This work presents the design of a control law based on the average model of a shunt active power filter considering an H-bridge neutral point clamped topology and its experimental validation. Therefore, the proposed controller is formed by three control loops, namely current (inner), regulation (outer), and balance control loops. The current loop aims to compensate both the displacement power factor and the harmonic distortion produced by nonlinear loads connected to the point of common coupling. To deal with harmonic current distortion, the current loop involves an adaptive mechanism based on a bank of resonant filters tuned at odd harmonics of the fundamental grid frequency. The regulation and balance loops are aimed to maintain the voltage of the capacitors forming the DC-link at a desired constant level. For this, proportional-integral controllers are designed. The design of all three loops considers the average model of the system. The performance of the proposed multi-loop control law is evaluated through numerical results and real-time experimental implementation, both considering a 2 kW academic benchmark with a constant switching frequency of 7 kHz. In order to provide harmonic distortion, a nonlinear load based on an uncontrolled diode bridge rectifier is considered. Additionally, step-load changes from 0.5 kW to 1 kW are considered for the nonlinear load. As a result, a suitable current tracking, voltage regulation, and balance are observed despite parametric uncertainties, load variations, and harmonic distortion. As a consequence, in steady state, simulation results indicate that the compensated grid current THD is 1.75%; meanwhile, the nonlinear load current THD is 52.5%. Experimental results indicate that the compensated grid current THD is 2.32%; meanwhile, the nonlinear load current THD is 53.8%.