EET103 TEKNOLOGI ELEKTRIK SISTEM SATU FASA EET103 TEKNOLOGI ELEKTRIK

SISTEM SATU FASA Pengenalan dan ciri-ciri sistem satu fasa Kebaikan dan keburukan sistem satu fasa Pengiraan voltan, arus dan kuasa

PENGENALAN DAN CIRI-CIRI SISTEM SATU FASA ALTERNATING CURRENT: a current or voltage varies periodically in magnitude and direction

PERBEZAAN AC DAN DC Difference between DC and AC: DC: a direct flow of electrons through a conductor such as a metal wire. A battery or DC generator usually provides a source of electrons and the potential or voltage between the positive (+) and negative (-) terminals.

AC (Alternating Current): a back-and-forth movement of electrons in a wire. When the force of a negative (-) charge is at one end of a wire and a positive (+) potential is at the other end, the electrons in the wire will move away from the (-) charge, just like in DC electricity. But if the charges at the ends of the wires are suddenly switched, the electrons will reverse their direction.

AC voltage (1 cycle):

Mathematics of AC voltages An AC voltage v(t) can be described mathematically as a function of time by the following equation: where A is the amplitude in volts (also called the peak voltage), ω is the angular frequency in radians per second t is the time in seconds

Since angular frequency is of more interest to mathematicians than to engineers, this is commonly rewritten as: Where f is the frequency in hertz (Hz).

AC voltage:

Amplitude is the maximum voltage reached by the signal Amplitude is the maximum voltage reached by the signal. It is measured in volts, V. Peak voltage (Vp) is another name for amplitude. Peak-peak voltage (Vp-p) is twice the peak voltage (amplitude). When reading an oscilloscope trace it is usual to measure peak-peak voltage.

RMS (effective) value: The root-mean-square (RMS) value of an alternating current is the steady direct current which converts electrical energy to other forms of energy in a given resistance at the same rate as the alternating current (AC). In power distribution work the AC voltage is nearly always given in as a root-mean-square (rms) value, written Vrms. For a sinusoidal voltage:

Vrms = 0.707 × Vpeak   and   Vpeak = 1.414 × Vrms

Frequency The number of complete cycles of alternating current or voltage completed each second Frequency is always measured and expressed in hertz (Hz).

Period An individual cycle of any sine wave represents a definite amount of TIME. The time required to complete one cycle of a waveform is called the PERIOD of the wave. The relationship between Period (T) in seconds and frequency (f) in Hz:

Frequency measurement:

Wavelength The time it takes for a sine wave to complete one cycle is defined as the period of the waveform. The distance traveled by the sine wave during this period is referred to as WAVELENGTH.

Wavelength measurement:

Alternating current values: PEAK AND PEAK-TO-PEAK VALUES:

Contoh (1) Rajah berikut menunjukkan satu kitar gelombang arus sinus. Berikan persamaan bagi arus tersebut sebagai fungsi masa. t (ms) i (mA) 170 -170 20 10

Penyelesaian: Persamaan umum bagi gelombang sinus ialah i(t) = Im sint Dari rajah gelombang diketahui; Im = 170 mA dan T = 20 ms = 0.02 s

Maka, frekuensi dapat dikira seperti berikut: f = 1/T = 1/0.02 = 50 Hz Seterusnya persamaan arus menjadi, i(t) = Imsint = 170 sin(2ft) = 170 sin(100t) mA

Contoh (2) Satu voltan ulang-alik bentuk sin mempunyai frekuensi 2500 Hz dan nilai puncak 15 V. Lukiskan bentuk satu kitar gelombang voltan tersebut.

Penyelesaian Dari soalan, diketahui nilai-nilai berikut: Vm = 15 V dan T = 0.4 ms Rajah umum gelombang sinus adalah seperti berikut: t (ms) v (V) 15 -15 0.4 0.2

Contoh (3) Satu voltan ulang-alik sinus diberikan oleh persamaan: v(t) = 156kos(800t) V Lukiskan rajah satu kitar gelombang voltan tersebut.

Penyelesaian: Diberi, v(t) = Vm kos(t) = 156 kos(800t) volt Maka, nilai puncak voltan, Vm = 156  = 2f = 800 f = 400 Tempoh bagi gelombang ini ialah; T = 1/f = 1/400 = 2.5 ms

Gambarajah gelombang voltan: v (V) 156 -156 0.625 1.25 2.5 t (ms) 1.875

INSTANTANEOUS VALUE The INSTANTANEOUS value of an alternating voltage or current is the value of voltage or current at one particular instant There are actually an infinite number of instantaneous values between zero and the peak value.

AVERAGE VALUE The AVERAGE value of an alternating current or voltage is the average of ALL the INSTANTANEOUS values during ONE alternation.

Effective and average value

Phase angle (sudut fasa): Apabila sesuatu gelombang sinus tidak melepasi nilai kosong pada t=0, maka persamaan gelombang tersebut mempunyai sudut fasa yang perlu dipertimbangkan. Sudut fasa menunjukkan ANJAKAN sesuatu gelombang dari sifar. Gelombang sinus boleh bermula dari apa-apa nilai seperti berikut. Ia tidak semestinya bermula dari sifar (atau dari nilai puncak bagi fungsi kos).

Persamaan gelombang berikut: ao adalah sudut fasa (phase angle) y = Ymsin(x + a) ao adalah sudut fasa (phase angle) x () 90 180 270 360 Ym -Ym a

Sine Waves In Phase (sefasa) When two sine waves are precisely in step with one another, they are said to be IN PHASE. To be in phase, the two sine waves must go through their maximum and minimum points at the same time and in the same direction.

Voltage and current are in phase

Sine Waves Out Of Phase (tidak sefasa) Voltage wave E1 which is considered to start at 0° (time one). As voltage wave E1 reaches its positive peak, voltage wave E2 starts its rise (time two). Since these voltage waves do not go through their maximum and minimum points at the same instant of time, a PHASE DIFFERENCE exists between the two waves. The two waves are said to be OUT OF PHASE.

Phase difference is 90o

GELOMBANG TIDAK SEFASA Dua gelombang sinus yang tidak sefasa boleh diwakilkan dengan persamaan: v(t) = Vm kost ; i(t) = Im kos(t + ) Arus i(t) MENDAHULU (leading) voltan v(t) dengan sudut . Dalam sebutan masa, arus mendahului voltan dengan tempoh (T/360) saat. Boleh juga disebut voltan MENGEKOR (lagging) arus dengan sudut 

Dua Gelombang Tidak Sefasa: Θ is phase difference v, i Vm Im -Vm -Im Gelombang V mencapai nilai puncak di t2 t  T Gelombang i mencapai nilai puncak di t1 v i

CONTOH (4) Lukiskan satu kitar gelombang arus sinus yang diberikan oleh persamaan i(t) = 70sin(8000t + 0.943 rad) mA. Tandakan nilai-nilai kritikal.

PENYELESAIAN Bentuk am gelombang arus ialah: i(t) = Im sin(t + ) = 70 sin(8000t + 0.943 rad) Dari persamaan diatas, nilai-nilai kritikal ialah: Im = 70;  = 2f = 8000;

f = 4000 Hz = 4 kHz; Maka, T = 1/f = 1/4000 = 0.25 ms; Dan,  = 0.943 rad = 54

Rajah gelombang sinus bagi arus: i (mA) t (ms) 70 -70 57 54 0.25 0.125

SISTEM SATU FASA Pengenalan dan ciri-ciri sistem satu fasa Kebaikan dan keburukan sistem satu fasa Pengiraan voltan, arus dan kuasa

KEBAIKAN DAN KEBURUKAN SISTEM SATU FASA Direct current has several disadvantages compared to alternating current. Direct current must be generated at the voltage level required by the load. Alternating current, however, can be generated at a high level and stepped down at the consumer end (through the use of a transformer) to whatever voltage level is required by the load.

The major advantage that AC electricity has over DC is that AC voltages can be transformed to higher or lower voltages. This means that the high voltages used to send electricity over great distances from the power station could be reduced to a safer voltage for use in the house. This is done by the use of a transformer. This device uses properties of AC electromagnets to change the voltages. It is easy to convert AC to DC but expensive to convert DC to AC.

SISTEM SATU FASA Pengenalan dan ciri-ciri sistem satu fasa Kebaikan dan keburukan sistem satu fasa Pengiraan voltan, arus dan kuasa

Z= Z  1. POLAR FORM Z :magnitude of Z  : angle of Z COMPLEX NUMBER 1. POLAR FORM Z= Z  Z :magnitude of Z  : angle of Z

Z = R + jX 2. RECTANGULAR FORM R: real value of Z X: imaginary value of Z j : operator valued √-1

3. EXPONENTIAL FORM Z = rej r : magnitude : angle

RECTANGULAR FORM TO POLAR FORM

POLAR FORM TO RECTANGULAR FORM

COMPLEX NUMBER ALGEBRA OPERATION To ADD two number: Transform to Rectangular To MULTIPLY two number: Transform to Polar To SUBTRACT two number:

SINUSOID-PHASOR TRANSFORMATION Time domain representation Frequency domain representation

Ohm’s Law in AC circuit

RESISTOR IN AC IN FREQUENCY DOMAIN:

V and I waveform for resistor : v, i v i t IN PHASE NO PHASE DIFFERENCE BETWEEN VOLTAGE AND CURRENT

INDUCTOR IN TIME DOMAIN: IN FREQUENCY DOMAIN:

GELOMBANG LITAR L ARUS MENGEKOR VOLTAN (ELI) v, i v i t 90º BEZA FASA SEBANYAK 90º = (1/4)T = 1/4f

KAPASITOR IN TIME DOMAIN: IN FREQUENCY DOMAIN:

GELOMBANG LITAR C v i t v, i Arus mendulu voltan sebanyak 90° (ICE)

GELOMBANG v-i BAGI R,L,C v, i v i t v, i v i t v, i v i t 90º V,I SEFASA v, i v i t 90º I MENGEKOR V SBYK 90º v i t v, i I MENDAHULU V SBYK 90º

Penentuan Mendulu/Mengekor

ARUS MENGEKOR VOLTAN Jika gelombang voltan mpy sudut fasa positif Dengan menganggap gelombang Arus sbg RUJUKAN: Jika gelombang voltan mpy sudut fasa positif Terletak disebelah kiri gelombang arus Gelombang voltan mendulu gelombang arus.

ARUS MENDULU VOLTAN Jika gelombang voltan mpy sudut fasa negatif Terletak disebelah kanan gelombang arus gelombang voltan mengekor gelombang arus.

REACTANCE AND IMPEDANCE AC CIRCUIT ELEMENT REACTANCE AND IMPEDANCE

REACTANCE All elements in AC circuit (resistor, inductor and capacitor) should have same unit before you do the analysis.

Inductor value (in henry) and capasitor value (in farad) must be transform into ohms (). Inductance and capacitance value in ohms are known as reactance which is inductive reactance for inductor, and capacitive reactance for capacitor.

Formula to get XL dan Xc: Symbol for inductive reactance is XL and for capacitive reactance is Xc.. Formula to get XL dan Xc: HAFAL!

CAPACITOR Series capacitors: Parallel capacitors:

INDUCTOR Series inductors: Parallel inductors:

IMPEDANCE Impedance is a element connecting the resistance, inductive reactance and capacitive reactance in time domain.

Impedance is represent by Z symbol: (ohms)  is angle between voltage and current Impedance is complex number because of magnitude and angle

Resistance impedance, ZR:

Inductive impedance, ZL

Capacitive impedance, Zc

KIRCHHOFF LAW IN AC ANALYSIS Transform circuit into frequency domain using these equation. Use KVL and KCL…

R-L CIRCUIT IN FREQUENCY DOMAIN + VL - R jL V = Vm + VR - I

CONTOH (1) : LITAR RL Given Vs = 40 cos (2000t - 60º). Find, Phasor voltage across R; Phasor voltage across L; Current, i(t) expression

Step 1: Circuit in frequency domain V s = 40 Ð -60 ° R=1000 j w L j1570.8 + V R - +

Step 2: Find circuit impedance

Step 3: Calculate current

Phasor current is;

(a) Phasor voltage across R,

(b) Phasor voltage across L,

Current, i(t) expression: »» Transform I in time domain

CONTOH (2) : LITAR RC Given VC = 60 cos(1000t - 33º). Find, Phasor current, I Phasor voltage across R Voltage source, vs(t).

Step 1: Circuit in frequency domain

Step 2: Circuit impedance (Z)

Step 3: Find I, VR,VS (a) Phasor current; (b) Phasor voltage across R;

(c) Source phasor voltage; Transform V into time domain;

IMPEDANCE TRIANGLE

IMPEDANCE TRIANGLE We also can get impedance by using impedance triangle: Galangan,Z  Reaktan, X  Perintang, R

Dari segitiga galangan; Ini bermakna, dengan mengetahui Galangan (Z), kita boleh juga mengetahui nilai perintang (R) dan Reaktan (X).

HUBUNGAN Z, R DAN X Hubungan Z dan R; Hubungan Z dan X;

AC Power Calculation

POWER IN AC CIRCUIT

INSTANTENAOUS POWER (KUASA SEKETIKA) Kuasa seketika yg diserap oleh setiap peranti elektrik adalah hasil darab Voltan seketika yg merintanginya dan Arus seketika yang melaluinya.

Dimana, Vm dan Im adalah Nilai Puncak (peak) bagi voltan dan arus. RMS VALUE Semua nilai Voltan dan Arus dalam pengiraan kuasa adalah menggunakan nilai RMS (root mean square). Iaitu: Dimana, Vm dan Im adalah Nilai Puncak (peak) bagi voltan dan arus.

Kuasa purata atau kuasa sebenar ditakrifkan sebagai: 1. AVERAGE POWER (KUASA PURATA) Kuasa purata atau kuasa sebenar ditakrifkan sebagai: Unit bagi kuasa purata ialah Watt.

Kuasa purata pada Perintang boleh juga diwakili oleh persamaan berikut: Kita tahu V=IR, maka kuasa purata turut diwakili oleh:

Kuasa purata ialah kuasa berguna yg. disebabkan oleh elemen Perintang. Dengan itu, kuasa purata bagi beban reaktif (L atau C) adalah Kosong.  ialah Sudut antara Voltan dan Arus, ATAU dikenali juga sebagai Sudut Galangan,Z.

Nilai  diperolehi seperti berikut:

CONTOH (1) Voltan sinus mempunyai amplitud maksimum 625 Volt dikenakan pada terminal yg mempunyai Perintang 50. Dapatkan kuasa purata yang dihantar kepada perintang tersebut.

PENYELESAIAN Nilai rms: Kuasa purata bagi perintang diperolehi:

Kuasa Reaktif ditakrifkan sebagai: 2. REACTIVE POWER (KUASA REAKTIF) Kuasa Reaktif ditakrifkan sebagai:

Kuasa reaktif juga merupakan kuasa yg disimpan oleh elemen reaktif iaitu L atau C. Maka, kuasa reaktif boleh juga dicari dengan:

CONTOH (2) Diberi v= 100 kos (t + 15º) dan i= 4 sin (t - 15º), Pada terminal rangkaian, dapatkan: Kuasa purata Kuasa reaktif i + v - Rangkaian

PENYELESAIAN Tukarkan persamaan arus, i dalam bentuk kos: i= 4 kos (t - 105º) Dari persamaan Kuasa Purata: Maka,

Dari pers. Kuasa reaktif: Maka,

Nilai kuasa purata, P= -100 W: Bermaksud kuasa purata telah dihantar balik dari beban kepada terminal bekalan. Nilai kuasa reaktif, Q=173.21 Var: Bermaksud kuasa reaktif telah diserap oleh beban.

AC POWER FORMULA AC power calculation can be done by using these formula: