Conventional harmonic source location methods based on single-shot sampling or short-term measurements offer limited reliability. Therefore, this paper proposes a harmonic source location strategy for distribution networks using group-sparse Bayesian learning under an edge-computing architecture. First, an edge-computing enabled hierarchical and partitioned framework for harmonic source location in distribution networks is established. The functions of edge nodes at various levels and their collaborative workflow are explicitly defined, enabling local processing of harmonic data and preliminary location. Second, a federated conditional diffusion model is proposed to generate missing harmonic measurements, enabling the effective reconstruction of incomplete harmonic measurement data. Then, a method for locating local harmonic source based on grouped sparse Bayesian learning is proposed. It constructs a typical-day confidence-interval measurement set from long-horizon harmonic monitoring data, applies group-sparse Bayesian learning to estimate the harmonic state interval, and further enables initial harmonic source location under limited measurement devices. Finally, the effectiveness of the proposed method is validated in a simulation environment. The simulation results demonstrate that, even under sparse and partially missing measurements, the proposed strategy can achieve accurate harmonic source location.

With the rapid development of cloud computing and big data technologies, the coordinated optimization of computational loads and energy management strategies across multiple data centers (DCs) has become crucial for enhancing resource efficiency and reducing operational costs. Therefore, a coordinated scheduling optimization method for multiple DCs considering cheating behaviors is proposed based on improved approximate dynamic programming with piecewise linear function approximation (PLF-IADP). First, a coordinated scheduling optimization model for multiple DCs based on asymmetric Nash bargaining theory is developed. The model is then transformed into two-stage reformulated optimization submodels to ensure solution quality while reducing computational complexity. In the first stage, a PLF-IADP-based coordinated optimization algorithm is proposed, enabling high-quality and efficient real-time optimization decisions under uncertain conditions. In the second stage, a cooperative game equilibrium solving algorithm that accounts for cheating behaviors, i.e., strategic misreporting of private cost information, is presented, ensuring the convergence and feasibility of the cost allocation strategy in the presence of cheating behaviors, while avoiding infeasible outcomes in extreme cheating scenarios. Case study results on a cooperative alliance consisting of multiple DCs demonstrate that the proposed method improves the performance of coordinated scheduling optimization in uncertain environments, ensures fair cost allocation based on DC contributions, and effectively mitigates the negative impact of cheating behaviors on the fairness and stability of the alliance.

With the penetration of distributed generation and power electronic devices in distribution networks continuing to increase, harmonic issues have become increasingly prominent. To accurately capture the harmonic distribution in distribution networks, harmonic state estimation must be conducted. However, this requires the reasonable deployment of sufficient measurement devices within the grid. Therefore, this paper presents a hierarchical and partitioned optimization strategy for multisource measurement configuration in harmonic state estimation of distribution networks. Firstly, various harmonic measurement devices, including phasor measurement units and power quality monitoring systems, are considered to construct a multi-source measurement hierarchical and partitioned configuration framework along with deployment guidelines. Secondly, a multisource harmonic measurement hierarchical and partitioned optimization strategy is proposed, targeting limited measurement resources, to achieve differentiated and collaborative deployment of measurement resources. Finally, the proposed strategy is validated in the modified IEEE 123-bus system. Simulation results demonstrate that, under the constraint of limited measurement devices, the proposed method ensures the maximum observability of the system, providing an economically viable monitoring solution for harmonic state estimation in distribution networks.

Mobile Energy Storage Systems (MESSs) are critical for improving distribution network resilience under extreme weather events. However, the mathematical model for MESS routing and scheduling is essentially a high-dimensional mixed-integer nonlinear stochastic optimization problem. To accurately and rapidly obtain the routing and scheduling of MESSs and the optimal operation of distribution networks, a bi-level optimization of MESS routing and scheduling based on a hybrid data-model driven approach is proposed. In the upper level, the data-driven approach is achieved by the graph attention network multi-agent conservative soft actor-critic reinforcement learning (GMARL) to determine optimal routing decisions for MESS in the transportation network while taking into account traffic flow and road repair time uncertainties. The proposed GMARL takes full advantage of a graph attention network for feature extraction, and adopts the multi-agent conservative soft actor-critic to mitigate overestimation caused by out-of-distribution experiences, thereby effectively coordinating multiple MESSs to achieve the optimal strategy. In the lower level, a mixed-integer second-order cone programming is formulated to obtain optimal scheduling strategies for MESSs, reconfiguration and optimal power flow in the distribution network. Upon determining the scheduling strategies and amount of load recovery, the reward function value for each MESS can be calculated and used to update the neural network parameters of GMARL, thereby further optimizing the routing strategies of MESSs. Finally, case studies on an IEEE 33-bus active distribution network and a 12-node transportation network are conducted to verify the effectiveness of the proposed approach.

To address the increased operational risk in distribution network caused by the grid integration of distributed wind power, a distribution network risk assessment method that combines a Dirichlet process mixture model (DPMM) with the cumulant method (CM) is proposed, to achieve effective quantification of operational risk. Firstly, a DPMM is employed to cluster wind power output data, and adaptive kernel density estimation is introduced to construct a probabilistic model of wind power output, thereby improving local fitting accuracy. Secondly, uncertainties arising from wind generation and load are considered, and a probabilistic power flow model for the distribution network is established based on the CM and the Gram–Charlier series expansion, in order to obtain the probability distributions of state variables and branch power flows. Then, distribution entropy theory is introduced to quantify the severity of limit violations for state variables such as voltage and power, so that operational risk assessment is enabled. Finally, simulations are conducted on a modified IEEE 34-bus distribution test system, and the results demonstrate the effectiveness of the proposed method.

With the rapid advancements of artificial intelligence, cross-regional collaboration among data centers (DCs) has emerged as an effective strategy to enhance resource utilization and reduce energy consumption. Without such collaboration, DCs may experience higher operational costs and energy consumption due to imbalances in computational load and disparities in regional electricity prices. Therefore, a triple-stage collaborative optimization method for cross-regional DCs considering optimal coalition matching is proposed. In Stage 1, a potential coalition search method for DCs is proposed, and the Bron-Kerbosch pivoting algorithm is employed to identify high-quality potential coalitions under multi-dimensional complementarity. Then, an optimal collaborative operation model for DCs incorporating fine-grained cooling system modeling is established in Stage 2, aiming to jointly optimize computational load scheduling and energy management. Based on this, an optimal dynamic coalition matching mechanism for DCs is proposed in Stage 3, integrating a rolling-horizon control strategy to adaptively update coalition structures and operation strategies under varying fluctuation levels. Case studies on ten heterogeneous cross-regional DCs demonstrate that the proposed method effectively reduces energy consumption, increases coalition profits and member satisfaction, thereby enhancing both economic performance and operational stability.

The large-scale integration of renewable energy sources has led to a significant increase in the number of harmonic sources within distribution networks. Concurrently, the altered supply modes introduced by renewable integration have caused dynamic changes in the network topology. Therefore, this paper proposes a three-phase distribution network harmonic source location method based on a physics informed topology adaptive graph convolutional network. Firstly, a harmonic pseudo-measurement method based on emission characteristics modelling is developed to address the shortage of harmonic measurements. Secondly, considering the dynamic changes in the distribution network topology, a multi-layer perception topology adaptive graph convolutional neural network is proposed, which is used to establish the mapping relationship between harmonic measurements and state variables. Meanwhile, the harmonic transfer equation and system parameters are embedded into the neural network training as physical constraints to ensure the results conform to physical properties. Then, a harmonic source identification criterion is established, and the long-term statistical index derived from the estimated harmonic injection current is used to locate harmonic sources in the distribution network. Finally, the effectiveness of the proposed method was verified in the IEEE 37-bus system and the actual system.

The advance progress of artificial intelligence and the computational resources have driven a marked increase in energy consumption by data centers. The coordinated scheduling optimization in energy-intensive data center has been extensively studied as a potential solution for cost reduction and efficiency improvement. In data center microgrid (DCM), complex computational workloads are often decomposed into tasks with dependency. It is worth exploring how task dependency influence the operation of DCM. In this paper, a coordinated scheduling optimization method of DCM considering task dependency is proposed. Through directed acyclic graph (DAG) theory, a task dependency-aware load model for DCM is constructed, achieving coupling between tasks and loads. Subsequently, a DCM collaborative optimization model is developed, ultimately realizing the coordinated scheduling optimization of tasks and power. By applying the Alibaba Cluster dataset, the simulation results validated the effectiveness of the methodology.

With the increasing frequency of large-scale black-start events in recent years, the rapid restoration of high-voltage transmission networks has become a critical technical challenge. This paper proposes a coordinated restoration strategy for 500 kV extra-high-voltage transmission networks (EHVTNs) and 220 kV high-voltage transmission networks (HVTNs), incorporating HVDC integration and emergency repair crew (ERC) scheduling. First, an integration and operational model for HVDCs is developed using the adjoint network method, which transforms complex self-impedance constraints into a mixed-integer linear programming formulation, enabling accurate and efficient HVDC integration. Second, fault repair priority indicators—derived from topological connectivity, reachability, and power flow betweenness—are introduced. Based on these indicators, an ERC scheduling optimization model is formulated to prioritize critical fault repairs and minimize overall restoration time. Then, by incorporating the synergistic effects of HVDC integration and ERC scheduling, a bi-level restoration optimization framework based on model predictive control is proposed to coordinate the restoration of EHVTNs and HVTNs. Finally, case studies on an actual 379-bus power system in China are conducted, and simulation results demonstrate that the proposed method reduces restoration time and improves restoration performance compared to conventional approaches, thereby providing effective technical support for rapid grid restoration following large-scale blackout events.

To address the challenge of imperfect market coordination in multi-energy-coupled integrated energy systems (IESs) under uncertainty, especially the unresolved conflicts among stakeholders and the insufficient protection of disadvantaged participants within current market frameworks, an energy management strategy based on data-driven and game theory methods is proposed. Firstly, to optimize the benefits for both individual and collective stakeholders, a tri-level multi-energy management model is developed using multi-game framework, providing a novel approach to capturing interactions among diverse entities. Secondly, to handle the uncertainty of renewable energy, a data-driven distributionally robust chance constraint (DRCC) method is introduced, which uniquely combines dynamic Bayesian network (DBN) with imprecise Dirichlet model (IDM) and applies it to mixed ambiguity set that integrates desirable properties of different ambiguity sets. Finally, fixed-point theory is used to establish the existence of game equilibrium, and a Gauss-Seidel algorithm with adaptive inertia weight, combined with the alternating direction method of multipliers, is proposed to solve the multi-game model while ensuring the privacy of all parties. Case studies demonstrate that the DBN-IDM reduces the conservatism of parameter selection for the DRCC, and the proposed energy management strategy and improved Gauss-Seidel algorithm enhance participant benefits and accelerate convergence.

Community integrated energy systems (CIESs) can serve as intermediaries to integrate flexible resources, such as electric vehicles, into distribution network (DN) operation. However, the coexistence of multiple stakeholders complicates pricing design. To address this issue, this paper proposes a tri-level non-cooperative game pricing framework involving the DN, CIESs, and flexible resources. A non-cooperative trading model between the DN and CIESs is developed, and a flexibility response model with global coupling constraints is formulated. In addition, the schedulable capacity of electric vehicle charging stations (EVCSs) is modeled based on individual EV charging/discharging characteristics using the Minkowski sum. The resulting generalized Nash equilibrium problem (GNEP) is reformulated as a variational inequality (VI), and solved by a distributed algorithm combining Gauss-Seidel and column generation with Dantzig-Wolfe decomposition (GS-DWD-CG). Simulation results show cost deviations within 1.6% from the centralized optimum for the DSO and CIESs, while FRH deviations are 5.4%-9.6%. Inter-CIES trading reduces total CIES cost by 10.60%, and EVCS aggregation reduces computation time by 97.59%.

To effectively enhance the resilience of the coupled energy-transportation network (CETN) after extreme events, this paper coordinates multi-type mobile emergency resources (MERs), including mobile energy storage systems (MESSs), line repair crews (LRCs) and road repair crews (RRCs), to support emergency load demand and repair faults. The collaborative scheduling strategy of MERs is influenced by various uncertainties, including the dynamic traffic flow distribution caused by urban users' travel behaviour, status changes of energy line outages and traffic road faults. Therefore, this paper proposes a hybrid data-model driven approach to solve the optimal routing and scheduling strategies of MERs accurately and efficiently. In the data-driven part, a novel graph diffusion attention network multi-agent reinforcement learning algorithm is proposed to optimize the MERs' routing strategies. The proposed algorithm incorporates a multi-task neural network architecture and various improvement strategies to enhance decision-making speed and training efficiency. In the model-driven part, the method of successive algorithm considering random utility is introduced to solve the transportation travel allocation model based on the modified semi-dynamic user equilibrium, obtaining road traffic flow distribution to get the next moment routing strategies of MERs. Additionally, the second-order cone relaxation and big-M method are employed to construct the MERs' scheduling problem as a mixed-integer second-order cone programming model to solve MERs' scheduling strategies. The effectiveness and scalability of the proposed approach are validated in two CETNs of different scales.

Harmonic state estimation in distribution networks is essential for identifying harmonic sources. However, issues such as limited measurement redundancy, asynchronous measurements, and unbalanced load distributions in three-phase networks undermine the reliability of existing methods in practical applications. To address these issues, this paper proposes an interval harmonic state estimation method in three-phase unbalanced distribution networks, integrating data from multiple sources. First, the interval multi-source harmonic measurement dataset is constructed by integrating asynchronous harmonic measurement data from multiple sources. The time asynchrony of measurement data from power quality monitoring devices is calibrated using the sliding window weighted dynamic time warping algorithm. Second, the interval harmonic state estimation model for the three-phase asymmetric distribution network is constructed. The model is solved using the interval-weighted least squares method, enhanced by the improved Krawczyk operator, thereby minimizing the expansion resulting from interval operations. Finally, the feasibility and accuracy of the proposed interval harmonic state estimation method are validated.

With the increasing integration of distributed energy and flexible resources, efficient coordination and trading mechanisms are urgently required in integrated energy distribution systems. This paper proposes a trading strategy based on a non-cooperative game-theoretic framework to model the multi-agent interactions among distribution network, integrated energy systems (IES), and distributed flexible resources. In the upper-level model, a dynamic game is formulated between the power grid and IESs, where the IESs incorporate distributionally robust chance constraints to handle renewable energy uncertainty. Distribution locational marginal price (DLMP) signals are generated as the outcome of this game. In the lower-level model, flexible resources adjust their energy demand in response to DLMP signals, thereby influencing price formation through demand-side decisions. A fixed-point iteration algorithm is employed to coordinate the bi-level model, and the alternating direction method of multipliers (ADMM) is used to solve the upper-level game in a distributed manner. Simulation results demonstrate that the proposed strategy effectively coordinates multi-agent behaviors, enhances system flexibility, and promotes the active participation of flexible resources in distribution-level market operations.

Hydrogen-enriched compressed natural gas pemetrated integrated energy system (HPIES) stands as a highly promising technique for enhancing energy efficiency and mitigating emissions, owing to its capacity to effectively address the issue of elevated hydrogen transportation expenses. Traditional integrated energy systems (IESs) fail to describe the impact of hydrogen blending on gas properties, gas transportation, and gas separation, and face economic challenges. Therefore, in this paper, a novel HPIES optimal scheduling model is established considering the multi-membrane hydrogen separation and the variable efficiency model of electrolyzer. Firstly, the HPIES model, considering variable hydrogen doping ratio and uncertain starting flow direction, is developed. Secondly, in HPIES, two kinds of membranes are combined to forma multi- membrane hydrogen separation model. The thermodynamics of the electrolyzer and the bubble coverage model are considered in the optimization of HPIES. Finally, the effectiveness of the proposed model is verified by taking IEEE 39 - bus power system and 20 - node natural gas system as an example. In addition, the results indicate that HPIES can accurately reflect the flow of the system, and it has led to a cost reduction of $439,156. Meanwhile, the model demonstrates that multi-membrane hydrogen separation can reduce 46.861 MW and 38.359 MW, respectively, in a single day compared to the other two membranes. The variable efficiency model of the electrolyzer can reflect the trend of changes in the electrolyzer.

Nowadays, integrated energy systems (IESs) have become an influential approach in the backdrop of energy interconnection and low-carbon energy concepts. This paper proposes a multi-energy trading strategy for IESs that simultaneously considers carbon emissions transaction (CET) and tradable green certificate (TGC) to promote low-carbon energy development further. Firstly, a multi-stage robust optimization method addresses uncertainties in renewable energy, loads, and electricity prices to ensure stable operation of the IES. Secondly, a trading mechanism is proposed by integrating CET with TGC to establish a coupled electricity-heat-carbon- green certificate market. Accordingly, a cooperative game framework among multiple IESs is modeled, which considers different contribution allocations while promoting the economic and low-carbon operation of IES. Finally, the model is solved using the alternating direction method of multipliers (ADMM) algorithm. The proposed strategy's effectiveness in improving the low-carbon economic operation of IESs has been proved through simulation studies.

To investigate the impact of conventional generator mechanical output uncertainty, caused by wind power fluctuations, on the transient stability of power systems. An affine algorithm (AA) is introduced to account for uncertainty in power system simulations. Firstly, affine numbers are used to represent the mechanical output range of conventional generators affected by wind power fluctuations. A dynamic characteristic model is then constructed based on wind turbine low voltage ride through (LVRT) parameters during voltage sags. Then, the problem of transient stability assessment under power system uncertainty is formulated as affine differential-algebraic equations (DAEs) that reflects the system's dynamic behavior. Finally, the trapezoidal integration method is employed to solve the affine differential equations, alternating between the differential and algebraic equations. The proposed method allows a rigorous analysis of the impact of uncertainty on system transient stability with only one simulation. A modified IEEE 39-bus system is used to compare the affine calculation results with the Monte Carlo (MC), demonstrating that the proposed algorithm has lower conservativeness and higher computational efficiency.

Under the background of energy interconnection and low-carbon electricity, integrated energy systems (IES) play an important role in energy conservation and emission reduction. To further promote the low-carbon transition of energy, this paper proposes a distributed robust optimal control strategy for IESs based on energy trading. Firstly, an IES model that includes an electric hydrogen module and gas hydrogen doping combined heat and power is established, and ladder-type carbon trading is introduced to reduce carbon emissions. Secondly, for the energy trading issues between photovoltaic (PV) prosumers and IES, a bi-level model is constructed using Stackelberg game method, where the IES acts as the leader and the PV prosumers as the followers. Noteworthy, a distributed robust optimization method is used to address the uncertainty of renewable energy and load. Additionally, the Nash bargaining method ensures an equitable balance of benefits among the various IESs and encourages them to participate in market transactions. On this basis, an intermediary transaction mode is proposed to address cheating behaviors in trading. Finally, the simulation results demonstrate that the proposed strategy not only effectively promotes cooperative operation among multiple IESs but also significantly reduces the system’s operating costs and carbon emissions.

The rise of electric vehicles (EVs) fosters closer integration between the power and transportation sectors. While implementing a fair EV charging pricing strategy optimizes the system economic performance, modeling EV users' behaviors and their elastic demand in response to charging prices remains a significant challenge. This paper proposes a novel pricing scheme for EV charging within power-transportation systems using a trilevel framework that considers the interactions among the power distribution network (PDN), charging network operator (CNO), and EVs. To capture the responsive behaviors of EVs, a user equilibrium (UE) model with price-elastic demand is formulated as a quasi-variational inequality (QVI). This approach reduces the tri-level pricing problem to a bi-level optimization problem by merging the middle and lower levels into an optimization problem with QVI constraints, thereby achieving mathematical tractability. The outer level optimizes energy dispatch in the PDN, while the inner level focuses on the CNO's pricing optimization in response to elastic EV demand. To solve the problem, a projection gradient algorithm and a tailored fixed-point algorithm are developed. Simulation results confirm the effectiveness and superiority of the proposed model and algorithms. Sensitivity analysis further shows that elasticity and regulation significantly affect system efficiency, demonstrating the model's robustness

To investigate the impact of uncertainty stemming from asynchronous measurement timings among various instruments on power system state estimation accuracy, the article employs the affine algorithm. This approach addresses the timing discrepancy between the state estimation moment and the actual measurement time. Firstly, the relevant historical measurement data are obtained through the historical load change curve, and the trend component of the measurement data is obtained by wavelet transform, so as to obtain the change rate of the measurement data. Then, the affine measurement at the time of state estimation is obtained by quantifying the change trend caused by the uncertainty of time deviation. Finally, utilizing the branch current as the state variable, the affine method is applied to obtain the estimation result. Through the IEEE33 node example, the affine estimation results under different time deviation ratios are compared, which verifies that th eproposed algorithm can track the time deviation changes of the measurement time and the state estimation time.