Principles and Practice ii) PT Connection
There are two most common PT combinations on three-phase, three-wire systems as shown in Figure 1-43. The vector diagrams are identical between PT configurations and the Open Delta is more common because it only requires two PTs, thereby dropping the cost by one-third.
Vca
59ca
Vab
59ab
PTab
59ab
PTbc
59bc
Vbc
59bc
3 WIRE DELTA WITH 3 PTs
PTca
59ca
B
C
A
Vca
59ca
Vab
59ab
PTab
59ab
PTbc
59bc
Vbc
59bc
59ca
3 WIRE DELTA WITH 2 PTs (Open Delta)
B
C
A
Figure 1-43: 3-Wire Delta PT C onfigur ations
The two most common PT configurations for four-wire, Wye systems are shown in Figure 1-44. The line-to-line voltage magnitudes and angles between the two configurations are identical and Open-Delta configurations commonly used if line-toneutral voltages are not required by the relay or application.
B B
C C
Vca
59ca
Vcn
59C
Vbn
59B
Vbc
59bc
A
Vab
59ab
Vca
59ca
Vab
59ab
Van
59A
PTab PTbc PTca PTab
59ab
PTbc
59bc
59an 59bn 59cn
59ca
59ab 59bc
59ca
4 WIRE WYE WITH 3 PTs
Vbc
59bc
4 WIRE WYE WITH 2 PTs (Open Delta)
Figure 1-44: 4-Wire Wye PT C onfigur ations
A
38

Chapter 1: Electrical Fundamentals
3-Wire Delta
2 PTs
4-Wire Wye
3 PTs
4-Wire Wye
2 PTs
Confusing line-to-ground and line-to-line setting values is the most common mistake related to voltages and relays. Review the manufacturer’s specifications to make sure the correct voltage levels are expected and set. Use the chart in Figure 1-45 for the most common PT secondary voltages. Calculate nominal PT secondary voltages by dividing the rated primary voltage by the PT ratio. Never mix Line-to-Line and Line-to-
Ground voltages when performing PT ratio calculations. For example, medium voltage
PT ratios are typically rated using line voltages (eg. 4200V / 120V = PT ratio 35:1) but substation PTs are typically rated using phase-to-neutral voltage ratios and secondary nominal voltages (E.g. 1200:1 PT ratio @ 67V = 80,400V / 67V Line-to-Neutral or
138,000V / 115V Line-to-Line)
Co NNECTIo NS
V
AB
, V
BC
, V
CA
V
AB
, V
CB
V
AB
, V
BC
V
AN
, V
BN
, V
CA
, V
CN
V
AB
, V
BC
, V
CA lINE -GRou ND No MINAl
N/A
69.28V or 66.40V or 67.0V
N/A lINE -lINE No MINAl
120V or 115V
120V or 115V or 116.04V
120V or 115V
Figure 1-45: Nominal PT Voltages
39

Principles and Practice
The electrical system can be affected by many problems, but protective relays are primarily designed to protect the electrical system and/or equipment from fault situations. The threephase electrical system typically has three phases that are connected together by highimpedance loads. A low impedance connection between phases and/or ground can cause extremely high fault currents, arc flashes, heat, and explosive forces, and catastrophic damage to equipment and personnel. A low impedance connection between phases and/or ground could be caused by a tree falling onto a transmission line, foreign material falling across a live bus, very humid conditions with insufficient clearance between phases, or failing insulation.
There are an unlimited number of scenarios that can cause an electrical fault which are typically categorized into four fault types. It is very common for an electrical fault to start in one category and cascade into another if the problem is not cleared in time. The most common fault types are:
Three-phase (3Ø or 3P) Faults occur when all three phases are connected together with low impedance. We typically create balanced 3Ø Faults when creating simulations which are the equivalent of leaving safety grounds on a system and then energizing that system.
Ra Xa Xd Ra Xa Xd B
A
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
B
A A
Ra Xa Xd Ra Xa Xd
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
A
Figure 1-46: Three-Phase Fault 3-Line Drawing
A three-phase fault causes all three currents to increase simultaneously with equal magnitudes. The magnitude of fault current will depend on the impedance and location of the fault, as well as the strength of the electrical system. The safety grounds connected to the grid in our example will cause much higher fault currents than the same safety grounds connected to an isolated generator. Similarly, a fault closer to the source (Figure
1-46 – Left Side) will produce more fault current than a fault at the end of the line (Figure
1-46 – Right Side) because there will be more impedance between the source and the fault in the second situation. The current will lag the voltage by some value usually determined by the voltage class of the system.
All three voltages will decrease simultaneously with equal magnitudes. The magnitude of fault voltage will depend on the impedance and location of the fault, as well as the strength
40

Chapter 1: Electrical Fundamentals of the electrical system. The voltage drop will not be as significant if the safety grounds are connected to the grid compared to the huge voltage drop that will be observed in an isolated system which could cause the voltage to drop to zero. Similarly, a fault closer to the source will create a larger voltage drop than a fault at the end of the line because there will be more impedance between the source and the fault.
The following phasor diagrams demonstrate the difference between a “normal” system and the same system with a three-phase fault. Notice that all phasors are still 120° apart, the voltages stayed at the same at the same phase angles, and the current magnitudes increased with a greater lag from the voltages.
Vcn
Vca
Ib
Ic
180
150
120
90 60
30
0
-120
-90 -60
-30
Ia
Van
Vab
Ib
Ic
Vca
Vcn
180
150
120
90 60
30
0
-120
-90 -60
-30
Vbc
Vbn
Van
Vab
Vbc
Vbn
Ia
Figure 1-47: Three-Phase Fault Phasor Diagram
It is always a good idea to simulate conditions as close to a true fault when performing tests and a 3Ø fault simulation should have the following characteristics:
• Prefault : nominal: 3Ø voltage magnitudes with 120° between phases in the normal phase rotation.
• Fault Voltage : Reduced, but identical, voltage magnitudes on all three phases with no change in phase angles from the prefault condition.
• Fault Current : Larger than nominal current on all three phases with identical magnitudes and 120° between phases with the normal phase rotation. The current should lag the voltage by 60 to 90°.
41

Principles and Practice
Phase-to-phase (P-P or Ø-Ø) faults occur when two phases are connected together with low impedance. A Ø-Ø fault can occur when a bird flies between two transmission conductors and its wing-tips touch both conductors simultaneously. Phase-to-phase faults are described by the phases that are affected by the low-impedance connection. The B-C fault in Figure
1-48 is a Ø-Ø fault that connects B-phase and C-phase.
Ra Xa Xd Ra Xa Xd B
A
C
Ra
Ra
Xa
Xa
Xd
Xd
Ra Xa Xd
Ra Xa Xd
B
C
B
A A
Ra Xa Xd Ra Xa Xd
C
Ra
Ra
Xa
Xa
Xd
Xd
Ra Xa Xd
Ra Xa Xd
B
C
A
Figure 1-48: Phase-Phase Fault 3-Line Drawing
The magnitude of fault current will depend on the impedance and location of the fault, as well as the strength of the electrical system. A fault closer to the source will produce more fault current than a fault at the end of the line because there will be more impedance between the source and the fault in the second situation. The fault current will lag the fault voltage by some value usually determined by the voltage class of the system.
If you follow the flow of current in Figure 1-48, you should notice that the current flows from the B-phase source into the fault, and then returns to the source via C-phase. Basic electrical theory states that the current flowing in a circuit must be equal, so the B-phase and C-phase currents must have the same magnitudes. However, relays monitor current leaving the source so the relay will see this fault as two equal currents with opposite polarity.
Therefore, when we simulate a P-P fault, the currents injected into a relay must have the same magnitudes and be 180° apart from each other. The current flowing through the actual fault will be equal to 2x the injected currents.
= =
Ifault Ib
180
150
120
90 60
30
0
-120
-90 -60
-30
Ic
= +
= − ° + Ic@30 °
Figure 1-49: Fault Current vs. Injected Current
= × − °
42

Chapter 1: Electrical Fundamentals
The effect of a P-P fault on the faulted voltages is even more complex. The faulted voltages will have equal magnitudes because the impedance between the source and the fault on each faulted phase should be equal. A fault closer to the source will create a larger voltage drop than a fault at the end of the line because there will be more impedance between the source and the fault.
The faulted voltage angles are also affected because the ratio of reactance and resistance in the circuit changes when the fault is introduced. There is a lot of information to consider when creating the correct voltage magnitudes and angles and we discuss the calculations in detail in Chapter 15: Line Distance (21) Element Testing . For our purposes in this chapter, it is important that you be able to recognize a Ø-Ø fault as the following phasor diagrams demonstrate. Notice that the faulted voltages have collapsed and come together to change the voltage triangle from an equiangular/equilateral triangle (three equal magnitudes and angles) in prefault to an acute, isosceles triangle (two equal magnitudes, two equal angles, and all angles are less than 90°).
Vcn
Vca
Ib
Ic
-150
150
120
90 60
30
0
-120
-90 -60
-30
Ia
Van
Vab
Ib
Vcn
Vca
-150
150
120
90
Vbc
-120
Vbn
-90
60
-60
30
0
-30
Ia
Van
Ic
Vab
Vbc
Vbn
Prefault or Normal Phase-Phase Fault
Figure 1-50: Phase-Phase Fault
It is always a good idea to simulate conditions as close to a true fault when performing tests and a Ø-Ø fault simulation should have the following characteristics:
1.
Prefault: nominal, 3Ø voltage magnitudes with 120° between phases in the normal phase rotation.
2.
Fault Voltage: Reduced, but identical, voltage magnitudes on both phases affected by the fault. The phase angle between the faulted phases should be less than 120°.
3.
The unaffected phase voltage should be identical to the prefault condition.
4.
Fault Current: Increased, but identical, current magnitudes on both phases affected by the fault. The phase angle between the faulted phases should be 180°.
5.
The unaffected phase current does not change between prefault and fault.
43

Principles and Practice
Phase-to-ground (P-G, P-N, Ø-G or Ø-N), or single-phase faults occur when any one phase is connected to the ground or neutral conductor with low impedance. A Ø-N fault can occur when a tree falls on a transmission line. Phase-to-ground faults are described by the phase that is affected by the low-impedance connection. The A-N fault in Figure 1-51 is a Ø-N fault that connects A-phase to the neutral.
B
A
Ra Xa Xd Ra Xa Xd
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
B
A A
Ra Xa Xd Ra Xa Xd
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
A
Figure 1-51: Phase-Ground Fault 3-Line Drawing
The magnitude of fault curren t will depend on the impedance and location of the fault, as well as the strength of the electrical system. A fault closer to the source will produce more fault current than a fault at the end of the line because there will be more impedance between the source and the fault in the second situation. The fault current will lag the fault voltage by some value usually determined by the voltage class of the system.
The fault only affects A-phase voltages and currents, so the B-phase and C-phase currents are nearly identical to the prefault values. The A-phase current will increase and lag the voltage at some value between 60 and 90°.
The B-phase and C-phase voltages will also be unaffected by the fault and they will have the same magnitude and phase angle during the fault as existed in prefault. The A-phase voltage magnitude will decrease, but the phase angle will not change between prefault and fault.
A Ø-N fault example is demonstrated in Figure 1-52. Notice that the faulted voltage has collapsed to change the voltage triangle from an equiangular/equilateral triangle (three equal magnitudes and angles) in prefault to an isosceles triangle.
44

Chapter 1: Electrical Fundamentals
Vcn
Vca Vcn Vca
Ib
Ic
180
150
120
90 60
30
0
-120
-90 -60
-30
Ia
Van
Vab
Ib
Ic
180
150
120
90 60
30
0
-120
-90 -60
-30
Van
Vab
Vbc
Vbn
Vbc
Vbn
Ia
Figure 1-52: Phase-Ground Fault
It is always a good idea to simulate conditions as close to a true fault when performing tests and a Ø-N fault simulation should have the following characteristics:
1. Prefault: nominal, 3Ø voltage magnitudes with 120° between phases in the normal phase rotation.
2. Fault Voltage: Reduced voltage the phase affected by the fault. The voltage angle is identical to prefault.
3. The unaffected phase voltages should be identical to the prefault condition.
4. Fault Current: Increased magnitude on the affected phase. The phase angle should lag the phase voltage by a value between 60 and 90°.
5. The unaffected phase currents do not change between prefault and fault.
45

Principles and Practice
Phase-to-phase-to-ground (P-P-G, P-P-N, Ø-Ø-G or Ø-Ø-N), or two-phase-to-ground faults occur when any two phases are connected to the ground or neutral conductor with low impedance. A Ø-N fault can occur when a tree falls on two phases of a transmission line.
Two phase-to-ground faults are described by the phases that are affected by the lowimpedance connection. The C-A-G fault in Figure 1-53 is a Ø-Ø-N fault that connects C and
A-phases to Ground.
Ra Xa Xd Ra Xa Xd B
A
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
B
A A
Ra Xa Xd Ra Xa Xd
C
Ra Xa Xd Ra Xa Xd
Ra Xa Xd Ra Xa Xd
B
C
A
Figure 1-53: Phase-Phase-Ground Fault 3-Line Drawing
P-P-G ground are very complex faults that are very difficult to reproduce without modeling software to calculate all of the fault quantities involved which is beyond the scope of this book. However, you should be able to see the characteristics of a P-P-G fault as shown in
Figure 1-54.
Vcn
Vca
Ib
Ib
Ic
180
150
120
90 60
30
0
-120
-90 -60
-30
Ia
Van
Vab
Vcn
Vca
Vbc
180
150
120
90 60
30
0
-120
-90 -60
-30
Vbn
Ia
Ic
Van
Vab
Vbc
Vbn
Figure 1-54: Phase-Phase-Ground Fault
46