The existing minimum demand inertia (MDI) assessment methods based on time-domain simulation of system frequency response are complex in modeling and time-consuming in computation. If incorporating the load-side resources, it will lead to further computation inefficiency. This paper proposes a fast assessment method (FAM) for MDI in power systems. A full-response analytical model (FRAM) of a multi-resource system considering the load-side inertia is developed. The analytical expression of the mapping relationship between the maximum frequency deviation and system inertia is derived, thus realizing the fast solution of the system MDI under frequency security constraints. Case studies based on the modified IEEE RTS-79 test system and a provincial power grid in China demonstrate that the proposed FAM can solve the MDI in milliseconds without being affected by the system scale while maintaining high accuracy. This can provide an accurate and rapid analytical tool for sensing inertia security boundary in grid inertia resource planning and operation scheduling.

Battery energy storage systems and distributed energy resources (DERs) on the load side can be aggregated into a virtual control unit (VCU) through virtual power plant (VPP) technology. The power system control center directly dispatches the VCU to participate in frequency security emergency control (FSEC). Due to the dual uncertainties of frequency regulation control commands and DER operating states, it is difficult to optimally disaggregate the VCU control tasks among control resources. To address this, an operational framework for VCU participation in FSEC is established based on “online budgeting and real-time matching.” A cluster-individual dual rolling control mode for control resources is designed. A method for determining the individual and cluster emergency control capacity of control resources is proposed based on transfer functions and resource operational domains. A cluster-individual control model for control resource participation in FSEC is then developed. This model incorporates power system emergency control performance requirements. An adaptive particle swarm optimization genetic algorithm (APSOGA) is applied to design a pre-computation solving mode. Simulation results demonstrate that the proposed method enables the VCU to effectively handle the uncertainty of power system control commands and DER operating states. It simultaneously maximizes VCU economic benefits while satisfying power system emergency control performance requirements. Compared to typical heuristic algorithms, the APSOGA with the pre-computation mode improves computation speed by 54.60 times and increases optimization revenue by at least 1.10%.

Aiming at the problems of low search efficiency, easy to fall into local optimum and long convergence time of the traditional ant colony algorithm in global path planning task, a comprehensive improvement method applied to the global path planning ant colony algorithm is proposed. The initial pheromone differential distribution mechanism is designed for the problem of low search efficiency; the adaptive heuristic function, expanded pheromone updating strategy, and adaptive pseudo-random state transfer rule are designed to solve the problems of the algorithm falling into local optimum easily and long convergence time. Matlab is utilized for simulation verification, and the path length, the number of iterations required for convergence and the number of inflection points are used as evaluation indexes to compare the basic algorithm, the literature algorithm and this paper's algorithm. The experimental results show that this paper's algorithm improves the convergence speed significantly, and the number of convergence generations is greatly reduced in different environments; in terms of the path length in complex environments, this paper's algorithm reduces 21.68% compared with the basic algorithm, and 13.56% compared with the literature algorithm; and the number of inflection points of the path is reduced in different environments to different degrees.

The dispatch problem of integrated energy systems faces a contradiction between the unified modeling and privacy protection issues as various energy systems belong to different sectors. An encrypted equivalent modeling method is proposed to construct the feasible region of district heating system (DHS) considering its thermal inertia and elasticity. A sensitivity modeling method is adopted to equivalently construct the feasible region of DHS and hide its absolute state information. The relative state information and structural parameters of DHS is further reduced and encrypted through the redundancy-constraintelimination technology and an equivalent constrainttransformation technique. Then, based on the DHS equivalent model, a non-iterative dispatch model was constructed for thermal and power systems. The dispatch model can fully utilize the elasticity of DHS and guarantee to obtain the global optimization. Case studies verifies the equivalence of the proposed encrypted feasible region model of DHS and the improvement in solving efficiency for the optimal dispatch problem. The solution time is reduced by two orders of magnitude compared to the heat-power iterative solution method. The redundancy-constraint-elimination technology further reduces the solution time by more than half. Economy and flexibility improvement brought by the elasticity of DHS to power systems are also verified.

With the evolution of power grid configurations, generation structures, and control methodologies during the transition to new power systems, the disturbance magnitude caused by single-component failures (e.g., DC blockings or large unit tripping) is increasing. Meanwhile, the antiinterference capability of the system, which is composed of factors such as system inertia and primary frequency regulation, is continuously declining. Against the backdrop of large-scale integration of renewable energy into the grid, the interruption of inter-regional connection lines can have a significant impact on system frequency. For the two-region power system, the spatiotemporal distribution characteristics of frequency are the key factors affecting the accurate description of the dynamic characteristics of its frequency response. Although existing analytical methods for twomachine frequency response can account for spatial distribution effects, they fail to analyze the impact of the initial states of internal dynamic components following a tieline interruption. To address these issues, this paper first couples two fundamental models to establish a two-machine equivalent system frequency full-response model that simultaneously considers spatial distribution and initial state changes. Secondly, through rigorous mathematical derivation, the closed-form solution of this two-machine equivalent system frequency full-response model is obtained, and analytical expressions for the frequency in each area are further derived. Finally, comparisons with results from various simulation models validate the accuracy and computational efficiency of the proposed method.

Benefit assessment, as the main means to measure the economy of the project, is the key to ensure that the virtual control unit participates in the frequency response control of the main network to realize the economy. The existing benefit assessment methods and indicator assignment methods are relatively mature, which provide reference for the research of this paper. In this paper, from the perspective of the power grid, in order to ensure the sustainable development of the project, the benefit assessment index system is constructed with economy as the main focus and environmental protection as the supplement; taking into account the degree of influence of the indexes, the hierarchical analysis method and entropy weight method are used for the assignment of the indexes. The example shows that the grid in the big disturbance using the program of transfer instead of cut, this benefit assessment model and method can realize the calculation of the various benefit indicators and the final benefit evaluation, for the virtual control unit to participate in the frequency response control of the main grid to provide a reference for the benefit assessment and measurement.

Amidst the rapid expansion of renewable energy sources, the application of virtual power plant technology to integrate distributed resources at the load side into virtual control units for participation in frequency response control can significantly augment the system's limited frequency regulation capabilities. As per established standards, these virtual control units primarily engage in system regulation through feedforward mechanisms, featuring intricate control architectures, rapid response times, and the capacity to intervene at the onset of disturbances. Conversely, conventional static evaluation methods, which concentrate on quasi-steady-state response power, offer an ambiguous depiction of the dynamic response process, thus failing to accurately capture the frequency response control performance of virtual control units. This study introduces an evaluation approach for the frequency response control performance of virtual control units from a dynamic perspective, utilizing transfer functions to ensure precise assessment. Drawing on current research into individual control models for distributed resources at the load side and relevant standards, the evaluation framework incorporates three dynamic parameters: speed of dynamic regulation, amplitude of dynamic adjustment, and cumulative dynamic effect. The actual values of these parameters are determined using the least squares fitting method. By aligning with grid requirements and incorporating convolution calculation techniques, benchmark values for the dynamic parameters are established. Based on a comparison of the actual and benchmark values, a set of evaluation indicators is developed. The viability and efficacy of the proposed method are demonstrated through comparative analysis.

Bulk power systems show increasingly significant frequency spatial distribution characteristics (FSDCs), leading to a huge difference in the frequency response between regions. Existing uniform-frequency models based on analytical methods are no longer applicable. This paper develops a reduced-order bus frequency response (BFR) model to preserve the FSDC and describe the frequency response of all buses. Its mathematical equation is proved to be isomorphic to the forced vibration of a mass-spring-damper system, and the closed-form solution (CFS) of the BFR model is derived by the modal analysis method and forced decoupling method in vibration mechanics. The correlation between its mathematical equation and the state equation for small-signal stability analysis is discussed, and related parameters in the CFS are defined by the eigen-analysis method without any additional devices or tools. Case studies show that the proposed reduced-order BFR model and its CFS can improve the solution accuracy while keeping the solution speed within milliseconds, which can preserve the significant FSDC of bulk power systems and represent a normalized mathematical description of distinct-frequency models.

Value of lost load (VoLL) is a fundamental parameter in the study of frequency security and operational control in power systems. Its stochastic characteristics are crucial for the analysis of new power systems. This paper investigates these stochastic characteristics of VoLL. From a temporal perspective, it examines the differentiated characteristics of VoLL across various electricity consumption sectors, as well as the time distribution stochastic characteristics of load components at different nodes in the power system. Using historical load data, the Kernel Density Estimation (KDE) method is employed to derive numerical features of the time distribution stochastic of VoLL at each node. From a spatial perspective, the study analyzes the stochastic characteristics of the spatial distribution of the lowest frequency points, which are influenced by the stochastic nature of large power loss disturbances. The stochastic characteristics of the spatial distribution of lost load quantities are derived, and by integrating the differences in load components across various nodes, numerical features of the spatial distribution stochastic of VoLL are obtained. The temporal and spatial distribution stochastic characteristics of VoLL are formulated in a stochastic convolution framework. The proposed theory is validated using the IEEE 39-bus test system, with results demonstrating that VoLL exhibits significant temporal and spatial distribution stochastic characteristics, with first and second moments during daily operations reaching up to 23.61 (sic)/kWh and 19.27(sic)(2)/kWh(2), respectively.

Existing regional inertia assessment methods mostly rely on actual measurement data and cannot consider the impact of disturbances on system partitioning, making it difficult to quickly and accurately assess the inertia of each region in the system. Based on this, this paper proposes an analytical assessment method for regional inertia in power systems considering spatial distribution. A multi-machine system frequency response analytical model (M-FRAM) was established to achieve analytical expressions for the frequency response of all units under different disturbance conditions. Based on the fuzzy C-mean algorithm to realize the online fast partitioning of the system, and use the parameter aggregation means to obtain the analytical expression of the regional frequency, and then realize the analytical calculation of the regional inertia. Case studies based on the IEEE 39-bus system show that the proposed method can quickly and accurately calculate regional inertia under various disturbance scenarios without relying on grid frequency measurement data. This method provides a faster and more accurate basis for assessing the spatial distribution of inertia and optimizing the allocation of inertia resources.

With the increase of the proportion of new energy capacity, the uncertainty of the frequency dynamic process of the power system after large disturbance is obviously enhanced, the deterministic analysis results have been unable to accurately and comprehensively characterize the frequency safety state and evolution situation of the system, and the time-domain simulation method also can not meet the needs of system analysis because of its low analysis efficiency. For this reason, the solution idea of extreme point analysis is selected, and an analytical method for estimating the probability of the frequency nadir after disturbance is proposed. Firstly, the statistical eigenvalues describing the uncertainty of the influencing factors of the frequency nadir are obtained by data-driven and model analysis, so as to provide input for probability estimation; Then, the probability density function(PDF) transformation of multivariate function is carried out based on the deterministic frequency nadir analytical formula: The PDF of the time of frequency nadir is obtained by using the central limit theorem, and then the PDF of the frequency nadir deviation is obtained by marginalization processing of the joint PDF of the constructed equidimensional variable group; And finally, the PDF of the frequency nadir value is obtained by convolution of the PDFs of the frequency nadir deviation and the initial frequency. The numerical results show that the proposed method can significantly improve the analysis efficiency while ensuring the estimation accuracy compared with the Monte Carlo method.

Along with the gradual deepening of the interaction between different energy systems, the coupling relationship between multi-energy loads is gradually complicated. However, there has been limited joint load forecasting research specifically focusing on the temporal-varying characteristics of coupling degrees. In this paper temporal variation characteristics of inter-correlations between electric and thermal loads are investigated first. A joint forecasting method for electric and thermal loads is proposed to improve the forecasting accuracy, with high adaptability to the coupling degrees. The proposed method consists of two improved modules. Temporal processing module is constructed based on hybrid neural networks (HNN), which can efficiently learn temporal information of forecasting objects. Then, the shared-soft module is introduced to improve the flexibility in mining shared information between subtasks of multi-energy load forecasts. To demonstrate the shared information captured by the proposed method, a coupling intensity index is proposed to enhance model interpretability, which can provide more coupling information to the power system operator. Comparing with other coupling extraction methods and prediction models, it is validated that the proposed method has a stronger shielding ability against inter-subtask interferences. In some cases, the MAPE of electric and thermal loads forecasting is reduced by 18.90 % and 15.18 % respectively. The proposed method can maintain accuracy facing different coupling degrees which contributes to improve the reliability of integrated energy system operation.

Distributed flexible resources on the load side of power systems can be aggregated into virtual control units (VCUs), which are directly dispatched by bulk power grids to participate in active power regulation at the distribution-grid level. However, existing dispatch methods fail to address the self-dispatch optimization challenges for fully-controllable and semi-controllable resources aggregated as VCUs, limiting the potential of loadside resources in the daily full-timescale frequency control ancillary services (FCASs). This study proposes aggregating electric vehicle (EV) battery swapping and charging stations (BSCSs) and small-scale battery energy storage stations (BESSs) into VCUs. To optimize the sequential strategies of these VCUs in responding to full timescale FCAS tasks in the day-ahead stage, two self-dispatch optimization frameworks are developed for the two forms of VCUs. A novel VCU operational mechanism is designed to ensure optimal coordination of multiple tasks by capturing the dynamic and time-varying regulation capabilities of distributed resources. To enhance the coordination of various flexible resources, the proposed framework introduces intra-station self-sufficiency and inter-station mutual aid as operational modes. Case studies for the two VCU configurations demonstrate the effectiveness of the approach. The results show that the VCUs can effectively evaluate and implement optimized allocation strategies allocation for grid dispatch tasks, balancing resource utilization between BESS clusters and BSCSs while accommodating the stochastic EV swapping demands faced by BSCSs.

With the increasing proportion of new energy sources, the power system has undergone various changes in terms of sources, grids, loads, and storage, making the dynamic process of system frequency more complex. It is necessary to study it from the perspective of the new situation. First, the uncertainty of disturbances is analyzed. By using high-order Gaussian fitting to analyze the differences between power generation and consumption, the probabilistic characteristics of disturbances are extracted, and the uncertainty is modeled with the characteristics of disturbances. Subsequently, the frequency response model of the power system is simplified and analyzed, resulting in an analytical formula related to the frequency nadir of the power system. Therefore, the probability of the frequency nadir is obtained from the probability of disturbances. Finally, a probability density transformation method is used to convert the probability density of disturbances into the probability density of the frequency nadir, completing the frequency nadir solution of the power system considering disturbance probability characteristics. The comparison between the simulation method and this method shows that it significantly improves computational efficiency while maintaining a minor error in results, providing effective data for the safety operation and backup planning of the power system.

In this work, a day-ahead dispatch optimization model with energy-type, power-type, and composite-type energy storage systems (ESSs) is established to participate in multiple frequency control ancillary services (FCASs), in wind-energy-integrated power systems. This model is designed to better handle the operational uncertainties of wind energy, mitigate operational risks and reduce carbon emissions. Leveraging the complementary features of different types of ESSs, the proposed operation strategies of regulation units can respond to multiple FCASs and achieve the optimal task allocation among different types of resources. Various uncertainty handling approaches are adopted to better cope with the randomness of step disturbances and wind power fluctuations. Furthermore, a new environmental factor is devised in the dispatch objective and the time-of-use carbon-price carbon emission trading (ToU-CET) and ladder-type CET (LT-CET) models are developed. They can incorporate dynamic carbon prices and leverage mechanisms to reduce carbon emissions during daily operations. The effectiveness of the proposed model is verified by case studies, and the decisions can help save energy and reduce carbon emissions in modern power systems with wind power generators with high security and reliability.

With the gradual increase of the penetration rate of new energy with uncertainty in the power system, the conventional units that are the main force of primary frequency regulation (P FR) have been replaced, resulting in the weak capacity of the power system for primary frequency regulation. Due to the large investment in supplementary source-side resources, a large number of load-side resources existing in the power system can be used to participate in PFR. Due to the insufficient capacity of individual load-side resources, it is difficult for them to be directly controlled by the power system. This paper proposes using a Virtual Control Unit (VCU) to aggregate various load-side resources, providing P FR for the power system. Since the capacity of each load-side resource is uncertain, the total capacity of VCU is also an uncertain quantity. The VCU uses tagging to categorize load-side resources based on their capacity characteristics. It then employs a two- level aggregation method to aggregate these resources. Since When aggregating all kinds of load-side resources, the VCU needs to report the total capacity to the power grid, thus making it necessary to evaluate its credible power capacity. Through case study analysis, it is shown that the proposed strategy can effectively aggregate a large number of load-side resources to participate in P FR, proving its effectiveness. Further, by utilizing two-level aggregation of load-side resources with tagging, the power capacity characteristics can be parsed into mathematical expressions, greatly simplifying the aggregation difficulty, demonstrating its superiority. Additionally, after risk analysis, the capacity reported by the VCU to the power grid can ensure the maximum expected profit of the VCU, ensuring the sustainability of the strategy.

A hierarchical approximate dynamic programming (ADP) strategy is presented to determine intra-day operations of distributed energy storage cluster for demand management and frequency response service. According to the principle of decomposition coordination, the intra-day operation problem is divided into cluster scheduling layer, subcluster control layer and terminal response layer, wherein a flexible allocation mechanism of primary frequency response (PFR) reserve is devised. The hybrid lookahead, myopic allocation and automatic control methods are adopted to achieve global coordination of cluster, local control of subcluster and automatic response of terminal. The results show that the proposed strategy can ensure the economic benefit and PFR service within a short computing time. Moreover, the flexible allocation mechanism can increase resource utilization and operational precision.

As the synchronous generators are gradually replaced by renewable energy like wind turbines, the problem of insufficient inertia of the power system is becoming more and more prominent. The distribution-side inertia gradually plays a greater role in the process of maintaining the frequency stability of the power system. However, the existing distribution-side inertia estimation methods are relatively rough, and it is necessary to realize the accurate estimation of the distribution-side inertia. Through the analysis of the distribution side load composition and the inertia resources of all kinds of load composition under the new situation, the composition of inertia of distribution side load is clarified. Combined with the operating characteristics and changing rules of various load components, the load operation scenarios are divided and clustered to provide the basis for the load structure forecast. Aiming at the complexity of multi-scene modeling and model redundancy, the method of inertia-oriented aggregation of load structures is presented. Based on the inertia properties of node load structure and load components, a distribution-side inertia estimation method is proposed. According to the IEEE standard model, the simulation results indicate that the aggregation of load structures can effectively reduce the analysis burden. Compared with the existing methods, the accuracy of distribution-side inertia estimation based on node load structure is significantly improved.

The evaluation of the electricity market is crucial for fostering market construction and development. An accurate assessment of the electricity market reveals developmental trends, identifies operational issues, and contributes to stable and healthy market growth. This study investigated the characteristics of electricity markets in different provinces and synthesized a comprehensive set of evaluation indicators to assess market effectiveness. The evaluation framework, comprising nine indicators organized into two tiers, was constructed based on three aspects: market design, market efficiency, and developmental coordination. Furthermore, a novel fuzzy multi-criteria decision-making evaluation model for electricity market performance was developed based on the Fuzzy-BWM and fuzzy COPRAS methodologies. This model aimed to ensure both accuracy and comprehensiveness in market operation assessment. Subsequently, empirical analyses were conducted on four typical provincial-level electricity markets in China. The results indicate that Guangdong’s electricity market performed best because of its effective balance of stakeholder interests and adherence to contractual integrity principles. Zhejiang and Shandong ranked second and third, respectively, whereas Sichuan exhibited the poorest market performance. Sichuan’s electricity market must be improved in terms of market design, such that market players can obtain a fairly competitive environment. The sensitivity analysis of the constructed indicators verified the effectiveness of the evaluation model proposed in this study. Finally, policy recommendations were proposed to facilitate the sustainable development of China’s electricity markets with the objective of transforming them into efficient and secure markets adaptable to the evolution of novel power systems.