A current controller for the modular multilevel converter operating under distorted grid voltage

Abstract

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

A model‐based controller for a single‐phase grid‐tied modular multilevel inverter with regulation and balance of energy

“…Therefore, the control scheme proposed here represents a more complete solution. As a consequence, not only the structure of the proposed controller differs with respect to that of Catzin Contreras et al, 25 but also the waveform of the circulating current suffers slight changes as it will be shown in the experimental results section.…”

“…The circulating current, as already defined in Catzin Contreras et al, 25 is obtained by adding the currents in the upper and lower arms, ie, i C ≜ i H + i L . The sum of Equations 1 and 2 gives model (7), which describes the dynamics of i C :…”

“…The present work represents an extension of Catzin Contreras et al, 25 where a simplified model was considered, that is, the capacitors on each cell were replaced by simple constant DC sources. The work in Catzin Contreras et al 25 only focused on the control of the output and the circulating currents, as there was no need to regulate nor balance the voltages in the DC sources.…”

“…The present work represents an extension of Catzin Contreras et al, 25 where a simplified model was considered, that is, the capacitors on each cell were replaced by simple constant DC sources. The work in Catzin Contreras et al 25 only focused on the control of the output and the circulating currents, as there was no need to regulate nor balance the voltages in the DC sources. In contrast, the control scheme proposed here includes mechanisms to guarantee the balance of the cell capacitor voltages in addition to the control of the output current and the circulating current.…”

“…The experimental tests include step changes in the load power and initial conditions considering unbalanced capacitor voltages to demonstrate the effectiveness of the voltage balancing mechanism. For the sake of comparison, the controller in Catzin Contreras et al 25 has been implemented, and both the circulating and the output currents responses are compared with those obtained with the proposed scheme.…”