sparsity‐promoting wide‐area control strategy, which requires few system observations, can reduce communication requirements and yield nearly optimal performance compared with centralized control [109]. Nevertheless, packet dropout still has the potential to affect the performance of this strategy.
1.2.2 Reliability of CPSs
Distributed renewable energy sources are increasingly connected to power distribution networks as a remedy for environmental and economic concerns [110–112]. However, their power outputs are dependent on the available intermittent natural resources, such as solar irradiation, wind velocity, and biofuel production [113–115]. The rapid deployment and commercialization of storage devices and electric vehicles (EVs) has become an attractive technological solution to facilitate the use of renewable energy sources, manage demand loads, and decarbonize the residential sector [115–117]. The above technological issues call for managing real‐time energy imbalance in DGSs to meet electricity demand over a long‐term horizon. In order to address the challenges of distributed control of energy sources, communication networks are being installed for accurate control of the different power sources and the timely operational scheduling of distributed generator (DG) units, with the objective of providing reliable and sustainable energy in a timely fashion [118–123]. However, most existing research works do not formally investigate the capability of communication networks in providing real‐time power management and promoting the optimal power dispatch [124–127]. The effective integration of communication networks into DG systems is a key step in the realization of future smart grids [90,128].
Most integrated system‐of‐systems models have been developed based on dedicated and closed communication networks, where the infrastructure is exclusively built for smart grid applications [90,128,129]. As the network is dedicated between the DG and the control center, the data exchange is assumed to be perfect and free of defects (e.g., induced time delays and packet dropouts [130–134]). However, experience has shown that dedicated communication networks are ill‐suited to future DG systems, which require a different, more complex but much cheaper network, as its dimension would be much larger [135–137]. Because of the low installation cost, high transmission speed, and flexible access, the open communication network has the highest potential for integration with future DGSs [82,84,138]. As end‐users have to share the limited bandwidth in the open communication networks, which could lead to local congestion, they can be unreliable and suffer from network‐induced delays and packet dropouts [139–141].
Existing research works [42,123,139–146] do not model explicitly and adequately the behaviors of transmission delays and packet dropouts. Most of the aforementioned models are limited to constant or less stochastic transmission delays, which are not true in reality [147,148]. The delays are described by discrete‐time models or are neglected by assuming that they are much smaller than the communication interval [17,123,149,150]. Packet dropouts are usually modeled by a two‐state Markov chain and the associated quantitative loss rates; the detailed state evolution is masked and only input/output information is made available. The state transition matrix is known by assuming that the evolutions of packet dropouts can be fully observed [123,140]. Additionally, the models of uncertain renewable power sources do not consider time‐correlated properties [42,123,139,142,143,151]. Consequently, the control schemes derived based on such assumptions can be very conservative and may not be readily applicable to real systems.
To bridge this gap, a generic and transparent mathematical model is necessary for the analysis of the impacts of integration of unreliable open communication networks (e.g., home area networks, neighborhood area networks, and WANs). The major challenges lie in the modeling and simulation of the interactions between degraded communication networks and DG systems, and the optimization of the real‐time energy management problem on such system platforms. Note that the specific requirements (i.e., high‐frequency data and data prediction) introduced by communication network integration need to be taken into account in this modeling, simulation, and optimization framework.
1.3 Opportunities for CPS Applications
1.3.1 Managing Reliability and Feasibility of CPSs
CPSs perform critical tasks in many industrial applications, for example, manufacturing systems [152], transportation systems [153,154], and power systems [18,155]. The components of control systems, that is, actuators and sensors, are subject to degradation when operating under severe working conditions [155–159].
Sudden load variations in electric power systems are often balanced by promptly changing the output of natural gas power plants following the LFC strategy [160]. However, the degradation of gas turbine compressors, that is, the deviation of compressor flow capacity and isentropic efficiency [161], and the degradation of PMUs, that is, measurement drifts and errors [162,163], reduce the LFC performance by decreasing the available balancing power, and by producing inaccurate frequency readings. Deteriorated LFC performance may result in power system failures because the system frequency exceeds its maximum allowable drop or fails to attain the steady‐state frequency tolerance band in the required time in compliance with ISO 8528‐5 [164]. As a result, power system failures are determined by the LFC performance, stemming from the partial information on the power system conditions, that is, the health indexes of gas turbines (flow capacity and isentropic efficiency), and measurement drift. Therefore, it is necessary to study these degradation processes to predict the real‐time LFC performance loss and ensure adequate LFC through proper maintenance activities.
Lifetime prognostic studies of gas turbines [165] have shown that the failure time of these systems varies between 24 000 h and 35 000 h. Such variability stems from different working conditions [166] and different starting points of the degradation paths [167]. Therefore, the degradation model should reflect the unit‐to‐unit variability in the degradation process of gas turbines [168]. Moreover, many condition‐based maintenance (CBM) models determine maintenance activities based on the estimated remaining useful lifetime (RUL) of gas turbines using health indexes (reduction in flow capacity and isentropic efficiency [161]) derived from on‐line measurements, for example, rotor speed, inlet temperature, and pressure [169,170]. Maintenance activities are scheduled based on the two health indexes. However, in control systems, failures are determined by the system performance [171] and not by the health indexes of individual components, that is, they are system‐level failures rather than component‐level failures [172–174]. Control systems may still operate normally even if the component health indexes exceed failure thresholds [157,175]. In addition, the feedback control mechanisms hide the explicit mapping from the individual component degradation state to the control performance loss [175]. It is easy to estimate the RUL of an individual component, but difficult for degraded control systems, because their failure time cannot be described by any particular distribution [171,176]. Therefore, when applied to degraded control systems, general CBM models should connect the component degradation and the control performance loss, so that maintenance activities depend on the reduction of control performance [176].
The Wiener process is often employed in degradation models because of its favorable mathematical properties; in particular, it can capture non‐monotonic degradation signals frequently encountered in practical applications, because consecutive independent increments are normally distributed [172]. Therefore, this stochastic process has been widely applied to characterize the path of degradation in realistic scenarios, where fluctuations are observed in the degradation process, for example, brake‐pad wear for automobiles [177], bearing degradation [174,178], gyroscopes in inertial navigation systems [172,179,180], contact image sensors in copy machines [181], the resistance of carbon‐film resistors [159], and the pitting corrosion process [167]. To overcome the aforementioned limitations, the Wiener degradation model with unit‐to‐unit variability is introduced to describe gas turbines exhibiting different lifetimes. The Wiener model considers the random starting time of the degradation process, which follows a non‐homogeneous Poisson process [167,182]. Furthermore, the drift parameter, which denotes the aging
