Three-phase four-wire (TPFW) distribution systems are prone to various power quality (PQ) issues, such as voltage fluctuations, poor power factor, unbalanced load conditions, and the presence of harmonics in current. Mitigation of these PQ problems using appropriate shunt compensator requires advanced control algorithms for control of three-phase voltage source converters (VSC) in a distribution system. In this paper, Chebyshev functional expansion based artificial neural network (ChANN) algorithm for shunt compensation using distribution static compensator (DSTATCOM) is proposed. The parameters of ChANN are trained in real time. Implementation results with linear and nonlinear loads are demonstrated on a prototype hardware designed and developed using dSPACE 1104, current and voltage sensors for the realization of DSTATCOM for TPFW system. A zigzag transformer is used along with conventional three-phase, three-wire (TPTW) DSTATCOM to reduce its overall rating. Suitable comparisons with conventional control techniques are also mentioned.