In this article, a novel distributed fuzzy load frequency control (LFC) approach is investigated for multiarea power systems under cross-layer attacks. The nonlinear factors existing in turbine dynamics and governor dynamics as well as the uncertain parameters therein are modeled and analyzed under the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy framework. The cross-layer attacks threatening the stability of power systems are considered and modeled as an independent Bernoulli process, including denial-of-service (DoS) attacks in the cyber layer and phasor measurement unit (PMU) attacks in the physical layer. By using the Lyapunov theory, an area-dependent Lyapunov function is proposed and the sufficient conditions guaranteeing the system’s asymptotically stability with the area control error (ACE) signals satisfying $\mathcal {H}_{\infty }$ performance are deduced. In simulations, we adopt a four-area power system to verify the resiliency enhancement of the presented distributed fuzzy control strategy against random cross-layer DoS attacks. Results show that the designed resilient controller can effectively regulate the load frequency under different cross-layer DoS attack probabilities.

With the participation of a significant number of plug-in electric vehicles (PEVs), it is really challenging to achieve economic-effective in load frequency control (LFC) while sustaining satisfiable system performance. To tackle this challenge, a new distributed economic model predictive control (DEMPC) strategy is proposed for the LFC with the large-scale PEV participation. In the light of the vulnerability of LFC to false data injection (FDI) attacks, a model-based χ ² intrusion detection unit is integrated with the proposed DEMPC. This model-based intrusion detection unit can not only monitor the FDI attacks, but also generate a model-based state prediction for the DEMPC once the data is identified as compromised. Then, an event-triggering mechanism is presented to reduce the computation and communication burdens of each area controller. Simulation studies of a four-area power system are conducted and the results validate the effectiveness of the proposed intrusion detection unit and event-triggering conditions for the DEMPC.

To further the penetration level of renewable energy sources (RESs) in power systems, the paper integrates wind turbines into conventional load frequency control (LFC). A resilient model predictive control (MPC) framework is constructed in the context of potential false data injection (FDI) attacks on vulnerable communication networks of multi-area power systems. To reduce the power generation cost, an economic cost function for MPC is firstly formulated. Then, a decentralized-model-based $\chi^{2}$ detection unit is presented to distinguish the attacked measurements sent from neighbors. Moreover, to reduce the computation burden of executing the distributed MPC strategy, an intensified event-triggered scheme that can handle incomplete and inaccurate modeling issues is proposed. Validation results illustrate the efficacy of the detection unit and the intensified event-triggered scheme, and conclude the relationships between alarming thresholds and key performance indicators. Note to Practitioners —This paper explores the applicability of LFC with the integration of wind turbines under economic MPC framework. Motivated by the underlying FDI attacks on vulnerable communication networks among different control areas, an intrusion detection unit is proposed to install at each controller side to realize resiliency enhancement. Different from the existing works, this paper meticulously investigates the relationships between alarming thresholds and key performance indicators (KPIs), aiming at providing some valuable references for power operators and managers. Besides, this paper proposes an intensified event-triggered scheme to relieve the computation burden of MPC algorithm. This intensified event-triggered scheme has two advantages. One is that it considers the historic released signals in event-triggered conditions, which makes sure the critical signals at crests or troughs of frequency dynamic curves can be triggered. The other advantage is that the supplementary event-trigged condition can well tolerant the incomplete and inaccurate modeling problems existing in conventional event-triggered conditions. Simulations verify the efficacy and feasibility of the resilient event-triggered MPC strategy for frequency regulation under FDI attacks.

Although distributed renewable energy sources (DRESs) provide a sustainable solution to future microgrids (MGs), their fluctuant power outputs can incur frequency instability. The work studies the load frequency control (LFC) for MGs with the integration of wind energy under a hierarchical architecture. At the DRES level, a model predictive control method is employed together with an intensified event-triggered scheme considering multiple historic released signals to improve the computation efficiency. At the MG level, robustness specification is addressed in mean-square asymptotic stability to relieve the fluctuations caused by wind power penetration. Furthermore, the phasor measurement unit (PMU) failure and intermittent transmissions are considered in the control design, leading to the resilient control policy. Besides, this article extends the applicability of conventional small-signal LFC model by adding an uncertain matrix to tolerant the parameter variation due to the shift of the steady-state operating point caused by wind energy integration. The closed-loop performance based on the deployed resilient LFC strategy is verified through hardware-in-the-loop experiments, by which the frequency regulations against PMU failures and intermittent communication at different levels are effectively exhibited.

Vibratory gyroscopes are the most ideal inertial sensors in the 21st century. The amplitude is an important index of vibratory gyroscopes. This article investigates an asynchronous tracking control approach for amplitude signals in vibratory gyroscopes. Since the manufacturing error of vibratory gyroscopes can result in the stochastic signal of the amplitude, Markov stochastic systems are adopted to approximate vibratory gyroscopes. Because the stochastic signal results in the amplitude jitter, a novel doubly fed tracking controller with the stochastic stability performance is proposed for reducing the amplitude jitter. In the practical application, regarding the known degree of the stochastic process, the partially unknown mode information is approximately given. By considering the asynchronous phenomenon between the system mode and controller mode, a hidden Markov model is constructed to name the resultant tracking error system. It is proved that the tracking error system is stochastically stable. Furthermore, the presented asynchronous tracking controller can well track the reference amplitude signal and significantly reduce the amplitude jitter. Finally, comparative results show the control precision of amplitude signals is significantly improved such that the better precision and performance of vibratory gyroscopes are achieved, which demonstrates the effectiveness and practicability of the proposed control approach.