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With technological advancements and cost reduction， the centralized integration of grid-forming energy storage system has significantly expanded. This integration notably impacts the short-circuit currents of power system， an effect that warrants careful consideration. This paper utilizes an electromechanical transient simulation model for grid-forming energy storage system to examine the amplitude and phase characteristics of short-circuit currents under various limiting strategies. Case simulations are conducted to assess changes in short-circuit currents at nearby buses under different scales of energy storage system integration， overcurrent capabilities， grid voltage levels， and operating conditions. This comprehensive analysis reveals the influence of energy storage integration system on the bus short-circuit currents and quantifies the contribution of grid-forming energy storage system to the short-circuit currents. Based on these findings， the paper offers recommendations for capacity allocation and placement of grid-forming energy storage system， taking into account their impact on short-circuit current levels.