HW3

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Homework # 3
AC Circuit Analysis
Due November 15 @ 10:00 AM
Problem 1. The operation of an electric oven has a maximum monthly demand of 200 kW and
380 inductive kVAR. In order to recover losses and encourage customers to operate with high power
factor, the power supply company penalizes with $ 500 per month for each kVAR that exceeds a
reference value calculated as 0.65 times the maximum active power.
(a) What is the power factor of the oven?
(b) What is the annual cost of the penalty?
(c) If the company can compensate the reactive power by installing a capacitor bank, at a cost of
$ 520,000 per each bank of 100 KVAR installed, and $ 1,030,000 for each bank of 200 KVAR
installed, what it is the annual savings obtained by the customer in every situation?
Problem 2. A positive phase sequence supply with Van = VF 0◦ [V] feeds a three-phase motor
connected in delta with a voltage of 440 [V] line-to-line, which consumes 4 [kVA] with a power factor
of 0.78 ↑. If it is connected, between a and b line, a 1.8 [kVAR] condenser and, between line c and
neutral conductor, a 800 [W] resistance, compute all currents (lines and neutral conductor).
Problem 3. A voltage source 12.47 / 7.2 [KVRMS ] supplies an unbalanced delta load, as follows:
• Phase AB: 1500 [kVA], FP = 0.95 ↑.
• Phase BC: 1000 [kVA], FP = 0.85 ↑.
• Phase CA: 950 [kVA], FP = 0.90 ↑.
For this system, compute:
(a) The currents in each phase.
(b) The M matrix corresponding to the following expression: IaAIbB
IcC
 = M
 IABIBC
ICA
 .
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