*4.2.1. The single phase-to-ground fault*

Using the numerical simulator a multitude of situation could be analyzed.

One of those situations is the one when the MVN has the null grounded trough compensation inductor and the MVN functions under resonance conditions, respectively overcompensated 10%.

Numerical Methods for Analyzing the Transients in Medium Voltage Networks 455

**Figure 9.** Time variation of the currents when MVN is 10% overcompensated and Rt = 1Ω, α = 0°

**Figure 10.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 1Ω, α = 0°

In these circumstances the evolution of voltages and currents during the transient is analyzed according to:


The first oscillogram, left side, is corresponding to the currents and the second corresponding to the voltages.

In these oscillograms I(S) represents the time variation of the current at the fault place, the zero sequence current of the faulty line is denoted as (I(R1a)+I(R2a)+I(R3a))/3, the zero sequence current is (I(R1b)+I(R2b)+I(R3b))/3 on the healty line, and the current trough the element for grounding the neutral point is I(L7).

In the oscillograms of the voltages , V(7), V(8) and V(9) represent, respectively, the voltages of the three phases and the zero sequence voltage of the MVN bars is represented by (V(7) + V(8) + V(9))/3.

In figures 9….20 the results correspond to the 10% overcompensated MVN with the neutral point grounded with compensation inductor. Only two values, 0 and 90°, of the initial phase of the voltage of the faulty line are taken into account. An intermediate value of 45° for this angle does not modify significantly the transient of the simple grounding fault.

From the oscillograms it can be observed that the initial phase of the faulty phase has great importance in the evolution of voltages and currents during the transient regime caused by the simple gounding fault.

Knowing, as accurate as possible, the evolution in time of the voltages gives the possibility of a good design for the MVN, strong enough to resist to the maximal applied voltage.

The maximal values of the currents are important for the correct evaluation of the mechanical forces acting on lines conductors, on the insulators and on the bars of MVN from the transformer station 110kV/MV.

The way that the electric contact is established, Rt , at the fault place, is very important in the transient evolution of the voltages and currents. If the resistance is over 100Ω the transient vanishes rapidly, in less than 5ms, and the maximal values of voltages and currents are not significant. This conclusion results by comparing oscillograms from Fig. 9 to Fig. 19, and, respectively, from Fig. 10 to Fig. 20.

overcompensated 10%.

analyzed according to:


corresponding to the voltages.

V(8) + V(9))/3.

the simple gounding fault.

the transformer station 110kV/MV.

respectively, from Fig. 10 to Fig. 20.

*4.2.1. The single phase-to-ground fault* 


element for grounding the neutral point is I(L7).

Using the numerical simulator a multitude of situation could be analyzed.


One of those situations is the one when the MVN has the null grounded trough compensation inductor and the MVN functions under resonance conditions, respectively

In these circumstances the evolution of voltages and currents during the transient is


The first oscillogram, left side, is corresponding to the currents and the second

In these oscillograms I(S) represents the time variation of the current at the fault place, the zero sequence current of the faulty line is denoted as (I(R1a)+I(R2a)+I(R3a))/3, the zero sequence current is (I(R1b)+I(R2b)+I(R3b))/3 on the healty line, and the current trough the

In the oscillograms of the voltages , V(7), V(8) and V(9) represent, respectively, the voltages of the three phases and the zero sequence voltage of the MVN bars is represented by (V(7) +

In figures 9….20 the results correspond to the 10% overcompensated MVN with the neutral point grounded with compensation inductor. Only two values, 0 and 90°, of the initial phase of the voltage of the faulty line are taken into account. An intermediate value of 45° for this

From the oscillograms it can be observed that the initial phase of the faulty phase has great importance in the evolution of voltages and currents during the transient regime caused by

Knowing, as accurate as possible, the evolution in time of the voltages gives the possibility of a good design for the MVN, strong enough to resist to the maximal applied voltage.

The maximal values of the currents are important for the correct evaluation of the mechanical forces acting on lines conductors, on the insulators and on the bars of MVN from

The way that the electric contact is established, Rt , at the fault place, is very important in the transient evolution of the voltages and currents. If the resistance is over 100Ω the transient vanishes rapidly, in less than 5ms, and the maximal values of voltages and currents are not significant. This conclusion results by comparing oscillograms from Fig. 9 to Fig. 19, and,

angle does not modify significantly the transient of the simple grounding fault.

**Figure 9.** Time variation of the currents when MVN is 10% overcompensated and Rt = 1Ω, α = 0°

**Figure 10.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 1Ω, α = 0°

**Figure 13.** Time variation of the currents when MVN is 10% overcompensated Rt = 10Ω, α = 0°

**Figure 14.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 10Ω, α = 0°

**Figure 11.** Time variation of the currents when MVN is 10% overcompensated and Rt = 1Ω, α = 90°

**Figure 12.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 1Ω, α = 90°

**Figure 11.** Time variation of the currents when MVN is 10% overcompensated and Rt = 1Ω, α = 90°

**Figure 12.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 1Ω, α = 90°

**Figure 13.** Time variation of the currents when MVN is 10% overcompensated Rt = 10Ω, α = 0°

**Figure 14.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 10Ω, α = 0°

**Figure 17.** Time variation of the currents when MVN is 10% overcompensated Rt = 100Ω, α = 0°

**Figure 18.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 100Ω, α = 0°

**Figure 15.** Time variation of the currents when MVN is 10% overcompensated Rt = 10Ω, α = 90°

**Figure 16.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 10Ω, α = 90°

458 Numerical Simulation – From Theory to Industry

**Figure 15.** Time variation of the currents when MVN is 10% overcompensated Rt = 10Ω, α = 90°

**Figure 16.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 10Ω, α = 90°

**Figure 17.** Time variation of the currents when MVN is 10% overcompensated Rt = 100Ω, α = 0°

**Figure 18.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 100Ω, α = 0°

If the MVN is functioning at resonance, the same simulation results are presented and, in addition, also the 45° value for the initial phase of the faulty phase voltage is presented.

The oscillograms show that the differences between the 10% overcompensated regime and

If the functioning regime is far from being at resonance the transient regim produced by simple grounding fault is very short and the variation of voltages and currents is less

The maximal value of the current at fault place is obtained for 90° (comparing α values 0°,

For Rt = 1Ω at α = 45° the current is twice its value at 0° and at 90° the current at the fault

If Rt becomes 10Ω the conclusions regarding the dependence of the current at the fault place on the phase α remain the same (higher α, higher value of the current) but with a decrease of about 25% of the maximal value of the current for a 10 times increase of the resistance at

**Figure 21.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 0°

the resonant regime are not significant.

place is four times greater than the same current if α = 0° .

important.

45°, respectively 90°).

the fault place.

**Figure 19.** Time variation of the currents when MVN is 10% overcompensated Rt = 100Ω, α = 90°

**Figure 20.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 100Ω, α = 90°

If the MVN is functioning at resonance, the same simulation results are presented and, in addition, also the 45° value for the initial phase of the faulty phase voltage is presented.

460 Numerical Simulation – From Theory to Industry

**Figure 19.** Time variation of the currents when MVN is 10% overcompensated Rt = 100Ω, α = 90°

**Figure 20.** Time variation of the voltages when MVN is 10% overcompensated and Rt = 100Ω, α = 90°

The oscillograms show that the differences between the 10% overcompensated regime and the resonant regime are not significant.

If the functioning regime is far from being at resonance the transient regim produced by simple grounding fault is very short and the variation of voltages and currents is less important.

The maximal value of the current at fault place is obtained for 90° (comparing α values 0°, 45°, respectively 90°).

For Rt = 1Ω at α = 45° the current is twice its value at 0° and at 90° the current at the fault place is four times greater than the same current if α = 0° .

If Rt becomes 10Ω the conclusions regarding the dependence of the current at the fault place on the phase α remain the same (higher α, higher value of the current) but with a decrease of about 25% of the maximal value of the current for a 10 times increase of the resistance at the fault place.

**Figure 21.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 0°

**Figure 24.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 45°

**Figure 25.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 90°

**Figure 22.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 0°

**Figure 23.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 45°

**Figure 24.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 45°

**Figure 22.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 0°

**Figure 23.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 45°

**Figure 25.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 90°

**Figure 28.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 0°

**Figure 29.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 45°

**Figure 26.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 90°

**Figure 27.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 0°

**Figure 28.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 0°

**Figure 26.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 90°

**Figure 27.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 0°

**Figure 29.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 45°

**Figure 32.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 90°

**Figure 33.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 0°

**Figure 30.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 45°

**Figure 31.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 90°

**Figure 32.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 90°

**Figure 30.** Time variation of the voltages when MVN is at resonance, Rt = 10Ω, α = 45°

**Figure 31.** Time variation of the currents when MVN is at resonance , Rt = 10Ω, α = 90°

**Figure 33.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 0°

**Figure 36.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 45°

**Figure 37.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 90°

**Figure 34.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 0°

**Figure 35.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 45°

**Figure 36.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 45°

**Figure 34.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 0°

**Figure 35.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 45°

**Figure 37.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 90°

**Figure 39.** Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 0°

**Figure 40.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 0°

**Figure 38.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 90°
