In this paper, we investigate the management of energy storage control and load scheduling in scenarios considering a grid-connected photovoltaic (PV) system using packetized energy management. The aim is to reduce an average aggregated system cost through the proposed packetized energy management controller considering household energy consumption, procurement price, load scheduling delays, PV self-sufficiency via generated renewable energy, and battery degradation. The proposed approach solves the joint optimization problem using established heuristics, namely genetic algorithm (GA), binary particle swarm optimization (BPSO), and differential evolution (DE). Additionally, the performances of heuristic algorithms are also compared in terms of the effectiveness of load scheduling with delay constraints, packetized energy transactions, and battery degradation cost. Case studies have been provided to demonstrate and extensively evaluate the algorithms. The numerical results show that the proposed packetized energy management controller can considerably reduce the aggregated average system cost up to 4.7%, 5.14%, and 1.35% by GA, BPSO, and DE, respectively, while meeting the packetized energy demand and scheduling delays requirements