Measuring generated power (kW) in a power plant and storing/logging values
which components would be needed to measure the generated power
  digitally in real time and take that measurement into something like
  an Arduino and/or Raspberry Pi so that I can log the values over time
  in custom software?


To calculate power you need to multiply (in real time) the voltage waveform and the associated current waveform. You need to sample at a fairly high rate in order to accommodate harmonics that may be present in your current waveform. Possibly as low as 1 kHz but preferably higher.

If your powergen system is three phase, depending on how it is wired, you may be able to take two voltage waveforms and two current waveforms into your digital system via analogue to digital converters.

Worst case is 3 phase and a neutral - you'll need three voltage ADCs and three current ADCs.

You use a voltage transformer to provide a low voltage (and isolated) AC representation of the voltage and you will probably use a CT to get a safe signal.

Use simultaneous sampling analogue to digital conveters (to avoid any incurrence of a phase angle error), multiply the relevant signals together inside your digital system to get an instantaneous power waveform then average that waveform to get average power.

Output that average power value in a way suitable for the target logging system. You can choose digital or analogue for this method but I would choose a digital comms method.