What is the power rating of the ground power unit for Bombardier Dash 8 Q400?
Specific information about requirements is difficult to find. However there is some information that is readily available concerning the Q400 and available ground power units.


The Q400 can start its engine with the onboard batteries, thus the necessary power requirement would not be nearly as big as with the A320 series.
Ground Power Units are usually supplied in 7,5, 15, 30, 60, 90, 120, 150 and 180kVA configurations
The Q400 is listed to have two TRUs which can output maximum of 300A 28VDC from a 115VAC (~73A) source. Source: Q400 Eletrical This would equal to a 90kVA Ground Power Unit, which according to Power Systems International provides 72A.
The Q400 has one 45kVA electrical generator per turbojet.
According to the Q400 Electrical document the Q400 has 24-volt NiCad batteries; Main and auxiliary, which both total to 80Ah.
The same document also states that the Q400 External Power Protection Unit does not monitor amperage, thus will not monitor total power. Some other system related with engine starting will most likely still monitor total power.
Aviation New Zealand provides the following details:



  "Small business jets fitted with 115 V 3 phase systems may be supplied by lower
  power units, typically 7.5 kVA and 15 kVA. Aside from over-power limits, all other
  parameters are likely to be similar to the above. " above=minimum 45kVA (as according to the document is specified in 
  ISO 6858:1982 (E): Aircraft Ground Support Electrical Supplies – General
  Requirements;)


Based on these details I think that the Q400 does not have specific external power requirements. Most likely a minimum of 7.5kVA is still recommended, as that is the lowest powered GPU I could find. However you might end up charging the batteries first, as the 7kW from the GPU might not be enough to start the engines. A 30kVA generator with 150% overload rating for 60 seconds is also most definitely enough since it can provide the exact 45kVA that is provided by the generators already in the engines of the Q400.

The best guestimate calculation I could come up of what the engines need to be started is:


  A320 CFM56 provides about 30000hp max, while the PW100 provides about
  5000HP
      The CFM56 is started by a APS3200 APU, which provides 447hp, of which about 330hp can be used by the compressor equaling to about
  240kW.
      Based on the hp difference of about 15%, we will assume the PW100 requires 
      only 15% of that power to start, which would be 36kW or ~40kVa. 
      Of course not all of the 240kW provided by APS3200 would be required for a     CFM56 to start, so I'm pretty confident that a Q400 engine will start with a 30kVa GPU.


I think in the end it might come up to the question of using the batteries more, thus them needing more maintenance. NiCd usually rated to 1500-2000 recharge cycles, on Q400 and aircraft batteries it is most likely even lower.