I'm allowing for approximately 150 years of technological advancement. This is in Earth's future, so I want to be realistic based off of what we are capable of now and projections for declining resources in the future. The space station is orbiting Earth, but at a distance, and doesn't rendezvous with the surface, so it can't refuel. Would solar power be adequate to sustain life support and other systems?
I can think of at least four power sources:
1) Solar Power, which is used in the International Space Station. Solar panels are, however, vulnerable to micrometeorites and fast ionized particles in the solar wind, but it would be possible to have microrobotic repair systems.
2) Catching He3 from the solar wind for fusion power. Since this He3 is ionized, it is possible to catch it with a magnetic field, similar to how a Bussard ramjet would catch ionized hydrogen (which might also be used, though pure hydrogen fusion is more difficult than He3 fusion). A magnetic field would be less vulnerable than a solar panel, and it might even protect the space station itself from fast ionized particles.
3) Using a giant wire loop to harvest energy as the station moves through the Earth's magnetic field (as described in David Brin's short story "Tank Farm Dynamo". This, however, has the side effect of slowing the station's orbital speed, leading to a slowly deteriorating orbit. Hence, it would only work in combination with something like a solar sail that adds speed to the orbit at the same rate. This solar sail could double as a solar panel, with the vulnerabilities mentioned above.
4) Power beamed from the surface as microwaves (assuming there is still a civilization on Earth). Microwaves have been suggested as a way to beam solar power from orbit to the Earth's surface, so would obviously also work in reverse. A microwave rectenna would be far less vulnerable than solar panels.
In terms of energy, solar is the way to go.
All the energy stored chemically and kinetically in all the planets, comets and asteroids together pales in comparison with the energy stored and provided by the sun.
If you haven't already familiarized yourself with the Kardashev scale, now is a good time. This is a paper from 1964, widely popular in science and sci-fi. One of the conclusions here is that if you are near a star, you should go solar - if you are using any other power source, you are likely primitive.
However, do take note of Shadowzee's answer - your energy source may be abundant, but nothing else will be. If you require continuous human occupation of the station you need to either constrain the timespan of the mission, or handwave where the food and water are coming from. Also the air slowly leaks away into space - in real life, a resupply mission usually includes some amount of atmospheric gases as well.
No. It's not about being able to have enough energy. There would simply not be enough resources available for a closed system like a space station to sustain itself. They would need to recycle their air, water and waste perfectly to ensure the system could sustain itself. They would not be able to support a large number of additional life, like children due to the limited resources or expand their living structure.
Parts wear out, things need to be fixed, you need to go outside. Things will be wasted. And since they can't recover them from the surface they are doomed once they run out of supplies eventually.
So power is the least of your worries. You need raw materials. Protection from micro comets. And some form of entertainment and exercise on board so your astronauts don't go mad with boredom.
If the space station is designed and built 150 years in the future there is a strong probability that fusion power will be perfected by then.
Presumably the water supply on the station will be extra large and will have more water than is needed for other purposes, so that from time to time some of the water will be broken down into hydrogen and oxygen and the hydrogen will be sued a a fusion fuel for the fusion power generator.
Presumably the space station will also also have giant solar panels for electricity, and maybe a giant mirror to focus sunlight to heat water for a steam turbine to generate electricity, so the station can use either solar power or fusion power or both at the same time.
And possibly your "space station" is actually a space habitat, a sort of space city with a population of thousands. If you are not familiar with concepts of space habitats you might want to learn about them. And if that space habitat was provided with space ships when it was built, it may sometimes send expeditions to rendezvous with asteroids and comets to bring back raw materials to be used by the habitat's 3D printers to make objects and replace matter lost from the habitat.
The amount of energy and thus fuel needed to rendezvous with an asteroid or comet tens or hundreds of millions of miles away and return with cargo might be far, far less than that needed to land on Earth just a few thousand miles below and take off again with supplies for the space station.
Fission would be perfectly viable in 150 years. We have existing systems that fit onto submarines and military ships now. Assuming realistic physics, fission will give you all the power you need or could want, up to the limits of how well you can afford to cool your reactor in space. I would assume active cooling, where heat is pumped into the radiators, not just passive cooling.
The basic objections on Earth and in the modern era to fission can be broken into two categories: Technological, which can probably be overcome in 150 years, and questions around handling waste. But if we're in space to that extent in 150 years, handling waste is easy. Earth may not be full of places we feel like we can stick waste, but space is. Space is already an irradiated wasteland, we can't really make it worse in that regard. Plus, we should not assume in 150 years that the same social attitudes are in play; if a space civilization literally depends on generating power to survive, they may have somewhat different opinions than those people on Earth who can afford to turn off all their machines and go stand outside, where clean water literally falls into their mouths if they wait long enough. That's not how it'll work in space.
Solar Thermal is the future
Don't forget solar power is not limited to photovoltaic collection. A water-based solar thermal plant which focuses unlimited solar energy using simple light-weight reflectors can generate massive amounts of mechanical energy which can be used to power low-tech electricity generating turbines as well as machinery such as hatches and tools. Since your station is isolated its water supply would have to be closed-loop which would not be a problem for internal steam circuits. Leakages of non-toxic water would simply be recollected by the environmental systems. Steam circuits would require heat radiation elements which could simply combine with the stations climate control coolant loops. In an extreme emergency steam could also be used as a propellant to alter the station's orbit.
Steam power technology isn't sexy so it rarely makes it into sci-fi milieus. But in reality it would be a smart use of simple physics for space-based colonies.