Sure - see page 5 of the rulebook, in the "Earning Cash" paragraph of the Phase 5: Bureaucracy section:
Earning cash: Starting with the first player, every player indicates
how many cities in his network he wishes (and is able) to supply with
electricity. He earns cash based on the number of cities he powers as
shown on the payment table. A player who does not supply any city gets
10 Elektro (the guaranteed minimum). The players remove the required
resources from the power plants that produced electricity this round
and place the used resources in the resource supply next to the board.
A player may choose (or only be able) to supply fewer cities than he
has in his network. The player is paid only for the supplied cities.
If a player produces more electricity than he has cities in his
network, the surplus is wasted. Every player can choose how many and
which of his power plants he uses, e.g. he does not have to supply all
of his cities.
So you can very much power 6 cities with enough electricity for 10. You just won't be able to store the extra electricity produced for future use (or save yourself any of the resources that it cost you to produce so much electricity).
See also the line "a player may choose to supply fewer cities than he has in his network. The player is paid only for the supplied cities." It seems pretty clear to me that you can undersupply your cities if you want, strange though such a course of action might seem!