Lecture Electric circuit theory: AC power analysis - Nguyễn Công Phương

Lecture Electric circuit theory: AC power analysis include all of the following content: Instantaneous and average power, RMS value, apparent power and power factor, complex power, power factor improvement.

Electric Circuit Theory

AC Power Analysis

Nguy ễ n Công Ph ươ ng

I Basic Elements Of Electrical Circuits

II Basic Laws

III Electrical Circuit Analysis

IV Circuit Theorems

V Active Circuits

VI Capacitor And Inductor

VII First Order Circuits

VIII.Second Order Circuits

IX Sinusoidal Steady State Analysis

X AC Power Analysis

XI Three-phase Circuits

XII Magnetically Coupled Circuits

XIII.Frequency Response

XIV.The Laplace Transform

XV Two-port Networks

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

P

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

Maximum Average Power Transfer (1)

+ –

P = I R

eq L

eq L

=

+

E I

eq Lm

Maximum Average Power Transfer (2)

eq L eq L

R P

P = I R

eq Lm

L

P R P X

Maximum Average Power Transfer (3)

0 0

Z Z For maximum average power transfer, the load impedance must

be equal to the complex conjugate of the equivalent impedance

= ×

E

Maximum Average Power Transfer (4)

R P

Maximum Average Power Transfer (5)

For maximum average power transfer, the load impedance must

be equal to the complex conjugate of the equivalent impedance

If Z L = R L ? → X L = 0

Maximum Average Power Transfer (6)

Ex 1

20

=

E − 45 V;o J = 5 60 Ao

Determine the load impedance Z2 that

maximize the average power What is

the maximum average power?

−

Z Z Z

Maximum Average Power Transfer (7)

Ex 1

20

=

E − 45 V;o J = 5 60 Ao

Determine the load impedance Z2 that

maximize the average power What is

the maximum average power?

Maximum Average Power Transfer (8)

Maximum Average Power Transfer (9)

Ex 2

Determine the load impedance Z that maximize the

average power What is the maximum average power?

1 Find the Thevenin equivalent

Maximum Average Power Transfer (10)

Ex 2

Determine the load impedance Z that maximize the

average power What is the maximum average power?

1 Find the Thevenin equivalent

Maximum Average Power Transfer (11)

Ex 2

Determine the load impedance Z that maximize the

average power What is the maximum average power?

1 Find the Thevenin equivalent

Maximum Average Power Transfer (12)

Ex 2

Determine the load impedance Z that maximize the

average power What is the maximum average power?

1 Find the Thevenin equivalent

Maximum Average Power Transfer (13)

Ex 2

Determine the load impedance Z that maximize the

average power What is the maximum average power?

1 Find the Thevenin equivalent

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

1 T eff

I i dt

T

→ = ∫

2 0

1 T eff

T

= ∫

2 0

RMS Value (2)

2

m rms

I

I =

2 0

1 1 cos 2

2

T m

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

2

m rms

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

Complex Power (2)

*

1 2

AC Power Analysis

1 Instantaneous and Average Power

2 Maximum Average Power Transfer

Power Factor Improvement (1)

C

Power Factor Improvement (2)

2

2

rms

rms C

C

Power Factor Improvement (3)