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Thursday, January 10, 2013

CHAPTER 7 POWER FACTOR CORRECTION




7.1       THE INCENTIVE


The larger consumers of electric power onshore pay not only for the energy they actually use (in kWh units) but also a contribution towards the capital cost of the supply system.  The amount paid for this element is usually based on the maximum kVA demand (note, not kW) over an accounting period.  This system of tariffs is further discussed in the manual ‘Onshore Electrical Systems’.





FIGURE 7.1
POWER TRIANGLE FOR INDUCTIVE LOAD

The kVA being demanded at any time is the vector combination OP of active power (kW) and reactive power (kvar), as shown in Figure 7.1.  The active power reflects the mechanical output of the various motors of an installation, together with lighting and heating, whereas the reactive power is required for their magnetisation.  It depends mainly on the total number and size of motors running at any instant and is independent of their loading.  From Figure 7.1 it can be seen that, the smaller the reactive element NP can be made, the nearer the kVA demand (OP’) can be made to approach the active load element (ON) and so achieve its least value for any given active load.

Ideally therefore the minimum running cost of an installation is achieved if the reactive loading (vars) can be eliminated altogether, so that the plant draws only active load from the system - that is to say, it runs at unity power factor so far as the supply system is concerned.  This is known as ‘power factor correction’.

It can be of great importance to onshore installations that take their power from an Area or Supply Authority and have to pay them for it under a tariff such as described above.  It is of less importance to an offshore installation which does not obtain its energy under a tariff, but a good power factor is nevertheless desirable as it uses plant more efficiently.  The methods described below will be found onshore but not offshore.

7.2       THE PRINCIPLE


It is shown in Chapters 9 and 10 of the manual ‘Fundamentals of Electricity 2’ that the current which flows in a purely inductive circuit when an a.c. voltage is applied lags 90° in phase on that voltage, whereas in a purely capacitive circuit the current leads 90°.




FIGURE 7.2
LAGGING, LEADING AND NET CURRENT

Figure 7.2 shows an a.c. voltage applied to both a purely inductive circuit (L) and a purely capacitive circuit (C) together.

The inductive current wave is IL (blue) the capacitive IC (red).  Since the former lags, and the latter leads, 90° on the voltage wave, they are 180° apart with respect to each other -that is to say, they are ‘anti-phase’, the positive parts of the one coinciding with the negative parts of the other.  The magnitudes of the two current waves depend on the impedance of the inductor (ZL) and that of the capacitor (ZC) according to the a.c. version of Ohm’s Law, namely:

 
In Figure 7.2 the dotted curve is the difference between the IL and IC curves - or more strictly the algebraic sum, since IC is negative with respect to IL at all points along it.  If there is little numerical difference between IL and IC (as shown in the figure), the difference curve will be very small indeed.  If IL > IC it will be in phase with IL (as shown), but if IL < IC it will be the other way up, in phase with IC.

In the special case where IL = IC numerically, there is no difference at all.  Between them the two circuits then draw no net current whatever from the mains, even though current passes through each and circulates between them, passing from one to the other and back again.  The circuits are said to be ‘in resonance’.


This suggests that, if we have a circuit containing inductance, such as a motor, which draws lagging reactive power (vars) from the mains, it can be completely offset by placing in parallel with it another circuit containing only capacitance.  The value of that capacitance is chosen such that the leading vars drawn by it just counterbalance the lagging vars drawn by the motor.  If this is done, the pair will between them draw no net vars from the mains, but reactive power will circulate back and forth between the two.  The capacitor can in fact be regarded as supplying all the magnetising vars to the motor, instead of the mains being called upon to do so.

Of course any active power needed by the motor for its driven load and losses will continue to be drawn from the mains.  It is only the demand for reactive power that has been completely removed from the mains and is now met from the capacitor.  Since only active power then comes from the mains, it is supplied at unity power factor, and the kVA demanded is reduced to the lowest value possible - namely equal to the kW demand.

7.3       THE PRACTICE


This description suggests a practical means of so correcting a motor that it draws only active power from the mains.




FIGURE 7.3
CAPACITOR CONNECTIONS TO A MOTOR

A 3-phase set of capacitors is connected in parallel with the motor terminals as shown in Figure 7.3.  They will be switched by the same contactor as is used to start the motor; this ensures that the capacitors are only in circuit when the motor itself is.  The capacitance value is chosen so that the reactive power in kvar (leading) drawn by the capacitors is as nearly as possible equal to the reactive power in kvar (lagging) drawn by the motor to magnetise itself.  And since this magnetising power is constant and does not vary with the motor loading, the chosen capacitors will compensate at all motor loads.  An example of the calculation for choice of capacitor size is given overleaf.


Example:

            Q         A 240 hp motor has a power factor of 0.8 at full-load and an efficiency of 85%.  What size of capacitors is required to provide full correction?

            A          240 hp = 180kWm. If efficiency is 85%, total input power is 180 ¸ 0.85 = 212kWe.

                        As power factor is 0.8, the total input kVA is 212 ¸ 0.8, or 265kVA.

                    

            This is the total leading reactive power to be supplied by the bank of three capacitors.  Each capacitor therefore should have a rating of 53kvar.  (Note that power capacitors, unlike those used in electronic circuits, are usually rated in ‘kvar’ at a stated voltage and frequency (or sometimes ‘kVA’), which is the same thing, as resistance is negligible.  Their capacitance in mF or mF can be calculated if desired, but it is not of any use in this calculation.)


Since the capacitors are connected directly to the motor terminals and therefore down-stream of the starting contactor, any charge left in them on switching off will be dissipated in the motor windings.


FIGURE 7.4

EFFECT OF POWER FACTOR CORRECTION BY CAPACITOR



It has already been explained in Figure 7.2 that the leading current drawn by a capacitor is completely opposite in sign to the lagging current drawn by an inductor.  In fact a leading current can be regarded as a negative lagging current.  Following this line of argument, the leading vars drawn by the capacitors can be regarded as negative lagging vars going in, or positive lagging vars coming out.  In the right-hand picture of Figure 7.4 the blue parts represent lagging vars, which now come from the capacitor to the motor, so cutting out the need to draw them from the mains.  This diagram explains perhaps more clearly how a capacitor bank corrects the power factor of a motor by providing its lagging vars for magnetising instead of the mains doing so.  As far as the mains are concerned, they see a motor which only requires active power and therefore operates at unity power factor.

In large industrial installations some of the bigger motors may be provided with individual capacitors, but with smaller machines a single capacitor bank might be installed to correct a group of motors.  In that case they would be sized to correct for an average number of motors running.  If more than the average number were on-line there would be some under-correction; if less, there would be over-correction.

Power factor correction is not confined to motors, though this is its main application.  Of interest may be the application to an induction furnace in a steelworks. Here a crucible containing steel pieces for melting is heated by induction from an alternating current flowing in a coil round the crucible.  When cold, the steel is highly inductive and so causes a heavy demand for reactive power in the heating coil, with a consequent low power factor.  As the steel heats, its magnetic properties change; the inductance drops, and with it the demand for reactive power.

If sufficient capacitors were installed to correct for the initial cold state (usually banks of several in parallel), there would be progressive over-correction as the steel became hotter.  This would require capacitors in the banks to be switched out in sequence.



FIGURE 7.5

INDUCTION FURNACE AUTOMATIC POWER FACTOR CONTROL


Figure 7.5 shows a typical automatic control system.  It monitors the reactive power being drawn and controls the number of capacitors needed as the melt progresses, so keeping the power demand from the mains as near unity power factor as possible all through the melting process.

7.4       CLOSENESS OF CORRECTION


Ideally a motor’s reactive power demand should be exactly nullified by the correcting capacitors, but this is not always practical, nor is it necessary.


FIGURE 7.6
UNDER-CORRECTION AND OVER-CORRECTION

Figure 7.6, which is a development of Figure 7.1, shows the kW, kvar and kVA of a motor uncorrected, slightly under-corrected and slightly over-corrected.  It is the purpose of power factor correction to reduce the kVA to the lowest possible level - ideally to equal the kW.  It can be seen from the figure that, so long as the under- or over-correction is not too large, the kVA does not differ much from the kW; indeed, the difference is a ‘second order’ effect.

Capacitors, although simple pieces of equipment, are nevertheless costly to provide and install, especially for high-voltage plant.  Therefore no more should be spent on them than will show an overall gain compared with the cost of a high maximum demand kVA charge.

This calls for a nice calculation which takes account of the tariff, the cost of the capacitor equipment and its installation.  A careful balance is required, and it will probably result in slight under-correction.  If circumstances subsequently alter, such as increased tariffs, further capacitors can always be added.

7.5       POWER FACTOR CORRECTION OF NETWORKS


So far this chapter has considered only local power factor correction of consumer equipment, mainly motors.  This may be required to achieve the minimum running cost for the consumer’s plant.

Supply authorities’ networks onshore should also be operated at as high a power factor as possible, both for economic reasons and more particularly to maintain voltage levels on the system.  How this is done is explained in the manual ‘Electrical System Control’.

In particular the use of the ‘synchronous condenser’ in this role is discussed in Chapter 1, para. 1.9, of that manual.

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