###### Abstract  
In this paper, a multivariable linear integral feedback regulation controller for a microgrid was proposed. Considering that the nominal structure model of the inverter could not effectively and in a timely manner deal with the impact of filter parameter uncertainty, there were changes in output power quality among different generation environments. To solve the constraints imposed by uncertain factors on the system, we formulated the following scheme. First, based on the analysis of the asymptotic stability and power characteristics of the nominal model, we added the microgrid filter parameter uncertainty to this model. Secondly, under the action of the bounded range, the performance characteristics of the optimal cost were analyzed, adjusted, and optimized. The controller adjusted parameters to ensure the stable operation of the microgrid system, and to achieve the voltage stability regulation and output power balance. Finally, we built a test system to verify the feasibility and effectiveness of the proposed linear integral controller in MATLAB/Simulink. linear integral regulation controller; nominal model; parameter uncertainty; bounded range analysis; output power balance +
Footnote †: journal: Applied Sciences  
design process of a smart microgrid is to establish a simulation nominal model under ideal conditions [6]. Using inherent stability analysis methods, such as eigenvalue analysis and singular value analysis, a controller is designed to verify the accuracy and robustness of the microgrid system model. However, the traditional synchronous reference frame phaselocked loop (SRF-PLL) method could lead to frequency fluctuations and degrade the system performance. To improve the power quality and recovery ability of the power injected into the grid in a distortion environment, frequency, voltage, and current deviation problems are studied as a key part of power system research. The authors [8] used a moving average filter (MAF) to eliminate the frequency fluctuation of the PLL, and to compensate for the harmonic distortion caused by the power grid voltage distortion, but the control effect on the current was small and the algorithm of the MAF was relatively complex. The authors [9] proposed a method for the stability domain in island and grid connection modes to optimize and calculate the maximum limit value of the stability domain and to achieve the robust stability of the system. However, this method was only suitable for calculating two known uncertain parameters. The work of [10] studied the multi-loop control scheme, which combined a repetitive controller (RC), resonant controller, and a grid voltage feed-forward controller. This work achieved the seamless conversion between the grid-connected and island modes and made the current stable, eliminating the harmonic distortion of voltage and frequency change. However, the requirement on the device level was high; it was limited to small electronic devices and practical projects. For current harmonics in [11], a design RC could compensate for the total harmonic distortion (THD) and improve the dynamic response. However, to precisely track the fundamental frequency and harmonics was very difficult, which limited the bandwidth of the controller and existing harmonics in order to eliminate the selected harmonic components. The authors of [12] used the harmony search (HS) algorithm based on H-infinity to optimize frequency and voltage, and to make the system more robust and stable. However, the algorithm does not consider the impact of time delay on the system failure or load change. The work in [13] can compensate for the total harmonic distortion (THD), but due to the high gain at the fundamental frequency and harmonic frequency, the zero steady-state tracking error was linearly eliminated. In [14] the authors designed harmonic compensators and configured them in a series with the tracking regulator of single-phase grid-connected inverters. This effectively attenuated the voltage distortion and accurately synchronized the tracking.