[Objective] High renewable energy penetration exacerbates power-system stability challenges， particularly concerning frequency security and short-circuit current adequacy. Conventional cost-driven scheduling methods may violate these dynamic security limits. However， directly embedding detailed nonlinear security models into scheduling model is computationally prohibitive. This study addresses this gap by proposing a practical and tractable solution framework to ensure the dynamic security of power systems with high renewable energy penetration. [Methods] A rescheduling-based iterative framework is proposed that enforces dynamic security through simulation-guided constraint generation. This method first solves a conventional scheduling model. Subsequently， high-fidelity dynamic security assessments—including frequency-response analysis and short-circuit analysis—are performed on the resulting schedule. Upon detection of security violations， sensitivity-based linear security constraints are generated and incorporated into the scheduling optimization formulation. This process iterates until all dynamic security criteria are satisfied. [Results] Simulations on the HRP-38 test system demonstrate that the proposed approach converges efficiently to schedules that are both secure and economically competitive. It effectively eliminates dynamic security violations while incurring only a modest increase in operational cost， thereby validating its capability to maintain system security while preserving economic efficiency. [Conclusions] The framework presented in this study offers a practical and tractable pathway to reliability-aware scheduling in systems with high renewable penetration.
[Objective] To address the variations in resource allocation and energy consumption behavior among prosumers in peer-to-peer （P2P） community energy trading scenarios， as well as the limited adaptability of traditional model-based methods in uncertain environments， this paper proposes a multi-agent reinforcement learning method that features both scalability and privacy protection capabilities. [Methods] First， three representative types of heterogeneous prosumer models are constructed. Second， a community energy trading model based on the mid-market rate pricing mechanism is established， and a flexibility incentive mechanism is introduced. Finally， the energy trading decision-making problem of prosumers is formulated as a partially observable Markov decision process， and a soft actor-critic algorithm based on dynamic mean-field （DMF-SAC） approximation is proposed to solve the energy management strategies of prosumers. [Results] Simulation results demonstrate that the proposed method outperforms baseline methods in terms of convergence performance， computational overhead， and operating costs. It also effectively improves the local consumption of distributed energy and enhances peak-shaving and valley-filling capabilities. [Conclusions] The proposed method effectively improves the efficiency and economic benefits of collaborative optimization for heterogeneous prosumers while balancing privacy protection and system scalability， which holds significant value for energy trading and management in community-based markets.
[Objective] To improve the low-carbon economy of park-level integrated energy systems under the “dual carbon” goals， a bi-level Stackelberg-Nash game optimization scheduling method integrating electricity-hydrogen coupling and green certificate-carbon trading is proposed. [Methods] A multi-energy flow coupling framework is first constructed， incorporating liquid-storage carbon capture， two-stage power-to-gas， and hydrogen-blended natural gas technologies， to achieve multi-energy complementarity and low-carbon synergy. Second， a synergistic green certificate-carbon trading mechanism is established， where green certificate revenues and tiered carbon costs are incorporated into the objective function to form a closed-loop market that incentivizes low-carbon operation. Furthermore， an “operator-user” bi-level Stackelberg-Nash game framework is developed： the upper level sets pricing and scheduling strategies， while the lower level adjusts energy consumption behavior. The game equilibrium is solved using the Alternating Direction Method of Multipliers. [Results] Case studies show that， compared with traditional master-slave game scheduling， the proposed method reduces total system cost by 7.9% and carbon emissions by 10.0%， while effectively improving renewable energy accommodation and multi-stakeholder coordination. [Conclusions] This method provides effective technical support for achieving the “dual carbon” goals in park-level integrated energy systems.
[Objective] In the context of carbon peaking and carbon neutrality goals and the ongoing construction of new-type power systems， the high penetration of renewable energy and stringent emission reduction requirements have revealed several critical deficiencies in conventional power system planning， including coarse-grained carbon accounting， poor coordination between market mechanisms and planning decisions， and insufficient low-carbon incentives on the demand side. To achieve coordinated low-carbon optimization across source-grid-load dimensions， it is imperative to develop a planning approach that can characterize nodal carbon responsibility while incorporating both green certificate trading and carbon emission trading mechanisms. Taking a regional transmission system as the research subject， this paper proposes a source-load coordinated bi-level low-carbon planning model that integrates carbon emission flow with the dual market mechanisms of green certificate trading and carbon trading. [Methods] From the perspective of the system planner， the upper-level model incorporates annualized investment costs， supply-side operating costs， and the net trading terms of carbon allowances and green certificates into a unified objective function， thereby coordinating generation expansion decisions with market signals. On the basis of carbon emission flow theory， a nodal carbon potential model is developed to characterize the spatiotemporal distribution of carbon responsibility across the network. The lower-level model formulates a differentiated demand response scheme driven by nodal carbon potential signals， which guides load shifting in both temporal and spatial dimensions toward low-carbon patterns； the source-load coupling is then solved through iterative coordination between the two levels. [Results] Case study results demonstrate that， compared with a conventional planning scheme， the proposed coordinated optimization reduces annual carbon emissions by 7.40% and total annual system cost by 1.13%， while increasing the renewable penetration rate from 51.45% to 54.98%. Under the guidance of nodal carbon potential， load is reduced during high-carbon periods and shifted to low-carbon periods， resulting in a 5.11% decrease in the demand-side carbon response assessment cost. [Conclusions] Green certificate trading and carbon emission trading reshape the power supply structure through investment incentives and emission constraints， respectively， whereas nodal carbon potential signals enable refined allocation of carbon responsibility from the system level to individual nodes. In conjunction with demand response， these mechanisms constitute a synergistic framework that effectively enhances system decarbonization performance while maintaining economic efficiency.
[Objective] With the large-scale integration of renewable energy sources， diverse flexible loads， and digital-intelligent equipment， traditional distribution network planning evaluation methods struggle to flexibly adapt to the multifaceted and differentiated characteristics of modern distribution networks. To achieve data-driven， scenario-based， and differentiated planning evaluations， this study constructs an indicator system tailored to new-type distribution networks and proposes a multi-scenario planning evaluation method based on Bayesian optimization and heterogeneous stacked ensemble learning. [Methods] First， a scenario-aware feature space is constructed via one-hot encoding to enable unified ensemble learning across multiple scenarios. Second， a two-layer stacked ensemble strategy is proposed： the first layer establishes a diverse base model pool comprising Random Forest， XGBoost， LightGBM， and CatBoost， balancing the variance reduction of Bagging with the bias reduction of Boosting； the second layer employs an XGBoost meta-learner for decision fusion to integrate complementary algorithmic strengths. Furthermore， Bayesian optimization based on Gaussian Process Regression is utilized to iteratively tune hyperparameters across all layers， enhancing overall model performance and generalization capability. [Results] Case study results demonstrate that the proposed integrated model achieves an accuracy of 91.33%， representing an average improvement of 12.35% over traditional single models. Across various scenarios， accuracy remains stable within a narrow range of 90.61%-91.99%， indicating no overfitting or maladaptation in specific scenarios. [Conclusions] The proposed method effectively integrates distribution network planning scenario characteristics and leverages the complementary advantages of multiple algorithms. It successfully addresses multi-scenario， high-dimensional， and nonlinear decision-making problems in distribution network planning， demonstrating robust overall performance and superior generalization capabilities.
[Objective] The large-scale integration of high-penetration renewable energy sources（RES）and power-electronic-interfaced devices has continuously displaced the conventional synchronous generators（SG）. This transition has led to a significant reduction in the equivalent rotational inertia of modern power systems， posing unprecedented challenges to frequency security and stable operation. This paper systematically reviews and critically analyzes the state-of-the-art research on power system inertia modeling， security assessment， and coordinated control. By identifying key scientific issues and technological bottlenecks associated with low-inertia power systems， this study clarifies future research priorities and establishes theoretical foundations and technical pathways to support the secure and stable operation of highly uncertain， low-inertia modern power systems. [Methods] This paper develops a comprehensive technical framework for the security and stability analysis of low-inertia modern power systems. First， the fundamental characteristics and operational mechanisms of such systems are examined， based on which a multi-dimensional inertia modeling framework is established， including equivalent inertia modeling of synchronous generators， modeling of power-electronic-interfaced devices， and multi-timescale dynamic modeling. Second， a unified security assessment framework covering diverse operating conditions is proposed， incorporating frequency security assessment， online dynamic security assessment， and assessment under uncertainty. Finally， coordinated control strategies are developed from both spatial and multi-timescale perspectives to enable the optimal coordination of heterogeneous resources—including wind power， photovoltaic systems， energy storage， and flexible loads—thereby supporting system planning and operation. [Results] This paper systematically summarizes the complete technical framework of low-inertia modern power systems， encompassing characteristic analysis， inertia modeling， security assessment， and coordinated control strategies. The presented review deepens the understanding of operational mechanisms and security challenges in low-inertia power systems and provides valuable references for both theoretical research and engineering practice. [Conclusions] The findings offer critical technical support for ensuring the secure， stable， and efficient operation of modern power systems with high penetration of renewable energy sources.
[Objective] To address the sub-synchronous wideband oscillation problem caused by the high penetration of grid-forming distributed energy resources in active distribution networks， traditional phasor measurement unit （PMU） placement methods based on pure topology suffer from severe dynamic monitoring blind spots. Therefore， an optimal PMU placement method considering wideband oscillation modal energy weighting is proposed. [Methods] This paper establishes a high-order nonlinear differential-algebraic equation model of an active distribution network containing multiple virtual synchronous generators （VSGs） to accurately screen high-risk wideband target modes by extracting the system state-space matrix. Subsequently， a modal energy-weighted Fisher information matrix （FIM） is formulated based on modal eigenvectors and the inverse of the damping ratio， enabling the quantitative evaluation of the spatial localization characteristics of nodal wideband dynamic observability. Building upon this， an improved greedy placement algorithm integrating dynamic FIM scores and static topological gains is proposed， incorporating a spatial large-adjacency penalty mechanism to strictly ensure the global dispersion of measurement nodes. [Results] Tests on a modified IEEE 33-node extreme weak-ring network demonstrate that， under the strict investment constraint of K=14， the proposed method achieves a significant advantage in capturing total wideband dynamic energy compared to traditional integer linear programming （ILP） and unweighted FIM algorithms. The comprehensive observability for the worst-case mode consistently exceeds the safety margin. Both time-domain reconstructed waveforms and empirical mode decomposition-Hilbert-Huang transform （EMD-HHT） frequency-domain integrations verify that the method effectively eliminates the transient monitoring blind spots inherent in traditional configurations. Furthermore， across 50 Monte Carlo parameter perturbation tests， the system maintains exceptional robustness with zero failures. [Conclusions] The proposed method breaks through the physical limitations of pure topological placement， overcomes the low-frequency bias trap of conventional full-state algorithms， and accurately identifies the antinodes of wideband resonant energy. It achieves superior robustness in full-band dynamic perception while ensuring a full-rank static topology， providing rigorous theoretical support for the planning of wide-area dynamic monitoring systems in next-generation distribution networks.
[Objective] To address the high penetration and low-inertia characteristics arising from the grid integration of large-scale renewable energy bases in “sandy-gobi-desert” regions， as well as the limitations of traditional dispatch methods that primarily focus on steady-state power balance and economic operation with insufficient attention to frequency security risks， this paper proposes an optimal dispatch method for concentrated solar power-photovoltaic hybrid power plants considering generalized inertia and rate of change of frequency hard constraints. [Methods] First， the optimal dispatch of concentrated solar power-photovoltaic hybrid power plants is modeled as a markov decision process. This model incorporates dynamic security constraints， such as the rate of change of frequency and generalized inertia， to achieve strict control over grid frequency security boundaries. Second， to efficiently solve this highly nonlinear scheduling model and overcome the limitations of the conventional twin delayed deep deterministic policy gradient （TD3） algorithm—specifically addressing the low utilization efficiency of historical information and the insufficient learning of critical disturbance samples—an improved TD3 algorithm integrating long short-term memory （LSTM） networks and a prioritized experience replay （PER） mechanism is proposed. [Results] Multi-scenario simulation results based on modified IEEE-30 and IEEE-57 bus systems demonstrate that， under the complete frequency-inertia constrained scenario， the proposed LSTM-PER-TD3 algorithm achieves zero frequency-limit violations and zero reserve shortage， with a total operating cost only 2.94% above the mixed integer linear programming （MILP） theoretical optimum. [Conclusions] Concentrating solar power plants possess dual advantages of thermal energy storage for time-shifting regulation and physical inertia support from synchronous units， which can firmly guarantee frequency security for high-penetration new energy bases. The developed LSTM-PER-TD3 optimization algorithm realizes efficient unit scheduling while balancing operational safety and economy. It provides theoretical foundations and technical support for active frequency support and intelligent economic scheduling of power systems with high-penetration new energy integration.
[Objective] To address the problem of critical load power restoration after distribution network faults， a coordinated power restoration strategy integrating electric vehicles （EVs） and emergency power supply vehicles （EPSVs） across multiple temporal domains is proposed. [Methods] A multi-temporal EV equivalent power source model is established to characterize the available power capacity of EV fleets under summer， winter， workday， and holiday scenarios. A load outage loss assessment model considering load importance， capacity， and outage duration is developed. On this basis， a two-stage EV-EPSV coordinated scheduling model is constructed and solved using genetic algorithm （GA） and adaptive large neighborhood search （ALNS）. [Results] Simulation results show that， compared with the EV-only scheme， the EV+EPSV heuristic scheme achieves a load outage loss saving rate of approximately 9.51%-16.19%， while the proposed coordinated scheme achieves a load outage loss saving rate of approximately 34.49%-70.36%. Under the same coordinated restoration framework， ALNS outperforms local search （LS） with a saving rate of approximately 15.97%-49.18%. [Conclusions] The proposed strategy can exploit the temporal complementarity between the rapid response of EVs and the mobile compensation capability of EPSVs， effectively reducing load outage losses and improving power restoration efficiency after distribution network faults.
[Objective] Energy flow calculation is fundamental to the planning and operation of integrated energy systems （IES）. The existing holomorphic embedding method requires significant computational effort and long solution times for large-scale IES due to the need for solving coefficient equations of power series and the Padé approximation process. [Methods] This paper proposes an energy flow calculation method for electrical-gas IES based on preconditioned bi-conjugate gradient stabilized （BICGSTAB） restarted holomorphic embedding. The method combines preconditioned BICGSTAB and total multiplication of polynomial （TMP） for grid-side holomorphic embedding power flow calculation， while employing the restarted holomorphic embedding method for gas network energy flow calculation. When solving the power flow at the grid side， the coefficient matrix for solving the power series coefficient equations is first preconditioned； then， the constant value dynamic update mechanism in the Holomorphic Embedding Load Flow Method based on constant values is used to solve the voltage approximation value by using Padé approximation and TMP. When solving the side energy flow of gas network， the restarted holomorphic embedding method is used to calculate the energy flow of gas network， so as to improve the calculation speed and convergence of energy flow. Finally， the proposed method is validated using the E39-G20 and E2383-G60 test systems. [Results] The results demonstrate that the proposed method achieves a maximum relative error of only 0.051 3% compared to the Newton-Raphson method， with a maximum computational speedup ratio of 358.0883. [Conclusions] The proposed method enables accurate and efficient energy flow analysis in the electricity-gas IES， maintains high IES energy flow solution accuracy under various operating conditions， and offers strong robustness， which can provide a new idea for the efficient calculation of IES energy flow.
[Objective] With the increasing continuous increase in electric vehicle penetration， the mismatch between charging resources and demand on expressways during peak travel periods is becoming increasingly prominent. To address this issue， this paper proposes a real-time charging navigation strategy for the entire charging process on expressways， considering secondary roads， regional distribution networks， and fast-charging stations within the secondary road network. [Methods] First， the expressway network considering secondary road networks， charging behavior of drivers， and the secondary distribution network are modeled based on the physical characteristics of the expressway network. Then， the multi-dimensional factors influencing users’ charging navigation decisions are converted into a multi-level road comprehensive impedance based on individual preferences， establishing a personalized dynamic road resistance （PDRR） model. Finally， through a two-stage real-time charging guidance， the navigation scheme is optimized with the goal of enhancing users' overall charging experience on the expressway network. In the first stage， the fast-charging station with the lowest comprehensive road resistance is preliminary selected based on real-time network information. In the second stage， an improved Floyd-Warshall algorithm is used to identify the route with the lowest weight in the PDRR model in real time and update it accordingly. Both stages incorporate individual preferences and real-time traffic information affecting various key factors of the user charging experience. [Results] Simulation results based on a real multi-level road network show that， compared with the strategy considering only the pure expressway road network， incorporating the secondary "road-network-station" factors reduces the average charging time of each charging station during peak hours by 53.97%， and increases the overall matching degree between the guidance scheme and user demand by 1.96%. [Conclusions] The proposed real-time charging navigation strategy can effectively reduce the overall charging cost， alleviate charging congestion on the expressway network during peak periods， and significantly improve the operational economy and reliability of fast charging stations.
[Objective] To improve the computational efficiency of dynamic analysis for large-scale renewable energy clusters， this paper investigates a typical renewable energy cluster connected to a 500 kV collection substation， and further studies cross-station and cross-type aggregation methods based on the existing single-machine equivalence of each station by unit type. [Methods] To address the errors caused by insufficient representation of spatiotemporal dynamic differences among heterogeneous equivalent units during further aggregation， an error-driven spatiotemporal aggregation equivalent modeling method for renewable energy clusters is proposed. In the temporal dimension， dynamic response differences among equivalent units are characterized to correct cross-station and cross-type dynamic behaviors. In the spatial dimension， the influence of the collector network is considered to calculate the equivalent impedance. Simultaneously， an error-threshold-driven mechanism adaptively updates model parameters according to operating conditions to balance accuracy and computational efficiency. [Results] Under different operating conditions and disturbance scenarios， the proposed method effectively captures the voltage dynamic response characteristics of the renewable energy cluster， and its adaptive parameter update capability is verified through threshold comparison and output fluctuation analysis. [Conclusions] The proposed method can effectively represent the spatiotemporal dynamic differences among cross-station and cross-type equivalent units. It reduces model complexity and improves computational efficiency while maintaining equivalence accuracy， providing an effective approach for dynamic analysis and equivalent modeling of large-scale renewable energy clusters.
[Objective] To mitigate the challenges posed to power grid security by the randomness and volatility of high-penetration wind and solar power output in clean energy bases， and to promote their efficient integration and advance carbon neutrality goals， multi-timescale nested optimization method for energy storage capacity configuration that considers the coordination of cascade hydropower and hybrid energy storage is proposed in this paper. [Methods] The proposed method accurately characterizes head loss， ramping constraints， and vibration safety intervals of hydropower units in a wind-solar-cascade hydropower system， and develops a two-stage optimization model. In the first stage， coordinated scheduling of cascade hydropower and pumped storage is employed to smooth long-period， large-amplitude fluctuations of wind and solar power. In the second stage， the fast response capability of electrochemical energy storage is utilized to compensate for short-term high-frequency， small-amplitude power disturbances. [Results] The simulation results demonstrate that the proposed method can fully exploit the coordinated advantages of hydropower regulation capability and hybrid energy storage. By leveraging pumped storage to smooth long-period large fluctuations and electrochemical energy storage to compensate for short-term high-frequency disturbances， a functional division and capacity matching between the two are achieved. Their complementary advantages lead to an optimal final configuration， which effectively suppresses power fluctuations across the full time scale of the system. As a result， the system’s curtailment rate is reduced to 0.10%， the load matching degree is improved to 99.85%， and the required rated power of the electrochemical energy storage accounts for less than 1% of the total installed capacity of the base. [Conclusions] The proposed optimization configuration method achieves synergistic complementarity between cascade hydropower and hybrid energy storage across multiple time scales， significantly improves wind and solar power integration and load matching capability， and greatly reduces the required capacity of electrochemical energy storage. It provides reliable technical support for energy storage capacity optimization and efficient renewable energy integration in clean energy bases.
[Objective] To exploit the dispatchable potential of electric vehicle （EV） clusters and address the insufficient consideration of renewable energy output uncertainty and user behavior heterogeneity， a Stackelberg game-based regulation strategy considering dispatchable potential is proposed for EV clusters and charging stations. [Methods] A dispatchable potential model for EV clusters is constructed across three dimensions： time， power， and energy. An aggregation model is then established based on the consistency principle to reflect the true regulation boundaries. On this basis， a bi-level game model with the charging station as the leader and the EV cluster as the follower is formulated. The upper level adopts two-stage robust optimization to handle photovoltaic output uncertainty， while the lower level establishes an optimal response model incorporating user response willingness and off-station charging demand. The bi-level model is equivalently solved using Karush-Kuhn-Tucker （KKT） conditions and robust decomposition. [Results] Simulations based on real-world charging data demonstrate that， compared with scenarios without cluster aggregation and without vehicle-to-grid （V2G）， the proposed strategy increases the charging station’s revenue by 9.6% and 10.5%， and reduces user costs by 11.3% and 29.1%， respectively. [Conclusions] The proposed strategy can effectively unlock the large-scale regulation capability of EV clusters， achieving a win-win situation for both the charging station and users. Furthermore， two-stage robust optimization enhances scheduling robustness under PV output uncertainty， while the V2G mode， combined with user behavior feedback， ensures the feasibility of regulation and user satisfaction.
[Objective] This paper aims to tap into the regulation potential of electric vehicles （EVs） within multi-market environments， to address the critical issues of information asymmetry and scheduling deviations between aggregators and users， and construct an optimal scheduling model that balances the interests of multiple parties. [Methods] A three-layer "electricity market-aggregator-user" Stackelberg game model is established. In this framework， the aggregator acts as the leader to coordinate revenues from the energy market， frequency regulation market， and green electricity certificate transactions. To handle price uncertainties， a robust optimization approach has been employed. Furthermore， an incentive-compatible mechanism based on the Vickrey-Clarke-Groves （VCG） theory is designed to eliminate the motivation for users to misreport their private information. To enhance model accuracy， a non-linear battery degradation model is introduced， and the game equilibrium is solved using backward induction combined with professional linearization techniques. [Results] Case studies demonstrate that the proposed mechanism reduces the system peak load by 17.4% and lowers the comprehensive costs for users by 16.27%. The analysis verifies that truthful reporting of private information is the optimal strategy for users under the VCG-based incentive mechanism. Notably， the aggregator can reduce physical execution deviations by over 80% by conceding less than 10% of its potential profits， indicating a high efficiency in risk mitigation. [Conclusions] The VCG mechanism effectively achieves risk isolation on the user side. The coupling of multiple markets and the application of robust optimization significantly bolster the aggregator’s resilience against market volatility. Moreover， it is identified that a battery cost below 1000 CNY/kWh serves as the economic threshold for the large-scale deployment of vehicle-to-grid （V2G） applications.
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