*4.2.2. The double phase-to-ground fault*

The same simulation model from Fig. 8 is used with the switch VSa closed, and after 20ms the switch VSb is connected also. VSGOL remains in "closed" position.

The double phase to ground fault was simulated for neutral point grounded by compensation inductor and, respectively, by resistor.

In both cases Rt was considered consecutively with 1Ω, 100Ω, 1000Ω trough VSa switch and with 1Ω trough VSb .

In both cases α = 90° was considered, but also α = 0° was imposed for the situation with compensation inductor.

Also the situation with isolated neutral point was simulated, with same Rt values , but only with α = 90°. (Curcanu et al., 2006).

The same symbols are used in oscillograms for the currents, just in addition the index "a" is used for the first faulty line (simulated by switch VSa) and the index "b" for the second faulty line (VSb). For the voltages the symbols are quite the same as those used previously.

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

*4.2.2. The double phase-to-ground fault* 

with 1Ω trough VSb .

compensation inductor.

previously.

with α = 90°. (Curcanu et al., 2006).

compensation inductor and, respectively, by resistor.

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

the switch VSb is connected also. VSGOL remains in "closed" position.

The same simulation model from Fig. 8 is used with the switch VSa closed, and after 20ms

The double phase to ground fault was simulated for neutral point grounded by

In both cases Rt was considered consecutively with 1Ω, 100Ω, 1000Ω trough VSa switch and

In both cases α = 90° was considered, but also α = 0° was imposed for the situation with

Also the situation with isolated neutral point was simulated, with same Rt values , but only

The same symbols are used in oscillograms for the currents, just in addition the index "a" is used for the first faulty line (simulated by switch VSa) and the index "b" for the second faulty line (VSb). For the voltages the symbols are quite the same as those used

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

**Figure 43.** Time variation of the currents when MVN is at resonance , Rt = 1000Ω, α = 0°

**Figure 44.** Time variation of the voltages when MVN is at resonance, Rt = 1000Ω, α = 0°

**Figure 41.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 0°

**Figure 42.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 0°

**Figure 43.** Time variation of the currents when MVN is at resonance , Rt = 1000Ω, α = 0°

**Figure 41.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 0°

**Figure 42.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 0°

**Figure 44.** Time variation of the voltages when MVN is at resonance, Rt = 1000Ω, α = 0°

**Figure 47.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 90°

**Figure 48.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 90°

**Figure 45.** . Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 90°

**Figure 46.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 90°

**Figure 47.** Time variation of the currents when MVN is at resonance , Rt = 100Ω, α = 90°

**Figure 45.** . Time variation of the currents when MVN is at resonance , Rt = 1Ω, α = 90°

**Figure 46.** Time variation of the voltages when MVN is at resonance, Rt = 1Ω, α = 90°

**Figure 48.** Time variation of the voltages when MVN is at resonance, Rt = 100Ω, α = 90°

The double phase to ground fault has less important transient effects than the single phase

When the simple phase to ground fault occurs than the value of initial phase α is importans, but its variation is totaly insignifiant in the double phase to ground fault. The value of the resistance at the fault place is important in both fault types, the maximal value of the fault currents and the zero sequence currents depending strongly on the electric resistance at the

The oscillograms for the MVN grounded trough resistor are presented in Fig. 51 ... Fig. 54. The fault is simulated with the switch VSa and for α = 90° the transient is most important.

The current flowing trough the grounding resistor is calculated also and this is important

**Figure 51.** Time variation of the currents when MVN is grounded trough resistor, Rt = 1Ω, α = 90°

double phase to ground fault gives a heavier transient for voltages than for currents.

is strongly decreasing from 1.8kA to 500A.

If the resistance at the fault place is increasing from 1Ω to 100Ω the current at the fault place

Oscillograms from Fig. 55 …Fig. 60 , for isolated neutral point of the MVN, show that the

There is not an important difference between the transient produced by the double phase to ground fault in MVN with isolated neutral point compared with the MVN grounded trough

because the value of this current is taken into account for the protection.

The resistance at the fault place is simulated with the switch VSa.

to ground fault.

fault place.

**Figure 49.** Time variation of the currents when MVN is at resonance , Rt = 1000Ω, α = 90°

**Figure 50.** Time variation of the voltages when MVN is at resonance, Rt = 1000Ω, α = 90°

The double phase to ground fault has less important transient effects than the single phase to ground fault.

When the simple phase to ground fault occurs than the value of initial phase α is importans, but its variation is totaly insignifiant in the double phase to ground fault. The value of the resistance at the fault place is important in both fault types, the maximal value of the fault currents and the zero sequence currents depending strongly on the electric resistance at the fault place.

The oscillograms for the MVN grounded trough resistor are presented in Fig. 51 ... Fig. 54. The fault is simulated with the switch VSa and for α = 90° the transient is most important.

The current flowing trough the grounding resistor is calculated also and this is important because the value of this current is taken into account for the protection.

The resistance at the fault place is simulated with the switch VSa.

476 Numerical Simulation – From Theory to Industry

**Figure 49.** Time variation of the currents when MVN is at resonance , Rt = 1000Ω, α = 90°

**Figure 50.** Time variation of the voltages when MVN is at resonance, Rt = 1000Ω, α = 90°

**Figure 51.** Time variation of the currents when MVN is grounded trough resistor, Rt = 1Ω, α = 90°

If the resistance at the fault place is increasing from 1Ω to 100Ω the current at the fault place is strongly decreasing from 1.8kA to 500A.

Oscillograms from Fig. 55 …Fig. 60 , for isolated neutral point of the MVN, show that the double phase to ground fault gives a heavier transient for voltages than for currents.

There is not an important difference between the transient produced by the double phase to ground fault in MVN with isolated neutral point compared with the MVN grounded trough

compensation inductor, but both cases are much heavier than the transient for MVN grounded trough resistor.

Numerical Methods for Analyzing the Transients in Medium Voltage Networks 479

**Figure 54.** Time variation of the voltages when MVN is grounded trough resistor Rt = 100Ω, α = 90°

**Figure 55.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 1Ω, α = 90°

**Figure 52.** Time variation of the voltages when MVN is grounded trough resistor Rt = 1Ω, α = 90°

**Figure 53.** Time variation of the currents when MVN is grounded trough resistor, Rt = 100Ω, α = 90°

grounded trough resistor.

compensation inductor, but both cases are much heavier than the transient for MVN

**Figure 52.** Time variation of the voltages when MVN is grounded trough resistor Rt = 1Ω, α = 90°

**Figure 53.** Time variation of the currents when MVN is grounded trough resistor, Rt = 100Ω, α = 90°

**Figure 54.** Time variation of the voltages when MVN is grounded trough resistor Rt = 100Ω, α = 90°

**Figure 55.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 1Ω, α = 90°

**Figure 58.** Time variation of the voltages when the neutral point of MVN is isolated, Rt = 100Ω, α = 90°

**Figure 59.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 1000Ω, α = 90°

**Figure 56.** Time variation of the voltages when the neutral point of MVN is isolated, Rt = 1Ω, α = 90°

**Figure 57.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 100Ω, α = 90°

**Figure 56.** Time variation of the voltages when the neutral point of MVN is isolated, Rt = 1Ω, α = 90°

**Figure 57.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 100Ω, α = 90°

**Figure 58.** Time variation of the voltages when the neutral point of MVN is isolated, Rt = 100Ω, α = 90°

**Figure 59.** Time variation of the currents when the neutral point of MVN is isolated, Rt = 1000Ω, α = 90°

Two possible situations are considered: C101a = C102a, and C102a = 0,1C101a.

**Figure 61.** Time variation of the currents, neutral point of MVN is grounded by resistor and Rt = 1Ω, α = 90°,

**Figure 62.** Time variation of the voltages, neutral point of MVN is grounded by resistor and Rt = 1Ω, α = 90°,

C101a = 9C102a

C101a = 9C102a

**Figure 60.** Time variation of the voltages when the neutral point of MVN is isolated, Rt = 1000Ω, α = 90°

The greater values of the currents at the two fault places, when the double phase to ground fault is produced, give high thermic solicitation to the instalation, as well as, higher values of the step voltages. This situatiom is dangerous for human being and animals, especially if this events are situated near the earth plate.

The time variation at the two fault places is far from being the same, no matter what grounding methos is used for the neutral point of the MVN.
