978-1-6654-3613-7/21/$31.00 ©2021 IEEE Finite-Time Nonlinear Observer Design for Uncertain DC Microgrids Feeding Constant Power Loads Shekoufeh Neisarian, Mohammad Mehdi Arefi, Navid Vafamand Shiraz University Shiraz, Iran {sh.neisarian, arefi, n.vafamand}@shirazu.ac.ir Mohammad S. Javadi INESC TEC Porto, Portugal msjavadi@gmail.com João P. S. Catalão FEUP and INESC TEC Porto, Portugal catalao@fe.up.pt Abstract—Due to the salient features of direct current (DC) microgrids (MGs) in integrating renewable energy sources, this paper offers a robust finite-time nonlinear observer (FTNO) for DC MGs comprising linear resistive and nonlinear constant power loads (CPLs) and a buck converter. It is assumed that the capacitor voltage is only accessible and the power system is subject to unknown time-varying uncertainties. A novel nonlinear observer is designed to estimate the inductance curren2t to prevent the ripples produced by current sensors and to eliminate the price of utilizing expensive sensors. The global finite-time stability analysis of the observer error dynamic is investigated via a Lyapunov function and an explicit finite convergence time (FCT) is derived. The convergence rate of the estimated current is tunable by adjusting the parameters in FCT. Eventually, simulations are carried out to confirm the superiority of the proposed observer performance in estimating unknown inductance current in a particular finite time. Keywords—Uncertain DC microgrid, Buck converter, Constant power load, Nonlinear observer, Adjustable finite convergence time. I. INTRODUCTION Microgrids (MGs) have been presented to provide an impressive way of integrating different kinds of distributed renewable energy [1]. The MGs are categorized into AC and DC ones. In applications involving DC electronic loads and renewable DC sources like wind and photovoltaics, the DC MGs are more appropriate and affordable than conventional AC MGs [1]. However, there is an increasing share of loads that are tightly controlled by power converters in DC MGs. Such loads are nonlinear since they act as CPLs. From the small-signal point of view, they expose negative incremental resistance which makes the overall system unstable. Recently, the stability issue of CPLs in the DC MGs has been extensively studied with several control methods proposed. Though, in those control approaches, it is presumed that all the system state variables are accessible and measurable [2], [3]. It is noteworthy that some papers like [4]– [7] considered disturbance observer or in [8], a finite-time disturbance observer is probed to compensate for the effects of disturbances and they are completely different from state observer. A literature search reveals that there have been only a few works on the estimation of unknown and unmeasured variables of DC MGs with CPLs by utilizing observers. For instance, a fuzzy observer is presented in [9], which cannot theoretically assure the estimate convergence. To the best of the authors’ knowledge, there are no researches on the design of finite-time nonlinear observers (FTNOs) for uncertain DC MGs feeding CPLs. The finite-time approach to design nonlinear observers has superiority towards asymptotic estimation. It is capable of fast estimating and is robust against uncertainties. This paper discusses the problem of global FTNO design for DC MGs with linear loads and CPLs subjected to unknown time-varying bounded matched disturbances and a finite convergence time (FCT) of estimation is extracted to give the freedom of adjusting the rate of convergence of estimation error. A complete mathematical proof of universal finite-time stability of the observer error dynamic is performed by properly introducing a Lyapunov function candidate. Simulation results display and confirm the effectiveness of the offered FTNO. The advantages and innovations of the proposed scheme are listed as below: • The inductance current is estimated in a specific finite estimation time and not only the ripples caused by deploying physical sensors are alleviated but also the expenses emanating from installing sensors are omitted. • An explicit finite convergence time of the observer error dynamic is extracted that gives the choice of adjusting the rate of convergence of the estimation process. • The estimation process is done as fast as possible • The stability analysis of the observer error dynamic is held globally. • The suggested approach is robust against uncertainties comprising external disturbances, perturbations, and unmodeled dynamics, which is not the case in the existing results. J.P.S. Catalão acknowledges the support by FEDER funds through COMPETE 2020 and by Portuguese funds through FCT, under POCI-01- 0145-FEDER-029803 (02/SAICT/2017). 2021 IEEE International Conference on Environment and Electrical Engineering and 2021 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe) | 978-1-6654-3613-7/21/$31.00 ©2021 IEEE | DOI: 10.1109/EEEIC/ICPSEurope51590.2021.9584484