Energy Syst DOI 10.1007/s12667-016-0217-5 ORIGINAL PAPER Second order sliding mode control of three-level four-leg DSTATCOM based on instantaneous symmetrical components theory Saber Bouafia 1 · Abdelkader Benaissa 1 · Said Barkat 2 · Mansour Bouzidi 1,3 Received: 23 December 2015 / Accepted: 1 August 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract In this paper, a second order sliding mode controller (SOSMC) is proposed to control a three-level four-leg DSTATCOM connected to three-phase four-wire dis- tribution system. The controller is designed in synchronous reference frame using super twisting algorithm based on symmetrical components theory. The proposed DSTATCOM control is aimed for the power factor correction in both capacitive and inductive operation modes. It has also purpose the regulation of excessive neutral cur- rent in the fourth wire of the distribution utility system under unbalanced loads or asymmetrical fault in the grid cases. This paper also presents a simplified three-level three-dimensional space vector modulation (3DSVM) with DC-bus capacitor voltages balancing strategy based on the effective use of the redundant switching states of the inverter voltage vectors. The effectiveness and validity of the proposed SOSMC sys- tem and 3DSVM are maintained by computer simulation. From simulation results, the comparison between the SOSMC, first order integral SMC, and conventional PI con- troller shows superiority of the SOSMC with high performance under both dynamic and steady state operations even in worst cases such as fault and unbalancing loads. Keywords Three-level four-leg DSTATCOM · Three-phase four-wire distribution system · Second order sliding mode controller · Three dimensional space vector modulation B Saber Bouafia bouafia.saber@gmail.com 1 Intelligent Control and Electrical Power Systems Laboratory (ICEPS), Djillali Liabes University, 22000 Sidi-Bel-Abbès, Algeria 2 Department of Electrical Engineering, Electrical Engineering Laboratory, University of Mohamed Boudiaf, 28000 M’Sila, Algeria 3 Department of Electrical Engineering, University of Kasdi Merbah, 30000 Ouargla, Algeria 123