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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