Min Xie Cyber-Physical Distributed Systems

1.2.1 Stability of CPSs

In power systems, communication delays always occur in the transmission of frequency measurements from sensors to the control center (S‐C channel), and control signals from the control center to the plant side (C‐A channel) [24][25]. In local networks, time delays are usually ignored because the control is mainly applied locally, and communication delays are negligible compared with the subsystem time constants [26]. In recent years, with the rapid development of wide‐area measurement systems (WAMSs), a large number of phasor measurement units (PMUs) have been deployed to facilitate the real‐time control of wide‐area power systems (WAPSs) to improve the load frequency control (LFC) performance [27][28][29]. However, when data packets are transmitted across a WAMS, communication delays may become significant and cannot be ignored [30][31][32].

The conventional control of WAPSs is centralized and employs dedicated communication channels over a closed communication network. However, new regulatory guidelines require coordination across multiple hierarchical levels of power systems for more effective market operations and, as a result, open communication infrastructures have been deployed to promote the control of these increasingly complex systems [33][34]. While open networks have economic, maintenance, and reliability advantages, they are subject to time delays that are inherently stochastic (e.g., multiple delays [35] and probabilistic interval delays [36]), and thus cannot be calculated based on the procedures for dedicated networks. Numerical investigations show that time delays the open communication network have the potential to destabilize a WAPS [37][38][39]. For instance, the deregulation of the power industry has pushed many tie lines between control areas to operate close to their maximum capacity. This is especially true for tie lines serving heavy load centers, for example, in southern California [40]. Under these circumstances, operational stresses, such as large time delays, increase the possibility of inter‐area oscillation, reducing the effectiveness of control system damping, and potentially leading to loss of system synchronism [41].

Recent studies on the LFC of WAPSs with communication delays have mainly focused on: 1) the influence of time delays on the WAPS and effective approaches for delay compensation [42][43]; 2) control methods for providing robust performance against delays (e.g., event‐triggered control methods [44], wide‐area phasor power oscillation damping controllers [45], and robust controllers [46][47]); 3) exact methods for evaluating the delay margin for stability, that is, the maximal allowable delay (upper bound on the time delays), when WAPSs and open networks are integrated [48][49][50]. A WAPS is unstable if the real‐time delays exceed the delay margin.

Two classes of methods are available for computing the delay margin in a WAPS for constant and time‐varying delays. Frequency‐domain direct methods quantify the delay margin based on computing critical eigenvalues for constant delays with a known upper bound, for example, the Schur‐Cohn‐based method for commensurate delays [51], Rekasius substitution [52], and the elimination of exponential terms in the characteristic equation [53]. Indirect methods can deal with time‐varying and constant delays; they are derived from Lyapunov stability theory [54][55][56], linear matrix inequality techniques [57][58][59], H‐infinity robust synthesis [60], and the dual‐locus diagram method [61].

These methods assume well‐defined time delay models, that is, constant [62], uniformly distributed [63], multiple [64], and probabilistic interval time delays [65], and require prior knowledge of the lower bound, upper bound, and parameters of the delay distribution. However, delays in an open communication network vary with the number of active end‐users [66] and media access control (MAC) protocols [67]; therefore, no prior knowledge of time delays is available, and they are intrinsically stochastic. These assumptions hinder the application to real systems and lead to excessively conservative results. To overcome these limitations, the LFC model of WAPSs should account for a real open communication network with various MAC‐level protocols. The TrueTime simulator has been used to extract realistic scenarios of networked control systems (NCSs), in which the characteristics of the random delays are unknown and are statistically inferred after collecting sufficient delay observations [68][69][70]. As a specific application of NCSs, insights obtained from the integration of traditional control systems and open communication networks can foster the integration of open communication networks and WAPSs. However, to the best of the author's knowledge, few studies have analyzed the stabilization of WAPSs via real open communication networks.

During the computation of the control signals, the prediction of the C‐A delay in the current period and the S‐C time delay in the successive period can greatly improve the controller performance. However, this possibility has not been investigated in previous works on delay margins or robust LFC strategies. Several methods for delay estimation are available, such as the Markovian model approach [71], backpropagation neural network prediction [72], adaptive wide‐area power oscillation damping [73], dynamic Markov jump filters [74], hidden Markov models (HMMs) [75][76], and the exponentially weighted moving average (EWMA) method [77]. Time delays depend on the underlying network state, which is ever‐changing and concealed [78][79]. Indeed, network states cannot be observed directly, but random time delays can be measured using the time‐stamp technique [80]. Therefore, the state variables of the open communication network can be estimated using the measured time delays; the transitions among these states can be modeled by a discrete HMM (DHMM). As a result, random delays are observations of the DHMM [81][82][83].

Traditionally, in HMM‐based delay models, random delays are mapped to a discrete observation space through scalar quantization techniques, for example, uniform quantization and k‐means clustering quantization [84][85][86][87]. Because the evolution of random delays is described by a finite‐state Markov chain, the communication network action can be learned via the DHMM [88][89][90]. In addition, DHMMs have been used for other applications in power systems, for example, the dynamic detection of transmission line outages [91], the generation of distributed photovoltaic systems [92], and residential energy use [93][94][95]. Chapter 3 introduces the missing data expectation maximization (MDEM)‐based Baum‐Welch algorithm [96][97][98] for the estimate of the parameters of the DHMM online, without previous knowledge of the state transition matrix. Following this step, the time delay can be predicted using the Viterbi algorithm [99]. The predictions are used as the inputs of the Smith predictor to compensate for time delays and improve the LFC strategy performance [100][101]. Our work improves the conventional Smith predictor, which simply employs the summation of the latest measured C‐A time delay and the S‐C time delay to construct the prediction [102]. The conventional Smith predictor cannot capture the evolution of the network states, which is the root cause of stochastic time delays.

The relationship between the delay margin and the controller gains can only help achieve a compromise between the LFC performance and the maximum allowable delay. However, the delay margin‐based method cannot compensate for random delays because it does not involve the real‐time prediction of delays in each period. Therefore, in Chapter 3, the Smith predictor estimates the real‐time delay, which is then integrated into the delay margin‐based method to enhance the frequency stabilization performance. The Smith predictor can also enhance the LFC performance of robust proportional‐integral‐derivative (PID) controllers, whose gains are tuned via robust evolutionary algorithms [103]. Improvements to control strategies currently implemented in real systems, e.g., delay margin‐based proportional‐integral (PI) controllers [104][105] and PID controllers [106], are presented to demonstrate the effectiveness of the proposed methodology for the control of WAPSs.

The power sector is experiencing a structural trend toward decentralization, stemming from the integration of large shares of renewable energy resources (RERs) [107]. This is fostered by distributed energy resources (DERs), which require the integration of power generation means located at or near the end‐user side [108][109]. However, the stochastic nature of RERs and the load demand induces system frequency fluctuations [110][111]. An effective control strategy is needed to maintain the system frequency at its nominal value by balancing the power generation and demand in real time. To this end, automatic generation control (AGC) schemes have been developed for damping frequency oscillations in distributed generation systems (DGSs) [112][113][114][115]. AGC is performed by computing control signals based on the system frequency and delivering balancing inputs to various energy storage systems (ESSs) to absorb (release) the surplus (deficit) power from (to) the grid [116][117][118]. However, the ubiquity of DERs across wide areas and the complex structure of DGSs hinder the development of dedicated communication infrastructures for DGSs with massive DERs [119][120][121][122].

Recently, AGC has been integrated with open communication networks because of its low cost, high speed, simple structure, and flexible access. Data exchanges among PMUs, generators, and the control center are provided by the open communication network in the form of time‐stamped data packets [123][124][125][126]. Stable AGC depends heavily on the performance of the open communication network [127][128][129][130][131][132][133][134][135]. Cognitive radio networks, cellular networks, local area networks (LANs), wide area networks (WANs), and wireless local area networks (WLANs) are employed as open communication infrastructures in these NCSs [136][137][138].

However, open communication networks are exposed to various types of degradation processes, such as network‐induced time delays [139][140][141][142], packet dropouts [143][144], failures of the communication infrastructure [145], uncertain communication links [146], and cyberattacks [147]. As a result, the measurement signals (control signals) received by the control center (ESS or generators) degrade, effective AGC cannot be carried out, and the system frequency response worsens [148][149][150][151][152]. Studying the performance of open communication networks is critical for understanding the occurrence of time delays and packet dropouts. To this end, medium access and packet transmission must be analyzed. The MAC layer is the lower layer of the data link layer of the Open System Interconnection model, and it is responsible for moving data packets among network interface cards across communication channels. Several MAC protocols, for example, carrier‐sense multiple access with collision detection (CSMA/CD, Ethernet), CSMA with arbitration on message priority (controller area network), and IEEE 802.11b/g (WLAN), prevent the collision of packets sent from different nodes across the same channel [153][154][155][156].

Time delays are variable, challenging to predict, deteriorate AGC performance, and reduce the stability region [157][158]. Packet dropouts refer to lost messages, which occupy network bandwidth but cannot reach the destination. They affect the operations of DERs and the reduction of frequency fluctuations, particularly in uncertain network environments. Optimal feedback AGC regulators for DERs have been investigated in numerous works for perfect communication networks, and the impact of transmission delays and packet dropouts on the controller cannot be captured [159]. Robust PID controllers against constant or uniformly distributed time delays [160][161][162][163] are designed to cope with perturbations of the control parameters. However, constant or uniformly distributed time delays cannot be generally assumed in realistic communication networks.

In addition, recent studies focusing on primary and secondary control levels have been extended to the power management level by considering fuzzy controllers [164][165], decentralized power management and sliding mode control strategies [166], static synchronous compensators [167], and two‐degrees‐of‐freedom feedback‐feedforward robust controllers [168][169]. The reactive power reference can be determined and controlled by a novel application of radial basis function neural networks [170][171][172] to improve the power sharing and stability of microgrids with multi‐DERs. To provide high reliability and robustness against network failure or time delays, droop‐based control schemes are designed to specify the frequency of each DER unit by using complementary loops and fuzzy logic controllers [173], robust H∞ controllers [174], and PI controllers [175][176]. On the other hand, novel approaches for mitigating the impact of random time delays quantify robust delay margins [177]. The delay margin‐based sparsity‐promoting wide‐area control strategy, which requires few system observations, can reduce communication requirements and yield nearly optimal performance compared with centralized control [178]. 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 [179][180][181]. However, their power outputs are dependent on the available intermittent natural resources, such as solar irradiation, wind velocity, and biofuel production [182][183][184]. 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 [185][186][187]. 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 [188][189][190][191][192][193]. 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 [194][195][196][197]. The effective integration of communication networks into DG systems is a key step in the realization of future smart grids [198][199].

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 [200][201][202]. 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 [203][204][205][206][207]). 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 [208][209][210]. 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 [211][212][213]. 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 [214][215][216].

Existing research works [217][218][219][220][221][222][223][224][225][226] 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 [227][228]. The delays are described by discrete‐time models or are neglected by assuming that they are much smaller than the communication interval [229][230][231][232]. 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 [233][234]. Additionally, the models of uncertain renewable power sources do not consider time‐correlated properties [235][236][237][238][239][240]. 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.

1.3.1 Managing Reliability and Feasibility of CPSs

CPSs perform critical tasks in many industrial applications, for example, manufacturing systems [241], transportation systems [242][243], and power systems [244][245]. The components of control systems, that is, actuators and sensors, are subject to degradation when operating under severe working conditions [246][247][248][249][250].

Sudden load variations in electric power systems are often balanced by promptly changing the output of natural gas power plants following the LFC strategy [251]. However, the degradation of gas turbine compressors, that is, the deviation of compressor flow capacity and isentropic efficiency [252], and the degradation of PMUs, that is, measurement drifts and errors [253][254], 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 [255]. 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 [256] 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 [257] and different starting points of the degradation paths [258]. Therefore, the degradation model should reflect the unit‐to‐unit variability in the degradation process of gas turbines [259]. 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 [260]) derived from on‐line measurements, for example, rotor speed, inlet temperature, and pressure [261][262]. Maintenance activities are scheduled based on the two health indexes. However, in control systems, failures are determined by the system performance [263] and not by the health indexes of individual components, that is, they are system‐level failures rather than component‐level failures [264][265][266]. Control systems may still operate normally even if the component health indexes exceed failure thresholds [267][268]. In addition, the feedback control mechanisms hide the explicit mapping from the individual component degradation state to the control performance loss [269]. 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 [270][271]. 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 [272].

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 [273]. 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 [274], bearing degradation [275][276], gyroscopes in inertial navigation systems [277][278][279], contact image sensors in copy machines [280], the resistance of carbon‐film resistors [281], and the pitting corrosion process [282]. 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 [283][284]. Furthermore, the drift parameter, which denotes the aging rate, is also variable and follows a normal distribution, where the mean denotes the average aging rate and the variance represents the variability in the aging rate [285][286][287][288][289]. These parameters can be estimated from the lifetime dataset via an expectation‐maximization (EM) algorithm [290][291][292][293][294][295].