Received March 2, 2021, accepted March 27, 2021, date of publication April 5, 2021, date of current version April 14, 2021. Digital Object Identifier 10.1109/ACCESS.2021.3071198 Mitigation of Complex Non-Linear Dynamic Effects in Multiple Output Cascaded DC-DC Converters SAJJAD AHMED 1 , (Graduate Student Member, IEEE), SYED ABDUL RAHMAN KASHIF 1 , NOOR UL AIN 1 , AKHTAR RASOOL 2 , MUHAMMAD SOHAIB SHAHID 1 , SANJEEVIKUMAR PADMANABAN 3 , (Senior Member, IEEE), EMRE OZSOY 4 , (Senior Member, IEEE), AND MUHAMMAD ASGHAR SAQIB 1 1 Department of Electrical Engineering, University of Engineering and Technology, Lahore 54890, Pakistan 2 Department of Electrical Engineering, Sharif College of Engineering and Technology, Lahore 55150, Pakistan 3 CTIF Global Capsule, Department of Business Development and Technology, Aarhus University, 7400 Herning, Denmark 4 Research and Development Design Center, Danfoss Drives A/S Ulsnaes 1, DK-6300 Graasten, Denmark Corresponding author: Sajjad Ahmed (sajjad.ahmed@uet.edu.pk) ABSTRACT In the modern world of technology, the cascaded DC-DC converters with multiple output configurations are contributing a dominant part in the DC distribution systems and DC micro-grids. An indi- vidual DC-DC converter of any configuration exhibits complex non-linear dynamic behavior resulting in instability. This paper presents a cascaded system with one source boost converter and three load converters including buck, Cuk, and Single-Ended Primary Inductance Converter (SEPIC) that are analyzed for the complex non-linear bifurcation phenomena. An outer voltage feedback loop along with an inner current feedback loop control strategy is used for all the sub-converters in the cascaded system. To explain the complex non-linear dynamic behavior, a discrete mapping model is developed for the proposed cascaded system and the Jacobian matrix’s eigenvalues are evaluated. For the simplification of the analysis, every load converter is regarded as a fixed power load (FPL) under reasonable assumptions such as fixed frequency and input voltage. The eigenvalues of period-1 and period-2 reveal that the source boost converter undergoes period-2 orbit and chaos whereas all the load converters operate in a stable period-1 orbit. The proposed configuration eliminates the period-2 and chaotic behavior from all the load converters and is also validated using simulation in MATLAB/Simulink and experimental results. INDEX TERMS Bifurcation, chaos, DC-DC power converters, non-linear dynamical systems. I. INTRODUCTION DC-DC converters are the inescapable components of mod- ern DC distribution systems. The non-linear behavior of those individual converter circuits is thoroughly carried out in the studies of power electronics circuits presented in refer- ence [1], [2]. The time-varying behavior of those converter circuits is because of the low and high-frequency oscilla- tions that result in multiple period bifurcations and chaos phenomena [3]. In the modern era of technology, most of the consumer devices are comprised of DC-DC converter circuits that necessitate the design engineers to mainly focus on the elimination of sub-harmonics [4]. So, it is important to go through the studies of the non-linear dynamics of those con- verter systems. The main advantages of the DC distribution systems include simplicity in the connectivity with renewable The associate editor coordinating the review of this manuscript and approving it for publication was Eklas Hossain . sources, higher efficiency, and a wide range of choices for the design parameters. The reliability and stability of DC power converters are the main issues that come across when they are used in the distribution systems. The design and stability of a single converter can be easily carried out. However, the main stability issues arise in a DC distribution system when the interaction of sub-converters takes place [5]. The DC converters connected in a cascaded style is the basic form in a DC distribution system where various renew- able energy sources deliver power to a shared DC bus and all the load converters take power from that bus [6]. Hence, it is the need of the hour to study the reliability and stability of cascaded DC-DC converter systems. The studies have proven that the non-linear dynamic effect is due to the cascaded configuration in the DC-DC converter systems [7]–[9]. These studies are only suitable for small-signal analysis about the stability of DC converter systems. Some models such as FPLs, impedance calculation criteria, and Thevenin network 54602 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 9, 2021