Many appliance identification systems use harmonics of current signals as features. However, the choice of the order and number of relevant harmonics for appliance identification task has never been demonstrated. Here, we propose to tackle this issue by analysing the relevance and redundancy of harmonics for this task using feature selection algorithms based on mutual information criterion. Six heuristic strategies based on this criterion were implemented and their selection results from high-dimensional feature vectors were compared. For the choice of a minimal subset of relevant harmonics, we propose a stopping criterion in the selection procedure. In order to validate the selected subset of harmonics, a hidden Markov model based-classifier was used and evaluated on PLAID dataset. Results highlight odd order harmonics relevance. Furthermore, the feature subset {1,2,3,4,5,7,9} was selected by three strategies as strongly relevant since this minimal subset is sufficient for essentially explaining appliances' signatures.