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Transformer Riddle No.89 - Transformer one phase broken
Would you please let me have enough information about the situation in which a 3 phase transformer has 1 phase broken and supplied with 2 phases while on its secondary side. it has:
First : a single phase load,
Second: A 3 phase load,
Special thanks for giving generously of your valuable time, intelect and friendship environment.

REGARDS,
KAZEMI
FROM IRAN

#1
Wed, November 21st, 2012 - 17:25
Unbalance loading/supplying study is done as important transformer abnormal conditions.
By definition, according to IEC 76, ‘normal’ service conditions for a power transformer are at an altitude of not greater than 1000 m above sea level, within an ambient temperature range of -25 to +40C, subjected to a wave shape which is approximately sinusoidal, a three-phase supply which is approximately symmetrical. As the conditions arising from the balanced three-phase load are those which would normally occur, it is only a question of superposing those arising from the single-phase load upon the normal conditions to obtain the sum total effects. For the purpose of this study it is only necessary to consider the more usual connections adopted for supplying three-phase loads. The value of current distribution is based upon the assumption that the single-phase currents are not sufficient to distort the voltage phasor diagrams for the transformers or transformer banks. This assumption would approximate very closely to the truth in all cases where the primary and secondary currents in each phase are balanced. In those cases, however, where the primary current on the loaded phase or phases has to return through phases unloaded on the secondary side, the distortion may be considerable, even with relatively small loads; this feature is very pronounced where three-phase shell-type transformers and banks of single phase transformers are employed.
There are many abnormal operation explanation as following which you can use for your especial concerned cases study.

(a) Star/star; single-phase load across two lines
With this method of single-phase loading the primary load current has a free path through the two primary windings corresponding to the loaded secondary phases, and through the two line wires to the source of supply. There is, therefore, no choking effect, and the voltage drops in the transformer windings are those due only to the normal impedance of the transformer. The transformer neutral points are relatively stable, and the voltage of the open phase is practically the same as at no-load. The secondary neutral point can be earthed without affecting the conditions. The above remarks apply equally to all types of transformers.

(b) Star/star; Single-phase load from one line to neutral
With this method of single-phase loading the primary load current corresponding to the current in the loaded secondary must find a return path through the other two primary phases, and as load currents are not flowing in the secondary windings of these two phases, the load currents in the primaries act as magnetising currents to the two phases, so that their voltages considerably increase while the voltage of the loaded phase decreases. The neutral point, therefore, is considerably displaced. The current distribution shown on the primary side is approximate only, as this will vary with each individual design.
The above remarks apply strictly to three-phase shell-type transformers and to three-phase banks of single-phase transformers, but three-phase core-type transformers can, on account of their interlinked magnetic circuits, supply considerable unbalanced loads without very severe displacement of the neutral point.

(c) Star/star with generator and transformer primary neutrals joined; single-phase load from one line to neutral
In this case the connection between the generator and transformer neutral points provides the return path for the primary load current, and so far as this is concerned, the other two phases are short-circuited. There is therefore no choking effect, and the voltage drops in the transformer windings are those on the one phase only, due to the normal impedance of the transformer. The transformer neutral points are relatively stable, and the voltages of the above phases are practically the same as at no-load. The secondary neutral point can be earthed without affecting the conditions.
The above remarks apply equally to all types of transformers.

(d) Delta/delta; single-phase load across two lines
With this connection the loaded phase carries two-thirds of the total current, while the remainder flows through the other two phases, which are in series with each other and in parallel with the loaded phase. On the primary side all three windings carry load currents in the same proportion as the secondary windings, and two of the line wires only convey current to and from the generator. There is no abnormal choking effect, and the voltage drops are due to the normal impedance of the transformer only. The type of transformer does not affect the general deductions.

(e) Star/delta; single-phase load across two lines
On the delta side the distribution of current in the transformer windings is exactly the same as in the previous case, that is, two-thirds in the loaded phase and one-third in each of the other two. On the primary side the corresponding load currents are split up in the same proportions as on the secondary, and in value they are equal to the secondary currents of the different phases multiplied by √3 and multiplied or divided by the ratio of transformation, according to whether the transformer is a step-up or step-down. The primary neutral point is stable.
The above remarks apply equally to all types of transformers.

(f) Delta/star; single-phase load across two lines
Single-phase loading across lines of this connection gives a current distribution somewhat similar to that of (a), except that the currents in the two primary windings are 1/√3 times those occurring with the star primary, while all the three lines to the generating source carry currents in the proportions shown instead of two lines only carrying currents as in the case of the star primary.
There is no choking effect, and the voltage drops in the windings are due only to the normal impedance of the transformer. The transformer secondary neutral point is relatively stable and may be earthed. The voltage of the open phase is practically the same as at no-load.
The above remarks apply equally to all types of transformers.

(g) Delta/star; single-phase load from line to neutral
With this connection and single-phase loading the neutral, primary and secondary windings on one phase only carry load current, and on the primary side this is conveyed to and from the generating source over two of the lines only. There is no choking effect, and the voltage drops in the transformer windings are those corresponding only to the normal impedance of the transformer. The secondary neutral point is stable and may be earthed without affecting the conditions. The voltages of the open phase are practically the same as at no-load. The type of transformer construction does not affect the general deductions.

(h) Interconnected star/star; single-phase load across two lines
With this connection and method of loading, all the primary windings take a share of the load, and although in phase C there is no current in the secondary winding, the load currents in the two halves of the primary windings of that phase flow in opposite directions, so that their magnetic effects cancel. There is no choking effect, and the voltage drops in the transformer windings are those due to the normal impedance of the transformer only. With three-phase shell-type transformers and three-phase banks of single-phase transformers the secondary neutral is not stable and should not be earthed unless the flux density is sufficiently low to permit this. With three-phase core-type transformers, however, the neutral is stable and could be earthed. The voltage of the open phase is practically that occurring at no-load.

(i) Interconnected star/star; single-phase load from one line to neutral
With this connection and method of loading a partial choking effect occurs, due to the passage of load current in each half of the primary windings corresponding to the unloaded secondary windings. The voltage of the two phases in question, therefore, becomes increased on account of the high saturation in the cores and the voltage of the windings corresponding to the loaded phase drops. Both primary and secondary neutrals are therefore unstable and should not be earthed. The above remarks apply strictly to three-phase shell type transformers and to three-phase banks of single-phase transformers. With three-phase core-type transformers the deflection of the neutral point is not so marked, and considerable out-of-balance loads can be supplied without any excessive deflections of the neutral points.

(j) Star/interconnected star; single-phase load across two lines
With this connection and method of loading the secondary windings on all three limbs carry load currents, and therefore all the primary windings carry corresponding balancing load currents. The current distribution is clearly shown on the diagram, from which it will be seen there is no choking effect, and the transformer neutral points are stable if three-phase core-type transformers are used, and so may be earthed. On the secondary side the voltage of the open phase is practically the same as at no-load. The voltage drops in the transformer windings are those due only to the normal impedance of the transformer.

(k) Star/interconnected star; single-phase load from one line to neutral
With this method of loading there is similarly no choking effect, as the primary windings corresponding to the loaded secondaries carry balancing load currents which flow simply through two of the line wires to the generating source.
The voltage drops in the transformer windings are those due only to the normal impedance of the transformer, and the voltages of the above phases are practically the same as at no-load. The secondary neutral is stable and can be earthed. The primary neutral can only be earthed, however, if the transformer unit is of the three-phase core type of construction.

(l) Delta/interconnected star; single-phase load across two lines
With this connection and loading the general effect is similar to the star/interconnected-star connection. That is, there is no choking effect, as the primary windings corresponding to the loaded secondaries take balancing load currents, although the primary current distribution is slightly different from that occurring with a star primary. The voltage drops in the transformer windings are those due only to the normal impedance of the transformer, while the voltage of the open phase is practically the same as at no-load. The secondary neutral is stable and can be earthed.

(m) Delta/interconnected star; single-phase load from one line to neutral
With this connection and method of loading the results are similar to those obtained with the star/interconnected-star, that is the primary windings corresponding to the loaded secondaries carry balancing load currents so that there is no choking effect. The voltage drops in the transformer windings are those due only to the normal impedance of the transformer, while the voltages of the open phases are practically the same as at no-load. The secondary neutral point is stable and can be earthed.

Reference:
The J & P Transformer Book (Martin J. Heathcote, CEng, FIEE)

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