The power sharing of PV sets with battery banks in a low voltage distribution network, is optimized with the aim of extending network lifetime. The network lifetime is analyzed using a probabilistic model, in which each PV-battery set has a certain failure probability of supplying power to any load demand center. This probability is assumed to be of normal distribution, that is related to other factors such as power rating, coverage availability, and battery DoD. To extend network lifetime, redundancies in power sharing are removed by activating different groups of PV sets at different times, with durations depending on their joint Gaussian probabilities in supplying the load demands. The contribution of each PV-battery set, is estimated in an intuitive method according to the evaluated probabilities, in which the network is converted into source nodes and load nodes distributed as an ad hoc network, with formulated Gaussian probabilities. An economic load dispatch is then evaluated among the selected PV sets of probabilities higher than a predefined threshold value, to optimize power sharing of the load. A case study of several PV-battery sets supplying several distributed loads, is analyzed and simulated, with formulated joint probabilities. It is found that lifetime is extended by 190% for three PV sets supplying two load centers.