This paper presents a tool to robustly allocate the allowable operating zones of active and reactive power trading margins for multi energy storage systems (ESSs) without violating typical distribution system constraints. This tool helps the distribution network operator (DNO) to facilitate ESS safe participation in day-ahead active and reactive power markets. It estimates the required ESS reactive power support to keep safe voltage margins. In order to avoid conservative results, an uncertainty budget designed by a fuzzy expert is imposed on the uncertainty domain. Case studies on one hundred different uncertainty scenarios are conducted on a real 41-bus Canadian system. Simulation results have shown that the proposed algorithm provides robust operating zones for ESSs with less conservatism.