Power help

Kost is also contradictory because he is stating "an ideal power supply", which doesn't exist even in the most expensive equipment.  The problem is that the audio electronics run half from the internal power supply and half from the incoming A/C current.  So anything external will definitely affect the sound (such as power cords, outlets, fuses, UPS).
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sleepwalker had a suggestion with the Eaton UPS.  That will provide 100% coverage (within battery limits).  The only other thing I can think of are the Furman power conditioners with the "current reservoir".  This is a capacitor inside the power conditioner that provides a smoother A/C voltage when there are dips in the incoming A/C current.  It may help fight the "hiccups" you are experiencing, but it will not do anything for the outages.  Two examples are Furman Elite-15 PFi ($750) and Furman Elite-20 PFi ($1299).

Why not check out a PS Audio Powerplant? It regenerates the incoming line voltage and produces a new clean sine-wave for your components.
  It regulates voltage, cleans dirty power from the grid, and lowers the noise floor.

Looks like those start at about $5k. That's a bit steep. Is that the only thing that actually works? 

A good UPS will cost somewhere in the neighbourhood of $1000 to $1500, depending on inverter output quality, battery capacity and inverter capacity. I was able to score a few surplus 1500VA Eaton 9130’s with one string of batteries (all you really need for hifi) for $250 each. It’s all time and place. The 9130 has 9-factor power quality correction (surges, brownouts, phase, blackout, transient noise and others), and produces the vitally important perfect sine wave output, free of harmonics. Just keep your ear to the ground on fleabay and Kijiji for similar deals.