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I have run the same calculation twice but they differ only in nbands
ALAT = 5.1690000000
k-Points NKPTS = 120 number of bands NBANDS= 60
energy without entropy= -61.901061 energy(sigma->0) = -61.901061
ALAT = 5.1690000000
k-Points NKPTS = 120 number of bands NBANDS= 31
energy without entropy= -61.915859 energy(sigma->0) = -61.915859
the calculation with 31 bands is lower, but I would assume that the calculation with 60 bands should be more accurate. Which energy is correct? Is it possible for a converged energy to be too low?

This depends not only on the number of bands but also the energy cutoff and the number of k-points are important quantities.
Taking into account more (empty) bands and a higher ENCUT may improve the description of your system. Too few bands and k-points might result in wrong total energies (which can be lower than a converged solution).
You should test the convergence of the total energy for your system with respect to these.

I should have added that at a slightly different lattice constant I converged the energy with respect to Kpoints and encut (prec=high encut=750). In addition these are computed with ialgo=48. If I switch to algo=normal nbands=31 and =60 get the same result as ialgo=48 and nbands=60. To follow up on your comment, given that my two calculations have the same kpoints and encut, which should be converged, is it possible to get an energy too low due to the choice of nbands?

Yes, at least I would not exclude this possibility ... but this might also depend on your system. I know some cases, where the choice of NBANDS is crucial.

please have a look at the 'Theoretical background' chapter of the online manual, to see why especially the RMM-DIIS algorithm is very sensitive to the number of unoccupied bands (a sufficient number of them has to be included to provide enough degrees of freedom for sub-space diagonalisation in the sub-space spanned by the trial wavefunctions)
http://cms.mpi.univie.ac.at/vasp/vasp/node180.html

i did read that section and I understand about insufficient degrees of freedom, but my confusion is that the correct value is above the incorrect value. If I use the Davidson approach, I can see how I can converge to an excited state, i.e. too high an energy, but I could not get too low an energy. I guess the bottomline is that RMM-DIIS should be used with caution.