Continued from part two – **Capacitor Banks In Power System (part two)**

## Maximum Permissible Current

**Capacitor units** shall be suitable for continuous operation at an RMS current of 1.30 times the current that occurs at rated sinusoidal voltage and rated frequency, excluding transients. Taking into account the capacitance tolerances of 1.1 CN, the maximum permissible current can be up to 143 IN.

These overcurrent factors are intended to take care of the combined effects of harmonics and overvoltage’s up to and including1.10 UN, according to IS 13340.

## Discharge Device

Each capacitor unit or bank shall be provided with a directly connected discharge device. The **discharge** device shall reduce the residual voltage from the crest value of the rated value UN to 50 V or less within 1 min, after the capacitor is disconnected from the source of supply. There must be no switch, fuse or any other isolating device between the capacitor unit and the discharge device.

A discharge device is not a substitute for short-circuiting the capacitor terminals together and to earth before handling.

**Where:**

**t** = time for discharge from UN Jr to UR(s),

**R** = equals discharge resistance

**C** = rated capacitance (pF) per phase,

**U _{N}** = rated voltage of unit (V),

**U**= permissible residual voltage

_{R}**k**= coefficient depending on both resistance and capacitor unit connections, Value of

**k**to be taken as per IS13340

## Configuration of Capacitor bank

A delta-connected bank of capacitors is usually applied to voltage classes of 2400 volts or less.

In a **three-phase** system, to supply the same reactive power, the star connection requires a capacitor with a capacitance three times higher than the delta connected capacitor. In addition, the capacitor with the star connection results to be subjected to a voltage √3 lower and flows through by a current √3 higher than a capacitor inserted and delta connected.

For Three Phase STAR Connection

Capacity of the capacitor bank C = Q_{c} / (2πF_{r}U_{r}^{2})

Rated current of the components I_{RC} = 2πF_{r}CU_{r} / √3

Line current I = I_{RC}

Three Phase Delta Connection

Capacity of the capacitor bank C = Q_{c} / (2πF_{r}U_{r}^{2}.3)

Rated current of the components I_{RC} = 2πF_{r}CU_{r}

Line current I = I_{RC} / √3

**Where,**

**U _{r}** = rated voltage, which the capacitor must withstand indefinitely;

**F**= rated frequeny

_{r}**Q**= generally expressed in kVAR (

_{c}**reactive power**of the capacitor bank)

While deciding the size of capacitor bank on any bus it is necessary to check the voltage rise due to installation of capacitors under full load and light load conditions. It is recommended to limit the voltage rise to maximum of 3% of the bus voltage under light load conditions. The voltage rise due to capacitor installation may be worked out by the following expression.

## Voltage Drop/Rise Due to Switching

Switching on or off a large block of load causes voltage change. The approximate value can be estimated by:

**Voltage change ≅ load in MVA/fault level in MVA**

Switching a capacitor bank causes voltage change, which can be estimated by:

**Voltage change ≅ capacitor bank rating in MVA /system fault level in MVA**

**Where,**

**% V _{C}** = % voltage change or rise due to capacitor

**% X**= % Reactance of equipment e.g. Transformer

If the capacitor bank is STAR connected than the required value of C will be higher in comparison to the value of C in DELTA connection for the same value of required kVAR. Higher value of C will cause higher voltage rise of the system causing nuisance tripping of the equipment provided with over voltage protection.

It is common practice to leave the star-connected capacitor banks ungrounded (there are separate reason for leaving it ungrounded) when used in the system or use delta-connected banks to prevent the flow of third harmonic currents into the power system through the grounded neutral.

Large capacitor banks can be connected in STAR ungrounded, STAR grounded or delta. However, the wye ungrounded connection is preferable from a protection standpoint. For the STAR ungrounded system of connecting single capacitor units in parallel across phase-to-neutral voltage the fault current through any incomer fuse or breaker of capacitor bank is limited by the capacitors in the two healthy phases. In addition the ground path for harmonic currents is not present for the ungrounded bank.

For STAR grounded or delta-connected banks, however, the fault current can reach the full short circuit value from the system because the sound phases cannot limit the current.

## Detuning of Capacitor Banks

In an industrial plant containing power factor correction capacitors, harmonics distortions can be magnified due to the interaction between the capacitors and the service transformer. This is referred to as harmonic resonance or parallel resonance. It is important to note that capacitors themselves are not main cause of harmonics, but only aggravate potential harmonic problems. Often, harmonic-related problems do not show up until capacitors are applied for power factor correction.

Impedance of the capacitor decreases with increase in frequency. Capacitor capacity to cancel out harmonic decreases with increase in frequency. This offer the low impedance path to harmonic currents. These harmonic currents added to the fundamental current of capacitors can produce dangerous current overloads on capacitor. Each of the harmonic currents causes the voltage drop across the capacitor. This voltage drop is added to the fundamental voltage. Thus in presence of harmonics higher voltage rating of capacitor is recommended. This overvoltage can be much above permissible 10% value when resonance is present.

Another important aspect is resonance which can occur when p.f. capacitors forms the series or parallel resonant circuit with impedance of supply transformer. If the resonance frequency of this LC circuit coincides with one of the harmonic present, the amplitude of the harmonic current flowing through LC circuit is multiplied several times damaging the capacitors, supply transformer and other network components.

## Precautions to be taken while switching ON a capacitor bank

Make sure that there is adequate load on the system. The normal current of the capacitor to be switched ON at 440 volts is say 100 amps. Therefore the minimum load current at which the capacitor should be switched ON is 130-150 amps.

If one capacitor unit is already on and a second one is to be added then minimum load current on this bus system must be equal to or more than the combined capacitor current of the two banks by at least a factor of * 1.35 to 1.5*.

After switching off the capacitor – wait for at least one minute before switching it on. Earth all the live terminals only after waiting for one minute before touching these with spanner etc. If above precautions are not observed, this could lead to dangerous situations both for plant and personnel.

Switch off the capacitors when there is not enough load. This is a MUST. If the capacitors are kept ON when there is no load or less load then Power factor goes to leading side and system voltage increases which may cause damage to the capacitors as well as other electrical equipments and severe disturbance can be caused.)

If the line voltages are more than the capacitor rated voltage, then do not switch on the capacitors. As the load builds up, the line voltage will fall. Switch on the capacitors then only.

### Operation of capacitor bank and co relatation with harmonics in the system

Harmonics can be reduced by limiting the non-linear load to 30% of the maximum transformer’s capacity. By doing this we ensure that power system does not exceeds the 5% voltage distortion level of IEEE Standard 519. However, with power factor correction capacitors installed, resonating conditions can occur that could potentially limit the percentage of non-linear loads to 15% of the transformer’s capacity.

F_{R} = √kVA_{SC} / kVA_{RC}

**Where,**

**F _{R}** = resonant frequency as a multiple of the fundamental frequency

**kVA**

_{SC}= short circuit current at the point of study

**kVA**= capacitor rating at the system voltage

_{RC}If **F**_{R} equals or is closed to a characteristic harmonic, such as the 5th or 7th, there is a possibility that a resonant condition could occur. Almost all harmonic distortion problems occur when the parallel resonance frequency is close to the fifth or seventh harmonic, since these are the most powerful harmonic current components. The eleventh and thirteenth harmonics may also be worth evaluating.

### True and displacement power factor specially with regards to variable speed drives?

Power factor of variable speed drives – With the six-step and current source inverters, the power factor will be determined by the type of front end used. When SCR’s are used, the power factor will be relatively poor at reduced speeds. When diodes with a dc chopper are used, the power factor will be the same as a PWM inverter, which is relatively high (near to unity) at all, speeds.

True power factor is the ratio of real power used in kilo watts (kW) divided by the total kilo volt-amperes. Displacement power factor is a measure of the phase displacement between the voltage and current at the fundamental frequency. True power factor includes the effects of harmonics in the voltage and current. Displacement power factor can be corrected with capacitor banks. Variable speed drives have different displacement power factor characteristics, depending on the type of rectifier.

PWM type variable speed drives use a diode bridge rectifier and, have displacement power factors very close to unity. However, the input current harmonic distortion can be very high for these variable speed drives, resulting in a low true power factor. True power factor is approximately 60% despite the fact that the displacement power factor is very close to unity. The true power factor can be improved substantially in this case through the application of input chokes or transformers which reduce current distortion.

Capacitor banks provide no power factor improvement for this type of variable speed drives and can make the power factor worse by magnifying the harmonic levels.