None of the example shots involve anything approaching "big production" lighting.¹ As far as I can determine, the largest modifier used in any of the shots would be something in the 70-80cm range — certainly no more than 100cm — and not particularly soft for its size either. A large beauty dish, small softbox or a small octa — even a small "hot" umbrella — will get you there.
The first set uses a small source from behind, about 45 degrees left and about head-height for a rim. That could be a standard reflector on a studio flash; it could be a bare speedlight (either zoomed all the way out or using a Sto-fen to get the spread). The main light is front left and low, almost on the ground. It's softish (as described above) but not nearly big enough or soft enough to make the shadows indistinct. The angle of wrap-around is small enough that about half of the torso's width is in full shadow on the wall. When you consider that the right side of the shadow begins when the left edge of the light is blocked, and the deepest shadow occurs when the entire light is blocked, either the light isn't particularly large or it is a (relatively) long way away.
The second set looks like it's using window light. Whether that's actual window light or a simulation thereof is another question altogether. It falls of rather quickly though, and you can simulate this light (if necessary) with a moderately sized softbox or umbrella. Or a bedsheet (or, if you need to spend money, something like a butterly silk, grid cloth or diffusion panel) over the window and a speedlight or flash head outside if there is a window but the sun and sky aren't cooperating.
The third looks like a beauty dish or a large fresnel high and right to me (and, again, the part of a beauty dish may be played by a small softbox or a small hot umbrella in your version), or perhaps a small skylight or high dormer window. The fourth could be stark sunlight above and behind the photographer's head, or a gridded reflector (no bigger than a beauty dish) coming from the same angle (which would be in keeping with the vignette — but then the vignette might have been added in post).
So there's nothing here you can't do with moderately-priced equipment (speedlights or entry-level studio flash, perhaps with battery power for location shooting if a generator isn't practical). Or with $20K worth of Broncolor equipment either, for that matter. But large modifiers and multi-kilowatt lights to feed them are not what you need. Go smaller, and be more careful with the placement of your lights.
¹ That's not to say that high-end equipment wasn't used; just that truckloads of unwieldy gear aren't necessary to get these shots.