Sequence Components. Do Three 3-Phase Values Sum to zero?
Rodney Hughes B.Eng-Elec FIEAust CPEng NER APEC IntPE Aus
Power System, Protection and IEC 61850 Specialist
Kirchhoff's Law tells us that the sum of the currents at any node must equal zero. Of course the current flow in/out of a node... i.e. any POINT in the system could be the actual wires or a fault path, but there must be equal currents flowing into the node and out .. the current can't just disappear!
Hence at a star point of three phases and a fourth connection to neutral, those four currents flowing in and out of the star POINT must sum to zero.
Ia + Ib + Ic + In = 0
But what if we only know the currents on the three lines: Ia, Ib, Ic. They do not necessarily add to zero because Ia + Ib + Ic = -In
In some cases, the three phasors may represent a perfectly normal system condition such as:
System Components is a mathematical treatment of the magnitudes and phase angles of the three individual phase measurements that allows us to know far more about the nature of the power system condition than just the measurements alone.
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Myths and Misunderstandings
Sequence Components does not state that the real system 3-phase currents sum to zero, or that real system 3-phase voltages sum to zero.
In fact, the Symmetrical Component formulas are because the system sometimes does NOT sum to zero across the three phases,
... or they DO sum to zero, but the phases are not equally balanced on all three phases!
We are not talking about d.c. offsets, inrush transients or decaying/decrement waveforms which may affect one or more phases differently to the other for a few, or indeed many cycles.
We are not talking about the “super-fast” so-called travelling wave disturbances when a fault occurs.
We are not talking about waveforms with harmonics.
We are talking about the normal system fundamental frequency r.m.s. currents or voltages that you can measure with a "voltmeter" or "ammeter" and a "phase angle meter"!
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A more complete explanation is provided in my technical reference web site, including a spreadsheet you can download to display the phasors graphically.
https://ideology.atlassian.net/l/cp/j8x0kGbV
I cater to service providers in ELECTRIC POWER ??: equipment procurement, design engineering, overseeing projects on behalf of the installing contractor, & related functions for primary power distribution & generation
2 年Rodney - Great article and very visual website (a lot of work was put into that site!). I have self-admittedly struggled with symmetrical components in keeping the visual aligned with the mathematical - and any such reference material is always helpful. Thank you.
Electrical Power Systems Engineer, specializing in utility transmission protection
2 年Just for fun, harmonics can be assigned a sequence. Given a set of positive sequence fundamental phasors, If we start at the fundamental, the harmonics of that positive sequence quantity occur in the order +, -, 0 and keep repeating. All harmonics that are a multiple of three (called triplen harmonics) can be considered zero sequence because they all line up in phase with each other. Because of this, they tend to accumulate in the neutral path. Negative sequence harmonics (2, 5, 8, 11…) result in counter rotating torques in three phase machines, which result in increased losses and reduction of max power output capability.