Calculating Equivalent Series Resistance and Inductance for Parallel Branches

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SUMMARY

To calculate the equivalent series resistance (Req) and inductance (X) for two parallel branches, the correct method involves using the combined impedance formula: Zeq = (R1+jX1)*(R2+jX2)/((R1+jX1)+(R2+jX2)). This approach accounts for the complex nature of the components, yielding accurate results. The simpler method, Req = R1*R2/(R1+R2), is insufficient as it does not consider the inductive reactance, leading to discrepancies in the results. The values of resistance (R) and reactance (X) should be expressed in per unit for consistency.

PREREQUISITES
  • Understanding of complex impedance in electrical circuits
  • Familiarity with per unit system in electrical engineering
  • Knowledge of series and parallel circuit analysis
  • Basic proficiency in converting between polar and rectangular forms
NEXT STEPS
  • Study the principles of complex impedance in AC circuits
  • Learn about the per unit system and its applications in power systems
  • Explore advanced techniques for calculating equivalent circuits in parallel configurations
  • Practice converting between polar and rectangular forms of complex numbers
USEFUL FOR

Electrical engineers, students studying circuit theory, and professionals involved in power system analysis will benefit from this discussion on calculating equivalent series resistance and inductance in parallel branches.

Physicist3
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Hi,

If I have two brances, branch 1 and branch 2 which are in parallel and each branch has a resistance and inductance, to calculate the equivalent series resistance and inductance, can I calculate the resistance and inductance separately e.g.

Req = R1*R2/R1+R2 (and same for X),

or do I have to do it combined E.g.

Zeq = (R1+jX1)*(R2+jX2)/(R1+jX1)+(R2+jX2), and then convert to polar etc and back to rectangular to find the equivalent R and jX values? The two methods give me different answers?

Sorry, forgot to add, the values of R and X are in PER UNIT
 
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Physicist3 said:
The two methods give me different answers?
And the second one is correct. That should answer if the first one works.
Note that there are brackets missing.
 

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