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A new passivity-based voltage tracker for islanded Direct Current (DC) microgrids is presented in this paper. The proposed design develops a new sufficient condition for passivity-based state feedback with proportional and integral control using the attracting ellipsoid method. In this paper, we consider the time behavior of the extended vector, which completely describes the principle properties of the closed-loop system such as the boundedness of the trajectories within some ellipsoid and the dependence of its “size” on the feedback gains. The next step, which we are realizing in this paper, is the minimization of the attractive ellipsoid by selecting the “best” admissible feedback parameters. Here, it is important to note that the applied feedback is of PD-type (proportional differential) on the system state and I-type (integral) on the output. This is a new construction of the suggested feedback which gives several advantages for a designer. The suggested control is decentralized and uses only the local states; it is cost-effective and avoids the time delays in the communication networks which are needed if centralized control is used. The suggested control is carried out in the bilinear matrix inequality (BMI) framework. Extensive simulation is performed on a test system composed of renewable energy sources, under plug and play (PnP) operations, and uncertainties in distribution lines and loads. The performance of the proposed decentralized voltage controller is compared with that of a voltage tracker present in the literature. The comparison shows the improvements introduced by the proposed control ensure the stability of the dc bus voltage and a quick response under different scenarios of operating conditions.

A theme that become common knowledge of the literature is the difficulty of developing a mechanism that is compatible with individual incentives that simultaneously result in efficient decisions that maximize the total reward. In this paper, we suggest an analytical method for computing a mechanism design. This problem is explored in the context of a framework, in which the players follow an average utility in a non-cooperative Markov game with incomplete state information. All of the Nash equilibria are approximated in a sequential process. We describe a method for the derivative of the player’s equilibrium that instruments the design of the mechanism. In addition, it showed the convergence and rate of convergence of the proposed method. For computing the mechanism, we consider an extension of the Markov model for which it is introduced a new variable that represents the product of the mechanism design and the joint strategy. We derive formulas to recover the variables of interest: mechanisms, strategy, and distribution vector. The mechanism design and equilibrium strategies computation differ from those in previous literature. A numerical example presents the usefulness and effectiveness of the proposed method.