This paper proposes a sensitivity-based optimization approach for the energy management and volt/var control of islanded networks powered by a thermal generator and several hybrid power plants (HPPs). Specifically, the method optimizes, in a 24-hour horizon, the active and reactive power of the HPPs, the output voltage of the thermal generator, as well as the settings of local voltage controllers e.g., step voltage regulators, capacitor banks, in order to minimize the generation cost of thermal generators and satisfy the following constraints: a) the technical limits of the diesel generators, b) the maximum direct penetration limits of the renewables, c) the state of charge limits of energy storage systems, d) the three-phase voltage limits of all the buses of the network. Simulations were executed in a modified islanded version of the IEEE 8500-node network, consisting of a diesel generator and multiple HPPs with various renewable generators and storage devices. According to the simulations, the proposed method minimizes the generation cost of diesel generators, while satisfying all the aforementioned technical constraints. In contrast to the existing optimization methods e.g., PSO, MINLP, which are practically inapplicable in large networks with a 24-hour optimization horizon, the proposed method presents very low computation time.