ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL ELECTRIC CIRCUITS EIGHTH EDITION

SINUSOIDAL STEADY – STATE POWER CALCULATIONS CHAPTER 10 SINUSOIDAL STEADY – STATE POWER CALCULATIONS © 2008 Pearson Education

Understand the following ac power concepts & how to calculate them in a circuit. instanteneous power Average(real) power Reactive power Complex power Power factor Understand the condition to deliver max. average power to a load & then how to calculate the load impedance. 3. In ac circuits, Understand how to calculate ac power with linear transformer and ideal transformer.

CONTENTS 10.1 Instantaneous Power 10.2 Average and Reactive Power 10.3 The rms Value and Power Calculations 10.4 Complex Power 10.5 Power Calculations 10.6 Maximum Power Transfer © 2008 Pearson Education

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10.1 Instantaneous Power The positive sign is used when the reference direction for the current is from the positive to the negative reference polarity of the voltage. The frequency of the instantaneous power is twice the frequency of the voltage (or current). © 2008 Pearson Education

10.1 Instantaneous Power Instantaneous power, voltage, and current versus ωt for steady-state sinusoidal operation © 2008 Pearson Education

10.2 Average and Reactive Power Average Power Average power is the average value of the instantaneous power over one period. It is the power converted from electric to non-electric form and vice versa. © 2008 Pearson Education

Note:

10.2 Average and Reactive Power This conversion is the reason that average power is also referred to as real power. Average power, with the passive sign convention, is expressed as © 2008 Pearson Education

10.2 Average and Reactive Power Reactive power is the electric power exchanged between the magnetic field of an inductor and the source that drives it or between the electric field of a capacitor and the source that drives it. © 2008 Pearson Education

10.2 Average and Reactive Power Reactive power is never converted to nonelectric power. Reactive power, with the passive sign convention, is expressed as © 2008 Pearson Education

Note:

Note:

Note:

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10.2 Average and Reactive Power Power Factor Power factor is the cosine of the phase angle between the voltage and the current: © 2008 Pearson Education

10.2 Average and Reactive Power The reactive factor is the sine of the phase angle between the voltage and the current: © 2008 Pearson Education

10.3 The rms Value and Power Calculations A sinusoidal voltage applied to the terminals of a resistor Average power delivered to the resistor © 2008 Pearson Education

10.3 The rms Value and Power Calculations The average power delivered to R is simply the rms value of the voltage squared divided by R. If the resistor is carrying a sinusoidal current, the average power delivered to the resistor is: © 2008 Pearson Education

rms value = effective value.

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a) max. amplitude 625 V vtg. Is applied to 50 Ω . Average power at this resistor? b) Repeat (a) by 1st finding IR. Sol.: rms value of vtg. = 625/√2 ≈ 441.94 V P = V2rms/R b) max. amplitude of ct. = 625/50 = 12.5 A rms value of ct. = 12.5/ /√2 ≈ 8.84 A Hence,

10.4 Complex Power Complex power is the complex sum of real power and reactive power. | S | = apparent power Q = reactive power θ P = average power A power triangle © 2008 Pearson Education

10.4 Complex Power Quantity Units Complex power volt-amps Average power watts Reactive power var Three power quantities and their units © 2008 Pearson Education

10.4 Complex Power Apparent Power is the magnitude of complex power. © 2008 Pearson Education

Remind: > 0 Lagging pf: ct. lags vtg. Hence inductive load < 0 Leading pf: ct. leads vtg. Hence capacitive load

PF lagging → inductive → reactive power +

Electric facilities( that is, refrigerators, fans, air conditioners, fluorescent lighting fixtures, & washing machines) & most industrial loads operate at a lagging power factor. Correction of power factor of these loads using capacitor. This method is often used for large industrial load.

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See:

10.5 Power Calculations(abbreviation.) The phasor voltage and current associated with a pair of terminals © 2008 Pearson Education

Load impedance: 39 + j26 Line impedance: 1 + j4 Effective(or rms) value of S. : 250 V

load1: lead pf 0.8, 8 kW av. Power absorbed load2: lag pf 0.6, 20 kVA absorbed c) S. freq.: 60 Hz . value of capacitor with pf = 1 if placed in parallel with 2 loads? c) S. freq.: 60 Hz

appearance power supplied to load, magnitude of current, av. power :

Place capacitor with 10 KVAR in parallel with existing load Place capacitor with 10 KVAR in parallel with existing load. Then pf = 1(그림10.15c) So capacitive reactance is

a) Power supplied to each impedance? b) Power of each source? c) Delivered av. power = absorbed av. power Delivered reactive power = absorbed reactive power

Reactive power delivered to (12 – j16)Ω

see: absorbed av. power:1950 W , delivered reactive power3900 VAR b) Complex power of independent S. see: absorbed av. power:1950 W , delivered reactive power3900 VAR Complex power of dependent S. 주: 5850 W 평균전력 공급, 5070 VAR 무효전력 공급 see: delivered av. Power:5850 W , delivered reactive power 5070 VAR

10.6 Maximum Power Transfer A circuit describing maximum power transfer © 2008 Pearson Education

10.6 Maximum Power Transfer Condition for maximum average power transfer The circuit with the network replaced by its Thévenin equivalent © 2008 Pearson Education

Proof: Let EE141

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a) ZL value to deliver max. power to ZL? b) av. power at a)? Sol.: a) Thevenin eqvalent cit. seen to a, b terminal

b) in Fig.

a) ZL to be able to max. power & then max. power(mW) b) load: 0 ~ 4000 Ω reactance: 0 ~ - 2000 Ω RL & XL to be able to transfer most av. power to load & then max. av. power? See:

See: P = I2eff RL See: P(no restriction) > P(restriction)

ZL phase is -36.87o. Magnitude of ZL changes until av. power becomes biggest under given restriction. Specfy ZL in rectangular form. Av. Power to delivered to ZL ? a) In case magnitude of ZL be varied but its phase not, The greatest power is transferred to load when magnitude of ZL is set equal to magnitude of ZTH ; that is, Therefore,

See: No restrictions on ZL

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Adjust RL until max. av. power is be delivered to RL. a) RL? b) max. av. power to be delivered to RL? sol.: a) Thevenin equivalent cit. so V20 Note that Vth = - V2

Fig. is used to determine the short ckt current. Using Rearranging, Therefore, RTh = VTh/I2 =

Pmax = I2R =

제출기일을 지키지않는 레포트는 사정에서 제외함 EE141 Home work Prob. 10.1 10.4 10.5 10.6 10.14 10.16 10.18 10.25 10.29 10.36 10.37 10.41 10.44 10.47 10.52 10.57 10.61 10.63 10.65 제출기한: 다음 요일 수업시간 까지 제출기일을 지키지않는 레포트는 사정에서 제외함 제출기한: 다음 요일 수업시간 까지 제출기일을 지키지않는 레포트는 사정에서 제외함 Prob. 9.1 9.3 9.5 9.8 9.9 9.11 9.22 9.23 9.24 9.27 9.29 9.33 9.45 9.47 9.51 9.54 9.57 9.61 9.62 9.64 9.72 9.74 9.79 EE141

THE END © 2008 Pearson Education