National Polytechnic School Department of Electrical Energy IEE584 Electric Machines

Dr. Franklin Quilumba 1

Homework 1

Due date: April 21, 2015 1. A certain 1-phase load draws 5 MW at 0.7 power factor lagging. Determine the

reactive power required from a parallel capacitor to bring the power factor of the parallel combination up to 0.9.

2. A balanced, symmetrical, 3-phase, 60 Hz source serves a balanced, symmetrical, 3-phase load; the line-to-line voltage at the load is 200 volts (RMS). The line current into the load is 10 Amps (RMS). (a) If the load power factor is 0.8 lagging, estimate the capacitance needed between each line to correct the power factor to unity. (Balanced 3-phase delta capacitors) (b) Estimate the value of the source side line current after the capacitors are installed.

3. Given a single-phase source of 2400∠0° V (RMS), with 3 loads in parallel: Motor: 100 kW at pf = 0.9 lagging Lights: 100 kW at pf = 1.0 Capacitors: 100 kVAr at pf = 0 leading Find: (a) Total complex power provided by the source (b) Magnitude of the source current (c) Power factor (pf) of the total load

4. Three loads are connected in parallel across a single-phase source voltage of 240 V (RMS). Load 1 absorbs 12 kW and 6.667 kVAr; Load 2 absorbs 4 kVA at 0.96PF leading; Load 3 absorbs 15 kW at unity power factor. Calculate the equivalent impedance, Z, for the three parallel loads, for two cases: (i) Series combination of R and X, and (ii) parallel combination of R and X.

5. Consider the balanced three-phase system shown in the Figure below. Determine v1(t) and i2(t). Assume positive phase sequence.

6. A 3-phase load draws 200 kW at a PF of 0.707 lagging from a 440-V line. In parallel

is a 3-phase capacitor bank that supplies 50 kVAr. Find the resultant power factor and current (magnitude) into the parallel combination.

7. An industrial load consisting of a bank of induction motors consumes 50 kW at a power factor of 0.8 lagging from a 220-V, 60-Hz, single-phase source. By placing a bank of capacitors in parallel with the load, the resultant power factor is to be raised

National Polytechnic School Department of Electrical Energy IEE584 Electric Machines

Dr. Franklin Quilumba 2

to 0.95 lagging. Find the net capacitance of the capacitor bank in microfarad that is required.

8. A 25-kVA load with power factor 0.80 lagging has a group of resistive heating units added at unity power factor. How many kW do these units take, if the new overall power factor is 0.85 lagging?