Title Analysis of Ferroresonance Phenomenon in 22 kV ......energies Article Analysis of Ferroresonance Phenomenon in 22 kV Distribution System with a Photovoltaic Source by PSCAD/EMTDC

Title Analysis of Ferroresonance Phenomenon in 22 kV DistributionSystem with a Photovoltaic Source by PSCAD/EMTDC

Author(s) Thanomsat, Nattapan; Plangklang, Boonyang; Ohgaki, Hideaki

Citation Energies (2018), 11(7)

Issue Date 2018-7-3

URL http://hdl.handle.net/2433/233941

Right

© 2018 by the authors. Licensee MDPI, Basel, Switzerland.This is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use,distribution, and reproduction in any medium, provided theoriginal work is properly cited. (CC BY 4.0).

Type Journal Article

Textversion publisher

Kyoto University

energies

Article

Analysis of Ferroresonance Phenomenon in 22 kVDistribution System with a Photovoltaic Source byPSCAD/EMTDC

Nattapan Thanomsat 1 ID , Boonyang Plangklang 1,* ID and Hideaki Ohgaki 2 ID

1 Department of Electrical Engineering, Faculty of Engineering, Rajamangala University of Technology,Thanyaburi, Pathumthani 12110, Thailand; [email protected]

2 Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 6110011, Japan;[email protected]

* Correspondence: [email protected]; Tel.: +66-86-899-2996

Received: 16 May 2018; Accepted: 29 June 2018; Published: 3 July 2018

Abstract: Overvoltage and overcurrent in the middle voltage (MV) 22 kV and low voltage (LV) 0.4 kVdistribution network with photovoltaic (PV) rooftop system of the Provincial Electricity Authority ofThailand (PEA) have been investigated in order to show that these unwanted situations are caused bythe ferroresonance phenomenon. This information would be useful to improve a better solution forthe system protection when PV rooftops are integrated into the PEA distribution system. The softwaretool, PSCAD/EMTDC is used to study the overvoltage at the high side of open-delta and open-wyedistribution transformer- and overcurrent at the low side of distribution transformer linked to thegrid system via three single-phase fuse cutouts. The ferroresonance phenomenon can be observedwhen the PV rooftop system is linked to the low voltage side of the distribution transformer via threesingle-phase fuse cutouts. The results show a good similarity with the results from the simulation ofthe MV side and LV side of distribution transformers. Finally, the physical phenomena described tothe overvoltage, overcurrent, and the destruction of the distribution transformer and other apparatusin load customers will occur when the system consists of the PV rooftop source, capacitance in longtransmission line, nonlinear distribution transformer with saturation characteristic and the usage ofsingle-phase switching cutouts in the system.

Keywords: ferroresonance; PV Rooftop system; PSCAD/EMTDC

1. Introduction

Ferroresonance is a special kind of resonance that occurs in the network with nonlinear elements,especially in transformers. When nonlinear inductance of the transformer core and the capacitanceof the network are equal, ferroresonance happens. This equality can occur when the transformer isaccidentally energized and de-energized in only one or two phases. Ferroresonance results in a highcurrent and voltage across the inductance core and leads to the damage of the transformer as shown inFigure 1. There are a lot of articles in the literature which have discussed this phenomenon, for instance,References [1–8], and numerous simulation results of the possible ferroresonance happening in thehigh voltage side of the distribution network have been reported in References [9–12]. Gonen T.reported that ferroresonance is a transient phenomenon caused by the interaction of system capacitancewith the nonlinear inductance of the transformer, energy source, and limited power losses [13].However, Garikoitz B., et al. showed that the influence of ferroresonance is not only limited to thecable capacitance consideration, but also to several constructive, design, operation, and protectiveparameters [14]. There are a lot of ferroresonances in the configuration of distribution transformers.

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Energies 2018, 11, 1742 2 of 24

In 2003, Jacobson D.A.N. determined that seven different types of electrical systems are affected byferroresonance phenomena [15].

Energies 2018, 11, x FOR PEER REVIEW 2 of 24

transformers. In 2003, Jacobson D.A.N. determined that seven different types of electrical systems are affected by ferroresonance phenomena [15].

Figure 1. The transformer explosion caused in middle voltage (MV) [16].

This phenomenon has been considered and concentrated by the large-scale electricity generators that produce and distribute energy to the end user. Nowadays, electricity is not only produced by large-scale producers but also by the small-scale end users. The development of the electricity generation technology and energy policies together with the environmental crisis have persuaded the end users to produce electricity from renewable energy by themselves. Therefore, ferroresonance caused by energizing and de-energizing transformers which are connected to these small-scale electricity producers must be of concern.

One of the small-scale electricity generation systems from renewable energy is the photovoltaic (PV) system, which directly converts solar energy into electricity. It is one of the significant and clean sources of renewable energy. In the year 2012, Thailand has successfully installed nearly 2300 MW of solar energy, 99 percent of which is in the form of commercially centralized installations (solar farms), while the housing-sized solar PV (solar rooftop) shares a very small percentage [17,18]. However, according to the explosive growth of urbanization in Thailand, which increases every year (approximately 1.6 percent per year [17]), the usage of rooftop solar energy dramatically increased. In contrast with this growth, the information about the end users that can produce electricity is not fully known by the provincial electricity authority of Thailand (PEA), which is the main electricity distributor in Thailand. Therefore, ferroresonance phenomena from accidentally energizing and de-energizing the distribution transformer should be awarded and concentrated. The study in Reference [19] confirmed that ferroresonance does exist in the power transformer, which is connected to the PV system. However, the complete distribution network is not considered. Moreover, the analysis of the ferroresonance effect on the load is still not considered. With more information on ferroresonance in distribution systems with PV systems connected to it, the PEA will be aware of the effect of this phenomenon on the transformers and the power qualities [20–29].

Based on these facts, the simulation-based study of the ferroresonance effects in the distribution network with PV system sources will be presented in this paper. The major contribution of this work is the analysis of the type of ferroresonance that occurs in systems together with its effect on the system. The frequency analysis technique known as the Fast Furrier Transformation (FFT) will be used to distinguish the type of ferroresonance in the frequency domain. After the introduction in the first part, the organization of this paper is arranged in 4 parts. In the second part, the preliminary and Theory of ferroresonance will be presented. System modeling and the simulation results will be mentioned, analyzed and discussed in the third and fourth part, respectively. Finally, the conclusion will be addressed in the last part.

Figure 1. The transformer explosion caused in middle voltage (MV) [16].

This phenomenon has been considered and concentrated by the large-scale electricity generatorsthat produce and distribute energy to the end user. Nowadays, electricity is not only producedby large-scale producers but also by the small-scale end users. The development of the electricitygeneration technology and energy policies together with the environmental crisis have persuadedthe end users to produce electricity from renewable energy by themselves. Therefore, ferroresonancecaused by energizing and de-energizing transformers which are connected to these small-scaleelectricity producers must be of concern.

One of the small-scale electricity generation systems from renewable energy is the photovoltaic(PV) system, which directly converts solar energy into electricity. It is one of the significant andclean sources of renewable energy. In the year 2012, Thailand has successfully installed nearly2300 MW of solar energy, 99 percent of which is in the form of commercially centralized installations(solar farms), while the housing-sized solar PV (solar rooftop) shares a very small percentage [17,18].However, according to the explosive growth of urbanization in Thailand, which increases every year(approximately 1.6 percent per year [17]), the usage of rooftop solar energy dramatically increased.In contrast with this growth, the information about the end users that can produce electricity is not fullyknown by the provincial electricity authority of Thailand (PEA), which is the main electricity distributorin Thailand. Therefore, ferroresonance phenomena from accidentally energizing and de-energizing thedistribution transformer should be awarded and concentrated. The study in Reference [19] confirmedthat ferroresonance does exist in the power transformer, which is connected to the PV system. However,the complete distribution network is not considered. Moreover, the analysis of the ferroresonanceeffect on the load is still not considered. With more information on ferroresonance in distributionsystems with PV systems connected to it, the PEA will be aware of the effect of this phenomenon onthe transformers and the power qualities [20–29].

Based on these facts, the simulation-based study of the ferroresonance effects in the distributionnetwork with PV system sources will be presented in this paper. The major contribution of this workis the analysis of the type of ferroresonance that occurs in systems together with its effect on thesystem. The frequency analysis technique known as the Fast Furrier Transformation (FFT) will beused to distinguish the type of ferroresonance in the frequency domain. After the introduction in thefirst part, the organization of this paper is arranged in 4 parts. In the second part, the preliminaryand Theory of ferroresonance will be presented. System modeling and the simulation results will bementioned, analyzed and discussed in the third and fourth part, respectively. Finally, the conclusionwill be addressed in the last part.

Energies 2018, 11, 1742 3 of 24

2. Preliminary and Theory

2.1. Ferroresonance in the Transformer

There are basically four different ferroresonance modes that can happen in a power system,that is, the fundamental mode, the subharmonic mode, the quasi-periodic mode and the chaotic mode,as shown in Figure 2.


2. Preliminary and Theory

2.1. Ferroresonance in the Transformer

There are basically four different ferroresonance modes that can happen in a power system, that is, the fundamental mode, the subharmonic mode, the quasi-periodic mode and the chaotic mode, as shown in Figure 2.

(a) Fundamental mode (b) Subharmonic mode

(c) Quasi-periodic mode (d) Chaotic mode

Figure 2. The ferroresonance modes and their frequency responses [30].

Fundamental mode

The signal has the same period as the power system (T). The frequency spectrums consist of the fundamental frequency component followed by the decreasing magnitude of the n -th odd harmonic.

Subharmonic

The signal has a period which is a multiple of the source period ( nT ). The frequency spectrums consist of the fundamental frequency component followed by the decreasing contents of the n -th subharmonic.

Quasi-periodic

The signal is not periodic but has the repetitive pattern. The frequency spectrums are discontinuous and defined as 21 mfnf , where n and m are integers.

Chaotic

The signal is not periodic and the frequency spectrums are continuous. In order to achieve the analytical solution of ferroresonance, the simplified equivalent circuit of

the transformer, which consists of a nonlinear inductance, equivalent capacitance, equivalent resistance, and energy source, is considered as shown in Figure 3.

Figure 2. The ferroresonance modes and their frequency responses [30].

• Fundamental mode

The signal has the same period as the power system (T). The frequency spectrums consist of thefundamental frequency component followed by the decreasing magnitude of the n-th odd harmonic.

• Subharmonic

The signal has a period which is a multiple of the source period (nT). The frequency spectrumsconsist of the fundamental frequency component followed by the decreasing contents of then-th subharmonic.

• Quasi-periodic

The signal is not periodic but has the repetitive pattern. The frequency spectrums arediscontinuous and defined as n f1 + m f2, where n and m are integers.

• Chaotic

The signal is not periodic and the frequency spectrums are continuous.In order to achieve the analytical solution of ferroresonance, the simplified equivalent circuit of the

transformer, which consists of a nonlinear inductance, equivalent capacitance, equivalent resistance,and energy source, is considered as shown in Figure 3.

Energies 2018, 11, 1742 4 of 24Energies 2018, 11, x FOR PEER REVIEW 4 of 24

Figure 3. The equivalent circuit of the transformer for ferroresonance analysis.

Suppose that the magnetization curve of the nonlinear inductance is represented in Figure 4, therefore, this curve can be approximated by the n th-order polynomial

nL bai (1)

where Li is a magnetizing current, is a magnetic flux in the transformer core, a is a coefficient of

the linear term that corresponds to unsaturated magnetizing inductance and b is a coefficient of the nonlinear term.

Figure 4. The magnetization curve of transformer inductance.

The analytical solution of ferroresonance in Figure 3 can be achieved by the harmonic balance method. The differential equation for the flux linkage with the magnetization curve approximated by Equation (1) is presented by

tEbaCdt

d

RCdt

dss

n cos)(112

2

(2)

In order to achieve the steady-state flux by the harmonic balance method, a simplified version of Equation (2) can be written in the form of Duffin’s equation [31,32]

tEdt

d

RCdt

dss

n cos1 22

202

2

(3)

where C

a0 and

C

b2 .


Suppose that the magnetization curve of the nonlinear inductance is represented in Figure 4,therefore, this curve can be approximated by the nth-order polynomial

iL = aφ + bφn (1)

where iL is a magnetizing current, φ is a magnetic flux in the transformer core, a is a coefficient ofthe linear term that corresponds to unsaturated magnetizing inductance and b is a coefficient of thenonlinear term.



Suppose that the magnetization curve of the nonlinear inductance is represented in Figure 4, therefore, this curve can be approximated by the n th-order polynomial

nL bai (1)

where Li is a magnetizing current, is a magnetic flux in the transformer core, a is a coefficient of

the linear term that corresponds to unsaturated magnetizing inductance and b is a coefficient of the nonlinear term.


The analytical solution of ferroresonance in Figure 3 can be achieved by the harmonic balance method. The differential equation for the flux linkage with the magnetization curve approximated by Equation (1) is presented by

tEbaCdt

d

RCdt

dss

n cos)(112

2

(2)

In order to achieve the steady-state flux by the harmonic balance method, a simplified version of Equation (2) can be written in the form of Duffin’s equation [31,32]

tEdt

d

RCdt

dss

n cos1 22

202

2

(3)

where C

a0 and

C

b2 .


The analytical solution of ferroresonance in Figure 3 can be achieved by the harmonic balancemethod. The differential equation for the flux linkage with the magnetization curve approximated byEquation (1) is presented by

d2φ

dt2 +1

RCdφ

dt+

1C(aφ + bφn) = ωsE cos ωst (2)

Energies 2018, 11, 1742 5 of 24

In order to achieve the steady-state flux φ by the harmonic balance method, a simplified versionof Equation (2) can be written in the form of Duffin’s equation [31,32]

d2φ

dt2 +1

RCdφ

dt+ ω2

0φ + ω22φn = ωsE cos ωst (3)

where ω0 =√

aC and ω2 =

√bC .

For the fundamental mode (n = 1, 3, 5, . . .), the steady-state solution of Equation (2) is written inthe form

φ = Φ sin(ωst + θ) = Φx sin ωst + Φy cos ωst (4)

where Φ =√

Φ2x + Φ2

y and θ = tan−1(

ΦyΦx

).

We substitute Equation (4) into Equation (2) and apply the approximation of termsinn(ωst + θ) with

sinn(ωst + θ) ∼= k1 sin(ωst + θ) (5)

where k1 = (−1)n−1

2n−2

(n

n−12

).

Then when we equate the sin ωst term and neglect cos ωst with the higher order terms,the following equations are obtained:

[−(ω2s − ω2

0) + k1ω22Φn−1]Φx −

( ωs

RC

)Φy = 0 (6)

[−(ω2s − ω2

0) + k1ω22Φn−1]Φy +

( ωs

RC

)Φx = ωsE (7)

When Equations (6) and (7) are solved for the coefficients Φx, Φy, the solution of Equation (4)can be obtained. Finally, the solution for the other modes of ferroresonance can be achieved withsimilar procedures.

Ferroresonance can be explained by using a graphical approach. Consider the V-I characteristicsof inductance and capacitance, as shown in Figure 5.


For the fundamental mode ( ,...5,3,1n ), the steady-state solution of Equation (2) is written in the form

ttt sysxs cossin)sin( (4)

where 22yx and

x

y1tan .

We substitute Equation (4) into Equation (2) and apply the approximation of term

)(sin tsn

with

)sin()(sin 1 tkt ssn

(5)

where

21

2)1(

2

1

1 nn

kn

n

.

Then when we equate the tssin term and neglect tscos with the higher order terms, the following equations are obtained:

0])([ 1221

20

2

ys

xn

s RCk

(6)

ERC

k sxs

yn

s

])([ 12

2120

2 (7)

When Equations (6) and (7) are solved for the coefficients yx , , the solution of Equation (4)

can be obtained. Finally, the solution for the other modes of ferroresonance can be achieved with similar procedures.

Ferroresonance can be explained by using a graphical approach. Consider the V-I characteristics of inductance and capacitance, as shown in Figure 5.

Figure 5. The graphical solution of a series ferroresonance circuit [33]. Figure 5. The graphical solution of a series ferroresonance circuit [33].

Energies 2018, 11, 1742 6 of 24

Since the inductive reactance of the transformer core consists of two regions, linear and nonlinearcharacteristics, the possible operation points are obtained as the intersection of VL and VS + VC areas follows:

• Point 1 is a stable non-ferroresonance mode. At this point, the circuit is working with the inductivemode and remains there in the steady-state.

• Point 2 is a stable ferroresonance mode. At this point, the circuit is working with the inductivemode with both high voltage and current. This solution also remains there in the steady-state.

• Point 3 is an unstable mode and the solution will not remain there in the steady-state.

2.2. The Distribution Transformer under the Emerged or De-Energized Modes

The delta and wye transformer connection with energy sources is modeled in the form of aninductor and capacitor network as shown in Figure 6a,b, respectively. These capacitors exist in theunderground cables or the overhead power lines with respect to earth. Whereas the inductors representthe magnetizing inductance of the transformers.


Since the inductive reactance of the transformer core consists of two regions, linear and nonlinear characteristics, the possible operation points are obtained as the intersection of

LV and

CS VV are as follows:

Point 1 is a stable non-ferroresonance mode. At this point, the circuit is working with the inductive mode and remains there in the steady-state.

Point 2 is a stable ferroresonance mode. At this point, the circuit is working with the inductive mode with both high voltage and current. This solution also remains there in the steady-state.

Point 3 is an unstable mode and the solution will not remain there in the steady-state.

2.2. The Distribution Transformer under the Emerged or De-Energized Modes

The delta and wye transformer connection with energy sources is modeled in the form of an inductor and capacitor network as shown in Figure 6a,b, respectively. These capacitors exist in the underground cables or the overhead power lines with respect to earth. Whereas the inductors represent the magnetizing inductance of the transformers.

(a) The line supplying a transformer with delta connected

(b) The line supplying a transformer with wye-ground connected

Figure 6. The transformer connection scheme.

From the connection scheme in Figure 6, the series circuit of the capacitor, inductor and supply source is used for analyzing the ferroresonance in each phase, as shown in Figure 7.

Figure 6. The transformer connection scheme.

From the connection scheme in Figure 6, the series circuit of the capacitor, inductor and supplysource is used for analyzing the ferroresonance in each phase, as shown in Figure 7.

Energies 2018, 11, 1742 7 of 24


(a) The ferroresonance circuits for each phase of the circuit in Figure 6a

(b) The ferroresonance circuits for each phase of the circuit in Figure 6b

Figure 7. The ferroresonance circuits for each phase of the circuits in Figure 6.

3. System Modeling for Simulation

In this section, the modeling of the distribution system with a PV connected system is arranged. Since an experiment with ferroresonance is a destructive experiment, the demonstration is simulated using the PSCAD/EMTDC software. In this study, three different cases are considered.

3.1. The System Under Considering

The system consists of a local load of the PEA network. Through the 22 kV distribution system, the local load has 3 transformers (one unit of 1 MVA and two units of 500 kVA) for condos, suburban homes and townhouses, and suburban homes with total installed PV rooftops, respectively. The total 500 kW installation capacity of the PV rooftop system consists of a PV array with Maximum Power Point Tracking (MPPT) and the simplified inverter without the anti-islanding system. The produced energy is incorporated into the 22 kV grid through the step-up transformer. The distribution line to the system consists of two underground cables of 20-km length and a PI transmission line section of 200-m length. Moreover, there are three cutout switches at every connection line, as shown in Figure 8.

Figure 8. The simulation system model.



In this section, the modeling of the distribution system with a PV connected system is arranged.Since an experiment with ferroresonance is a destructive experiment, the demonstration is simulatedusing the PSCAD/EMTDC software. In this study, three different cases are considered.


The system consists of a local load of the PEA network. Through the 22 kV distribution system,the local load has 3 transformers (one unit of 1 MVA and two units of 500 kVA) for condos, suburbanhomes and townhouses, and suburban homes with total installed PV rooftops, respectively. The total500 kW installation capacity of the PV rooftop system consists of a PV array with Maximum PowerPoint Tracking (MPPT) and the simplified inverter without the anti-islanding system. The producedenergy is incorporated into the 22 kV grid through the step-up transformer. The distribution line to thesystem consists of two underground cables of 20-km length and a PI transmission line section of 200-mlength. Moreover, there are three cutout switches at every connection line, as shown in Figure 8.


(a) The ferroresonance circuits for each phase of the circuit in Figure 6a

(b) The ferroresonance circuits for each phase of the circuit in Figure 6b



In this section, the modeling of the distribution system with a PV connected system is arranged. Since an experiment with ferroresonance is a destructive experiment, the demonstration is simulated using the PSCAD/EMTDC software. In this study, three different cases are considered.


The system consists of a local load of the PEA network. Through the 22 kV distribution system, the local load has 3 transformers (one unit of 1 MVA and two units of 500 kVA) for condos, suburban homes and townhouses, and suburban homes with total installed PV rooftops, respectively. The total 500 kW installation capacity of the PV rooftop system consists of a PV array with Maximum Power Point Tracking (MPPT) and the simplified inverter without the anti-islanding system. The produced energy is incorporated into the 22 kV grid through the step-up transformer. The distribution line to the system consists of two underground cables of 20-km length and a PI transmission line section of 200-m length. Moreover, there are three cutout switches at every connection line, as shown in Figure 8.

Figure 8. The simulation system model. Figure 8. The simulation system model.

Energies 2018, 11, 1742 8 of 24

3.2. Simulation Case I: The Effect of Ferroresonance on the High Voltage (HV) Side of theDistribution Transformer

The purpose of Case I is to consider the effect that ferroresonance causes due to the connectionof a 1 MVA and 500 kVA transformers to a PV system. The single line diagram of this case is shownin Figure 9 and its corresponding series inductance and capacitance (LC) ferroresonance circuit ismodeled in Figure 10. Moreover, the required parameters and data are summarized in Table 1.


3.2. Simulation Case I: The Effect of Ferroresonance on the High Voltage (HV) Side of the Distribution Transformer

The purpose of Case I is to consider the effect that ferroresonance causes due to the connection of a 1 MVA and 500 kVA transformers to a PV system. The single line diagram of this case is shown in Figure 9 and its corresponding series inductance and capacitance (LC) ferroresonance circuit is modeled in Figure 10. Moreover, the required parameters and data are summarized in Table 1.

Figure 9. The single line diagram of the 1 MVA and 500 kVA transformer connections.

RR

L

RR

L

A B C

RL

RR

L

XC

XC

XC

XM

XM

XM

Vgrid

Figure 10. The series LC ferroresonance circuit for Case I.

Table 1. The parameters for simulation Case I.

Name Parameter Value

Vgrid Base MVA (3 phase) 10 MVA

Base voltage (L-L, RMS) 32 kV Base frequency 50 Hz

Cable 1 Steady-state frequency 50 Hz

Segment length 20 km


Segment length 20 km T1 Transformer MVA 500 kVA

RL RRLVA

us

Cable_1

C1Cable_1S1 A1

C2

S2 A2

C3

S3 A3

C1Cable_1S1A1

C2

S2A2

C3

S3A3

BRKL01_1

BRKL01_2

BRKL01_3

A

B

C

A

B

C

#2#1

22.0 [kV]0.4 [kV]

500 [kVA]umec

VT01a

VT01b

VT01cP+jQ

0.01 [MW] /ph0.005 [MVAR] /ph

BRKL02_1

BRKL02_2

BRKL02_3

C1Cable_2S1 A1

C2

S2 A2

C3

S3 A3

Cable_2

C1Cable_2S1A1

C2

S2A2

C3

S3A3

A

B

C

A

B

C

#2#1

22.0 [kV]0.4 [kV]

1000 [kVA]umec

VT02a

VT02b

VT02cP+jQ

0.01 [MW] /ph0.005 [MVAR] /ph

underground cable 20 km


Vload02

Vload01

C1Cable1S1 A1

C1Cable1S1A1


C1Cable1S1 A1

C1Cable1S1A1

overhead line 200 m

PEA's 22 kVDistribution System



3.2. Simulation Case I: The Effect of Ferroresonance on the High Voltage (HV) Side of the Distribution Transformer

The purpose of Case I is to consider the effect that ferroresonance causes due to the connection of a 1 MVA and 500 kVA transformers to a PV system. The single line diagram of this case is shown in Figure 9 and its corresponding series inductance and capacitance (LC) ferroresonance circuit is modeled in Figure 10. Moreover, the required parameters and data are summarized in Table 1.


RR

L

RR

L

A B C

RL

RR

L

XC

XC

XC

XM

XM

XM

Vgrid




Vgrid Base MVA (3 phase) 10 MVA

Base voltage (L-L, RMS) 32 kV Base frequency 50 Hz




Segment length 20 km T1 Transformer MVA 500 kVA

RL RRLVA

us

Cable_1

C1Cable_1S1 A1

C2

S2 A2

C3

S3 A3

C1Cable_1S1A1

C2

S2A2

C3

S3A3

BRKL01_1

BRKL01_2

BRKL01_3

A

B

C

A

B

C

#2#1

22.0 [kV]0.4 [kV]

500 [kVA]umec

VT01a

VT01b

VT01cP+jQ

0.01 [MW] /ph0.005 [MVAR] /ph

BRKL02_1

BRKL02_2

BRKL02_3

C1Cable_2S1 A1

C2

S2 A2

C3

S3 A3

Cable_2

C1Cable_2S1A1

C2

S2A2

C3

S3A3

A

B

C

A

B

C

#2#1

22.0 [kV]0.4 [kV]

1000 [kVA]umec

VT02a

VT02b

VT02cP+jQ

0.01 [MW] /ph0.005 [MVAR] /ph



Vload02

Vload01

C1Cable1S1 A1

C1Cable1S1A1


C1Cable1S1 A1

C1Cable1S1A1

overhead line 200 m

PEA's 22 kVDistribution System


Energies 2018, 11, 1742 9 of 24



VgridBase MVA (3 phase) 10 MVA

Base voltage (L-L, RMS) 32 kVBase frequency 50 Hz

Cable 1Steady-state frequency 50 Hz


Cable 2Steady-state frequency 50 Hz


T1

Transformer MVA 500 kVAPrimary voltage 22 kV

Secondary voltage 0.4 kVType: Delta-Wye groundBase operation frequency 50 Hz

T2

Transformer MVA 1 MVAPrimary voltage 22 kV

Secondary voltage 0.4 kVType: Delta-Wye groundBase operation frequency 50 Hz

Load 1 Customer Load 1 0.01 MW + 0.005 MVAR per phaseLoad 2 Customer Load 2 0.01 MW + 0.005 MVAR per phase

Three single-phase circuit breakers (BRK) are connected with underground cables (BRKL01_1,BRKL01_2, BRKL01_3, BRKL02_1, BRKL02_2, and BRKL02_3). The measuring equipment isrepresented by VT01a, VT01b, VT01c, VT02a, VT02b, and VT02c. Single-phase circuit breakers areconsequently switched from phase C, A and B for de-energization. After that, they are switched fromphase B, A and C for energization.

3.3. Simulation Case II and Case III: The Impact of the PV Rooftop System on the Distribution Transformer andSuburban Homes

The purpose of Case II is to consider the effect of ferroresonance that is caused by the cuts in thePV system at the interconnection transformers 500 kVA LV and suburban home sides. The purpose ofCase III is to consider the effect of ferroresonance that is caused by the cuts in the PV system at theinterconnection transformer 500 kVA LV side with the increasing installation capacity of the PV systemstep by step and to observe the effects of the change. The single line diagram for expressing thesetwo cases is shown in Figure 11 and its corresponding series LC ferroresonance circuit is modeled inFigure 12. Additionally, the required parameters and data are summarized in Table 2.


Figure 11. The single line diagram of a PV rooftop system with a 500 kVA transformer and a light load connected.

A B C

R=

0

XC

XC

XC

XM

XM

XM

Vpv

Figure 12. The series LC ferroresonance circuit for Cases II and III.

Three single-phase circuit breakers are connected with the transmission line PI section (BRKA, BRKB, and BRKC). The measuring equipment is represented by Ea, Eb, Ec, Ia, Ib, Ic, VLoad and ILoad. Single-phase circuit breakers are consequently switched from phase B, C and A for de-energization. After that, they are switched from phase A, C and B for energization.

4. Simulation Results and Discussion

The simulation results from the model in Section 3 are considered, analyzed and discussed in this section.

4.1. Case I: The Ferroresonance Effect on the 500 kVA and 1 MVA Transformer with Condos, Suburban and Town House Loads

For Case I, the single-phase de-energization and energization at BRKL01 and BRKL02 illustrate the ferroresonance overvoltage of the 1 MVA and 500 kVA transformers. The simulation results also show that the overvoltage occurs between 0.25–0.7 s as seen in Figures 13 and 14, respectively.

GT

+

20

.0 [m

F]

2

I D

D2

I

D2

I

D2

I

D2

I

D2

I

800.0

30.0

Ga1

Ga2

Gb1

Gb2

Gc1

Gc2

D

sb Vboost

500 [uH]

500 [uH]

500 [uH]

10

.0 [m

F]

10

.0 [m

F]

10

.0 [m

F]

BRKA

BRKB

BRKC

Isa

Isb

Isc

P+jQ0.01 [MW] /ph0 [MVAR] /ph

ILo

ad

VLoad

A

B

C

A

B

C

COUPLEDPI

SECTION

A

B

C

3 P

ha

seR

MS

3 Phase RMS

a VA

Ea

Eb

Ia

Ib

IcBRK3Vabc

Ec

A

B

C

A

B

C

#2 #1

0.4 [kV]22.0 [kV]

500 [kVA]umec

Figure 11. The single line diagram of a PV rooftop system with a 500 kVA transformer and a lightload connected.

Energies 2018, 11, 1742 10 of 24


Figure 11. The single line diagram of a PV rooftop system with a 500 kVA transformer and a light load connected.

A B C

R=

0

XC

XC

XC

XM

XM

XM

Vpv


Three single-phase circuit breakers are connected with the transmission line PI section (BRKA, BRKB, and BRKC). The measuring equipment is represented by Ea, Eb, Ec, Ia, Ib, Ic, VLoad and ILoad. Single-phase circuit breakers are consequently switched from phase B, C and A for de-energization. After that, they are switched from phase A, C and B for energization.


The simulation results from the model in Section 3 are considered, analyzed and discussed in this section.

4.1. Case I: The Ferroresonance Effect on the 500 kVA and 1 MVA Transformer with Condos, Suburban and Town House Loads

For Case I, the single-phase de-energization and energization at BRKL01 and BRKL02 illustrate the ferroresonance overvoltage of the 1 MVA and 500 kVA transformers. The simulation results also show that the overvoltage occurs between 0.25–0.7 s as seen in Figures 13 and 14, respectively.

GT

+

20

.0 [m

F]

2

I D

D2

I

D2

I

D2

I

D2

I

D2

I

800.0

30.0

Ga1

Ga2

Gb1

Gb2

Gc1

Gc2

D

sb Vboost

500 [uH]

500 [uH]

500 [uH]

10

.0 [m

F]

10

.0 [m

F]

10

.0 [m

F]

BRKA

BRKB

BRKC

Isa

Isb

Isc

P+jQ0.01 [MW] /ph0 [MVAR] /ph

ILo

ad

VLoad

A

B

C

A

B

C

COUPLEDPI

SECTION

A

B

C

3 P

ha

seR

MS

3 Phase RMS

a VA

Ea

Eb

Ia

Ib

IcBRK3Vabc

Ec

A

B

C

A

B

C

#2 #1

0.4 [kV]22.0 [kV]

500 [kVA]umec


Table 2. The parameters for simulation Cases II and III.


PV module data

Ref. irradiance 1000 W/m2

Ref. Temperature 25 CEffective area per cell 0.01 m2

Series resistance per cell 0.02 ΩShunt resistance per cell 1000 Ω

Diode ideality factor 1.5Band gap energy 1.103 eV

Saturation current at reference conditions per cell 1 × 10−12 kAShort circuit current at the ref. conditions per cell 0.0025 kA

Temperature Coefficient of photocurrent 0.001 A/K

Coupled PI Section Line Rated Frequency 50 HzLine Length 0.2 km

T3

Transformer MVA 500 kVAPrimary voltage 0.4 kV

Secondary voltage 22 kVType: Wye ground—DeltaBase operation frequency 50 Hz

Load 3 Customer Load 3 0.01 MW per phase

Three single-phase circuit breakers are connected with the transmission line PI section (BRKA,BRKB, and BRKC). The measuring equipment is represented by Ea, Eb, Ec, Ia, Ib, Ic, VLoad and ILoad.Single-phase circuit breakers are consequently switched from phase B, C and A for de-energization.After that, they are switched from phase A, C and B for energization.


The simulation results from the model in Section 3 are considered, analyzed and discussed inthis section.

4.1. Case I: The Ferroresonance Effect on the 500 kVA and 1 MVA Transformer with Condos, Suburban andTown House Loads

For Case I, the single-phase de-energization and energization at BRKL01 and BRKL02 illustratethe ferroresonance overvoltage of the 1 MVA and 500 kVA transformers. The simulation results alsoshow that the overvoltage occurs between 0.25–0.7 s as seen in Figures 13 and 14, respectively.

Energies 2018, 11, 1742 11 of 24


Figure 13. The ferroresonance overvoltage at the HV side transformer 1 MVA.

Figure 14. The ferroresonance overvoltage at the HV side transformer 500 kVA.

However, ferroresonance does not occur when the distribution transformer is not in the saturation region and the three-phase circuit breaker is connected and disconnected at the same time. These characteristics are shown in Figures 15 and 16, respectively.

Figure 15. The three-phase circuit breaker disconnecting and connecting without the saturation transformer 1 MVA at the HV side.

Main : Voltage at primary of transformer 1 MVA

Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-300

-200

-100

0

100

200

300

Inp

ut V

olta

ge

[kV

]

VT02a VT02b VT02c

Main : Voltage at primary of transformer 500 kVA

Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-80

-60

-40

-20

0

20

40

60

Inpu

t V

olta

ge

[kV

]

VT01a VT01b VT01c


Time [s] 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

Inpu

t V

olta

ge [

kV]

VT02a VT02b VT02c








Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-300

-200

-100

0

100

200

300

Inp

ut V

olta

ge

[kV

]

VT02a VT02b VT02c


Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-80

-60

-40

-20

0

20

40

60

Inpu

t V

olta

ge

[kV

]

VT01a VT01b VT01c


Time [s] 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

Inpu

t V

olta

ge [

kV]

VT02a VT02b VT02c


However, ferroresonance does not occur when the distribution transformer is not in thesaturation region and the three-phase circuit breaker is connected and disconnected at the sametime. These characteristics are shown in Figures 15 and 16, respectively.







Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-300

-200

-100

0

100

200

300

Inp

ut V

olta

ge

[kV

]

VT02a VT02b VT02c


Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-80

-60

-40

-20

0

20

40

60

Inpu

t V

olta

ge

[kV

]

VT01a VT01b VT01c


Time [s] 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

Inpu

t V

olta

ge [

kV]

VT02a VT02b VT02c

Figure 15. The three-phase circuit breaker disconnecting and connecting without the saturationtransformer 1 MVA at the HV side.

Energies 2018, 11, 1742 12 of 24


Figure 16. The three-phase circuit breaker disconnecting and connecting without the saturation transformer 500 kVA at the HV side.

4.2. Case II: The Ferroresonance Effect on the 500 kVA Transformer LV Side with Suburban Home Load and the Total 500 kW Installation Capacity of PV Rooftop Systems

In Case II, the de-energization and energization in the phase by phase scheme are illustrated. First, the BRKB opens at 0.3 s. The corresponding phase voltage and current are shown in Figure 17.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 17. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB open circuit is at 0.3 s.

The frequency analysis results is shown in Figure 17. The corresponding frequency spectrums are obtained as shown in Figure 18.


Time [s] 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-30

-20

-10

0

10

20

30

Input

Volt

age

[kV

]

VT01a VT01b VT01c

PV_Rooftop_01 : Line current at LV side of transformer 500 kVA

Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cur

ren

t [k

A]

(kA

)

Ia Ib IcPV Rooftop 01 : Voltage at LV side of transformer 500 kVA

Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inp

ut V

olt

ag

e [

kV]

Ea Eb Ec

PV_Rooftop_01 : Voltage at LV side of transformer 500 kVA

Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inpu

t V

olta

ge [

kV]

Ea Eb EcPV_Rooftop_01 : Line current at LV side of transformer 500 kVA

Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic

Figure 16. The three-phase circuit breaker disconnecting and connecting without the saturationtransformer 500 kVA at the HV side.

4.2. Case II: The Ferroresonance Effect on the 500 kVA Transformer LV Side with Suburban Home Load and theTotal 500 kW Installation Capacity of PV Rooftop Systems

In Case II, the de-energization and energization in the phase by phase scheme are illustrated.First, the BRKB opens at 0.3 s. The corresponding phase voltage and current are shown in Figure 17.


Figure 16. The three-phase circuit breaker disconnecting and connecting without the saturation transformer 500 kVA at the HV side.

4.2. Case II: The Ferroresonance Effect on the 500 kVA Transformer LV Side with Suburban Home Load and the Total 500 kW Installation Capacity of PV Rooftop Systems

In Case II, the de-energization and energization in the phase by phase scheme are illustrated. First, the BRKB opens at 0.3 s. The corresponding phase voltage and current are shown in Figure 17.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 17. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB open circuit is at 0.3 s.

The frequency analysis results is shown in Figure 17. The corresponding frequency spectrums are obtained as shown in Figure 18.


Time [s] 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-30

-20

-10

0

10

20

30

Input

Volt

age

[kV

]

VT01a VT01b VT01c


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cur

ren

t [k

A]

(kA

)

Ia Ib IcPV Rooftop 01 : Voltage at LV side of transformer 500 kVA

Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inp

ut V

olt

ag

e [

kV]

Ea Eb Ec


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-0.40

-0.20

0.00

0.20

0.40

Inpu

t V

olta

ge [

kV]


Time [s] 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic

Figure 17. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB opencircuit is at 0.3 s.

Energies 2018, 11, 1742 13 of 24

The frequency analysis results is shown in Figure 17. The corresponding frequency spectrums areobtained as shown in Figure 18.Energies 2018, 11, x FOR PEER REVIEW 13 of 24

(a) Phase A

(b) Phase B

(c) Phase C

Figure 18. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB open circuit is at 0.3 s.

From the results in Figures 17 and 18, it is clearly seen that phase A and C are affected by the ferroresonance. Their voltage consists of the fundamental mode ferroresonance while the current consists of the combination of fundamental mode and quasi-periodic mode ferroresonances.

Secondly, a phase C is consequently disconnected by opening BRKC at time 0.4 s. The corresponding phase voltage and current are shown in Figure 19.

The frequency analysis of the results is shown in Figure 19. The corresponding frequency spectrums are obtained as shown in Figure 20.

(a) Phase A

FFT of Voltage phase A100.0

0.01 2 3 4 5 6 7

% [1] 41.0841

FFT of current phase A100.0

0.01 2 3 4 5 6 7

% [1] 57.574

FFT of Voltage phase B100.0

0.01 2 3 4 5 6 7

% [1] 39.6773

FFT of current Phase B100.0

0.01 2 3 4 5 6 7

% [1] 6.89177

FFT of voltage phase C100.0

0.01 2 3 4 5 6 7

% [1] 48.0503

FFT of current phase C100.0

0.01 2 3 4 5 6 7

% [1] 317.331


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec

PV Rooftop 01 : Line current at LV side of transformer 500 kVA

Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic

Figure 18. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKB open circuit is at 0.3 s.

From the results in Figures 17 and 18, it is clearly seen that phase A and C are affected by theferroresonance. Their voltage consists of the fundamental mode ferroresonance while the currentconsists of the combination of fundamental mode and quasi-periodic mode ferroresonances.

Secondly, a phase C is consequently disconnected by opening BRKC at time 0.4 s.The corresponding phase voltage and current are shown in Figure 19.


(a) Phase A

(b) Phase B

(c) Phase C

Figure 18. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB open circuit is at 0.3 s.

From the results in Figures 17 and 18, it is clearly seen that phase A and C are affected by the ferroresonance. Their voltage consists of the fundamental mode ferroresonance while the current consists of the combination of fundamental mode and quasi-periodic mode ferroresonances.

Secondly, a phase C is consequently disconnected by opening BRKC at time 0.4 s. The corresponding phase voltage and current are shown in Figure 19.

The frequency analysis of the results is shown in Figure 19. The corresponding frequency spectrums are obtained as shown in Figure 20.

(a) Phase A


0.01 2 3 4 5 6 7

% [1] 41.0841


0.01 2 3 4 5 6 7

% [1] 57.574


0.01 2 3 4 5 6 7

% [1] 39.6773


0.01 2 3 4 5 6 7

% [1] 6.89177


0.01 2 3 4 5 6 7

% [1] 48.0503


0.01 2 3 4 5 6 7

% [1] 317.331


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic

Figure 19. Cont.

Energies 2018, 11, 1742 14 of 24


(b) Phase B

(c) Phase C

Figure 19. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC open circuit is at 0.4 s.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 20. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC open circuit is at 0.4 s.


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 44.2473


0.01 2 3 4 5 6 7

% [1] 156.305


0.01 2 3 4 5 6 7

% [1] 39.6512


0.01 2 3 4 5 6 7

% [1] 6.66635


0.01 2 3 4 5 6 7

% [1] 39.6512

Figure 19. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC opencircuit is at 0.4 s.

The frequency analysis of the results is shown in Figure 19. The corresponding frequencyspectrums are obtained as shown in Figure 20.


(b) Phase B

(c) Phase C

Figure 19. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC open circuit is at 0.4 s.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 20. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC open circuit is at 0.4 s.


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 44.2473


0.01 2 3 4 5 6 7

% [1] 156.305


0.01 2 3 4 5 6 7

% [1] 39.6512


0.01 2 3 4 5 6 7

% [1] 6.66635


0.01 2 3 4 5 6 7

% [1] 39.6512

Figure 20. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKC open circuit is at 0.4 s.

Energies 2018, 11, 1742 15 of 24

From the results in Figures 19 and 20, it can be clearly seen that only phase A is affected byferroresonance. Its voltage consists of fundamental mode ferroresonance while the current consists ofthe combination of fundamental mode and quasi-periodic mode ferroresonances.

Finally, phase A is disconnected by opening BRKA at time 0.5 s. The corresponding phase voltageand current are shown in Figure 21.


From the results in Figures 19 and 20, it can be clearly seen that only phase A is affected by ferroresonance. Its voltage consists of fundamental mode ferroresonance while the current consists of the combination of fundamental mode and quasi-periodic mode ferroresonances.

Finally, phase A is disconnected by opening BRKA at time 0.5 s. The corresponding phase voltage and current are shown in Figure 21.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 21. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA open circuit is at 0.5 s.

The corresponding frequency spectrums of Figure 21 are obtained and shown in Figure 22.

(a) Phase A


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0 C

urr

en

t [k

A]

(kA

)Ia Ib Ic


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge [

kV]

Ea Eb Ec


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 39.324


0.01 2 3 4 5 6 7

% [1] 6.42465

Figure 21. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA opencircuit is at 0.5 s.



From the results in Figures 19 and 20, it can be clearly seen that only phase A is affected by ferroresonance. Its voltage consists of fundamental mode ferroresonance while the current consists of the combination of fundamental mode and quasi-periodic mode ferroresonances.

Finally, phase A is disconnected by opening BRKA at time 0.5 s. The corresponding phase voltage and current are shown in Figure 21.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 21. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA open circuit is at 0.5 s.


(a) Phase A


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge [

kV]

Ea Eb Ec


Time [s] 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 39.324


0.01 2 3 4 5 6 7

% [1] 6.42465

Figure 22. Cont.

Energies 2018, 11, 1742 16 of 24


(b) Phase B

(c) Phase C

Figure 22. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA open circuit is at 0.5 s.

From the results in Figures 21 and 22, the voltage and current of all phases are not affected by ferroresonance.

After all the circuit breakers are disconnected, the connection characteristics of each phase are considered. First, the BRKA is closed at 0.6 s. The corresponding phase voltage and current are shown in Figure 23.

(a) Phase A

(b) Phase B


0.01 2 3 4 5 6 7

% [1] 39.4034


0.01 2 3 4 5 6 7

% [1] 7.02954


0.01 2 3 4 5 6 7

% [1] 39.3804


0.01 2 3 4 5 6 7

% [1] 6.16561


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge

[kV

]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic

PV Rooftop 01 : Voltage at LV side of transformer 500 kVA

Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic

Figure 22. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKA open circuit is at 0.5 s.

From the results in Figures 21 and 22, the voltage and current of all phases are not affectedby ferroresonance.

After all the circuit breakers are disconnected, the connection characteristics of each phase areconsidered. First, the BRKA is closed at 0.6 s. The corresponding phase voltage and current are shownin Figure 23.


(b) Phase B

(c) Phase C

Figure 22. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA open circuit is at 0.5 s.

From the results in Figures 21 and 22, the voltage and current of all phases are not affected by ferroresonance.

(a) Phase A

(b) Phase B

(c) Phase C


0.01 2 3 4 5 6 7

% [1] 39.4034


0.01 2 3 4 5 6 7

% [1] 7.02954


0.01 2 3 4 5 6 7

% [1] 39.3804


0.01 2 3 4 5 6 7

% [1] 6.16561


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

ltage

[kV

]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olt

age

[kV

]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olt

age

[kV

]

Ea Eb Ec


Time [s] 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rre

nt

[kA

] (k

A)

Ia Ib Ic

Figure 23. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA closecircuit is at 0.6 s.

Energies 2018, 11, 1742 17 of 24



(c) Phase C

Figure 23. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA close circuit is at 0.6 s.


(a) Phase A

(b) Phase B

(c) Phase C

Figure 24. The frequency spectrum of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA close circuit is at 0.6 s.

From the results in Figures 23 and 24, only phase A is affected by the ferroresonance. Its voltage consists of the fundamental mode ferroresonance while the current consists of the combination of the fundamental mode and quasi-periodic mode ferroresonances.

Second, the BRKC is closed at 0.7 s. This connection yields the voltage and current as shown in Figure 25.

(a) Phase A


0.01 2 3 4 5 6 7

% [1] 43.534


0.01 2 3 4 5 6 7

% [1] 145.333


0.01 2 3 4 5 6 7

% [1] 39.5469


0.01 2 3 4 5 6 7

% [1] 7.03912


0.01 2 3 4 5 6 7

% [1] 39.5327


0.01 2 3 4 5 6 7

% [1] 6.40018


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge

[kV

]


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic

Figure 24. The frequency spectrum of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKA close circuit is at 0.6 s.

From the results in Figures 23 and 24, only phase A is affected by the ferroresonance. Its voltageconsists of the fundamental mode ferroresonance while the current consists of the combination of thefundamental mode and quasi-periodic mode ferroresonances.

Second, the BRKC is closed at 0.7 s. This connection yields the voltage and current as shown inFigure 25.


(c) Phase C

Figure 23. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA close circuit is at 0.6 s.


(a) Phase A

(b) Phase B

(c) Phase C

Figure 24. The frequency spectrum of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKA close circuit is at 0.6 s.

From the results in Figures 23 and 24, only phase A is affected by the ferroresonance. Its voltage consists of the fundamental mode ferroresonance while the current consists of the combination of the fundamental mode and quasi-periodic mode ferroresonances.

Second, the BRKC is closed at 0.7 s. This connection yields the voltage and current as shown in Figure 25.

(a) Phase A


0.01 2 3 4 5 6 7

% [1] 43.534


0.01 2 3 4 5 6 7

% [1] 145.333


0.01 2 3 4 5 6 7

% [1] 39.5469


0.01 2 3 4 5 6 7

% [1] 7.03912


0.01 2 3 4 5 6 7

% [1] 39.5327


0.01 2 3 4 5 6 7

% [1] 6.40018


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic

Figure 25. Cont.

Energies 2018, 11, 1742 18 of 24


(b) Phase B

(c) Phase C

Figure 25. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC close circuit is at 0.7 s.

The corresponding frequency spectrums of Figure 25 using FFT are shown in Figure 26.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 26. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC close circuit is at 0.7 s.


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 41.2048


0.01 2 3 4 5 6 7

% [1] 91.0408


0.01 2 3 4 5 6 7

% [1] 7.20637


0.01 2 3 4 5 6 7

% [1] 39.8952


0.01 2 3 4 5 6 7

% [1] 232.812


0.01 2 3 4 5 6 7

% [1] 45.8282

Figure 25. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC closecircuit is at 0.7 s.



(b) Phase B

(c) Phase C

Figure 25. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC close circuit is at 0.7 s.


(a) Phase A

(b) Phase B

(c) Phase C

Figure 26. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKC close circuit is at 0.7 s.


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 0.810

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

ren

t [k

A]

(kA

)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 41.2048


0.01 2 3 4 5 6 7

% [1] 91.0408


0.01 2 3 4 5 6 7

% [1] 7.20637


0.01 2 3 4 5 6 7

% [1] 39.8952


0.01 2 3 4 5 6 7

% [1] 232.812


0.01 2 3 4 5 6 7

% [1] 45.8282

Figure 26. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKC close circuit is at 0.7 s.

Energies 2018, 11, 1742 19 of 24

From the results in Figures 25 and 26, phase A and phase C are affected by ferroresonance.Their voltage consists of the fundamental mode ferroresonance while their current consists ofa combination of the fundamental mode and quasi-periodic mode ferroresonances.

Finally, the BRKB is closed at 0.8 s. This connection yields the voltage and current as shown inFigure 27.


From the results in Figures 25 and 26, phase A and phase C are affected by ferroresonance. Their voltage consists of the fundamental mode ferroresonance while their current consists of a combination of the fundamental mode and quasi-periodic mode ferroresonances.

Finally, the BRKB is closed at 0.8 s. This connection yields the voltage and current as shown in Figure 27.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 27. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB close circuit is at 0.8 s.


(a) Phase A


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0 C

urr

ent

[kA

] (k

A)

Ia Ib Ic


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

rent

[kA

] (k

A)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 44.1801


0.01 2 3 4 5 6 7

% [1] 141.737

Figure 27. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB closecircuit is at 0.8 s.



From the results in Figures 25 and 26, phase A and phase C are affected by ferroresonance. Their voltage consists of the fundamental mode ferroresonance while their current consists of a combination of the fundamental mode and quasi-periodic mode ferroresonances.

Finally, the BRKB is closed at 0.8 s. This connection yields the voltage and current as shown in Figure 27.

(a) Phase A

(b) Phase B

(c) Phase C

Figure 27. The voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB close circuit is at 0.8 s.


(a) Phase A


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inpu

t V

olta

ge [

kV]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cu

rren

t [k

A]

(kA

)

Ia Ib Ic


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Cu

rre

nt [

kA]

(kA

)

Ia Ib Ic


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

Inp

ut

Vo

lta

ge

[kV

]

Ea Eb Ec


Time [s] 0.800 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Cur

rent

[kA

] (k

A)

Ia Ib Ic


0.01 2 3 4 5 6 7

% [1] 44.1801


0.01 2 3 4 5 6 7

% [1] 141.737

Figure 28. Cont.

Energies 2018, 11, 1742 20 of 24


(b) Phase B

(c) Phase C

Figure 28. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer 500 kVA when the BRKB close circuit is at 0.8 s.

From the results in Figures 27 and 28, phases A, B and C are affected by the ferroresonance. Their voltage consists of the fundamental mode ferroresonance while their current consists of a combination of the fundamental mode and quasi-periodic mode ferroresonances. However, the effect of this phenomenon exists for a short time.

Furthermore, the ferroresonance that occurs in the system leads the voltage and current at the suburban home to have fluctuations as shown in Figure 29.

Figure 29. The voltage and current at the simulation load of a Suburban home.

For the HV side of the distribution transformer, its voltages are not affected by ferroresonance since it is connected to the grid. However, the currents fluctuate due to this phenomenon, as shown in Figure 30.

Figure 30. The voltage and current at the HV side of the distribution transformer.


0.01 2 3 4 5 6 7

% [1] 43.6869


0.01 2 3 4 5 6 7

% [1] 152.53


0.01 2 3 4 5 6 7

% [1] 43.4256


0.01 2 3 4 5 6 7

% [1] 139.894

PV_Rooftop_01 : Voltage at Point of common coupling

Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

40

Vol

tag

e a

t P

CC

[kV

]

Vpcc

Figure 28. The frequency spectrums of the phase voltage and current at the LV side (0.4 kV) transformer500 kVA when the BRKB close circuit is at 0.8 s.

From the results in Figures 27 and 28, phases A, B and C are affected by the ferroresonance.Their voltage consists of the fundamental mode ferroresonance while their current consists ofa combination of the fundamental mode and quasi-periodic mode ferroresonances. However, the effectof this phenomenon exists for a short time.

Furthermore, the ferroresonance that occurs in the system leads the voltage and current at thesuburban home to have fluctuations as shown in Figure 29.


(b) Phase B

(c) Phase C








0.01 2 3 4 5 6 7

% [1] 43.6869


0.01 2 3 4 5 6 7

% [1] 152.53


0.01 2 3 4 5 6 7

% [1] 43.4256


0.01 2 3 4 5 6 7

% [1] 139.894


Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

40

Vol

tag

e a

t P

CC

[kV

]

Vpcc


For the HV side of the distribution transformer, its voltages are not affected by ferroresonancesince it is connected to the grid. However, the currents fluctuate due to this phenomenon, as shown inFigure 30.


(b) Phase B

(c) Phase C








0.01 2 3 4 5 6 7

% [1] 43.6869


0.01 2 3 4 5 6 7

% [1] 152.53


0.01 2 3 4 5 6 7

% [1] 43.4256


0.01 2 3 4 5 6 7

% [1] 139.894


Time [s] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

-40

-30

-20

-10

0

10

20

30

40

Vol

tag

e a

t P

CC

[kV

]

Vpcc


Energies 2018, 11, 1742 21 of 24

4.3. Case III: The Effect of Ferroresonance When Increasing the Capacity of PV Rooftop Systems from 1 kW to500 kW

In Case III, the effects of the PV system connection at the 500 kVA transformer LV side with thestep by step increasing of the installed capacity of the PV system are shown in Table 3.

Table 3. The simulation results of the increasing installation capacity of the PV system.

PV InstallCapacity

(kW)

Vmax (kV, L-L) atTerminal Point of

Transformer

Imax (kA) atTerminal Pointof Transformer

Vload Max.(kV, L-L)

Iload Max.(kA)

Max. HDof Voltage

(%)

FerroresonancePhenomena

1 0.578 3.476 0.566 0.098 27.8 Y2 0.578 3.665 0.576 0.100 31.4 Y3 0.580 3.739 0.577 0.100 33.2 Y4 0.580 3.741 0.577 0.100 33.2 Y5 0.580 3.742 0.581 0.100 33.2 Y6 0.580 3.743 0.577 0.100 34.1 Y7 0.580 3.746 0.577 0.100 33.1 Y8 0.580 3.748 0.577 0.100 33.1 Y9 0.580 3.753 0.577 0.100 33.1 Y10 0.580 3.758 0.577 0.100 33.1 Y20 0.603 3.986 0.601 0.104 32.8 Y30 0.612 4.103 0.609 0.106 32.5 Y40 0.619 4.132 0.617 0.107 33.3 Y50 0.639 4.274 0.638 0.111 33.2 Y60 0.659 4.366 0.658 0.114 32.6 Y70 0.660 4.374 0.658 0.114 31.8 Y80 0.660 4.383 0.658 0.114 33.9 Y90 0.668 4.524 0.668 0.116 34.2 Y

100 0.690 4.728 0.688 0.119 34.7 Y200 0.640 4.279 0.639 0.111 31.7 Y300 0.677 4.507 0.674 0.117 35.1 Y400 0.698 4.647 0.696 0.121 36.3 Y500 0.716 5.302 0.715 0.124 37.8 Y

Because the installation of the PV systems grid connected in Thailand is preferred from a minimumof 1 kW, Table 3 shows that a 1 kW PV system can lead to ferroresonance phenomena in the distributiontransformer. In addition, the voltage and current values at the terminal transformer LV side are high.If the installed capacity of the PV system increases, the current in this area also increases and directlyaffects the distribution transformer.

From these results, the researcher found that the simulation results are different in some cases.The reasons for the differences are summarized as follows:

(1) The effect of the underground cable and distribution transformer configuration.(2) The effect of magnetizing the core saturation from the distribution transformer used for the

voltage divider.(3) The effect of the supply voltage to a transformer primary winding that is connected to a ground

or neutral separated wye or delta connection.(4) The effect of the increase of the voltage source in the system which, in this case, is the PV rooftop

system on the LV side.

The results reveal that the ferroresonance overvoltage and overcurrent phenomena can happenin this system under the saturation transformer with the capacitance of the 20 km undergroundcable, the capacitance of the 200 m transmission line PI section, the nonlinear characteristic of the1 MVA and 500 kVA transformer, and the PV system source. Moreover, the major principle of theferroresonance phenomena is an unbalanced switching operation. If there are differences in switchingcutouts disconnected and connected, they will cause damage to the power system. The ferroresonanceovervoltage will be 30–150 kV in the MV side, and the overvoltage will be 0.5–1 kV; the overcurrent will

Energies 2018, 11, 1742 22 of 24

be 2–6 kA in the LV side. The effect of this situation is the generation of the destruction of the electricalequipment and protection system. For this reason, the phenomena will not happen when three-phasedisconnected switching cutouts are operated at the same time. However, when three-phase switchingcutouts are operated at the same time, resonance transience will happen and can produce harmonicdistortion of the current in the distribution network as demonstrated in Figures 23–25.

To prevent ferroresonance occurring in a transformer accidentally energized in only one or twophases (see Figure 3), the practical solutions consist of the following:

1. Lowering the value of the capacitance between the circuit breaker and transformer below itscritical value by using, for example, a circuit breaker cubicle closer to the transformer or placingcircuit breakers just upstream of the transformers and closing them only when the voltage hasbeen restored to all three-phases.

2. Avoiding use of the transformers delivering an active power which is lower by 10% than its ratedapparent power.

3. Avoiding no-load energizing.4. Prohibiting single-phase operations or fuse protection, blowing of which results in

single-pole breaking.5. Prohibiting live work on a cable-transformer assembly when the cable length exceeds a certain

critical length.6. Resistance-earthing of the neutral of the supply substation.7. Solidly earthing the neutral (permanently or only during energizing and de-energizing operations)

of a transformer whose primary is wye-connected (available neutral).

5. Conclusions

This paper presents the analysis of ferroresonance phenomena in 0.4/22 kV distributiontransformers with a PV system source using the software simulation approach. The results explainthat ferroresonance overvoltage and overcurrent will occur when the system consists of a PV rooftopsource, the capacitance in a long transmission line, a nonlinear distribution transformer with saturationcharacteristic and the usage of single-phase switching cutouts in the system. In addition, when theinstalled capacity of the PV system increases, the current at the terminal distribution transformeralso increases and causes damage to the distribution transformer. Typically, for the three-phasesswitching cut-out and cut-in, ferroresonance will not occur. To prevent ferroresonance in a PVgrid connected system, many solutions can be applied. The usage of the three-phase switchingcutouts for connecting and disconnecting the system or the multi-pole breaking switchgear is oneof the solutions. Installing the ferroresonance suppression circuit to the transformer also preventsthe derogation. If the single-phase switching cutouts is installed, the proper sequent switchingmust be considered. In addition, the distribution transformer must be in the normal condition(without saturation characteristic). Moreover, a wide overview of this phenomenon that resulted fromsimulation studies can help the operator in electrical maintenance departments to get quick possiblesolutions to the problem. Therefore, it will allow the analysis of the risks and the evaluation of thesolution to be completed efficiency.

Author Contributions: N.T. designed, performed and analyzed data from the simulations; B.P. and H.O. assistedfor the data analysis and provided the suggestions for the writing.

Funding: Rajamangala University of Technology Thanyaburi, Thailand.

Conflicts of Interest: The authors declare no conflict of interest.

Energies 2018, 11, 1742 23 of 24

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Title Analysis of Ferroresonance Phenomenon in 22 kV ......energies Article Analysis of Ferroresonance Phenomenon in 22 kV Distribution System with a Photovoltaic Source by PSCAD/EMTDC