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How to compute time-averaged power in a frequency domain solution?
Posted Sep 3, 2014, 2:29 p.m. EDT Low-Frequency Electromagnetics, Results & Visualization Version 4.4 6 Replies
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I am attempting to compute the time-averaged power delivered to a resistive load domain but cannot figure out a reliable way to do so. Any help would be appreciated.
I am modeling inductive coupling between two coils of wire in the Magnetic & Electric Fields interface. The bottom coil is driven by a voltage source imposed by terminals. The top coil is connected to a resistor, where that resistor is simply modeled as a domain with lower conductivity. I'm solving my model in the frequency domain and would like to compute the time-averaged power delivered to that load resistor. I cannot attach my full model, but a toy model is attached to illustrate the situation.
I've tried multiple tactics to compute the power delivered to the load, but none quite work. Here are a few of my attempts:
1) Compute the voltage across the load by averaging the voltage on each boundary and computing the difference. Compute the current through the load by integrating the surface current through a boundary. Compute power delivered to the load as (1/2)*real(conj(V)*I). This gives an okay estimate sometimes, but often has significant error due to varying voltage and current distributions on the load boundaries. In many cases, this can even report more power going into the load than is being provided by the source.
2) Integrate the resistive losses (mef.Qrh) within the load domain. This gives a much more accurate estimate of power delivered to the load, but only at a specific instant in time (i.e., at phase = 0 degrees). If there is a way to compute the time average of these resistive losses, then that'd be perfect, but I cannot find a way to compute the time average for a frequency domain solution.
3) Utilize the time-averaged power flow variables (mef.Pox). Unfortunately, these essentially average to zero on any given boundary and thus appear useless to me.
So how does one go about computing the average power delivered to a resistive load domain? I've been struggling with this question and would appreciate any advice.
Thank you.
I am modeling inductive coupling between two coils of wire in the Magnetic & Electric Fields interface. The bottom coil is driven by a voltage source imposed by terminals. The top coil is connected to a resistor, where that resistor is simply modeled as a domain with lower conductivity. I'm solving my model in the frequency domain and would like to compute the time-averaged power delivered to that load resistor. I cannot attach my full model, but a toy model is attached to illustrate the situation.
I've tried multiple tactics to compute the power delivered to the load, but none quite work. Here are a few of my attempts:
1) Compute the voltage across the load by averaging the voltage on each boundary and computing the difference. Compute the current through the load by integrating the surface current through a boundary. Compute power delivered to the load as (1/2)*real(conj(V)*I). This gives an okay estimate sometimes, but often has significant error due to varying voltage and current distributions on the load boundaries. In many cases, this can even report more power going into the load than is being provided by the source.
2) Integrate the resistive losses (mef.Qrh) within the load domain. This gives a much more accurate estimate of power delivered to the load, but only at a specific instant in time (i.e., at phase = 0 degrees). If there is a way to compute the time average of these resistive losses, then that'd be perfect, but I cannot find a way to compute the time average for a frequency domain solution.
3) Utilize the time-averaged power flow variables (mef.Pox). Unfortunately, these essentially average to zero on any given boundary and thus appear useless to me.
So how does one go about computing the average power delivered to a resistive load domain? I've been struggling with this question and would appreciate any advice.
Thank you.
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6 Replies Last Post Sep 9, 2014, 2:01 a.m. EDT
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Posted:
10 years ago
2) Integrate the resistive losses (mef.Qrh) within the load domain. This gives a much more accurate estimate of power delivered to the load, but only at a specific instant in time (i.e., at phase = 0 degrees). If there is a way to compute the time average of these resistive losses, then that'd be perfect, but I cannot find a way to compute the time average for a frequency domain solution.
Hi KG,
As you integrate Qrh over the domain, you get the constant value, not phase dependent. Am i missing something?
Best Regards,
Dima.
--
Dima Apter
www.a2z-consulting.com
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Posted:
10 years ago
Maybe you're right, Dima. The attached model is a much simpler check of simply one resistive block with AC voltage applied across it. In this case, the values make sense: (Power In) = (Resistive Losses) = 2 W.
In my initial coils model, however, the same calculations give (Power In) = 0.38 W, and (Resistive Losses) = 0.51 W. Clearly something is wrong because this says more power is being lost to heating than is being provided by the input terminals. I thought my issue was that the computed resistive losses were for phase = 0 degrees... but maybe the issue is somewhere else?
In my initial coils model, however, the same calculations give (Power In) = 0.38 W, and (Resistive Losses) = 0.51 W. Clearly something is wrong because this says more power is being lost to heating than is being provided by the input terminals. I thought my issue was that the computed resistive losses were for phase = 0 degrees... but maybe the issue is somewhere else?
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Posted:
10 years ago
What is the frequency in the initial model? Maybe some skin effect - meshing issue?
--
Dima Apter
www.a2z-consulting.com
--
Dima Apter
www.a2z-consulting.com
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Posted:
10 years ago
The initial model is run at only 100 Hz. So skin depth should be about 6 mm, and the conductor dimensions are 4 mm by 10 mm. So I don't think there should be any skin effect - meshing issues. I should run again at finer meshes, though, to see if that corrects the issue. My computer is tied up at the moment, but I'll test this when I get the chance and report back.
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Posted:
10 years ago
Upon tinkering with mesh size, I see that the problem may be in my Tx_Power calculation. Refining my mesh leaves mef.Qrh about the same, but my value for Tx_Power changes significantly. Since I'm using terminals for the inputs, I thought I could just compute the input power as:
Tx_Power1 = (1/2)*real(conj(mef.V0_1)*mef.I0_1)
Tx_Power2 = (1/2)*real(conj(mef.V0_2)*mef.I0_2)
Tx_Power = Tx_Power1 + Tx_Power2
That gives the answer I'd expect in the basic resistor model I tested, but apparently is not working here. I'm still looking into it.
Tx_Power1 = (1/2)*real(conj(mef.V0_1)*mef.I0_1)
Tx_Power2 = (1/2)*real(conj(mef.V0_2)*mef.I0_2)
Tx_Power = Tx_Power1 + Tx_Power2
That gives the answer I'd expect in the basic resistor model I tested, but apparently is not working here. I'm still looking into it.
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Posted:
10 years ago