Load side participation can provide support to the power network by appropriately adapting the demand when required. In addition, it may allow for an economically improved power allocation. In this study, we consider the problem of providing an optimal power allocation among generation and on-off loads within the secondary frequency control timeframe. In particular, we consider a mixed integer optimization problem which ensures that secondary frequency control objectives, i.e. generation-demand balance and frequency attaining its nominal value at steady state, are satisfied. We present analytic conditions on generation and on-off load profiles such that an ϵ-optimality interpretation of the steady state power allocation is obtained, providing a non-conservative bound for ϵ. Moreover, we develop a hierarchical control scheme that provides on-off load values that satisfy the proposed conditions. Furthermore, we study the interaction of the proposed control scheme with the physical dynamics of the power network and provide analytic stability guarantees. Our results are verified with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, where it is demonstrated that the proposed algorithm enables an optimality interpretation of the steady state power allocation.