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Introduction

Switching-on Transients in a Power Capacitor

Single capacitor-bank switching

Capacitor switching with already connected parallel banks.

Switching-off transients

Harmonic Resonance

Protection of shunt capacitor banks

Application of LT capacitor across Induction Motors
 
 

       The steady-state aspects of capacitor application to distribution feeders have been default with in the earlier part. This second part of the article attempts to take a look at the peculiar transient problems as well as abnormal conditions involved in power capacitor applications briefly. Capacitor protection is also touched upon briefly. Some important points on the application of LT capacitor in the industry to improve the power factor of induction motors are also included.

1.  Switching-on Transients in a Power Capacitor. 

1.1 Single capacitor-bank switching  

A simplified model of a single bank capacitor switching at a point on the feeder where the voltage before switching on is and system reactance is Xsc= wLsc (Xsc is the short circuit reactance at that point.) is shown in fig 1. The phase variable  is included to take in to account the fact that the instantaneous voltage at the switching instant can be anywhere on the voltage wave.

Assuming that Xsc is much less than Xc, the steady state voltage across C will be . But since capacitor voltage can not change instantaneously, there must be a transient oscillation term to adjust the initial condition voltage across C. Hence the voltage across C is 

The transient term in practice will be damped by the circuit resistance and will die down in a few a.c cycles. The corresponding current through the breaker and capacitor will be 

The transient current will have maximum amplitude when i.e. for voltage maximum switching. Also, the transient current will have a large amplitude since  is usually large. The problem is more severe in the case of switching on large capacitor banks at a high short circuit capacity point.

The current waveform with is shown in fig 2.

It is clear from the figure that the maximum r.m.s. value of inrush current for switching at voltage maximum can be

Where I_rated is the rated rms current of capacity, Xsc is the short circuit reactance at the point of application of capacitor, Q_sc is the short circuit MVA and Q_c is the capacitor MVA rating.

The short time rating of breaker as well as the capacitor must be sufficient to withstand this high frequency inrush current which may last for several a.c. cycle.

High frequency current flow in capacitor causes considerable thermal overloading in the capacitors. Also,an examination of the voltage equation will show that, in the extreme case of voltage maximum switching, the instantaneous voltage of the capacitor may reach a maximum of 2Vm many times in the first few a.c cycles. This will lead to severe strain on the capacitor dielectric leading to a loss of life of the capacitor.

1.2 Capacitor switching with already connected parallel banks.

The above mentioned problem of high valued high frequency inrush current and over voltages is made more severe by the presence of already energised parallel banks. Refer to fig 3. Lsc refers to the short circuit i0nductance at the point of connection and Lc refers to the small inductance of the loop formed by the energised bank and the bank to be energised.

The transient will be severe when  degrees i.e. voltage maximum switching. The zero initial condition on C₂ forces C₁ to discharge in to C₂ through Lc during the transient condition. The inductance Lc being small, the transient current component arising out of the local oscillation in the loop will be of very high magnitude compared to the transient current covered in section 1.1. Also the local current & voltage oscillations will be poorly damped. The oscillation will contain two frequency components in addition to 50Hz components of  and approximately and the second of these will be the more serious transient.

Some form of transient current limiting and damping of oscillations will be required to safe guard the capacitors and switching equipments against these high frequency inrush transients. The worst case condition will be when the last bank is being switched on with all the other banks is being switched on with all the other banks already energised. Current limiting and damping of oscillations can be done by introducing a reactor in serious with the capacitor. The value of reactor is chosen to limit the current (transient current amplitudes will be proportional to ) and the resistance present in the reactor will usually be sufficient to provide good damping to the oscillations. The value of reactor usually adopted has about 4 to 6% MVA rating of the capacitor bank rating. This value is arrived at from harmonic current limiting considerations as explained later, but this value is found to be appropriate for inrush current limiting and damping also.

Connecting a 6% reactor in series with capacitor produces a 6% rise in 50Hz voltage across capacitor. Hence the capacitor has to be rated for 106% of normal system voltage. Otherwise, the normally available 10% over voltage capability of capacitors will be taken up by the 6% voltage rise leaving only a 4% margin for system over voltage conditions. 

2.  Switching-off transients

Switching off a capacitor is associated with the normal transient recovery voltage oscillations across the circuit breaker gap and RRRV considerations are the same as in any other applications. But a more serious problem of over voltages can come up with capacitor switching.

Consider the circuit in fig 4. 

Assuming arc extinction at current zero, capacitor will hold a voltage of Vm forever (unless there is leakage or there is re strike). Hence at the next negative maximum of input the voltage across the breaker will be 2Vm and there may be a re strike at this point. If there is a re strike, one half cycle (at the oscillation frequency ) current will flow into capacitor, charging it up to 3Vm before the breaker can clear at current zero. If this happens, at the next negative maximum, the breaker will have 4V_m across it and a re strike is again possible which will charge up the capacitor to 5 V_m. Such successive re strikes will lead to dangerous over voltage in the system. 

The breaker selected must be capable of withstanding the increased voltage level of 2V_m across it after a half cycle of clearing point. Also there must be proper discharging arrangement for the capacitors to avoid over voltages as well as to reduce the inrush current at the next switching on. Usually this discharging is accomplished through discharge resistance provided for the purpose or through a potential transfer which any way is needed for protection system.

3. Harmonic Resonance

A non-linear load takes a non-sinusoidal current from a sinusoidal supply voltage. The non-sinusoidal current can be resolved in to various harmonic components. The triplen harmonic currents are suppressed usually by proper transformer connections.

Hence, the power network currents can contain harmonics (including even harmonics) at non-triplen orders if there are nonlinear loads. Loads like saturated transformers and machines, welding units, arc furnaces, rectifier and inverter units, battery charging equipment, thyristorised power converters and motor control equipment, static VAR compensators etc. are nonlinear and introduce harmonic currents into the distribution network and elsewhere. The flow of harmonic currents in the line impedance produces harmonic voltages along with the fundamental frequency voltage at all points in the system. Also, tooth ripple in generation & machines, variation in air gap reluctance in a synchronous machine, non-sinusoidal flux distribution in a generator etc. crate harmonic voltages in the system. In addition to these, flux distortion in a synchronous machine from sudden load changes and magnetising inrush of transformers etc. can create harmonics in the system during transient conditions.

Harmonic voltage at the point at which a capacitor is connected will provide high valued harmonic currents in the capacitor since capacitive impedance decreases with frequency. This will cause over heating of capacitor and possible damage. 

But a much more severe problem is one of harmonic resonance. Consider in fig 5. Here, the capacitor is connected across a nonlinear load which is simulated by two current sources one at fundamental frequency and one at the 5^th harmonic i.e. instead of representing the load directly, its effect is taken care of by assuming two current sources which will have the same current as in the load. For illustration purpose the current taken by the load is assumed to have only two components –one at fundamental frequency and one at 5^th harmonic. 

The total voltage across capacitor can be found by using super position theorem. The three circuits are shown in fig 6. 

The MVAR rating of capacitor at 50 Hz will be much less than short circuit capacity at the point of connection and hence  will be much greater than 50 Hz. Hence Capacitive impedance will dominate in fig 6(a) and inductive impedance will dominate in fig 6(b).Solving these two circuits will give the power frequency voltage across capacitor which will be close to the rated value. But in fig 6(c), frequency of source is 5 times the fundamental frequency and this source will meet with considerable impedance – specifically, it will meet with infinite impedance if C& L_SC can resonate at 250 Hz. Hence even for small harmonic currents, large harmonic voltages can appear across capacitor at near anti-resonant conditions. Consequently there will be large harmonic currents in the line as well as capacitor causing damage to the capacitor due to over heating and excessive stress on insulation. The harmonic over voltage created thereby can affect the other equipments connected on the line too.

The solution lies in offering allow impedance (preferably zero impedance) shunt path for the harmonic currents to flow. This can be accomplished by connecting a reactor in serious with capacitor has 4% MVA rating of the capacitor rating such that the circuit resonates at 5^th harmonic. Thus, connecting the reactor effectively reduces the fifth harmonic voltage to zero. The line current will be at 50Hz, required to supply the 50Hz current component of the load and capacitor-reactor combination. The fifth harmonic current required by the load comes from the capacitor. The capacitor- reactor combination acts as compensation equipment at power frequency and as a filter at 5^th harmonic

Another major application of power capacitors is evident from the above. They can , in combination with suitable reactors, be used as effective harmonic voltage suppressors in distribution systems with a predominance of nonlinear loads which take large amounts of harmonic currents.

Rectifier and thyristor circuits introduce another kind of distortion in to the 50 Hz voltage wave in addition to drawing harmonic currents. They introduce sharp spikes in to the voltage wave due to commutation transients. A directly connected capacitor (without a series reactor) will in general smoothen the waveform due to the natural tendency of capacitors to resist sharp changes in voltage. But this may result in an increase of 3^rd, 5^th harmonics in voltage waveform due to a possible anti-resonance between this capacitor and system inductance. The problem can be solved by two banks of capacitor with a series reactor, designed to eliminate the predominant harmonic in one of them.

Dangerous harmonic resonance conditions can arise when a transformer is switched on across a capacitor bank, which is already energised. The switching inrush of the transformer is rich in harmonics and the capacitor along with system inductance will amplify the harmonics currents in to large harmonic voltages if anti resonant conditions exist. This will result in tripping of capacitor on over current or over voltage indications every time the transformer is switched on. Series reactor can alleviate the problem in most of the cases. 

4.  Protection of shunt capacitor banks.

The protection scheme for capacitor banks installed at the substations will generally consist of

1. Neutral unbalance over current protection.
2. Time delayed over voltage protection. 
3. Three phase definite time over current relay with high instantaneous units.
4. A single pole thermal over load relay.
5. A time delayed non-volt relay.
6. A back up neutral displacement over voltage relay.

5.  Application of LT capacitor across Induction Motors.

The following points are note worthy in connection with LT capacitor application across induction motors.

The full load PF of a squirrel cage motor is between 80 to 90%. Generally the motors do not operate at full load and consequently have a lower operating P.F. However even though the PF of a squirrel cage motor varies materially from no load to full load, the total KVAR demand of the motor does not vary much over this range. Hence LT capacitors with a rating equal to or slightly less than magnetising KVAR of the motor should be capable of maintaining the PF above 95% throughout the operating range. Capacitors with a rating greater than magnetising VARS of the motor can cause over-voltages at motor terminals and self-excitation in the machine. Capacitors connected to the motors and switched with the motor as a unit will help to remove overcompensation in the system during light load conditions. However excessive inrush current transient torque in the motor, over-voltage due to self-excitation etc can result especially when large capacitors are used in this mode.

A capacitor switched along with the motor can prolong the time constant of open circuit e.m.f of the machine on switching off the supply to the unit. If the unit is switched on immediately after switching off, large equalising currents will flow in to the unit due to magnitude & phase difference between applied voltage and back e.m.f. in the machine. The capacitor places a minimum limit on the time between a switch-off and switch on of the motor. Needless to mention that capacitor switched along with the motor can not be employed in drives which are to be restarted frequently or reversed (by plugging) frequently.

Some problems can arise if capacitor is switched along with the motor and the motor has star-delta starter. Over voltage for a few cycles to two to three times the rated voltage due to self excitation can occur when switching from star to delta and the line is broken before the neutral. If the neutral connection is broken before line, series resonance between capacitor and winding may occur giving rise to over-currents and over-voltages. These problems can be avoided by connecting the capacitor on the line side of contactors or by using 6 terminal capacitors.