Concept explainers
The missing values in the given table.
Answer to Problem 4PP
Primary | Secondary | Load |
EP = 23000 V | EP = 120 V | EP = 208 V |
IP = 0.626A | IP = 120.08 A | IP = 69.33 A |
EL = 23000 V | EL = 208 V | EL = 208 V |
IL = 1.084 A | IL = 120.08 A | IL = 120.08 A |
Ratio = 191.52:1 | Z = 3 Ω |
Explanation of Solution
In the figure, three single-phase transformers have been connected to form a delta–wye bank.
The primary is connected to a three-phase line of 23000 V.
The secondary voltage is 208 V.
A three-phase resistive load with an impedance of 3 Ω per phase is connected to the secondary of the transformer.
The primary windings of the three single-phase transformers are connected to form a delta connection. In a delta connection, the phase voltage is equal to line voltage.
The secondary windings are connected as a wye. In a wye connection, the phase voltage is less than the line voltage by a factor of 1.732 (the square root of 3). Therefore, the phase value of the primary voltage can be calculated using the formula
The turns ratio can be calculated by comparing the phase voltage of the primary with the phase voltage of the secondary:
The load is connected directly to the output of the secondary. The line voltage applied to the load must therefore be the same as the line voltage of the secondary:
The load bank is connected in a delta connection. The voltage across the phase of the load bank will equal to the line voltage.
The phase current of the load can be calculated using Ohm’s law:
The amount of line current supplying a delta-connected load will be 1.732 times the phase current of the load:
Since the secondary of the transformer is supplying current to only one load, the line current of the secondary will be the same as the line current of the load:
The phase current in a wye connection is equal to the line current.
The phase current of the transformer primary can now be calculated using the phase current of the secondary and the turns ratio. Because the primary has a higher voltage than the secondary, it will have a lower current. (Volts times amperes input must equal volts times amperes output.)
All the transformed values of voltage and current take place across the phases, the primary has a phase current of 6.68 A. In a delta connection, the line current is 1.732 times the phase current:
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Chapter 29 Solutions
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