wwhitney
Senior Member
- Location
- Berkeley, CA
- Occupation
- Retired
Hello,
I am a little surprised by the result at the end of this, so I'm asking if my analysis method is sound and the result is correct.
- Let's say a transformer secondary coil is an idealized voltage source. For a single coil, that's a 2-wire single phase source. If we apply a linear load, it is characterized by its impedance. The power flow out of the coil must match the power flow into the load at all points in time. If the impedance is purely resistive, the power flow out of the coil is always non-negative. If the impedance has a reactive component, the current/voltage phase angle will be non-zero but at most 90 degrees, so while the power flow will be instantaneously into the coil at some points in a cycle, the average power out of the coil over one cycle will still be non-negative.
- Now say we have an open delta secondary (two coils), and a linear load applied across the "phantom" coil. The load still sees a 2-wire single phase source. If the load is resistive, then its current will be in phase with the voltage across this "phantom" coil. The current through each of the two actual coils will be 60 degrees out of phase with the current. The average power flow over a cycle from each actual coil will be positive (and equal in this case).
- Now suppose the load across the phantom coil has sufficient reactance that the phase angle of the load current is above 30 degrees relative to the voltage supplied to the load. In the actual coils, this >30 degree phase angle will add in one coil to the 60 degree offset from the previous case, and subtract in the second coil. So one coil will have a >90 degree phase angle between I and V, while the other will have a phase angle between -30 and 30 degrees. In the first coil, the integral of I dot V will be negative over a cycle, so power will flow into the coil on average over a cycle. Power will flow out of the second coil on average over a cycle, supplying power both to the load and to the first coil.
Is that correct?
Thanks,
Wayne
I am a little surprised by the result at the end of this, so I'm asking if my analysis method is sound and the result is correct.
- Let's say a transformer secondary coil is an idealized voltage source. For a single coil, that's a 2-wire single phase source. If we apply a linear load, it is characterized by its impedance. The power flow out of the coil must match the power flow into the load at all points in time. If the impedance is purely resistive, the power flow out of the coil is always non-negative. If the impedance has a reactive component, the current/voltage phase angle will be non-zero but at most 90 degrees, so while the power flow will be instantaneously into the coil at some points in a cycle, the average power out of the coil over one cycle will still be non-negative.
- Now say we have an open delta secondary (two coils), and a linear load applied across the "phantom" coil. The load still sees a 2-wire single phase source. If the load is resistive, then its current will be in phase with the voltage across this "phantom" coil. The current through each of the two actual coils will be 60 degrees out of phase with the current. The average power flow over a cycle from each actual coil will be positive (and equal in this case).
- Now suppose the load across the phantom coil has sufficient reactance that the phase angle of the load current is above 30 degrees relative to the voltage supplied to the load. In the actual coils, this >30 degree phase angle will add in one coil to the 60 degree offset from the previous case, and subtract in the second coil. So one coil will have a >90 degree phase angle between I and V, while the other will have a phase angle between -30 and 30 degrees. In the first coil, the integral of I dot V will be negative over a cycle, so power will flow into the coil on average over a cycle. Power will flow out of the second coil on average over a cycle, supplying power both to the load and to the first coil.
Is that correct?
Thanks,
Wayne
