ECCJ / TextReport / India / Energy Manager System in Japan,Appendix 1~4

ECCJ / TextReport

India

Example Problem (10): Electric devices

Select the most suitable phrases or words from the answer group for the blanks in the next text regarding the load and efficiency of power transformers, and mark their symbols. Calculate the values for { A | ab.c } to { G | ab.c } . Calculate the value to one more digit than the number of significant digits in the answer, and then round to the last digit needed for the answer. For the square roots of 3, you may use the value of 1.732.

The total loss of a power transformer consists of no-load loss and load loss. The main portion of no-load loss is iron loss and it is constant regardless of the amount of load. The load loss is the sum of copper loss and { 1 }. It varies in proportion to the square of load current. The loss of auxiliary equipment such as cooler for the transformer is { 2 } in the total loss. The efficiency of transformer takes on a maximum at a load point where load loss is equal to no-load loss. Because of the improvement of { 3 } material, the no-load loss of transformers has decreased recently, and there is a tendency that load point of the maximum efficiency is shifted toward { 4 }. The efficiency itself has been also improved.

In the case of a 6 kV distribution transformer, the load point for the maximum efficiency used to be around 75 % of the rated load and the maximum efficiency available was in the 97 % range. However, of this type of transformers in these days, a 100 kV•A single-phase transformer for instance, the no-load loss is 300 W while the load loss at the rated load is 1600 W. Therefore, the highest efficiency is given at the load point of { A | ab.c }[%] , and its value is { B | ab.c }[%].

Consider a case where single-phase transformers of the same rating and same performances are connected in star connection while a three-phase balanced load of the same level and same power factor is applied to each of them. Its efficiency varies depending on the type of connection in the transformers. Suppose that the 100 kV•A single-phase transformer noted above has a three-phase balanced load of 150 kV•A with a power factor of 1. Now calculate the efficiency in the following cases.

When connecting a three-phase load to three transformers in connection, the load shared by each transformer is 50 kW and the load loss of each transformer is { C | abc } [W]. Hence, the total efficiency in this case is { D | ab.c }[%].

When connecting a three-phase load to two transformers in V-V connection, the load current of each transformer is equal to the three-phase line current or { E | ab.c }[%] of the transformers’ rated current, while the load loss of each transformer is { F | a.bc } [kW]. Hence the total efficiency in this case is { G | ab.c } [%].

In these cases the no-load loss of the three transformers in connection is bigger than that of the two transformers in V-V connection, but the efficiency is higher in the former. This can be explained by the fact that in the V-V connection, a phase difference between voltage and current of { 5 } [rad] develops in the transformers and it adversely affects the utilization factor of the transformers.

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