How can I safely install drywall anchors around an electrical panel?
If your hollow walls do not have wooden studs, the studs are most likely steel (at least in the US).

You are right to be concerned about the extensive wiring near an electrical panel. Numerous wires may be exiting in virtually any direction. You could check out where wires exit by turning off the main power switch and then removing the panel face plate. You will be able to see the directions most of the wires follow. Caution! There is still live power coming into the main breaker, even when that breaker is off.

If the wiring is up to code, cables are supposed to be recessed from the front edge of the metal stud by at least 1.25 inches (NEC 303.4(D)). This leaves you some room to drill and install anchors in the drywall, although I would avoid drilling very close to the panel (as you suggest).

For extra safety, you may wish to turn off the power when you are drilling on that wall, take care not to allow the drill to penetrate much beyond the drywall and, if you seem to hit anything other than drywall, check to make sure it is not a cable before progressing.

You can mount things on steel studs, but you need special screws, not wood screws. Also, if mounting on steel studs, be sure the screws are not so long that they penetrate the steel more than about 1/2 inch at most (longer provide no additional holding power in steel studs).

While steel toggles and expanding anchors should not hit wiring if it has been properly spaced, consider the plastic expanding type if you want additional safety. 



I would avoid the tubular type plastic anchors except for the lightest of loads. And do not use the steel hammer-in type anchors!

Note: If you think you might have hit a cable, be sure the power is off and call an electrician to check it out before proceeding!

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