Gautam C. Das

Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Electrical Engineering


Induction motors and transformers are among the earliest electrical equipment to be manufactured. The squirrel-cage induction motor has been studied very widely from the time of Tesla and Ferraris in 1889. The operation of a squirrel-cage induction motor with an unbalanced supply voltage has also been studied in great detail. Yet there is little mention of an induction motor operating on an open-delta or vee-connected transformer bank in textbooks. The open-delta transformer connection is the equivalent of the delta-delta connection with one transformer removed. The vee-connection is equivalent to a star-delta connection with one transformer removed; the primary neutral must be connected. However, both of these connections behave identically as far as the output is concerned. Hence, as a general term open-delta will be used throughout the discussion. Open-delta connections are used in emergencies where one of a group of three delta-delta connected transformers becomes defective and has to be removed from service. The remaining two transformers transmit three-phase power with a reduced load capacity. Such connections are also used in areas where the load is expected to increase. A third transformer can be readily added converting the open-delta to a delta-delta or wye-delta, thereby increasing the load ca pa city. Open-delta transformer banks are quite commonly used by rural electric co-operatives. It is cheaper to install an open-wye open-delta bank. The loads are often house-hold loads, small motors, and seasonal pumps; the slight unbalance introduced due to an open-delta secondary is usually not serious. Open-delta transformer banks, as can be seen, are used to supply three-phase induction motors. However, due to the lack of sufficient published works and detailed studies, there may be a substantial waste in transformers and/or motor capacity. The author, therefore, chose to investigate the development of an equivalent circuit for an induction motor supplied by an open-delta transformer bank, and to study the performance of the induction motor. Finally, a family of curves was developed for easy evaluation of the voltage unbalance factor. Unbalance factor plays an important part in determining the performance of the motor operating under unbalanced voltage conditions. Unbalance factor is defined as the ratio of the negative to positive-sequence voltage.

Library of Congress Subject Headings

Electric transformers
Electrostatic induction



Number of Pages



South Dakota State University