See also answers to What technologies enable or at least help satellite operation in Very Low Earth Orbit (VLEO)?
- "powered" means "thrust via reaction mass of some kind being pushed via use of power by the spacecraft continuously, and
- "a continuously varying orbit" means continuously actively altering it's otherwise natural orbit (which already continuously varies due to several effects)
and it seems that they do, then the answer to "How many existing satellites..." is probably zero.
@OrganicMarble points out that:
GOCE continuously thrusted to maintain, not change its orbit.
and links to this answer to What is the most aerodynamic Satellite?
I mentioned that:
...there are groups of satellites that have adjusted their attitude to make their solar panels interact with weak atmospheric drag to either drift slowly forward or backward over time compared to their nominal attitude in order to spread out within their orbital plane after being launched and deployed together. I'm still looking forward to a clarification from you on exactly will or won't count as "powered".
and now remember, I was thinking of the CYGNSS constellation. From How can the CYGNSS spacecrafts (actually) measure ocean roughness?:
above: screen shots from CYGNSS_FactSheet_October2014
They did use a little electrical power to perform attitude adjustments to increase or decrease atmospheric drag mostly from the solar panels, but it was not powered flight.
From this answer to Rocket to launch 8 cubesat to LEO at an equidistant distance:
Here is an example of a simulation of the use of alternating between high and low drag configurations to achieve equal spaced phasing and then to maintain it using small station-keeping drag adjustments:
Figure 8: Time-discretized high-drag commands are assigned to achieve desired slots (b) with commands
Figure 9: Attitude modes of Dove satellite enable large drag area ratios (a) Orthographic projections with cross-sectional areas. (b) High-drag and low-drag attitudes
But I could be wrong!
If someone thinks of something that meets your criteria, or something new is put in space that does, then new answers can be posted.