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1 AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor Complex Power Dr. Nik Rumzi Nik Idris SEE 1023 Circuit.

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Presentation on theme: "1 AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor Complex Power Dr. Nik Rumzi Nik Idris SEE 1023 Circuit."— Presentation transcript:

1 1 AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor Complex Power Dr. Nik Rumzi Nik Idris SEE 1023 Circuit Theory

2 2 Instantaneous, Average and Reactive Power + v(t) i(t) Passive, linear network Instantaneous power absorbed by the network is, p =v(t).i(t) Let v(t) = V m cos ( t + v ) and i(t) = I m cos( t + i ) Which can be written as v(t) = V m cos ( t + v i ) and i(t) = I m cos( t)

3 3 p = V m cos( t + v – i ). I m cos( t) v i Instantaneous Power (p) Example when v i = 45 o positive p positive p = power transferred from source to network negative p negative p = power transferred from network to source 45 o

4 4 v(t) = V m cos ( t + v i ) and i(t) = I m cos( t) p = V m cos( t + v – i ). I m cos( t) p = p = P + Pcos(2 t) Qsin(2 t) Using trigonometry functions, it can be shown that: = AVERAGE POWER (watt) = REACTIVE POWER (var) Which can be written as

5 5 p =

6 6 Example for v - i = 45 o

7 7 p = P = average power Q = reactive power p = P + P cos(2 t) Q sin(2 t)

8 8 P = AVERAGE POWER Q = REACTIVE POWER p = P + P cos(2 t) Q sin(2 t) Useful power – also known as ACTIVE POWER Converted to other useful form of energy – heat, light, sound, etc Power charged by TNB Power that is being transferred back and forth between load and source Associated with L or C – energy storage element – no losses Is not charged by TNB Inductive load: Q positive, Capacitive load: Q negative

9 9 Power for a resistor p = Voltage and current are in phase, p = P = average power = Q = reactive power = 0

10 10 Power for an inductor p = Voltage leads current by 90 o, P = average power = 0 p = Q = reactive power = v i

11 11 Power for a capacitor p = Voltage lags current by 90 o, P = average power = 0 p = Q = reactive power = v i

12 12 Apparent Power and Power Factor Consider v(t) = V m cos ( t + v ) and i(t) = I m cos( t + i ) We have seen, = APPARENT POWER Is known as the APPARENT POWER VA

13 13 Apparent Power and Power Factor We can now write, The term POWER FACTOR is known as the POWER FACTOR lagging pf For inductive load, ( v i ) is positive current lags voltage lagging pf leading pf For capacitive load, ( v i ) is negative current leads voltage leading pf

14 14 Apparent Power and Power Factor

15 15 Apparent Power and Power Factor I rms = o V rms = o Load + Source + V L Active power absorbed by the load is 250(5) cos (50 o )= 1250(0.6428) = watt Power factor of the load = cos (10-(-40)) = cos (50 o ) = Apparent power, S = 1250 VA Reactive power absorbed by load is 250(5) sin (50 o )= 1250(0.6428) = var (lagging)

16 16 Complex Power Defined as: (VA) Where, and If we let and (VA)

17 17 Complex Power (VA) Where,

18 18 Complex Power The complex power contains all information about the load I rms = o V rms = o Load + Source + V L We have seen before: Active power, P = watt Apparent power, S = 1250 VA Reactive power, Q = var watt var S S = ( j957.56) VA S = o VA |S| = S = Apparent power S = o (5 -40 o ) VA = 1250 VA With complex power, 50 o

19 19 Complex Power Other useful forms of complex power We know thatPQ

20 20 Complex Power Other useful forms of complex power We know that For a pure resistive element,For a pure reactive element,

21 21 Conservation of AC Power Complex, real, and reactive powers of the sources equal the respective sums of the complex, real and reactive powers of the individual loads

22 22 Conservation of AC Power Complex, real, and reactive powers of the sources equal the respective sums of the complex, real and reactive powers of the individual loads S s = P s +jQ s = (P 1 + P 2 + P 3 ) + j (Q 1 + Q 2 + Q 3 ) But

23 23 Maximum Average Power Transfer Max power transfer in DC circuit can be applied to AC circuit analysis ZLZL + V I Z Th V Th + AC linear circuit average What is the value of Z L so that maximum average power is transferred to it?

24 24 Maximum Average Power Transfer ZLZL + V I Z Th V Th + average What is the value of Z L so that maximum average power is transferred to it?

25 25 Maximum Average Power Transfer ZLZL + V I Z Th V Th + average What is the value of Z L so that maximum average power is transferred to it? Z Th = R Th + jX Th Z L = R L + jX L P max when and

26 26 Maximum Average Power Transfer ZLZL + V I Z Th V Th + average What is the value of Z L so that maximum average power is transferred to it? P max when and X L = X Th, R L = R Th


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