Each elements of power system will present impedance to different phase sequence components of current which may not be the similar. For instance, the impedance which any part of equipment offers to the positive sequence current will not essentially be the same as offered to negative sequence or zero sequence current. Therefore, in unsymmetrical fault calculations, each part of equipment will have three values of impedance one corresponding to each sequence current viz.
- Positive sequence impedance (Z1)
- Negative sequence impedance (Z2)
- Zero sequence impedance (Z0)
The impedance offered by a circuit or equipment to positive-sequence current is said to be positive sequence impedance and it is represented by Z1. Likewise, impedances presented in any circuit or equipment to negative-sequence and zero-sequence currents are named as negative sequence impedance (Z2) and zero sequence impedance (Z0) respectively.
The following points may be noted:
- In a 3-phase balanced system, each portion of the equipment or circuit offers only one impedance, that is, the one offered to positive sequence or normal sequence current. This is anticipated because of the nonexistence of negative and zero sequence in the 3-phase balanced system.
- In a 3-phase unbalanced system, each part of the equipment or circuit will have three values of impedance viz. positive sequence, negative Sequence Impedance and zero sequence impedances.
- The positive and negative sequence impedances of linear, symmetrical and static circuits. (e.g., transmission-lines, cables, transformers and static loads) are identical and are the similar as those used in the analysis of balanced conditions. This is owing to the fact that impedance of such circuits are independent of the phase order, provided the voltages applied are balanced. It may be noted that positive and negative sequence impedances of rotating machines (e.g., synchronous and induction motors) are normally different.
- The zero sequence impedance depends upon the path taken by the zero sequence current. As this path is normally different from the path taken by the positive and negative sequence currents, therefore the zero sequence impedance is usually difference from positive or negative sequence impedance.
Sequence Impedance of Power System Elements
The design of impedances in various elements of power system (e.g., Generators, Transformers, Transmission lines etc) to positive sequence, negative sequence and zero sequence currents are considerable importance in determining the fault current in a 3-phase unbalanced system. An entire concern about this topic does not covered in this post; but short preliminary explanations may be of interest here.
The following are the three main parts of equipment will be considered for Sequence Impedance of Power System Elements
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- Synchronous Generators
- Transformers
- Transmission lines
Synchronous Generators
These positive, negative and zero sequence impedances of rotating machines are generally different. The positive sequence impedance of a synchronous generator is equal to the synchronous impedance of the machine. The zero-sequence impedance is much less than the positive-sequence impedance. The zero sequence impedance is a variable item and if its value is not given, it may be assumed to be equal to the positive sequence impedance. In simple:
Negative-sequence impedance
Zero-sequence impedance = variable item
= may be taken equal to positive-sequence impedances, if its value are not given
It might be advisable to mention here that any impedance Ze in the earth connection of star connected systems has the effect to introduce an impedance of 3 - Ze per phase. It is because the three equal zero-sequence currents, being in phase, do not sum to zero at the star-point, but they flow back along the neutral connection.
Transformers
Since the transformers have same impedance with reversed phase rotation their positive-sequence and negative-sequence impedances are equal, this value being equal to the impedance of the transformer. However, the zero-sequence impedance depends upon earth connection. If there is a through circuit for earth current, zero-sequence impedance will be equal to positive-sequence impedance, or else it will be infinite. In simple,
Positive-sequence impedance = Negative-sequence impedance
= Impedance of transformers
Zero-Sequence impedance = positive-sequence impedance, in case there is circuit for earth current
= Infinite, if there is no through circuit for earth current.
Transmission Lines
The positive-sequence and Negative-sequence impedances of a line are the same, this value being equal to the normal impedance of the line. This is projected because the phase rotation of the currents does not make any difference in the constants of the line. However, the zero-sequence impedance is usually much greater than the positive-sequence or negative-sequence impedance. In simple:
Positive-sequence impedance = Negative-sequence impedance
= Impedance of the line
Zero-sequence impedance = variable item
= may be taken as three times positive-sequence impedance if its values are not given.
