Lec 20.pptx
- 1. Course: Introduction to Power Engineering Course Instructors: Ms. Nisma Saleem Lecture No. 20
- 2. Power System Analysis (Fault Analysis)
- 3. Contents • Asymmetrical fault analysis • Symmetrical components • Sequence impedances • Sequence impedance of power system elements • Sequence networks • Sequence networks of synchronous generators • Sequence networks of power system • Unsymmetrical faults on three phase system
- 7. Symmetrical Components • The Symmetrical Components consist of three subsystems for an unbalanced three-phase system. They are: • Positive sequence components • Negative sequence components • Zero sequence components Positive sequence components:
- 8. Symmetrical Components Negative sequence components: Zero sequence components:
- 9. Symmetrical Components • Three voltage phasors Va , Vb , and Vc of an unbalanced set can be expressed in terms of their symmetrical components as following:
- 10. Symmetrical Components Representing Vb and Vc in terms of Va, we get:
- 11. Symmetrical Components In matrix form:
- 14. Sequence Impedances • In unsymmetrical fault calculations, each piece of equipment will have three values of impedance—one corresponding to each sequence current viz. (i) Positive sequence impedance (Z1) (ii) Negative sequence impedance (Z2) (iii) Zero sequence impedance (Z0) • The impedance of a circuit when positive sequence currents are flowing is called positive sequence impedance. • When only negative sequence currents are flowing the impedance is termed as negative sequence impedance. • With only zero sequence currents flowing the impedance is termed as zero sequence impedance
- 15. The following points may be noted : (a)In a 3-phase balanced system, each piece of equipment or circuit offers only one impedance the one offered to positive or normal sequence current. This is expected because of the absence of negative and zero sequence currents in the 3-phase balancedsystem. (b)In a 3-phase unbalanced system, each piece of equipment or circuit will have three values of impedance viz. positive sequence impedance, negative sequence impedance and zero sequence impedance. (c)The positive and negative sequence impedances of linear, symmetrical and static circuits (e.g. transmission lines, cables, transformers and static loads) are equal and are the same as those used in the analysis of balanced conditions. This is due to the fact that impedance of such circuits is independent of the phase order, provided the applied voltages are balanced. It may be noted that positive and negative sequence impedances of rotating machines (e.g. synchronous and induction motors) are normally different. (d)The zero sequence impedance depends upon the path taken by the zero sequence current. As this path is generally different from the path taken by the positive and negative sequence currents, therefore, zero sequence impedance is usually different from positive or negative sequence impedance.
- 16. 18.7 Sequence Impedances of Power System Elements • The concept of impedances of various elements of power system (e.g. generators, transformers, transmission lines etc.) to positive, negative and zero sequence currents is of considerable importance in determining the fault currents in a 3-phase unbalanced system. (i) Synchronous generators (ii) Transformers (iii) Transmission lines
- 17. (i) Synchronous generators. • The 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 negative 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 short :
- 18. (ii)Transformers. • Since transformers have the same impedance with reversed phase rotation, their positive 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 otherwise it will be infinite. In short,
- 19. (iii) Transmissionlines. • The positive sequence and negative sequence impedance of a line are the same; this value being equal to the normal impedance of the line. This is expected 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 or negative sequence impedance. In short :
- 20. Sequence Network • Since each sequence current causes a voltage drop of that sequence only, each sequence current can be considered to flow in an independent network composed of impedances to current of that sequence only. • The single phase equivalent circuit composed of the impedances to current of any one sequence only is called the sequence network of that particular sequence. • Therefore for every power system we can form three- sequence networks. These sequence networks, carrying current Ia1, Ia2 and Ia0 are then inter-connected to represent the different fault conditions.
- 21. Sequence Network of synchronous machine • An unloaded synchronous machine having its neutral earthed through impedance, Zn, is shown in figure below. • A fault at its terminals causes currents Ia, Ib and Ic to flow in the lines. If fault involves earth, a current In flows into the neutral from the earth through Zn.
- 22. Sequence Network of synchronous machine • Positive Sequence network:
- 23. Sequence Network of synchronous machine • Negative Sequence network:
- 24. Sequence Network of synchronous machine • Zero Sequence network: • The zero sequence currents flow through the neutral impedance Zn and the current flowing through this impedance is 3Ia0.
- 25. Sequence network of Power system One line diagram of a small power system Corresponding reactance diagram (positive sequence diagram)
- 26. Sequence network of Power system Positive sequence diagram Corresponding negative sequence diagram
- 27. Sequence network of Power system Corresponding Zero sequence diagram The reactances of generator, motor and transmission line will be different in the given data for zero sequence network along with the neutral reactance
- 28. Sequence network of Y-∆ transformers • The sequence equivalent circuits of three phase transformers depend of the connections of primary and secondary windings. • Different combinations of Y and delta windings determine the configurations of zero sequence circuits and the phase shift in positive and negative sequence circuits. • Five possible connections of two winding transformers are summarized along with their approximate zero-sequence circuits in the given figure (resistance and magnetizing current paths are omitted from each circuit)
- 29. Sequence network of Y-∆ transformers • The sequence equivalent circuits of three phase transformers depend of the connections of primary and secondary windings. • Different combinations of Y and delta windings determine the configurations of zero sequence circuits and the phase shift in positive and negative sequence circuits. • Five possible connections of two winding transformers are summarized along with their approximate zero-sequence circuits in the given figure (resistance and magnetizing current paths are omitted from each circuit)