This document discusses concepts of power in single-phase and three-phase AC circuits. It begins by explaining real and reactive power, power factor, and the power triangle in single-phase circuits. It then introduces three-phase circuits, describing how they consist of three single-phase voltages 120 degrees out of phase. Wye and delta connections are discussed, along with how they affect phase and line voltages and currents. One-line diagrams are introduced as a simplified way to represent balanced three-phase systems. Equations for real, reactive and apparent power in three-phase circuits are provided.

1. BAB 1. KONSEP DASAR
1.1 Daya Listrik pada Rangkaian 1
Fasa
1.2 Rangkaian Tiga Fasa
1.3 Daya Listrik pada Rangkaian 3
Fasa

2. BAB 1. 1
 Daya Listrik pada Rangkaian 1 Fasa
Real (Active) and Reactive Power
Real (Active) and Reactive Loads
Power Triangle
Real (Active) and Reactive Power Flow

3. Sine Wave Basics (Review)
 RMS – a method for computing the effective value of a time-varying e-m
wave, equivalent to the energy under the area of the voltage waveform.

4. Real, Reactive and Apparent
Power in AC Circuits
 in DC circuits: P=VI but…= in AC circuits: average
power supplied to the load will be affected by the phase
angle  between the voltage and the current.
 If load is inductive the phase angle (also called
impedance angle) is positive; (i.e, phase angle of
current will lag the phase angle of the voltage) and the
load will consume both real and positive reactive power
 If the load is capacitive the impedance angle will be
negative (the phase angle of the current will lead the
phase angle of the voltage) and the load will consume
real power and supply reactive power.

5. Resistive and Reactive Loads

6. Impedance Angle, Current Angle
& Power
 Inductive loads  positive impedance angle
current angle lags voltage angle
 Capacitive loads  negative impedance angle
current angle leads voltage angle
 Both types of loads consume real power
 One (inductive) consumes reactive as well while
the other (capacitive) supplies reactive power

7. Tegangan, Arus dan Daya
 First term is average or Real power (P)
 Second term is power transferred back and forth
between source and load (Reactive power Q)

8. More equations
 Real term averages to P = VI cos (+)
 Reactive term Q = VI sin (+ for inductive load,
- for capacitive load)
 Reactive power is the power that is first stored and then released
in the magnetic field of an inductor or in the electric field of a capacitor
 Apparent Power (S) is just = VI

9. Tegangan, Arus dan Daya sbg Fungsi Waktu

10. Tegangan, Arus (sefasa) dan Daya sbg Fungsi
Waktu

11. Tegangan, Arus (lag 90°) dan Daya sbg Fungsi
Waktu

12. Loads with Constant Impedance
 V = IZ
Substituting…
 P = I2Z cos 
 Q = I2Z sin 
 S= I2Z
 Since… Z = R + jX = Z cos  + jZ sin 
 P = I2R and Q = I2X

13. Review V, I, Z
 If load is inductive then the Phase Angle
(Impedance Angle Z) is positive, If phase
angle is positive, the phase angle of the current
flowing through the load will lag the voltage
phase angle across the load by the impedance
angle Z.

14. Complex Power
 S = P + jQ
 S = VI cos + j VI sin
S = VI (cos + j sin)
 S = VI ej
 S = VI
I = I- dan V = V0o)
S = VI*
 Since S=√(P2 + Q2)
Rangk. Induktif
I-

V0°
S
P
Cos 


15. Complex Power and Key
Relationship of Phase Angle to V&I
 S = P + jQ
 S = VI* (complex conjugate operator)
 If V = V30o and I = I15o
THEN….. COMPLEX POWER SUPPLIED TO
LOAD = S = (V30o)(I-15o) = VI (30o-15o )
= VI cos(15o ) + jVI sin(15o )
 NOTE: Since Phase Angle  = v - i
S = VI cos() + jVI sin() = P + jQ

16. The Power Triangle

17. Aliran Daya Aktif


 0
V
V
BILA SEPHASE DENGAN , BERARTI
DAYA LISTRIK DIBANGKITKAN (SUMBER
ADALAH GENERATOR) DAN MENGALIR MENUJU
SISTEM (ARUS KELUAR DARI TERMINAL
POSITIP)
P = Re (VI*) MEMPUNYAI TANDA POSITIP.



 I
I

cos
I

V
I

cos
I V

18. Aliran Daya Aktif



 I
I
BILA MEMPUNYAI BEDA PHASE 180°
TERHADAP , BERARTI DAYA LISTRIK DISERAP
(SUMBER ADALAH MOTOR), DAN ARUS MENUJU
TERMINAL POSITIP DARI SUMBER.
P = Re (VI*) MEMPUNYAI TANDA NEGATIP.


 0
V
V

cos
I
V
I


cos
I
V

19. Aliran Daya Reaktif


 0
V
V
DAYA REAKTIF SEBESAR I2 XL (DENGAN
TANDA POSITIP) DIBERIKAN PADA INDUKTANSI
ATAU INDUKTANSI MENYERAP DAYA REAKTIF.
ARUS TERBELAKANG (LAGGING) 90°
TERHADAP
Q = Im (VI*) MEMPUNYAI TANDA POSITIF



 90
I
I
V
I

90
L
X

V
I

20. Aliran Daya Reaktif



 I
I
DAYA REAKTIF SEBESAR I2 XC (DENGAN TANDA
NEGATIF) DIBERIKAN PADA KAPASITOR ATAU
SUMBER MENERIMA DAYA REAKTIF DARI
KAPASITOR.
ARUS MENDAHULUI (LEADING) 90° TERHADAP
Q = Im (VI*) MEMPUNYAI TANDA NEGATIF.


 0
V
V V
I

90
I V

21. Contoh soal 1
 V = 1200o V
 Z = 20-30o 
 Calculate current I, Power Factor (is it leading or
lagging), real, reactive, apparent and complex
power supplied to the load

22. BAB 1.2
 Rangkaian Tiga Fasa (3-)
What are they?
Benefits of 3- Systems
Wye (Y) and delta () connections
One line diagram (of a balanced 3 phase
system)

23. What does Three-Phase mean?
 A 3- circuit is a 3- AC-generation system
serving a 3- AC load
 3 - 1- AC generators with equal voltage but
phase angle differing from the others by 120o

25. Balanced 3 phase systems
SISTEM TEGANGAN TIGA FASA YANG
SEIMBANG TERDIRI DARI TEGANGAN SATU
FASA YANG MEMPUNYAI MAGNITUDE DAN
FREKWENSI YANG SAMA TETAPI ANTARA
SATU DENGAN LAINNYA MEMPUNYAI BEDA
FASA SEBESAR 120°.

26. Tegangan & Arus 3 Fasa
 Balanced
Same amplitude
120° phase diff.
 Phase shift
ia lags ua angle j
 Phase sequence
abc

27. Fasor Tegangan/Arus
 Urutan Fasa abc
 Seimbang: Ia+ Ib+ Ic=0
 No return current
Losses reduced
No return conductor
a
b
c

28. Benefits of 3- circuits
 GENERATION SIDE:
 More power out
 Constant power out (vs. pulsating sinusoidal)
 ………
 LOAD SIDE:
 Induction Motors (no starters required)

29. Common Neutral
 A 3- circuit can have the negative ends of the
3- generators connected to the negative ends
of the 3- AC loads and one common neutral
wire can complete the system
 If the three loads are equal (or balanced) what
will the return current be in the common neutral?

30. If loads are equal….
 the return current can be calculated to be…
 ZERO!
 Neutral is actually unnecessary in a balanced
three-phase system (but is provided since
circumstances may change)

31. Wye (Y) and delta () connection

32. Delta ()

33. Hubungan Y
n : TITIK NETRAL
Vab=Vbc=Vca = VL : TEGANGAN ANTAR
FASA
Van=Vbn=Vcn = Vp : TEGANGAN FASA

34. Hubungan Arus dan Tegangan
 Bila IL adalah Arus Saluran dan Ip adalah Arus
Fasa, maka berlaku :
 IL = Ip
 VL = √3 Vp
 Dimana VL, Vp, IL , Ip adalah harga efektif dari
tegangan dan arus

35. Diagram Fasor (Hub. Y)
Sumber = Beban
Vab
30o
o
p
cn 120
V
V 

o
p
an 0
V
V 

o
p
bn V
V 120




36. Hubungan ∆
TITIK NETRAL tidak ada
Iab=Ibc=Ica = Ip : ARUS FASA
Ia=Ib=Ic = IL : ARUS SALURAN

37. Hubungan Arus dan Tegangan
 Bila VL adalah Tegangan Antar Fasa dan Vp
adalah Tegangan Fasa, maka berlaku :
 VL = Vp
 IL = √3 Ip
 Dimana VL, Vp, IL , Ip adalah harga efektif
dari tegangan dan arus

38. Diagram Fasor (Hub. ∆)
o
p
bc I
I 120



o
p
ca I
I 120


Sumber ≠ Beban
o
p
ab I
I 0


b
I
o
30
o
p
bc I
I 120



o
p
ca I
I 120


o
p
ab I
I 0


a
I
o
30

39. One-Line Diagram
(of a BALANCED 3 PHASE SYSTEM)
 since all phases are the same (except for phase
angle) and loads are typically balanced only one
of the phases is usually shown on an electrical
diagram… it is called a one-line diagram
 Typically include all major components of the
system (generators, transformers, transmission
lines, loads, other [regulators, swithes])

40. Daya pada Rangkaian 3 Fasa
=uiR
=uiL

41. Daya 3 Fasa

42. Daya 3 Fasa
 ptotal(t)= pa(t)+ pb(t)+ pc(t)
 Daya 3 fasa = Jumlah Daya tiap-tiap Fasa
 ptotal(t)=constant
If voltages and currents balanced
cosj need not be zero
Constant ptotal(t) => constant torque

43. p
p
p
p
p
p
Sin
I
V
Q
Cos
I
V
P
j
j
j
j
3
3
3
3


L
p
L
p I
I
V
V 
 ;
3
3
; L
p
L
p
I
I
V
V 

Untuk Sistem 3 fasa seimbang
φp adalah sudut antara
Arus Fasa (Lagging) dan
Tegangan Fasa
Hubungan Y
Hubungan ∆

44. Rumus Daya 3 Fasa
p
L
L
p
L
L
Sin
I
V
Q
Cos
I
V
P
j
j
j
j
3
3
3
3


L
L I
V
Q
P
S
3
2
2



Watt
Var
VA