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

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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.

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.

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

Impedance Angle, Current Angle & Power Inductive loads positive impedance angle current angle lags voltage angle Capacitive loads negative impedance angle

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 = I 2 Z cos Q = I 2 Z sin S= I 2 Z Since Z = R + jx = Z cos + jz sin P = I 2 R and Q = I 2 X

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 e j S = VI I = I - dan V = V 0 o ) S = VI* Since S= (P 2 + Q 2 ) Cos P S I - V 0 Rangk. Induktif

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

16 The Power Triangle

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

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

19 Aliran Daya Reaktif V V 0 I I 90 X L I 90 V DAYA REAKTIF SEBESAR I 2 X L (DENGAN TANDA POSITIP) DIBERIKAN PADA INDUKTANSI ATAU INDUKTANSI MENYERAP DAYA REAKTIF. ARUS I TERBELAKANG (LAGGING) 90 TERHADAP V Q = Im (VI*) MEMPUNYAI TANDA POSITIF

20 Aliran Daya Reaktif I I V V 0 I 90 V DAYA REAKTIF SEBESAR I 2 X C (DENGAN TANDA NEGATIF) DIBERIKAN PADA KAPASITOR ATAU SUMBER MENERIMA DAYA REAKTIF DARI KAPASITOR. ARUS MENDAHULUI (LEADING) 90 TERHADAP I Q = Im (VI*) MEMPUNYAI TANDA NEGATIF. V

21 Contoh soal 1 V = o V Z = o 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 120 o

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 i a lags u a angle j Phase sequence abc

27 Fasor Tegangan/Arus c a Urutan Fasa abc Seimbang: I a + I b + I c =0 No return current Losses reduced No return conductor b

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 = V L : TEGANGAN ANTAR FASA Van=Vbn=Vcn = V p : TEGANGAN FASA

34 Hubungan Arus dan Tegangan Bila I L adalah Arus Saluran dan I p adalah Arus Fasa, maka berlaku : I L = I p V L = 3 V p Dimana V L, V p, I L, I p adalah harga efektif dari tegangan dan arus

35 Diagram Fasor (Hub. Y) V o cn Vp 120 V ab 30 o V o an Vp 0 V 120 bn V p o Sumber = Beban

36 Hubungan TITIK NETRAL tidak ada Iab=Ibc=Ica = I p : ARUS FASA Ia=Ib=Ic = I L : ARUS SALURAN

37 Hubungan Arus dan Tegangan Bila V L adalah Tegangan Antar Fasa dan V p adalah Tegangan Fasa, maka berlaku : V L = V p I L = 3 I p Dimana VL, Vp, IL, Ip adalah harga efektif dari tegangan dan arus

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

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 =ui R =ui L

41 Daya 3 Fasa

42 Daya 3 Fasa p total (t)= p a (t)+ p b (t)+ p c (t) Daya 3 fasa = Jumlah Daya tiap-tiap Fasa p total (t)=constant If voltages and currents balanced cosj need not be zero Constant p total (t) => constant torque

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

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

45 TUGAS PELAJARI CONTOH SOAL (HAND OUT)

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