I have an earth-like world orbiting an M7 red dwarf on the outer edge of the habitable zone(0.0443AU). Since red dwarfs emit more infrared light than visible light, solar panels would probably not be as efficient.
Assuming that a civilisation around it builds a space station the size of the ISS, how much more solar panels would be needed to generate enough power for it? Would a civilisation around a red dwarf even develop solar panels or would they use a different energy source entirely?
In the absense of the fancy chemistry required to make narrow-bandgap photovoltaic cells, you can always use solar thermal instead. Here's a nice ilustration of von Braun's proposed space station:
(wikimedia info. Original artist Chelsey Bonestell.)
There are no photovoltaics here, because this proposal was made in '52 and solar cells in space didn't arrive til '58. Instead, at the "top" of the ring you can see a circular collector with a parabolic cross section. The white line along the bottom of the collector is a mercury tube. The parabolic concentrator focusses sunlight on the tube, which heats up and produces high pressure mercury vapor which you can use to run a mercury gas turbine which in turn drives a generator. You'll need big radiators to condense the mercury for the next cycle.
There's scope to improve this technology too... here's a 1988 NASA report: Solar dynamic power system definition study. Solar-heated Stirling engines present the opportunity for lighter and more efficient power generation than turbines or the then-available photovoltaics. Around a red star, there'd be little competition for this kind of power generation until much more advanced material science arrived.
As a handy side-effect, this kind of power generation requires somewhat more hands-on maintenance than handy solid-state solar panels, being rather more complex and having a lot of moving parts. This can justify a human sapient biological presence in space, whereas around Earth solar power combined with microelectronics meant it made a lot more sense to keep the meatbags on the surface.
I read this a few days ago. It more or less is a complete answer.
A recent study in Scientific Reports looked at the efficiency of solar panels under a range of stellar spectra, particularly comparing the sun and Proxima Centauri. Their study focuses on organic photovoltaics (OPVs), which are both light and flexible.
You can tune the band gap of OPVs. The team found that while a wider band gap works well for sunlight, the light of Proxima Centauri would require a narrow band gap. For example, a simulated wide band gap solar cell has a theoretical efficiency of 18.9% for sunlight, but only 0.9% for Proxima Centauri. In contrast, a narrow band gap model has a theoretical efficiency of 12.6% for Proxima Centauri.
Whether it's a red dwarf, A yellow dwarf (Our sun) or a supergiant ALL stars are White in realistic space.
The solar energy they produce via their intensity, would only require a distance change. a weaker star requires closer proximity. The Photovoltaic effect converts visible light and Some IR into power.
Also Photovoltaic may not be needed. Parabolic mirror reflectors, multiple units can yield thermal energy to an engine generator either a turbine or a stirling. 
There are smaller than one way to generate solar energy in space. Solar electric, which we call solar panels is one way. Solar thermal, using the heat of the solar energy was already mentioned. An option that I think might actually be dominant for space-based civilization is thermao electric. Here we use heat to directly produce energy.
You are discussing settling a red dwarf star. The first issue that comes to mind is that those are often flare stars that can experience mass ejections which can raise their brightness and energy output by orders of magnitudes. We don't quite understand why this happens and young ones are usually more active, but we have seen very old ones still do occasional flaring. In a way occasional flaring is actually worse. If you have massive flares every other day, your infrastructure is built for this. If you have a massive flare every thousand years, this is an existential risk to your civilization.
The next factor is that it outputs most of its energy in the infrared as you already mentioned.
Furthermore, if one wants to do energy production for an advanced civilization, one must understand the geometry of the situation one is in. Basically, your source of life is a spherical hot object. Given that this object gives off its heat as radiation the intensity of this radiation scales with the inverse of the distance squared. As an example, consider that sunlight at Earth has a strength level of one. If we move out to double this distance, we don't have half the sunlight, we have one quarter. Conversely, if you move into half the distance, you have four times the energy. At 1% of the distance, you have 10,000 times the energy.
Luckily, we can transmit energy much more efficiently than light just spreading out from the sun. The laser beam can be or target for several astronomical units. If one works with ultraviolet laser frequencies, putting 50 m mirror relay stations every few astronomical units will give you a powerful space-based energy grid. This is how you actually do space-based solar correctly. You place generator stations as close to the sun as you can get away with. They generate lasers, those lasers transport the energy to receiver stations elsewhere in the system.
The economics of this are amazing. Imagine that only 1% of the solar input actually ends up as usable energy where you need it. If we now put our generator at the 1% off the distance between the Earth and the Sun, we still get the same energy from this generator as we would have gotten from 100 generators in the position where we we'll have our infrastructure. And I think realistic efficiency rates for the system are probably between 30 and 60%.
In this situation, thermo-electric elements make sense. They are relatively inefficient at low temperatures, but if you get them to several thousand Kelvin, they become impressively efficient. Cheap mirrors and a close distance to the star can easily create the temperature of the stars surface on your generator. Expect efficiencies between 70 and 90% here.
Notably, those systems are also more flare resistant than the alternatives. There are no moving parts unlike in thermal electric systems. They don't require complex material science, unlike solar panels.
Given your risk of flares, you likely want warning systems. Your power satellites are likely grouped together in tight constellations. If your solar monitors detect the flare is incoming, you maneuver them behind each other. One satellite in the constellation is a hydrogen storage tank with a tungsten shield. This shield has little holes in it. For the duration of a flare, we hide the satellites behind this one and slowly bleed hydrogen through the shield to keep it cool.
Alternatively you could of course consider your power satellites disposable and just launch new ones. If you have self-replicating machines, this might actually be the economical option. A big advantage of using lasers to transfer the energy out to your habitat stations, is that you don't lose as much in the case of a flare. You'll probably want backup systems for energy. A simple solution would be to rotate the counter rotating shells of your habitat stations slightly faster. Built a generator in there. You will probably only lose a few percent of gravity if you run your habitat off its own rotational energy for a few days or even weeks.
If you find that solar energy is too much of a hassle or a danger, gravitational energy can also be used. Pick one of the outer planets or a big comet. Place a mass driver on it. Shoot rocks off this planet and target a place near your infrastructure in the inner system. The rock will develop a lot of kinetic energy falling into the gravity well of the Sun. Have it impact a target big enough to vaporize it and The Rock. Do this within a magnetic fields and the resulting plasma will generate electricity for you.
