Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2640-2645 2640  
  

www.etasr.com Shrivastav et al.: Performance Analysis of Transient Current Limiters in a Distribution System 
 

Performance Analysis of Transient Current Limiters 
in a Distribution System 

 

Alok Kumar Shrivastav 
Electrical Engineering Dpt 

Techno India Batanagar 
Kolkata, India 

alok5497@gmail.com 

Pradip Kumar Sadhu  
Electrical Engineering Dpt 

Indian Institute of Technology (ISM) Dhanbad 
Jharkhand, India 

pradip_sadhu@yahoo.co.in 

Ankur Ganguly 
Electrical Engineering Dpt 

Techno India Batanagar 
Kolkata, India 

anksjc2002@yahoo.com 
 

 

Abstract—In this study, a simple, but effective method is 
presented for the limitation of the Y-yg transformers transient 
current. One of the main privileges of this method is its simple 
topology. It does not need any control circuit or measurement 
unit. The method is based on a three-phase thyristor bridge with 
a low resistance reactor. Since the number of thyristors is 
minimized, the voltage ripple, electrical losses and the 
malfunction probability owing to device failure are decreased 
considerably. The proposed method is simulated and validated by 
MATLAB simulation and conventional methods test results. It is 
shown that the proposed configuration is effective for the 
transient current limitation of Y-yg transformers 

Keywords- transient current limiter; TCL; stability analysis; 
fast Fourier transform; FFT; harmonic restraint, error analysis 

I. INTRODUCTION 
Nowadays power systems have been commonly operated 

with the maximum possible capacity and closer to their 
stability boundaries due to various reasons such as rapid 
increase in electricity demand and deregulation of electricity 
markets. This decreases the power system marginal security in 
case of instabilities. Under such circumstances, when a circuit 
breaker is charged, a high transient current flows for a little 
time until normal flux conditions are established. During most 
practical system conditions, this transient current’s value is 
high. This transient current, rich in all harmonics, has been 
found to cause wide raging disturbances in power system and 
power supplies [1]. In recent years, some solutions have been 
recommended to overcome the problem with diode bridge-DC 
reactors and voltage source PWM converters. In addition, a 
control strategy has been proposed for the assessment of 
SAPFs (shunt active power filters), based on the Lyapunov 
control theory, defines a stable operating region for the 
interfaced converter during the integration time with the utility 
grid [2]. Authors in [3] developed a wye-delta multi-function 
balance transformer based power quality control systems 
(MBT-PQCS). In [5], authors formulated the indirect matrix 
converter (IMC)-based unified power quality conditioner 
topology for a photovoltaic (PV) system for solving the power 
quality functionalities. In [6], an exhaustive simulation model 
based on mathematical model of a three-phase, shunt active 
power filter has been developed. In [9], the performance of the 

transformer magnetic flux under phase-hop condition is 
investigated and compared with different operating conditions 
using finite elements. These methods have some drawbacks 
like voltage drop, while they need bypass resistance, additional 
control circuits and switching devices. In [10], two different 
types of measurement equipment are presented comparatively 
for power quality assessment. In [12], shunt compensation 
based power quality enhancement is shown. However, the 
controller stability is not discussed in any of the available 
research methods. 

This paper’s objective is to investigate stable and harmonic 
free, transient current limiters (TCLs). In this context, two 
different types of TCLs based three-phase converter were 
proposed, twelve pulse and six-pulse. The first stage had 
presented the mathematical and simulation considerations of 
transients that occur during closing of circuit breaker and 
energizing of transformer and the second stage address the 
comparative loom of stability and the total harmonic distortion 
(THD) between twelve-pulse and six-pulse converter based 
three-phase thyristor bridge system. 

II. SERIES TCL FOR THREE-PHASE Y-YG TRANSFORMER 
Transient current in circuit breaker results from any abrupt 

change in the magnetizing voltage. The transient current 
waveform consists of a large and long lasting AC component 
and harmonics [16]. The TCL, has a low resistance coil in 
order to gain better results. The series TCL connected to three-
phase breaker and primary side of three single-phase 
transformers operates in two modes, charging mode and 
discharging mode [16]. The present mathematical statement in 
charging mode is composed, as takes after [16]. 

( / )
1

2 2)

2
2 2

2
( ) sin( )

( ) (

sin( )
( ) ( )

R L t TF

TF

VVp
i t e wt

RR wL

VVp
wt

RR wL






 
    
  

 
  

(1) 

where 
TCLP RRR   (Rp is the resistance in the primary side of 

the transformer and RTCL is the reactor resistance), 
L=Lp+LTCL+Lm (Lp is the leakage spillage inductance in the 
essential side of the transformer and LTCL is the reactor 



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www.etasr.com Shrivastav et al.: Performance Analysis of Transient Current Limiters in a Distribution System 
 

inductance and Lm is the charging inductance of the 
transformer), VTF is the forward thyristor voltage drop and Vp is 
the crest plentifulness of the utility voltage. 

 

 

Fig. 1.  Three single phase TCL connected in series with Y-yg transformer 

III. PPOPOSED TCL 
As shown in [16] the transient current of the three-stage 

transformer can be controlled by utilizing twelve thyristors of 
the arrangement TCL. Through these thyristors, considerable 
current of the loaded transformers flows. Therefore, they are 
costly as well as unstable. Hence, to make the system stable 
and harmonics free, a modified circuit is proposed which is 
shown in Figure 2 [16]. 

 

 
Fig. 2.  Proposed TCL connected to Y-yg transformer 

IV. CHARGING MODE 
According to Figure 3, the coil in comparison by neglecting 

R1 and L1 is communicated as, charging method of conducting 
coil [7] and can be written as follows: 

1
1

1
1

sin( 30) 2 2

2 2

LL p p

TF TCL TCL

di
V wt R i L

dt
di d

V L R i
dt dt



   

  
   

(2) 

Differentiating (2) leads to the following equation: 

1
1

2 2
1 1

2 2

sin( 30) 2 2

2

LL p p

TCL TCL

di
wV wt R i L

dt

d i di d
L R

dtdt dt



   

 

   (3) 

 

 
Fig. 3.  Coil charging mode 

It is clear that 

     1 m ci t i t i t       (4) 

cciR
dt

d


      (5) 

and 

* m mm
m

di did d
L

dt di dt dt

 
      (6) 

Utilizing (4), (5) and (6) the accompanying comparison can be 
represented as  

1 2 3 4( ) sin( )
Ft Gt

m m m mi t i e i e i wt i      

dt

d

L

R

dt

di
R

dt

d

m

c
c


 1

2

2
    (7) 

Supplanting (7) in (3), we get (8) 

2 2
1 1 1

2 2

1 1

cos( 30) 2 2

2( )

LL p p TCL

c
TCL c

m

di d i d i
wV wt R L L

dt dt dt
Rdi di d

R R
dt dt L dt



    

 

 (8) 

Comparing (2) with (8) can be revised in the accompanying 
structure  

EwtDCi
dt

di
B

dt

id
A  )sin(1

1

2

1
2

   (9) 

where 

C

TCLp
m

R

LL
LA




2

 

mTCLp
c

TCLp
m LLL

R

RR
LB 22)

2
( 




 
2 p TCLC R R   

2 2 2

2( )
c m

LL
c

R L w
D V

R


  



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2

30

cos

TF

LL

E V

V

D

 



 
 



 

Using Laplace transform, (9) can be rewritten, as follows 

2 '

2 2

( ( ) (0) (0)) ( ( ) (0)) ( )

sin( ) cos( )

A s I s sI I B sI s I CI s

s w E
D

Ss w

 
     





  (10) 

Consequently 

 
 

  
 

  

 

2 2 2 2 2 2

2

sin coss
I s D D

s As Bs C s As Bs C

E

s As Bs C

  
 

  
     

 

 (11) 

Utilizing the inverse Laplace transform, the transient 
current somewhere around 0 and T/4 can be dictated by the 
accompanying equation. 

1 2 3 4( ) sin( )
Ft Gt

m m m mi t i e i e i wt i       (12) 

where 

1 2 2 2 2

( ) c o s ( )

( ) ( ) ( ) ( ) (
m

E D F S i n D w
i

F F G F G F w F G F w

  
   

     

 
2 2 2 2 2

sin( ) cos( )

( ) ( )( ) ( )( )
m

E DG Dw
i

G G F G F G w G F G w

  
   

       


















23243 )22()(4

2

wwFGGFw

wD
im

 

4m

E
i

GF


 

2 4

2

B B A C
F

A

  


 
2 4

2

B B A C
G

A

  


3 2

4 2 3 2

(2 2 ) cos( ) (2 ( )) sin( )
cos( )

4 ( ) (2 2 )

w FG w w F G

w F G wFG w

 


  


    
As given in (12), the charging mode somewhere around 0 

and T/4 comprises of two exponential and one sinusoidal 
segment. Since F and G are negative, these two exponential 
parts will tend to decay. 

V. STABILITY ANALYSIS 
The performance and stability analysis of the process under 

investigation are carried out using the simulated model that is 
formulated based on the physical properties of the real process. 
Figures 4 to 8, illustrate the impact of TCL on voltage stability 
of grid-connected photovoltaic system by conventional linear 
stability analysis tools like Bode, Nyquist and Nichols Chart.  

A. Bode Plot Analysis  
This method is very helpful for determining the stability of 

a system. It is a logarithmic plot, so they collapse a wide range 
of frequencies on the horizontal axis and a wide range of gains 
on the vertical axis into a completely viewable plot. From (11) 

Bode analysis is done to check the stability of the system 
shown in Figures 1-2. Result shows that the preceding system 
is unstable but the modified system shown in the Figure 2 is 
stable considering the same gain margin and other parameters 
are also constant. 

 

 
Fig. 4.  Bode diagram for line current stability of Figure 1 

 

 
Fig. 5.  Bode diagram for line current stability of Figure 2 

B. Nyquist Plot Analysis 
This is a parametric plot of a frequency response obtained 

from (11), used for assessing the stability of the system shown 
in Figures 1-2. In, Nyquist plot, if TGH contour does not 
encircle the critical point and the open loop system doesn’t 
possess any open loop pole at the right half of s-plane then the 
system is stable. Figures 6-7 illustrate the stability of the model 
presented in Figures 1-2. 

C. Nichols Plot Analysis 
In this method, derived from (11), considering constant-

magnitude loci and constant phase-angle loci in the log-
magnitude versus phase diagram. The magnitude in dB 
monotonically decreases with increase in frequency. A 



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comparative stability analysis of Figure 1–2 is shown, which 
implicates the results shown in figure 8 is unstable and figure 9 
is stable considering the same value of gain margin. 

 

 

Fig. 6.  Nyquist diagram for line current stability of Figure 1 

 

 

Fig. 7.  Nyquist diagram for line current stability of Figure 2 

VI. TOTAL HARMONIC DISTORTION ANALYSIS 
In this paper, fast Fourier transform (FFT) method has been 

applied for harmonic assessment in single-phase signals of 
Figure 1 and Figure 2. By this fundamental technique, the 
amplitude and phase angle of harmonic components can be 
individually determined. The results show that the proposed 
TCL circuit shown in Figure 2 is more efficient than the system 
shown in Figure 1. Figures 10-11 show the FFT output and 
THD analysis for 50 and 60Hz for TCL systems in Figures 1 
and 2 respectively. 

 

 

Fig. 8.  Nichols diagram for line current stability of Figure 1 

 

 

Fig. 9.  Nichols diagram for line current stability of Figure 2 

VII. RESULTS AND DISCUSSION 
The simulations are carried out in Matlab. The comparative 

analysis and simulation parameters are given in Tables II-III. 
Figures 4–5, Figures 6–7 and Figures 8-9 show the close loop 
stability of the system shown in Figure 1 and Figure 2 using 
conventional methods such as Bode, Nyquist and Nichols. As 
shown in Figures 4, 6 and 8, the close loop system becomes 
unstable without using modified TCL or it can be stable using 
the conventional TCL as shown in Figures 5, 7 and 9. Figure 
10 (a)-(c) shows the harmonic distortion of Figure 1 at different 
frequency. Figure 11 (a)-(c) illustrates the harmonic analysis 
for the transformer current using conventional TCL shown in 
Figure 2. A comparison of these figures shows that using the 
proposed TCL results in the reduction of the THD amplitude. 
The system harmonic parameters up to sixteenth order with and 
without using the proposed TCL are listed in Table I. This test 
verifies the effectiveness of the proposed TCL for limiting the 
unwanted harmonics. The results show that the transient 
current has been limited significantly, which will downsize the 
nominal values of all circuit elements owing to the new current 
scale. Evidently, this is gained in the cost of adding the TCL. 

 



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(a) 

 
(b) 

 
(c) 

Fig. 10.  (a) FFT output, (b) THD analysis at 50Hz, (c) THD analysis at 
60Hz for TCL system shown in Figure 1 

TABLE I.  COMPARATIVE PARAMETER ANALYSIS 

Parameters Figure2 Figure3 
Sampling time 5.49369e-007 s 6.56117e-007 s 

Samples per cycle 30337.8 25402 
Total Harmonic 

Distortion (THD) 
28.65% 0.19% 

Maxm frequency used 
for THD calculation 

910020.00 Hz 761940.00 Hz 

 

TABLE II.  SIMULATION PARAMETERS 

Parameters Value Parameter Value 

Rp 0.65Ω LTCL 0.8H 

R1 0.05Ω RTCL 0.03Ω 

Lp 0.0025H VTF 10V 

L1 0.001H ω 314.15 

Lm 0.9H S 20 MVA 

Rc 2000Ω VLL 2000(Vrms) 

 

 
(a) 

 
(b) 

 
(c) 

Fig. 11.  (a) FFT output, (b) THD analysis at 50Hz, (c) THD analysis at 
60Hz for TCL system shown in Figure 2 

 

TABLE III.  COMPARISON OF SYSTEM STABILITY AND HARMONIC 
ANALYSIS WITH AVAILABLE TECHNIQUES 

System Analysis Stability Analysis THD Analysis 

Proposed Method System Stable 0.19% 
 [4] N.A 4.05% 
 [5] N.A 4.3% 
 [2] N.A 16.5% 
 [3] N.A 22.3% 
 [6] N.A 30.8% 

VIII. CONCLUSIONS 
In this paper, a comparative study between two efficient 

TCLs, based on a three-phase thyristor bridge system for the 
mitigation of transient occurs during the closing of circuit 
breaker and charging of transformer has been proposed. The 
main advantage of the proposed limiter is that it can 
automatically provide high impedance to restrain the transient 
current phenomenon and it will not cause distortion in the 
steady-state load voltage or current waveforms. The proposed 
TCL has a simple topology, does not need any controlling 



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circuit and uses fewer thyristors than other TCLs. In addition, it 
gives a stable output, lower voltage drop, ripple, and lower 
harmonic distortion for transformers. The simulation results 
show the effectiveness of the proposed TCL. Moreover, this 
technique is shown to be effective in stability analysis of power 
systems in distribution area.  

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