Further refinements of Young’s type inequality for positive linear maps

Here, an improved control strategy is proposed, which adopts a non‐linear robust backstepping controller to eliminate DC circulating current in a parallel uninterruptible power supply (UPS) system. The traditional active and reactive power sharing control can ideally suppress the AC circulating current, but cannot effectively restrict the DC circulating current. Based on the traditional active power and reactive power sharing control (TAPRPSC) of the parallel UPS system, the proposed control strategy is used in each parallel inverter module to suppress the DC component disturbance in the inverter output voltage, which varies within a certain range. Hence the desirable steady‐state and dynamic performance of the system can be obtained. Moreover, the Lyapunov method is utilized to ensure the stability and robustness of the system. A parallel system of two UPS inverters with the proposed control strategy is built by Matlab/Simulink, and further experiments are carried out on the semi‐physical simulation platform of the Modelling Tech. Both the simulation and experimental results verify the effectiveness of the proposed control strategy for DC circulating current suppression and ideal output voltage tracking.

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“…With Young's inequality [27], (17) can be acquired as:

\begin{equation}{\dot V_2} \le - \left( {{k_1} - \frac{a}{2}} \right) \times e_1^2 - \left( {{k_2} - \frac{a}{2}} \right) \times e_2^2 + \left( {\left| {{d_1}} \right| - {d_{\max }}} \right) \times \left| {{e_2}} \right|\end{equation}

…”

Section: The Proposed Improved Backstepping Control For DC Circulatio...mentioning

confidence: 99%

Design and analysis of robust backstepping controller for DC suppression of parallel UPS inverter system

Zhou

Yang

et al. 2022

IET Power Electronics

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“…For further reading related to generalized refinement of Young's inequality, the reader is referred to recent papers [4], [3], [9], [10] and [11]. One goal of this paper is to show the general refinements form governing Theorem 1.3.…”

Section: Theorem 11 ([1]mentioning

confidence: 99%

A new generalization of refined young inequalities for τ-measurable operators

Amine

Akkouchi

2021

Filomat

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“…For example, putting P = 2, A = 2 1 1 1 and B = 1 1 1 1 . However, Lin [4] showed that the inequality (7) can be squared under the same conditions as in it,…”

Section: Introductionmentioning

confidence: 99%

“…For more information about operator inequalities involving positive linear maps, we refer the readers to [7][8][9][10][11] and references therein.…”

Section: Introductionmentioning

confidence: 99%