirbelstrom,
Attached is sequence diagram.
I have some doubts about SKM calculation.
1- I did not understand why prefault voltage Term ET-A
is different of prefault BUS-A.
2- What is the meaning:
ALL BUSES REPORTED AT TIME = 0.5 CYCLES
short circuit 522A refers to 8 cycles !!

Thank you Odlanor for your helpful comments to my posting.
Your sequence diagram correctly shows negative sequence impedance of the zig-zag transformer in parallel with its positive sequence impedance. I did not show Z1 & Z2 of the Zig-Zag transformer because they are 9999%.
Your questions have made me look closer at how SKM PTW reports the results of a single phase to earth ( SLG ) short-circuit using PTW’s Comprehensive short-circuit program.
Your Quest 1.
The zig-zag transformer is modelled as a Ynd1.
( YNd1 = primary star earthed, secondary delta not earthed and 30 degrees behind primary )
Z1 = Z2 = 9999 + j 9999 %
Z0 = 1.0000 + J 10.0000 %
The Zig-Zag transformer primary bus is BUS-A
The Zig-Zag transformer secondary bus is Term ET-A

However when I rerun the study I get :
BUS-A 1.0 per unit volts at 0 degrees, and
Term ET-A 1.0 per unit volts at 0 degrees. ?
See attached report.

Your Quest 2.
PTW calculates the asymmetrical rms short-circuit current for the worst-case situation when the voltage wave is at zero and the current lags the voltage by 90 degrees. This occurs ½ cycle after the fault inception.
In accordance with IEC Standards, PTW also calculates the peak short-circuit current for the same condition.

The attached Excel spreadsheet shows how the formula for I asym rms is derived and also the Iasym rms at various times after the SLG fault inception at BUS-A.
I have also attached the single-line diagram annotated with the I asym rms at various times after fault inception.


Do you have SKM PTW software, if so I can send you the PTW model ?

Attached is the excel spreadsheet with calcs for Iasym rms at various times after SLG fault inception.

EddyWirbelstrom
1- Rerun with Term ET-A 1.0 per unit volts at -30 degrees.

2- Is it correct? I guess should be
ET-A 8cycle-174A 1/2cycle-500.57A
GenA 8cycle-348A 1/2cycle-750.85A

3- I do not have SKM software.