This paper presents the concept of an advanced rail balancer (ARB) for next-generation traction substations (TSSs), along with its control algorithm based on a novel advanced resonant controller. The ARB utilises a cascaded H-bridge (CHB) converter topology and is designed to effectively address several key issues in modern TSSs, including load current symmetrisation in the distribution power grid, reactive power compensation, harmonic currents from railway vehicles and active filtering of higher-order harmonics in the grid current. The proposed asymmetric control of the ARB converter includes individual ARB phase current control using an advanced resonant controller. The resonant controller algorithm provides the desired frequency response without offset and uses direct latency compensation to mitigate the effects of low switching frequency and large control sampling times. Experimental results show very good performance of the proposed control algorithm, especially for grid current harmonics filtration with low ARB switching frequency, large sampling times and control latency.