This paper analyzes the neutral current reduction performance of a three-phase four-leg solid state transformer (SST) under different degrees of unbalanced load. Several kinds of control strategies are presented, such as the neutral current elimination controls that rely on phase shifting, voltage amplitude, phase shifting, and voltage amplitude combination control. A neutral current minimization control, which ensures the SST output voltages complying with the EN 50160 output voltage unbalance standard, is also developed. These control approaches simply build on the balanced voltage control providing voltage references which slightly unbalance the voltage amplitude and phase angle or both. The effectiveness of the proposed strategies is validated through tests on a downscaled prototype. Simulation results for the neutral current minimization control of the SST applied to a real urban distribution network with distributed loads are presented. The results of this analysis show that overall the neutral current minimization results in an energy saving from both reduced losses in the distribution cables and reduced power consumption in the load.