Transformers

Problem 618: The current densities in the primary and secondary windings of a step down transformer are 1250 and 1500 A per square inch, respectively. The ratio of transformation is 10:1 and the mean length per turn of the primary is 15% greater than that of the secondary. If the primary winding resistance is 20 ohms, calculate the resistance of the secondary windings.

Problem 619: A certain transformer has a ratio of 8 is to 1. The primary winding resistance is 0.00283 ohm per turn and has 1155 more turns than the secondary winding. If the copper losses in the primary is 20% less than in the secondary, find resistance of the secondary winding.

Problem 652: A 1000 kVA, 6,600 /400 volts 60 cycle single phase core type transformer has the following average daily load: Full load at 0.8 pf for 8 hours, Half load at 0.707 pf for 10 hours, No-load for 6 hours. Calculate the ratio of full load copper loss to the iron loss for the transformer to be most economical for the above loading.

Problem 654: A 6.9 kV/600 V, multi-tap, single-phase distribution transformer is connected to the far end of a distribution line for which the rear end voltage is maintained at 6.9 kV. The equivalent impedance of the transformer referred to low voltage side is 0.05 + j0.25 \(\Omega\) per phase. The impedance of each line is 1+ j2 \(\Omega\). It is required to maintain a terminal voltage of 600 V when the line current of 300 A at 80% pf lagging is delivered to the load. What approximate percentage tapping is required in the primary side? Neglect changes in impedance due to changes in turns ratio.

Problem 657: A 3-phase, 60 Hz transformer has primary, secondary and tertiary windings. The primary winding is delta connected and rated 6,600 V. The secondary winding is delta connected and rated 1000 V. The tertiary winding is wye connected and rated 440 V. If the secondary winding has a 3-phase balanced load of 100 kVA at 80% pf lagging and the tertiary winding has a balanced 3-phase load of 50 kW at unity pf, what is the current in the primary winding and its operating pf?

An open delta bank, consisting of two single-phase transformers is operating with a balanced three-phase load of $50$ kVA, $440$ V at $0.8$ pf lagging and a single-phase load of $10$ kW resistive connected across c-a leg. Determine the minimum ratings of the two transformers. Assume a phase sequence of a-b-c.

An open-delta connected transformer bank serves a balanced $3$-phase load of $40$ kVA at $230$ V and $0.866$ pf lagging. Solve for the real power and pf at which each transformer is operating.

An open delta, three-phase transformer consisting of two single-phase transformers is operating with a balanced three-phase load of $50$ kVA, $440$-V at a lagging pf of $0.8$. Determine the operating pf of each transformer.

Two single-phase transformers are connected in V (open delta) and serving a delta connected impedance load, each impedance is equal to $16 \angle 36.87^\circ$ ohms. If the transformer voltages impressed on the impedances are: $V_{ab} = 240 \angle 0^\circ$, $V_{bc} = 240 \angle 240^\circ$, $V_{ca} = 240 \angle 120^\circ$ volts. Solve for the kVA delivered by each transformer.

A $500$-kVA single-phase transformer "A" with percentage impedance of $0.010 + j0.05$ is connected in parallel with a $250$-kVA transformer "B" with a percentage impedance of $0.015 + j0.04$. If the transformers are serving a single-phase load rated $800$-kVA, $80\%$ lagging pf, determine the operating pf of each transformer. Assume the transformers have the same turns ratio.

The MERALCO has two single-phase transformers with equal turns ratio and ratings and are operated in parallel to supply a load of $280$ kW at $0.80$ lagging pf. Transformer A has a resistance of $2\%$ and a reactance of $8\%$. Transformer B has a resistance of $1\%$ and a reactance of $6\%$. Determine the power delivered by the transformers A and B to the load.

Two single-phase transformers with equal ratings and turns ratio are operated in parallel to supply a load of $180$ kW at a lagging pf of $0.90$. Transformer A has a resistance of $1\%$ and a reactance of $6\%$. Transformer B has a resistance of $2\%$ and a reactance of $5\%$. Calculate the power delivered by each transformer.

Two single-phase transformers A and B are connected in parallel to serve a $600$-A single-phase load at $0.80$ pf lagging. The equivalent impedance of the transformers are $2 + j3$ and $2.3 + j5$ ohms, respectively. Determine the ratio of the kW output of transformer A to the kW output of transformer B. Assume the transformers have equal ratings and turns ratio.

Two transformers are connected in open delta and deliver a balanced three-phase load of 245 kW at 460 volts and a power factor of 0.707. Calculate the power delivered by the individual transformers.

A 500 kVA, 34.5/13.8 kV, 3-phase transformer is delta-wye connected. The primary and secondary winding resistances are 35 ohms and 0.876 ohm per phase, respectively. Calculate the percent efficiency at full load and unity power factor if the core loss is 3 kW.

In a transformer, the core loss is found to be 60 watts at 30 Hz and 90 watts at 40 Hz measured at the same maximum flux density. Compute the eddy current and hysteresis losses at 60 Hz in watts.