Chapter 1

Introduction
1.1. Overview and Application of SCBs
Capacitor banks are of two types 1) series capacitive element banks 2) Shunt Capacitive element
banks. Both these configurations depend on the method of connecting with in the system. SCBs
lessen line current and line losses and also improve potential profile and power factor. Series CBs
improves the potential profile of the system, however they have no control over the current flow as
these CBs are configured in series. Moreover, potential across the capacitive element bank rises up to
15 times of its rated potential. Hence the use of series CBs is confined to specific high potential
systems only.
A SCB is a power-system component that improves potential profile [1], power factor
improvement [2] and/or power loss reduction [3]. We have been adopting shunt capacitive element
units to fulfil the capacitive reactive power needs or power factor improvement. The application of
shunt capacitive element units has availed great popularity because they are quite less expensive,
simple to use and are placed at optimally located in the electrical power system. Its installation in the
existing system has additional advantages on the electrical proficiency of the system such as:
improved potential regulation at the load side, reduction of system losses and lessening of huge
investments in electrical systems. Primarily the weakness of the shunt capacitive element units lies
in their reactive power generation because it is relative to the square of potential, and as a result
when potential is least and electrical system need them most, they are not delivering the required
value of the reactive power.
SCBs are also exposed to serious faults. The major fault that appears inside a SCB is element/unit
failure. This element failure not only deprives the power system of KVAR but also a considerable
loss to the economy [4]. If SCB is exposed to that fault for longer duration, the phase –line voltage is
redistributed and healthy elements/units experience overvoltage, hence, the outage time of a SCB is
decreased if the fault is not properly identified [5]. Hence to ensure maximum availability of SCB in
our power system Fault identification of SCBs is necessary.
A SCB has large number of power capacitors. It is extremely difficult to monitor each and every
capacitor by physical inspection. On the other hand, relying on power system protection devices to
trip SCB in case of fault appearance from service is an out-dated practice. Instead SCB faults should
be quickly and correctly detected by the system only designed for SCB protection [6][7][8]. SCB
protection is a two stage process and it is known to be a very time consuming process [ 9]. The first
1
step taken by the protection scheme is to identify the number of faulty elements or units and to locate
the exact place of fault. After proper fault identification, data is fed to microcontroller based
protection relays. SCB Fault identification is the vital part of the protection of SCBs. Fault
Identification methodology serves as the brain for SCB protection. SCB protection schemes are
installed for instability provoked inside the SCB itself. In case of fault, the first step taken by the
protection scheme is to isolate the unit or element inside the SCB, so that it might not result in
damaging of the entire SCB unit. In case the fault excites to the greater extent, protection scheme
trips that SCB from the service that might bring a calamitous failing, and also provide warning to
announce instability within the SCB [10]. But all this can be only possible if we can properly locate
the fault and its place of occurring.
SCB fault identification schemes can be deceived by undetectable faults. Sometimes same number of
elements fail in both wyes of SCB. This type of failure cause same magnitude of neutral current to
flow. When current reaches at neutral point, due to same in magnitude neutral currents cancel each
other. Hence apparently no fault is detected by fault identification scheme. This problem arises due to
back-end mathematic algorithm. The mathematical analysis of fault identification system to remove
undetectable faults is the primary research issue of this thesis.
Parameters of SCB are very important while performing fault identification methodology. Parameters
show considerable deviation from normal value during fault condition. This thesis also discuss in
details all SCB parameters and their affect on SCB performance.
Different type of SCBs behave differently during fault. The thesis also provide comparative analysis
of Externally fused and Fuseless SCBs parameters and also provide sound reasons of their behavior.
The above mentioned reasons provide base for our problem statement.

1.2. Problem statement

The recent research has succeed to locate the exact phase at which the fault occurs, however, the fault
identification has serious limitations that lead us towards undetectable faults. In [11] a differential
current measurement approach is employed for fault identification. However, this identification
scheme uses more CTs and less sensitive in a sense that this scheme is silent about fault appearance
in both sides of the SCB simultaneously. In [12] neutral compensation technique is used to locate
faulty elements but this methodology also has an issue regarding fault location during ambiguous
indications. [13] covers different SCB types. However it does not propose to identify fault in both
halves of SCB simultaneously. [14] uses neutral compensation approach to find faulty phase but it is
silent about fault identification during same capacitive reactance change in both halves of SCB. All
above cases provide a research gap. The parameters of SCB at fault are not discussed in detail in

2
above discussed papers. The parameters of SCB provide all the necessary information about SCB
during fault operation. This research gap provides the basis of following problem statements.
1) Fault identification methodology is not sensitive enough to identify fault in both halves of
SCB without ambiguous indication (same number of faulty elements on both halves of SCB).
2) All SCB parameters are not discussed in detail to show their deviation from normal behavior
during fault.

1.3. Objective of Research

1) To propose fault identification methodology that is sensitive enough to identify fault in both
halves of SCB without ambiguous indication.
2) To discuss all SCB parameters in detail to show their deviation from normal behavior during
fault.

1.4. Scope of Research

The scope of research is limited to mathematical analysis of fault identification methodology of
SCB protection.

3
Chapter 2
Literature Review
2.1. The capacitive element unit and SCB configurations
2.1.1. The capacitive element unit

The capacitive element unit is the substantial element of a SCBs. The capacitive element unit is
developed of individual capacitive elements, configured in parallel/series configurations, within a
steel case. Internally the discharge element is a resistor that lessens unit residual potential up to 50V
or less with in 5 minutes. Capacitive element units are made in huge number of potential ratings
(240V to 24kV) and ratings (2.5 KVAR to nearly1,000 KVAR)[15].

Disscharge Resistor
16.6kV 16.6kV
625MVAR 625MVAR
Single capacitor
unit
16.6kV 16.6kV Having 12
625MVAR 625MVAR capacitors

16.6kV 16.6kV
625MVAR 625MVAR

16.6kV 16.6kV
625MVAR 625MVAR

Figure 1. single-⌀ of a split-wye grounded 115 KV-5MVAR Bank

Source IEEE guide for SCB protection C37.99 2012

2.1.2. Shunt capacitive element unit features

Protection of shunt capacitive element units demands us comprehending the merits and limitations of
capacitive element unit and related electrical devices that include: one by one capacitive elements,
bank switching equipment fuses, potential and current sensor elements. Capacitive elements are
demanded to operate at or below their rated potential and frequency since they are massively
4
responsive to these parameters; the reactive power produced by a capacitive element is relative to
above factors.
Standard sizes of the capacitive elements manufactured for shunt installation to AC electrical systems
are detailed in IEEE Standards 18-2012 and IEEE Standards 1036-2012 [16][17]. These standards
also provide instructions for application guidelines. Here are the standards which specify that:

 Shunt capacitive element units need to be designed for uninterrupted service up to 110% of
rated RMS potential and crest potential not over-exceeding of rated RMS potential and it
should reckon the elevated frequency components but omitting momentary bursts.

 The shunt capacitive element units should master to combat 135% of nominal current.

 Shunt capacitive element units must not impart below 100% or more than 115% of reactive
power at rated sinusoidal potential and frequency [18].
Shunt capacitive element units are not at their best for uninterrupted utility up to 135% of the
rated reactive power made by inter -composed impacts of:

 Potential in oversupply of name-plate rating at rated frequency, but not over 110% of the
rated RMS potential.

 Elevated frequency potentials overlapping on rated frequency.

 Reactive power formulation gap of up to 115% of the rated reactive power.

Huge range of VAR and potential ratings allows protection engineer can design an economical
(No. of units inserted in the SCB, the complex SCB design, schedule maintenance) and the
aftermaths of an element or unit failing. For example, owing to the blown fuse in externally
-fused bank, one entire unit goes disengaged. If engineer has designed the SCB with a few units
of large KVAR rating, a substantial magnitude of KVAR might go out of use. Large magnitude
of KVAR (capacitance) loss will deprive us of available potential support, capacity of reactive
power management, or usefulness of elevated frequency filtering.
Many factors dominate the design of a SCB, advancements in the dielectric has majorly
lessened element failings inside a SCB unit. In the early history, the SCB units employed Kraft
paper with PCB impregnate as a fundamental dielectric material. Kraft paper was of supreme
refined quality, but the paper had still much non-uniformity in it [19]. Now a days the power
capacitors are built with propylene film and films are impregnated with fluids such as faradol and
dielectric constant at 60 Hz is 2.27[20][21]. Due to such advancements the dielectric losses are
5
 reduced to 0.12KW/KVAR for externally fused SCBs and 0.2KW/KVAR for fuseless SCBs [22].
Due to dielectric advancement the dissipation factor has also reduced to 0.004 for 60Hz and
0.00001 for 1 MHz[23].The dissipation factor for power capacitors is
i 2 ESR
tg ∂= 2 2.1
i XC
Where ESR is equivalent series resistance i 2 is ideal capacitive current and X C is ideal capacitive
reactance.
The discharge factor in case of parallel equivalent resistance is
I Loss
tg ∂= 2.2
IC

Where ILOSS is current decreased due to capacitance loss and I C is ideal capacitor current[24]. 2.1
and 2.2 show that increase in failures of capacitors will result in decrease in parallel capacitance
as a result loss current will increase and ideal capacitor current will decrease. This will increase
the dissipation factor. 2.1 and 2.2 also show that main reason reason for capacitor discharge is
abnormality of capacitive reactance and capacitive current that create overvoltage [25]. SCBs
avoid weaker spots in the dielectric material, SCB units had numerous layers of paper
interpolated among foil layers. When dielectric material of this type went out of order, the foil
layers did not band together to form a firm connection. Instead, the cellulose extended to arc,
originating carbonizing of the paper that provoked gas inside the airtight SCB unit. In many
cases, this gas buildup provoked entire unit to breach by one, originating in continuing series of
element failings.
Now a days dielectrics are fabricated with a few-layer technology of impregnated polypropylene
film. Film layers are fabricated to be slim and failings in the capacitive element provoke the foils
to band together, as a result a firm connection is established eliminating the danger of arc and
carbonizing. These stages of a fuse blowing must be understood.

2.2. SCBs configurations

Fuses are put in place in capacitive elements and they are sited optimally (internally on the capacitive
element unit on single element or outwards) is a major design technique and it needs to be mastered
before further working on shunt banks. They also footprint the out of order mode of the capacitive
element and influence the configuration for shunt capacitive elements:

6
 • External fuse - A separate fuse, on the exterior side is put in place between the capacitive
element and the capacitive element bank fuse bus bar, predominantly protects individual
shunt capacitive element. The shunt capacitive element is also designed for a correspondingly
high potential since the exterior side fuse can deal a high potential fault. Exercising
capacitive elements with the huge possible potential rating will result to shunt capacitive unit
with the lowest number of series series-parallels.

A defect in a capacitive element unite the foils together and roots short circuit currents to drift
between capacitive elements configured in parallel in identical formation. The halting capacitive
elements in the bank hold in operation with an elevated potential across them than before the fault. If
a second element also go out of order this also puts potential pressure on remaining capacitive
elements. Subsequent faults inside the identical bank will incite the fuse to trip, drawing out the
capacitive element and indicating the failed one.

2.2.1. Externally-fused SCBs

These units are equipped adopting one or more series formation of parallel -configured capacitive
elements per phase as visible in figure 2. The instability signaling magnitude truncate as number of
series formations of capacitive elements is heightened or as number of capacitive elements in parallel
within a series formation is elevated. Nevertheless, reactive power rating of isolated capacitive
element might crave being smaller since a least number of parallel elements is vital to grant SCBs to
keep on activity with one fuse or unit out.

Single capacitor
unit
Having 12
capacitors

Figure 2.Externally-fused SCBs

Source: IEEE guide for SCB protection C37.99 2012

7
2.2.2. SCBs with internal fuses

Single capacitive element has a fuse inwardly the capacitive element. The fuse is a primitive part of
the wire competent to restrict the current and summed up in a wrapper that can endure the heat
provoked by the arc. When fault arises in capacitive element, the fuse takes out the struck element
only allowing remaining elements, configured in parallel in identical configuration, keep on activity
but with a little bit elevated potential across them.

Single capacitor
F4 F12 F11
unit
Having 9
capacitors

F7 F8 F6

F5 F10 F9

Figure 3. Internally-fused SCBs with single unit separately shown

Source: IEEE guide for SCB protection C37.99 2012

A common capacitive element bank that uses capacitive elements with an internal fuse is visible in
figure 3. Generally, shunt capacitive elements that are inwardly fused are equipped with less
capacitive elements in parallel and more series formations of elements. The capacitive elements are
traditionally large because entire unit is not predictable to break down.

2.2.3. Fuse-less SCBs

Fuse-less shunt capacitive elements have massive identically to Externally-fused banks as shown in
figure 4. To make a SCB, capacitive elements are organized in series chains between phase and
neutral, as visible in figure 4. Protection is set up on capacitive elements (inside unit) deteriorating
in a shorted mode, adopting short circuit in the formation. Once the capacitive element waste away,
the capacitive element unit keeps on its activity but the potential across collapsed capacitive element
is then re-distributed among additional capacitive element formations that are configured together in
the series [26]. Consider an example in which a SCB has 6 capacitive element units that are
configured in series and one by one unit comprises of 8 element formations in series, there is a net
magnitude of 48 element formations configured together in series. If one capacitive element waste
8
away, potential stress (48/47=1.021×100=102.1%) will be on the remaining elements. Hence 2%
elevation in potential. The capacitive element bank goes on performing its job; nevertheless, but
chronological wasting of elements will aftermath the eradication of the bank. The design not
accommodating fuses is not typically employed for system potentials lessened than about 34.5kV.
Experiments say that there shall be more than 10 elements associated in series so that the capacitive
element bank does not have to be redirected from operation for the wasting away of isolated element,
since potential stress across additional elements would elevate by a factor of e(e-1) where ‘e’ is the
number of elements in chain. The discharge energy is trivial because not a single capacitive element
unit is configured directly in parallel. The surplus benefit of units without fuses is that the fault
identification is not required to achieve organization with the fuses.

Single capacitor
unit
Having 12
capacitors

Figure 4.Fuse-less SCBs with single unit separately shown

Source: IEEE guide for SCB protection C37.99 2012

2.2.4. Un-fused Shunt SCBs

Un-fused SCBs configuration is shown in figure 5. Contradicting with the Fuse-less configuration
having units that are configured in series, the un-fused SCBs are formulated in a series/parallel
configuration of the capacitive element units. The un-fused configuration is frequently adopted on
units below 34.5kV, where a series chain of capacitive element units are not advised to design or
higher potentials units with trivial parallel energy. This configuration is not required as many
capacitive element units configured in parallel as SCB with external fuses [27].
9
 Single capacitor
unit
Having 12
capacitors

Figure 5.Un-fused SCBs with single unit separately shown

Source: IEEE guide for SCB protection C37.99 2012

2.3. Design of the SCB

The protection of shunt capacitive element units needs total grip of the foundation of capacitive
element bank construction and capacitive element unit configuration. Shunt capacitive element units
are systems of series /parallel configured units. Capacitive element units are standardized in parallel
form a formation, and series configured formations form a uni-phase capacitive element bank.

It is highly recommended that least number of units must be configured in parallel so that if one
capacitive element unit waste away in a formation it must not provoke a potential stress more than
110% of the rated potential on surplus capacitive elements of the formation. Identically, last number
of the series configured formations is such that the total bypass of formation do not disturb the ones
staying in operation to a lasting over-potential of more than 110%.

The ultimate number of capacitive element units that are inserted in parallel per formation is
determined by certain requirements. When single unit of SCB is wasted away, the left over
magnitude of capacitive elements in identical parallel formation tolerate some magnitude of charge.
The charge will dissipate in a form of a high frequency momentary bursts current that goes through
wasted away capacitive element unit and its fuse. Fuse holder and the wasted away capacitive
element unit must be able to handle this discharge momentary bursts.

The discharge momentary bursts from a bulk quantity of wasted away parallel capacitive elements
can be severe is enough to part into pieces the wasted away capacitive element unit or the expulsion
fuse holder, which will result in disaster to the rest of the units or provoke a serious bus break down
10
internally the bank. To lessen the practicability of wasting away of the expulsion fuse holder, or
breakage of the capacitive element case, the protection engineers have put a limit to the overall
ultimate energy stored in a parallel configured formation to 4,659 KVAR [27]. In order not to cross
this periphery, the technique of more capacitive element formations of a less potential rating
configured in series with less units are configured in parallel per formation is established.
Nevertheless, this might elevate the problem of decrease in the impression- ability of the instability
detection system. A double Y configuration is the best available answer and might provide a
enhanced instability detection system. Another adequate option is the insertion of current limiting
fuses.

The peerless configuration for a SCBs primarily depends upon the best handling of the provided
potential rating of capacitive element units, fuses, and protective relaying. Usually all substation
units are configured in wye distribution capacitive element units, nevertheless, might configured wye
or delta. There are units which prefer an H configuration on one by one and e phase also adopting a
CT in the associated branch to get informed about the instability and use protective techniques.

2.3.1. Units configured in grounded Wye

Grounded wye capacitive element units consist of series and parallel-configured capacitive element
units per phase and they bring for least impedance path from phase-ground [28]. Generically bank
configurations are visible in Figure 6. Here are the merits of the grounded capacitive element units
are:
 Low-impedance path to ground which allows for essential its own protection from lightening
surge currents and protection from surge potentials. Shunt capacitive element units can serve
without surge arresters because of the fact that they can suck in the surge.

 They are also inserted as a filter for high frequency currents because of the fact they serve for
low-impedance path for high frequency currents and hence they can be proficiently inserted
as filters in configurations with elevated frequency content. Nevertheless, care is essential to
handle resonance between the SCBs and the electrical system.

 Diluted momentary bursts recovery for circuit breakers and additional switching devices.

Few disadvantages for grounded wye SCBs are:

11
  They are greatly influenced by the interference on telecom circuits owing to elevated
frequencies;

 They can motivate potential disorder and/or over-operation on protective equipment owing to
circulation of inrush currents and elevated frequencies.

 They also require for phase-configured series reactors to lessen the potentials coming out on

the CT secondary which is a consequence of high frequency, high magnitude currents.

2.3.2. Multiple units configured in series phase-ground Double- wye

Once a capacitive element gets big, thereby building the parallel energy exceeds (above 4,650
KVAR) for the capacitive elements units or fuses, the SCB might be divided into two split-wye parts
as shown in figure 6. The grounded single- wye bank will behave exactly alike the grounded double-
wye bank. The two neutrals are configured with a common joint to ground. The double- wye
configuration provides a healthier and more speedy configurations for fault identification with a non-
complicated, non-compensated relay, since any null-sequence component system strike both wyes
evenly, but a wasted away capacitive element unit will be detected instability in the neutral. Time
organization might need to grant a fuse, in or on an away capacitive element unit, to blow.
Configuring it without a fuse, the time lag might modify trivial or short since no fuse organization is
vital. If current through the string surpass the uninterrupted proficiency of the SCB unit, more chains
need to be given in parallel.
Phase A
Phase B

Phase C

.
(a)
12
 PHASE A
PHASE B
PHASEC

(b)

Figure 6(a). Un-grounded wye SCB units arranged un-grounded single- wye
Figure 6(b). Un-grounded wye SCB units arranged un-grounded double- wye
Source: IEEE Standards for application of SCBs C37.48 2010
2.3.3. Units configured in un-grounded wye

Bank systems configured in un-grounded wye manner are visible in figure 7. Un-grounded wye units
provide great hindrance towards null- sequence currents, third elevated frequency currents. They also
restrict the huge capacitive element discharge currents when system ground failings occur. Another
profit is that over-potentials appearing at the CT secondary sides do not go greater in magnitude
regarding grounded configurations. Nevertheless, the neutral should be properly insulated for high
line potential, since it is right away goes phase potential when SCB is activated, or when single
capacitive element waste away in SCB setting up for operation with an individual formation of units
[29]. For units higher than 15kV, this might be uneconomical.

Multiple units configured in series phase to neutral single- wye configuration. SCBs units
with externally applied fuses, internally applied fuses, or absent fuses can be configured to form the
bank. For fault identification systems that are conscious to system potential instability, two
possibilities are there for us, either fault identification time lag is set sufficiently long enough so that
line protections eradicate ground failings, or the capacitive element bank is tripped.
Multiple units configured in series phase to neutral double- wye configuration. As per IEEE
standards when a capacitive element bank goes beyond the ultimate 4,650 KVAR per formation, the
SCBs is split intentionally into two wye parts. As long as the two neutrals are not grounded, the bank
has some of the characteristics of un-grounded single-wye SCBs. These two neutrals might be

13
configured together through CT or VT. Same like for any un-grounded wye SCB, neutral CTs are
properly insulated from ground for full line-ground potential. Identical criteria holds for the phase
Phase A
Phase B

Phase C

(a)
PHASE A
PHASE B
PHASEC

(b)

Figure 7(a). Un-grounded wye SCB units arranged un-grounded single- wye
Figure 7(b). Un-grounded wye SCB units arranged un-grounded double- wye
Source: IEEE Standards for application of SCBs C37.48 2010
2.3.4. Shunt capacitive element units configured in delta configuration

Delta configured SCBs are shown in figure 8. SCBs units that are configured in delta design are more
functioned only at distribution potentials and are set with an only series formation of capacitive
elements rated at line-line potential [30]. With only one series formation of units, the major
advantage that happen that no over-potential elevate across the fully operational capacitive element
units from isolation of a wasted capacitive element unit. Hence, the need of fault and instability
detection is not the requirement

14
 C2

Figure 8. delta configured SCBs

Source: Northeast power systems
2.3.5. Units configured in H-Bridge configuration

H-Bridge configured SCBs are shown in figure 9. Few enlarged SCBs units also practice an H-
Bridge in all phases having installed CT configured among two legs to examine the current flowing
through every leg [31]. When all capacitive elements are up to the mark, null current flow through
the CT. In case capacitive elements waste away, current will pass through CT. H-bridge
configuration can be responsive. This special design is practiced on big units having many SCBs
units operated in parallel

Figure 9. H-Bridge configured SCBs

Source: IEEE Standards for application of SCBs C37.48 2010

2.4. Protection of SCBs

The protection of SCBs involves [32]:

15
  Protection of the SCBs against failings happening within the SCBs involving those inside the
SCBs unit.
 Protection of the SCBs against system disruption and failings. The adopted protection
scheme for a SCBs relies on SCB configuration: the capacitive element banks unit is
grounded or not and the nature of system grounding.

2.5. SCBs protection

The protection of shunt capacitive element units against system intrinsic failings mainly relies on
protective equipment that functions in a coordinated terminology. The protective devices that guard a
SCBs from internal failings are mainly as following:
1) Separate fuses
2) Fault identification to give warning.
3) Overcurrent devices for bank failing protection.

Eradication of wasted away capacitive element by its fuse ends in elevation of the potential stress
across the operational elements that consequences in an instability inside the bank. An over-potential
condition prevailing for long time, higher than 10%, on any element will be restricted by the
employing protective relays that disconnect the SCB.

Fault identification finds magnitude of parameters altered that emerged from the wasting away of a
capacitive element or unit and dis-function the bank from functioning when the originating potential
becomes over-limiting on the remaining fully functioning capacitive element units.

Fault identification typically comes with the prime protection for arcing failings within a SCBs and
other issues that might affect the function of a SCBs unit. Arcing failings might incite a significant
damage in the minute fraction of a second. The fault identification must be the lowest possible
intentional detainment in order to derogate the magnitude of harm to the SCBs in the case of external
arcing.

In most SCBs units, an external arc inside the capacitive element bank may not end in enough change
in phase current to function the main failing protection (typically an overcurrent relay). Impression-
ability demands for proper SCBs protection for above said situation might be broad, typically for
SCBs with various series configurations. Based on the impression- ability demand a protection
scheme is developed in which specific potential or current parameter of the SCBs is evaluated and

16
cross compared to SCB stable circumstances. SCBs protection does have many configurations, which
depends on the capacitive element bank typical design and grounding method. A number of
protection systems are employed for Internally-fused, Externally-fused, fuse less, or un-fused SCBs.

2.6. SCBs element failing mode

To expand the efficiency of fault identification it is vital to take a deep look on the wasting away of
the shunt capacitive element. In Externally-fused, Fuse-less or un-fused capacitive element banks, the
wasted element is short-circuited originating in the welding of both electrodes. The weld arc most of
the time happens at the point of fault (the element waste away short-circuited). This short circuit
disturbs the complete formation of elements, thereby elevating potential stress on functioning SCBs
formations. Few more capacitive element waste away until the external fuse completely isolates the
unit. The external fuse will perform its action once a SCBs unit goes short circuited, thereby
disengaging the wasted away unit.

SCBs that are Internally-fused have specially manufactured fused capacitive elements that are
disengaged when an element wasting happens. The danger of successive failings is shrink since the
fuse will disengage the wasted away element within a few seconds. Failing of an element
consequences in less instability than compared with the entire unit failing in case of Externally-fused
banks (since the quantity of capacitance taken away by a blown fuse is lower), and therefore a highly
responsive fault identification system is employed when units with internally-fused configuration are
employed.

2.7. Intrinsic instability and system instability

Practically, instability signal detected by instability relay is consequence of wasting away of

operating capacitive elements and the system fault that is cited internally and SCBs instability.
Primarily the instability condition that prevails on all SCBs configurations is owing to system
potential redistribution on the healthy elements and capacitive element production margin. Secondary
instability mistakes are brought in by detecting equipment margins and change and by relative
variations in capacitance owing to deviations in shunt capacitive element unit temperatures in
capacitive element banks. This crucial instability mistake might force to stop instability relay
functioning, or to induce a invalid functioning.

If the intrinsic instability mistake magnitude surpass 50% of the warning value, compensation is
applied in order to adequately warning for the fault as in case of one element as defined. In some
particular settings, a different SCBs design can heighten the impression- ability without providing
17
compensation. For instance, a wye configured SCBs is divided into a wye-wye SCBs, consequently
duplicating the impressionability of the protection and smooth the system potential instability result.

Employing neutral instability terminology system with compensation for intrinsic instability is
typically needed for big units. Neutral instability provoked signal generated by loss of one or two
separate capacitive elements is insignificant in comparison to the intrinsic instability, and the second
one appears to be unnoticeable. Instability compensation needs to be adopted if the intrinsic
instability surpasses ½ of desire value. Elevated frequency potentials and currents might affect the
function of the instability relay and can be eradicated by exercising frequency band-pass or other
adapted filtering.

2.8. Considerations of instability for trip relays

The time detainment of the instability trip relay should be diminished to cut down harm from an
arcing failing inside the SCB configuration and forestall exposure of rest of the shunt capacitive
elements to over-potential circumstances outside their allowed boundaries.

The instability trip relay needs sufficient time detainment to avert invalid functioning owing to inrush
current and the system ground failings, switching of other configured device, and non-simultaneous
pole function of the energizing switch. For the majority of usages, 0.1s should be enough. For
instability relaying schemes that would function on a system potential instability, a detainment
somewhat longer than laborious protection failure , clearing time is needed to avert tripping owing to
a system failing. Longer detainments raise possibility of catastrophic SCBs faults.
With grounded capacitive elements, the fault of one pole of SCBs switching equipment or a single
phasing from a blown SCBs fuse will permit null- sequence currents to go in system ground relays.
SCBs relaying, including the operating time of the switching equipment, needs to be interconnected
with operation of the system ground relays to avert tripping system load. The instability trip relay
configuration needs a walkout option to advert accidental closedown of SCBs switching element if a
trip owing to instability happened.

2.9. Considerations of instability for warning relays

To permit the impacts of intrinsic instability within the SCBs, the instability relay warning should be
set to function at ½ of the magnitude of the instability signal defined by the computed warning terms

18
that are based on an idealized SCBs. The warning needs adequate time detainment to overrule
external disruption.

2.10. SCB Fault Identification methodologies

The first step in SCB protection is to detect the fault provoked inside SCB. The table below can
make
us understand how SCB protection works.
Type of SCB and condition Type of fault identification Remarks
Externally fused SCB and due Neutral current protection, After proper fault
to fault fuse externally neutral voltage protection or identification data is set to
installed voltage differential protection microcontroller based digital
At unit will first blow will identify the number of relays that will sound alarm or
fuse failures to find faulty trip the SCB.
units
In Fuseless SCB due to Neutral current protection, After proper fault
absence of fuse capacitor itself neutral voltage protection or identification data is set to
blows and acts as short circuit voltage differential protection microcontroller based digital
and causes voltage stress on will identify the number of relays that will sound alarm or
healthy elements faulty elements trip the SCB.

Three basic fault identification schemes are applied that are discussed below.
2.10.1. Voltage Differential method

The voltage differential method uses tap voltage to apply voltage divider rule.

19
 Phase A
Phase B

Phase C

X1
V BUS

V TAP

X2

Neutral point

Figure 10. Derivation of voltage differential method

Source: IEEE Standards for protection of SCBs C37.99 2012

Considering figure10 parameters are

VTAP= Tap voltage
VBUS= bus voltage
VN = Neutral voltage

X 1 , X 2 = Reactance of upper half and lower half as indicated

Applying voltage divider rule on fig 10, following relation is obtained.

VTAP   VN X2

VBUS  VN X1  X2 2.3
For solidly grounded banks VN=0 in 2.1 we get
VTAP X2

VBUS X1  X2 2.4
Consider k-factor, where
X2
K
X1  X2 2.5

20
The equation 2.2 can be written in terms of k-factor as follows
VTAP  k  VBUS  0 2.6
The above signal stays zero as long as there is no fault in SCB and X 1 and X2 do not change
The protection operating signal can be defined as
VOP  VTAP  k  VBUS 2.7
The above equation represents voltage differential method because it results in difference of two
voltages. Voltage differential method is suitable for grounded banks as indicated by derivation of
methodology. As it employs only magnitude of two voltages this methodology is immune from
transients and high frequency components.
2.10.2. Neutral voltage instability method

Considering figure 11 parameters are

VA ,VB ,VC = Phase voltage

I A , I B , I C = Phase currents

VN = Neutral voltage

X A , X B , X C = Reactance indicated phase

Applying KCL at neutral point

I A  I B  IC  0 2.8
The phase currents can be solved as follows
VA  VN VB  VN VC  VN
IA  IB  IC 
 jXA        jXB         jXC

21
 VA
VB
VC

VC

XA XB XC

Neutral point

Figure 11. Derivation of Neutral voltage fault identification method

Source: IEEE Standards for protection of SCBs C37.99 2012

Inserting values of IA , IB , IC in 2.6 following equation is formed

2.9
When there is no fault in SCB and all phase impedances are equal equation 2.6 can be written as
3  V0  3  VN  0 2.10
Equation 2.8 shows that zero sequence voltage and neutral voltage are equal during normal operation
Hence final equation is as follows:
3  V0  3  VN  VOP 2.11
2.10.3. Neutral Current instability method

Considering figure 12 parameters are

I A , I B , I C = Phase currents

I A1 , I B1 , I C1 I A2 , I B 2 , I C 2 = Line currents

I N = Neutral current

X A1 , X B1 , X C1 X A2 , X B 2 , X C 2 = Reactance of indicated split wye

22
The derivation in neutral current fault identification method is done on the basis of difference in
neutral current

PHASE A
PHASE B
PHASEC

XA1 XB1 XC1 XA2 XB2 XC2

IA1 IB1 IC1 IA2 IB2 IC2

IN through CT

Figure 12. Derivation of Neutral current fault identification method

Current at neutral CT of fig.12 is equal to

I N  I A1  I B1  I C1 2.12
Equation 2.10 can be written in terms of k-factors for left half wye
I N  I A  K A  I A  K B  I C 3  K C   
Where
X A2 X B2 XC2
KA  KB  KC 
X A1  X A 2 X B1  X B 2 X C1  X C 2
The final equation for fault identification becomes

I OP  I NF   KA  I A  KB  I B  KC  I C 
2.13
I NF =Neutral current during fault stage
Where

2.11. Investigation of Fault Identification schemes for different SCB

configurations

Fault identification schemes employed for different configurations are as follows.

23
2.11.1. . Fault Identification for un-grounded single- wye SCB

The merest system to detect instability in single un-grounded wye elements is to evaluate the SCBs
neutral potential or null-sequence potential. If the SCBs is in uniformly configured and the system
potential is balanced, neutral potential will appear as null value[33]. A variation in any phase of the
SCBs lead towards neutral potential or null-sequence potential.

(a) (b)

Figure 13(a) Un-grounded single- wye SCB protection using neutral potential instability
Figure 13(b) Un-grounded single- wye SCB protection using more VTs
Source: Schweitzer Engineering Laboratories

A system that evaluates the potential in the way between the capacitive element neutral and ground
adopting a VT detector and an over-potential relay with a third elevated frequency filter is visible in
figure 13(a). It is fairly straight-forward but endures in the case of system potential re-distribution
stress and intrinsic instability. The potential-sensors equipment is typically a VT but we can also be a
capacitance potential based element or resistive element in nature. The potential-measuring element
must be chosen for the least potential proportion securable, while still being in a position to resist
momentary bursts and uninterrupted over-potential circumstances to get ultimate instability detection
impression- ability. Nevertheless, a VT applied for this purpose needs to be sized for full system
potential since the neutral potential is under certain circumstances, elevate as high as 2.5 per unit in
switching process.

A null- sequence element that eradicates the system instability can be gained adopting three
potential-measuring elements with their higher end side potential wye-configured from line towards
ground, and the secondary side configured in a collapsed delta configuration. The potential source
VT in some configurations operate as a tapping in SCBs or adopt the VT of the SCBs bus.
24
Protection scheme of Neutral instability relay configuration for un-grounded wye SCBs, adopting 3-
phase potential transformers with their secondary sides configured with collapsed delta configuration
to over-potential relay is visible in figure 13(b). Comparing to the configuration in figure 13(a), this
configuration has the benefit that it is not responsive to system potential instability. Also, the
instability potential heading to the over-potential relay is 3Vn(Neutral Potential) as visible from
figure 13(a).for the VT proportion, there is the benefit of three times increase in impression- ability
factor comparable with the single neutral-ground VT configuration. Potential transformers need to be
sized for line-line potential.

(a) (b)
Fig 14(a) Un-grounded single- wye SCB fault identification by connecting VTs at mid-phase
Figure 14(b) Un-grounded single- wye SCB fault identification by connecting VTs at per-phase
Source: Schweitzer Engineering Laboratories
Advanced digital protection relays can compute the null-sequence potential from per phase potential
as visible in figure 14(a), ridding of the requirement of extra auxiliary VTs to get null- sequence
potential. figure 14(b) presents identical method but adopting VT on the SCBs bus [34].
Even though configurations visible in figure 13(b), 14(a) and 14(b) get rid of system instability, they
could not get rid of the intrinsic capacitive element instability. Protection configuration that
eliminates the system instability and even up for the intrinsic capacitive element instability is visible
in Figure 15.

Figure 15 is a modification of the potential differential configuration for grounded elements. The
most beneficial system to get rid of the system instability is to divide the SCBs in two split-Wyes;
nevertheless, it is not recommended. The system instability comes out as a null-sequence potential,
both at the SCBs terminal and at the SCBs neutral. SCBs terminal null-sequence portion is gained
from 3 line VTs having higher potential side configured in Wye and their secondary side configured
in collapsed delta. The deviation potential between the neutral instability signal owing to system
instability and computed null-sequence from the terminal VT will be evened up for all circumstances

25
of the system instability. The left over error coming out at neutral owing to the producers’ capacitive
element margin is then evened up by phase shifting equipment.

Figure 15. Compensated neutral potential instability method

Source: Technical article on unbalance protection schemes of SCBs
2.11.2. . Fault Identification for un-grounded double- wye SCB

Un-grounded SCBs can be split into two equal sections. This bank configuration intrinsically evens
up for system potential instability; nevertheless, impacts of the producers capacitive element margin
will impact relay function until steps are taken to even up for above said error.

Three configurations of supplying fault identification for double- wye un-grounded elements are
visible in figure 16(a), which adopt a CT that joins the two neutrals and also employ overcurrent
relay (might a shunt or might a potential relay) [35]. The configuration visible in figure 16(b) adopts
a VT configured among two neutral points and an over-potential relay. The CT scheme used in figure
16(a)
is most efficient because system is unaffected by the harmonics. The impact of system potential
instability are averted by both configurations and CT configuration is untouched by third
fundamental frequency currents or potentials once they are balanced. CT and VT needs to be sized
for system configurations [36].
Neutral current is 1/2 of that single grounded SCBs of the identical rating. Nevertheless, the CT ratio
and relay size might picked out for the hoped impression- ability since they are not exposed to
switching surge currents or single phase currents as in case of grounded neutral configuration.
Even though a low ratio VT will be worthy, a VT sized for system potential is needed for the un-
grounded neutral. Hence, a high turn ratio should be consented. The main problem with the use of
VT is that VT cannot be able to detect very small signals because in modern fuseless SCB
26
configurations very small neutral current is generated and when that current is converted into
potential by the use of resistive burden, signal loses its strength and VT is unable to detect that
signal. Hence faults remain undetectable and sensitivity is compromised.

(a) (b)
Figure 16(a) Un-grounded double- wye SCB fault identification using neutral current instability
Figure 16(b) Un-grounded double- wye SCB fault identification using neutral potential instability
Source: Schweitzer Engineering Laboratories
2.11.3. Fault Identification configuration for grounded single- wye SCB

An instability in SCBs will induce current to pass in the neutral. Fault Identification founded on a CT
employed on the link between the SCBs neutral point and ground point is visible in figure 17(a). This
CT has unexpected higher over-potential and current demands. CT ratio is chosen that provide both
required overcurrent proficiency and convenient warning for protection.
The CT has a resistive burden at the output and responsive potential protection relay. Owing to
existence of elevated frequency currents (especially third null-sequence elevated frequency which
goes through neutral-ground link), protection relay needs to be tuned cut down its impression- ability
to frequencies except power frequency[37].
The potential across the resistive burden of CT acts in identical phase with neutral-ground current.
This neutral-ground current is vector magnitude of 3- ∅ currents. These vectors undergo 90 degree
phase shift with system phase-ground potentials. This configuration might be counter balanced for
the power system potential instability, by taking into account the 90 degree out-phasing, and is not
uncommonly adoptable for enormous capacitive elements that demand responsive adjustments.

Every time when SCBs are switched on, momentarily instable capacitive element charging currents
diffuse in phase points and in capacitive element neutral points. In the case when the parallel SCBs is
operating, the magnitude of these currents might rise up to thousands amps, forcing the relay to
malfunction and CT break.

27
 (a) (b)

Figure 17(a) Grounded single- wye SCB fault identification using neutral potential instability
Figure 17(b) Grounded single- wye SCB fault identification using neutral current instability
Source: Schweitzer Engineering Laboratories
An instability potential fault identification configuration for single grounded wye configured SCBs
adopting capacitive element tapping point potentials is visible in figure 17(b). An instability in the
SCBs will induce instability in potentials on tapping-point of 3- ∅. The protection configuration
comprises of a potential measuring element configured among the capacitive element’s midway point
and ground on all phases. A time detainment potential relay with a third elevated frequency filter is
configured to the collapsed delta secondary sides. Latest digitized protection relays adopt the
computed null sequence potential instead as visible in figure 17(b).
2.11.4. Fault Identification for grounded double- wye SCB

Configuration in which a CT is configured on one by one neutral of two parts of a double- wye SCBs
is visible in figure 18. The neutrals are configured to a common ground. CT secondary sides are
cross-configured to an over current relay so that protection relay is irresponsive to any outside impact
that influences both parts of the SCBs in the identical way. CTs might be exposed to switching
momentary bursts currents, hence, surge protection is needed. They should be rated for single- ∅ load
currents if feasible [36]. Willingly, the links from neutral-ground points of two wyes might be in
different direction through CT [38].

28
 Figure 18. Un-grounded split-wye SCB protection employing CT
Source: Technical article on unbalance protection schemes of SCBs
2.11.5. Fault Identification using Potential Differential configuration for grounded -wye
SCBs
On big SCBs with huge magnitude of capacitive elements, it is hard to detect the loss of one or two
shunt capacitive elements as the signal generated by the instability is lost in the intrinsic SCBs
instability. Potential differential gives a responsive and competent way to counterbalance for both
system and the intrinsic SCBs instability in grounded wye capacitive elements [39]. The potential
differential configuration for a single- wye-configured SCBs is visible in Figure 19. The potential
differential configuration for a double- wye configured bank in visible in figure 20.

The configuration adopts two VT’S per phase with one VT configured to a tapping on SCBs and
other is configured to bank bus in single- wye elements and also for double- wye elements, at
identical tapping on second bank. Then potential of both VT’s are cross compared, a signal
developed owing to the wasting away of single capacitive elements or units is gained.
The SCBs tapping potential is found by linking a potential-measuring element at two points, one at
ground point and second at the end of parallel formations of capacitive elements. This is a mid-point
tapping where the potential is evaluated at right mid-point of phase and ground. Willingly, tapping
potential might evaluated at low potential capacitive elements ( capacitive shunt) at neutral point of
the phase

29
 Figure 19. Potential differential fault identification configuration for single- wye banks
Source: Technical article on unbalance protection schemes of SCBs
After testing all shunt capacitive elements are operational and no fuses have functioned, the potential
magnitudes at the starting are adapted to be the identical. At first the magnitude of difference
potential at SCBs tapping and the bus (for single- wye elements) signal is evaluated and it comes out
0. Also, shunt capacitive element margin and introductory system potential instability is
counterbalanced. If the system potential instability changes a little bit, the protection relay system is
still counterbalanced because a given percentage in bus potential leads to the identical percent
variation at capacitive element bank tapping. Any later potential deviation between capacitive
element tapping potential and the bus potential will rise owing to the instability induced by loss of
capacitive elements inside that specific phase. For double- wye elements, tapping potential is cross-
compared to relating tapping-wye potential.

Latest digitized protection relay dynamically counter balance minute errors brought in by measuring
element change and temperature deviations between capacitive elements within the SCBs. If we
tapping the SCBs at the mid-point the impression- ability will be identical for faults intrinsic and
extrinsic the tapping part. If SCBs is provided tapping below or above mid-point, impression- ability
for faults intrinsically the tapping part will high (or low) than for faults extrinsically the tapping part.
This deviation might excite complications in accomplishing an adequate relay setting. Impression-
ability belonging to the midpoint tapping and low-potential capacitive elements at neutral point of the
phase will be identical. Tapping across the lower-end series formations or a mid-point tapping is not
adoptable for Fuse-less shunt capacitive element configurations with more strings, since the strings
are not configured to one by one other at the tapping point. Tapping across the lower-end capacitive
elements is appropriate for Fuse-less shunt capacitive elements.

30
 Figure 20. Potential differential fault identification configuration for grounded double- wye banks
Source: Technical article on unbalance protection schemes of SCBs

2.12. Final Comments After Investigation

SCB type Literature Review regarding fault
identification
[11] uses H-Bridge SCBs configuration for fault Investigating [11] findings are as follows:
identification
Rating of H-Bridge SCBs is as follows: 1. [11] performs fault identification is
Operating Operating Capacitor done with Neutral compensation
voltage MVAR Strings potential scheme.
345kV 66 2 per phase 2. It successfully identifies the faulty
345kV 137 4 per phase phase.
345kV 190 6 per phase 3. This scheme is immune to harmonics
because harmonics at neutral CT are
cancelled due to equal in magnitude
and opposite in direction.
4. It is more sensitive for small SCBs as
compared to large SCBs because in
large SCBs 1 or 2 element failures do
not cause much instability in reactance.
Hence such element failure is difficult
to detect using the proposed
methodology of [11].
5. The major loop hole of this scheme is
when fault appearance in opposite
diagonals is ignored.

31
[12] performs fault identification in four Investigating [12] findings are as follows:
configurations 1. [12] use Neutral potential compensation
SCB type MVAR& operating scheme for all grounded SCB
kV configurations.
Single grounded SCB 27MVAR , 88kV 2. [12] use Neutral current compensation
Double grounded SCB 109MVAR , 230kV scheme for un-grounded SCB
H-bridge SCB 131MVAR , 345kV
Double un-grounded 9MVAR , 33kV
configurations.
SCB 3. Results of [12] show that Neutral
potential compensation for fault
identification is 50% slow process.
4. Results of [12] show that Neutral
potential compensation is more suitable
for faulty phase identification than
faulty elements identification because it
left failed elements undetected.
5. Results of [12] show that Neutral
current compensation is most suitable
for faulty elements identification and it
has 90% fast as compare to old
techniques.
6. No calculations are performed for
simultaneous fault appearance in both
wyes of SCB

[13] uses four SCB configurations for fault Investigating [13] findings are as follows:
identification
SCB type & Voltage Operating MVAR 1. [13] employs Voltage differential
Fuseless Single 27 MVAR,145 kV scheme for all grounded SCB
Grounded SCB configurations.
Fuseless Single 27 MVAR,145 kV 2. [13] performs calculations for failed
Un-Grounded SCB elements in configurations discussed.
Fuseless parallel 16 MVAR,145 kV 3. [13] used voltage differential technique
Grounded Wye SCB is most suitable for grounded SCBs
Fuseless double 36 MVAR,145 kV because it is not susceptible to
Grounded Wye SCB transients and higher frequency
components because these components
are cancelled out at ground point.
4. [13] used voltage differential technique
is not very sensitive because at ground
point voltage appearance across
resistive burden is negligible due to
single element failure and remains
undetectable.
5. No calculations are performed for
simultaneous fault appearance in both
wyes of SCB.
32
 [14] uses two types of SCBs for faulty phase Investigating [14] findings are as follows :
identification
SCB type MVAR & kV 1. [14] employs Neutral potential
Grounded single wye 27 MVAR , 139kV compensation method for fault
Externally fused SCB identification single Ungrounded
Grounded single wye 28 MVAR , 139kV SCBs.
internally fused SCB 2. Elements in parallel with the faulty
elements short out due to application of
overvoltage across them.
3. Overall reactance of SCB decreases.
4. The total current increases.
5. The voltage across healthy elements
also increase.
6. The proposed methodology of [14]
only simulates the fault identification
in half-wye. No case is simulated for
fault identification simultaneously in
both halves of SCB.

2.13. Fault identification schemes with ambiguous indication

Fault identification in ungrounded SCBs need further refinement. A mix of capacitive element
wasting away rise to the ambiguous indications regarding the operation of the SCBs. For example,
during safety state service, unnoticeable current passes through CT between neutrals of an un-
grounded split-wye SCBs for a stable bank, and this consideration is accurate. Nevertheless, the
trivial magnitude of current flow through CT when same number of capacitive elements/units are
wasted away on the identical phase and on both wyes of the SCBs as visible in figure 21. In figure.
21 C-ΔC represents same number of failed elements on both sides of SCBs that lead same
capacitance change on both sides. This situation is strictly unrequired as this particular indication is
evidently misleading and need to properly identified.

33
These misleading indications can be a trouble. If same number of elements/units continue to fail on
both sides of SCB, the potential stress on SCB elements/units can reach to such high level that entire
SCB can go out of service.

C-ΔC C-ΔC

IN through CT

(Figure 21. Y-Y configured banks with ambiguous indications)

34
Chapter 3
Methodology

3.1. Mathematical Modeling for Fault Identification in Externally-fused

SCBs
3.1.1 Mathematical Modeling for Left Half Section of SCB

The protection for one by one configuration fusing methods (Externally-fused banks employ fuse as
their primary source of protection) size of SCB, method of grounding and installation of CT or VT
[40].
Fault identification of SCB has following purposes:
1).To detect a single element or single unit failing depending upon the configuration of SCB (single
unit failing in case of Externally-fused SCB and single element failing in case of Fuse-less SCB)
2).To perfectly detect more than one elements or units depending upon the configuration of SCB for
correct warning condition [41].
The scope of this research thesis is limited to fault identification and analysis
The proposed scheme is primarily based on the derivation of neutral current. As shown in the Fig
22, first of all neutral current is found using Kirchhoff’s law
I N  I L1  I L 2  I L 3 (3.1)
Then applying the current division method in figure 22

 X R1   X R2   X R3 
IN      I1     I2     I3
 X L1  X R1   X L2  X R2   X L3  X R3  (3.2)
Then the evaluated neutral current equal to:
I N  K1 I1  K 2 I 2  K3 I 3 (3.3)
Where
X RN
KN 
X RN  X LN (3.4)
Now It is assumed that fault appears at the left section of the SCB. This fault will change the value
of reactance of XLN to XLFN.As a result new K factor is produced which is termed as K FN having the
following value:
X R1
K F1 
X R1  X FL1 (3.5)

35
 XA1 XB1 XC1 XA2 XB2 XC2

IA1 IB1 IC1 IA2 IB2 IC2

IN through CT

Fig 22 (Un-grounded wye double bank with neutral compensation protection)

The new equation for the neutral current will be as following
I NF  K F 1 I1  K 2 I 2  K 3 I 3 (3.6)
Where INF=Neutral current at fault condition. At this stage it is essential to define neutral
compensation current which is the difference in magnitude of neutral current and the neutral current
at the fault stage.
I NCOMP  I NF  I N (3.7)
This neutral compensation will be the key factor in finding the number of faulty units in SCB. By
putting the values of INF and IN, following equation is formed.
I NCOMP   K F1  K1  I1
(3.8)
Upon further solving the equation by submitting the values of K F1 and K1 desired final result are;
( X R1   X LF 1  X L1 
I NCOMP  I1 
 X R1  X LF 1    X R1  X L1  (3.9)
For double-wye SCBs in symmetrical configuration, reactance of both sides are equal in absence of
fault:
X R  X L   By putting X R1  X L1 , equation (3.10) is formed;

36
 I NCOMP  I1 
 X LF 1  X L1 
2   X R1  X L1 
(3.10)
In case of SCB, X=C because the major portion of reactance is capacitance. So, the final equation
will have the following shape

I NCOMP  I1 
 CLF1  CL1 
2   CR1  CL1 
(3.11)
For un-even Double-wye configurations following equation for left half of SCB is
(CR1   CLF 1  CL1 
I NCOMP  I1 
 CR1  CLF1    C R 1  CL1 
(3.12)
From (3.12) following parameters are required to locate the fault.
CR1=Capacitance of the right half of the capacitive element bank in healthy condition
CLF1= Capacitance of the left half of the capacitive element bank in faulty condition
CL1=Capacitance of the left half of the capacitive element bank in healthy condition
I1=phase current of the capacitive element bank at fault
All these parameters will provide I NCOMP. The smallest value of the I NCOMP will be the value when
only one capacitive element unit is at fault. The main advantage of the proposed scheme is that all
the values will be in per unit system and complex calculation of series and parallel combinations of
SCB are avoided.
3.1.2. Mathematical Modeling for Right Half Section of SCB

The proposed scheme is primarily based on the derivation of neutral current. As shown in the figure
22, first of all neutral current is found using (3.1)
I N  I L1  I L 2  I L 3
Then applying the current division method in fig 22
 X L1   X L2   X L3 
IN     I1     I2     I3
  X L1  X R1    ( X L2  X R2 )   ( X L3  X R3 )  (3.13)
Then the evaluated neutral current can be found using (3.3)
I N  K1 I1  K 2 I 2  K3 I 3
According to (3.4)
X RN
KN 
X RN  X LN
Now It is assumed that fault appears at the right section of the SCB. This fault will change the value
of reactance of XLN to XLFN.As a result new K factor is produced which is termed as K FN having the
following value:
37
 X L1
K F1 
X R1  X FL1 (3.14)
The new equation for the neutral current will be as following
I NF  K F 1 I1  K 2 I 2  K 3 I 3 (3.15)

Where INF=Neutral current at fault condition. Using (3.7) we have;

I NCOMP  I NF  I N
By putting the values of INF and IN, following equation is formed.
I NCOMP   K F1  K1  I1
Upon further solving the equation by submitting the values of K F1 and K1 desired final result are;
( X L1   X RF 1  X R1 
I NCOMP  I1 
 X L1  X RF 1    X L1  X R1  (3.16)
For double-wye SCBs in symmetrical configuration, reactance of both sides are equal in absence of
fault:
XR  XL

X R1  X L1 , equation 3.17 is formed;

By putting

I NCOMP  I1 
 X R1  X RF 1 
2   X R1  X LFI 
(3.17)
In case of SCB, X=C because the major portion of reactance is capacitance[42]. So, the final
equation will have the following shape

I NCOMP  I1 
 CR1  CRF 1 
2   CR1  CLFI 
(3.18)
For un-even Double-wye configurations following equation for right half of SCB is
(CL1   CRF 1  CR1 
I NCOMP  I1 
 CL1  CRF 1    C L1  CR1 
(3.19)
From (3.19) following parameters are required to locate the fault.
CR1=Capacitance of the right half of the capacitive element bank in healthy condition
CRF1= Capacitance of the right half of the capacitive element bank in faulty condition
CL1=Capacitance of the left half of the capacitive element bank in healthy condition
I1=phase current of the capacitive element bank at fault
All these parameters will provide I NCOMP for the right half of the Shunt capacitive element bank
.The smallest value of the INCOMP will be the value when only one capacitive element unit is at fault.

38
3.2. Fault analysis parameters for Externally-fused SCBs
Parameters in (3.12) and (3.19) can be found using IEEE standards 2012 equations .The equations
in IEEE standards 2012 are also employed for detailed fault analysis of Externally-fused SCBs. All
these equations provide per unit values. The value 1 shows normal condition. Any value greater or
less than 1 show increasing or decreasing value of the parameter respectively.
3.2.1. Parallel formation capacitance
The capacitance of parallel formation of capacitive elements that include
blown fuses.
Pa  n
Cg    
Pa (3.20)
3.2.2. Affected wye capacitance
The per unit split phase –neutral capacitance of series/parallel formation of
capacitive elements that include blown fuses.
(3.21)
3.2.3. Affected phase capacitance
The per unit phase –neutral capacitance of series/parallel formation of
capacitive elements that include blown fuses

Cp   
 Cs   Pa  Pt  Pa
Pt (3.22)

3.2.4. Neutral-to-ground potential

For grounded banks G=0 and for un-grounded banks G=1.This parameter
provides value of neutral-ground potential.
3
Vng  G  1
 2  Cp  (3.23)
3.2.5. Potential on affected phase
The potential from line to neutral of the affected phase that contains blown
fuses. The operation of the fuses lessens the capacitance of the phase and increases the potential
stress across that phase as a result this parameter show values greater than 1.
Vln  1  Vng (3.24)

3.2.6. Potential on affected series formation

39
 The potential on the affected series formation with blown fuses.
Vln   Cs
Vcu 
Cg if Cg>0 (3.25)
Vln  S otherwise
3.2.7. Current through affected capacitive element(s)
The current through the individual capacitive element units
with blown fuses.
Iu  Vcu  1 (3.26)

3.2.8. Current in affected wye

This parameter provides the value of split-phase current with blown fuses.
Iy  Cs  Vln
(3.27)
3.2.9. Current in affected phase
This parameter provides the value of phase current with blown fuses.
Iph  Cp  Vln
(3.28)

3.3. Mathematical Modeling for Fault Identification in Fuse-less SCBs

3.3.1 Mathematical Modeling for Left Half section of the SCB

The principle to find fault identification in Fuse-less SCB is same, but it is a bit more complex
procedure as the equations get more and more complex. The reason is because of the fact that all
elements are of Fuse-less in nature and unlikely the Externally-fused banks, it is essential to locate
single faulty element inside the SCB unit. As a result, the protection scheme employed for Fuse-less
banks becomes more sensitive in nature. Secondly, IEEE standards 2012 [41] suggests that the
Fuse-less bank must be split into strips as shown in figure 23. The proposed methodology is as
follows;
As shown in the Fig 23, first of all neutral current is found using Kirchhoff’s law
I N  I L1  I L 2  I L 3  
Putting the values of currents following equation is formed;

IN  
 X3 / / X4     X7 / / X8     X 10 / / X 12  
  I1     I2     I3
   X 3 / / X 4    X 1 / / X 2       X 7 / / X 8    X 5 / / X 6       X 11 / / X 12    X 9 / / X 10   

(3.29)
40
Owing to the bank half wye is further split into two strings, the equation is becoming more complex.
The evaluated neutral current can be found using (3.3)
I N  K1 I1  K 2 I 2  K3 I 3
According to (3.4)
X RN
KN 
X RN  X LN

X1 X2 X5 X6 X9 X10 X3 X4 X7 X8 X11 X12

IL1 IL2 IL3 IR1 IR2 IR3

IN Through CT

Fig 23 (Un-grounded split-wye Fuse-less SCB)

Now it is assumed that fault appears at the left section of the SCB. This fault will change the value
of reactance of X1 TO X1F.As a result new K factor is produced which is termed as K FN having the
following value:

K F1 
 X3 / / X4 
  X 3 / / X 4    X 2 / / X 1F   (3.30)

41
The important thing to be noted that in Fuse-less SCB the proposed scheme should be able to locate
fault in string of the SCB as shown in figure 23. In figure 23 fault is assumed in left most string of
the SCB. That’s why the above k-factor equation has become more complex.
Equation (3.7) for the neutral current will be as following:
I NF  K F 1 I1  K 2 I 2  K3 I 3  
Equation (3.8) is employed for neutral compensation current is;
I NCOMP  I NF  I N   
This neutral compensation will be the key factor in finding the number of faulty elements in SCB.
By putting the values of INF and IN, following equation is formed;
I NCOMP   K F 1  K1  I1
(3.31)
Upon further solving the equation by submitting the values of K F1 and K1, the desired final result in
equation form.

I INCOMP  I1 
 X 3 / / X4   X 1 / / X 2   –   X 3 / / X 4    X 2 / / X IF  
 X 3 / / X 4    X 2 / / X 1F     X 3 / / X 4    X 2 / / X 1  
(3.32)
In a SCB X=Capacitance, hence for the sake of easiness final equation is modified as follows.

I INCOMP  I1 
C 3 / / C4    C1 / / C2   – C 3 / / C4    C2 / / C IF  
 C3 / / C4    C2 / / C1F     C3 / / C4    C2 / / C1  
(3.33)
From above equation following parameters are required to get the results.
C3, C4, C1, C2=capacitance of the indicated strings of the SCB
I1=phase current of the capacitive element bank at fault
All these parameters will provide I NCOMP. The smallest value of the I NCOMP will be the value when
only one capacitive element is at fault.
3.3.2 Mathematical Modeling for Right Half Section of SCB

As shown in the figure 23, first of all neutral current is found using (3.1)
I N  I L1  I L 2  I L 3  
Putting the values of currents following equation is formed;

IN  
 X1 / / X 2     X5 / / X 6     X 9 / / X 10  
  I1     I2     I3
   X 3 / / X 4    X 1 / / X 2       X 7 / / X 8    X 5 / / X 6       X 11 / / X 12    X 9 / / X 10   

(3.34)
Owing to the bank half wye is further split into two strings, the equation is becoming more complex.
The evaluated neutral current as per (3.3)
I N  K1 I1  K 2 I 2  K3 I 3

42
Where k-factor acoording to (3.4) is
X RN
KN 
 X RN  X LN 
Now it is assumed that fault appears at the left section of the SCB. This fault will change the value
of reactance of X1 TO X1F.As a result new K factor is produced which is termed as K FN having the
following value:

K F1 
 X3 / / X4 
  X 3 / / X 4    X 2 / / X 1F   (3.35)
In Fuse-less SCB the proposed scheme should be able to locate fault in string of the SCB as
shown in figure 23. In figure 23 fault is assumed in first right string of the SCB. That’s why the
above k-factor equation has become more complex.
The equation for the neutral current will be (3.7):
I NF  K F 1I1  K 2 I 2  K 3 I 3   
The equation for neutral compensation current is (3.8)
I NCOMP  I NF  I N                               
This neutral compensation will be the key factor in finding the number of faulty elements in SCB.
By putting the values of INF and IN, following equation is formed;
I NCOMP   K F 1  K1  I1
(3.36)
Upon further solving the equation by submitting the values of K F1 and K1, the desired final result in
equation form.

I INCOMP  I1 
 X 3 / / X4    X1 / / X 2   –   X 3F / / X 4    X 2 / / X 1  
 X 3F / / X 4    X 2 / / X 1    X 3 / / X 4    X 2 / / X 1  (3.37)
In a SCB Z=Capacitance, hence for the sake of easiness final equation is modified as follows.

I INCOMP  I1 
C 3 / / C4    C1 / / C2   – C 3F / / C4    C2 / / C1  
 C3 F / /C4    C2 / / C1    C3 / / C4    C2 / / C1  (3.38)
From above equation following parameters are required to get the results.
C3F =capacitance of the indicated faulty string of the SCB
C3, C4, C1, C2=capacitance of the indicated strings of the SCB
I1=phase current of the capacitive element bank at fault
All these parameters will provide I NCOMP. The smallest value of the I NCOMP will be the value when
only one capacitive element is at fault.
3.4. Fault analysis parameters for Fuse-less SCBs

43
Parameters in (3.33) and (3.38) can be found using IEEE standards 2012[41] equations .These
equations are also employed for detailed fault analysis of Fuse-less SCBs. All these equations
provide per unit values. The value 1 shows normal condition. Any value greater or less than 1 show
increasing or decreasing value of the parameter respectively.
3.4.1. Total elements in a string
This equation tells about total elements in a string.
E  S  Su (3.39)
3.4.2. Affected string capacitance
The per-unit capacitance of affected string of capacitive element units
E
Cst 
E e (3.40)

3.4.3. Affected wye capacitance

The per-unit capacitance of the half wye containing affected string.
Sl  1    Cst
Cy 
Sl (3.41)

3.4.4. Affected phase capacitance

The per-unit capacitance of the phase containing affected string.

Cp 
 Cy  Sl   Sp   Sl
Sp (3.42)

3.4.5. Potential on the affected phase

The potential from line to neutral on affected phase. Failing of capacitive
elements cause increase in phase capacitance and decrease in potential stress across affected phase.
Vln  1  Vng (3.43)

3.4.6. Current in affected wye

The per-unit current in affected half wye affected phase.
Iy  Cy  Vln (3.44)

3.4.7. Current in affected phase

The per-unit current in affected affected phase.
Iph  Cp  Vln (3.45)
3.4.8. Difference current
The difference of neutral current between equal wyes.
44
 Id  Vln   1  Cp 
(3.46)

3.4.9. Neutral Current

The instability current that flows into neutral owing to appearance
3  Vng   G   Sp   Sl  
In 
Sp (3.47)
3.4.10. Ground Current
The per-unit current that flows into ground in grounded banks. This parameter
is useful when relay utilizes ground to neutral protection scheme.
Ig   1  G    1  Iph 
(3.48)

3.4.11. Neutral-ground potential

For un-grounded banks its value depends upon Cp. For grounded banks its
value is always null.
(3.49)

45
Chapter 4
Calculations and Results discussions
The IEEE standards for power capacitive elements 2012 provide a comprehensive guidance for
SCBs fault identification and the most reliable way of possible calculations for determining
imbalance parameters owing to the failings in SCB. Figure 24 shows the SCB under consideration.
The SCB of figure 24 is working in a 138kV nominal phase potential. The complete specifications
of figure 24 SCB are shown in table1. The protection system rating is also provided in table 1.

46
Phase A
Phase B
Phase C

7 7
Units Units

S=5

Fig 24 (138 kV, 50 MVAR Split-wye un-grounded Externally-fused SCB)

Source: Schweitzer Engineering Laboratories
Table 1 (SCB configuration under consideration)
blown fuses (n) 0,1,2 and so on
SCB MVAR 50.0 MVAR
Parallel-units per phase(Pt) 14
Parallel-units per phasein left wye (Pa) 8
System nominal phase-phase potential 138 kV
Rated bank system potential 151 kV
Un-grounded bank Grounded=0,un-grounded=1

47
 Capacitive element bank rated potential 132kv

Rated current KVAR 191.4 A

Capacitive element unit rating 17.4 kV
KVAR 238.1KVAR
No of units 210
Neutral CT 300:1

Maximum system operating potential 105% (145 kV)

4.1. Calculations and results for Externally-fused SCBs

4.1.1. Null fuse failings (n = 0)—normal condition

The best way to start fault identification and fault analyzing of SCB in figure 24 is to start with finding
all the parameters of SCB of figure 24 behaving in normal condition. Once all the parameters of SCB of
figure 24 in normal conditions are found, the deviation of the parameters behaving at fault can be easily
monitored. The equation employed for fault identification and fault analysis employ per unit values. The
value 1 shows normal condition. Any value greater or less than 1 show increasing or decreasing value of
the parameter respectively.
All the parameters shown in table 2 at n=0(no fault condition) except (Vng=0V ) have value 1 which
show that during no fault condition SCB is behaving normally. Values in table 3 are found by using
equation 12. Ratio of INCOMP/Iphase=0 shows no fault is currently induced in SCB. The purpose of dividing
INCOMP with Iphase is to locate the exact phase of fault because I phase will only change in case of fault. I phase
for non -faulty phases will always be 1(per unit system).
Values computed in table 2 are fed to microcontroller based instability relays. The instability relay of
protection system must have a strong organization with the one by one SCB unit fuses so in case of any
fault fuses must isolate the wasted capacitive unit to avoid failing of the entire SCB. [A reliable fuse
operation provides an easy visual inspection for identifying wasted capacitive element unit or
element[43].The instability relay must have the enough sensitivity to warning for single wasted capacitive
unit in a formation. It must also trip the bank if the wasted unit creates a potential stress greater than
110% across the fully –operational units. If it is not performed the entire formation or SCB can go out of
service.
110% of the capacitive element unit rated potential is 17.4 kV × 1.1 = 19.14 kV.
From table 4 it is evident that capacitive element rated potential is 17.4 kV. Potential on formation
with no fuse failings is 16.74 kV. At 105% system potential, the capacitive element units are operating at
96.2% of rated potential. The primary neutral-to ground potential is 0V. From these calculations we see

that we no fault occurs potential stress across one by one unit is well within the limits .

48
4.1.2. Fuse failings within a single formation (n = 1,2)—fault condition

Initially it is assumed fault is provoked in the left wye of the phase A of SCB of figure 24. Parameters of
SCB are calculated during fault condition and values are tabulated in table 2 for n=1(single fuse failing)
and for n=2(double fuse failing).
4.1.2.1. Fault identification and Fault analysis with one SCB unit failing (n=1)

It is clear from table 3 that as fault is provoked in phase A of SCB of figure 24 and one fuse fails (n=1) ,
the ratio INCOMP/IA attains some value indicating no of faulty units as well as faulty phase. No of faulty
units depend upon the ratio INCOMP/IA. The value of ratio INCOMP/IA obtained in table 4 is the smallest value
because only one unit has wasted. For more than 1 fuse blow INCOMP/IA will attain higher values. INCOMP/IB
and INCOMP/IC are equal to 0. This shows no fault is induced in phase B and phase C. With increase in
number of faulty units this ratio will continue to rise as seen from graph 2.
The next step is to analyze the SCB during fault operation. The basic purpose for analyzing SCB in
per unit quantities is to analyze one by one e parameter in an easy way. Referring to table 2 for n=1 as
one fuse has blown, one unit of SCB goes out of service formation, wye and phase capacitance are
dropped by 1.5% respectively. This means the loss of KVAR proficiency of SCB. On the other hand,
potential stress across affected series formation and phase increase by 6.6 % and 0.5% respectively.
Current through affected wye and affected phase is also dropped by 1.1% respectively. All these
parameters lead SCB to instability and after the threshold limit based on the computed values the SCB
will be tripped from service. The parameters variation of single fuse failure n=1 can also be visualized
by graph 1.
After per-unit values are now converted into primary values for one fuse failing (n=1), it can be seen
from table 4 with one fuse blown within a parallel formation, the potential on the affected formation (the
formation experiencing the fuse failing) rises to 17.85 kV. This is 102% of the capacitive element unit
potential rating. This shows that affected formation is experiencing 6.6% increase in potential stress. The
primary neutral-to ground potential is 425 V. The potential across affected phase also rises up to
84.14kV (0.5% increase). The current through the affected capacitive elements rise up to 15.159A (1.1%
increase). This condition must be known to maintenance personnel by warning.
4.1.2.2. Fault identification and Fault analysis with one SCB unit failing (n=2)

Table 3 shows that upon two unit failings (n=2) the ratio has increased to 8.13×10-3. As the no. of units
will continue to fail the ratio will continue to increase indicating maintenance personnel about
uninterrupted failing. Table 3 also showed that the calculations are indicating fault only in the affected
phase, thus indicating towards exact faulty phase. With increase in number of faulty units this ratio will
continue to rise as seen from graph 2.
Upon fault analyzing the SCB using Table 2 for n=2, it is clear that with two fuse failings SCB
parameters are more disturbed. SCB is losing capacitance. Wye and phase capacitance are dropped by
3.2%. It is a considerable drop in capacitance and it will considerably affect the KVAR rating .One
49
major issue is the great increase of potential across the affected series formation that is 14% which is
totally an unwanted condition because it might damage the entire series formation. Current in affected
wye and phase also drops by 2.2%.
Referring table 4 with two fuses blown within a single formation, the potential on the affected
formation rises to 19.11 kV, which is 109.7%(14% increase) of rated potential. This is nearly equal the
tripping threshold value. The current through affected SCB formation rises up to 16.23A (2.2% increase).
The neutral-ground potential has gone up to 909V. The potential across affected phase also rises up to
84.63kV (1.1% increase). It means, the SCB must be tripped before further units failings in the SCB. The
above results show that without fault identification and fault analysis of SCB, it is not easy for
maintenance personnel to locate the faulty phase.

Table 2 (Externally-fused SCB per unit-values of different parameters for n=0, 1, 2)

SCB parameters equations SCB parameters SCB parameters SCB parameters SCB parameters
at n=0(null fuse at n=1(single at n=2 (double
failing) fuse failing) fuse failing)
Parallel 1 0.929 0.857
formation
capacitance
S  Cg Affected wye 1 0.985 0.968
Cg  capacitance
Cg  ( S  1)  1
(Cs  Pa ) Pt  Pa Affected phase 1 0.985 0.968
Cp  capacitance
Pt
3 Neutral-to- 0 5.076 ×10-3 1.011
Vng  G  1 ground potential
2  Cp
Vln  1  Vng Potential on 1 1.005 1.011
affected phase
Vln  S Potential on 1 1.066 1.141
V ln  affected series
Cg if Cg>0 formation
Vln  S otherwise
Iu  Vcu  1 Current through 1 1.066 1.141
affected
element(s)
Iy  Cs  Vln Current in 1 0.9899 0.978
affected wye
Iph  Cp  Vln Current in 1 0.9899 0.978
affected phase

50
 Externally fused SCB Parameters variation in Per-unit value with increase in
faulty units
3

2.5
Per-unit value of each parameter

1.5

0.5

0
0 1 2 3 4 5
phase capacitance voltage on affectedNumber
units of phase
Faultycurrent
units curretnt through affected units

Graph 1 Externally-fused SCB per unit-values of different parameters for n=0, 1, 2

Table 3 (SCB Fault Identification calculations)

No of fuses INCOMP/IA INCOMP/IB INCOMP/IC
blown( N)
0 0 0 0

1 3.7×10-3 0 0

2 8.13×10-3 0 0

3 3.1×10-2 0 0

4 4.55×10-2 0 0

5 9.48×10-2 0 0

51
 Externally fused SCB INCOMP/IPHASE
ratio with increase in faulty units
0.1

0.09

0.08

0.07

0.06
INCOMP/IPHASE
ratio value

0.05

0.04

0.03

0.02

0.01

0
0 1 2 3 4 5 6

Number of faulty units

Graph 2 (Externally fused SCB INCOMP/IPHASEratio with increase in faulty units)

Table 4 (Externally-fused SCB primary values of different parameters for n=0, 1, 2)

SCB parameters equations SCB SCB SCB SCB parameters at
parameters parameters at parameters at n=2(double fuse
n=0(null fuse n=1(single fuse failing)
failing) failing)

Vng  PRI  Vng  SYS  VLN Potential 0 424.954 V 909.954 V

neutral-
ground
Vln  PRI  Vln  SYS  VLN Potential on 83.72 kV 84.14 kV 84.63 kV
affected
phase
Vcu  PRI  Vcu  U  VOLTS Potential on 16.74 kV 17.85 kV 19.11 kV
affected
formation
Iu  PRI  Iu  U  IRATE Current 14.22 A 15.159 A 16.23 A
through
affected
capacitive
element(s)

4.2. Calculations and results for Fuse-less SCBs

Using the equations provided in IEEE standards 2012 [41], the required parameters are computed. The
SCB chosen for analysis and fault identification is usually installed at 220kV grid stations shown in figure

52
25. The specifications of Fuse-less SCB and its protection system are given table 5. Table 5 also provides
the rating of the protection system employed. For Fuse-less systems CT of low value is employed for
increased sensitivity. Low value of CT permits the detection of small magnitude of current flow in the

53
neutral.

54
 Fig 25 (230 kV, 60.0 MVAR Split-wye un-grounded Fuse-less SCB)
Source: Schweitzer Engineering Laboratories

The specifications of SCB of fig.24 are as follows.

Table 5 (Fuse-less SCB configuration under consideration)

System nominal potential 230 kV
Rated bank system potential 250 kV
Rated 3 phase KVAR 60000
Series formations (S) 10
Parallel strings per phase(Sp) 2
Parallel strings in left wye (Sl) 1

Series elements per-units (Su) 4

Parallel elements per formation (N) 8

Bank Rating 50.0 MVAR

Rated current KVAR 115.5 A
Capacitive element unit rating 14.4KV
Capacitive element unit KVAR 833.33 KVAR
Capacitive element rating 3.6 kV
Neutral CT ratio 25:5

Maximum system operating potential 105% (241.5 kV)

4.2.1. For Zero Failed Element (e=0) —Normal condition

Zero element failing is the condition when the SCB is behaving properly and no fault is induced. One
by one parameter of SCB shown in figure 25 is evaluated in per-unit value.
Values in table 7 are found by using equation 3.33. Ratio of I NCOMP/Iphase =0 shows no fault is
currently induced in SCB. The purpose of dividing I NCOMP with Iphase is to locate the exact phase of
fault because Iphase will only change in case of fault. I phase for non -faulty phases will always be 1(per
unit system). The smallest value of INCOMP/Iphase will indicate single element failing.
Upon analyzing Table 6 values for null element failing (e=0) it is visible that all the parameters
of SCB are operating normally. The table 4 shows that SCB is providing full capacitance and owing
to null failed elements there is no potential stress across capacitive elements. The neutral current
flowing between equal wyes is also 0A, which shows the fully operational condition of SCB.
Per unit quantities for e=0, 1, 7, 8 are converted into primary quantities and shown in table
8.Table 8 shows the potential on one by one element with null failed elements (e=0) is 3486 V at
105% nominal system potential. This is 96.8% of the rated element potential. Vng-PRI =0
represents the condition of null stress potential. In-PRI =0 and Id-PRI =0 also show that there is no
current flow. Vln-PRI 139.4 kV is also at normal value. The above analysis shows that at null fault

55
element condition the rated element potential is well within the safe limits and system is working
quite properly.

4.2.2. For Failed Elements (e=1, 7, 8) —fault condition

To locate faulty element, it is assumed that fault is appeared on a single element in left wye of phase
A of Fuse-less SCB shown in figure 25.

4.2.2.1. Fault identification And Fault Analysis With One SCB Element Failing (e=1)

It is clear from table 7 that as fault is provoked in phase A of SCB by one element failing, the ratio
INCOMP/IA attains 1.6×10-3 value indicating no of faulty elements as well as faulty phase. No of faulty
elements depend upon the ratio INCOMP/IA. The value of ratio INCOMP/IA obtained in table 7 is the
smallest value because only one element has wasted. For more than 1 element failing INCOMP/IA will
attain higher values. INCOMP/IB and INCOMP/IC are equal to 0. This shows no fault is induced in phase B
and phase C. This ratio will continue to rise with increase in element failures as seen by graph 4.
Upon analyzing the per unit values of table 6 it is clear as one element wastes away , affected
phase capacitance increases by 2.6% . Potential on affected phase is decreased by 0.4% owing to
which elevated magnitude of current (2.1%) start to flow through the faulty phase and hence wye
current and phase current also get elevated. Owing to fault occurrence difference current also start
to flow which was 0A in fully-operational condition. Potential across affected elements is also
increased by 2.1%.The varying trend of parameters can be visualized by seeing at graph 3.
Referring to table 8 shows that the single element failing has increased Vng-PRI =593.32V For
a single failed element, the potential on the affected elements rises to 3545 V, which is 98.5%(2.1%
increase) of the rated element potential. The new value of In-PRI =0.718A which was previously
0A. The new value of Id-PRI =1.436A which was also previously 0A. The fault analysis show that
all SCB parameters have shown deviation from normal values and fault identification scheme is
sensitive enough to locate even a single element failing. This condition must be known to
maintenance personnel.
4.2.2.2. Fault identification And Fault Analysis With Seven SCB Elements Failing (e=7)

Situation becomes more complex with increase in element failings. For seven failed elements
calculations are shown in table 6.
Table 7 shows that upon seven elements failings the ratio has increased to 2.396×10-2.As the no.
of elements will continue to fail the ratio will continue to increase indicating elements failure. It can
be easily seen from graph 4 that upon 7 elements failure the curve has attained higher value.

56
 Upon analyzing the table 6 we see that as elements failing is increased, the capacitance of the
faulted phase increases by 10.6% and current flow through faulty phase increases by 6.8% which is
a considerable amount. Difference current is also more elevated. Potential across the affected phase
drops by 3.7%.Similarly all the parameters can be seen to show considerable deviation. The varying
trend of parameters can be visualized by seeing at graph 3.
Referring table 8 with seven failed elements, the potential on one by one element rises to 3942 V.
This is 109.5% (10.6% increase) of the rated element potential. The computed value of potential
across the element is nearly equal the tripping threshold (110%).The new value of Id-PRI =12.207 A
(10.2% increase) which shows the difference current has increased to the greater magnitude. The new
value of Vng-PRI =4.761 ×103.All the values are showing considerable deviation.
4.2.2.3. Fault identification And Fault Analysis With Eight SCB Elements Failing (e=8)

Table 7 shows that upon eight elements failings the ratio has increased to 2.94×10-2. As the no. of
elements will continue to fail the ratio will continue to increase indicating maintenance personnel
about uninterrupted failing.
Upon analyzing the table 6 we see that as elements failing is further increased, the capacitance of
the faulted phase increases by 12.5% and current flow through faulty phase increases by 8% which
is a considerable amount. Difference current is also more elevated. Potential across the affected
phase drops by 4%. Similarly all the parameters can be seen to show considerable deviation.
Referring table 8 with eight failed elements, the potential across the remaining elements in the
string rises to 4016 V. This is 111.5% of the rated element potential. Upon eight elements failing,
tripping threshold (110%) has surpassed. So it is recommended to trip the SCB. The new value of Id-
PRI =14.456A (11.87%) which shows the difference current has increased to the greater magnitude.
The new value of Vng-PRI =5.577 ×103. All the values are showing considerable deviation. To
determine the trip threshold, find a current instability point halfway between seven and eight unit
failings.

Table 6 (Fuse-less SCB per unit-values of different parameters at fault)

SCB parameters equations(per-unit SCB SCB SCB SCB SCB
value) parameters parameters at parameters at parameters at parameters at
null element one element seven element eight element
failing failing failing e=7 failing
e=0(per-unit e=1(per-unit (per-unit e=8(per-unit
value) value) value) value)
E  S  Su Total 40 40 40 40
elements in a
string
E Affected 1 1.026 1.212 1.25
Cst  string
E e capacitance

57
 Sl  1  Cst Affected wye 1 1.026 1.212 1.25
Cy  capacitance
Sl

Cp 
  Cy.Sl   Sp  S  Affected
phase
1 1.013 1.106 1.125
Sp capacitance
3 Neutral-to- 0 0.00425 0.034 0.04
Vng  G  ground
 2  Cp   1 potential
Vln  1  Vng Potential on 1 0.996 0.966 0.96
the affected
phase
Ve  Vln  Cst Potential on 1 1.021 1.171 1.2
affected
elements
Iy  Cy  Vln Current in 1 1.021 1.171 1.2
affected wye
Iph  Cp  Vln Current in 1 1.009 1.068 1.08
affected
phase
Ig   1  G    1  Iph  Ground 0 0 0 0
current
3  Vng  G   Sp  Sl  Difference 0 0 0.051 0.06
Cp  Neutral
Sp current
between wyes
Id  Vln   1  Cp  Difference 0 0.0013 0.102 0.12
current

58
 Fuseless SCB Parameters variation in Per-unit value with increase in faulty
elements
1.4

1.2
Per-unit value of each parameter

0.8

0.6

0.4

0.2

0
0 1 2 3 4 5 6 7 8

Number of Faulty Elements

Phase Capacitance Line-Neutral Voltage

Voltage on affected elements Phase current
Graph 3 (Fuse-less SCB per unit-values of different parameters at fault)

Table 7 (SCB Fault Identification calculations)

No of elements failing(e) INCOMP/IA INCOMP/IB INCOMP/IC

0 0 0 0
-3
1 1.6×10 0 0
2 3.2×10-3 0 0
-3
3 4.96×10 0 0
-3
4 6.75×10 0 0
5 8.6×10-3 0 0
6 1.053×10-2 0 0
7 2.396×10-2 0 0
8 2.94×10-2 0 0

59
 Fuseless SCB INCOMP/IPHASE
ratio with increase in faulty elements
0.04

0.03

0.03
INCOMP/IPHASE

0.02
ratio value

0.02

0.01

0.01

0
0 1 2 3 4 5 6 7 8 9
Number of faulty Elements

Graph 4 (Fuseless SCB INCOMP/IPHASE ratio with increase in faulty elements)

Table 8 (Capacitive element bank different parameters primary values under consideration)
SCB parameters equations(primary Neutral- SCB SCB SCB SCB
value) to- parameters parameters at parameters at parameter
ground at one one element seven element s at eight
current element failing failing e=7 element
failing e=1(primary (primary failing
e=1(primar values) values) e=8
y values) (primary
values)
Iph  PRI Potentia 0 0 0 0
ING  Ig   Sl l
2 neutral-
Iph−PRI ground
× Sl
2
Vng  PRI  Vng  SYS  VLN Neutral 0 593.32 A 4.761 ×103 5.77
current A ×103 A
between
wyes
Id  PRI  Iph  Iph  PRI  Id Potentia 0 1.436 12.207 14.456
l on
affected

60
 phase
Vln  PRI  Vln  SYS  Vln Potentia 139.4kV 1.388×102kV 1.347 1.339
l on ×102kV ×102kV
affected
element
s
 Vln  PRI  Neutral- 3.486 kV 3.545×103k 3.942×103k 4.016×
VePRI 2  Ve    to- V V 103kV
 2  ground
potentia
l

4.3. Comparison of parameters of SCB during fault appearance

4.3.1. Voltage on affected elements
The mathematical analysis show that upon fault appearance
Fuseless SCB show rise in voltage on affected elements. This trend for 230 kV, 60 MVAR SCB can
be seen as orange line in graph 5. [14] also simulated voltage on affected elements for 139 kV, 28
MVAR SCB. [14] results can be seen as blue line in graph 5. Calculated results in this research and
[14] results have similarity in a sense that both are showing increasing voltage on affected elements.
The results shown have a clear cut reason that can be explained using the results provided in table 6.
Fuseless SCBs rise in capacitance can be justified using ohms law. In case Fuseless SCBs the relation
between voltage on affected elements, capacitance is as follows.
voltage on affected elements=Voltage line−neutral × String capacitance
This shows that
Voltage on affected elements/units ∞ string capacitance
It is clear from table 6 that with increase in faulty elements string capacitance show rising behavior,
hence, voltage on remaining affected elements show rising trend.

61
 Fuseless SCB comparison graph with increase in failed elements
28 MVAR ,139 KV SCB 60 MVAR , 230 KV SCB

1.8

1.6

1.4

1.2
Voltage in per-unit

0.8

0.6

0.4

0.2

0
0 1 2 3 4 5 6

Number of failed elements

Graph 5 SCB voltage on affected elements with increase in faulty elements comparison

4.3.2. Neutral current between wyes variation

The second major parameter is Neutral current
between wyes. Neutral current appears when any power system is unbalanced. This happens due to
change in system reactance. Specifically discussing SCB, neutral current appears when any
element/unit goes out of order and SCB capacitance changes. This cause change in phase current as
well as neutral current.
This shows that
Neutral current ∞ Variation∈capacitance /reactance
Table 6 show that Fuseless SCBs show increase in capacitance due to elements failure, hence neutral
current is showing increasing trend as shown in graph 6. Table 2 show that Externally fused SCBs
show increasing value of neutral current with increase in faulty units. Calculated results in this
research and [14] results have similarity in a sense that both are showing increasing neutral current.
The reason behind this is already explained.

62
 SCB Neutral current variation for increase in faulty elements
28 MVAR , 139 KV 60 MVAR , 230KV

1.6

1.4

1.2
PER UNIT CURRENT

0.8

0.6

0.4

0.2

0
0 1 2 3 4 5 6

Number of Faulty elements

Graph 6 SCB neutral current with increase in faulty elements comparison

63
Chapter 5
Conclusion
SCBs are the backbone of the power system providing reactive power compensation to the system.
Now a days many power electronic devices are in use like converters, inverters etc. Moreover,
different type of loads like household, industrial and commercial are of inductive nature. Therefore,
efficiency and economics of power system relies heavily on reactive power compensation. For
reactive power compensation SCBs are installed.
SCBs face problem due to element/unit failure. Element/unit failure does not allow SCB to
function properly. Un –identification of faulty elements/units will allow voltage stress as per IEEE
C37.99 2012 on healthy elements as a result healthy elements can also fail. The worst situation
happen when whole SCB need to be tripped from service. Hence timely and correct fault
identification is required. To remove such faults, faulty elements first need to be identified. For that
purpose fault identification schemes are employed. The thesis has employed neutral current
compensation technique which is the latest technique in practice for fault identification. The
technique works on the principle of neutral current. When any element/unit fails, there is a change in
reactance of SCB. This change cause neutral current flow in neutral. The magnitude of neutral
current is used to detect number of faulty elements/units. This scheme is also immune to harmonics
because higher frequency components are cancelled-out at neutral point. Moreover, this scheme is
most sensitive because it can detect minor changes in reactance, hence, 1 element failure can also be
easily detected. The thesis also show that voltage unbalance protection scheme is technical not
suitable for SCB fault identification due to harmonics and un-detectable faults.
The primary objective of the thesis is to provide refinement in Fault identification during
ambiguous indications. Ambiguous indications in which fault appears on both sides of SCB lead
towards undetected faults. Existing SCB protection techniques are not sensitive enough to locate
faulty unit/element during ambiguous indications. The fault identification technique developed using
neutral current compensation in this research identifies fault using neutral compensation current
which is the difference in neutral current between fault stage and neutral current during normal
condition. The equation for neutral current compensation is so intelligently designed that it is
unaffected by fault appearance in any other phase. Hence fault identification during ambiguous
indication is properly indicated. Hence thesis correctly identifies the fault identification, hence saving
time and saving entire SCB failure.
The second objective of thesis was Fault analysis of parameters of SCB. Fault analysis of Externally-
fused SCB show that they use fuse as their primary source of protection. When fault arises
Externally-fused SCB parameters show considerable deviation from normal performance. Affected
64
phase capacitance and affected phase current is decreased. The potential-stress across the fully-
operational series formation of units is elevated.
Fuse-less SCB require more sensitive and complex protection as compared to Externally-fused SCB
because in Fuse-less SCBs single element failing detection is required. Fuse-less SCBs are
configured with more complexity as per IEEE standards. For Fuse-less SCB show that affected phase
capacitance and affected phase current is increased. The potential-stress across the fully-operational
series elements is elevated.

65
 References
[1] S. Sithole, N. Mbuli & JHC. Pretorius,” Potential Regulation in the Douglas Area Using SCBs
and Controllable Shunt Reactors,” Institute of Electrical and Electronics Engineers, November
2013.pp. 85-90.

[2] A. Taye,” Design and Simulation of Automatic Power Factor Correction for Industry
Application,” International Journal of Engineering Technologies and Management Research , Vol
5(2). pp. 10-21 October 2018.

[3] Y. Xu , Dong Z. Y., Wong K. P., Liu E., & Yue B.” Optimal Capacitive element Placement to
Distribution Transformers for Power Loss Reduction in Radial Distribution Systems,” IEEE
Transactions on Power Systems, January 2013, vol 28(4). pp 4072–4079

[4] I. Daut , Bahaudin R. C., Hadzer C. M. Hardi, S. Hashim, N. Nisja, I,” Investigation on the effect
of shunt capacitive element and shunt filter on elevated frequency in distribution system,” 2008
IEEE 2nd International Power and Energy Conference, September 2008. pp 684-688 .

[5] IEEE Standards for operation and application of SCBs, IEEE std C37.48 , 2010.

[6] T. Zhao, Y. P. Liu and F. C. Lv, “A Feasibility and Method Research on the On-line Monitoring
of Parallel Compensation Capacitors,” Proceeding of 2012 IEEE International Conference on
Condition Monitoring and Diagnosis, September 2012, Bali, Indonesia, pp. 748-751.

[7] A. Lu, “Power Station Substation and Power System Reactive Power,” China Electric Power
Press, 2006, pp. 146-156.

[8] Q. L. Jia, D. L. Yuan and Y. F. Luan, “System Simulation, Analysis and Design based on
Matlab7.X／Simulink／Stateflow,” Xi'an University Press,2008.

[9] S. R. McCormick, K. Hur, S. Santoso, A. Maitra, and A. Sundaram, “Capacitor bank predictive
maintenance and problem identification using conventional power quality monitoring systems,”
IEEE PES General Meeting, June 2004, Vo1.2 ,pp. 1846-1850.

[10] S. Samineni and C. A. Labuschagne, “Apparatus and method for identifying a faulted phase in a
shunt capacitor bank,” US Patent 8 575 941, November, 2013.
66
[11] M. Ellis, D. Meisner & M. Thakur, “Innovative Protection Schemes for H-Configuration Fuse-
less Grounded Shunt Capacitive Element Bank,” IEEE Protective Relay Engineers 2012 65th Annual
Conference, Feb. 2012 . pp 449–458.

[12] J. Schaefer, S. Samineni, C. Labuschagne, S. Chase, and D. Hawaz, “Minimizing capacitor bank
outage time through fault location,” in Protective Relay Engineers, 2014 67th Annual Conference
for, March 2014, pp. 72–83.

[13] Terrence Smith, “Determining Settings for Capacitor Bank Protection,” IEEE Transactions on
Power Delivery, July 2010 .pp. 40-45.

[14] S. Samineni and C. A. Labuschagne, “Princples of Shunt capacitor bank application and
protection,” 63rd Annual Conference for Protective Relay Engineers, March 2010. pp. 100-125

[15] R. Horton, “Unbalance protection of fuse-less, split-wye, grounded, shunt capacitor banks,”
IEEE Transactions on Power Delivery, July 2002. pp 700-716.

[16] IEEE Standards for series power capacitors , IEEE std P824, 2015.

[17] IEEE Standards for application of shunt capacitor banks, IEEE std 1036, 2010.

[18] J. Wang, M. Ibrahim & Z. Gaji, “Internal Failing Detection and Protection on Capacitive
element Banks,” 13th International Conference on Development in Power System Protection, Feb.
2016. Pp. 200-207.

[19] K. Younsi, Y. Zhou, and S. Soliman, "Methods and systems for monitoring capacitor banks,"
US Patent 8466689, June, 2013.

[20] Power Capacitors and harmonic filters buyer's guide, ABB, Document No. IHSM 9543 32-
00en, September 2013.

[21] Power Capacitors and Capacitor Banks, Selected Projects, Siemens Energy, Article No.
EMTS-B 10015-00-4AUS.

67
[22] J. G. Drobny, Polymers for electricity and electronics. New Jersey: Wiley, 2012.

[23] T. Longland, T. W. Hunt, and W. A. Brecknell, Power Capacitor Handbook. UK:

Butterworths, 2014.

[24] K. Younsi, Y. Zhou, and S. Soliman, “Methods and systems for monitoring capacitor banks,”
US Patent 8466689, June 2013.

[25] Z. Achillides, G. E. Georghiou, and E. Kyriakides, “Partial discharges and associated transients:
the induced charge concept versus capacitive modeling,” IEEE Transactions on Dielectrics and
Electrical Insulation, December 2008, vol. 15, no. 6, pp. 1507-1516.

[26] E. Clark, “Fundamentals of Adaptive Protection of Large Capacitor Banks - Accurate Methods
for Canceling Inherent Bank Unbalances,” 2007 60th Annual Conference for Protective Relay
Engineers , May 2007. pp. 7-15.

[27] T. S. Sidhu, M. R. D. Zadeh, S. Member, and P. P. Parikh, “Enhanced Fault-Location

Scheme for Double Wye Shunt Capacitor Banks,” in IEEE Transactions on Power Delivery,
Febuary 2017, vol. 32, no. 4, pp. 1872–1880.

[28] A. L. P. de Oliveira, A. L. M. Pereira, “Introduction of the Mechanically Switched Capacitors

(MSCs) application on Power Transmission Systems,” IEEE/PES Transmission and Distribution
Conference and Exposition: Latin America (T&D-LA), July 2010. pp. 400-406.

[29] Dawalibi, “Farid Paul, Sharon Tee, Simon Fortin, and Nathalie Grignon. Inadequacies of the
Industry-Standard IEEE C37.99-2000 Concerning Grounding Neutrals of Shunt Capacitors in High-
Voltage Substations,” IEEE Transactions on Power Delivery, july 2011.pp 317-330.

[30] Benton Vandiver, “Optimizing HV capacitor bank design, protection, and testing,” 2018 71st
Annual Conference for Protective Relay Engineers (CPRE), July 2018 .pp 120-137.

[31] Roy Moxley, Jeff Pope, and Jordan Allen. Capacitor Bank Protection for Simple and Complex
Configurations. IEEE Transactions on Power Apparatus and Systems, December 2012, pp.1-7.

68
[32] S. Samineni, C. Labuschagne, J. Pope, and B. Kasztenny,“Fault location in shunt capacitor
banks,” Developments in Power System Protection DPSP Managing the Change, 10th IET
International Conference on, March 2010, pp. 1–5.

[33] Robert Frye, Jay Hicks, Elmo Price. Achieving Optimum Capacitor Bank Protection and
Control. IEEE Transactions on Power Delivery, july 2012. pp. 57-65.

[34] Smith Jobes, “Optimum Settings for Capacitor Bank Protection,” IEEE Transactions on Power
Delivery, July 2010 .pp. 45-50.

[35] Felix Nepveux, Protection Of Tuned Capacitor Banks. IEEE Transactions on Power Apparatus
and Systems, May 2007. pp. 30-37.

[36] Joseph Schaefer , Satish Samineni, Casper Labuschagne, Steven Chase, and Dereje Jada Hawaz,
“Minimizing Capacitor Bank Outage Time Through Fault Identification,” IEEE Transactions on
Power Apparatus and Systems, May 2014 .pp. 1-10.

[37] IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power
Systems,” IEEE Std 519-2014 (Revision of IEEE Std 519-1992), pp. 1–29, June 2014.

[38] Natarajan, “Protection Of Shunt Capacitors,” Power Engineering (Willis), August 2005. pp.1-6.

[39] B. Kasztenny, J. Schaefer, E. Clark, “Fundamentals of Adaptive Protection of Large Capacitive

element Banks,” 60th Annual Georgia Tech Protective Relaying Conference Atlanta , December
2007. pp. 126-157.

[40] Wei-Jen Lee, Narayanan K., Maffetone T., & Didsayabutra P. The design of a capacitive
element bank early warning system. IEEE Transactions on Industry Applications, Vol 39(2) . pp
306–312.

[41] IEEE Guide for the Protection of Shunt Capacitor Banks, IEEE Std C37.99-2012 (Revision of
IEEE Std C37.99-2000), pp. 1–151, March 2013.

[42] C70 Capacitor Bank Protection and Control System, UR Series Instruction Manual, Section
9.1.6, GE Digital Energy, November 2014

69
[43] IEEE Standard for Shunt Power Capacitors,” IEEE Std 18-2012 (Revision of IEEE Std 18-
2002), pp. 1–39, Feb 2013.

70