ET201: THREE PHASE SYSTEMS (ANSWER FOR DISCUSSION EXPERIMENT 4)

(ii)       Current

Figure 1.1.4 (b) shows the current in star connection. The value of line current (I_R, I_Y , I_B ) and phase current (I_r , I_y , I_b) are the same.

     

Line current,      I_L:  I_R , I_Y , I_B

Phase current, I_PH :  I_r , I_y , I_b


So, current element in star connection:

              I_L = I_PH


Neutral current (I_N) is the sum of the three current i.e. I_R, I_Y, and I_{B ;} having same magnitude but 120^o difference in phase. Therefore mathematically, the sum of these vectors will make neutral current I_N equals zero.

       I_N = I_R + I_Y + I_B = 0 

ET201: THREE PHASE SYSTEMS (PART 4)

a)                  Three phase emf generation

Let us consider Red (R) phase taken as reference and the coil rotates clockwise as indicated in Figure 1.1.2 (c) to (e), the induced voltage (emf) waveform for R (e_R), Y(e_Y)  and B(e_B)  can be derived separately. Figure 1.1.2 (f) shows the combination of the RYB waveform; therefore it is called the three phase waveform.

Figure 1.1.2. Emf waveform; (c) R phase  (d) Y phase (e) B phase (f) Three phase

ET201: THREE PHASE SYSTEMS (PART 3)

1.1.2        Generation of three phase voltages (emf).

In a single phase AC system, alternating voltage may be generated by rotating a coil in magnetic field or by rotating a magnetic field within a stationary coil. The value of the voltage generated depends, in each case, upon the number of turns in the coil. Consider a case of a single phase alternator with one armature winding only. If the number of armature windings is increased, then it becomes polyphase alternator and it produces as many independent voltage waves as the number of windings or phases. These windings are displaced from one another by equal angles, the values of these angles being determined by the number of phases or windings. In fact, the word “polyphase” means poly(many) and phase(winding or circuit).

A three phase alternator, as the name shows, has three independent armature windings which are 120 electrical degrees apart. Hence, the voltages induced in the three windings are 120⁰ apart in time phase. In Figure 1.1.2(a) is shown a two pole, stationary-armature, rotating-field type three phase alternator. It has three armature coils RR’, YY’ and BB’ displaced 120⁰ apart from one another. Figure 1.1.2(b) is shown a pole, stationary-magnet, rotating coils type.

Figure 1.1.2. (a) Rotating-field, stationary coils   (b)Rotating- coils, stationary field

ET201: THREE PHASE SYSTEMS (PART 2)

1.1.1    Three phase system advantages

There are several reasons why three phase system is superior to single phase system for transmission and distribution of electricity;

a)   In a balanced three phase system, the conductors need be only about 75% the size of conductors for a single phase two-wire system of the same power (KVA) rating. This helps to reduce the cost because less copper (or aluminium) is needed.

b)    The power delivered by a single-phase system pulsates and falls to zero three times during each cycle. The power delivered by a three-phase circuit pulsates also, but it never falls to zero

Figure 1.1.1. Three phase power never falls to zero

a)     The horsepower rating of three phase motors and the KVA (kilo-volt-amp) rating of three phase transformers is about 150% greater than for single-phase motors or transformers with a similar frame size.

b)   The efficiency and power factor of three phase motors much better than single phase motors for the same power transferred.

c)   Three phase motors have the ability to “self-start”; caused by the phase difference between three phase coils, but not in single phase motors.

d)  Three phase transformers are lighter, more efficient and cheaper compared to single phase transformer for the same size.

e)     When connected in parallel, single phase generator present difficulties which do not occur with three phase generators.

h)  The instantaneous three phase power flow is constant.  This is advantageous for both the end user and the generator, which does not have to supply a pulsating torque.