This paper presents a current controller for the single-phase grid-connected modular multilevel converter of 2n + 1 levels. The controller is designed based on the mathematical model of the converter. It has the aim of injecting an almost pure sinusoidal current with a proper phase, despite the low-frequency harmonics present on the grid voltage. Also, a loop for the circulating current is developed to keep this variable close to a constant value for proper internal operation of the converter. The overall current controller comprises injected and circulating current loops. Out of these loops, a voltage reference for each converter arm is built, which is then used in a phase-shift carrier-based pulse-width modulation to generate the switching sequences. These are then used to command the modules conforming the converter. Experimental results in a 7-level modular multilevel converter (n = 3) operating under harmonic distortion in the grid voltage are obtained from a hardware-in-the-loop test bench to validate the performance of the proposed current controller. n, number of cells in one arm of MMC; L, inductance of each arm; i P , i N , upper and lower arm currents; E, DC-link voltage value; v S , distorted grid voltage; e P , e N , total inserted voltage for the upper and the lower arms; v Ci , i-th (i ∈ 1, … , 2n) capacitor voltage of MMC; u i , i-th switching signal of MMC; C, capacitors' capacitance; z i , capacitors' scaled energy; i 0 , injected current to the AC side; e D , difference between the produced voltages of the lower and the upper arms; i T , circulating current; e T , total voltage produced by the upper and lower cells; z P , z N , upper and lower cells' scaled energy; z T , total scaled energy stored in the upper and the lower cells; z D , difference between the scaled energy of the upper and the lower cells; 0 , fundamental frequency of the grid voltage; i * 0 , reference for the injected current; P 0 , constant load power reference; v S,RMS , RMS value of the grid voltage;v S,1 , estimation of the grid voltage fundamental component; t, time; i * T , reference for the circulating current; e * D , e * T , steady-state expressions for e D and e T ;ĩ 0 , error of the injected current loop; D , harmonic disturbance in the injected current loop; R D , damping gain of the injected current loop;̂D, estimate for the harmonic perturbations grouped in D ; k, odd harmonics number; D,k , estimation gains for the resonant filters; s, complex variable; f 0 , fundamental frequency (in Hz) of the grid voltage; T kr , desired response time for each harmonic component; i0

Summary A controller based on the model is presented for a single‐phase grid‐tied inverter of 2N + 1 levels, which is based on the modular multilevel converter (MMC) topology, where N is the number of cells per arm. This is referred to as an MMC‐based inverter in this paper. The controller has the purpose to assure a good performance of the converter operation both internally and during grid connection. For this, the proposed controller involves four control loops, namely, overall energy regulation, energy balance between arms, circulating current, and injected current loops. Notice that the proposed controller by itself guarantees voltage regulation at the arms level only. To guarantee individual regulation of each cell capacitor voltage, the proposed controller is then combined with the phase‐shifted carrier‐based pulse‐width modulation (PSC‐PWM) scheme. Experimental evidence is exposed to assess the performance of the proposed control scheme. The experimental setup considers a grid‐tied inverter based on an MMC of seven levels (N = 3). The proposed controller and the experimental prototype are implemented in a hardware‐in‐the‐loop platform. The experimental tests include responses to step changes in the load power and unbalance in the initial capacitor voltages.