A guide identifies the optimal approach to prevent problems when selecting new or upgrading existing capacitor banks

Capacitor banks have been used for many years to compensate the fundamental reactive power required by resistive-inductive loads. They are essential for an economic operation of the electrical system. However, non-linear loads are becoming predominant in today’s electricity system. Capacitor banks must now be designed to cope with two basic challenges these non-linear loads bring about. They have to withstand excess harmonic current, and they have to avoid the risk of resonance with inductances in other appliances in close (electrical) proximity.

Basics: Characteristics of inductance and capacitanceInductance is the electrical analogue to the inertia of mass in a mechanical system. A reactor, i.e. a component with a defined and intentional inductance value, represents the electrical equivalent of a flywheel with a defined inertia. Of course, anything that has a mass also has certain inertia and, in thesame manner, any conductor has a parasitic inductance.

Both the inductance L and the capacitance C represent reactive components with a particular reactance. Capacitive reactive power input is the equivalent of inductive reactive power output and vice versa. Reactive power has, in effect, no clearly definable direction of flow

Therefore, the inductive reactance XL is proportional to frequency f, while the capacitive reactance XC is inversely proportional to frequency f. For any parallel combination of L and C, there will be a frequency f0, at which reactance of L and of C are equal. This is the resonant frequency. This frequency, at which the LC combination oscillates

With respect to leading currents, it may seem a bit difficult to imagine how a capacitive current can ‘know’ in advance what the voltage that drives it will do a quarter of a period later but, in a manner of speaking, this is actually what happens. To be precise, it is any change of current that is lagging or leading in relation to the corresponding voltage change, e.g. the zero crossing. It originates from the energy being stored in the capacitance and from the special characteristics of the waveform.

Electrical capacitance corresponds to the resilience (elasticity) of a mechanical component. A capacitor can be produced with a defined capacitance, corresponding to a spring in a mechanical system. Just as every material has some degree of resilience (elasticity), there is also a certain parasitic capacitance between any two pieces of conducting material.The question is whether this parasitic reactance is large enough to play a role in practical engineering. At high voltages or high frequencies, they often are. However, this is not normally the case at low voltage levels and mains frequency.

When the energy stores are a capacitor and an inductor, the tension in the extended/compressed spring correlates with the positive/negative voltage in the capacitor and the speed of the mass is the current, also swapping polarity at regular intervals. This means every 90°, all changes of the dimensions (tension/voltage and velocity/current) follow a sine function. Given a 90° phase shift, it can also be said that one of the dimensions follows a cosine function. Assuming linear and loss-free components at any point in time with the oscillation results in the internal energy being constant at any point in time. With actual components, losses do occur and the phase displacement of current against voltage in an inductive/capacitive component becomes less than ±90°. However, these losses are in general rather low; the influence of non-linearity in reactor core materials is largely negligible for technical purposes if the reactor is properly designed.

What is special about the sine wave?Sine voltages drive sine currents, and sine currents produce sine voltage drops. Is this true for the sine waveform only or for any function? To answer directly, it is in fact a peculiarity of the sine wave. See the examples for other waveforms in Figures 1 and 2. Instantaneous voltage values are proportional to the instantaneous current values only for resistive elements, so that any voltage curve produces a current curve of the same shape and vice versa. For reactive loads, the instantaneous voltage is proportional to the rate of change of current with respect to time di/dt (in the case of an inductance L) or the current is proportional to the rate of change of instantaneous voltage with respect to time du/dt (in the case of a capacitance C).

The sinusoidal voltage and current curves have the same shape for resistive and reactive components, but with a phase shift. For reactive components, the voltage is proportional to the rate of change of the current. However, the rate of change of a sinusoid is described by a cosinusoid, which has the same shape and merely a different start point.

What is reactive power?In resistive loads, the instantaneous values of voltage and current are proportional to each other (Figure 4). In reactive components they are not (Figure 6). In the latter case, if one of the dimensions has a sinusoidal wave shape, so does the other but with a phase shift between the two. Hence, during two sections of every AC period, they have the same sign, but during the other two sections, their signs are different. During these periods of opposite voltage and current polarities, the product of them, the power, is negative, so a power consumer in fact temporarily turns into a power ‘supply.’ The electrical energy absorbed a quarter period before was not consumed (e.g. converted into another form of energy, such as heat), but was stored and is now recovered and fed back into the network. The real ‘active’ energy transferred during each full period equals the integral of power. That is the area below the voltage multiplied by current curve (shaded areas in the figures), with the parts below the abscissa to be subtracted from those above. Therefore, fundamental reactive power is an oscillation of energy.

So far, the definition of reactive power, as it relates to sinusoidal voltages and reactive loads, is still relatively simple. However, reactive power is also present in phase angle controlled resistive loads (e.g Incandesecent lamp with dimmer).Figure 7 provides the explanation. Viewed from the simple point of view of the load (top row in Figure 7), there is no reactive power—current is in phase with voltage (despite the distorted wave shape) and the displacement power factor is unity. Nevertheless, all loads exist in a common system, and should be examined from the system perspective, shown in the lower row of Figure 7. Now the voltage waveform is again sinusoidal and the displacement power factor is now lagging by 0.8 (see the W, VA, and VAR measurements).

Why compensate?There are many simultaneously active loads in a conventional electricity network. Many are resistive, some have a capacitive component, i.e. (leading), and others have an inductive component, i.e. (lagging). Resistive-inductive loads prevail in most networks, resulting in a resistive-inductive overall current (Figure 5). This incessant, undesired, oscillation of energy results in an additional flow of current in cables and transformers. It causes additional resistive-losses and uses a potentially large portion of their capacity. Therefore the basic reasons for compensating are to avoid:Undesired demand on transmission capacity (additional current)Energy losses caused by such loadsAdditional voltage drops caused by such loads.

These extra voltage drops in the system are significant; a reactive current flowing in a resistance causes a genuine power loss. Even where the impedance is largely reactive, rapid changes in the reactive current may cause flicker. A good example of this is a construction crane connected to a relatively small distribution transformer when building is erected. The cranes are usually driven by relay-controlled three-phase induction motors that are quite frequently switched from stop to start, from slow to fast, and from downwards to upwards. The start-up currents of these motors are very high, several times the rated current, and have a very high inductive component, the power factor being around cos ≈ 0.3 (or even smaller with bigger machines). The voltage drop in the transformer is also largely inductive, so it has more or less the same phase angle as the start-up current of the motor. It will add much more to the flicker than the same current drawn by a resistive load (Figure 8). Fortunately, this also means that this flicker can easily be mitigated by adding a capacitor to compensate the inductive component of the motor’s start-up current.

How to compensate under today’s conditionsControl and regulation of reactive powerIt is normally desirable to compensate reactive power. This is quite easy to achieve by adding an appropriate capacitive load parallel with the resistive-inductive loads so that the inductive component is offset. While the capacitive element is feeding its stored energy back into the mains, the inductive component is drawing it, and vice versa, because the leading and the lagging currents flow in opposite directions at any point in time. In this way, the overall current is reduced by adding a load. This is called parallel compensation.

To do this, knowledge of how much inductive load in installation is must, otherwise overcompensation may occur. In that case, the installation would become a resistive-capacitive load, which in extreme cases could be worse than having no compensation at all. If the load—more precisely its inductive component varies, then a variable compensator is required. Normally this is achieved by grouping the capacitors and switching each group on and off via relays / contactors. This of course causes current peaks along with the consequent wear of the contacts, risk of contact welding, and induced voltages in paralleled data lines. Care must be taken in timing the switch on. When voltage is applied to a fully discharged capacitor at the instant of line voltage peak, the inrush current peak is equal to that of a short circuit. Even worse, switching on a short time after switching off, the capacitor may be nearly fully charged with the inverse polarity, causing an inrush current peak nearly twice as high as the plant’s short circuit current peak! If there are many switch-mode power supply loads (SMPS) being operated on the same system, then a charged compensation capacitor, reconnected to the supply, may feed directly into a large number of discharged smoothing capacitors, more or less directly from capacitance to capacitance with hardly any impedance in between. The resulting current peak is extremely short but extremely high. Much higher in fact than in a short circuit! There are frequent reports about the failure of devices, especially the contacts of the relays controlling the capacitor groups, due to short interruptions in the grid which are carried out automatically, e.g. by auto-reclosers, to extinguish a light arc on a high or medium voltage overhead line. It is often suggested that this doubling of peak value cannot occur with capacitors that are equipped with discharge resistors in accordance with IEC 831. However, the standard requires that the voltage decays to less than 75 V after 3 minutes, so they have little effect during an interruption as short as a few tens of milliseconds up to a few seconds.

If, at the instant of re-connecting the capacitor to the line voltage, the residual capacitor voltage happens to equal the supply voltage, no current peak occurs. At least this is true if the compensator is viewed as a pure capacitance and the incoming voltage as an ideal voltage source, i.e with zero source impedance. However, if the self-inductance of the system is taken into account, certain resonances between that and the capacitance may occur. Assume the following case: the residual voltage of the capacitor is half the peak value and equal to the instantaneous line voltage, which is at 45° after the last zero voltage crossing, i.e.

However, this is not the case, because the capacitor has been disconnected from the supply up to this point. At the instant of connection—ignoring the system’s inductance—the current would rise up to this value immediately, and nothing would happen that would not have also happened in the steady state. Nevertheless, a real system is not free of inductance, so the current will assume this value only hesitantly at first, then accelerate and—again due to the inductance, its ‘inertia’—shoot beyond the target up to nearly double the expected value. It will then come down again and thus perform a short period of oscillation that may be attenuated down to zero well within the first mains cycle after connection. The frequency of such oscillation may be rather high, since the mains inductance is low, and may cause interference with other equipment in the installation. Only if the instantaneous line and residual capacitor voltages are both at their positive or negative peaks at the instant of re-connecting the capacitor—at which point the instantaneous current would be zero anyway—will the resistive-inductive current start without oscillation.

In actuality, there are two conditions to be fulfilled. Firstly, the sum of voltages across the capacitance and its serial reactance (be it parasitic or intentional detuning) must be equal to the line voltage. Secondly, the supposed instantaneous current, assuming connection had already taken place and is well established, has to equal the actual current, which of course is zero until the instant of switching. This second condition is fulfilled only at line voltage peak, which therefore has to equal the capacitor voltage. To achieve this, the capacitor is pre-charged from a supplementary power source. This practice has a secondary, albeit minor, advantage. It ensures that there is always the maximum possible amount of energy stored in the capacitor while not in use, so that at the instant of turn-on it may help to mitigate some fast voltage dips and prevent the subsequent flicker.

Relays, however, are too slow and do not operate precisely enough for targeted switching at a particular point in the wave. When relays are used, measures have to be taken to attenuate the inrush current peak. Such devices include inrush limiting resistors and detuning reactors. The latter are frequently used for other reasons and are occasionally required by utilities. Although this series reactor replaces the inrush current peak at switch-on with a voltage peak (surge) at switch-off, it is still the lesser evil, since the reactive power rating of the reactor is just a fraction of the capacitor rating and the energy available is therefore less.

Electronic switches, such as thyristors, can be easily controlled to achieve accurate point-on-wave switching. It is also possible to control switching so as to mitigate a fast flicker caused by a large, unstable inductive load, such as the crane motor mentioned previously, an arc furnace, or a spot welder.

An alternative option frequently applied in some parts of Europe is FC/TCR compensation, the paralleling of a Fixed Capacitor with a Thyristor Controlled Reactor.

Centrally or dispersed reactive compensation?The reason why commercial electricity users normally compensate, is because some utilities charge for reactive power. This reactive power rate compensates for ‘useless use’ of the distribution system and is generally not as high as the active power rate, but significant nonetheless. In some countries, the practice of charging for reactive power is declining. Likewise, power factor compensation is becoming less common. Electricity users see this as an advantage, but in fact, it places an increased load on a system that is often working quite close to its maximum.

The traditional approach is to place one large static compensator at the point of common coupling, the utility entry, and correct the power factor there to the level required to avoid charges (usually cos = 0.90 or cos = 0.95). The alternative approach is to disperse compensation near resistive-inductive loads and, in the extreme case, to an individual appliance that draws reactive current.

Centralised compensation is often believed to be cheaper. This is because the central unit is less costly to purchase than spreading the same reactive power rating across the plant in small dispersed units. A lower installed compensation capacity can also be chosen because it is assumed that not every reactive current consumer will be active simultaneously. However, central compensation does nothing to reduce the losses caused by reactive power inside the local network. It merely reduces the power factor charge levied by the utility. In a system with dispersed compensation, the reactive current only flows in the short distances between the local compensation units and the appliances, while in a system with centralised compensation, the reactive current flows through every cable and every transformer between the inductive appliances and the point of common coupling. Centralised compensation also has some of the other disadvantages of reactive power, namely transmission capacity demand and voltage drop.

Apart from the financial and energy efficiency arguments, there are technical arguments for and against centralised compensation. For example, if the aggregate load on a transformer is capacitive, the output voltage rises above nominal. This effect is sometimes used to offset the voltage drop in a heavily loaded transformer. The load is simply overcompensated so that the overall load appears capacitive to the transformer. This reduces the inductive voltage drop in the transformer [2]. In cases where a frequently switched heavy load causes a flicker problem, this may be a more sturdy and reliable solution than electronic flicker compensators and may also be considerably more cost-efficient in cases where a degree of compensation would be needed in any case.However, in general terms, the overvoltage of a transformer under capacitive load is a risk that should be avoided or must be at least adequately dealt with by, for example, using a slightly higher than nominal voltage rating (≈6 per cent). It is sometimes necessary or desirable to apply compensation at MV level and it is attractive to connect LV capacitors via a MV/LV transformer rather than paying the higher price for MV capacitors. In such a case, the transformer load is capacitive and the output voltage may be higher than expected. This can be dealt with by proper selection of components with adequate voltage rating or by selecting the transformer ratio, by the use of taps, to normalise it. The latter is preferable since it avoids running the transformer in an over-excited state with consequently higher losses. This approach can be appealing on paper yet prove to be a false economy. Although the installation cost is reduced, the running costs are increased. Reactive current in the installation is transformed twice—from the installation LV to the system MV and from system MV to capacitor LV— with two load losses to be paid for by the consumer.

In a decentralisation scheme, each and every resistive-inductive load, however small, may be compensated by integrating a capacitor into it. This has been accomplished quite successfully, for instance, in luminaires with one or two fluorescent lamps and magnetic ballasts. In Germany and Switzerland, this is frequently implemented as serial compensation, where one out of every two lampand- ballast circuits is left uncompensated and the other one is (over-) compensated by means of a series capacitor, dimensioned in such a way as to draw precisely the same amplitude of current as the uncompensated branch, but with the inverse phase angle.

For asynchronous induction machines however, individually local compensation is problematic. If the capacitor is located before the motor switch, then it may easily remain connected when the motor is off, leaving the system overcompensated. If the capacitor is located after the motor switch so that it is disconnected from the motor, then there is a risk of self-excitation in the machine as it decelerates.Voltage is generated although the device has been isolated from the supply, including overvoltage in the event that the capacitance has been wrongly dimensioned.

Reactive power is not always undesirable. Rather, the proper amount of capacitive reactive power needs to be generated to offset the inductive reactive power and, in cases where resistivecapacitive loads prevail, the reverse is true. However, the latter is not always recommended, as capacitive reactive power can bring along technical advantages. For example, it can be used for exciting asynchronous generators such as wind turbines and cogeneration plants if these are connected directly to the system without an inverter. It even becomes an absolute necessity in situations where such generators are supposed to feed an island network. Otherwise there is no excitation, no voltage, and no supply, even while the machine is running.

DetuningDetuning refers to the practice of connecting each compensation capacitor in series with a reactor. One reason for detuning—the attenuation of inrush currents—has already been discussed. However, the basic reason why detuning is recommended by all compensator suppliers and most utilities—and why many consumers have already adopted it—is the problem of voltage disturbances on the network. Modern electronic loads draw harmonic currents, cause harmonic voltage disturbance, and impose high frequency noise on the network. As the reactance of a capacitor is inversely proportional to the frequency, these high frequencies can cause the current rating of the capacitor to be exceeded. This is prevented by the presence of a detuning inductor. The reactive power rating of the detuning reactor is usually 5 per cent, 7 per cent, or 11 per cent of the reactive power of the compensation capacitor. This percentage is also called the ‘detuning factor.’

When discussing ratings, there is often considerable confusion as to whether the reactive power indicated on the rating plate of a compensator refers to the rated mains voltage or to the rated capacitor voltage (which is higher), and whether or not the detuning factor has been taken into account. In fact, the stated reactive power should always refer to the combined unit—compensator plus detuning reactor—at supply voltage and fundamental frequency.

Since the reactance of a reactor rises proportionally with the frequency while that of the capacitor drops, an 11 per cent detuning factor at 50 Hz already becomes ≈100 per cent at 150 Hz1. This means that the inductive reactance and the capacitive reactance are equal (in resonance) and cancel each other out. This provides an option to design detuning factors to ‘suck out’ a particular harmonic from the network, while performing the basic compensation function as well. Generally, however, in order to prevent capacitor and reactor overload, it is preferable to avoid detuning factors that place the resonant frequency on one of the predominant harmonic frequencies. Rather, the detuning factor is chosen so that the capacitor/inductor combination becomes inductive for frequencies just below the lowest occurring harmonic and above (Figure 9). This avoids resonances (Figure 10) that might otherwise occur between the capacitor and other elements of the system. This is especially true of the stray inductance of the nearest transformer being excited by one or another harmonic. In the figures, the amplification factors are plotted against the frequency. The amplification factor here is to be understood as the ratio of the system’s behaviour as it is, compared to the same system’s behaviour in the absence of the compensator.

But this is not the only reason for detuning. Nowadays capacitors may also easily be overloaded by the higher frequencies omnipresent in the networks. These are often higher than even the most common harmonics. Even small high frequency voltages superimposed on the supply voltage—so small that they are not visible in the voltage recordings of a high-class network analyser (Figure 11)— can drive high currents through the capacitors.

On the left is an 11 W fluorescent lamp operated with a magnetic ballast but without compensation. However, the very high amount of reactive power requires compensation by capacitors. On the right, the lamp system current (the serial connection of lamp and ballast, paralleled with the appropriate capacitor) is a bizarre zigzag rather than the desired approximate sine wave. This additional mixture of higher frequency currents must be flowing through the capacitor, since nothing else has changed in the wiring. Measurements confirm this. Since the current on the left is almost sinusoidal, the difference between the power factor (also called load factor LF) and the cos (also called displacement power factor DPF) is small. On the right, however, it is significant. The reason is that the power factor is the ratio of real (50 Hz) power to apparent power, including fundamental reactive power, harmonic power, and noise power, while the cos —displacement factor—only includes the fundamental reactive power caused by a phase shift between voltage and fundamental current. The capacitor is intended to carry reactive current (left), but is also a sink for harmonic currents (right) if not detuned.

This is the second reason for the widespread detuning practice today and reveals how important it may be for the life of a capacitor designed for 50 Hz. The experiment can be repeated with similar results in nearly all modern networks. Simply connecting a capacitor to the line voltage and recording the current will give similar readings everywhere. It is very impressive to let the capacitor current flow through an appropriately dimensioned loudspeaker. The noise is truly awful, but it changes back again to a calm and quiet 50 Hz hum as soon as the capacitor is ‘detuned’ with a reactor.

The present example also makes the above mentioned serial compensation practice for fluorescent lamps appear quite advantageous, as it represents a compensating capacitance with a detuning factor of 50 per cent, and this even with a reactor that is already in place and need not be added.

ConclusionsInductive load components prevail over capacitive load components in most networks. This results in an undesired oscillation of energy, bringing along an additional flow of current in cables and transformers. It causes additional resistive-losses and uses a potentially large part of their capacity. Compensating the inductive load component avoids:

Undesired demand on transmission capacity (additional current)Energy losses causedAdditional voltage drops.

Doing this properly requires knowledge of the amount of inductive load in the installation; otherwise, over-compensation may occur, which in extreme cases can be worse than having no compensation at all. A variable compensator is required in case the inductive load component varies.

Variable compensation can be achieved by grouping the capacitors and switching each of those groups on and off separately. The switching system should be precise enough for targeted switching at a certain point in the wave. The resistive-inductive current will only start without oscillation if, at the moment of switching, the instantaneous line and residual capacitor voltages are both at their positive or negative peaks. If not, resonance between the self-inductance of the system and the capacitance may occur. The frequency of such oscillation may be rather high and may cause interference with other equipment in the installation. Therefore, variable compensation units should preferably be designed using semiconductor switches, such as thyristors, and intelligent control algorithms. Relays are too slow and do not operate precisely enough. But if relays are used, measures have to be taken to attenuate the inrush current peak, such as inrush limiting resistors or detuning reactors.

Compensation capacitors should always be detuned in order to avoid resonance with harmonics and overload by high frequency current. Indeed, modern electronic loads draw harmonic currents, cause harmonic voltage disturbance, and impose high frequency noise on the network. As the reactance of a capacitor is inversely proportional to the frequency, these high frequencies can cause the current rating of the capacitor to be exceeded. This is prevented by the presence of a detuning inductor. The reactive power rating of the detuning reactor is usually 5 per cent, 7 per cent, or 11 per cent of the reactive power of the compensation capacitor.

Compensation capacitors can be centralised or dispersed. The traditional approach is to place one large static compensator at the point of common coupling and correct the power factor there to the level required to avoid charges. The alternative approach is to disperse compensation near resistiveinductive loads and, in the extreme, to an individual appliance that draws reactive current. In the first case, the installation cost will be lower. One large unit will be cheaper than the sum of several small units. Moreover, the installed compensation capacity can be lower because it is assumed that not every reactive current consumer will be switched on simultaneously. However, it is far from certain that centralised compensation will also have the lowest Total Cost of Ownership (TCO). With centralised compensation, reactive current will still flow between the appliances and the compensator at the point of common coupling. This means that in the local private network, all disadvantages of reactive power remain, namely energy losses, capacity demand for cables and transformers, and voltage drop. For this reason, the TCO of dispersed compensation will in some cases be lower than the TCO of centralised compensation. There are indeed some additional technical arguments to be made in favour of either centralised or dispersed compensation. For asynchronous induction motors, for instance, individual decentralised compensation is problematic.

Authored by_

Manas Kundu, Director Energy Solutions, International Copper Association India (ICAI)

# Power factor correction in a harmonic-rich environment

By

Posted on