In energy communities with high penetration of renewables, electricity supply can become scarce during certain periods. In such cases, the objective of a resource allocation algorithm can be to minimize the disutility of the worst-off user of the community. This paper presents the problem of finding an optimal max-min fair allocation of available energy. A mixed-integer linear formulation is used to tackle the problem, so that the worst-off user's disutility is minimized. The allocation results are compared to the standard approach that optimizes the system's Social Welfare. The users' disutility function models for electricity consuming devices, are based on their time-under-unsatisfied-demand, which is a measurable and comparable metric and does not rely on the user's self reported valuation for energy consumption.