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Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

(OP)
An islanded powerhouse consists of unearthed star-connected generators directly connected to a 11kV bus.
The 11kV bus is earthed via an earthing transformer as shown in the attached simplified three-line diagram sketch and the attached single line diagram.
The impedance values were chosen to simplify and are not the actual values. Actual values are shown below.
SKM / PTW program confirms the magnitude and direction of the phase currents for a single phase to earth short-circuit shown in the attached sketch.

I would like to verify the PTW results by manual calculations based on a sequence impedance diagram.
Can anyone suggest the layout for the sequence impedance diagram ?
How is the earthing transformer and unearthed generator  represented in the sequence impedance diagram ?

The actual values are not needed, however they are :

Generator – Star connected, unearthed
Sn = 3295 kVA, Un = 11000V
Rg = R1 = R2 = 0.01 pu
x"d = X1 = 0.166 pu
x"q = X2 = 0.186 pu
ro = 0.01 pu
xo = 0.01 pu

Zigzag earthing transformer
Ro = 0.83 Ohm        ( 0.0069 pu on 1000 kVA )
Xo = 2.048 Ohm    ( 0.0169 pu on 1000 kVA )
R1 = R2 = 999999 Ohm
X1 = X2 = 999999 Ohm

I will attach the single-line-diagram and PTW report in separate postings.

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

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?  http://www.eng-tips.com/faqs.cfm?fid=1287
 

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

EddyWirbelstrom,
This is Matlab calculation- PART I

% 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 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

 

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

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

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

EddyWirbelstrom,
This is Matlab calculation- PART II
% 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
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

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

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: 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.

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

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 !!


 

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

(OP)
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 ?
 

RE: Zigzag Earthing Transformer - Unearthed Generator - SLG Fault

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.




       

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