{'fraction_non_alphanumeric': 0.02470660901791229, 'fraction_numerical': 0.0, 'mean_word_length': 5.585365853658536, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lyapunov Stability and Performance Analysis of the Fractional Order Sliding Mode Control for a Parallel Connected UPS System under Unbalanced and Nonlinear Load Conditions

Parallel-connected uninterruptible power supply (UPS) systems have been used to maintain power supply to the critical load in order to increase power capacity and system reliability. This paper presents a robust and precise voltage control strategy for parallel-connected UPS systems. Each parallel-connected UPS system consists of a three-phase inverter with an output inductor-capacitor (LC) filter directly connected to an AC common bus in order to feed the critical load. Fractional-order sliding mode control (FOSMC) is proposed to maintain the quality of the output voltage despite linear, unbalanced and/or nonlinear load condition. The Riemann-Liouville (RL) fractional derivative is employed in designing the sliding surface. The voltage control strategy effectively eliminates the parametric uncertainties, external disturbances, and reduce the total harmonic distortion (THD) of the output voltage. Furthermore, it also maintains very good voltage regulation such as dynamic response and steady-state error under the nonlinear or unbalanced load conditions. The stability of the proposed controller is proven by applying Lyapunov stability theory. Droop control approach and virtual output impedance (VOI) loop are investigated to guarantee the accurate active and reactive power-sharing for parallel-connected UPS system. Finally, the implementation of the control scheme is carried out by using MATLAB/Simulink real-time environment.