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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.


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


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]

STe

3

AV

Tm

Ef0

Tmw

Ef Ifw

( S

yn

cM

/c)

Mu

ltim

ass

Te

Wra

dT

mT

mi

Te

i

460 MVA 13.8 kV

GRAND RAPIDS

V

A

w

Ef

Vs

TE

1.0

Tmi

w

Wrefz0

z

Hydro Gov 1

w Tm

Wref

z

zi Hydro Tur 1

Vs

PSS1A Vs

V

A

36

9.5

3 [o

hm

]5

44

.87

[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


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


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


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.


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)


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


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



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


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)


Ferroresonance

Normal state

SVC Connected

Sustained state

Change arrangement


-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


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

http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6910351

[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.


23

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