Looking through the community discussions, powerd seems to be a cpu hog, at least intermittently. I haven't had a problem with configd. (On a mac book pro, El Capitan) I was recently getting spinning pinwheels, and using activity monitor, I noticed powerd often using 99% of the cpu, > 80% consistently, while plugged into power or on battery. Then I went into terminal, and ran "top -o cpu" , confirmed the cpu usage and noted the pid number. I then did "q" to quit out of top, then re-ran top, with "top -pid 47" (47 was the process id for powerd for me). I then closed the activity monitor window, and watched in terminal, and saw the cpu usage for powerd go to 0! Activity monitor was still running, just the main window was closed, even the icon in the dock reflecting cpu usage showed less cpu usage... So my problem is related to activity monitor and having the main window open(?)
So one suggestion is closing activity monitor and use top in terminal to see if that effects powerd or configd cpu usage, and you can try closing other apps. Another suggestion is go into the console log and filter by powerd or configd, and see if any messages there help you. I had:
6/24/16 10:30:30.000 AM kernel[0]: process powerd[47] thread 545 caught burning CPU! It used more than 50% CPU (Actual recent usage: 56%) over 180 seconds. thread lifetime cpu usage 430.788554 seconds, (382.646944 user, 48.141610 system) ledger info: balance: 90004015609 credit: 429784906407 debit: 339780890798 limit: 90000000000 (50%) period: 180000000000 time since last refill (ns): 160437242725
6/24/16 10:30:33.561 AM spindump[778]: Saved cpu_resource.diag report for powerd version ??? (???) to /Library/Logs/DiagnosticReports/powerd_2016-06-24-103033_Bobs_MBP.cpu_resource. diag
Finally, since your problem seems to be power related, have you tried resetting the SMC?
Reset the System Management Controller (SMC) on your Mac - Apple Support
If you still have a problem after that, less likely to be helpful but worth a try, reset the nvram. How to Reset NVRAM on your Mac - Apple Support