I'm using a mod (RemoteTech-v1.5.1) that requires communication link networks to be established.  The easiest way to do that is to orbit 3-4 satellites in equatorial orbit around Kerbin at approximately the same orbit period and spaced apart.

Current testing of the Valkyrie III line of communication satellites reveals a problem with battery reserve power.  Reserve battery is 610 units large and it runs out of electrical power while passing behind Kerbin (first estimate is approximately 2/3 through the transit).  That means periodic blackouts during at least part of their orbit and they will not be able to link to the other units in the solar system.

Valkyrie satellite is at around 506-510k meters altitude (Ap/Pe).  Orbit velocity is approximately 1785 m/s.  Kerbin's diameter is 1.2 Mm.  To cross 1.2 Mm at 1785 m/s takes 673s.  Approximate orbit time is 64.5 minutes.

Planned power usage is (2) Comms DTS-M1 running (0.82/s each), (1) Communotron 16 (0.13/s each), and (1) Reflectron DP-10 (0.01/s).  That gives a total of about 1.78/s - so the 610 units in the battery lasts for only 343s (of the ~673s transit, oops!).

So in order for things to work correctly, I need around 1400 battery power, plus enough solar cells to recharge the batteries before each dark side pass.  A stack of seven Z-200 Rechargeable Battery Bank would do the job.  Definitely not the most cost efficient, but they are available early on in the tech-tree.

Planned payload (est. cost of 7810):

(1@60) DP-10 - 500km range (used for launch)
(1@300) C16 - 2.5 Mm range (activated at 80km altitude)
(2@600) DTS-M1 - 50 Mm range (one pointed to KSC, one to "Active Ship")

(18@100) OX-STAT PV Panel
(7@360) Z-200 Battery Packs
(1@600) Small Inline Reaction Wheel

(2@425) FL-T200 Fuel Tank
(1@750) LV-909 LFE

Lower stages (est. 9750 recoverable, 1950 non-recoverable):

(1@400) TR-18A Stack Decoupler
(2@700) Mk2-R parachute
(4@850) FL-T400 Fuel Tank
(1@950) LV-T45 LFE
(6@600) TT-38K Radial Decoupler

(6@325) RT-10 SRBs (disposable)

That puts the total lift costs at around 20280 including fuel (19510 dry).  This is a successful design that seems to work well for the purpose, but I will need to test it out with the (7) battery packs instead of just (3) packs.  Still, that's only 40kg on top of 5705kg launch weight, so it won't affect things.

Naturally, I'm low on funds at the moment in career mode after launching (5) of the Valkyrie III series.  So I will need to go complete a few contracts, then launch a few of the Valkyrie IV line of communications relays.

Additional lessons learned:

The number of OX-STAT PV panels that you will need is an art and not a science.  You need to assume that your satellite will be in the worst possible configuration to get power (engine towards the star).  My designs with 18 or 24 panels and a 1.8/s drain often resulted in an orbiting brick.  No power to do anything with it at all, even if it had a line of sight to the ground station.

For the Hermes line of 1.5Mm relay stations, I'm going with (36) PV panels.  Twelve are on the sphere of the Stayputnik Mk I, the other (24) are at the bottom of the T400 fuel tank that is used for maneuvering fuel.  These also have about 2200 units of battery capacity.

After putting a satellite into orbit and before leaving it alone for a while, I reorient it to be side-on and "vertical" to the star.  Then I leave the SAS running in hopes that it will stay mostly oriented properly to the star.

If your satellite does run out of power you either have to wait for it to (eventually) turn around as it orbits, or send out a Kerbal on a EVA to push it around.  A satellite that has its engines pointed at the star should slowly get back into a side-on position as it makes its way around the orbit.

Advanced Comm Satellite Theory:

#1 - You always need a Reflectron DP-10 to get off the launchpad and downrange into space.  It only has a 500km range, so you will want to deploy other antennas as soon as possible once you hit 75km altitude (out of the atmosphere).  It only pulls 0.01 EC/s, which is very minor.

#2 - You always need a Communotron 16 running.  This is a 2.5Mm (25km) range that draws 0.13 EC/s.

#3 - Ideally, you should have (3) Comms DTS-M1.  One to link to KSC when it is in view, two to link to the other two equatorial orbit satellites.  These are directional and have a range of 50 Mm (50000 km).

#4 - You should have one Reflectron KR-7.  This should link to the actively piloted vessel.  KR-7 is directional with a range almost twice that of the DTS-M1 (90 Mm or 90000 km).

That's (4) running at 0.82 EC/s, plus the Comm 16 running at 0.13 EC/s plus the DP-10 at 0.01 EC/s. For a total draw of 3.42 EC/s.  Assuming 3.5 EC/s, a 1000km altitude orbit will require 2900 EC of reserve battery power.  A synchronous orbit at 2868.75 km requires 4200 EC of reserve battery power.