1. Power System Protective Relaying-Part Two
Wei-Jen Lee, Ph.D., PE
Professor of Electrical Engineering Dept.
The Univ. of Texas at Arlington

2. Definition Quantity in per unit =
Quantity in percent = (Quantity in per unit)*100

3. Advantages More meaningful when comparing different voltage levels
The per unit equivalent impedance of the transformer remains the same when referred to either the primary or the secondary side
The per unit impedance of a transformer in a three-phase system is the same, regardless the winding connection
The per unit method is independent of voltage changes and phase shifts through transformers

4. Advantages
Manufacturers usually specify the impedance of the equipment in per unit or percent on the base of its nameplate ratings
The per unit impedance values of various ratings of equipment lie in a narrow range

5. General Relations Between Circuit Quantities

6. General Relations Between Circuit Quantities

7. General Relations Between Circuit Quantities

8. Base Quantity Selections
VA, V, I, and Z are four power quantities
One has to select two base quantities and derive the other two

9. Base Conversion

10. Example One: Base Conversion
A 50-MVA, 34.5:161 kV transformer with 10% reactance is connected to a power system where all the other impedance values are on a 100 MVA, 34.5 or 161 kV base. The reactance of the transformer under new base is:

11. Example Two: Base Conversion
A generator and transformer, as shown below, are to be combined into a single equivalent reactance on a 100 MVA, 110 kV (high voltage side) base.

12. Example Two: Base Conversion
The transformer is operated at 3.9 kV tap.
New base voltage at high side is 110 kV.
The base voltage at low side is:
110*3.9/115 = 3.73 kV

13. Transformer Polarity

14. Transformer Polarity
The ANSI/IEEE standard for transformers states that the high voltage should lead the low voltage by 30o with Y-D or D-Y banks.

15. Relay Polarity
Relays that sense the direction of current (or power) flow at a specific location and, thereby, indicate the direction of the fault, provide a good example of relay polarity.
A directional-sensing unit requires a reference quantity that is reasonably constant against which the current in the protected circuit can be compared.

16. Relay Polarity Definition of maximum torque line and zero torque line
Solid state units can have adjustments for (1) the maximum torque angle and (2) the angle limits of the operating zone

17. Relay Polarity

18. Relay Polarity
In Fig. (A), the maximum operating torque or energy occurs when the current flow from polarity to non-polarity (Ipq) leads by 30o the voltage drop from polarity to non-polarity (Vrs). The minimum pick up of the directional unit is specified at the maximum torque.
Higher current will be required when Ipq deviates from the maximum torque line.

19. Relay Polarity
For ground fault protection, the 60o unit of Fig. (B) is used with a 3Vo reference and the zero unit of Fig. (C) with a 3Io current reference.
The Fig. (C) is also used for power or var applications.

20. Maximum torque occurs when
Relay Polarity
Connection
Unit Type
Phase A
Phase B
Phase C
Maximum torque occurs when
30o
Fig. 3.7C
Ia, Vac
Ib, Vba
Ic, Vcb
I lags 30o
60o Delta
Ia-Ib, Vac
Ib-Ic, Vba
Ic-Ia, Vcb
I lags 60o
60o Wye
Ia, -Vc
Ib, -Va
Ic, -Vb
90o-45o
Fig. 3.7A
(max. torque: 45o)
Ia, Vbc
Ib, Vca
Ic, Vab
I lags 45o
90o-60o

21. The 90o-60o Connection for Phase-Fault Protection

22. The 90o-60o Connection for Phase-Fault Protection

23. Directional Sensing for Ground Faults: Voltage Polarization

24. Directional Sensing for Ground Faults: Voltage Polarization

25. Directional Sensing for Ground Faults: Current Polarization

26. Symmetrical Components

27. Zero Sequence Current and Voltage for Ground Fault Protection

28. Sequence Networks
Single-Line Diagram

29. Sequence Networks
Positive Sequence Network

30. Sequence Networks
Negative Sequence Network

31. Sequence Networks
Zero Sequence Network

32. Sequence Network Reduction
Consider faults at bus H for the positive sequence network of the sample system. The Z1 is equal to the parallel of (Xd”+XTG+X1GH) and (Z1S+XHM)

33. Fault Studies for Relay Settings and Coordination
Three-phase fault studies for applying and setting phase relays
Single-phase-to-ground fault studies for applying and setting ground protection relays
Fault Impedance: Faults are seldom solid, but involve varying amount of resistance.
It is generally ignored in protective relaying and faults studies for high voltage transmission or sub-transmission system.

34. Fault Studies for Relay Settings and Coordination
In distribution systems, very large or basically infinite impedance can exist. High impedance fault detection relay may be necessary for distribution system.
For arcing fault, the arc resistance varies a lot. However, a commonly accepted value for currents between 70 and 20,000 A has been an arc drop of 440 V per foot, essentially independent of current magnitude. Therefore,

35. Fault Studies for Relay Settings and Coordination
In low voltage (480 V) switchboard-type enclosures, typical arc voltages of about 150 V can be experienced.
Substation and Tower-Footing Impedance is another highly variable factor. Several technical papers have been written and computer programs have been developed in this area with many variables and assumptions. The general practice is to neglect these in most fault studies and relay applications and settings.

36. Fault Studies for Relay Settings and Coordination

37. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Three-Phase Faults

38. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Three-Phase Faults
Three-Phase faults are assumed to be symmetrical.
The positive-sequence network can be used to calculate the fault current.
Since Ia, Ib, and Ic are balanced, only I1 appears in the circuit. If there is fault impedance ZF among phases, Z1 should be changed to Z1 + ZF. V-( Z1 + ZF) I1=0 or

39. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Single Phase-to-Ground Faults

40. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Single Phase-to-Ground Faults
A phase-a-to-ground fault is represented by connecting the three sequence networks together (either with or without fault impedance).

41. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Single Phase-to-Ground Faults

42. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Phase-to-Phase Faults
- It is convenient to show the fault between phases b and c with fault impedance of ZF.

43. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Phase-to-Phase Faults

44. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Phase-to-Phase Faults

45. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Phase-to-Phase Faults

46. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Phase-to-Phase Faults
Assume Z1 = Z2, then I1 = V/2Z1. Just considering the magnitude,

47. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Double Phase-to-Ground Faults
The connection for this type of fault is similar to the phase-to-phase fault with the addition of the zero sequence impedance in parallel with the negative sequence impedance.

48. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Double Phase-to-Ground Faults

49. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Double Phase-to-Ground Faults

50. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Double Phase-to-Ground Faults (Solid faults)

51. Fault Studies for Relay Settings and Coordination
Sequence Interconnections for Double Phase-to-Ground Faults (Line-to-line fault impedance: ZF and phase-to-ground fault impedance: ZFG)

52. Example: Fault Calculations on a Sample System

53. Example: Fault Calculations on a Sample System
Step One: Transfer all the constants to a common base
- VG:
- VS: No change
- Two winding Transformer:

54. Example: Fault Calculations on a Sample System
Step One: Transfer all the constants to a common base
- Three winding transformer:

55. Example: Fault Calculations on a Sample System
Step One: Transfer all the constants to a common base
- Line Impedance:

56. Example: Fault Calculations on a Sample System
Develop sequence network for different fault conditions (Fault at point “G”).
Positive & negative sequence network

57. Example: Fault Calculations on a Sample System
Develop sequence network for different fault conditions (Fault at point “G”).
Zero sequence network

58. Example: Fault Calculations on a Sample System
For the fault at G, the right side impedance (j j j0.03=j0.2481) is parallel with left side impedance (j0.20+j0.1375=j0.3375).

59. Example: Fault Calculations on a Sample System
The right side network is reduced for a fault at bus G by first paralleling X0S + ZH with ZL and then adding ZM and X0GH (The equivalent impedance is equal to j0.6709). Paralleling with the left side impedance (XTG = j0.1375), the zero sequence impedance X0 = j

60. Example: Fault Calculations on a Sample System
Three-phase fault at Bus G
The division of current from the left (IaG) and the right (IaH) are:

61. Example: Fault Calculations on a Sample System
Single-phase-to-ground fault at Bus G

62. Example: Fault Calculations for Autotransformers
Autotransformers have become very common in recent years.
Consider a typical autotransformer in a system, as shown in the figure, and assume that a single-phase-to-ground fault occurs at the H or 34.5 kV terminal

63. Example: Fault Calculations for Autotransformers

64. Example: Fault Calculations for Autotransformers

65. Example: Fault Calculations for Autotransformers
The sequence networks are shown below:

66. Example: Fault Calculations for Autotransformers
When the fault happens at Bus H, the equivalent sequence impedance for the networks are:
Positive & negative sequence network
Zero sequence network

67. Example: Fault Calculations for Autotransformers
Single-phase-to-ground fault at H:

68. Example: Fault Calculations for Autotransformers
Fault current distribution

69. Example: Open-Phase Conductor
A blown fuse or broken conductor that opens one of the three phases results in a serious unbalance that has to be detected and resolved as soon as possible.
The sample system (Assume phase a open at “H”)

70. Example: Open-Phase Conductor
The positive sequence network (X-Y indicates the fault location)

71. Example: Open-Phase Conductor
The negative sequence network (X-Y indicates the fault location)

72. Example: Open-Phase Conductor
The zero sequence network (X-Y indicates the fault location)

73. Example: Open-Phase Conductor
It is necessary to consider the load current in this case. (This is similar to two-phase-to-ground fault calculation)

74. Example: Open-Phase Falling to Ground on One Side
Same sample system as before.
Assume phase a conductor on the line at bus H opens and falls to ground on the H side (right side).

75. Example: Open-Phase Falling to Ground on One Side
Same sequence network
Since this is a simultaneous fault (an open phase fault and a phase-to-ground fault), we can insert three ideal transformers at H to isolate the open phase fault and phase-to-ground fault. (Load current can be ignored)

76. Example: Open-Phase Falling to Ground on One Side

77. Example: Open-Phase Falling to Ground on One Side

78. Example: Open-Phase Falling to Ground on One Side
The other possibility is that the open conductor falls to ground on the line side. We can use the same approach as before. However, the load must be considered in the fault current calculation.