1. ELEC1300 1 Electrical Engineering 1 Friday Revision Lecture 11 Maximum Power Transfer theorems in a.c. Circuits And Power in a.c. Circuits Semester 2, 2014

3. ELEC1300 2014 Announcements 3 Week 12: Lab 6 (AC Power, Reactive Power) – Complicated lab – Read notes – Watch video Pre Lab 6 Quiz, due 2pm Mon 27 Oct

4. ELEC1300 2014 Outline Further notes on Reactive Power Compensation RMS Values Maximum Power Transfer Real, Reactive and Complex Power Lab 6: Power in AC Circuits 4

5. ELEC1300 2014 Reactive Power Compensation Example V s (Voltage supply, 11kVrms) Load A: Induction furnace, 500kVA, PF= 0.6 lagging Load B: 300kW Motor, PF=0.8 lagging Load C: Capacitor for ‘reactive power compensation’ Questions: 1.Without compensation (Load C absent) find the overall real power, reactive power, power factor and |I s |? 2.Find the value for the capacitance, as load C, that will improve the power factor to 0.9. What is |I s |in this case? 5 ISIS VSVS Load A Load B Load C

6. ELEC1300 2014 Reactive Power Compensation Example Method: 1.Draw up power table 2.Compute all elements in table 6 ISIS 11kV A: 500kVA 0.6pf B: 300kW 0.8pf C ItemP (kW) Q (kVAR) |S| (kVA) pf cos(θ) θ 5000.6A 3000.8B 53.13° 300 400 36.87°375225 A+B600625866.390.692546.17°

7. ELEC1300 2014 Reactive Power Compensation Example Method: 1.Draw up power table 2.Compute all elements in table 3.Derive further quantities needed 7 ItemP (kW) Q (kVAR) |S| (kVA) pf cos(θ) θ 5000.6A 3000.8B 53.13° 300 400 36.87°375225 A+B600625866.390.692546.17° Without compensation: real power = 600kW reactive power = 625kVAR power factor = 0.6925 (lagging) |I s |= 866.39 (kVA)/11kV = 78.76 A

8. ELEC1300 2014 Reactive Power Compensation Example Method: 1.Draw up power table 2.Compute all elements in table 3.Derive further quantities needed 4.Extend table to include compensation 8 ItemP (kW) Q (kVAR) |S| (kVA) pf cos(θ) θ 5000.6A 3000.8B 53.13° 300 400 36.87°375225 A+B600625866.390.692546.17° 00C-90° A+B+C600 0.9 25.84° 290.59 666.67 -334.41

9. ELEC1300 2014 Reactive Power Compensation Example 9 ISIS 11kV 500kVA 0.6pf 300kW 0.8pf C Method: 1.Draw up power table 2.Compute all elements in table 3.Derive further quantities needed 4.Extend table to include compensation 5.From Q c and line voltage, find C

10. ELEC1300 2014 RMS Values Suppose v(t) is a periodic “sawtooth” waveform. What is the period of v(t) ? What is the r.m.s. value of v(t)? If v(t) is the voltage across an 8  resistor, what is the average power? 10 12V v(t)v(t) t 5mS10mS15mS

11. ELEC1300 2014 Maximum Power Transfer Theorem in a.c. Circuits Maximum power will be delivered to a load when the load impedance is the complex conjugate of the Thévenin or Norton impedance of the a.c. circuit. So if: Z Th = (3 + j4)  then Z L = Z Th = (-j5)  then Z L = Z Th = 5  then Z L = 11

12. ELEC1300 2014 Example: 2009 Final Exam 1.Find the impedance, which when connected across points a and b, will give maximum power transfer 2.Find the real power in the load under this condition. 12 2k2k 10H 5F5F 4cos(200t+30 ° )A a b