@Alex 11
Hmm, would it be too obvious to point out that:
In order to stop a panel from generating *any* power, you'd need to cover it with a lot of dust.
The arrays would be big. No, let's rephrase that. The arrays would huge. Massively so. We're not just talking about a handful of panels clustered together covering a few sq.m of desert.
In order to ensure a consistent power supply around the clock, you'd need arrays distributed all around the globe.
In order to provide a level of redundancy so that arrays can be taken off-grid for maintenance, and to allow for a level of demand growth before additional arrays need to be built, there'd be more arrays available at any moment than would be required just to meet the existing power requirements.
So, short of a massive and sudden dust storm, it'd take a while for normal levels of windblown dust to completely knock out one panel, and even longer to knock out an entire array in a single location. Even if you did then knock out the entire array at location A, the chance that the arrays in locations B, C, D....ZZ9 Plural Z Alpha have also been knocked out is, I would suspect, rather slim.
OK, but what if today's the day the gods of fate roll snake-eyes and it all goes fruit-shaped? Would it be too much to imagine each panel incorporating a battery backup, so that if it not only loses all of its own power but also any power from the grid, it is still able to perform a few cycles of self-cleaning?
You're also assuming that cleaning dust off a panel requires electrical power... I'd then suggest that an army of Mrs Mopps be held on a state of constant alert by the electricity company, ready to be drop-shipped into the heart of any array beset by excessive levels of dust, armed with industrial sized yellow cloths and beer-keg sized bottles of Mr Sheen. Or, more realistically, you employ groups of locals to maintain the arrays, performing preventative cleaning so that, short of the aforementioned massive storm, the dust levels wouldn't be allowed to build up to the point where it became an issue, and so that, in the event of the aforementioned storm, the dust could start to be cleaned off again as soon as the storm abated.