Power factor correction in a harmonic-rich environment

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.

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