The wide application of energy conversion facilities on the demand side, such as combined heat and power units, has accelerated the integration of multiple energy carriers in the form of energy hub (EH). EH can flexibly schedule its electricity and gas consumption patterns to provide demand response (DR) services to the electricity system. However, DR can introduce significant uncertainties in gas demands, posing challenges to the real-time balance of the integrated electricity and gas systems (IEGSs). The gas stored in the pipeline (i.e., linepack) is a promising flexible resource to accommodate the gas demand uncertainties during the DR. However, using linepack is challenging due to the complex physical characteristics of gas flow dynamics. This article proposes a coordinated optimal control framework for both EH and IEGS, focusing on leveraging the linepack flexibility to enhance DR capabilities. First, a multilevel self-scheduling framework for the EH is developed to comprehensively explore the DR potential. The gas flow dynamic constraints are then formulated to ensure that the fluctuating gas demand can be accommodated by the linepack in the IEGS. The second-order cone (SOC) relaxation is adopted to convexify the nonlinearity in the motion equation of gas flow dynamics. To tackle the overall mixed-integer SOC programming problem, an enhanced Benders decomposition strategy that incorporates the lift-and-project cutting plane method is developed, along with a novel solution procedure. The proposed method is validated using the IEEE 24-bus Reliability Test System and the Belgium natural gas transmission system to demonstrate its effectiveness.

The interdependency among the electricity, gas, heat, and cooling energy systems is ever-increasing. The flexible energy utilization patterns on the demand side and gas flow dynamics in the transmission system bring both opportunities and challenges to the reliable operation of integrated energy systems (IES). For example, if the electricity supply is interrupted, the gas system can ramp up the gas supply to the gas-fired units using linepacks. By this means, the reliability of the electricity system at this moment can be improved, while the gas system's capability of withstanding future risks may be undermined. Therefore, the operational reliability between different energy systems and time periods should be carefully balanced. This article proposes an operational reliability evaluation framework for the IES considering flexibilities from both the demand side and transmission system. First, the flexibilities of end-users and linepacks are explored based on the Energy Hub and gas flow dynamics models. Then, the reliability models of IES components are developed using the discretized-time Markov process to characterize the temporal state evolution in the operational horizon. A look-ahead contingency management scheme of the IES is then proposed to minimize the electricity and gas load curtailments. Taking account of all the possible system states, the operational reliabilities of the IES are evaluated using the time-sequential Monte Carlo simulation. Finally, the proposed method is validated by using the IEEE Reliability Test System and the practical Belgium gas transmission system.

Considerable research efforts have been expended in modeling load-sharing systems. The existing models, however, have various limitations, such as being limited to the exponential time-to-failure distribution, constant component performances, or performances without constraints. In this article, we make contributions by modeling a dynamic load-sharing system (DLSS), where the performance of each component is dynamic according to prespecified load-sharing principles and is limited by its capacity constraint. Moreover, the capacity constraint of a component can reduce due to degradations. In the proposed model, increasing failure rates are also involved since the surviving components must share the load of the failed component and continue working with increasing stresses. When the desired performance for a component exceeds the limitation, the entire system fails. An extended Markov process (EMP) method is proposed for evaluating the reliability of the considered DLSS with nonrepairable components. The proposed analytical method is flexible in handling arbitrary component time-to-failure distributions and in handling diverse load allocation mechanisms. Numerical studies of a power transmission system and a water transmission system are provided to validate the proposed method and its advantages. Effects of several model parameters are also investigated through case studies.

Rapidly increasing distributed energy resources (DERs) bring more fluctuating output power to the distribution network and put forward a higher requirement on local regulation resources for maintaining the network's balance. Heating, ventilation, and air conditioning (HVAC) loads account for more than 40% of power consumption in modern cities and have huge regulation potential as flexible loads. However, HVACs equipped with inverter devices have rarely been studied for providing regulation services in the local electricity market (LEM), even though they have exceeded regular fixed-speed HVACs. To address this issue, this article proposes a real-time LEM and a distribution network's optimization framework to exploit the regulation potential of inverter-based HVACs considering multiple DERs. This LEM can avoid iterations in real time and significantly decrease the difficulty related to the participation of small end-users in urban distribution networks. Moreover, in this article, we propose a transactive capacity evaluation method to assist end-users in deciding their inverter-based HVACs regulation capacities in the real-time LEM, which considers buildings’ thermal features, users’ multiple comfort requirements, and dynamic ambient temperature. On this basis, a multilevel bidding strategy is developed for inverter-based HVACs to decrease energy cost, increase fluctuating DERs local utilization rate, and alleviate the distribution network's congestion. Finally, a realistic distribution network is utilized to verify the effectiveness of the proposed methods.

A large variety of real engineering systems operate with multiple performance measures that are multistate in nature. These systems are usually modeled as multiperformance multistate systems (MPMSSs). However, existing MPMSS models fail to consider an important aspect, i.e., the performance conversion process. For example, in a combined heat and power (CHP) generating unit, apart from the output heat and electricity, decision-makers are also interested in the unit's capacity to convert gas into electricity and heat. The latter is related to the performance conversion process. This article proposes a framework for the reliability evaluation of performance conversion-based MPMSS. In the proposed MPMSS model, the couplings among different types of performances inside the components are quantified into the multistate performance conversion matrix. The performance conversion structure functions are proposed to derive system performance conversion capability based on the conversion capabilities of the components. Two reliability evaluation methods considering the steady-state performance conversion process and the continuous-time performance conversion process are proposed, respectively. Numerical examples are given to demonstrate the developed methods.

While a number of network systems are running under certain stress with a limited lifetime, it is still unknown how to predict the lifetime–stress relation of complex systems. We develop a percolation-based approach to build an operational lifetime–stress model for complex networks, which captures the spatial and temporal reliability characteristics of the system. In this article, the general analytical expression for the entire operational lifetime–stress relation has been presented, which suggests that the load stress and the number of nodes in the network impact the operational lifetime in the same manner. The size effect found here in the lifetime–stress relation is observed for the first time, to our best knowledge. For 2-D lattices, we show that the lifetime–stress relation can be regarded as the combination of two parts—an approximately linear region for small stress, and nonlinear region for large stress. We also analyze the lifetime–stress function of Beijing road network and the western United States power grid. Our article might help to develop acceleration testing methods, which will facilitate better design of reliable complex systems.

As an extension of binary system model, multistate systems (MSSs) are more flexible for modeling reliabilities of real-life engineering systems. In the conventional MSS theory, it is usually assumed that the performance of the system and components can be characterized by one measure. However, the assumption is difficult to be satisfied for some complex engineering systems that have different forms of performances at the same time. For example, the integrated energy system can supply various forms of energy simultaneously, including electrical power, natural gas, and heat. Therefore, the conventional MSS is difficult to model the system with multiple performances. In this article, a general multiperformance measure MSS model is proposed. The fundamental assumptions and key definitions are provided for such systems. The ordering methods to compare performance measure vectors are introduced. The concepts of separability, monotonicity, relevancy, coherency, and equivalency of the component and the system are developed to characterize the system properties. Examples are given to illustrate these definitions.

A module of a fault tree is an independent subtree that has no input from the rest of the tree and no output to the rest, except the top events. Modularization is an important technique to reduce the computation cost for large, complex fault tree analysis. This article presents a new linear-time algorithm that is more efficient and easier to code for finding modules existing in fault trees. Two main stages are included in the proposed algorithm: branching and transforming. To demonstrate the efficiency and applicability of the proposed algorithm, comparisons are performed between the proposed algorithm and other linear-time algorithms for finding modules in fault trees. Results have shown the superiority and effectiveness of the proposed algorithm.

The emerging concentrating solar power plant (CSPP) represents one of the promising technologies for promoting solar power applications. In this paper, risk-constrained day-ahead scheduling strategies for a virtual power plant (VPP) integrating a CSPP with some responsive residential and industrial loads are proposed considering the uncertainties from electricity price, thermal production of the solar field of the CSPP, and participation factor of residential demand response. The well-established information gap decision theory (IGDT) is utilized to hedge against the risk caused by these uncertainties. Based on IGDT, both a robust scheduling strategy for the risk-aversion decision maker and an opportunistic scheduling strategy for the opportunity-seeking decision maker are presented for hedging the profit risk of the VPP against variations of electricity price, thermal production, and demand response. Simulation results show that the presented IGDT-based method can act as an effective tool for managing risks from uncertainties, and also demonstrate that the RA VPP should focus more on the thermal production of the CSPP so as to guarantee the desired profit, whereas the OS VPP should pay more attention to the market price so as to achieve a windfall profit.

Multistate series-parallel system (MSSPS) is a widely used model for representing engineering systems, whose reliability has been extensively analyzed. Universal generating function (UGF) is an efficient method for evaluating the reliability of MSSPS. However, when facing the large-scale MSSPS, where the number of system components and possible states are enormous, calclating the exact system reliability can be rather time-consuming. To evaluate the reliability of large-scale MSSPS more efficiently, this paper proposes an approximation method, named continuization discretization approximation (CDA) method. The CDA approach consists of continuization and discretization processes. The continuization process applies Gaussian approximation method based on the central limit theory and the UGF technique to evaluate parallel subsystems. While the discretization process discretizes the continuous distribution to a discrete one, and proposes an algorithm to evaluate the series subsystems efficiently. The efficiency and accuracy performance of the CDA method can be adjusted by parameters according to the computational resource and the system scale. The newly proposed method is compared to the existing methods in evaluating the large-scale MSSPS. Numerical examples show that the CDA method has evident advantage in computational efficiency with satisfactory accuracy performance.

The wide-area measurement system provides a new data acquisition and supervisory control tool for a power system, and the data acquisition level is increased dramatically with its development in the smart grid environment. Huge data associated with the power system operation are acquired, which are beneficial for enhancing situational awareness of a power system concerned. Identifying the coherency among synchronous generators using real-time signals from phasor measurement units (PMUs) is one of the major tasks of situational awareness in power system operation. Given this background, a data-driven coherency identification methodology is proposed based on the spectral clustering algorithm. First, several trajectory dissimilarity indices for the rotor angle and rotor speed trajectories of generators as measured by PMUs are presented based on the trajectory similarity theory. Second, a decision-making method based on the Gini coefficient and Kendall rank correlation coefficient is presented for integrating multiple indices describing trajectory dissimilarities. Third, the spectral clustering algorithm is presented to identify the coherency of synchronous generators, and silhouette is presented for determining a reasonable number of coherent groups. Finally, oscillation events happened/simulated in two actual power systems, i.e., Guangdong power system in China and Western Interconnection power system in North America, are utilized to demonstrate the effectiveness of the proposed data-driven coherency identification methodology.

Warm standby redundancy is a fault-tolerant technique balancing the low economical efficiency of hot standby and the long recovery time of cold standby. In this paper, motivated by practical engineering systems, a general demand-based warm standby system (DB-WSS) considering component degradation process is studied. A series of intermediate states exists between perfect functionality and complete failure because of degradation processes. A lot of existing analytical reliability assessment techniques are focused on conventional binary-state models or exponential state transition distributions for a system or its components. In this paper, a novel reliability evaluation approach based on the multistate decision diagram for DB-WSS is proposed. The proposed technique can handle arbitrary distributions of degradation processes for multistate components or systems. Moreover, considering the imperfect switch of the warm standby component, the start failure probability is taken into account in the warm standby system. Numerical studies are given to illustrate the proposed approach.

Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties. First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle. Finally, an efficient algorithm is designed to extract probability boxes ($p$-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system availability and reliability estimation. The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.

Generation expansion planning (GEP) is the problem of finding the optimal strategy to plan the construction of new generation while satisfying technical and economical constraints. In the deregulated and competitive environment, large-scale integration of wind generation (WG) in power system has necessitated the inclusion of more innovative and sophisticated approaches in power system investment planning. A bi-level generation expansion planning approach considering large-scale wind generation was proposed in this paper. The first phase is investment decision, while the second phase is production optimization decision. A multi-objective PSO (MOPSO) algorithm was introduced to solve this optimization problem, which can accelerate the convergence and guarantee the diversity of Pareto-optimal front set as well. The feasibility and effectiveness of the proposed bi-level planning approach and the MOPSO algorithm have been verified by a numerical test system.

The multi-state$k$-out-of-$n$system model finds wide applications in industry, and has been extensively studied in recent years. This model has also been generalized to the multi-state weighted$k$-out-of-$n$system model. Recursive methods, and universal generating functions (UGF) are two primary algorithms for exact performance evaluation of multi-state$k$-out-of-$n$systems. However the computational burden becomes the crucial factor when there is a “dimension damnation” problem caused by the increase in the number of components in the system, and the number of possible states a component may be in. In situations wherein exact values of system reliability are not necessary, we may use more efficient algorithms to approximate system reliability. In this paper, we develop a comprehensive framework for reliability approximation of multi-state weighted$k$-out-of-$n$systems. Two fuzzy based multi-state weighted$k$-out-of-$n$system models are defined. Procedures for building these two models from the conventional models are also introduced. The fuzzy recursive methods, and fuzzy UGF techniques are developed to evaluate such systems. The clustering technique, and curve fitting method are used to determine the fuzzy weights, and probabilities of states in the models.

A multi-state system (MSS) model is a more flexible tool for representing engineering systems than the conventional binary system model, which has been widely studied in recent research. The multi-state weightedk-out-of-nsystem model is the generalization of the multi-statek-out-of-nsystem model, where the componentiin statejcarries a certain utility. In this paper, we propose a multi-state system structure called hierarchical weighted multi-statek-out-of-nsystems. In such a system, the structure of the system can be decomposed into different hierarchical levels, and a subsystem at each level can be represented using a multi-state weightedk-out-of-nstructure. The proposed system structure can find applications in many real life systems, and a municipal infrastructure is a typical example of such a structure. The definition of the hierarchical multi-state weightedk-out-of-nsystem model is proposed in this paper. Universal generating functions (UGF) are used to evaluate reliabilities of the defined systems. Moreover, to reduce computational complexity, recursive algorithms are developed to obtain lower, and upper bounds of the defined system reliabilities.

Compared with a binary system model, a multi-state system model provides a more flexible tool for representing engineering systems in real life. In conventional multi-state theory, it is assumed that the exact probability and performance level of each component state are given. However, it may be difficult to obtain sufficient data to estimate the precise values of these probabilities and performance levels in many highly reliable modern engineering systems. New techniques are needed to solve these fundamental problems. A general fuzzy multi-state system model is proposed in this article to overcome these deficiencies. The basic definitions and assumptions of such systems are introduced. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Future research directions include performance evaluation algorithms for the defined fuzzy multi-state systems.