The increase in the penetration rate of renewable energy exacerbates the rise in system short-circuit level. Thus, short-circuit constraints (SCCs) are crucial in the co-optimization of transmission and generation expansion planning. The deregulated environment further complicates this process by assigning responsibilities for transmission and generation to separate market entities. This paper proposes a multi-period co-optimization method of transmission and wind turbine generation expansion planning to address this challenge. The transmission expansion planning (TEP) problem limits the short-circuit level, which could be elevated by lines, synchronous generators, and wind turbine generators. The method is formulated as a tri-level mixed-integer linear programming (MILP) problem, where an equilibrium problem with equilibrium constraints is formed at the second and third levels. This problem is restructured into a MILP problem with Nash equilibrium conditions via complementarity problem reformulation. We propose an iterative algorithm targeting the SCCs to solve it. The effectiveness of the proposed method is validated on the IEEE 24-bus reliability test system through comparisons with three existing TEP methods, analyzing the impact of SCCs and generation expansion planning on TEP and the system operating cost under a deregulated environment.

The capacity market provides economic guidance for generation investment and ensures the adequacy of generation capability for power systems. With the rapidly increasing proportion of renewable energy, the adequacy of flexibility and resilience becomes more crucial for the secure operation of power systems. In this context, this paper incorporates the flexibility and resilience demand into the capacity market by formulating the capacity demand curves for ramping capability, inertia and recovery capabilities besides the generation capability. The guidance on generation investment of the capacity market is also taken into account by solving the generation investment equilibrium among generation companies with a Nash Cournot model employing an equivalent quadratic programming formulation. The overall problem is established as a trilevel game and an iterative algorithm is devised to formulate the capacity demand curves in the upper level based on Genco's investment acquired from the middle and lower levels. The case study further demonstrates that to incorporate flexibility and resilience demand into the capacity market could stimulate proper generation investment and ensure the adequacy of flexibility and resilience in power systems.

Low frequency transmission systems (LFTS) can increase the transmission distance and capacity of submarine cables for offshore wind farms by reducing capacitive current, but they also weaken transient stability and fault ride-through (FRT) in permanent-magnet synchronous generator (PMSG) systems. During a voltage sag, the grid-side converter loses most of its active-power transfer capability, while the machine-side converter still keeps nearly constant mechanical power input, which causes DC-bus overvoltage. To address this problem, this paper proposes a coordinated control strategy based on a dual second-order generalized integrator phase-locked loop (DSOGI-PLL) for directdrive PMSG turbines under LFTS without extra hardware. The DSOGI-PLL improves phase tracking and harmonic suppression, while the proposed control shifts DC-bus voltage regulation to the machine-side converter and makes the grid-side converter prioritize reactive current support. Simulation results show that the strategy can suppress DC-bus overvoltage and maintain stable operation under asymmetrical faults and harmonic interference.

The increasing penetration of inverter-based resources (IBRs) aggravates harmonic, frequency and voltage instability in modern power systems. While harmonic stability has been extensively studied, the theoretical understanding of frequency-voltage stability remains limited. This letter investigates system frequency and voltage dynamics under power disturbances by the PQ/omega U transfer function, and uncovers the anti-diagonal mapping relationship between dq-admittance and frequency-voltage stability. The results reveal that a main-diagonally dominant dq-admittance implies that the system frequency and voltage are primarily impacted by reactive and active power, respectively. Conversely, an anti-diagonally dominant dq-admittance indicates that frequency and voltage are more sensitive to active and reactive power, respectively. The proposed theory enables frequency-voltage stability assessment based on the dominance pattern of dq-admittance, providing a new perspective for understanding frequency and voltage dynamics. The analysis is validated using three representative IBR-based test systems.

Extreme weather events have become increasingly frequent in recent years, leading to widespread outages and substantial economic losses in power systems. While existing studies primarily focus on failure prevention, emergency response, and post-event recovery coordination, limited attention has been given to real-time optimal scheduling that incorporates probabilistic failure risk and resilience-oriented economic measures such as insurance. This paper proposes a data-driven hierarchical dispatch framework designed to enhance system resilience while reducing overall operational costs and load losses. First, an LSTM-Bayesian hybrid model is developed to estimate component failure probabilities under ice- and snow-related meteorological conditions. To accurately localize and quantify potential faults, a dynamic line vulnerability index is further introduced, capturing temporal variations in weather-induced stress. Building on these risk assessments, a resilience insurance purchasing strategy is formulated to mitigate the financial impact of extreme-weather-induced outages. The proposed framework is validated on the different node systems. Simulation results demonstrate that the coordinated dispatch strategy, integrating both probabilistic fault modeling and resilience insurance, significantly enhances system performance: load shedding is reduced by approximately 62.63% during fault conditions, dispatch costs are lowered, and insurance payouts decrease by 15% compared with an uninsured scenario. These findings highlight the effectiveness of combining data-driven risk analysis with resilience economics to support robust and sustainable grid operation under extreme weather events.

This paper addresses the optimal scheduling of low-cost, zero-carbon microgrids by proposing a novel ensemble deep learning-based electricity price prediction algorithm, BiLSTM-Adaboost. Under controlled conditions with the same network depth and 500 training rounds, our approach outperforms over ten classical and advanced electricity price prediction methods in terms of accuracy. Building on these high-precision forecasts, we introduce an advanced multi-objective optimization algorithm, A-MOEA/DD, specifically designed for zero-carbon microgrid scheduling. The integrated system encompasses wind and photovoltaic power generation, water electrolysis hydrogen production, hydrogen storage tanks, advanced hybrid hydrogen gas turbines, and carbon sequestration. Focusing on minimizing both overall operating costs and power imbalances, the algorithm executes 1,000,000 evaluations with a population size of 100, yielding 71 Pareto front solutions, thereby surpassing the performance of more than 10 state-of-the-art multi-objective optimization algorithms. Notably, the combined process of electricity price prediction and microgrid scheduling optimization is completed in under 15 minutes, demonstrating its practical applicability as an effective and reliable solution for real-time, low-cost, zero-carbon microgrid operations. To meet this practical need, this study proposes a reliability-oriented decision-making scheme based on the Pareto front. Meanwhile, three extended experimental studies were conducted to further investigate the generalization capability of the proposed prediction algorithm on datasets of varying sizes, and to elucidate the rationale for parameter choices in the prediction and optimization processes.

In the context of energy trading in distribution systems, rural prosumers exhibit distinct agricultural behavioral tendencies. Meanwhile, driven by multidimensional factors, prosumers show heterogeneous preferences for electricity generated from different sources. However, traditional energy trading models generally fail to establish detailed modeling of agricultural production behaviors and neglect the impacts of multidimensional driving factors on prosumers’ electricity preferences. To address this problem, an innovative peer-to-peer (P2P) energy trading model for rural prosumers is proposed, which systematically incorporates both agricultural behavioral tendencies and electricity use preferences. Specifically, agricultural loads are modeled in detail, and agricultural behavior tendencies are incorporated. Moreover, a novel energy preference model is established. Electricity is classified according to its generation source to capture prosumers’ differentiated preferences for various energy types. Since prosumers’ preferences for different types of electricity are affected by multidimensional factors, fuzzy logic is employed to quantify these preferences. A dynamic pricing mechanism is developed to match the categorized energy, and the alternating direction method of multipliers (ADMM) is adopted to solve the model for protecting privacy. Finally, case studies show that the proposed model facilitates the enhancement of social welfare and the improvement of rural prosumers’ energy structure.

Hydrogen energy storage systems (HESS) hold significant potential for facilitating the large-scale integration of renewable power. However, existing operation models for water electrolysis devices often oversimplify the start-up process and lack the ability to capture multi-timescale power fluctuation, limiting their effectiveness in providing rapid flexibility. To address these limitations, this paper establishes an operation model for water electrolyzer that incorporates multiple start-up process, ensuring applicability across various electrolysis techniques. Furthermore, a multiple time-resolution uncertainty model is introduced to capture the fluctuation of wind power. Based on them, an adaptive robust unit commitment (UC) model is developed, incorporating the fast switching of electrolyzers during re-dispatch. The proposed optimization problem is efficiently solved using a nested column-and-constraint generation (NC&CG) algorithm. Case studies conducted on the modified IEEE-RTS 79 system validate the effectiveness and feasibility of the proposed method. The results demonstrate that the model considering multiple start-up process reduces total costs by 19.2% and wind curtailment by 92.7% compared to conventional approaches. When integrated with the multi-resolution uncertainty framework, an additional 68.9% reduction in wind curtailment is achieved, leading to an optimal total cost. Sensitivity analysis highlights the influence of electrolyzer technical characteristics. For instance, increasing the ramping rate from 15%/min to 20%/min enhances the tracking of rapid wind power fluctuation. Moreover, PEM, with its wider operation range and faster response, consistently outperform AEC across different wind volatility scenarios. This study underscores the necessity of high-fidelity modeling and multiple time-resolution analysis for unlocking the flexibility, particularly the fast-ramping potential, of HESS in renewable energy integration. The findings provide theoretical insights for the design and operation of HESS, supporting their large-scale deployment in future power systems

In stochastic planning for large-scale renewable energy bases, scenario reduction is widely employed to mitigate computational burden without sacrificing planning optimality. Existing data-driven techniques predominantly minimize statistical discrepancy between original and reduced scenario sets, yet such fidelity offers no theoretical assurance of decision quality in the underlying planning problem. Therefore, this paper proposes a decision-driven three-layer framework for scenario reduction of renewable energy bases. In the upper layer, candidate representative scenario subsets are generated and screened through an optimization-driven search. The middle layer embeds a refined planning model for large-scale renewable bases, incorporating the operational characteristics of transmission corridors. The lower layer evaluates the obtained configuration against all original scenarios to assess the operational reliability. Finally, a hybrid solution strategy that combines an enhanced simulated annealing algorithm with the Gurobi solver is developed to coordinate these layers. Case studies based on real data of western China show that the proposed method attains a total cost of 6.141 billion yuan, reducing costs by 14.9 % and 19.5 % compared with K-means and KDE, respectively.

This letter proposes an adaptive predispatch-hazard-redispatch (PHR) framework for multi-stage reserve dispatch in power systems. Unlike existing two-stage predispatch-redispatch and multi-stage heuristic threshold-based approaches, the PHR framework adopts adaptive redispatch weights to balance reserve adequacy assurance and computational cost. The complex multi-stage PHR structure is formulated as a policy graph and solved via a graph stochastic dual dynamic programming approach. Multiple strategies are explored to dynamically adjust redispatch weights based on system flexibility and uncertainty. Case studies on an IEEE 39-bus system demonstrate 70.0-86.5% cost reduction compared to benchmark methods while maintaining computational tractability.

ABSTRACT The secure operation of the fractional frequency transmission system faces significant challenges during grid‐side asymmetric faults. This vulnerability stems from two critical technical barriers: the frequency disparity between interconnected grids obscures post‐fault interaction mechanisms, complicating system response analysis and the inherent complexity of modular multi‐ level matrix converter introduces substantial analytical difficulties in fault characteristic identification. This paper proposes a 2D phasor analytical framework that systematically decouples the interactive relationships within M 3 C. Through an iterative analytical approach, the investigation reveals the dynamic cross‐coupling mechanisms between ripples and harmonics under asymmetric faults, particularly addressing the nonlinear interactions between bridge‐arm current and submodule capacitor voltage. The proposed method realises the modelling of multi‐component under‐grid‐side asymmetric faults, precisely delineates the internal coupling modes and further reveals the fault transmission mechanism in the form of a generalised model introduced by fault participation factors. The effectiveness of the proposed method and the accuracy of the analysis are validated through case studies involving three fault scenarios in MATLAB/Simulink.

Traditional offshore wind turbines typically use grid-following (GFL) control strategy, which struggle to actively support the stable operation of power system with high wind power penetration. In contrast, grid-forming (GFM) strategy offers support capabilities similar to synchronous machine. Consequently, in large-scale, long-distance offshore wind low-frequency transmission system, hybrid operation of GFL/GFM-PMSG presents a competitive solution. Furthermore, under large-signal disturbances such as offshore wind power fluctuations and low-frequency transmission line faults, analyzing the impact mechanisms of the proportion configuration index of GFM-PMSG and system parameters on stability margin becomes crucial. This paper develops a dynamic model for offshore wind low-frequency transmission, considering various hybrid distributions of GFL/GFM-PMSG and incorporating the multifrequency coupling effects. To address the model's high order and strong nonlinearity, the fuzzy Lyapunov theory is improved using tensor space theory of membership function, which reduces conservativeness and lowers exponential complexity to a linear level. Additionally, the adjoint sensitivity analysis method defines a generalized damping index, quantitatively uncovering the relationships between different proportion configuration index, control parameters, and stability margin. Thus, the comprehensive strategy is proposed to enhance the large-signal stability of the hybrid system. At last, the proposed theory and analysis are validated through simulation and experiment.

The uncoordinated charging of large-scale electric vehicles (EVs) tends to cause severe network congestion, posing a significant threat to the secure and reliable operation of power distribution networks. To address this issue, this paper proposes a distribution locational marginal price (DLMP) based congestion management method, utilizing differentiated congestion prices to incentivize EV aggregators (EVAs) to actively adjust charging patterns, thereby mitigating network congestion. In this model, an improved power flow method based on continuous implicit linearization is employed, which integrates network loss modeling and dynamically updates the linearization point, thus guaranteeing the accuracy of power flow approximation and price signal calculation. Moreover, both the uncertainty of EVA parameters and its impact on the safety constraints of the grid are characterized by robust ambiguity sets within the congestion management model, ensuring the reliability of the proposed pricing mechanism in guiding EV charging behavior in uncertain environments. Furthermore, a two-layer iterative algorithm is designed to facilitate bidirectional coordination between the distribution system operator (DSO) and EVAs. The outer layer updates network-related coefficient matrices to improve accuracy in grid state estimation, while the inner layer uses the alternating direction method of multipliers (ADMM) to iteratively adjust DLMPs while preserving the privacy of EVAs. Numerical results demonstrate that the proposed method can incentivize EV charging pattern adaptation and effectively relieve network congestion.

Modular Multilevel Matrix Converter (M3C) is the key frequency converter of flexible low-frequency ac transmission system, but the inter-arm balancing strategy is usually complicated due to its degree of freedom of difference-mode terms of submodule capacitor voltage. To solve this issue, the input, output and circulating current model and internal energy dynamics model of M3C are firstly established based on the two-dimensional sequence analysis method. Then, the M3C arm power equation is derived considering the difference-mode terms of submodule capacitor voltage to reveal the inter-arm self-balancing phenomenon, and its influencing factors are analyzed. Accordingly, a novel control scheme for high-voltage, high-capacity scenarios is designed. The outer loop eliminates the eight inter-arm voltage balancing controllers required in conventional control scheme. Finally, the inter-arm self-balancing of M3C is verified in MATLAB/Simulink. The result shows that the proportional gain inner-cycle current control is the major influence factor of inter-arm self-balancing, and the self-balancing performance declines with the proportional gain increasing for typical control bandwidth.

Low-frequency transmission system (LFTS) has become a highly competitive technical solution for the long-distance transmission of renewable energy. Its power-electronic nature makes LFTS at risk of experiencing wideband oscillations. Impedance analysis method is a simple and efficient method for stability analysis of power system. Proposing the impedance model of modular multilevel matrix converter(M3C), which is the key device of LFTS, is the basis of applying the impedance method to stability analysis of LFTS. The paper analyzes the structure of M3C and the small-signal propagation process within it. The equation set of small-signal model is derived and the impedance model of M3C based on harmonic state-space (HSS) method is proposed. Furthermore, a cross-hybrid impedance model for stability analysis of LFTS for renewable energy transmission is proposed. The model can efficiently characterize the frequency-domain admittance characteristic of M3C. Finally, the simulation verification based on Matlab/Simulink has been carried out, which verified the accuracy of the impedance model proposed.

The secure operation of the fractional frequency transmission system faces significant challenges during grid-side asymmetric faults. This vulnerability stems from two critical technical barriers: the frequency disparity between interconnected grids obscures post-fault interaction mechanisms, complicating system response analysis and the inherent complexity of modular multi- level matrix converter introduces substantial analytical difficulties in fault characteristic identification. This paper proposes a 2D phasor analytical framework that systematically decouples the interactive relationships within M3C. Through an iterative analytical approach, the investigation reveals the dynamic cross-coupling mechanisms between ripples and harmonics under asymmetric faults, particularly addressing the nonlinear interactions between bridge-arm current and submodule capacitor voltage. The proposed method realises the modelling of multi-component under-grid-side asymmetric faults, precisely delineates the internal coupling modes and further reveals the fault transmission mechanism in the form of a generalised model introduced by fault participation factors. The effectiveness of the proposed method and the accuracy of the analysis are validated through case studies involving three fault scenarios in MATLAB/Simulink.

With the accelerating global shift toward carbon neutrality and the rapid adoption of new energy vehicles, developed regions are entering a phase of heightened energy demand. This evolution has introduced a competitive dynamic between energy aggregators and new energy vehicle owners, underscoring the need for effective regulatory oversight. This study models the trading relationship between energy aggregators and new energy vehicle owners as a constrained, nonlinear multi-objective optimization problem. The model accounts for both electricity and hydrogen transactions, incorporating contract and spot market interactions with upstream suppliers, along with the diverse charging schedules of new energy vehicles. To manage the model’s complexity, simplification strategies were applied, and an integrated algorithm, I-IMTCMO-BS, was proposed. Experimental results show that the algorithm generated 285 high-quality approximate Pareto solutions, outperforming 12 benchmark multi-objective optimization algorithms in feasibility and dominance. Furthermore, a market supervision mechanism based on Pareto classification is introduced to evaluate transaction outcomes as positive, acceptable, or unacceptable as a basis for informed regulatory intervention. Overall, the research offers a full-process analytical framework and algorithmic toolkit for market regulators tasked with managing the emerging dynamics between energy aggregators and new energy vehicle owners an issue poised to become increasingly relevant in the global clean energy transition.

Ensuring the resilience of power grids against potential terrorist attacks is a critical challenge for modern energy systems. This study proposes an innovative three-stage evaluation method to identify the weakest bus in a power grid, considering the total number of affected line disconnections, the total impacted load, and the geographical extent of disruption. Experimental validation using an improved IEEE 30-bus system demonstrates the method's effectiveness in accurately pinpointing the most vulnerable bus. Based on this assessment, a five-objective optimization framework is developed, incorporating three strategic planning measures: backup power supply deployment, preset transmission line reinforcement, and double-circuit line construction. To efficiently solve this complex sparse multi-objective mixed-integer programming problem with 490 decision variables, we introduce a novel evolutionary algorithm, PSL-SCEA. By leveraging a population of 50 individuals over 1,000,000 evolutionary evaluations, the proposed method successfully generates 15 Pareto-optimal solutions. The results demonstrate a well-balanced trade-off between economic feasibility and grid robustness, providing a strategic foundation for enhancing power grid resilience against potential disruptions. This study also investigates the scalability of the proposed method by applying it to the larger-scale IEEE 57-bus system, resulting in a set of 37 Pareto-optimal solutions.

Distributed energy resources (DERs) struggle to enter wholesale markets due to their small, stochastic nature. This paper proposes an aggregator based framework and clearing model for distributed PV storage systems. It defines access mechanisms using “aggregator trading, separate settlement” and develops a day ahead clearing model incorporating grid and unit constraints. Aggregators participate via a “quantity bidding without price” strategy. IEEE30 node simulations demonstrate enhanced resource consumption and identify a critical storage capacity ratio that optimizes economic benefits and congestion relief. This study provides a theoretical and empirical reference for normalized aggregator market operations.