Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.     

Load frequency control for wind-integrated multi-area power systems: An area-based event-triggered sliding mode scheme

This paper deals with the load frequency control problem of multi-area power system with doubly-fed-induction-generator-based wind farm. An area-based event-triggered (ET) sliding mode control scheme is proposed to restore the nominal frequency by transmitting less information. The main feature of area-based ET scheme is that each area will transmit its states information to the controller independently via its own triggering mechanism. By flexibly selecting triggering thresholds, the area-based ET scheme can meet the unbalanced network resources among different areas. Meanwhile, the designed sliding mode controller can effectively suppress the fast fluctuation resulting from load and wind generation to achieve frequency restoration and maintain the tie-line power at its scheduled value. The optimization algorithm on the sufficient conditions is given. Finally, the proposed control scheme is illustrated via a three-area power system and IEEE 39-bus system.     

Load frequency control for multi-area power system based on Markov model

The usage of communication networks provides a backbone of integration of information technologies and load frequency control (LFC) scheme. Time delays introduced by network environments taking the new challenge for dynamic performances and even the stability of closed-loop LFC scheme. This paper focuses on the stability and stabilization of multi-area LFC schemes for power systems with the introduction of communication networks and renewable energies. Markov theory is exploited in this paper for describing the discrete time-delay mechanism. Then, by utilizing Wirtinger-based inequality, and constructing a novel Lyapunov functions, the results of robust stability and stabilization criteria are derived in terms of linear matrix inequality (LMI). Finally, simulation results are provided to demonstrate the effectiveness and superiority of developed results.     

Sparsely distributed sliding mode control for interconnected systems

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.     

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.     

Sampled observer-based adaptive decentralized control for strict-feedback interconnected nonlinear systems

This paper investigates the decentralized tracking control problem for a class of strict-feedback interconnected nonlinear systems with unknown parameters, where the system states are unmeasurable and the interconnections are unknown. Different from the existing results, where the output is available all the time, we consider the case that the output is only available at the sampled instants, which means the failure of existing methods. By introducing a kind of sampled observer for each subsystem, the system states and unknown parameters are jointly estimated. Based on which, a totally decentralized output feedback control scheme is developed to achieve the desired tracking performance by applying backstepping technique, where a compensation mechanism is utilized to address the unknown interconnections from other subsystems. Subsequently, by using Lyapunov stability theory, it is proved that all the signals in the closed-loop system are bounded and the tracking errors converge to an adjustable neighbourhood of the origin. Finally, an example is used to illustrate the effectiveness of the proposed method.     

Constrained load/frequency control problems in networked multi-area power systems

In this paper, we present a supervisory discrete-time predictive control strategy for load/frequency control problems in networked multi-area power systems subject to coordination constraints. Coordination between the control center and the spatially distributed areas is accomplished via data networks subject to communication latency modeled by time-varying time-delay. The aim here is finding supervising strategies able to reconfigure, whenever necessary in response to unexpected load changes and/or faults, the nominal set-points on frequency and generated power to the generators of each area so that viable evolutions would arise for the overall power system and a new sustainable equilibrium is reached. In order to demonstrate the effectiveness of the strategy, examples on a four-area power system are presented.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

Distributed control for spatially interconnected time-varying delay systems under input saturation

This paper presents the distributed control design for a class of spatially interconnected continuous-time time-varying delay (SICTD) systems under input saturation. A distributed controller and distributed anti-windup compensator (AWC) are proposed based on the distributed structure of the SICTD system. Then, a sufficient condition is derived to guarantee the asymptotic stability and $H_{\infty }$ performance of the closed-loop system under the saturation constraints. We have also provided an algorithm for obtaining the AWC parameters by employing the elimination lemma and the cone complementary linearization approach. The proposed anti-windup compensation methodology can also be employed to compensate for the actuator saturation of the spatially interconnected delay-free systems. Finally, two practical examples are presented to verify the effectiveness of the proposed AWC design method.     

Formation control for a string of interconnected second-order systems via target feedback

This paper investigates the formation control of interconnected second-order systems. Each agent is assumed to be capable of measuring its own absolute velocity and the relative positions with respect to its neighboring agents, whereas the target formation is described by absolute positions of all agents in a global coordinate. For such formation control problems, no distributed control policy was reported in existing literature. This paper focuses on the string connection structure of the agents and proposes a distributed control policy that takes the form of purely state feedback without incorporating any feed-forward component. The closed-loop system equation is characterized by an oscillation matrix whose entries are the feedback controller gains. Formation control is accomplished by formulating the agents’ target positions as feedback controller gains. Moreover, it is shown that for agent models described by double integrators, each of the agents located at the two endpoints of the string structure should know its own absolute position. For a class of agent models where each agent’s acceleration depends on its own position, the control laws do not need to use the absolute position. For both system models, the target formations that are asymptotically reachable by the proposed control laws are specified explicitly. Numerical simulations have been conducted to illustrate the effectiveness of the theoretical results.     

Decentralized partial-variable periodic intermittent control for a class of interconnected fractional-order systems

This paper investigates the problems of stability and decentralized control for a class of interconnected fractional-order systems. Firstly, model of the interconnected fractional-order system is established. In the meantime, a decentralized periodic intermittent control technique based on partial variables of the system is developed, and the time cost in the control process and the control cost can be saved by this technique. Secondly, stability criteria by using stability theory of fractional-order systems are derived, respectively. Related results can also be used for estimating regions of stability and applied to practical systems such as the power system, the wireless power transfer(WPT) system and the brushless DC motors (BLDCM) system. Besides, in order to reduce the conservatism of the results, the relevant inequality technique is introduced during the derivation process. At last, illustrative examples are given to demonstrate effectiveness of the obtained results. Compared with existing literatures, simulation results indicate that the conservatism of the results is decreased obviously, and the proposed control scheme can indeed save the time cost and the control cost.     

Event-triggered dynamic output feedback tracking control for large-scale interconnected systems with disturbances

This paper is concerned with the event-triggered dynamic output feedback tracking control for large-scale interconnected systems with disturbances. For each node, a novel event-triggered mechanism is driven by local relative output tracking error to determine whether the signal will be transmitted. A two-step optimization is applied for dynamic output feedback controller design which guarantees robust stability of the system with an optimal H_∞ disturbance attenuation level. Finally, a simulation example of master-slave multiple vehicles is given to illustrate the effectiveness of the proposed scheme.     

Fault-tolerant safe control design of switched and interconnected nonlinear systems

This paper provides novel fault-tolerant safe control (FTSC) strategies for switched and interconnected nonlinear systems. With several switching and interconnection situations considered, the proposed corresponding strategies ensure that the state never enters the unsafe set and asymptotically converges to the origin in the presence of faults. This relies on a proposed concept named “fault-tolerant control Lyapunov-Barrier functions (FTCLBF)”. Two practical examples are taken to demonstrate the efficiency of the proposed method.     

A note on L2-gain analysis for power systems with delayed load frequency control schemes

This paper investigates $L_2$-gain analysis of power systems with delayed load frequency control schemes. Based on a new delay form, new functionals which may be more general than some existing Lyapunov-Krasovskii functionals are developed. Then, new $L_2$-gain criteria are derived with the help of the functionals. Finally, some comparisons are made to show that the obtained criteria are effective.     

Decentralized adaptive tracking quantized control for interconnected pure feedback time delay nonlinear systems

This paper focuses on the problem of adaptive tracking quantized control for a class of interconnected pure feedback time delay nonlinear systems. To satisfy the requirement of prescribed performance on the output tracking error, a novel asymmetric tangent barrier Lyapunov function is developed. The decentralized adaptive controller is designed via backstepping method. To deal with the uncertain interconnected nonlinear functions, we design a new virtual control input in the first step. Instead of estimating the bound of each unknown function, we use the adaptive method to estimate the bound of the composite function which is composed of the unknown functions. Thus the over parameterization problem is avoided. It is proved that the output of each subsystem satisfies the prescribed performance requirement and other state variables are bounded. Finally, the simulations are performed and the results verify the effectiveness of the proposed method.     

Fault-tolerant control for a class of linear interconnected hyperbolic systems by boundary feedback

This paper considers a fault-tolerant control problem for a class of interconnected linear hyperbolic partial differential equation systems. Both subsystem faults and coupling faults are considered. Firstly, the well-posedness of the faulty system is analyzed by using semigroup theory. Secondly, for the fault-free case, a stabilizing boundary feedback control based on small-gain theorem is proposed. Consequently, in the presence of faults, fault recoverability conditions are established that maintain the stability of the faulty systems. The fault-tolerant control strategies are also provided. A heat exchanger example is taken to illustrate the effectiveness and practicality of the proposed methods.     

Networked load frequency control of multi-area uncertain power systems via adaptive event-triggered communication scheme

Load frequency control of power systems is a very important approach to keep stability and security. Unfortunately, the traditional load frequency control is not effective because of the introduction of communication networks in multi-area power systems. In order to overcome this difficulty, sampling-based load frequency control for multi-area power systems is studied via an event-triggered detector. Unlike published works, an adaptive law for event-triggered scheme is given. Since multi-area power systems with event-triggered scheme are hybrid systems, there are a lot of challenges for analysing load frequency control problem. Some lemmas and a new Lyapunov function are developed to overcome these challenges. The obtained stability and stabilization criteria can provide a tradeoff to balance the required communication resources and the desired control performance. Numerical examples verify effectiveness of the obtained results.     

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.