CHAPTER 5 SWITCHING ON - ASYMMETRY

5.1       SWITCHING ON - SINGLE-PHASE

When a current is switched on in a d.c. inductive circuit, it rises from zero and gradually approaches its steady value, the rate depending on the inductance and resistance of the circuit, as explained in the manual ‘Fundamentals of Electricity 1’.  The behaviour when an a.c. circuit is switched on is however quite different, and there is no time delay in the build-up of current.

 

FIGURE 5.1

SWITCHING ON - 90° LAG

Figure 5.1(a) shows the voltage in an a.c. circuit having inductance only and little resistance.  This is the condition for a 90° lag, and the current peaks occur at the same instants as the voltage zeros.  Figure 5.1(b) shows the corresponding current wave both before and after the current is switched on, which is assumed to occur at the point M at one of the voltage zeros.  The dotted wave in Figure 5.1(b) is what the current should be doing after switching on - namely lagging 90° behind the voltage.

But this would entail the current jumping suddenly from zero at point M just before the switch-on to its maximum an instant after - which it clearly cannot do.  What happens is that the current grows so that the whole current waveform moves bodily upward (in this case) by an amount equal to its amplitude, as shown in full line in Figure 5.1(b). If this

displaced wave is examined closely, it will be seen that there is no jump at the moment of switch-on (M) - it is zero immediately before and immediately after - and it also lags 90° on the voltage wave, its peaks coming opposite the voltage zeros.

It is completely asymmetrical at the instant of switching on, but it gradually regains symmetry a few cycles later; the more resistance that is present, the quicker symmetry is restored.  Where, as here, the displacement is complete and equal to the a.c. amplitude, the wave is said to be ‘100% asymmetrical’.

If, instead, the current had been switched on at the point N at one of the voltage peaks, as in Figure 5.1(c), the effect would be different.  At a voltage peak the current with a 90° lag would in any case be zero so there would be no need for any sudden change at the moment of switch-on - it would be zero both immediately before and immediately after the switching.  There would therefore be no asymmetry to compensate for a jump, and the current would start and remain symmetrical throughout; it would be ‘0% asymmetrical’.

With 100% asymmetry the current peak is about double the symmetrical peak, and this itself is √ 2 times the symmetrical rms value.  So the asymmetrical peak is 2√ 2 or 2.83 times the rms.  In practice, because the current has already started to regain symmetry by the time the first peak appears, the ‘doubling factor’ is usually taken to be 2.55.

Figures 5.1(b) and 5.1(c) are the two extreme cases with a 90° lag; switching at the instant of voltage zero and at the instant of a voltage peak.  The general case would be somewhere in between, where there would be partial asymmetry, something between 0% and 100%.

FIGURE 5.2

SWITCHING ON – GENERAL CASE (PARTIAL ASYMMETRY)

With the general case of a circuit having both inductance and resistance the power factor would be higher than zero and the current lag would be less than 90° (see Figure 5.2).  In this case the current has to jump from zero before the switch-on to a point something less than peak value immediately after.  Therefore the asymmetry to compensate for this jump is less than a full amplitude (100%), as shown in Figure 5.2.  There is then ‘partial asymmetry’, between 0% and 100%.

5.2       SWITCHING ON – 3 PHASE

All the above discussion has been about a single-phase voltage being switched onto a circuit.  However, most switching on platform and shore equipment is 3-phase.  In a 3-phase circuit the voltage phases are 120° apart so that, even if at the instant of switching one of them occurs at a voltage zero or voltage peak, the other two will not be so, and they will be at voltage points somewhere between zero and peak.  Therefore, even if one phase of current is wholly asymmetrical or wholly symmetrical, the other two will be partially asymmetrical.  This is shown in Figure 5.3 where red-phase current is 100% asymmetrical; the other two in that case will be 50% asymmetrical in the opposite direction.

FIGURE 5.3

SWITCHING ON - 3-PHASE (PF ZERO)

The problem of asymmetry on switching on is an important one in platform and shore networks, especially under conditions of sudden short-circuit.  Whatever the calculated short-circuit current is, the peak current which flows in the first cycle of short-circuit, where the power factor may be typically about 0.15, will be about 2.55 times the calculated rms current, and this could put damaging strain upon busbars and other distribution equipment unless it is allowed for in design.  Switchgear which operates very quickly - that is, within the first few cycles of a short-circuit - will have to handle and clear this excessive asymmetrical current in at least one pole, and as the instant of short-circuit would be entirely random, it might occur in any pole.  For this reason all main switchgear is given two breaking current ratings: an rms symmetrical breaking capacity and a peak asymmetrical breaking capacity, which is about 2.55 times the symmetrical; this is not usually given on the nameplate.

CHAPTER 10 QUESTIONS

10.1     QUESTIONS

1.            What do you understand by ‘active power’?  What type of circuit absorbs only active power?  What is the relationship between current and voltage in a circuit passing only active power?

2.            What do you understand by ‘reactive power’?  What is the relationship between current and voltage in a circuit passing only reactive power?  In what unit is reactive power measured?

3.           What is ‘apparent power’?  What is its relation to active and reactive power?

4.            In a 3-phase system with line-to-line voltage V_L and balanced line current I_L at a phase angle j, write down expressions for (a) active power, (b) reactive power and (c) apparent power, giving the correct units.

5.            Describe the meaning of ‘power factor’.  A single-phase circuit, supplied at 250V has a resistance of 40 ohms and an inductive reactance of 30 ohms in series.  What is (a) the power factor and (b) what active power flows?

6.            In a 250V single-phase system carrying a current of 50A at a power factor of 0.75 what is (a) the active power and (b) the reactive power?  Give the units in both cases.

7.            In a 3-phase system the line voltage is 11kV and the line current 200A at a power factor of 0.8.  What is the total active power transmitted?

8.                What is the power factor of a 50Hz single-phase circuit consisting of a 50 ohm resistor and a 0.1H inductor in series?

9.              In the circuit of Q.8 what is (a) the active power P and (b) the reactive power Q transmitted when a current of 25A is flowing?

10.             

 

In the balanced 3-phase system shown in the figure determine:

(a)    the line currents I_L

(b)    the overall power factor

(c)    the total active power P

(d)    the total reactive power Q

11.         What difference would it make if the generator in Q.10 were delta-connected?

12.         A purely reactive (90° lagging) a.c. circuit is switched on at an instant when the voltage is passing through zero.  Sketch the ensuing current wave.

13.         When a balanced 3-phase system is switched on, why do the initial currents in the three phases show different degrees of asymmetry?

14.         To what uses can a diode be put in simple power supply or control circuits?

15.         How is an a.c. current converted into d.c.?  What element is used to do this?  If a single-phase a.c. current of 10A (rms) undergoes half-wave rectification, what d.c. current level is achieved?

16.         With a 3-phase, full-wave rectifier what a.c. voltage (rms) must be applied in order to achieve 24V d.c. output?

17.         How can a rectifier bridge be adapted to give a variable d.c. output?

18.         Why is high voltage used to generate large bulk quantities of electricity?

19.         A platform has a 6.6kV generation and a 440V distribution system.  An oil transfer pump is driven by a motor rated at 1 200kW.  At what voltage would you expect it to operate?  Why?

20.         A system has six motors with nameplate ratings 200 hp, 150 hp, 2 x 100 hp, 80 hp and 50 hp.  What is the total full-load output in kW_m ?

21.         What different types of instrument can be used to measure alternating voltages and currents?  What voltage or current will they indicate?  What do you expect to notice about their scales?

22.         Why cannot a moving-coil instrument be used to indicate a.c. directly?  How can it be made to do so?

23.         What type of instrument would you use to indicate watts on a 3-phase a.c. system?

24.         What type of instrument would you use to indicate vars on a 3-phase a.c. system?

25.         Why are transducers often used in modern instrumentation?