Distributed computing faces a persistent multi agent trust dilemma. In the computation process, participants may maliciously attack the system for personal gain by providing false data. Blockchain provides a possible solution for this problem with its immutability and multi-party consensus. However, existing blockchain data throughput has long been queried owing to its exorbitant time and energy costs by consensus mechanisms. This paper proposes a light blockchain structure in distributed computing scenarios. A No-Proof consensus (NPC) mechanism is designed for distributed computing problems with no extra proving process such as Proof-of-Work or Proof-of-Stake. This consensus mechanism notices that the distributed computing result has proven to be valid in the computation process automatically, which does not need to be verified again in the consensus mechanism. Further, the single-threaded data processing ability of the blockchain structure certainly leads to low efficiency when applied to distributed computation problems. An NPC-based blockchain is constructed in this paper to solve this problem. In this structure, the distributed computing is done off chain, and an oracle is designed to upload the computing results to the blockchain asynchronously. Upon the contribution in this paper, a distributed energy trading model is provided as a case study to verify the superiority of the designed blockchain in contrast with other similar structures.

Decreasing the randomness of renewable energy sources is the priority for the stability of novel power systems. Renewable energy prediction models have been studied extensively with higher precision. However, these models have become much more complicated and opaquer, meanwhile accuracy improvements almost reach the convergence. Major prediction deviations are still inevitable and how the deviations occurred is inexplicable in those black-box models. This prediction interpretability problem arises puzzling power system operators. Specifically, advanced solar power forecasting technologies have proposed multimodal prediction models that involve various input forms, such as remote-sensing cloud images, exacerbating the forecast opacity. Hence, this study focuses on the interpretability issue of deep-learning-based multimodal solar power predictions, and proposes a post-hoc local traceability method. Based on neural-backed decision trees, the method can decouple solar power forecast outputs into an inference hierarchy and weather transition probabilities. Effects of multimodal inputs can be also quantified with Shapley values in the method. By providing qualitative results of input effects and the prediction inference process, the proposed method increases local interpretability while maintaining forecast accuracy.

Refrigerators, as a type of thermostatically controlled load (TCL), have good capacities to participate in demand response (DR) programs. However, existing methods have paid little attention to refrigerator parameter estimation and have rarely focused on retrofit-free control strategies. These control strategies often take the refrigerator’s temperature set-point or the compressor ON/OFF status as decision variables, requiring retrofitting the thermostatic controller. To address this issue, this paper proposes a 2R1C model for the refrigerator, which facilitates parameters estimation and scheduling strategy design. Based on the 2R1C model, a least-square-estimation (LSE)-based parameters estimation method is proposed to improve the accuracy and efficiency. In addition, a price-based scheduling method is proposed for an actual retrofit-free refrigerator that uses the main-power ON/OFF status as the decision variable, which can be easily implemented through an external power socket. By establishing a temperature-ramp-oriented thermostat control model considering the main-power ON/OFF status, the scheduling model is developed and linearized into a mixed integer linear program (MILP). The optimization, simulation, and practical control of an actual refrigerator verify the effectiveness of the proposed method.Note to Practitioners—This paper addresses the optimal scheduling problem of the refrigerator participating in DR, applicable to the majority of practical refrigerators. Existing optimal scheduling strategies for refrigerators suffer from two main issues. Firstly, most of these strategies assume that the thermal parameters of refrigerator loads are given, leading to inaccuracies due to the neglect of parameter estimation. Secondly, the majority of control strategies define the decision variable as the refrigerator’s power consumption rather than the temperature set-point, which deviates from the actual mode in which refrigerators indirectly control power through temperature set-points. This paper proposes a modeling approach based on 2R1C for the mode in which practical refrigerator control power indirectly through temperature set-points. On this basis, a parameter estimation strategy is designed, and an optimization strategy based on MILP is developed with the main-power ON/OFF status of the refrigerator as the decision variable. Compared to traditional methods, the proposed approach can be implemented through an external power socket, making it suitable for the vast majority of refrigerators without the need for retrofitting. In future research, we aim to extend this single refrigerator scheduling strategy to the control of a large number of refrigerators and even clusters of other TCLs, achieving more complex application scenarios.

Probabilistic energy flow (PEF) calculation is a fundamental task for the operation and planning of both natural gas systems (NGSs) and integrated energy systems considering uncertainties. Traditional Monte Carlo simulation (MCS) based PEF approach requires repeated energy flow calculations based on a large number of random samples, leading to a huge computation burden. Hence, this paper proposes a convex multiparametric programming (MPP) based fast PEF calculation method for NGSs. First, we develop an energy function based convex optimization model whose optimal solution is equivalent to the solution of deterministic energy flow equations. Then, we propose a convex MPP model with uncertain boundary conditions (such as the gas injections/loads) as the parameters. A multiparametric quadratic approximation algorithm is further introduced to solve the proposed MPP and obtain the analytical energy flow expression. This analytical expression characterizes the mapping relationship between the energy flow solution and uncertain parameters. Finally, we establish an online PEF calculation framework, in which the repeat energy flow calculations can be efficiently performed by merely substituting the uncertain parameters into the analytical energy flow expression obtained offline. Case studies on multiple NGSs verify the effectiveness of the proposed method. Note to Practitioners—This paper introduces a novel approach for efficient PEF calculation in NGSs that addresses the computational challenges posed by traditional methods. Conventional MCS-based PEF approaches involve numerous energy flow calculations with massive stochastic scenarios, resulting in significant computational burdens. The key contribution of our work is to equivalently reformulate the original PEF problem as an energy function based convex MPP model, which incorporates uncertain boundary conditions (e.g., gas injections/loads) as its parameters. Then, a multiparametric quadratic approximation algorithm is suggested to obtain the parametric solution of this MPP, which is essentially an analytical expression of the energy flow solution as a function of uncertain parameters. This allows for efficient repeated energy flow calculations by simply substituting uncertain parameters into the pre-determined expression obtained offline. Thus, the online PEF computational efficiency can be significantly improved. We conduct case studies on several benchmark NGSs to validate the effectiveness and scalability of the proposed method. Numerical results show that the online PEF computation efficiency of the proposed method is approximately 2-3 orders of magnitude faster than that of the NR-MCS method.

In this paper, the robust control of multi-channel nonlinear delay system is discussed. Firstly, a four-order dynamical model of wind turbine nonlinear system suffers from time-varying delay and match disturbances is established. Then, a channel-dependent fuzzy sliding-mode function is designed and the sliding dynamic is obtained. Meanwhile, the stability analysis of sliding dynamic is proved and the channel-dependent sliding parameters are solved. Furthermore, a fuzzy sliding mode controller is proposed to ensure the sliding surface is reachable. Additionally, an adaptive fuzzy sliding mode controller is presented to deal with the situation that the upper bound of the disturbance is unknown. Finally, a numerical simulation and a semi physical simulation are implemented to demonstrate the effectiveness of the algorithm.Note to Practitioners—This paper was motivated by the issue of the robust control of multi-channel wind turbine nonlinear system. Different from traditional controlled system, the wind turbine nonlinear system often suffers from the delay and disturbances. This paper designs a new fuzzy-sliding-mode strategy to address the above issues. Firstly, we established a four-order nonlinear dynamic of wind turbine system under the time-varying delay and match disturbances. In order to obtain the sliding dynamic, a channel-dependent fuzzy sliding-mode function is presented. For ensuring the sliding surface is reachable, a fuzzy sliding mode controller is proposed. In order to handle the upper bound of the disturbance is unknown, an adaptive fuzzy sliding mode controller is presented. Both simulation and experiment indicate that proposed approaches are feasible and effective.

Reactive power optimization (RPO) is a key task in the operation and control of active distribution networks (ADNs). The nonlinear power flow constraints and the integers introduced by voltage regulator (VR) constraints make the nonconvex RPO model difficult to solve. In this paper, a RPO model is proposed considering the nonuniform tap ratios of VRs. The three phases in VRs are independently controlled and the phase coupling effects are strictly considered. Moreover, to deal with the bilinear relationship among continuous complex voltage phasors and discrete tap ratios, the voltage phasor matrix is decoupled into real and imaginary parts, and a status variable method is proposed to exactly linearize the bilinear terms. Further, the nonlinear power flow constraints are relaxed to a set of second-order cone constraints without neglecting the coupling effect among the three phases and are proved to be equivalent to the semi-definite constraints, which does not require the rank-1 verification and is more efficient and scalable. Thus, the original nonconvex RPO for three-phase unbalanced ADNs is simplified to a mixed-integer second-order cone programming (MISOCP) model. Case studies validate the model’s effectiveness, and the computational efficiency meets practical requirements. Note to Practitioners—This paper simplifies the complex problem of reactive power optimization for active distribution networks with unbalanced three-phase power flows. We offer a novel RPO model improving the typically nonconvex and nonlinear optimal power flow problem, and addressing the particular challenges imposed by voltage regulators optimization with nonuniform tap ratios. Independent control of the VR phases and accurate incorporation of phase coupling effects have been realized, greatly simplifying the optimization process. The transformation of nonlinear power flow constraints into a computationally efficient set of second-order cone constraints eliminates the need for cumbersome rank-1 verification. Our mixed-integer second-order cone programming model integrates smoothly with standard optimization procedures, improving voltage regulation and network stability. The effectiveness and efficiency of the approach have been validated in case studies, offering a viable tool for industry application.

Congestion analysis is critical for power system analysis and operation, but the integration of renewable energy sources (RESs) and energy storage systems (ESSs) will bring great uncertainty and computational challenges. In this study, we propose an accelerated simulation method for long-term congestion assessment in power systems characterized by a high proportion of RESs and ESSs. Our approach includes an affine adjustable robust congestion assessment model capable of identifying congestion in each sampling. The model utilizes automatic generation control to address uncertainties associated with RESs and incorporates multi-period coupling constraints for components with chronological characteristics. Additionally, the Cross-Entropy-Latin Hypercube Sampling (CE-LHS) algorithm is employed to expedite convergence during sampling generation in sequential Monte Carlo Simulation (SMCS). Numerical results from several test systems demonstrate the effectiveness and computational enhancements achieved by the proposed technique. Note to Practitioners—This paper presents an accelerated method for long-term congestion assessment in power systems with high-proportional RESs and ESSs. A robust optimization model with multi-period coupling constraints is proposed to establish operational boundaries for long-term congestion analyzes. Building on SMCS, the CE-LHS algorithm is integrated to improve convergence performance. CE produces the optimal parameter distribution of the system, while LHS effectively mitigates the truncation effect associated with CE. The application future of this method is not limited to power systems, it can also be utilized in other industrial systems characterized by significant uncertainty, such as energy systems, structural facilities, and automated control systems.

Solving large-scale stochastic dynamic economic dispatch problems involving energy storage over multiple time periods is inherently challenging. Decomposing the optimization problem across time scales to achieve parallel optimization is an effective strategy for enhancing computational efficiency. However, the introduction of energy storage complicates this task significantly due to its non-convex characteristics. To address this challenge, this paper presents a novel strategic two-stage Diagonal Quadratic Approximation Method (DQAM) that transforms the original problem into a two-stage structure amenable to parallel solving. In this structure, each sub-problem focuses on a single time period, effectively handling the mixed-integer and strong temporal coupling characteristics of energy storage. This extension broadens the applicability of the original DQAM to non-convex problems. Numerical results under various conditions demonstrate the effectiveness and performance of the proposed two-stage DQAM, achieving significantly improved solution efficiency while maintaining good solution accuracy. Leveraging computational processor and memory resources, the proposed method can achieve a maximum enhancement of 36.86 times in computational efficiency on large-scale systems with multiple time periods. Note to Practitioners—With the increasing scale of power systems and the growing penetration of renewable energy, the accuracy and real-time requirements for economic dispatch solutions have been continuously enhanced. Solving large-scale optimization problems over multiple time periods in power grids has become more challenging, especially with the additional computational burden introduced by the deployment of energy storage to mitigate renewable energy fluctuations. The configuration of energy storage generates a large number of binary decision variables, which results in the original problem becoming a large-scale mixed-integer programming model which is difficult to solve. This paper proposes a strategic two-stage DQAM to solve the stochastic dynamic economic dispatch problem with energy storage, utilizing a two-stage structure to determine an approximate energy storage optimization schedule through an optimization approximation function. Subsequently, the equivalent dynamic economic dispatch problem is transformed into a sizable form with smaller and more easily solvable sub-problems. By relaxing the temporal coupling constraint, the computational efficiency is significantly improved. Test results on systems of various scales and time periods demonstrate that the two-stage DQAM reduces computation time in all scenarios.

Multi-energy systems with energy storage can coordinate various energy carriers to facilitate the integration of large amounts of distributed energy sources and promote the overall efficiency of energy use, which needs distributed dispatch with the requirement of security and privacy. This paper studies the distributed economic dispatch based on information from neighboring agents only. In order to handle the non-convexity due to the complementarity constraint of energy storage, it is proved that simultaneous charging and discharging is suboptimal for the multi-energy systems. Based on this, an equivalent convex problem is reformulated. A scalable distributed algorithm based on parallel ADMM and dynamic consensus mechanism, termed DEED-ADMM, is then proposed. It is shown that DEED-ADMM is scalable in terms of per-agent energy consumption and computational complexity with centralized methods. Moreover, under general convex cost functions, convergence properties of DEED-ADMM are theoretically analyzed by adopting the Lyapunov-based approach. It is proved that the primal problem and the dual problem can be simultaneously solved. Finally, case studies demonstrate the effectiveness of the proposed algorithm. Note to Practitioners—This paper is motivated by the problem of coordinating various energy carriers as well as energy storage in multi-energy systems to promote the overall efficiency of energy use. The coupling among different energy carriers and the complementarity constraint of non-simultaneous charging and discharging of battery storage make the problem non-convex. Existing distributed approaches require stringent assumptions on the cost functions, or suffer from a heavy computational burden. To address the above challenges, a fully distributed algorithm is developed, which is scalable and suitable for large-scale systems. Moreover, it is the first distributed algorithm that solves the economic dispatch problem and the dual problem simultaneously in multi-energy systems with general convex cost functions. Practitioners can easily adjust the coefficients of the proposed algorithm to guarantee convergence for the IEEE 30-bus or even 116-bus systems, as long as the economic dispatch problem is feasible. Our future work will focus on designing resilient mechanisms under potential attacks and considering more practical situations such as power loss.

Optimization problems arise in various domains, ranging from power systems to resource allocation and large network management. An effective solution to these problems in a distributed manner has become a crucial research area due to the increasing scale and complexity of modern systems. In this article, we propose a novel local projection global tracking (LPGT) decentralized algorithm based on the Alternating Direction Method of Multipliers for general optimization problems. Unlike existing distributed methods that require problem-specific adaptations or centralized coordination, LPGT provides tailored solutions for handling generic local equality and inequality constraints, as well as global coupled equality and inequality constraints. Moreover, a projection-based analytical scheme is designed to handle generic local equality and inequality constraints without iterative subproblem solvers, and a fully decentralized deviation tracking mechanism is constructed to enforce both global coupled equalities and inequalities constraints via agent communications, eliminating the need for a central coordinator. Case studies for a local energy trading model are proposed to verify the feasibility and applicability of the algorithm.

Data centers (DCs) play a crucial role in the modern digital era. High service reliability is critical for DCs to provide the desired quality of service. This work models the task execution progress from a novel perspective of process sequence dependency, which fully considers the execution sequence of all constituent processes for the completion of a task. Subsequently, an innovative sequence-dependency-concerned process migration mechanism is established, by which the characteristics of sequence-free tasks, sequence-strict tasks, and sequence-relied tasks are meticulously portrayed. Furthermore, taking a district’s single-point and multi-point power supply failures into account, by exploring the roles of power supply systems, backup power systems, and uninterruptible power supply systems of DCs with different power supply importance levels, a data-density-based dispatch model is proposed under district power supply failure. Finally, considering prediction errors of photovoltaic power and process arrival rate in practical DC operations, a two-stage robust optimization model is proposed and a nested column-constraint generation algorithm is employed for problem solutions. Simulation results verify the presented task migration mechanism can effectively conduct economic task reallocation following the task completion priority and sequence dependency requirements.

The vigorous development of electric vehicles (EVs) is an important means of reducing carbon emissions and mitigating environmental problems such as the greenhouse effect. Battery swapping stations (BSSs) can both provide battery swapping services for large-scale EVs and charge batteries centrally. As the supply of fully charged batteries in the BSS shrinks, it becomes necessary to schedule the charging of the depleted batteries rapidly that users have swapped for fully-charged ones. The charging schedule for depleted batteries must be made without knowledge of future battery arrivals. In this context, this paper develops a mathematical model for online charging scheduling of BSSs, formulates the charging strategy as a two-dimensional rectangle packing problem, and quickly calculates the scheduling arrangement of batteries by partitioning the remaining available capacity of a BSS. Since there are limited battery types within the BSS which can provide battery replacement services, this paper supplements the proposed model with known battery types, which improves the utilization of the available capacity of BSSs. Finally, numerical results verify the effectiveness of the proposed model.Note to Practitioners—Electric vehicles (EVs) are becoming an alternative way to reduce carbon emissions in transportation systems. Herein, the optimal battery charging problem is the core problem when it comes to dispatching a huge number of EVs. Up to now, battery-swapping is widely used for EVs due to its simple, convenient way. Furthermore, a business model for the battery swapping stations (BSSs) is brought up, where EV users send their depleted batteries to the BSS and the BSS provides the users with a fully charged replacement battery from its warehouse, which only takes a few minutes. Since the maximum charging power of the BSS is limited by the capacity of the transformer connecting the BSS to the power grid, the BSS will adopt an optimal charging schedule that maximizes the charging benefit for large quantities of depleted batteries in the warehouse. However, the challenge is that the charging schedule for depleted batteries must be made without knowledge of future battery arrivals because the EV behaviors are difficult to predict. To address this problem, this paper developed an online charging scheduling algorithm, which formulates the charging strategy as a two-dimensional rectangle packing problem. The proposed method can provide battery replacement services in real-time and solve quickly without any information about incoming depleted EV batteries. The proposed model and method have been tested on the system with different numbers of batteries to show the effectiveness. Besides, the online two-dimensional rectangle packing problem can provide an online decision for BSSs.

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM.Note to Practitioners—Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

Due to the spatially and temporally transferable workloads, data centers (DCs) become increasingly important in demand response (DR) implementations. By making full use of their owned DCs, data center operators (DCOs) are significant DR resource providers. To fully exploit the DR capability of the DCO on different time scales, we present a two-stage scheduling model for DCOs and the system operator (SO). In the DR scheduling, the SO formulates DR compensation prices first, and then each DCO decides its best-response power demands accordingly. Considering the profit-hunting property of the SO and DCOs, a two-stage DR Stackelberg game model is proposed. Furthermore, the existence and uniqueness of the Stackelberg equilibrium are proved. Finally, to protect the data privacy of DCOs, we design a Kriging-metamodel-based algorithm which avoids the DCO privacy exposure to the SO in the optimization process. Simulation results prove the accuracy and the calculation efficiency of the proposed Kriging-metamodel-based algorithm.Note to Practitioners—DCs play an increasingly important role in the power balance of grids in recent years. Existing studies focusing DCs’ DR participation generally consider the single-stage DR participation of DCs which ignores the role of DCOs in unified scheduling and management of their owned DCs. Considering the impacts of service request submitting time on the DR capabilities of DCs, this work proposes a novel two-stage DR scheduling model in the account of the unified scheduling role of DCs. Then, a Stackelberg game model is further proposed to characterize the profit-hunting property of the SO and DCOs. Finally, a privacy-protected algorithm is designed to address the optimization problem without explosions of DCO’s sensitive data. Simulation results show the effectiveness of the proposed model and algorithm in encouraging DCOs to adjust their energy consumption plans according to the SO’s request. Moreover, it is proven that the proposed algorithm can achieve global optimization with effective data privacy protection and low computation cost. Simulation results suggest that the proposed method can obtain a high-quality solution for a Stackelberg game model with privacy protection.

This paper proposed sufficient conditions of the zero duality gap for the second-order conic programming approach of the DC optimal power flow that quadratically embeds the transmission loss. The mechanism of the changes for locational marginal price with differently selecting the slack bus is revisited, based on which a load-weighted distributed slack bus method is introduced. Furthermore, a second-order conic programming-based convexification method is proposed by employing the duality analysis. A favorable property of the proposed method is that mild sufficient conditions of the zero duality gap can be derived by the analysis of Karush-Kuhn-Tucker conditions. Numerical results illustrate the effectiveness of the proposed method and physically prove the proposed sufficient conditions. Compared with traditional and similar market-clearing methods, the proposed method has better performance on convergence, robustness, and accuracy. Note to Practitioners—This paper was motivated by the problem of the pricing mechanism in the deregulated electricity market but it is also applicable to rapidly solving the power flow of power systems with sufficient reactive power. Existing approaches use the B-coefficient to estimate the transmission loss in the model non-linearly. In this paper, an improved approach considering transmission loss is proposed, which further introduces the distributed slack bus method and subsequently employs the second-order cone programming algorithm. The proposed method hedges the risk of appearing multiple solutions or lack of accuracy. Rigorous mathematical proofs are derived to support the method. For industrial practice, three sufficient conditions suitable for different kinds of power systems are given, indicating when the proposed approach can be efficiently applied. The proposed method can be integrated into the existing electricity market trading platform for independent system operators and facilitates real-time market clearing and electricity price calculation. Future research is expected to improve the accuracy of the model based on nodal power balance equations.

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. Note to Practitioners— This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

Energy storage (ES), with its flexible characteristics, has been gaining attention in recent years. The ES planning problem is highly significant to establishing better utilization of ES in power systems, but different market regulations impact the ES planning strategy. Thus, this paper proposes a novel ES capacity planning model under the joint capacity and energy markets, which aims to minimize the total cost for power consumers. The great challenge is that the ES planning model has a large number of time periods, which significantly increases the problem dimensionality. In order to alleviate the computational burden, a fully parallel algorithm is proposed to temporally decompose the original problem into a series of small sub-problems, which can be solved in parallel. Moreover, we find that the corresponding analytical solutions to the sub-problems remarkably accelerate the calculation speed while ensuring accurate results. Finally, numerical results verify the effectiveness of the proposed model. Note to Practitioners—Energy storage (ES) has become more and more essential to guaranteeing power balance in power and energy systems by shifting peak loads to valley loads. However, investors may face challenges to ES capacity planning due to the lack of business models. To address this challenge, price tariffs should be carefully investigated. In the practical power system, the market price should consider both the energy price and capacity price for industries and big companies. In the energy market, investors can gain a profit by selling energy at the peak load (high price) and buying energy in the valley (low price). It should be noted that the energy market cannot recover the ES investment cost, but investors can, in fact, reduce their capacity cost since ES can reduce the peak load. Consequently, we have designed a new business model for ES planning under joint capacity and energy markets to analyze the profits via the two market regulations. The computational burden is another challenge for the proposed multi-period convex optimization model. The model must consider a long-term simulation, potentially containing thousands of time periods, which can be difficult to solve. In order to alleviate the computational burden resulting from the long-term market simulation, we further propose a fully parallel algorithm to solve the proposed business model for ES quickly. To sum up, the proposed model and method have been tested on a practical company with a practical price tariff in China to show their effectiveness.

Since wind resources increase with altitude, many wind turbines are installed in high-altitude areas, where blade icing may occur frequently in cold weather. Ice accretion on wind turbines can lead to severe aerodynamic performance degradation or even shutdown. Furthermore, considering the spatiotemporal uncertainty of wind resources, wind power prediction (WPP) in cold weather will be extremely complex. However, existing methods mostly focus on icing-related shutdown detection of wind turbines and pay little attention to the associated WPP during cold weather. To address this problem, a novel Bayesian deep learning-based WPP (BDL-WPP) model is proposed. First, hybrid features related to WPP are extracted based on the actual operational characteristics of wind turbines, and the whole process of blade icing and de-icing is considered for the first time. Then, a BDL-WPP model is proposed based on the extracted features. In order to process the time series information within the BDL framework, a variational Bayesian gated recurrent unit is developed to implement the proposed BDL-WPP model. Finally, a posterior inference algorithm is derived for the BDL-WPP model based on stochastic variational inference. The proposed method is tested on a real-world provincial grid, and the results show that its mean absolute error is consistently below 0.025 under both normal and icing conditions, verifying its effectiveness.

The ongoing process of decarbonizing the power system and the frequent occurrence of extreme weather have led to a significant increase in operating uncertainty and greatly reduced the system controllability. An effective risk assessment and early-warning tool will significantly assist system operators in monitoring and controlling power systems. However, existing methods mainly rely on simplified analytical conditional probability models to describe the component failure probability under different operating conditions and are not suitable for low-probability risk assessment. Inspired by the idea of Bayesian statistics, a Bayesian deep learning-based probabilistic risk assessment and early-warning model considering meteorological conditions is proposed in this article. A new Bayesian neural network (BNN) is proposed which efficiently utilizes expert experience and domain knowledge as prior to model the contingency probability. And a hybrid neural network is developed to rationally utilize the multisource heterogeneous data and comprehensively analyze the historical and forecast information. Finally, a novel risk assessment and early-warning model for high-impact, low-probability extreme events is proposed, which can predict the risk for the nextntime-steps. The proposed method is tested on a modified IEEE 118-bus system and a real-world provincial grid, and the results verify its effectiveness.

Electric vehicles (EVs) have been gaining great popularity in recent years, but the lack of adequate infrastructure and the long battery charging time have hindered their further development. Therefore, a battery charging and swapping system (BCSS) can solve this problem by arranging battery charging and distributing the battery swapping system (BSS) to various locations while participating in the demand response of both power and transportation networks through time-of-use tariffs and congestion price. To optimally achieve the combined operation of BCSSs, this paper proposes a hybrid swapped battery charging and logistics dispatch model in the continuous-time domain. Specifically, the battery charging system will arrange the optimal battery charging strategy by a rectangle packing algorithm. Furthermore, the logistics system will set up a transportation dispatch model for the battery charging system to deliver the charged batteries from the battery charging system to the battery swapping system and then retrieve them. The combined model is involved in the demand side response considering the price. Simulation studies for different cases verify the effectiveness of the proposed model.

Shipboard integrated power systems (SIPSs) are usually equipped with multiple pulsed power loads (PPLs). In complex scenarios with strict operational requirements, the performance of the SIPS is greatly affected by the output energy of PPLs, especially in achieving high suppressive capability in a short period. To maximize the short-time output efficiency of PPLs in emergency situations, the aperiodic scheduling method is studied, aiming at optimizing the coordination of multiple PPLs and energy storage. The proposed aperiodic scheduling model aims to maximize the total utility of PPLs in the given period. The model fully considers constraints related to energy storage, system power balance, aperiodic charging and discharging process, time sequence, and charging power. To solve this complex non-linear model, a bi-layer dynamic programming algorithm is proposed. Simulation tests of SIPS performance are carried out to validate the advantage of the proposed method. The results show that the performance of single PPL and multi PPLs with aperiodic scheduling is improved by 42.3% and 25.7% respectively compared with periodic scheduling.

Data centers (DCs) have been playing a significant role in demand response (DR) programs in recent years due to their considerable DR capability. DCs are in the charge of the DC operator (DCO), who is responsible for making a reasonable allocation of computing tasks to provide DR resources. To relieve the transmission pressure of power systems, the system operator (SO) encourages DCOs to participate in the DR programs. To maximize the total welfare, a detailed DR scheduling model of DCOs and SO is proposed for the coordinative optimization. Considering the privacy issue of DCOs, a two-level distributed scheduling algorithm based on the alternating direction multiplier method (ADMM) is designed for privacy protection and distributed autonomy. Simulation results show that the proposed coordinative optimization algorithm can effectively realize the maximization of total social welfare with data privacy protection. For a power system with multiple DCOs, reasonable scheduling of DCO’s DR resources can reduce the peak-valley difference of system loads reliably and economically.

In this paper, a hybrid machine learning model is applied to evaluate the relationship between random initial states and the power system’s vulnerability to cascading outages. A cascading outage simulator (CS), which uses off-line AC power flows, is proposed for generating training data. The initial states are randomly selected and the CS model is deployed for each initial state, where power system generation and loads are adjusted dynamically and power flows are redistributed to quantify the vulnerability metric. Furthermore, the proposed hybrid machine learning model deploys a combined Support Vector Machine (SVM) classification and Gradient Boosting Regression (GBR) to improve the learning precision. The classification model is trained by SVM, which divides the data into two categories with and without load shedding. Then, GBR is adopted only for the data with load shedding to determine the relationship between input power outage states and the vulnerability metric. The proposed vulnerability analysis approach is applied to several test systems and the results are analyzed. Note to Practitioners—The power system vulnerability can be quantified by cascading outage simulations. However, there are two challenges: i) there are a huge number of possible initial states and we cannot enumerate all these initial states for the cascading outage simulation. Neither can we precisely quantify the bus vulnerability. ii) The cascading outage simulation may be time-consuming for large-scale power systems, which is challenging for the online application. To address the above challenges, we expect to design a machine learning technique to predict the power system vulnerability, which can train the model in an offline way and then use it for the online application. Firstly, since there is not enough operation data from practical power systems, we develop a cascading outage simulator, using off-line AC power flows, for generating synthetic training data. Secondly, we observe that the training precision by directly applying the regression model may be very poor because the output of the machine learning model may take on an uneven distribution concerning input parameters. Thus, we propose a hybrid machine learning model with a combined classification and regression method, where the classification model is employed to remove the data without the load shedding, and the regression model then determines the relationship between input power outage states and the vulnerability metric. The proposed model and method have been tested on several systems including a practical large-scale Polish power system to show the effectiveness.

This article investigates the resiliently distributed fixed-time control of frequency recovery and power allocation in a multi-terminal high voltage direct current (MTDC) system against denial-of-service (DoS) attacks. An MTDC system typically consists of several AC areas, on which the DoS attacks may cause communication faults by blocking communication channels, preventing certain AC areas from sending message and damaging related facilities. A novel distributed security control scheme is proposed in this paper, which introduces attack detection method and communication repair mechanism to restore the paralyzed topology caused by DoS attacks. By extension, a resiliently distributed fixed-time control is presented under this frame. The proposed control scheme can not only realize frequency restoration but also accomplish active power sharing under DoS attacks. Furthermore, different from existing control strategies, the advanced scheme can guarantee the convergence time without considering the initial value, which helps improve the robustness and stability of the MTDC system. The resilient stability of the proposed scheme is proved by Lyapunov-Krasovskii stability theory. Finally, case studies on an MTDC system are conducted to demonstrate the effectiveness and validity of the proposed controller. Note to Practitioners—MTDC system is a large-scale power system connecting various AC grids. It has the characteristics of distributed and high intelligence, which is prone to be attacked by an adversary. As an index to measure the safe and stable operation of MTDC system, frequency is the focus of this paper. We propose a novel topology recovery mechanism for MTDC systems under DoS attack and design a resilient fixed-time secondary frequency controller based on the idea of multi-agent. The experimental results show that under DOS attack, the proposed topology recovery mechanism and controller can recover the frequency to the rated value in a fixed time and realize the proportional distribution of active power. In practical application, engineers can learn from the controller to resist DoS attack and realize the stable operation of large-scale distributed power system.

Load aggregators (LAs) play a key role in fully tapping the demand response (DR) resources of small and medium-sized end-users to enable a more flexible power grid. In the ancillary service market, the LA can provide DR to the system by aggregating the resources of its users. In response to the issued DR program, end-users offer to provide DR resources. To help optimize the user bidding strategy, an evolutionary game model is presented here in view of the bounded rationality of bidders. A combined Q-learning and compound differential evolution (CDE) algorithm is proposed to deal with the problems of incomplete information and uncertainties in the opponents’ decision-making, and prevent the evolutionary stable strategy (ESS) from falling into a local optimum. Moreover, a cloud-computing-based framework is designed and agent servers are introduced to protect data privacy. Numerical results show that by adopting the proposed algorithm, the user's bidding price keeps slightly lower than the opponents’ price which guarantees its revenue remains on a high level. This indicates that the proposed algorithm has good adaptability for addressing incomplete information and uncertainties in opponents’ decision-making.

As an auxiliary to the electricity market, the traditional frequency regulation market (FRM) lacks reliable data storage ways and direct transaction channels for buyers and sellers, and the cost-sharing method of frequency regulation (FR) service is still unfair. To this end, this article proposes a general and decentralized FRM framework based on multiblockchain techniques. According to the scheduling sequence of transactions, the FR services are divided mainly into before-the-fact transactions (BFTs) and after-the-fact transactions (AFTs). We construct a combinatorial double-auction model for BFTs and propose a novel cost-sharing model based on triggers for AFTs. Taking Pennsylvania-New Jersey-Maryland as an example, we design a consensus algorithm for the on-chain transaction process and cost sharing. Numerical results on both types of transactions show that the proposed auction model can meet the different needs of FR buyers. The proposed sharing method highlights that triggers from frequency events should result in higher costs. The consensus algorithm also improves the fault tolerance and throughput of transactions.

Integrated energy systems become more and more important to realize the energy complementary property. Micro-integrated energy system, served as the terminal integrated energy system, will have the electricity delivered directly to the local customers by energy hubs (EHs). Here, the data and information of the EHs during the operation are confidential and should be kept by each owner. Therefore, this article designs a dual-decomposition-based distributed algorithm to address this problem, where the optimal consensus problem is used for the dual problem to update the multipliers. The primary and dual problems are alternatively solved until the Karush-Kuhn-Tucher condition is satisfied. For the proposed distributed algorithm, the feasibility can be strictly guaranteed during the iteration process. Moreover, theorems and lemmas are proved for the linear convergence rate. The numerical results verify the effectiveness of the proposed algorithm.

Nowadays, the entire world is facing challenges in energy and environment. To resolve these problems, the power systems are interconnected to promote the development of renewable energy sources (RESs). However, the economic dispatch (ED) problem for the global energy interconnection (GEI) should tackle two issues: 1) handle the uncertainty from RES and allocate the responsibility among the interconnected countries and 2) protect the information privacy through the dispatch. Motivated by the above, this article proposes a zonally adjustable robust decentralized ED model for the GEI. In the model, each country is only responsible for its own uncertainty, and tie-line power flows remain unchanged under uncertainties. Moreover, an alternating direction method of multipliers (ADMM)-based fully distributed algorithm is used, in which only limited information should be exchanged between neighboring countries. Finally, a case study on the Northeast Asian countries verifies the effectiveness of the proposed method. Note to Practitioners-Since the renewable energy generation has a spatial correlation among regional countries, global energy interconnection (GEI) aims to combine several power systems together to promote the renewable energy accommodation. However, two problems need to be considered: 1) Information Privacy: The information privacy of the power system in each country should be preserved, which prevents the GEI from conducting a centralized optimal dispatch framework and 2) Uncertainty: The uncertain output of renewable energy resources brings challenge to the power system secure operation. The main contribution of this article is to set up a zonally robust decentralized optimization for the GEI, where the zonally robust economic dispatch (ED) is conducted by the area control error (ACE) system to manage the difference between scheduled and actual generation under the uncertainties, and the alternating direction method of multipliers (ADMMs) algorithm is adopted for decentralizing the zonally adjustable robust ED model, which only needs limited information. In particular, this article uses a real-world example from Northeast Asian Countries to help engineers understand the advantages of the GEI and the new dispatch framework.

An isolated power system (IPS) usually operates in an islanded mode. Because of the lack of support from an external power grid, stability is a prominent issue for IPSs. This article proposes a novel stability analysis approach for IPSs based on the input-to-state stability (ISS) theory. Compared with existing stability analyses that use simulations and direct methods, the proposed method decomposes the stability analysis process by considering the ISS properties of subsystems and a network equation that reflects their connections. Thus, it has good adaptability for the stability analysis of systems with flexible operating conditions. Algorithms are presented for estimating the ISS properties of subsystems, and asymptotic gains in a piecewise linear form are adopted. The small gain theorem is used for the decomposed stability analysis, and a practical algorithm to numerically check the small gain condition is presented. Time-domain simulations were performed with a test system to verify the effectiveness of the proposed decomposition-based stability analysis approach.Note to Practitioners—Power systems used in shipboards, airplanes, remote areas, and so on are usually classified as isolated power systems (IPSs). The continuity of power supply in IPSs is the prerequisite of fulfilling certain tasks. Due to the lack of support from the bulk power grid, the normal operation of IPSs can be threatened by various external disturbances, such as disasters, battle damages, device failures, and so on. To maintain the survivability and reliability of IPSs under extreme conditions, fast reconfiguration and emergency control approaches are often performed, which lead to system topology changes and frequent connection/disconnection operation of devices in IPSs. Because of the limited generation capacity of an IPS, a stability analysis after an emergency is important for ensuring that the IPS can perform tasks normally, and can provide guidance for designing fast reconfiguration and emergency control strategies. However, current stability analysis approaches have limited applicability or are overly conservative for analyzing the stability of IPSs. To address the challenge of changeable topologies for the stability analysis of an IPS, this article proposes a decomposition-based analysis approach using input-to-state stability (ISS) theory. By decomposing the entire system into several subsystems, the system’s stability can be checked through the ISS properties of subsystems and their connections. The ISS properties of subsystems can be estimated offline, which saves time for online calculation. To reduce the conservativeness of stability analysis, the asymptotic gains in piecewise linear form are adopted in this article. Practical algorithms are designed for efficiently checking the proposed decomposition-based stability conditions. The research outcome provides a fast and flexible stability analysis approach that can adapt to the frequent changes in the operating conditions of IPSs.

To increase the resilience of shipboard power systems, this paper presents an optimal defense strategy to protect critical lines against attacks. In the modeling, an attack is considered to destroy one critical bus, which may result in that all lines are connected to this bus will be out of service unless protection is enabled. Furthermore, after one true attack occurs, the network restoration is performed as soon as possible to pick up the critical loads and maintain system operation. To address the uncertain location of the attacks, a tri-level robust optimal defense strategy is set up to protect the critical lines under the worst attack. Moreover, a nested column-constraint generation method is employed to solve this model. A 60-bus shipboard power system is studied to demonstrate the effectiveness of the proposed model and the defense method.

This paper first presents a comprehensive model of the gas system with detailed formulations on pipelines, short pipes, resistors, valves, compressors, and compressor stations. Furthermore, an optimal energy flow model is proposed for integrated power-gas generation and transmission systems. Specifically, on the generation side, gas-fired units couple the two energy systems as the power generation and gas sink; on the transmission side, gas compressor stations link the two energy systems as the power demand and gas transportation. However, gas flow equations are nonlinear and gas flow directions also need to be optimized. Logical programming and tailored piecewise linearization techniques are performed, leading to a mixed-integer linear program (MILP). Only a logarithmic number of binary variables are introduced to represent the nonlinear quadratic function, and thus, the MILP model can be solved very efficiently. Numerical results on four power-gas test systems demonstrate the effectiveness of the proposed approach.

Look-ahead unit commitment (LAUC) is recently introduced among independent system operators (ISOs) in the U.S. to increase generation capacity by committing more generators after day-ahead unit commitment when facing various uncertainties in the power system operations. However, as the share of intermittent renewable energy increases significantly in the power generation portfolio, the load continues to fluctuate, and unexpected events and market behaviors happen nowadays, the ISOs are facing new critical challenges to maintain the reliability of power system. To systematically manage these uncertainties and corresponding challenges, new advanced approaches are urgently required to improve current LAUC models and solution methods. Therefore, in this paper, we first propose a new formulation to represent forbidden zones and dynamic ramping rate limits, which help capture the system operation status more accurately and hedge against the uncertainties more effectively, and then correspondingly propose a data-driven risk-averse LAUC model. Our computational experiments show how the size of data influences operational decisions and how the inclusion of forbidden zones and dynamic ramping provide better decisions.

State estimation is a fundamental function in modern energy management system, but its results may be vulnerable to false data injection attacks (FDIAs). FDIA is able to change the estimation results without being detected by the traditional bad data detection algorithms. In this paper, we propose an accurate and computational attractive approach for FDIA detection. We first rely on the low rank characteristic of the measurement matrix and the sparsity of the attack matrix to reformulate the FDIA detection as a matrix separation problem. Then, four algorithms that solve this problem are presented and compared, including the traditional augmented Lagrange multipliers (ALMs), double-noise-dual-problem (DNDP) ALM, the low rank matrix factorization, and the proposed new “Go Decomposition (GoDec).” Numerical simulation results show that our GoDec algorithm outperforms the other three alternatives and demonstrates a much higher computational efficiency. Furthermore, GoDec is shown to be able to handle measurement noise and applicable for large-scale attacks.