Air Core reACtors

introduction to switching of shunt Capacitor Banks

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Shunt capacitor banks are commonly installed in power systems to provide reactive compensation, reducing costs and optimizing power transmission. Some advantages of shunt capacitor bank installation are: > Compensation of the system’s inductive reactive

power

> Power factor correction

> Voltage control

> Harmonic filtering

However, the switching of shunt capacitor banks may cause thermal, mechanical and dielectric stresses in the other substation equipment. For this reason, transient studies are recommended to identify and quantify the transient duties that may arise in the system and to prescribe economical corrective measures whenever deemed necessary. The results of a switching transient study can affect operating procedures as well as the equipment in the system. The main objectives of the transient study are listed below:

> Identify the nature of transient duties that can occur for any realistic switching operation. This includes determining the magnitude, duration, and frequency of the oscillations.

> Determine if abnormal transient duties are likely to be imposed on equipment by the inception and/or removal of faults.

> Recommend corrective measures to mitigate transient overvoltages and/or overcurrents. This may include solutions such as resistor pre-insertion, tuning reactors, appropriate system grounding, and application of surge arresters and surge protective capacitors.

> Recommend alternative operating procedures to minimize transient duties (if applicable).

> Register the study results on a case-by-case basis in readily understandable form for those responsible for design and operation. Such documentation usually includes reproduction of wave shape displays and interpretation of, at least, the limiting cases.

The philosophy of mitigation and control of switching transients results in the application of one or more of the following methods:

1. Synchronized closing control for breakers and switches

2. Inrush current limiting reactors (damping reactors)

3. Temporary insertion of resistance between circuit elements (for example, the insertion of resistors in circuit breakers)

4. Surge arresters

5. Surge capacitors

6. Tuning reactors

7. Damped filters

8. Surge protective circuits

This paper presents the procedures for calculation and specification of damping reactors for limitation of inrush current of shunt capacitor banks.

sHuNt CAPACitor BANKs

There are three basic capacitor bank configurations:

1. Grounded wye

2. Ungrounded wye

3. Delta-connected

Grounded-Wye Capacitor Bank

Ungrounded-Wye Capacitor Bank

Delta-Connected Capacitor Bank

UN / fN / Scc UN / fN / Scc

UN / fN / Scc

Delta-connected capacitors are generally used at low voltages (e.g., 2.4 kV) where a standard capacitor rating is not available for a wye connection. Usually, wye-connected capacitor installations are less complicated to construct and more economical.

Concerning the grounding of the shunt capacitor banks, the advantages of the grounded-wye arrangement compared to the ungrounded-wye are as follows:

> Initial cost of the bank may be lower since the neutral does not have to be insulated from ground at full system BIL, as in the case with floating neutral arrangements.

> Recovery voltages due the capacitor switching are reduced.

> Mechanical duties may be less severe for the structure.

On the other hand, the disadvantages of the grounded-wye compared to the ungrounded-wye are as follows:

> High inrush currents may occur in substation grounds and structures, which may cause instrumentation problems.

> Grounded neutral may draw zero-sequence harmonic currents and cause telephone interference.

> The grounded-wye connection provides a low impedance fault path to ground and may require resetting of ground relays on the system. This is one of the reasons why grounded-wye banks are not generally applied to ungrounded systems.

> The grounded-wye arrangement usually makes current-limiting fuses necessary due to the line-to-ground fault magnitudes.

Grounded-wye, ungrounded-wye and delta-connected capacitor banks may also be subject to ferroresonant overvoltages if they are switched together with transformer banks of certain winding connections with single-pole switching devices or if a stuck pole should occur on a three-phase device.

Calculation of the Wye-Connected shunt Capacitor Bank ratingsThe ratings of a wye-connected shunt capacitor bank can be calculated as follows:

1. Rated three-phase reactive power :

2. Rated capacitive reactance per phase :

3. Rated capacitance per phase :

4. Rated current per phase :

The maximum continuous current of a wye-connected shunt capacitor bank depends on the:

> Voltage variations (typically, ±5% or ±10%)

> Tolerance of the equipment manufacturing (typically, -0/+15% for capacitors)

> Total voltage distortion due to harmonic resonances (typically, from 10 to 20%)

Therefore, the maximum continuous current can be estimated as follows:

The international standards indicate some guidelines for calculation of the effective current for wye-connected shunt capacitor banks, which are summarized in the table below:

The overcurrent factors for correction of the rated current are presented below:

Application examplesTwo installations of high voltage wye-connected shunt capacitor banks with associated current limiting reactors are shown in the pictures below:

245 kV capacitor bank with associated series damping reactor

132 kV capacitor bank with associated series damping reactor

sWitCHiNg of sHuNt CAPACitor BANKs

introductionThe switching of shunt capacitor banks has long been recognized as a potential source of voltage and current surges. Inrush currents associated with energization of single capacitor bank are about 5 per unit at frequencies of 200 to 600 Hz depending upon source impedance and bank size and its configuration. In comparison, energization of back-to-back capacitor banks and discharge of shunt capacitor banks to faults can produce transient currents of 40 to 100 per unit at frequencies of 2 to 20 kHz.

It is well known that restrikes during opening of shunt capacitor banks can cause severe problems on systems due to the possible escalation of overvoltages to as high as 4 per unit or more. In addition, the switching surges produced may propagate into the system and cause damages in power transformers and reactors at the remote end of radial transmission lines.

As mentioned in the previous section, various methods are currently in use to minimize switching transients, such as the using of pre-insertion resistors and current limiting reactors. Nowadays, the problems associated with restriking on switching capacitor banks are not of great concern, since the SF6 breakers are generally restrike-free. However, restrikes have been occasionally reported which have resulted in damage to system equipment.

requirements of Control systems and switching DevicesFor control of both inrush currents and overvoltages on switching of shunt capacitor banks, the optimum closing time for each pole would be at voltage zero between the poles of the switching device. For this reason, the control system and the switching device must have a capability of closing with an accuracy of approximately ±1 msec. A system with this degree of accuracy will limit switching surges to approximately the same order of magnitude as one with pre-insertion resistors or current limiting reactors. For these cases, no overvoltages would be expected, since the phase-to-earth and phase-to-phase overvoltages would be typically 1.2 per unit and 2.0 per unit respectively (e.g., normal system overvoltages). In addition, inrush currents would be reduced to insignificant values, particularly for back-to-back capacitor banks.

However, if errors are greater than approximately 1.4 msec, the prospective phase-to-phase overvoltage at a remote terminal could be greater than 4 per unit. At this level, phase-to-earth connected surge arresters, limiting phase-to-earth voltage to 2.0 per unit per phase, would begin to limit the phase-to-phase overvoltages.

grounded and ungrounded Neutral Capacitor BanksThe optimum closing time of wye-connected capacitor banks depends on whether its neutral is grounded

or ungrounded. For grounded neutral banks installed on grounded neutral systems, the optimum closing time would be at phase voltage zero at each pole. For ungrounded neutral banks, the optimum closing time is dependent upon the pole closure sequence.

Random closing is satisfactory for the first pole since no current flow is established. Assuming the first pole remains conducting, the second to close must close at voltage zero of the phase-to-phase voltage appearing across the pole. The third pole must close at voltage zero of the 1.5 per unit voltage appearing across that pole. Of course, if two poles close simultaneously, then the voltage across each pole will be 0.87 per unit and the third pole to close would experience a 1.5 per unit voltage.

When it is anticipated that the capacitor bank will be re-energized after a short-time after the de-energization (not a common requirement), then a trapped charge may be presented on the capacitor bank, and therefore, the optimum closing time depends on the magnitude of the trapped voltage. In this case, monitoring of both the source side and the load side voltages are necessary in order to establish the voltage across the open contacts of the breakers.

Since the optimum closing time for all three poles for either a grounded or ungrounded neutral bank is variable, it is recommended to use circuit breakers with the capability of independently closing the three poles. However, controlled switching is limited to applications in which the introduction of time delays between the closing time of the first, second and third poles are suitable. If there is some possibility of restriking on opening, then a rough control of the opening operation may be desirable such that contact parting is achieved well before a current zero. This would provide a maximum gap and dielectric strength across the switching device at the time of maximum recovery voltage and essentially eliminate reignitions and restrikes, and therefore, overvoltages.

Capability of Capacitors and switching DevicesThe circuit breakers and capacitors are the most sensitive equipment concerning the transient currents and voltages associated with the switching of shunt capacitor banks.

The capacitors are generally designed to withstand an overcurrent up to 100 times its rated current. The level of overcurrent is closely related with the life expectancy of the capacitor unit. For transient currents of 100 times the rated current, the maximum number of switchings shall not exceed 1000 times per year. However, for transient currents of 30 times the rated current, the maximum number of switching increases up to 100,000 times per year. [5]

For circuit breakers, according to international standards, the transient current and frequency shall not exceed the figures presented in the table below.

Table 04 – Transient capability of circuit breakers

Calculation of transient Currents of shunt Capacitor BanksThe determination of transient currents associated with energization and discharge of shunt capacitor banks should always be done by using appropriate software, such as ATP (Alternative Transient Program). However, the calculation of inrush and outrush currents may be acceptable, if the complete set of data required for a reliable digital simulation is not available.

As guideline, this section describes a simplified calculation procedure for current limiting reactors to be installed in series with shunt capacitor banks in order to keep the transient currents within the admissible values for the equipment (capacitors and switching devices).

energization of single shunt capacitor banks (inrush Currents)The inrush currents associated with energization of single capacitor banks are about 5 per unit at frequencies of 200 to 600 Hz, depending on the source impedance, bank size and configuration. Due to the high value of equivalent inductance of the system, this transient current does not cause relevant stresses on the equipment.

The source impedance (or system impedance) depends on the short-circuit power of the system at the capacitor bank busbar, given by:

The total time-varying current during the energization of single capacitor banks is compound by two components: steady state and transient period. The steady state component, which oscillates at 50 or 60 Hz, is generally neglected in the calculation of the inrush currents.

The transient component of the inrush current is given by:

The surge impedance of circuit, the peak value of the inrush current and its undamped natural frequency are given by:

> Surge impedance of the circuit

> Peak value of the inrush current

> Natural frequency of undamped oscillations

Since the magnitude and frequency of the inrush current associated with energization of single capacitor banks are not significant, the use of a current limiting reactor or pre-insertion resistors may not be necessary. However, for a system with very high short-circuit power (e.g., small source impedances) damping reactors may be required. The calculation of the reactance to be introduced in the circuit to limit the inrush current magnitude and frequencies to admissible values for the capacitor and switching devices are as follows:

> Criteria of maximum current

> Criteria of maximum frequency

Application examplesEnergizating a single capacitor bank, 138 kV, 30 MVAr, grounded-wye, connected to a 138 kV busbar with symmetrical short-circuit level of 20 kA and maximum operating voltage of 145 kV.

By installing a damping reactor of 0.571 Ω (1.515 mH) per phase, the calculated inrush current is 2.4 kAp at 708 Hz. This case was also performed in the software ATP and same results are presented below. It can be noticed that the simulated inrush current is a bit smaller than the calculated value, due to the effective resistances of the source, reactor and capacitor, which have not been considered in the calculations.

Picture 05 – Circuit for analysis of energization of single capacitor bank

Phase-to-earth voltage at capacitor bank bus

Inrush current associated with energization of the single capacitor bank

UN

CB

Due to the high currents and frequencies, the energization of back-to-back capacitor banks always requires the insertion of damping reactors or pre-insertion resistors. The calculation of the reactance to be introduced in the circuit to limit the inrush current magnitude and frequencies to admissible values for the capacitors and switching devices are as follows:

> Criteria of maximum current

> Criteria of maximum frequency

The equivalent inductance and capacitance are given by:

> Equivalent inductance of the circuit

> Equivalent capacitance of the circuit

remarks: a. It was assumed the installation of identical current

limiting reactors in series with each phase of the capacitor bank.

b. For “N” capacitor banks of the same size, the equivalent capacitance is given by:

Application examplesEnergizing two back-to-back capacitor banks, 138 kV, 30 MVAr, grounded-wye, connected to a 138 kV busbar with symmetrical short-circuit level of 20 kA and maximum operating voltage of 145 kV.

By installing a damping reactor of 0.571 Ω (1.515 mH) per phase, the calculated inrush current is 3.3 kAp at 2000 Hz. This value is greater than the one obtained for a single capacitor bank due to the contribution of the capacitor bank in operation in the same bus at the instant of the energization. In addition, the damping of the oscillations is faster due to the higher effective resistance value of the reactor at a higher frequency.

energization of back-to-back capacitor banks (inrush Currents)It is common to divide large capacitor banks in smaller shunt capacitor banks, to provide flexibility and reliability to the reactive compensation system. However, when two or more capacitor banks are in back-to-back configuration, the inrush currents associated with energization of a capacitor bank with other ones in operation can achieve up to 100 per unit at frequencies of 2000 to 20,000 kHz. It may produce high mechanical and dielectric stresses on the capacitor bank components and other equipment in its vicinity.

The total time-varying current during the energization of a capacitor bank is compound by three components: steady state, contribution of the system and contribution of the capacitor banks in operation in the same bus. Each component has a different peak value and frequency. Since the third component is more significant than the other ones, the steady state component and the contribution of the system to the inrush current may be neglected.

Therefore, the inrush current associated with energization of the capacitor bank “N”, with “N-1” capacitor banks in operation in the same bus, is given by:

The surge impedance of circuit, the peak value of the inrush current and its undamped natural frequency are given by:

> Surge impedance of the circuit

> Peak value of the inrush current

> Natural frequency of undamped oscillations

Phase-to-earth voltage at capacitor bank bus

Picture 05 – Circuit for analysis of energization of back-to-back capacitor banks

UN

CB CB CB

Discharge of shunt Capacitor Banks to faults (outrush Currents)When a short circuit occurs near to the shunt capacitor bank, it will discharge its energy through the low impedance path provided by the fault. The magnitude and frequency of the outrush current are of the same order as the inrush currents associated with energization of back-to-back capacitor banks, which can achieve up to 100 per unit at frequencies of 2000 to 20,000 kHz.

The worst condition is when the voltage across the capacitor bank is in its peak value. So the outrush current due to the discharge of the capacitor bank to fault is given by:

The surge impedance of circuit, the peak value of the inrush current and its undamped natural frequency are given by:

> Surge impedance of the circuit

> Peak value of the inrush current

> Natural frequency of undamped oscillations

Due to the high currents and frequencies, the discharge of a single capacitor banks to a fault always requires the insertion of damping reactors or pre-insertion resistors. The calculation of the reactance to be introduced in the circuit to limit the inrush current magnitude and frequencies to admissible values for the capacitors and switching devices are as follows:

> Criteria of maximum current

> Criteria of maximum frequency

Application examplesOccurrence of a three-phase-to-ground fault in a 138 kV busbar with a symmetrical short-circuit level of 20 kA and one single capacitor banks, 138 kV, 30 MVAr, grounded-wye, in operation at the instant of the fault.

By installing a damping reactor of 0.571 Ω (1.515 mH) per phase, the calculated outrush current to the fault is 6.7 kAp at 2000 Hz. As per single capacitor banks, the simulated value is smaller than the calculated value due to effective resistance of the system components. In addition, the damping of the oscillations is faster due to the higher resistance value of the reactor at high frequency of the discharge.

iNflueNCe of tHe Q-fACtor of tHe reACtor

Up to now, no dissipative elements have been considered in the previous presented analysis, but practical circuits have losses arising primarily from system and equipment resistances, iron losses in transformers and shunt reactors. In addition, system loads represent very important dissipative elements.

The dissipation is accommodated by including resistances in the circuit. In making transient analysis, all losses usually are neglected in the first instance, which simplifies the calculations. Moreover, this approach leads to conservative results with more severe overvoltages. Once the general behavior of the circuit has been established, the modification introduced by the system losses can be considered separately. Introducing resistance always has the effect of damping out the natural oscillations of a circuit. How quickly it occurs will depend on the amount of the losses or, in other words, the value of resistance relative the values of inductance and capacitance.

Concerning the air-core current limiting reactors installed in series with the shunt capacitor banks, their losses are represented by insertion of a series resistance in the circuit. Both the reactance and the AC series resistance of a damping reactor depend on the frequency, and the relation between them provides the Q-factor of the reactor, given by:

The damping of the inrush and outrush currents is evaluated by the Q-factor value at transient frequency. Typically, the Q-factor of a damping reactor decreases with the increasing of frequency. The effective resistance depends on various factors, such as: reactor design, geometry of the coil (diameter and height), number and size of internal conductors of the winding, material of the conductor (aluminum or cooper) and numbers of turns of each layer of the winding.

Inrush current associated with energization of the back-to-back capacitor banks

Outrush current of single capacitor bank during a fault at system

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Therefore, the Q-factor of damping reactors depends on their ratings. For reliable analysis, the manufacturer should be contacted to provide the typical values for a previously specified current limiting reactor.

The Q-factor at fundamental frequency of a damping reactor can be calculated by the relation between the rated reactive power and the total active losses per phase, as follow:

In some cases, power resistors may be installed in parallel with the current limiting reactors to reduce the Q-factor to very small values. In other cases, pre-insertion resistors are installed in the circuit breakers to provide high damping during energization of the shunt capacitor banks. During normal operation, these resistors are by-passed to reduce the total power losses of the circuit.

Application examplesEnergizating a single capacitor bank, 138 kV, 30 MVAr, grounded-wye, connected to a 138 kV busbar with symmetrical short-circuit level of 20 kA and maximum operating voltage of 145 kV.

By installing a damping reactor of 0.571 Ω (1.515 mH) per phase and running this case in the software ATP with two different effective resistances (or Q-factor), the inrush currents obtained from simulations are plotted in the curves below.

simBology

refereNCes

[1] ANSI/IEEE C57.16/1996 – Standard Requirements, Terminology and Test Code for Dry-Type Air-Core Series Connected Reactors.

[2] IEC 60289/1988 – Reactors.

[3] ANSI/IEEE C37.012/1979 – Application Guide for Capacitance Current Switching for AC High Voltage Circuit Breaker Rated on a Symmetrical Current Basis.

[4] IEC 62271-100 – High Voltage AC Circuit-Breakers

[5] Manoeuvre et protection des batteries de condensateurs MT. Cahier Technique Nº 189. Group Schneider. 1997.

[6] Capacitive Current Switching – State of Art. Electra Nº 155. 1994.

[7] ATP Rule and Theory Book.

To request technical information, please contact us by e-mail:aircorereactors.itr@areva-td.com

Representation Description Unity

UN Rated system voltage (kV)

UMAX Maximum system operating voltage (kV)

fN Rated system frequency (Hz)

Natural system frequency (rad/sec)

SCC Rated system three-phase short-circuit power (MVA)

ICC Rated system three-phase short-circuit current (kA)

XSIST Equivalent system reactance (Ω)

LSIST Equivalent system inductance (mH)

XCN Rated shunt capacitor bank reactance (Ω)

SC3Ø Rated three-phase shunt capacitor bank power

(kVAr)

CN Rated shunt capacitor bank capacitance (μF)

ICN Rated shunt capacitor bank current (A)

IRMS Design shunt capacitor bank current (A)

N Number of parallel shunt capacitor banks

fMAX Maximum circuit breaker operating frequency (kHz)

IMAX Maximum circuit breaker breaking/making current

(kAp)

LR Rated current limiting reactor inductance (μH)

FQ Current limiting reactor Q-Factor

R Current limiting reactor AC resistance (Ω)

t Time (seg)

Z0 Surge impedance of the circuit (Ω)

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Inrush current for a damping reactor with an effective resistance of 60 mΩ at 708 Hz

Inrush current for a damping reactor with an effective resistance of 1500 mΩ at 708 Hz