electric circuit analysis, power balance in the electric circuit, electric circuit simulation, circuit elements currents and voltages

QuickField offers an opportunity to include an electric circuit into the analyzed model. This example demonstrates the accuracy of the embedded circuit simulation.

Problem type:
Plane-parallel problem of AC Magnetics.

Geometry:
As it is explained in the Solution section below, the field model geometry is not affecting the circuit simulation. Here is the circuit schema.

Given: R = 20 Ohm X_{L} = 10 Ohm X_{C} = 2 Ohm
Current source I = 4 A (RMS) @ 0°
Voltage source U = 60 V (RMS) @ 30°
Frequency f = 50 Hz

Task:
Calculate currents and voltages in the circuit elements, check the power balance.

Solution:
QuickField could solve only coupled field-circuit problems, and the field problem should be AC or Transient Magnetic. So we created fictitious AC Magnetic problem with one block, not connected to the circuit, just to agree with this requirement. All following considerations and results relate to the circuit simulation only.

Total power is determined as S = U * I' = P + i*Q,
where U - voltage [V], I' - complex conjugate of current [A], P - average active power [W], Q - reactive power [V·Ar].

Results:

Complex power in voltage source V S(V) = 60@30° * 10.58@(-79.1°) = 634.8@(-49.1°) = 415.6 - i*479.8 [V·A].

Measured RMS values of voltages and currents, average values of powers.

Voltage V, V

Current I, A

Real power P, W

Reactive power Q, V·Ar

R

80 @ 0°

4 @ 180°

320

0

L

105.8 @ 10.9°

10.58 @ 100.9°

0

1119.4

C

52.9 @ 169.1°

10.58 @ 79.1°

0

-559.7

V

60 @ 30°

10.58 @ -100.9°

415.6

-479.8

I

185 @ 6.2°

4 @ 0°

-735.6

-79.9

Power balance

0

0

*Mathematical Methods for Physicists. A Comprehensive Guide. 7th Edition. George Arfken, Hans Weber, Frank Harris, p 937-938. ISBN 978-0-12-384654-9.