A calculation method based on adaptive tensor convolution is proposed for constructing and quantifying the density flexibility region of distribution systems in transmission-distribution coordinated dispatch. This density flexibility region is a two-dimensional power region integrating operational security constraints and feasible combination density, which can depict the adjustable power range of the system and quantify the flexibility redundancy at each operating point. Local aggregation of flexibility resources is achieved through convolution, and an adaptive weighting function constructed from electrical distance and power factor angle is introduced to characterize the nonlinear coupling relationships among flexibility resources. Furthermore, tensor convolution operation is employed to extend the high-dimensional combinatorial space. The feasible region distribution is obtained through constraint filtering and tensor summation operations, thereby forming a global density flexibility region encompassing multiple flexibility resources. Case studies are carried out on the IEEE 33-bus system and a 38-bus distribution network in Guizhou. The results show that the flexibility region area obtained by the proposed method is 1.17 times that obtained by Latin hypercube sampling, and the computation time is only 5% of that of Latin hypercube sampling. Moreover, the flexibility region composed of discrete flexibility resources features dual density centers.
Under the "dual carbon" goals, an optimal scheduling method for the integrated energy system (IES) is proposed to promote its stable, low-carbon, and efficient operation, considering source-load uncertainty and green certificate-carbon trading. Firstly, to address the source-load uncertainty of the IES, the Latin hypercube sampling (LHS) method and the Kantorovich distance-based scenario reduction technique are adopted on the source side to characterize the output uncertainty of renewable energy. On the load side, an integrated demand response (IDR) model is established based on the coupling characteristics and response differences of various loads across multiple time scales. Secondly, the interaction mechanism between the green certificate market and the carbon trading market is analyzed. By converting held green certificates into carbon emission offsets via the Chinese certified emission reduction (CCER) mechanism, a novel framework for the green certificate-carbon collaborative trading mechanism is established. Finally, multiple time scales scheduling model for the IES is established, incorporating source-load uncertainty and the green certificate-carbon collaborative trading mechanism. Simulation results show that, under source-load uncertainty, the IES fully exploits multi-energy complementarity advantages, improving energy utilization efficiency by 10.03%. Guided by the green certificate-carbon collaborative trading mechanism, the total operating cost and carbon emissions of the IES are reduced by 3.35% and 11.99%, respectively.
With the widespread integration of flexible resources such as distributed energy storage and controllable loads, the scheduling of modern power systems faces new challenges. On the one hand, the emergence of new grid architectures, such as microgrids and regional autonomous grids, is driving a shift in scheduling model from traditional centralized management to distributed scheduling. On the other hand, the large-scale integration of uncertain renewable energy sources significantly increases the complexity of deterministic scheduling. Therefore, a distributed optimization scheduling strategy for flexible resources that accounts for the uncertainty of renewable energy sources is proposed. Firstly, based on the Wasserstein distance, a fuzzy set of forecast errors is established to provide an approximate quantification of renewable energy uncertainty. Secondly, distributionally robust chance constraints are constructed to characterize the impact of uncertainty on system operations. Then, a distributed scheduling model is developed that incorporates the operational characteristics of flexible resources, including energy storage systems, electric vehicles, and controllable loads. To address the adverse effects of discrete controllable loads on algorithmic convergence, an improved consensus alternating direction method of multipliers (C-ADMM) is proposed, incorporating a branch-and-bound framework. Finally, the effectiveness of the proposed method is verified using a modified IEEE 30-bus system. Case study results show that the proposed strategy reduces the maximum economic cost by 2.07% compared with robust optimization under different fuzzy set radii, and decreases the maximum average constraint violation probability by 56.86% compared with stochastic optimization under various wind power forecast error distributions. Compared with the traditional C-ADMM, the improved C-ADMM reduces the convergence metric from 1.14 to 0.015.
Compared with traditional resources, load-side resources are diverse, and their regulatory capacity is uncertain, making it difficult for them to participate in energy and peak regulation markets simultaneously. To address the challenge that the uncertainty of load-side resources cannot be accurately described by a known probability distribution, a day-ahead joint bidding strategy of electricity energy and peak regulation markets based on the distributional robust chance constraint (DRCC) and risk expectation is proposed. Firstly, a data-driven approach is employed to characterize the uncertainty in the adjustable capacity of load-side resources. An ambiguity set based on the Wasserstein distance is constructed, which does not require prior assumptions about the specific probability distribution of the underlying random variables. Then, the bidding strategy of load-side resource integrators is proposed to minimize the risk expectation. Finally, the effectiveness of the proposed model is assessed by case studies. The proposed method overcomes the problem that the robust model is too conservative, and its computational adaptability is better than that of the stochastic model, achieving a good balance between robustness and economy.
Against the backdrop of China's ''carbon emission peak and carbon neutrality'' goals, the low-carbon transformation of the integrated energy system (IES) is imperative. However, the uncertainties in renewable energy output and load demand, as well as the correlation characteristics between sources and loads and among different loads, pose significant challenges to the configuration and optimization of the system. To address this, a low-carbon configuration and optimization method for IES considering source-load correlation is proposed. Firstly, a flexible carbon capture power plant and a multi-utilization structure for hydrogen energy are introduced to carry out the low-carbon transformation of the IES, constructing a coupled operational model for various devices. Secondly, a sample matrix considering source-load correlation is generated using the Nataf transformation combined with Latin hypercube sampling and singular value decomposition. The final typical source-load scenarios are then obtained through the K-means clustering algorithm. On this basis, a bi-level optimization configuration model for the IES is established. The planning level aims to minimize the system's annualized comprehensive cost, while the operational level focuses on minimizing the system's total annual operating cost. The dual-level model is solved using an iterative approach that combines particle swarm optimization with mixed-integer linear programming. The results of the case study indicate that the configuration considering source-load correlation is more reasonable. A rational allocation of the flexible carbon capture and hydrogen multi-utilization structure can effectively enhance the low-carbon economy of the IES.
With the continuous rise of renewable energy penetration in China's power system, thermal-wind-storage systems need to carry out joint frequency regulation response according to their unit characteristics. To improve the automatic generation control (AGC) response capability and economy of units, a joint frequency regulation optimization method for thermal-wind-storage systems is proposed, which considers the output characteristics of thermal-wind units and the state of charge (SOC) recovery of energy storage. Firstly, the boundary conditions for initiating SOC recovery at each energy storage station are defined based on operating conditions including the predicted output of wind turbines and the available capacity of energy storage. Secondly, based on this boundary and real-time frequency regulation commands, a multi-objective optimization model is established with three objectives: minimizing the output deviation of thermal units, minimizing the response cost, and maximizing the SOC recovery efficiency of energy storage. A combination scheme of fuzzy preference selection method and weighted sum method is applied to the objective function values of the solution set from the model, and the optimal scheduling strategy is obtained through scoring and ranking. Finally, a case study on a typical regional power grid verifies that the proposed model can effectively reduce the output deviation caused by thermal units, improve frequency regulation stability, decrease frequency regulation response cost, enhance frequency regulation economy, improve frequency regulation sustainability of energy storage resources, and strengthen overall system frequency regulation capability.
To meet the "dual carbon" goals, the transformation of mining energy systems is required. The issues of scattered source-load distribution and insufficient multi-energy synergy in underground coal mines located in central and western China are adddressed in this paper. An optimization method for multi-energy station configuration based on regional source-load distribution is proposed. Firstly, three types of energy stations are defined in this study: energy-consuming stations, energy-exporting stations, and small-scale thermal stations. This architectural design takes into account the distinct load characteristics and resource endowments of core production areas, auxiliary industrial areas, and logistic areas. Secondly, refined production-consumption models are established. These models incorporate mining-excavation-transport equipment, drainage systems, ventilation systems, renewable energy systems, and energy conversion systems. Mine safety requirements and auxiliary equipment operation rules are also integrated into the models. The optimization objective is set to minimize the total annual comprehensive cost. Through this method, the capacity of equipment and the strategies for cross-regional electricity/heat exchange are optimized. A western coal mine with an annual output of 5 million tons is selected as a case study to verify the proposed model. Four configuration scenarios are considered in the analysis: scenarios without power generation equipment, with power generation equipment, with full equipment and adjusted maintenance periods, and with full equipment while considering renewable energy uncertainty. Additionally, a special scenario with 30% load fluctuations is included. Simulation results indicate that local energy consumption efficiency is significantly improved by the regional synergistic architecture. The cost of purchased electricity is reduced by 64.29% through the system. A 61.44% reduction in the total cost is achieved by adjusting maintenance periods to align with peak-valley price periods, in comparison with the first scenario. The system cost is increased by 7 500 yuan due to renewable energy fluctuations. Nevertheless, the economic viability and operational reliability of the system are maintained under load uncertainty conditions. The effectiveness of the proposed configuration method is verified by these results.
To improve the low-carbon and economic operation performance of park-level integrated energy systems (PIES), a low-carbon economic dispatch method considering flexible equipment operation and energy storage configuration is proposed. Firstly, the traditional combined heat and power (CHP) system is retrofitted with the Kalina cycle and electric boiler technologies. Turbine waste heat is recovered to decouple inherent heat-power coupling constraints, significantly enhancing the output flexibility of CHP units. Secondly, additional energy storage is configured in the park to boost wind power accommodation and improve system reliability and operational flexibility. Furthermore, a tiered carbon trading mechanism is introduced for coordinated optimal scheduling with flexible-output CHP and energy storage devices. The total operational cost is categorized into energy procurement cost, equipment operation & maintenance cost and energy sales revenue, and a low-carbon economic dispatch model is constructed with the objective of minimizing total system cost. Case study results verify that the proposed model effectively improves equipment operational flexibility and system stability, cuts carbon emissions and overall operating costs, and provides theoretical references for the sustainable development of park-level integrated energy systems.
Under the context where the dual-carbon goals fuel the transformation of energy structure and large-scale hydro-photovoltaic complementary bases in Southwest China are emerging as the core of inter-regional energy transmission,the large-scale integration of renewable energy reduces the synchronous support capability of the sending-end power grid.Traditional thermal power units respond slowly in frequency regulation,and photovoltaic generation can only provide short-term support due to energy constraints,leading to frequency regulation power deficits and instability during cross-regional transmission.To address these issues,this paper develops a new mode that utilizes active power reserves of hydro-photovoltaic complementary bases to ensure frequency security in long-distance transmission.Firstly,an active power-frequency coupled active support control strategy for the hydro-photovoltaic complementary system is proposed,and models of photovoltaic virtual inertia and hydropower frequency response are constructed.Then,taking the cross-regional sequential control signal of the DC system as a disturbance,a frequency response model of the sending-end power grid that takes into account the frequency regulation capability of hydro-photovoltaic complementation is established.The external transmission capacity of frequency regulation active power is quantitatively analyzed,and parameter sensitivity analysis is performed.Finally,simulations are carried out using MATLAB/Simulink.The results show that under the hydro-photovoltaic complementary mode,the nadir frequency of the sending-end power grid is significantly improved,with a steady-state frequency deviation of-0.190 Hz,which is superior to the-0.517 Hz observed with thermal power alone.Increasing grid damping and inertia can mitigate frequency drops;however,due to the dependence of photovoltaics on solar irradiance,their long-term active power modulation capability is limited.The conclusion indicates that large-scale hydro-photovoltaic complementary bases can serve as new regulation resources for long-distance active power support,positively contributing to the frequency stability of the sending-end power grid and providing technical support for secure and stable cross-regional transmission of renewable energy.
Electrical distance is widely used as edge weights in spectral clustering for transmission network partitioning. However, the propagation risk of cascading failures is seldom embedded into the graph model. The emergency support potential of flexible resources also remains underutilized. As a result, power imbalance and excessive load shedding may occur in sub-networks after partitioning. In this paper, an active partitioning optimization method is proposed for transmission networks to prevent cascading failures in high-risk lines. A line fault propagation interaction matrix is built through Monte Carlo simulation, and a propagation risk index is defined accordingly. The propagation risk index is combined with line loading rate to form a comprehensive risk metric. The comprehensive risk metric is mapped onto graph edge weights via a Gaussian kernel function. An initial partitioning scheme is then generated by spectral clustering. A cut-set screening strategy based on source-load balance constraints is further developed. Heuristic boundary correction and electric vehicle aggregator (EVA) emergency support are introduced to guarantee power equilibrium in each sub-network. The method is tested on the IEEE 39-bus system under high-risk line fault scenarios. Compared with the natural evolution of cascading failures, power balance is achieved in all sub-networks after active partitioning, and load shedding is significantly reduced. Multi-strategy coordination is shown to be effective in preventing cascading failure propagation.
The performance of a straight waveguide phase modulator is influenced by insertion loss and half-wave voltage, which in turn can lead to the degradation of fiber optical current transformers (FOCTs). Therefore, elucidating the impact patterns of insertion loss and half-wave voltage on the system error of FOCTs is crucial for further enhancing the performance of phase modulators. Based on the analysis of the working principle of the direct-coupled waveguide phase modulator, the theoretical models for both insertion loss and half-wave voltage of the modulator are established. Experiments are conducted to observe the variations of insertion loss and half-wave voltage under different environmental conditions, and to ascertain the influence of these variations on the system error of FOCTs. A long short-term memory neural network is utilized for error compensation of insertion loss and half-wave voltage in the direct-coupled waveguide phase modulator. The results show that after error compensation, the output error of the system under variable temperature conditions is within 0.05% and meets the accuracy requirements of the 0.2-class current sensor.
With the continuous increase in renewable energy penetration and the widespread integration of distributed resources in the power grid, the interaction between transmission and distribution networks has become increasingly complex, and traditional dispatching approaches have been found inadequate in balancing the overall overall economic efficiency and system security. To address the challenge of coordinated transmission and distribution networks scheduling under high renewable energy penetration, a distributionally robust optimal scheduling method for transmission and distribution coordination that considers the power curtailment strategy is proposed in this paper. In the proposed method, a local affine control strategy, coupled with curtailment mechanism, is introduced to form a collaborative response mechanism with adjustable resources. At the modeling level, uncertainty constraints are reconstructed using a distributionally robust chance-constrained approach based on Wasserstein distance, and are transformed into a set of linear constraints through conditional value-at-risk approximation, enabling their incorporation into a convex optimization framework. A distributed optimization algorithm based on heterogeneous decomposition is employed, through which global resource coordination is achieved via the alternating iteration of boundary prices and exchanged power. Simulation studies are conducted on the modified T39-D33 and T118-D69 test systems. The results demonstrate that the proposed method is effective in handling renewable generation fluctuations, fully utilizing the bi-directional reserve support capabilities of coordinated transmission and distribution networks, and promoting secure and economically efficient operation under integrated scheduling.
In response to the demand for optimizing the allocation of energy resources in rural areas, a Pareto optimal operation method for the rural integrated energy system (RIES) is proposed, aiming to achieve the upgrading of rural energy structure, enhance energy utilization efficiency, and promote sustainable agricultural development. The research scope includes the construction of the energy supply model for RIES, the construction of the Pareto optimal model, and the design of optimization algorithms. Firstly, based on the ecological circulation characteristics of "straw-biogas-fertilizer-carbon", the energy supply model for RIES is constructed, clarifying the flow of energy conversion and utilization within the system. Secondly, considering the characteristics of agricultural production, a Pareto optimal model is constructed with the objectives of minimizing the total system operating cost, maximizing carbon reduction, and minimizing power outage rate. To solve this model, a multi-objective multi-verse optimizer (MOMVO) algorithm based on composite chaotic mapping and improved nonlinear convergence factor is designed to improve the search efficiency and quality of the algorithm. Through the case study of a certain agricultural comprehensive park in Hebei province, the results show that the optimization method proposed in this paper can effectively achieve the optimal balance of economic efficiency, carbon reduction and negative carbon capacity, and autonomy of RIES.
Lightning weather is frequently accompanied by heavy rainfall, resulting in the bridging of the insulator umbrella skirt of the transmission line by rain columns. Under the impact of lightning, the "bridging effect" may occur. Simultaneously, under the influence of multiple factors, the internal insulation of porcelain insulators deteriorates, forming zero-value insulators and further reducing the insulation performance. In this paper, 35 kV porcelain insulators on transmission lines with an operating life exceeding 15 years are selected, and tests on the lightning impulse discharge characteristics under heavy rainfall conditions in different zero-value positions are conducted. The research indicates that for the porcelain insulator string, whether with or without zero-value insulators, the rain flashover voltage decreases as a power function with the increase of rainfall intensity and the conductivity of rainwater. The rain flashover voltage of the intact insulator string is more significantly affected by rainfall intensity and the conductivity of rainwater. When the zero-value insulator is in different positions, the rain flashover voltage gradually decreases with the increase of rainfall intensity and the conductivity of rainwater, and a saturation trend is observed. When the zero-value insulator is located at the high-voltage end, the rain flashover voltage is the highest, and the influence of rainfall intensity and the conductivity of rainwater are significant. In this paper, the parameters of the rain shield are optimized. After its arrangement, the rain flashover voltage significantly increased by an average of 100.2%, and a clear saturation trend is presented with the increase of the outer diameter. Before and after the installation of the rain-shedding shields, obvious changes occurr in the development path of the electric arc, and the development time is significantly shortened. Compared to the condition before installing the rain-shedding shields, the arc length decreased by 39.99% and the arc propagation speed increased by 180.02% after installation.
Thermally induced defects in the encapsulated insulation layer of dry-type transformers are prominent.To detect abnormal heating of winding insulation materials in a timely manner,this paper proposes an inorganic thermochromic coating-based temperature measurement method for the encapsulated insulation layer of dry-type transformer windings and investigates its performance.The inorganic temperature-indicating material is synthesized via the liquid-phase method,and its structure and micromorphology are characterized by Fourier transform infrared spectroscopy,thermogravimetry-differential thermogravimetry(TG-DTG),and other techniques,revealing the discoloration mechanism of the material.Considering the discoloration temperature range and sensitivity,the optimal mass ratio of the components(oxalic acid,potassium oxalate,and cobalt carbonate)is determined.Temperature-indicating coatings are prepared using two different basecoats,and their composition ratios are optimized according to discoloration,adhesion,hydrophobicity,and electrical properties.The results show that coatings using RTV-Ⅱ as the basecoat have a discoloration temperature of 103～120℃and a grade 1 adhesion level.The static contact angle is greater than 100° both before and after discoloration,and the surface flashover voltage exceeds 9 kV/cm.The coating achieves the best comprehensive performance when the ratio of the basecoat to thermochromic material is 10∶3.After thermal aging at 60～80℃for 168 h,no obvious degradation is observed in its discoloration and electrical insulation performance.The results can provide technical support for the temperature detection and overheating warning of thermally induced defects in the encapsulated insulation layer of dry-type transformer windings.
To address the issue of harmonic source localization in low-observability power distribution systems, a hierarchical localization method based on physical network structure information is proposed. Firstly, according to the physical characteristics of distribution networks, the distribution rules of harmonic voltages and currents under radial topology are analyzed. Then, measurement points are reasonably placed to partition the network and construct a new topology. Based on harmonic current path identification, the number of harmonic sources and their located sections are determined. Finally, precise estimation is carried out in the determined sections to obtain the specific locations of harmonic sources. The model is established and solved based on mixed integer quadratic programming (MIQP), and simulations are implemented in MATLAB. Taking the IEEE 33-bus system as an example, the effectiveness and accuracy of the proposed method are verified by comparison with existing methods. The results demonstrate that the hierarchical harmonic source localization method presented in this paper can solve harmonic source localization problems that are closely aligned with real-world scenarios, achieving localization of harmonic sources in low-observability distribution systems where both the number and location of harmonic sources are unknown.
There is uncertainty in the output of wind farms, and there are also certain correlation in time and space. The random variables brought by these wind farms are introduced into the system, which may bring certain deviations to the calculation of the transient stability constrained optimal power flow (TSCOPF) if their temporal and spatial correlations are not adequately taken into account. Therefore, a TSCOPF model and calculation method considering the spatio-temporal correlation of wind power output are proposed. Firstly, a wind power output model containing spatio-temporal correlation is constructed to consider the correlation between wind farm power output in time and space dimensions. Secondly, a probability constraint is constructed based on the joint chance constraint (JCC) theory and a TSCOPF model based on JCC theory is established on this basis. Then a mix sample average approximation (MSAA) is used to process JCC, and JCC problem is transformed into a linear programming (LP) problem, which is solved by the CPLEX solver. Finally, simulation analysis is carried out at the improved IEEE 39-bus system, and the simulation results show that the proposed method can obtain the optimal operation scheme while ensuring system safety and stability.
The construction scale of communication base stations is increasing, and the reliability of power supply in distribution networks is enhancing. Therefore, backup energy storage resources of base stations are commonly experiencing idle conditions. Dispersed and low-capacity backup energy resources of base stations can be aggregated and utilized through the form of a virtual power plant (VPP). This paper presents a methodology for calculating the dynamic minimum backup time of communication base stations based on the availability index. The method aims to accurately evaluate the dispatchable capacity of an individual energy storage base station. This paper employs VPP technology to efficiently aggregate the dispatchable capacity of distributed base station backup energy storage. Thereby a base station backup energy storage VPP is formed and participates in the power market as a qualified entity. An economic dispatch model is proposed for a backup energy storage VPP to participate in both price arbitrage and frequency regulation ancillary services to maximize operational revenue. Case studies demonstrate that dynamic evaluations of minimum backup time enhance the accuracy of dispatchable capacity assessments in comparison to fixed-time methodologies. The energy storage VPP of base stations optimizes energy storage utilization and maximizes operational revenue through collaborative participation in price arbitrage and frequency regulation services.
Multi-source self-adaption STATCOM and line commutated converter (SLCC) technology can overcome the inherent shortcomings of conventional line commutated converter (LCC) based high-voltage direct current (HVDC) transmission technology. In the "embedded" scenario, the topology and control strategy of a symmetrical unipolar SLCC-HVDC is proposed, which possesses significant technical and economic advantages. Then, the operating principles of SLCC are analyzed. During the non-commutation process, the SLCC can directly control the grid current through the static synchronous compensator (STATCOM) supplementing current. During the commutation process, the SLCC need to passively absorb the commutation current from the grid, while the grid current can still be indirectly controlled through changing the commutation angle. Finally, the operation characteristics of the traditional LCC and the SLCC under the symmetrical unipolar topology are compared. Both the commutation angle and the commutation voltage drop of the SLCC-HVDC are smaller than the LCC-HVDC and the reactive power of the SLCC-HVDC can be adjusted smoothly. Under transient condition, the fluctuation of the commutation angle is smaller, taking less risk of commutation failure. For the harmonic characteristics, SLCC-HVDC obviously decreases the harmonics compared with the LCC-HVDC during the unsymmetrical operation, thus is supposed to possess more flexible operation modes.
To more effectively cooperation response of adjustable resources within the integrated energy system, a two-layer optimization method based on chance constraints for integrated demand response (IDR) in industrial parks is proposed. Firstly, based on the integrated energy system framework of the industrial park, an incentive-based integrated demand response strategy is developed, along with an interactive response framework involving the industrial park operator, load aggregator and the main grid. Then, to address the uncertainty in load response, the chance constraint method is introduced,and coordinated response strategy between air-conditioning and aluminum electrolysis load is proposed to improve response reliability. Finally, a two-layer optimization method is established, with the industrial park operator as the upper layer and the load aggregator as the lower layer. The model is solved using a hybrid approach that embeds the Gurobi solver within a particle swarm optimization algorithm. The simulation results show that the proposed two-layer optimization method can achieve a coordinated response of energy conversion equipment and multiple loads. It reduces the response cost of the industrial park and improves the reliability and economic efficiency of integrated demand response.
