International Journal on Electrical Engineering and Informatics - Volume 9, Number 1, March 2017
Mitigation of Ferroresonance By FACTS In Electrical Network
Salman Rezaei
Technical office, Kerman Power Generation Management Co. Kerman, Iran
Abstract: Catastrophic circumstances and equipment failures continue to occur due to
Ferroresonance even though this phenomenon has been extensively investigated since, many
years ago. This study enhances mitigation of Ferroresonance by means of Flexible AC
Transmission System. Static var compensator is used to suppress Ferroresonance along with
controlling voltage and reactive power in the network. Manitoba Hydro 230 kV electrical
network has experienced Ferroresonant states several times. In this paper, by means of
PSCAD/EMTDC simulation software, Ferroresonant states are recognized and analyzed in
Manitoba Hydro network. Ferroresonant states are classified in adequate modes by
Ferroresonance detection tools. Power and control circuit of SVC is designed and
Ferroresonant states are examined in presence of SVC.
Keyword: Ferroresonance, Ferroresonance detection tools, Damping reactor, Static Var
Compensator PSCAD/EMTDC
1. Introduction
Manitoba Hydro network experienced Ferroresonant states in 1995. Explosion of voltage
transformer due to opening grading capacitor circuit breakers, breaker failed to latch while
attempting to energize a 1500 kW induction motor at the Dorsey converter station. Result of
such experiences caused to adapt some mitigation options against Ferroresonance like; Bus
enhancement project and sectionalizing the bus bar, replacing PT with CVT, and permanently
connected 200 Ω loading resistors installed on the 4.16 kV sides of station service transformers
in Dorsey station. As the network arrangements and faults which result in Ferroresonance are
not predictable; in addition, using permanent resistors overshadows energy optimization, an
online-flexible device is required to mitigate all types of Ferroresonance.
Manitoba Hydro electrical network consists of five 230 kV power sources like; Vermillion,
Dorsey, Ridgeway, Rosser, (voltage source) and Grand Rapids (generator and equivalent
circuit mode) Furthermore, Ashern station comprises an overvoltage-damping reactor, and
Silver station with 2×230/66 kV, YNd, 50 MVA transformers are modelled in simulation [11].
This study is performed to follow previous Ferroresonance mitigation methods. One of the
latest published papers [1] represents a flexible method, which uses resistors and two back-to-
back controlled one-way conduction switches to control Ferroresonance of different types.
In this paper, basic aspects of SVC is explained. Then network is examined in an
arrangement, which causes Ferroresonance like; breaker phase failure and changing line
arrangement. Ferroresonance detection tools like; FFT, phase plan diagram, and frequency
deviation measurement are used to recognize different types of Ferroresonance. Effect of
manual operation of damping reactor is examined to mitigate Ferroresonance; in addition, a
Static Var Compensator (SVC) is designed in the network to suppress all types of
Ferroresonance, which are emerged in different arrangements. Practical aspects of power and
control circuit of SVC are explained and variable parameters are adjusted. The results are
compared between damping reactor and SVC; furthermore, advantage of using SVC in the
network is explained.
2. Theoretical approach
A. Basic principle and operational aspects of SVC
Static Var Compensator is basically a shunt connected variable Var generator whose output
is adjusted to exchange capacitive or inductive current to the system. One of the most widely
Received: May 2nd
, 2016. Accepted: February 23rd
, 2017
DOI: 10.15676/ijeei.2017.9.1.1
1
used configurations of the SVC is the TSC-TCR type in which Thyristor switched Capacitor
(TSC) is connected in parallel with Thyristor Controlled Reactor (TCR). The magnitude of the
TCR is inductive susceptance BL (α) which a function of the firing angle α as follow [2].
𝐁𝐋 (𝛂) =𝟐𝛑−𝟐𝛂+𝐬𝐢𝐧𝟐𝛂
𝛑𝐗𝐒 (1)
The magnitude of TSC is:
𝐁𝐂 =𝟏
𝐗𝐂 𝐒𝐭𝐞𝐩𝐬 (2)
Then, the effective shunt susceptance of SVC is:
𝐁𝐒𝐕𝐂 = 𝐁𝐂 − 𝐁𝐋 (𝛂) (3)
Where 𝛑
𝟐≤ 𝛂 ≤ 𝛑 , 𝐗𝐒 =
𝐕𝐒𝟐
𝐐𝐋 , VS is SVC bus bar voltage, QL is MVA rating of reactor.
(a)
(b)
Salman Rezaei
2
(c)
(d)
Figure 1. SVC of the TCR-TSC type. (a) Electrical connections. (b) Reactive power exchange
characteristic of an SVC of the TCR-TSC type. (c) SVC at mid-point of the line. (d) Phase and
power diagram.
As it is shown in Figure 1a, power circuit of 12-pulse Thyristor Switched Capacitor (TSC)
/Thyristor Controlled Reactor (TCR) Static VAR Compensator includes nine single phase
transformers so that primary winding is connected in star and the secondary windings in star
and delta to eliminate 6(2k − 1) + 1 , 6(2k − 1) − 1 (k = 1, 2, 3) harmonics due to 30°
phase difference between star and delta secondary windings. TCR and TSC are divided in to
two identical groups which are connected to star and delta secondary windings [3]. Delta
connection of TCR and TSC branches eliminates 3k k(1, 3, 5, 7, … ) harmonics. RC snubber
circuit across Thyristors in TCR is used to protect the Thyristor against over voltages.
Furthermore, parallel resistance across capacitor in TSC acts as a damping resistor and fixes
the voltage across capacitor. One of the most significant aspects of SVC transformer is to
prevent saturation of iron core. Saturated core causes Ferroresonance and instability of SVC
operation [4]. Saturation characteristic of transformer is defined by the magnetizing parameters
which are obtained by Φ-I Curve Data of transformer. They are defined and calculated as
follow.
Air Core Reactance (XAIR): specifies slope of the characteristic in saturated area. It is
obtained based on the two highest points in Φ-I Curve Data.
XAIR =∆∅Max
∆IMax×
ω
ZBase (4)
Rated Magnetizing Current (IMR): Adjustment of the magnetizing current determines the
horizontal position along the V = 1.0 pu voltage line of the effective knee point. That is, an
increasing value of magnetizing current will tend to make the saturation characteristic less
sharp. It is calculated using a point (ΦM, IM) closest to the rated flux ΦR where IR is rated power
of transformer.
∅R = ∫V√2
√3 sin (ωt) (5)
IMR =∅R
∅M×
IM
IR (6)
Knee Point (XKNEE): Adjustment of the Knee Voltage vertically shifts the Y-intercept of
the air core reactance line. It is calculated based on the highest point in Φ-I Curve Data.
Mitigation of Ferroresonance By FACTS In Electrical Network
3
XKNEE =∅Max−LAIR∙IM
∅R×
IM
IR (7)
Saturation of transformer core and occurrence of Ferroresonance in SVC transformer
cannot be damped by control circuit. As will be shown later, magnetizing characteristic
obtained by the above method is used in SVC transformer in this study. Magnetizing
parameters are chosen so to prevent Saturation of transformer core.
SVC includes a control circuit to maintain the voltage in nominal value. It is accomplished
by controlling required value of susceptance which is provided by TSC-TCR. Hence, a non-
linear susceptance characteristic is required for TSC and TCR. This study uses non-linear TCR
susceptance (BTCR) in control circuit. It is calculated as follow [5].
BTCR =BSVS−NC×BC1(1−
NC×BC1B∆t
)
1−2NC×BC1+BL
B∆t
(8)
Where:
BTCR: Output non-linear TCR susceptance [pu]
BSVS: SVC susceptance order (reference) [pu]
NC: Number of TSC stages currenty switched on (in use)
BL: Output susceptance of TCR inductor [pu]
B∆t =−1
XLPS (9)
XLPS: Transformer leakage reactance (Primary - Secondary)
𝐵𝐶1 =1
𝑁𝐶(𝑇𝑀𝑉𝐴𝑀𝑇𝑆𝐶
+𝑋𝐿𝑃𝑆) (10)
TMVA: SVC transformer 3-phase MVA rating
MTSC: Total MVAR all capacitor stages
Figure 1b shows Reactive power exchange characteristic of an SVC TCR-TSC type. When
the SVC has to supply reactive power in power system, a number of TSCs are switched in. The
TCR firing angle is then adjusted so that the amount of reactive power absorbed by the TCR
precisely offsets the excess of reactive power supplied by the TSCs. Hence, the total reactive
power, which SVC of the TCR-TSC type exchanges with the power system is as follow.
𝑄𝑇 = |𝑄𝐿| − |𝑄𝐶| (11)
In case of increasing the number of TSCs to supply reactive power, the TCR firing angle is
set to 180°, and then another TSC must be switched in. On the other hand, In case of
decreasing the number of TSCs the TCR absorbs the maximum amount of reactive power (i.e.,
when the TCR firing angle is 90°), and then a TSC must be switched out. In both cases, the
TCR firing angle is readjusted so that the TCR absorbs just the right amount of the reactive
power supplied by the TSCs to meet the reactive power requirement of the power system.
Conversely, when the SVC has to absorb reactive power, all TSCs in the SVC are switched
out. Then, the TCR firing angle is adjusted so that the TCR absorbs all the reactive power
supplied by the power system to which the SVC is connected [6].
Consideration of SVC at mid-point of a two-end supplied transmission line (where the
voltage collapse is maximum) is the most suitable place which causes voltage improvement.
Impedance of the line is divided as shown in Figure. 1c. Voltage and current in phase diagram
(Figure.1d) are calculated as follow.
V1S = V2S = Vcosδ
4 , I1 = I2 = I =
4V
Xsin
δ
4 (12)
Active power at bus 1 and 2 are equal and calculated as follow.
P1 = V1SI1 = VI1cosδ
4, P2 = V2SI2 = VI2cos
δ
4 (13)
Salman Rezaei
4
P = 2 (V2
X) sin
δ
2 (14)
Injected reactive power by SVC at the mid-point of the transmission line is calculated as
follow.
Q = VIsinδ
4=
4V2
X(1 − cos
δ
2) (15)
As can be seen in the above, compensation at mid-point of transmission line increases the
capability of the line to transmit active power. This is accomplished by increasing the
demanded reactive power from SVC and power sources.
Analysis of equal area criterion shows that increasing the active power to 2Pmax increases
transient stability so that deceleration area (A2) is extended. The area of A2ext shown in power
curve is added to A2 which represents deceleration area in the system without SVC (Figure. 1d).
The ability of SVC to vary the amount of transferred active power by controlling reactive
power is used to damp power oscillation in the network. As power oscillation is a dynamic
phenomenon, shunt compensator requires reactive power variations according to power angle
variations. In case of power oscillation, when dδ
dt> 0 the capability of transferring active power
is increased by injecting reactive power in the network to suppress rotor acceleration and
compensates excessive mechanical power of the turbine. Conversely, when dδ
dt< 0 the
capability of transferring active power is decreased by absorbing reactive power from the
network to moderate insufficient mechanical power of the turbine.
As will be shown in the study, Ferroresonance in the network causes increasing the voltage
and power oscillation. The mentioned above characteristics of SVC are used to control the
magnitude of voltage and damp power oscillation. It results in mitigation of Ferroresonance.
B. Practical time domain analysis
In order to analyse Ferroresonance in time domain a typical non-linear series RLC circuit is
considered as shown in Figure. 2 [9].
Figure 2. Series RLC Ferroresonant circuit example
Inductor voltage is calculated as follow.
VL = √Vh2 − (I × R)2 +
I
ωC (16)
It is also a nonlinear function of current as follow.
VL = ωf(I) (17)
Frequency of waveform can be deviated from nominal frequency in Ferroresonance so that
frequency deviation (Fr.d) can be defined as follow.
Fr. d = |FFr − Fnom| (18)
Where:
FFr = frequency of waveform in Ferroresonance
Resulted waveform is decomposed to its number of harmonics using FFT (Fast Fourier
Transform). Measurement is done by evaluation of samples which are taken in specific
Mitigation of Ferroresonance By FACTS In Electrical Network
5
sampling interval; hence, discrete Fourier Transform is used with a certain sampling rate to
illustrate harmonic components on harmonic spectrum.
VLk = ∑ VLne−j2πkn
N K = 0 … N − 1N−1n=0 (19)
N = number of samples
Then, Total Harmonic Distortion is calculated so integer harmonics, which obtained from
FFT are considered in the following formula.
THD = √∑ (individual (h)
individual (1))
2xh=2 (20)
x = number of harmonics
In order to determine Ferroresonance of different types, THD and Fr.d are used as criteria
which specified in Table 1.
Table 1. Criteria to determine Ferroresonance mode
Ferroresonance
mode
Fr.d dFr. d
dt
THD
(%)
Harmonic
spectrum
Fundamental zero zero 50 > Discrete
harmonic constant zero 50 > Discrete
Quasi-periodic variable Not zero 100 > Discrete
Chaotic variable Not zero 100 > Continuous
Fundamental Ferroresonance is detected when frequency of waveform remains at power
frequency (Fr.d is zero) and the value of THD is more than 50%. Harmonic Ferroresonance is
detected when frequency of waveform is deviated from power frequency and remains constant
(Fr. d is not zero and dFr.d/dt is zero); furthermore, the value of THD is also more than 50%.
In most cases, fundamental and harmonic Ferroresonance contain odd harmonics; hence,
harmonic spectrum is discrete.
Quasi-periodic and chaotic modes are emerged when dFr.d/dt is detected and calculated as
follow. dFr.d
dt= T ×
Fr.d(t)−Fr.d(t−∆t)
∆t (21)
Where:
T = time constant
t − ∆t = previous time step
∆t = time step interval
Furthermore, the value of THD is increased more than 100% where chaotic mode contains
a continuous harmonic spectrum.
In addition to above mentioned tools, Phase plan diagram plots voltage versus flux to show
the status of closed shapes in normal or Ferroresonant states.
3. Ferroresonant configurations
In this part, Manitoba Hydro is examined to find Ferroresonant configurations. Several
simulations are performed in different arrangements. In the following, some states which, lead
in Ferroresonance are explained.
A. Ferroresonance in case of breaker phase failure
This is mostly a common configuration in grounded-wye systems that feed three-phase
power transformers under no-load or light-load conditions [12]. Star-grounded transformers in
Silver station are supplied from a circuit breaker via a 64km line, which is taped from A3R-
A4D double circuit line (Figure 3a). Phase A of the breaker is failed to close while attempting
to energize no-load transformers. Ferroresonant circuit is formed according to Figure. 3b where
Salman Rezaei
6
the current passes through phase-to-phase capacitances of transmission line and winding of
interrupted phase. Occurring Ferro resonance in this configuration strongly depends on the
length of line between source and transformer. As it is shown in Figure. 3c, the waveform of
current is misshaped and its magnitude is increased in the time of 0.1 s. As it is shown in
Figure. 3d, increased magnetizing current up to 150 Apick prim (pick value in primary side)
crosses assumed capacitance line of the system in nonlinear area of the curve. Hence, operating
point of the system is located at nonlinear area and Ferroresonance occurs in the system. Due
to asymmetrical conditions, the magnitude of current is increased and sinusoidal waveform is
misshaped differently in each phase of HV side of transformer. It is notified that, the value and
waveform of voltage is not varied as well as current.
(a)
(b)
(c)
#1 #2
460 [MVA]13.8 [kV] / 230.0 [kV]
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Mu
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460 MVA 13.8 kV
GRAND RAPIDS
V
A
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Ef
Vs
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1.0
Tmi
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Wrefz0
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Hydro Gov 1
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Wref
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]5
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[H]
V
A
V
A
GRAPD
GRG1
GRG2
CHARGE-GRAPT RGRAPD
TimedBreaker
LogicOpen@t0
RGRAPD
0.00005 [uF]50 [ohm]
0.00005 [uF]
V
A
V
A
ASROS
ASDOR
C-ASROSR-ASROS
C-ASDOR
V
A
V
A
ASHERN
ASG1A
ASG2A
G1AG...
A3RA4D1
V
A
A3R02
A3RA4D2
NodeName
P = 178.1Q = -146.9
V
A
TimedBreaker
LogicOpen@t0
BRK6
BRK6G1A
G2A
ROSSER ENDDORSEY-RIDGEWAY
ASHERN ST.
A3R
A4D
GRAND RAPIDS
SILVER TAP
A3R
A4D
VERMILLION TAP
GRANDRAPIDS
TimedBreaker
LogicOpen@t0
GRANDRAPIDS
VTIT 3
IfEfEf0
VrefVS
Exciter_(AC1A)
1.0
n1_right
DAMPING REACTOR
Mitigation of Ferroresonance By FACTS In Electrical Network
7
(d)
Figure 3. Breaker phase failure in Silver station. (a) Part of Manitoba Hydro network under
study in PSCAD/EMTDC. (b) Ferro resonant circuit in grounded winding. (c)Value and
waveform of current in HV side of transformer in case of Ferro resonance. (d) Magnetizing
curve and assumed capacitance line of the system in Ferro resonance
Ferroresonance detection tools determine two modes of Ferroresonance in this configuration.
at the beginning of Ferro resonance (after 0.1s), odd and even orders of harmonics are
presented in waveform of current in HV side for about 0.2s nevertheless, harmonic spectrum is
discontinuous in this time (Figure. 4a). Fr.d and dFr.d/dt vary irregularly for about 0.2s (Figure.
4b). Hence, quasi-periodic mode is presented in this period temporarily. After that, even orders
are eliminated and frequency variation is suppressed; hence, Ferroresonance is changed to
fundamental mode in sustained state. Phase plan diagram (V-Φ) shows well-balanced circles in
normal state (Figure. 4c) where as, the circles are misshaped according to type of
Ferroresonance. Time-division of the plot can be set equal to the period of power frequency.
The plot shows misshaped and regular circles, which are repeated in each time division (Figure.
4d). These characteristics are the evidence of existing Ferroresonance with fundamental mode.
(a)
0 200 400 600 800 1000 1200 1400 1600 1800 20000
2000
4000
6000
8000
10000
12000
Frequency (Hz)
Am
plitu
de
Frequency Response
Salman Rezaei
8
(b)
(c)
(d)
Figure 4. Ferroresonance detection tools in Ferro resonance in case of breaker phase failure.
(a) Frequency spectrum of L1 phase in temporary state. (b) Frequency, Fr.d and THD
measurement. (c) Phase plan diagram in normal state. (d) Phase plan diagram in sustained
Ferro resonant state
Mitigation of Ferroresonance By FACTS In Electrical Network
9
B. Ferroresonance in case of changing line arrangement
Changing line arrangement in the network might lead in configuration which causes
Ferroresonance. One of the most probable Ferroresonant configurations resulted by changing
line arrangement is formed when a double circuit transmission line is terminated by a saturable
transformer. Capacitive coupling between double circuit lines and saturable iron core make a
Ferroresonant circuit [10].
As it is shown in Figure 3a, in Manitoba Hydro, transformers in Silver station are energized
by a double circuit line. In addition, Grand Rapids is connected to Ashern station by another
double circuit line. In order to emerge Ferroresonance, many statuses of the same configuration
are examined. In all statuses, both lines are remained energized. Hence, capacitive coupling of
lines is not the only reason of occurring Ferroresonance.
The Ferroresonant state mentioned above has been completely explained in [8]; hence, the
results of simulation are briefly explained as follow.
In case of changing the arrangement by opening breakers, A3R and G1A lines are changed
to an open-end line whose voltage is increased and causes saturation of transformer core. It
results in increasing and misshaping voltage and current waveforms in addition, power
oscillation in effect of increasing Fr.d in the network.
(a)
(b)
Salman Rezaei
10
(c)
(d)
Figure 5. Electrical parameters in Ferroresonance in case of changing line arrangement (a)
Value of voltage, current and active power. (b) Frequency, Fr.d and THD measurement. (c)
Frequency spectrum of L1 phase. (d) Phase plan diagram in Ferroresonance.
Irregular variation of Fr.d causes increasing the value of dF.rd/dt; furthermore, the value of
THD is more than 100% and harmonic spectrum is continuous; hence, chaotic mode is
presented in this configuration. Phase plan diagram shows irregular circles, which are not
repeated in each time division of the plot. It is also the evidence of existing Ferroresonance
with chaotic mode.
4. Mitigation of Ferroresonance in the network
Ashern station is located at the mid-point of the Manitoba hydro network. G1A-G2A
double circuit line with a length of 230 km from Grand Rapids and A3R-A4D double circuit
line with a length of 200 km from Rosser station are connected to Ashern station. Hence, this
station is a suitable place to compensate line parameters. A damping reactor is located at
Ashern station to mitigate over voltages (Figure. 3a). In this section, mitigation of
Ferroresonance by means of damping reactor and then designation of SVC in Ashern station is
analysed.
0 200 400 600 800 1000 1200 1400 1600 1800 20000
2
4
6
8
10
12
14x 10
4
Frequency (Hz)
Am
plitu
de
Frequency Response
Mitigation of Ferroresonance By FACTS In Electrical Network
11
A. Mitigation of Ferroresonance by damping reactor
Damping reactor with a combination of RLC elements and specific values is shown in
Figure 6a. Simulation result shows that damping reactor with existing parameters is not able to
mitigate Ferroresonances. It just decreases the magnitude of voltage and current. Regarding the
magnitudes of parameters in Ferroresonance in Silver station (section 3.B), the magnitude of
voltage and current is decreased to 331 kVpick prim and 0.587 kApick prim respectively (Figure. 6b).
The magnitude of parameters follows power oscillation. For instance, active power of damping
reactor oscillates from -2.4 to 3.1 MW and absorbs reactive power of about 62 to 77 MVAR.
The value of THD and Fr.d are reduced significantly when Grand Rapids is in generator mode
in the time after 1 s (Figure 6c).
Ferroresonance is mitigated when the magnitudes of reactor parameters are changed
according to table 2.
Table 2. previous and new values of parameters of damping reactor
parameters R11(Ω) R21(Ω) L21(H) C31(µF)
Previous value 3.7×106
2.814 2.833 0.0015
New value 580 1 4 0.0015
(a)
(b)
n1
0.0015 [uF]
2.814 [ohm] 2.833 [H]
3.7e+6 [ohm]
SASREEA
R21 L21
C31
R11
SASNEUT
73.45 [MVAR]1.588 [MW]
V
A
TimedBreaker
LogicOpen@t0
SASREEA
TimedBreaker
LogicOpen@t0
SASNEUT
Damping Reactor
SASREDA
TimedBreaker
LogicOpen@t0
SASREDA
Salman Rezaei
12
(c)
(d)
Figure 6. Damping reactor in Ashern station. (a) Single line diagram. (b) Voltage and current
waveforms in Silver station with previous values. (c) Electrical parameters of damping reactor
with previous values (d) Electrical parameters of damping reactor with new values.
Mitigation of Ferroresonance By FACTS In Electrical Network
13
As shown in Figure. 6d, the magnitude of voltage and THD are reduced to 1.000 pu and 0.07%
respectively. In order to suppress over voltage and mitigate Ferroresonance, damping reactor
absorbs active and reactive power from the network with a value of 92 MW and 140 MVAR
respectively. It is noted that absorbed active power is just reduced to 85 MW in no-
Ferroresonant state. Inflexible behaviour of damping reactor in different states and excessive
consumption of energy in normal and Ferroresonant states are the mean major problems of
using damping reactor.
B. Mitigation of Ferroresonance by Static Var Compensator
As it was seen in advance, the configurations which lead in Ferroresonance are not
predictable. Changing line configurations and plant outage are mostly performed automatically
in the network, in addition; breaker phase failure and over voltages happen accidentally. Hence,
an online-flexible device is required for automatic mitigation of Ferroresonance, which caused
by different arrangements and unwanted accidents. SVC is explained in two sections as follow.
- Power circuit
As was explained in section 2, SVC of the TCR-TSC type (Figure. 1a) is used in Ashern
station. The value of TCR and TSC sections are chosen to compensate the reactive power in
the specific area of the network to maintain the magnitude of voltage in range of nominal value.
It is examined in the most severe reactive power demand and also in Ferroresonant states;
hence, results in selection of 200 MVAR for both TCR and TSC sections. Increasing number
of TSC stages causes flexible control on reactive power. Examination of 6 stages results in the
most flexible control with the value of 200 MVAR. Rated power of transformer depends on
power of TCR and TSC stages. Voltage of secondary and tertiary windings depends on
optimum selection of insulation level for TCR and TSC sections. Increasing ratio of
transformer by decreasing the voltage in secondary and tertiary windings decreases required
insulation level for TCR and TSC sections; whereas, decreasing the ratio results in decreasing
copper loses and thermal rating of devices; hence, a practical compromise must be taken.
Saturation characteristic of transformer core (Figure. 7a) is formed by calculating magnetizing
parameters based on Φ-I curve data (section 2.A). The parameters are chosen so transformer
core is not saturated. Hence, stability of SVC is certified against any faults and over voltages in
the network. Some important technical characteristics of SVC are summarized in table 3.
Table 3. Technical characteristics of SVC in Ashern station
No. Char. Text Unit Value
1 3 Phase Transformer Power MVA 350
2 3 Phase Transformer voltage kV Y/y/Δ230/66/66
3 Number of Capacitor Stages - 6
4 Total value of TCR MVAR 200
5 Value of all Cap. Stages MVAR 200
6 Parallel Res.across Each Cap. Stage Ω 5000
7 Air Core Reactance pu 0.4
8 Inrush Decay Time Constant s 0.18
9 Knee Voltage pu 1.7
10 Shunt loss conductor Mho 0.00001
11 Transformer Magnetizing Current % 0.5
In the following, effect of parallel resistance across each capacitor stage is examined to
damp Ferroresonance. Different values of resistance are listed against variation of voltage,
THD, Fr.d and power losses in sustained state. They are summarized in table 4.
Salman Rezaei
14
Table 4. Variation of electrical parameters versus parallel resistance to damp Ferroresonance
Resistance
(Ω)
Voltage
(pu)
THD
(%)
Fr.d
(Hz)
Ploss (MW)
500 1.006 0.133 0.001 50
700 1.007 0.145 0.003 36
1000 1.006 0.150 0.000 25.5
1300 1.007 0.140 0.004 20
1600 1.008 0.150 0.001 16.6
2000 1.007 0.132 0.002 13.7
2500 1.008 0.411 0.004 11.7
3500 1.006 0.422 0.004 8.9
As shown in table 4, by increasing the value of damping resistance values of voltage, THD,
and Fr.d are remained in acceptable range in sustained state however, the value of active power
of SVC is decreased significantly. It must be noted that, increasing damping resistance
increases some parameters in transient state at the beginning of energizing. Like; voltage (1.5
pu) and Fr.d (5 Hz) however, transient time is about 50 ms; hence, the values are tolerable. The
most challenging case happens in Silver station where the value of energizing current in HV
side of transformer is increased by increasing damping resistance. It results in increasing
differential current and probable operation of differential protection of transformer. As
decreasing power losses causes increasing the risk of mis-operation of differential relay a
practical compromise must be taken. Figure. 7b and c show that transient value of current in
Silver station with resistance value of 500 and then 5000 Ω is increased from 179 Apick prim to
1.34 kApick prim respectively.
(a)
(b)
Mitigation of Ferroresonance By FACTS In Electrical Network
15
(c)
Figure 7. Transient values of voltage and current in Silver station. (a) Saturation characteristic
of SVC transformer. (b) Damping resistance with a value of 5000 Ω. (c) Damping resistance
with a value of 500Ω
- Control circuit
Control circuit of SVC is a feedback-based circuit, which measures reactive power and rms
value of voltage. Then, ISVCpu =Qpu
Vpu is calculated and multiplied in a droop value, which
regulate control signal. Then, the control signal is subtracted from actual rms value of voltage
and passes through low pass and notch filters to filter out interferences. The control signal is
compared with reference value to make an error value. The error value is controlled by PI
controller to control the values of required susceptance (BSVS). Then, non-linear TCR
susceptance (BTCR) is calculated based on BSVS according to equation (8). As it is shown in
Figure. 8, in order to generate firing angle of TCR, BTCR is divided by Output susceptance of
TCR inductor (BL). Resulted value which is normally ranged from -1 to 1 makes firing angle
from 180 to 90 respectively by a non-linear transfer function. TSC stages are also switched in
by BTCR value which is changed to a positive digital level. The stage is switched out when
digital level which is obtained by
BTCR − BL gets a negative value.
The values of P.Gian and T.Const of PI controller, in addition; Droop value are ramped by
multiple run in a Ferroresonant configuration (section 3.B) which is present at the beginning of
simulation. It is performed to choose optimum values based on measured parameters in
sustained state as shown in the following tables. Table 5 shows measured values versus P.Gian
variations whereas, T.Const and Droop values are remained constant at 0.1 and 1%
respectively. As shown in the table, the value of 1.0 results in minimum values of electrical
parameters and stabilizing time. Hence, it is chosen as optimum value.
Table 5. Variation of P.Gian versus electrical parameters of SVC
P.Gian Voltage
(pu)
THD
(%)
Fr.d
(Hz)
Ploss
(MW)
S. time
(s)
0.1 1.010 1.02 0.021 6.5 1.82
0.4 1.007 0.95 0.013 6.5 2.32
0.8 1.007 0.95 0.002 6.2 2.71
1.0 1.007 0.40 0.002 6.1 0.63
1.4 1.008 0.42 0.009 6.2 1.35
1.8 1.008 0.42 0.002 6.1 0.81
2.2 1.013 1.65 0.154 6.3 0.75
2.6 1.022 5.31 0.623 7.4 1.38
Salman Rezaei
16
Table 6 shows variation of T. Const where P. Gian and Droop are set to 1 and 1%
respectively. As shown in the table, the value of 0.1 results in minimum values of electrical
parameters and stabilizing time. Hence, it is chosen as optimum value.
Table 6. Variation of T.Const versus electrical parameters of SVC
T.Const Voltage
(pu)
THD
(%)
Fr.d
(Hz)
Ploss
(MW)
S. time
(s)
0.01 1.008 0.93 0.005 6.5 1.68
0.05 1.008 0.93 0.005 6.5 1.25
0.10 1.007 0.40 0.002 6.1 0.63
0.50 0.992 0.36 0.005 5.9 3.31
1.00 1.021 0.05 0.009 6.0 2.12
1.50 1.020 0.09 0.020 6.0 2.41
2.00 1.020 0.08 0.021 6.0 2.72
2.5 1.014 0.08 0.017 5.9 3.21
Figure 8. Control circuit of SVC in Ashern station
Table 7 shows percent variation of Droop where P.Gian and T.Const are set to 1 and 0.1
respectively. As shown in the table, decreasing Droop value results in decreasing stabilizing
time. Although Droop value of 0.1% causes minimum values of parameters and closest value
I
PBSVS
D-
F
+
Vre
f
D-
F
+
RMSvoltage
Vref
ReacPower
RMSvoltageMax
D
E0.8
N
D
N/DISVC
*
200.0
N
D
N/D
DroopCalculation
MeasuredReactive Power
MeasuredVoltage (pu)
VoltageReference (pu)
Low PassFilter90Hz
Notch filters60Hz 120Hz
Rated ReactivePower (MVar)
PI Controllerof
VoltageFeedback
To PreventDivision by 0
BSVS
Nc
BL
TCR/TSCBTCR
CAPS_ON
Btcr
D-
F
+
Bl
*.013
AORDN
D
N/D
Bl
Btcrn
CapOn
CapOff
CSW
CAPS_ON
Bl
CS
+
- NC
KB
AlphaOrder
Signal: capacitor bank switch on capacitor bank switch off
Capacitorswitching logic
CapsON - number ofTSC units in use
Capacitorbank
switching
Non-linear transfer function alpha = f (B_TCR_ref)
Non-linearsusceptancecharacteristic
BSVS
KB
Voltage Ref...
2
0
Vref
1
pu
Fireangle
Pgain
A
B
Ctrl
Ctrl = 11
0
1
MultipleRun
Ch. 1
Ch. 2
Ch. 3
V1
Meas-Enab
.
.
.DAMPINGREAC...
meas.multirun
0
Disable Enable
Multiple RunSVC Coefficients
Pgian, Tconst, Droop
THD
RMSvoltage
Pgain
A
B
Ctrl
Ctrl = 1
0
1
DAMPINGREAC...
voltage multirun
0
Disable Enable
En
ab
leP
ga
in
A
B
Ctrl
Ctrl = 1
run1
run1
SVC : C...
5
0
Pgain
1
EnableDroop
Frd
Mitigation of Ferroresonance By FACTS In Electrical Network
17
of voltage to reference value, it is not stable in some other states; hence, the value of 0.5% is
chosen as optimum value.
Table 7. Variation of Droop versus electrical parameters of SVC
Droop Voltage
(pu)
THD
(%)
Fr.d
(Hz)
Ploss
(MW)
S. time
(s)
0.1 1.001 0.39 0.004 6.0 0.62
0.5 1.005 0.42 0.004 6.1 0.62
1.0 1.007 0.40 0.002 6.1 0.63
2.0 1.016 0.50 0.006 6.3 0.71
3.0 1.022 0.52 0.004 6.5 0.73
4.0 1.030 0.58 0.007 6.6 1.31
5.0 1.035 0.60 0.008 6.8 1.71
6.0 1.043 0.60 0.017 5.9 3.21
- Examination of SVC in Ferroresonance
In this section, SVC with designated setting parameters of control system is examined in
Ferroresonant states which were explained in advance. Ferroresonance in case of breaker phase
failure (section 3.A) happens in Silver station in the time of 0.3 s. SVC is put in to service in
the time of 0.7 s. values of currents in HV side of transformer are increased and waveforms are
misshaped differently. Due to existing unbalance condition, the value and features of
waveforms are different in each phase. Transient state of interrupted phase A is suppressed
after 0.5 s whereas, two other phases get their sustained state in the time of 1.6 s and 1.8 s
respectively (Figure. 9a). The values of three phase currents are 22, 32, 19 Apeak prim in HV side
of transformer. THD value is reduced to 2% whereas, this value is about 0.1% in Ashern
station. In order to show variation of V-Φ in each state, a 3 dimensional phase plan diagram is
used in this section. As shown in phase plan diagram of phase C (Figure. 9b), voltage and flux
get their final values in the time of 1 s after connecting the SVC. As can be seen in Figure. 9c,
magnetizing current follows the total current of transformer in opposite direction however, flux
value of iron core is not able to follow instantaneous variations of magnetizing current in
transient state; hence, it is kept in a range of about + 600 wb-N in this time.
(a)
0 200 300 600 700 1000 1200 1400 1600 1800 2000
-100
-250
25
100
0 200 300 600 700 1000 1200 1400 1600 1800 2000-100
-50
0
50
Cu
rren
t (
A)
0 200 300 600 700 1000 1200 1400 1600 1800 2000-50
-25
0
25
50
70
Time (ms)
SVC ConnectedBreaker failure
Ferroresonance
Normal stateSustained state
Transient time 0.9 s
Sustained state
Transient time 1.1 s
Transient time 0.5 s
A
B
C
Salman Rezaei
18
(b)
(c)
-3 -2 -1 0 1 2 3
x 105
-600-400-20002004006008000
300
700
1000
1500
2000
2500
Voltage (V)Flux (wb.N)
Tim
e (
ms)
Transient time
1 s
SVC Connected
Normal state Breaker failure
Ferroresonance
Sustained state
C
Mitigation of Ferroresonance By FACTS In Electrical Network
19
(d)
Figure 9. Mitigation of Ferroresonance by SVC in case of breaker failure in Silver station. (a)
Waveform of currents in Silver station. (b) Phase plan diagram. (c) Value of flux and mag.
current of three phases. (d) Electrical parameters of SVC in Ashern station
Figure 9d shows electrical parameters of SVC. Voltage gets its final value of about 1.006
pu in the time of 1.1 s (0.4 s after connecting SVC). The values of THD, Fr.d, and active power
are increased temporarily while connecting the SVC however, the values are tolerable. SVC is
connected to the network in step 5 of TSCs. fire angle of TCR is reduced to 90° to absorb
maximum value of reactive power. As the voltage must be more reduced, TSC is changed to
step 4 and then 3 in the time of 1 s. As it is expected, fire angle is reduced to 90° while
reducing number of TSCs. thereafter, the TCR firing angle is readjusted to absorb just right
amount of the excessive reactive power supplied by the TSCs to meet the reference value of
voltage.
Another Ferroresonant state which was explained in section 3.B is examined in presence of
SVC. Ferroresonant arrangement is formed in the time of 1.2 s when Grand Rapids station is in
generator mode. As it was mentioned in advance, waveform of parameters is increased and
misshaped symmetrically in all three phases along with power oscillation in the time of
Ferroresonance. SVC is connected in the time of 2.2 s so that Ferroresonance is mitigated after
a transient time of about 0.5 s. Figure. 10a and b show voltage, current and phase plan diagram
of phase A in HV side of transformer in Silver station. Figure 10c shows that flux density of
Salman Rezaei
20
iron core follows power oscillation as well as magnetizing current and is damped to a value of
about 400 wb.N while connecting SVC to the power system. Figure. 10d shows electrical
parameters of SVC in the time before and after connection of SVC to the system. Voltage,
THD, and Fr.d get their sustained value of 1.008 pu, 0.8% and 0.02 Hz respectively in the time
of about 3 s whereas, sustained value of active power is about 6.5 MW. TSCs are still switched
out after connecting SVC whereas, fire angle is readjusted to get a value of about 138° to
absorb reactive power of 150 MVAR in order to meet the reference value of voltage.
(a)
(b)
(c)
1200 1700 2200 2700 3300-4
-2
0
2
4x 10
5
Vo
lta
ge (
V)
1200 1700 2200 2700 3300
-500
0
500
Time (ms)
Cu
rren
t (
A)
Transient time 0.5 s
Ferroresonance
Normal state
SVC Connected
Sustained state
Change arrangement
Transient time 0.5 s
-4-2 0 2 4
x 105
-1000-50005001000
500
1200
1500
2200
2700
3000
3500
Voltage (V)Flux (wb.N)
Tim
e (
ms) SVC Connected
Transient time
0.5 s
A
Normal stateChange arrangement
Ferroresonance
Sustained state
Mitigation of Ferroresonance By FACTS In Electrical Network
21
(d)
Figure 10. Mitigation of Ferroresonance by SVC in case of changing line arrangement. (a)
Waveform of voltage and current in Silver station. (b) Phase plan diagram. (c) Value of flux
and mag. current of three phases. (d) Electrical parameters of SVC in Ashern station
As it was shown in the study, SVC is an online-flexible device which is able to mitigate all
types of possible Ferroresonant states along with compensating reactive power. Unlike
proposed flexile method [1], SVC does not need any necessary change in power and control
system to mitigate different types of Ferroresonance. TSC stages and fire angle of TCR are
adjusted based on Ferroresonance of different types which proportionally depends on the value
of over voltages in the network. In compare with damping reactor in Ashern station, SVC just
absorbs 6% of active power to mitigate the same Ferroresonant state.
5. Conclusion
Static Var compensator as an online-flexible device is proposed in this paper to mitigate all
types of Ferroresonance which are caused by unpredictable states like, breaker failure or
changing line arrangement in Manitoba Hydro network. Ferroresonance is recognized by
detection tools and classified in adequate modes. Damping reactor which is located in Ashern
station, is examined with new parameters to mitigate Ferroresonance. Then, SVC with power
and control circuits is designed in Ashern station to mitigate Ferroresonance. Parameters of
SVC are examined to find optimum values. Finally, Ferroresonant states are examined in
presence of SVC. It is concluded that, in compare with damping reactor and other proposed
flexible methods, SVC absorbs low active power without any necessary change in parameters
to mitigate all different types of Ferroresonance along with compensating reactive power
automatically.
6. References
[1]. Wenxia Sima, Ming Yang, Qing Yang, Tao Yuan, Mi Zou: “Simulation and experiment
on a flexible control method for ferroresonance”, IET Generation, Transmission &
Distribution., 2014, Vol. 8, Issue: 10 pp. 1744-1753
Salman Rezaei
22
[2]. S. Punnepalli, G. Srinivasulu Reddy “Effective way to damping power oscillations using
Static Var Compensator with fuzzy logic controller”, IJTPE Journal., December 2012,
Vol. 4, Issue 13, No. 4 pp. 89-94
[3]. Narain G. Hingorani, Laszlo. Gyugyi: “Understanding FACTS: Concepts and Technology
of Flexible AC Transmission Systems”, Book of power engineering December 1999,
Wiley-IEEE Press, Section. 5, pp. 143–151
[4]. R. Gagnon, P. Viarouge, G. Sybille, E Tourkhani: “Identification of Ferroresonance as
the Cause of SVC Instability in a Degraded Series Compensated Network”, IEEE Power
Engineering Society Winter Meeting 2000, vol.2, pp. 1377 - 1382
[5]. Manitoba HVDC Research Centre, “PSCAD X4 Online Help”, Last Updated: 2012-06-
12
[6]. Festo Didactic Ltée/Ltd, Quebec, Canada: ”tatic Var Compensator (SVC)”, Courseware
Sample, Order no.: 86370-10, First Edition Rev. Level: 01/2015, ISBN 978-2-89640-540-
4
[7]. V. Valverde, G. Buigues, A. J. Mazón, I. Zamora, I. Albizu: “Ferroresonant
Configurations in Power Systems", (ICREPQ’12), Santiago de Compostela (Spain), 28th
to 30th March, 2012
[8]. Salman Rezaei: “Impact of Ferroresonance on protective relays in Manitoba Hydro 230
kV electrical network” presented at the 2015 IEEE 15th
International Conference on
Environment and Electrical Engineering Rome-Italy
[9]. D.A.N Jacobson, "Field Testing, Modelling, and Analysis of Ferroresonance in a High
Voltage Power System," Ph.D. dissertation, Dept. elect. and comp. Eng. Univ. Manitoba,
Aug. 2000.
[10]. D.A.N Jacobson and L. Marti, "Modeling Ferroresonance in a 230 kV Transformer-
Terminated Double-Circuit Transmission Line" Proc. 1999, IPST Conf., Budapest-
Hungary
[11]. EMTP works version 2.0.2, examples, “Ferro-Demo”, Data case given by D.A.N
Jacobson
[12]. Garikoitz Buigues, Inmaculada Zamora, Victor Valverde, Angel Javier Mazon, José
Ignacio San Martin: “Ferroresonance in three phase power distribution transformers:
Sources, Consequences, and prevention”, 19th
International Conference on Electricity
Distribution, Vienna, 21-24 May 2007, Paper No. 0197
Salman Rezaei received associate diploma from Chamran University,
Kerman, Iran in 2004 and B.Sc. from Mehriz-Azad University, Mehriz, Yazd,
Iran in 2010. He has been working in Kerman Combined Cycle Power Plant
since 2005. He was a laboratory technician and then electrical engineer of
technical office. His activities include protective relaying, testing electrical
devices, generator transformer and protective relays, electrical studies and
simulation of distributed resources and electrical projects. He also cooperates
with Kerman Nemad Niroo Co. Representing engineering services for
energy as Manager of electrical department. His research interests include simulation and
design of protective systems, Ferro resonance, and nonlinear dynamic.
Mitigation of Ferroresonance By FACTS In Electrical Network
23