Concept explainers
A transformer whose nameplate reads 2300/230 V, 25 kVA operates with primary and secondary voltages of 2300 V and 230 V rms, respectively, and can supply 25 kVA from its secondary winding. If this transformer is supplied with 2300 V rms and is connected to secondary loads requiring 8 kW at unity PF and 15 kVA at 0.8 PF lagging, (a) what is the primary current? (b) How many kilowatts can the transformer still supply to a load operating at 0.95 PF lagging?
(a)
Find the value of primary current for the given data.
Answer to Problem 51E
The value of primary current for the given data is
Explanation of Solution
Given data:
Primary voltage of the transformer
Secondary voltage of the transformer
Apparent power can supplied by the transformer from its secondary winding
Required average power for load 1
Power factor of the load 1
Required apparent power for load 2
Power factor of the load 2
Formula used:
Write the expression transformer ratio as follows:
Here,
Write the expression transformer ratio as follows:
Here,
Write the expression for current in terms of average power and voltage as follows:
Here,
PF is the power factor.
Write the expression for current in terms of apparent power and voltage as follows:
Here,
Calculation:
Modify the expression in Equation (3) for the current drawn by the load 1 as follows:
Substitute
Modify the expression in Equation (4) for the current drawn by the load 2 as follows:
Substitute
As the secondary current of the transformer is the sum of the currents drawn by the two loads, write the expression for secondary current of the transformer as follows:
Substitute
Substitute 2300 V for
Rearrange the expression in Equation (2) for the primary current of the transformer as follows:
Substitute
Conclusion:
Thus, the value of primary current for the given data is
(b)
Calculate the average power can be supplied by the transformer to a load of 0.95 lagging along with the existing loads.
Answer to Problem 51E
The average power can be supplied by the transformer to a load of 0.95 lagging is
Explanation of Solution
Given data:
Consider the load operating at 0.95 lagging as load 3.
Power factor of the load 3
Formula used:
Write the expression for maximum rated secondary current of the transformer as follows:
Write the expression for average power in terms of voltage, current, and power factor as follows:
Calculation:
Substitute
From the given data, write the expression for current drawn by the load 3 as follows:
Substitute 0.95 for
Write the expression for secondary current of the transformer by considering load 3 as follows:
Substitute
The absolute value of the new secondary current of the transformer is equal to the maximum rated secondary current of the transformer. Therefore, write the expression as follows:
Substitute
Simplify the expression as follows:
Simplify the quadratic expression and find the value of current drawn by the load 3 as follows:
Ignore the negative value and consider the positive value for the current drawn by the load 3 as follows:
Modify the expression in Equation (6) for the average power that can be supplied for the load 3 along with the two loads as follows:
Substitute
Conclusion:
Thus, the average power can be supplied by the transformer to a load of 0.95 lagging is
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Chapter 13 Solutions
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