Virtual inertia has been extensively implemented in power systems with distributed energy resources, especially wind energy conversion systems. This paper proposes an optimal virtual inertia planning strategy for stability enhancement of power system, which is penetrated with large volume of renewable resources provided by doubly fed induction generators (DFIGs). The stability of DFIG is first analyzed and the concept of critical frequency drop is proposed. Moreover, the intersection area between the two predefined operation curves of DFIG is defined as the stability margin and it is calculated in the form of a function of local virtual inertia. Subsequently, a virtual inertia planning strategy is proposed, wherein a coherency index that considers the homogeneity of the stability margin at each node is presented, followed by a nonconvex optimization problem. The problem is simplified with the Lyapunov function method and resolved. Two case studies are conducted to verify the effectiveness and performance of the proposed approach: a 12-bus system and the IEEE-118 bus system. Both cases show that with the proposed approach, the system stability margin coherency level is enhanced and the general stability is promoted.

In this paper, a distributed predefined-time fractional-order sliding mode controller (DPTFOSMC) is proposed for performance improvement of power system. The proposed DPTFOSMC is designed based on the multi-agent framework and distributed control theory, which can reduce the pressure of central controller in communication and calculation, thus obtaining fast and coordinated response. The DPTFOSMC can achieve the advantages of sliding mode control (SMC) with fast response and strong robustness for the power system. In addition, the power system under the proposed DPTFOSMC can be stabilized in stable range within a predefined time which is directly equal to the tunable parameter, thus meeting the high requirement for convergence time of the power system. The prescribed performance function (PPF) is carried out to design the DPTFOSMC, which can ensure that the power system can achieve the expected transient and steady responses. Meanwhile, fractional calculus is implemented to devise the DPTFOSMC to eliminate the chattering phenomenon of conventional SMC. The Lyapunov function is adopted to analysis the predefined-time stability of the power system under the proposed DPTFOSMC. Simulations are taken to validate the effectiveness and superior performance of the proposed DPTFOSMC for the power system. The results show that the DPTFOSMC can ensure the power system to achieve superior performances than the existing control methods.

This paper proposes a fractional-order sliding mode controller (FOSMC) for fixed-time stability of multimachine power systems. Fractional calculus has been applied in sliding mode control (SMC), which can better suppress the chattering phenomenon than traditional integer-order SMC. Hence, a FOSMC is proposed to regulate the excitation of synchronous generators to improve the transient stability of the power system. In addition, the FOSMC can maintain the multimachine power systems stabilization in an upper bound and measurable convergence time independent of the initial operating conditions of the power system. The Lyapunov function is implemented to demonstrate the stability of multimachine power systems under the FOSMC, and the upper bound convergence time of the power system is generally estimated. The New England 10-machine 39-bus power system is taken into simulation to test the effectiveness and superior performances of the FOSMC than existing control methods under different operating conditions. Meanwhile, the FOSMC with different orders are presented to verify that the FOSMC can better restrain the chattering phenomenon than traditional integer-order SMC. Simulation results show that the FOSMC can effectively reduce the chattering phenomenon and ensure the power system stabilization in an upper bound time, thus enhancing the dynamic performances of the power system.

The frequency and voltage restoration along with power sharing is imperative for the safe, reliable and stable operation of the islanded AC microgrids (MGs). In this paper, a novel distributed fractional-order predefined-time sliding mode controller (DFOPTSMC) is proposed as a secondary controller for the islanded AC MGs. The proposed DFOPTSMC can ensure that frequency and estimated average voltage (EAV) converge to reference value along with accurate power sharing within a setting predefined time. The fractional calculus algorithm is implemented to design the DFOPTSMC, which increases the degree of freedom of parameter adjustment and greatly enhances the flexibility of the DFOPTSMC. In addition, a distributed predefined-time observer is presented to achieve the EAV within a setting predefined time. The upper bound convergence time of the islanded AC MGs under the proposed DFOPTSMC is directly equal to a tunable parameter, thus overcoming the disadvantages of finite-time control and fixed-time control. The Lyapunov function is applied to present rigorous proof to analyze the stability of the islanded AC MGs under the proposed DFOPTSMC. An islanded AC MG is taken into simulation on the Matlab/Simulink 2021a platform and the experimental platform to test and verify the effectiveness and superior performance of the proposed DFOPTSMC. The results indicate that the proposed DFOPTSMC can significantly enhance the dynamic performances of the islanded AC MGs.