_Article_  
**Power Quality Improvement with a Pulse Width Modulation Control Method in Modular Multilevel Converters under Varying Nonlinear Loads**  
**[PERSON] 1,*, [PERSON] 2(r), [PERSON] 3(r), [PERSON] 4,*(r) and [PERSON] 5**  
1 Department of Engineering and Architecture, The University of Trieste, 34127 Trieste, Italy  
2 UNIDEIM, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal; [EMAIL_ADDRESS]  
3 Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland; [EMAIL_ADDRESS]  
4 Management and Production Technologies of Northern Aveiro--ESAN, 3720-509 Oliveira de Azemeins, Portugal  
5 Faculty of Engineering of the University of Porto and INESC TEC, 4200-465 Porto, Portugal; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS] (M.M.); [EMAIL_ADDRESS] (E.M.G.R.)  
Received: 3 March 2020; Accepted: 5 May 2020; Published: 9 May 2020  
**Abstract:** In order to reach better results for pulse width modulation (PWM)-based methods, the reference waveforms known as control laws have to be achieved with good accuracy. In this paper, three control laws are created by considering the harmonic components of modular multilevel converter (MMC) state variables to suppress the circulating currents under nonlinear load variation. The first control law consists of only the harmonic components of the MMC's output currents and voltages. Then, the second-order harmonic of circulating currents is also involved with both upper and lower arm currents in order to attain the second control law. Since circulating current suppression is the main aim of this work, the third control law is formed by measuring all harmonic components of circulating currents which impact on the arm currents as well. By making a comparison between the switching signals generated by the three proposed control laws, it is verified that the second-order harmonic of circulating currents can increase the switching losses. In addition, the existence of all circulating current harmonics causes distributed switching patterns, which is not suitable for the switches' lifetime. Each upper and lower arm has changeable capacitors, named \"equivalent submodule (SM) capacitors\" in this paper. To further assess these capacitors, eliminating the harmonic components of circulating currents provides fluctuations with smaller magnitudes, as well as a smaller average value for the equivalent capacitors. Moreover, the second-order harmonic has a dominant role that leads to values higher than 3 F for equivalent capacitors. In comparison with the first and second control laws, the use of the third control-law-based method will result in very small circulating currents, since it is trying to control and eliminate all harmonic components of the circulating currents. This result leads to very small magnitudes for both the upper and lower arm currents, noticeably decreasing the total MMC losses. All simulation results are verified using MATLAB software in the SIMULINK environment.  
**Keywords:** modular multilevel converter; control laws; harmonic component; second-order harmonic; circulating currents