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Positive Sequence Impedance vs. Negative Sequence Impedance Concept 3
- Thread starter EddyPach
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Eddypach- not an easy thing to do via the forum, but I'll give it a shot. Considering a three-phase system, symmetrical components (positive sequence, negative sequence, and zero sequence) allow one to analyze power system operation during unbalanced conditions such as those caused by faults between phases and/or ground, open phases, unbalanced impedances, and so on. The positive sequence set consists of the balanced three-phase currents and line-to-neutral voltages supplied by the system generator. They are always equal in magnitude and phase displaced by 120 degrees rotating at the system frequency with a phase sequence of normally a, b, c. The sequence currents or sequence voltages always exist in three's, never alone or in pairs.
The negative sequence set is also balanced with three equal magnitude quantities at 120 degrees apart but with the phase rotation or sequence reversed, or a, c, b. (If the positive sequence is a, c, b as in some power systems, then negative sequence will be a, b, c.) For the negative sequence set, again the sequence currents or sequence voltages always exist in three's, never alone or in pairs.
The members of the zero-sequence set of rotating phasors are always equal in magnitude and always in phase. Once again, if zero sequence currents or zero sequence voltages exist, they must exist in all three phases, never alone or in one phase.
In transformers, lines, etc., the phase sequence of the current does not change the impedance encountered, so positive sequence impedance equals negative sequence impedance; X1 = X2. System generators do not generate negative sequence currents, but negative sequence can flow in their windings. For rotating machines X2 = 1/2(X"d + X"q). Except for calculating faults very near machine terminals, can assume X"d=X"q, so X2 = X"d.
Zero sequence for transformers is equal to the positive & negative sequence and is the transformer leakage impedance, except in core-type transformers where Xo = .85 to .9 times X1. For estimating open lines Xo = 3 or 3.5 times X1 is commonly used. Zero sequence impedance of generators is low and variable depending on winding design.
The negative sequence set is also balanced with three equal magnitude quantities at 120 degrees apart but with the phase rotation or sequence reversed, or a, c, b. (If the positive sequence is a, c, b as in some power systems, then negative sequence will be a, b, c.) For the negative sequence set, again the sequence currents or sequence voltages always exist in three's, never alone or in pairs.
The members of the zero-sequence set of rotating phasors are always equal in magnitude and always in phase. Once again, if zero sequence currents or zero sequence voltages exist, they must exist in all three phases, never alone or in one phase.
In transformers, lines, etc., the phase sequence of the current does not change the impedance encountered, so positive sequence impedance equals negative sequence impedance; X1 = X2. System generators do not generate negative sequence currents, but negative sequence can flow in their windings. For rotating machines X2 = 1/2(X"d + X"q). Except for calculating faults very near machine terminals, can assume X"d=X"q, so X2 = X"d.
Zero sequence for transformers is equal to the positive & negative sequence and is the transformer leakage impedance, except in core-type transformers where Xo = .85 to .9 times X1. For estimating open lines Xo = 3 or 3.5 times X1 is commonly used. Zero sequence impedance of generators is low and variable depending on winding design.
- Thread starter
- #3
Yes you can. In our transformer specifications we have two statements regarding the symmetrical components.
Under the TESTS heading:
Impedance and load loss at rated current on the rated voltage connection and on the tap extremes. Test sheet impedance values shall include both the positive sequence and zero sequence network values.
And under the RATINGS heading:
The zero sequence impedance of any autotransformer equivalent-impedance-leg shall be positive or the least negative values possible without increasing the cost of the transformer(s).
Under the TESTS heading:
Impedance and load loss at rated current on the rated voltage connection and on the tap extremes. Test sheet impedance values shall include both the positive sequence and zero sequence network values.
And under the RATINGS heading:
The zero sequence impedance of any autotransformer equivalent-impedance-leg shall be positive or the least negative values possible without increasing the cost of the transformer(s).
redtrumpet
Electrical
See also:
1. Westinghouse (now ABB) Electrical Transmission and Distribution Reference Book
2. Elements of Power System Analysis, W. D. Stevenson
3. Alternating-Current Circuits, Kerchner and Corcoran
4. Analysis of Faulted Power Systems, P. M. Anderson
for more on symmetrical components.
1. Westinghouse (now ABB) Electrical Transmission and Distribution Reference Book
2. Elements of Power System Analysis, W. D. Stevenson
3. Alternating-Current Circuits, Kerchner and Corcoran
4. Analysis of Faulted Power Systems, P. M. Anderson
for more on symmetrical components.
Tgott this is a good explanation.
As a minor comment I will add that the sequence impedance method is a good approximation for linear systems,symmetric and sinusoidal steady state.
For many analysis problems, such as grounding, the symmetrical component may not be the preffer or accurate method recommended.
A good reference books in this subjet are:
"Analysis of Faulted Power System by P. Anderson, IEEE Press"
"Power System Grounding & Transient, Skis Meliopoulus, Marcel Decker"
As a minor comment I will add that the sequence impedance method is a good approximation for linear systems,symmetric and sinusoidal steady state.
For many analysis problems, such as grounding, the symmetrical component may not be the preffer or accurate method recommended.
A good reference books in this subjet are:
"Analysis of Faulted Power System by P. Anderson, IEEE Press"
"Power System Grounding & Transient, Skis Meliopoulus, Marcel Decker"
jbartos
Electrical
- Jan 15, 2000
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Suggestion: There are also some related postings in this Forum, e.g.
Three Phase Fault Calc Using Symmetrical Componets
etc.
Essentially, an unbalance system (power supply - load) is transformed into positive, negative and zero symmetrical components, in general. All components are treated simultaneously to obtain solution(s) to various problems, e.g. fault analysis, understanding of zero sequence currents flow, etc. However, there are some disadvantages to their usage, namely, more complex calculations especially for multi-phase systems with the larger number of phases, and nonlinear loads.
Three Phase Fault Calc Using Symmetrical Componets
etc.
Essentially, an unbalance system (power supply - load) is transformed into positive, negative and zero symmetrical components, in general. All components are treated simultaneously to obtain solution(s) to various problems, e.g. fault analysis, understanding of zero sequence currents flow, etc. However, there are some disadvantages to their usage, namely, more complex calculations especially for multi-phase systems with the larger number of phases, and nonlinear loads.
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