A common method for controlling a group of parallel converters in decentralized control strategy structure in an island microgrid, the use is the droop-down characteristics of frequency ω-P and voltage E-Q. However, the problem with using this method is that the reactive power is not properly distributed (in proportion to the capacity of the micronutrients) between the micronutrients, which may lead to overload in the converters. Microgrids may also suffer from dynamic stability problems such as power fluctuations, which can be increased by switching between active and reactive power control. To avoid this problem, the X / R ratio of transmission lines is an important parameter that should be carefully considered in the design of micronutrient controllers. By linearizing and simplifying conditions, the control system conversion function model becomes a single input-single output system, which is efficient enough to show the relationship between control parameters such as slope of droop characteristics and derivative sentences, virtual impedance, and voltage controllers. Using this model, stability conditions for different parameters are analyzed. Also, to improve power distribution stability, common droop strategies are modified by adjusting the slope as well as adding nonlinear sentence sections. This approach reduces the coupling between active and reactive power control and reduces the dependence of power distribution on grid parameters such as the X / R ratio. To evaluate the reliability of the proposed model, the simulation results in a sample island microgrid in MATLAB software are presented.

Non-cooperative intelligent control agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR control system based on the FNEP for a linear time-invariant system. For this purpose, two control strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) problem (i.e. a supervisory problem), and the second one is a decentralized control problem (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the optimal solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two problems are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR controller is presented. It is shown that the theorems could be extended from a two-agent control system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

multivariate control charts such as Hotelling's T2 and X2 are commonly used for monitoring several related quality characteristics. These control charts use correlation structure that exists between quality characteristics in an attempt to improve monitoring. The purpose of this article is to discuss some issues related to the G chart proposed by Levinson et al. [9] for detecting shifts in the process variance-covariance matrix. They use a G statistic which is distributed as a chi-square with p(p+1)/2 degrees of freedom where p denotes the number of variables under study. The authors show through simulation that the chi-square distribution only holds for certain cases. The results could be important to practitioners who use G chart for monitoring purposes.

Condition monitoring is the foundation of a condition based maintenance (CBM). To relate the information obtained from the condition monitoring to the actual state of the system, it is usually required a stochastic model. On the other hand, considering the interactions and similarities that exist between CBM and statistical process control (SPC), the integrated models for CBM and SPC have been developed. These models apply control charts as a condition monitoring technique, and the inference about the operational states of the system is based on the collected information about the quality of the produced items. Finally, it is decided whether to implement certain type of maintenance actions. This paper describes the application of multivariate control charts as a condition monitoring technique for CBM purposes. To this end, an integrated model is developed, while it is used a chi-square control chart. Also, to determine the inspection time points, a constant hazard policy is applied.

This article presents a new multivariate non-parametric control chart in Phase II based on depth functions. The proposed statistic is an affine invariant and asymptotically free distribution. Indeed, the asymptotic distribution of the proposed statistic is derived under the in-control process. Based on simulation studies, the performance of the proposed statistic, using several depth functions, has been evaluated and compared with three competing statistics. The results show that the introduced statistic performs adequately and, in some cases, outperforms the competing statistics. A real dataset has been analyzed based on the proposed chart.

multivariate control chats are generally used in situations where the simultaneous monitoring or control of two or more related quality characteristics is necessary. In most processes in the real world, distribution of the process characteristics are unknown or at least non-normal, so the non-parametric or distribution-free charts are desirable. Most non-parametric statistical process-control techniques depend on ranks. In this survey, we apply the fuzzy set theory to deal with the circumstances that the values of each characteristic are presented in linguistic form, so we propose non-parametric multivariate control charts based on sign and Wilcoxon signed-rank tests. The performance of the proposed charts is investigated in a simulation study. Numerical examples are used to demonstrate the effectiveness and performance of the proposed charts.