Electrical Engineering

, Volume 100, Issue 3, pp 2117–2127 | Cite as

Analysis of faults in active distribution network with and without synchronous generator using instantaneous symmetrical components in time domain

  • Vladica Mijailović
  • Dragan Ćetenović
  • Aleksandar Ranković
  • Predrag Petrović
  • Dimitrije Rozgić
Original Paper


The paper demonstrates the application of instantaneous symmetrical components method for the analytical calculation of all types of short-circuit currents in faulted distribution feeder with and without three-phase synchronous distributed generation (DG) connected. In active distribution systems, time-domain short-circuit current analysis is required in the processes of protective devices coordination and fault localization. In terms of the impact on the fault current, synchronous generator is the most critical DG type. The method enables encompassing initial conditions (load currents and voltages) before the fault occurs, critical conditions at the moment of fault occurrence, shunt parameters of network elements and the degree of voltage unbalance present in the feeder. Also, the procedure that we propose enables calculation of short-circuit current when the fault arc resistance cannot be neglected. Comparison with results of the fault current calculations based on the IEC methodology was performed through simulation tests and results.


Short-circuit current Active distribution network Symmetrical components Time domain Synchronous distributed generator 

List of symbols



\(U_i ({i=a,b,c})\)

The root-mean-square (rms) value of phase i voltage waveform

\(\alpha _0\)

Initial pre-fault voltage angle (the phase angle determining the magnitude of the three-phase voltages at \(t=0)\); \(\omega =2\cdot \pi \cdot f_n \), \(T=1/{f_n },\;f_n =50\,\hbox {Hz};\)

\(U_{ns} ,\;S_s^{''} ,\;T_{as}\)

Supplying network parameters (nominal voltage, sub-transient short-circuit power, short-circuit time constant, respectively)

\(U_{nG} ,\;S_{nG} ,\;x_{nG}^{''} ,\;T_{aG}\)

Distributed generator parameters

\(S_{nT} ,\;m_T ,\;x_T ,\;r_T\)

Distribution transformer parameters








Distribution feeder length


Laplace transformation of a function f(t)

\(u_{f,x} (t)\)

Instantaneous voltage of x-sequence at the point of failure, \(x=\{{p,\;n,\;0}\}\)

pn and 0

Subscripts (denoting positive, negative and zero sequences, respectively)

\(u_a (t)\), \(u_b (t)\), \(u_c (t)\)

Instantaneous voltage of phase a, b and c, respectively

\(e_{q,x} (t)\)

Instantaneous voltage of x-sequence, \(q=\{ {s,\;\mathrm{DG}}\}\), \(x=\{ {p,\;n,\;0} \}\)

Subscript s

Supplying network

Subscript \(\mathrm{DG}\)

Serial connection of distributed generator and distribution transformer

\(i_{v,x} (t)\)

x-sequence of the current flowing through the point of fault

\(i_{\mathrm{DG},x} (t)\)

x-sequence of the current flowing from DG

\(i_{k,x} (t)\)

x-sequence of the current flowing from the supplying network

\(I_{k,p} (0), I_{\mathrm{DG},p} (0)\)

Initial values of the currents \(i_{k,p} (t)\), \(i_{\mathrm{DG},p} (t)\), respectively

\(u_{C1,x} (t), u_{C2,x} (t)\)

Instantaneous voltage of x-sequence across shunt capacitance \(C_1 \) and \(C_2 \), respectively

\(U_{c1,p} (0), U_{c2,p} (0)\)

Initial values of the voltages \(u_{c1,p} (t)\), \(u_{c2,p} (t)\), respectively

\(i_{C1,x} (t), i_{C2,x} (t)x\)

x-sequence of the current flowing through shunt capacitance \(C_1 \) and \(C_2 \), respectively

\(K_{i,x} (s)\)

Functional coefficient of x-sequence in Laplace domain, \(i=\{ 1,2,3,4,5,6 \}\)


Complex value of grounding impedance


Serial resistance of x-sequence per feeder unit length


Serial inductance of x-sequence per feeder unit length


Shunt capacitance of x-sequence per feeder unit length



This study is the part of the Project No. III-42009 financed by Ministry of Education and Science of the Republic of Serbia. The authors hereby express their sincere gratitude for the support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Vladica Mijailović
    • 1
  • Dragan Ćetenović
    • 1
  • Aleksandar Ranković
    • 1
  • Predrag Petrović
    • 1
  • Dimitrije Rozgić
    • 1
  1. 1.Faculty of Technical SciencesUniversity of KragujevacČačakSerbia

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