Symmetrical component example: can't understand solution

In summary, the conversation discusses the calculation of the zero sequence circuit for example 6.1 from Stevenson's Power System Analysis book. The solution involves changing bases and reflecting impedances for T1 and T2, respectively, using their respective MVA ratings and voltage levels. The MVA rating of T2 is used to convert the 0.1 pu reactance to the voltage level of the motor circuit.
  • #1
ffp
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Ok, now I'm studying symmetrical components. Im using Stevenson's Power System Analysis book and example 11.9 asks for the zero sequence circuit of the example 6.1 in the same book.

Here's the example and the solution:
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Here's example 6.1, so we can see what is the circuit:
SmartSelect_20230123_225223_Moon+ Reader Pro.jpg


Here's the beggining of the solution, where I'm stuck...

SmartSelect_20230123_225443_Moon+ Reader Pro.jpg


I believe de X of T1 (0.0857 pu) is found by changing bases (Xpu=OLDpu x OLDbase/NEWbase). So 0.1 is the pu of T1, 300 is the Sbase (MVA) of the generator (and hence, system) and 350 is the Sbase (MVA) of T1. Is that right?

If so, why is X of T2 calculated differently, I believe by reflecting impedances? If that's really what he's doing, why is he using 13.2 and 13.8?

I'm really lost here with this example.
 

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  • #2
ffp said:
I believe de X of T1 (0.0857 pu) is found by changing bases (Xpu=OLDpu x OLDbase/NEWbase). So 0.1 is the pu of T1, 300 is the Sbase (MVA) of the generator (and hence, system) and 350 is the Sbase (MVA) of T1. Is that right?
Yes. Both T1 and the generator have the same voltage rating(and are at the same voltage level in the line diagram). This is why only the ratio of MVA ratings is used to find the new pu reactance.
ffp said:
If so, why is X of T2 calculated differently
The MVA rating of T2 is same as the base MVA (300MVA). The 0.1 pu reactance of T2 is w.r.t its own ratings (300MVA, 13.2kV). To convert it properly according to the motor citcuit voltage level, it is divided by the motor circuit voltage level (and then squared).
 

FAQ: Symmetrical component example: can't understand solution

What are symmetrical components?

Symmetrical components are a mathematical tool used in power systems to simplify the analysis of unbalanced three-phase systems. They decompose an unbalanced set of phasors into three sets of balanced phasors: positive sequence, negative sequence, and zero sequence components.

Why are symmetrical components used in power systems?

Symmetrical components are used in power systems to simplify the analysis and understanding of unbalanced systems. By converting an unbalanced system into balanced components, it becomes easier to analyze faults, load flow, and other phenomena using simpler, well-understood techniques.

How do you calculate symmetrical components?

To calculate symmetrical components, you use a set of transformation equations that convert the original unbalanced phasors into their symmetrical components. This involves using a transformation matrix that relates the original phasors to the positive, negative, and zero sequence components.

What is an example of symmetrical components in practice?

An example in practice could involve an unbalanced three-phase system where the voltages or currents are different in each phase. By applying the symmetrical components method, you can decompose these unbalanced voltages or currents into balanced sets, making it easier to analyze the system's behavior and identify issues.

What are common pitfalls when solving symmetrical component problems?

Common pitfalls include incorrect application of the transformation matrix, misunderstanding the physical meaning of the components, and not properly accounting for the phase shifts between the components. Ensuring a clear understanding of the theoretical basis and careful application of the mathematical steps can help avoid these issues.

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