example symmcomp
DESCRIPTION
Example of application of symmetrical componentsTRANSCRIPT
Consider a thevenin source supplying a delta/wye-grounded transformer, and assume a SLG fault at the wye-grounded side of the transformer
For simplicity, we’ll neglect all resistances, and assume j1 ohm reactive impedance for each element, in all sequence networks. The symmetrical component networks for this fault condition are connected in series as seen from the fault location, as follows:
At the fault location,
Current at the fault location, on the faulted phase
Current at the fault location, on the unfaulted phases:
XS XT
SLG Fault1 pu
/ wye-gndSource
j1 pu j1 pu1 pu
j1 pu j1 pu-ve seq
j1 pu j1 pu0-seq
If1
If2
If0
IS1
IS2
IS0
+ve seq
Next, consider current seen on the source side of transformer terminals (i.e. on the side of the delta-connected winding):
Consider if the result is reasonable.
Consider the following winding configuration, where the voltage on the delta side lags that on the wye-connected side by 30 degrees. With a fault on Phase a on the wye-side, current is expected to flow between phases a & b on the delta side. However current in Phase ‘c’ ought to be zero!!!
Va
Vc
Vb
va
vc
vb
Similarly, if on the other hand the voltage on the delta connected side were to lead that on the wye-connected side by 30 degrees, as shown below:
Then a fault on Phase a on the wye-side should result in current between phases a & c on the delta side, and no current in Phase ‘b’!!!
**** What’s wrong? ***
ANSWER: We have not taken into account the phase shift resulting from the delta-wye transformation.
Let’s say we consider the case where the voltage on the delta-connected side lags the voltage on the wye-connected side by 30 degrees.
Then, in the positive sequence mode, Va_delta_pos = Va-wye_pos * e-j30
whereas in the negative sequence mode, Va_delta_neg = Va-wye_neg * e+j30
Hence
Finally,
Va
Vc
Vb
vavc
vb
Thus, as expected, Ia = -Ib, and Ic = 0
In this case, let’s check for energy balance:
Three phase power at the sending end
Three-phase power at the receiving end