Line To Line To Line Fault MCQ Quiz - Objective Question with Answer for Line To Line To Line Fault - Download Free PDF

Explanation:

Fault Current in Synchronous Generators:

Definition: When a fault occurs at the terminals of a synchronous generator, the generator's response to the fault depends on the type of fault. Fault current is the current that flows during a fault condition, which is significantly higher than the normal operating current. The magnitude of the fault current depends on the type of fault and the impedance of the system.

Correct Option Analysis:

The correct option is:

Option 1: Three-phase fault.

Among all types of faults that can occur in a power system, a three-phase fault generates the highest fault current. This is because a three-phase fault involves all three phases of the system, creating a condition where the impedance of the fault path is minimum. As a result, the current during a three-phase fault is maximum compared to other types of faults.

Why Three-Phase Fault Produces Maximum Fault Current:

• Symmetrical Nature: A three-phase fault is a balanced fault, meaning all three phases are equally affected. This symmetry ensures that the fault current magnitude is uniform across all three phases, leading to the highest possible current flow.
• Minimum Fault Impedance: During a three-phase fault, the impedance of the fault path is at its lowest, as all three phases are directly short-circuited. Lower impedance results in higher current flow as per Ohm's Law (I = V/Z, where I is current, V is voltage, and Z is impedance).
• Generator's Response: Synchronous generators are designed to supply balanced three-phase power. When a three-phase fault occurs, the generator supplies maximum current to the fault because the fault aligns with the generator's natural three-phase configuration.

Implications of Three-Phase Fault:

• It is the most severe type of fault in terms of current magnitude and system impact.
• Protection systems, such as circuit breakers and relays, are designed to detect and isolate three-phase faults quickly to prevent damage to equipment and ensure safety.
• System studies and fault analysis prioritize three-phase fault scenarios to design robust protection schemes and ensure system stability.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Double line to ground fault.

A double line to ground fault involves two phases and the ground. While this type of fault results in a higher fault current than single line to ground or line-to-line faults, it does not exceed the fault current produced by a three-phase fault. The presence of ground in the fault path increases impedance compared to a three-phase fault, reducing the current magnitude.

Option 3: Line to line fault.

A line-to-line fault involves a short circuit between two phases. The fault current in this scenario is lower than that of a three-phase fault because only two phases are involved, and the impedance in the fault path is higher. Line-to-line faults are less severe than three-phase faults in terms of current magnitude and system impact.

Option 4: Line to ground fault.

A line-to-ground fault occurs when one phase is short-circuited to the ground. This type of fault has the highest impedance among all fault types, resulting in the lowest fault current. While line-to-ground faults are common in power systems, their impact is less severe compared to other faults.

Conclusion:

Among all types of faults, a three-phase fault produces the maximum fault current due to its symmetrical nature and minimum fault impedance. This makes it the most severe fault type in terms of system impact, requiring robust protection systems to mitigate its effects. Understanding the characteristics of different fault types is essential for designing effective power system protection schemes and ensuring system stability.

Among the given faults, LLLG or 3 phase fault is the most severe and least likely to occur in the power system. LG or line to ground fault is most common and occurs frequently.

Symmetrical Fault:

The faults which involve all three phases are known as the symmetrical fault. Such types of faults remain balanced even after the fault. The symmetrical faults mainly occur at the terminal of the generators.

• The three-phase line to the ground fault (LLLG): The three-phase line to ground fault includes all the three-phase of the system. The LLLG fault occurs between the three phases and the ground of the system. The probability of occurrence of such type of fault is nearly 2 to 3 percent.

Unsymmetrical Fault:

The fault gives rise to unsymmetrical current, i.e., current differing in magnitude and phases in the three phases of the power system are known as the unsymmetrical fault. It is also defined as the fault which involves one or two phases such as LG, LL, LLG fault. The unsymmetrical makes the system unbalanced. 

• Single Line to Line Ground (SLG): The single line of ground fault occurs when one conductor falls to the ground or contact the neutral conductor. The 70 – 80 percent of the fault in the power system is the single line-to-ground fault.
• Line to Line Fault (LL):  A line-to-line fault occurs when two conductors are short-circuited. The major cause of this type of fault is the heavy wind. The heavy wind swinging the line conductors which may touch together and hence cause short-circuit. The percentage of such types of faults is approximately 15 – 20%.
• Double Line to line Ground Fault (LLG): In double line-to-ground fault, the two lines come in contact with each other along with the ground. The probability of such types of faults is nearly 10 %.

Frequency of occurrence:

• Among the given faults, LG or line to ground fault is most common and occurs frequently.
• The order of frequency of occurrence is given below.

LG > LL > LLG > LLLG

Severity of faults:

• Among the given faults, LLLG or 3 phase faults are most severe. LG or line to ground fault is least severe.
• Line to line fault is more severe than line to ground fault while double line to ground fault is one level severe than LL.
• The order of frequency of occurrence is given below.

LLLG > LLG > LL > LG

Conclusion: Among the given faults, LLLG or 3 phase fault is the most severe and least likely to occur in the power system. LG or line to ground fault is most common one and least severe. The line to line fault is more severe than the line to ground fault while the double line to ground fault is one level severe than LL.

The terminal voltage of the generator = 0.9 pu

I = 1.0 pu, p.f = 0.8 lag

Equivalent diagram can be drawn as

I = 1.0∠-cos^-1 (0.8) = 1.0∠-36.86° = 0.8 - j0.6

Apply KVL,

\( {E_g^{"}} =V_t+ jI_LX_d^{''}\)

E^II_g = 0.9 + 0.15 ∠90 × 1.0 ∠-36.86°

= 0.9 + (0.8 + j0.6) × ( j0.15 )

= 0.99 + j0.12

E^II_g = (0.99 + j0.12) pu

\({I_g^{"}} = \frac{{{E_g}}}{{j0.15 + j0.1}}\)

\( = \frac{{0.99 + j0.12}}{{j0.25}}\)

= (0.48 - j3.96) pu

Sub-transient current in the generator due to fault is: I^II_g = 3.9889 pu

When a 3-phase short circuit fault occurs on bus-2, its voltage directly falls to zero i.e., ΔV₂ is largest.

Whereas for bus-1 and bus-2, their respective voltages sag due to fault on bus-2.

The more is the short circuit capability of a bus, the less would be the per unit equivalent impedance between the bus and the ground.

Therefore, more will be the strength of the bus i.e., due to fault on other bus, the sag in voltage of a bus would be less, if it has larger/greater short circuit capability.

Voltage at bus B after 3 – phase fault at A  \(= 0.8\;p.u.\)

\(\begin{array}{l} {V_B}\; = \;V\left( {prefault} \right)\;-\;{Z_{12}}\; \times \;{I_{f\left( B \right)}}\\ 0.8\; = \;1.0\;-\;{Z_{12}}\; \times \;10\\ {Z_{12}}\; = \;0.02\;p.u.\\ {V_A}\; = \;1.0\;-\;\left( {0.02\; \times \;8} \right)\\ {V_A}\; = \;0.84\;p.u \end{array}\)

Note:

For the voltage magnitude at bus B during a three-phase fault at bus A. So we use fault current of bus A

For the voltage magnitude at bus A during a three-phase fault at bus B. So we use fault current of bus B

Concept :

As shown in the phasor diagram 

• Current I₂ & I₄ have phase difference of 180°. So that they cancel out each other.
• Magnitude of the current I₁ is more than current I₃. Also I₁ is more lagging than I₃
• So that  fault is located at point Q.

Fault current is inversely proportional to reactance during fault.

\(\Rightarrow I_f\propto\frac{1}{X}\)

Voltage at bus B after 3 – phase fault at A  \(= 0.8\;p.u.\)

\(\begin{array}{l} {V_B}\; = \;V\left( {prefault} \right)\;-\;{Z_{12}}\; \times \;{I_{f\left( B \right)}}\\ 0.8\; = \;1.0\;-\;{Z_{12}}\; \times \;10\\ {Z_{12}}\; = \;0.02\;p.u.\\ {V_A}\; = \;1.0\;-\;\left( {0.02\; \times \;8} \right)\\ {V_A}\; = \;0.84\;p.u \end{array}\)

Note:

For the voltage magnitude at bus B during a three-phase fault at bus A. So we use fault current of bus A

For the voltage magnitude at bus A during a three-phase fault at bus B. So we use fault current of bus B

Among the given faults, LLLG or 3 phase fault is the most severe and least likely to occur in the power system. LG or line to ground fault is most common and occurs frequently.

Symmetrical Fault:

The faults which involve all three phases are known as the symmetrical fault. Such types of faults remain balanced even after the fault. The symmetrical faults mainly occur at the terminal of the generators.

• The three-phase line to the ground fault (LLLG): The three-phase line to ground fault includes all the three-phase of the system. The LLLG fault occurs between the three phases and the ground of the system. The probability of occurrence of such type of fault is nearly 2 to 3 percent.

Unsymmetrical Fault:

The fault gives rise to unsymmetrical current, i.e., current differing in magnitude and phases in the three phases of the power system are known as the unsymmetrical fault. It is also defined as the fault which involves one or two phases such as LG, LL, LLG fault. The unsymmetrical makes the system unbalanced. 

• Single Line to Line Ground (SLG): The single line of ground fault occurs when one conductor falls to the ground or contact the neutral conductor. The 70 – 80 percent of the fault in the power system is the single line-to-ground fault.
• Line to Line Fault (LL):  A line-to-line fault occurs when two conductors are short-circuited. The major cause of this type of fault is the heavy wind. The heavy wind swinging the line conductors which may touch together and hence cause short-circuit. The percentage of such types of faults is approximately 15 – 20%.
• Double Line to line Ground Fault (LLG): In double line-to-ground fault, the two lines come in contact with each other along with the ground. The probability of such types of faults is nearly 10 %.

Frequency of occurrence:

• Among the given faults, LG or line to ground fault is most common and occurs frequently.
• The order of frequency of occurrence is given below.

LG > LL > LLG > LLLG

Severity of faults:

• Among the given faults, LLLG or 3 phase faults are most severe. LG or line to ground fault is least severe.
• Line to line fault is more severe than line to ground fault while double line to ground fault is one level severe than LL.
• The order of frequency of occurrence is given below.

LLLG > LLG > LL > LG

Conclusion: Among the given faults, LLLG or 3 phase fault is the most severe and least likely to occur in the power system. LG or line to ground fault is most common one and least severe. The line to line fault is more severe than the line to ground fault while the double line to ground fault is one level severe than LL.

Concept :

As shown in the phasor diagram 

• Current I₂ & I₄ have phase difference of 180°. So that they cancel out each other.
• Magnitude of the current I₁ is more than current I₃. Also I₁ is more lagging than I₃
• So that  fault is located at point Q.

When a 3-phase short circuit fault occurs on bus-2, its voltage directly falls to zero i.e., ΔV₂ is largest.

Whereas for bus-1 and bus-2, their respective voltages sag due to fault on bus-2.

The more is the short circuit capability of a bus, the less would be the per unit equivalent impedance between the bus and the ground.

Therefore, more will be the strength of the bus i.e., due to fault on other bus, the sag in voltage of a bus would be less, if it has larger/greater short circuit capability.

Fault current is inversely proportional to reactance during fault.

\(\Rightarrow I_f\propto\frac{1}{X}\)

Z = 0.2 pu

4 parallel identical generators are connected to a common bus and a symmetrical fault occurred at the end of the line.

E_R1 = 1.0 pu

As E_R1 not given assuming E_R1 = 1 pu

\({Z_{eq}} = \frac{Z}{4}\), as 4 identical generators are connected to a common bus

L-L-L fault is occurring at the line end as the fault is a symmetrical fault.

So, the fault current is

\({I_F} = \frac{{{E_{R1}}}}{{{Z_{eq}}}}\)

\( = \frac{{1.0}}{{\frac{{0.2}}{4}}}\)

= 20 p.u

I_F = 20 pu

The terminal voltage of the generator = 0.9 pu

I = 1.0 pu, p.f = 0.8 lag

Equivalent diagram can be drawn as

I = 1.0∠-cos^-1 (0.8) = 1.0∠-36.86° = 0.8 - j0.6

Apply KVL,

\( {E_g^{"}} =V_t+ jI_LX_d^{''}\)

E^II_g = 0.9 + 0.15 ∠90 × 1.0 ∠-36.86°

= 0.9 + (0.8 + j0.6) × ( j0.15 )

= 0.99 + j0.12

E^II_g = (0.99 + j0.12) pu

\({I_g^{"}} = \frac{{{E_g}}}{{j0.15 + j0.1}}\)

\( = \frac{{0.99 + j0.12}}{{j0.25}}\)

= (0.48 - j3.96) pu

Sub-transient current in the generator due to fault is: I^II_g = 3.9889 pu

Voltage at bus B after 3 – phase fault at A  \(= 0.8\;p.u.\)

\(\begin{array}{l} {V_B}\; = \;V\left( {prefault} \right)\;-\;{Z_{12}}\; \times \;{I_{f\left( B \right)}}\\ 0.8\; = \;1.0\;-\;{Z_{12}}\; \times \;10\\ {Z_{12}}\; = \;0.02\;p.u.\\ {V_A}\; = \;1.0\;-\;\left( {0.02\; \times \;8} \right)\\ {V_A}\; = \;0.84\;p.u \end{array}\)

Note:

For the voltage magnitude at bus B during a three-phase fault at bus A. So we use fault current of bus A

For the voltage magnitude at bus A during a three-phase fault at bus B. So we use fault current of bus B