Solution Found!
Three single-phase two-winding transformers, each rated 25
Chapter , Problem 3.36(choose chapter or problem)
Three single-phase two-winding transformers, each rated 25 MVA, 34.5/13.8 kV, are connected to form a three-phase \(\Delta-\Delta\) bank. Balanced positive-sequence voltages are applied to the high-voltage terminals, and a balanced, resistive Y load connected to the low-voltage terminals absorbs 75 MW at 13.8 kV. If one of the single-phase transformers is removed (resulting in an \(\text { open- } \Delta\) connection) and the balanced load is simultaneously reduced to 43.3 MW (57.7% of the original value), determine
(a) the load voltages \(V_{a n}, V_{b n}, \text { and } V_{c n}\);
(b) load currents \(I_{a}, I_{b}, \text { and } I_{c}\); and
(c) the MVA supplied by each of the remaining two transformers. Are balanced voltages still applied to the load? Is the \(\text { open- } \Delta\) transformer overloaded?
Questions & Answers
QUESTION:
Three single-phase two-winding transformers, each rated 25 MVA, 34.5/13.8 kV, are connected to form a three-phase \(\Delta-\Delta\) bank. Balanced positive-sequence voltages are applied to the high-voltage terminals, and a balanced, resistive Y load connected to the low-voltage terminals absorbs 75 MW at 13.8 kV. If one of the single-phase transformers is removed (resulting in an \(\text { open- } \Delta\) connection) and the balanced load is simultaneously reduced to 43.3 MW (57.7% of the original value), determine
(a) the load voltages \(V_{a n}, V_{b n}, \text { and } V_{c n}\);
(b) load currents \(I_{a}, I_{b}, \text { and } I_{c}\); and
(c) the MVA supplied by each of the remaining two transformers. Are balanced voltages still applied to the load? Is the \(\text { open- } \Delta\) transformer overloaded?
ANSWER:Step 1 of 5
Calculate the \(3 - \phi kVA ratings {S_{3\phi }}\).
\({S_{3\phi }} = 3{S_{1\phi }}\)
\({S_{3\phi }} = 3\left( {25} \right)\)
\({S_{3\phi }} = 75\;{\rm{MVA}}\)
Calculate the line-line voltage rating.
\(\frac{{{V_{HLL}}}}{{{V_{XLL}}}} = \frac{{\left( {34.5} \right)\sqrt 3 }}{{\left( {13.8} \right)\sqrt 3 }} = \frac{{59.756}}{{23.90}}\)
Calculate the line-line voltage rating for each single-phase transformer.
\(\frac{{{V_{HLL}}}}{{{V_{XLL}}}} = \frac{{\frac{{59.756}}{3}}}{{\frac{{23.90}}{3}}}\)
\(\frac{{{V_{HLL}}}}{{{V_{XLL}}}} = \frac{{19.9\;{\rm{kV}}}}{{7.96\;{\rm{kV}}}}\)
Assume Base values as the ratings of the transformer.
Base value of voltage in Low voltage side, \({V_{{\rm{base,XLL}}}} = 7.96\;{\rm{kV}}\).
Base value KVA rating, \({S_{{\rm{base}},3 - \phi }} = 75\;{\rm{MVA}}\).
Step 2 of 5
(a)
Apply balanced Positive sequence voltages to these connections.
\({V_{ab}} + {V_{bc}} + {V_{ca}} = 0\)
Calculate the load voltages of Y -connection resistive load.
\({V_{an}} = \frac{{{V_{ab}}}}{{\sqrt 3 }}\)
\({V_{an}} = \frac{{13.8\;{\rm{kV}}}}{{\sqrt 3 }}\)
\({V_{an}} = 7.96\angle 0^\circ \;{\rm{kV}}\)
Similarly,
\({V_{bn}} = 7.96\angle - 120^\circ \;{\rm{kV}}\)
\({V_{cn}} = 7.96\angle 120^\circ \;{\rm{kV}}\)