[Objective] To accurately reflect the carbon emission differences on the load side， fully account for the total carbon emissions generated during system operation， and explore the potential of low-carbon demand response， a low-carbon operation optimization model for multi-energy microgrids considering indirect carbon emissions from electricity transactions is proposed. [Methods] First， an operation optimization model of multi-energy microgrids was established based on the energy flow constraints of electricity， heat and gas， as well as the complementary demand response characteristics of multi-energy carriers. To precisely differentiate carbon accounting responsibilities among load-side entities， indirect carbon emissions from purchased electricity were quantified according to power transaction paths， and the source and path allocation of purchased power were incorporated into optimization decisions. Furthermore， a low-carbon operation optimization model for multi-energy microgrids integrating demand response was developed. The model was formulated in the MATLAB environment using the YALMIP toolbox and solved by the CPLEX solver. [Results] Compared with the conventional demand response scheme without indirect carbon emission costs， the daily system operation cost decreases by 3.90%， and the total system carbon emissions drop by 552.63 kg， representing a reduction of 50.84%. In contrast to the regional average carbon emission factor method， the indirect carbon emissions of the system under the power transaction contract path are reduced by 547.46 kg， achieving a decline of 44.23%. [Conclusions] The proposed method provides theoretical and model references for the economical and low-carbon operation of multi-energy microgrids， and effectively stimulates the enthusiasm of end-users for low-carbon response.
[Objective] With the integration of high-penetration distributed photovoltaic generation into distribution networks，the directional identification of feeder terminal units （FTU） is susceptible to phase-angle deviation and communication abnormalities. As a result，graph-theory-based centralized protection may suffer from maloperation or failure to operate under information distortion conditions. To address this issue，a multi-stage adaptive protection improvement scheme incorporating fault evolution characteristics is proposed. [Methods] First，a fault identification matrix is constructed based on the distribution network topology matrix and the directional overcurrent information uploaded by FTU，so as to obtain the preliminary fault section. Then，for multiple fault sections appearing in the preliminary identification result，an evaluation function is introduced to screen candidate fault combinations，thereby reducing the risk of over-range operation caused by remote FTU information distortion. Furthermore，for scenarios in which an upstream line fault is misidentified as a fault in the studied section，or an independent terminal-line fault is missed，secondary verification is performed using the residual overcurrent characteristics after the initial isolation，so as to realize secondary accurate identification of the fault range. [Results] A 10 kV distribution network is built based on the PSCAD/EMTDC simulation platform，and the problems of failed fault clearance or insufficient protection action range caused by the upload of incorrect information in the traditional scheme are analyzed. The simulation results show that the scheme can accurately identify the residual fault current through secondary verification and supplement the actual fault section for clearance，effectively dealing with various FTU information distortion conditions. [Conclusions] The improved centralized protection scheme significantly enhances the fault tolerance，protection action reliability and selectivity of the system compared with the traditional centralized protection scheme. Compared with the scheme that solely relies on FTU identification information，this scheme has strong topological adaptability，simple criteria，and reduces the risk of protection failure in active distribution networks.
[Objective] Wind farms will operate in an off-grid state when faults occur or maintenance is performed on transmission lines， where the system exhibits weak support capability and is susceptible to small-signal instability. To maintain the stable hot-standby operation of off-grid wind farms and realize rapid grid reconnection after fault clearance for reducing wind curtailment losses， this paper proposes a sequence impedance modeling and small-signal stability analysis method for off-grid wind farms. [Methods] First， based on the harmonic linearization method， sequence impedance models are established for virtual synchronous generator （VSG）-controlled grid-forming wind turbines and grid-following wind turbines with reactive power compensation strategies. The coordinated operation mechanism is clarified， in which grid-forming wind turbines provide active frequency and voltage support while reactive power compensation wind turbines accurately match the system reactive power demand. Second， according to the circuit superposition theorem， the complex overall sequence impedance model of the off-grid wind farm is decomposed into subnetworks dominated by grid-forming wind turbines and reactive power compensation wind turbines. Combined with the Nyquist criterion， a systematic small-signal stability analysis method is proposed to reveal the influence of key parameters on the system stability-instability evolution law， providing a theoretical reference for the selection of key parameter ranges and system stability evaluation. [Results] Matlab/Simulink simulation results verify that the proposed method can effectively judge the small-signal stability of off-grid wind farms. Voltage amplitude and line impedance parameters have significant effects on system stability， and optimizing the ranges of core parameters can ensure the reliable black start and subsequent stable hot-standby operation of wind farms in off-grid mode. [Conclusions] The proposed method provides solid theoretical support and technical guidance for the small-signal stable operation of wind farms during off-grid black start and hot-standby conditions. Meanwhile， it can serve as a general modeling framework for the small-signal stability analysis of off-grid power systems composed of other types of new energy equipment.
[Objective] To address the limitation that local optimization search methods for alternating-current optimal power flow （AC-OPF） generally converge only to local optima and struggle to obtain higher-quality feasible solutions， this paper investigates a method that can deterministically escape from an obtained local optimum and continue searching for better solutions. [Methods] An augmented quotient gradient system （AQGS） bifurcation-based superior solution search method （ABS） was proposed based on the bifurcation behavior of the AQGS. By analyzing the bifurcation-induced disappearance mechanism of stable equilibrium points corresponding to suboptimal solutions in AC-OPF， this study revealed the influence of penalty-parameter adjustment on the equilibrium-point structure of the AQGS. Furthermore， the saddle-node bifurcation between a stable equilibrium point and a type-1 unstable equilibrium point was exploited to eliminate the stable equilibrium point corresponding to the current local optimum， thereby guiding the system trajectory to converge to a new optimal solution. [Results] The proposed method was validated on multi-solution test systems with 2， 3， 9， and 300 buses. Numerical results show that ABS successfully obtains feasible local optima with lower objective function values from given local optima in all tested cases， achieving maximum objective-function improvements of 2.92%， 0.21%， 27.60%， and 2.46%， respectively. [Conclusions] The proposed ABS method uses the bifurcation behavior of the AQGS to achieve deterministic escape from local optima and improve solution quality. It provides a new analytical perspective and computational method for multi-solution search and local optimum improvement in AC-OPF， verifying its effectiveness in complex multi-solution power flow optimization problems.
[Objective] To address severe net load fluctuations， high renewable curtailment， and voltage deviations in active distribution networks caused by penetration of distributed generation （DG）， this paper proposes a hierarchical coordinated multi-objective optimization method that integrates energy storage system （ESS） scheduling with active distribution network operational optimization. [Methods] A hierarchical optimization framework based on an iterative coordination mechanism was established. In the upper layer， a composite objective considering ESS economic benefits and net load peak-shaving performance was formulated. A dynamic weighting adjustment mechanism based on load fluctuation characteristics was introduced， and an improved whale optimization algorithm （IWOA） was employed to determine the day-ahead charging and discharging strategies of the ESS. In the lower layer， a multi-objective model aimed at minimizing network power losses， node voltage deviations， and renewable energy curtailment was constructed. An improved multi-objective particle swarm optimization （IMOPSO） algorithm was adopted to coordinate reactive power compensation devices， distributed generation outputs， and ESS power allocation. Coordination between the two layers was achieved through alternating iterations and information feedback. [Results] Simulation results on an improved IEEE 33-node active distribution network system using MATLAB demonstrate that the proposed method yields a daily energy storage revenue of RMB 427.4 and a peak-shaving and valley-filling rate of 15.1%. It reduces total network loss to 1，796.3 kWh， total renewable energy curtailment to 1，725.2 kWh， and the sum of squared voltage limit violations to 0.001， thereby effectively alleviating voltage deviations. The method exhibits strong adaptability and outstanding comprehensive benefits under diverse load fluctuation conditions. [Conclusions] The proposed hierarchical coordinated optimization framework effectively addresses the operational challenges introduced by high DG penetration， significantly enhancing the operational efficiency and renewable energy accommodation capability in active distribution networks. The method features satisfactory computational efficiency and practical applicability， providing robust technical support for optimal operation under complex conditions.
