Stability Issues Research Articles

Stability Analysis of Nondifferentiable Systems

ABSTRACTDifferential equations with right‐hand side functions that are not everywhere differentiable are referred to as nondifferentiable systems. This paper introduces three novel methods to address stability issues in nondifferentiable systems. The first method extends the linearization method as it fails when the equilibrium is in a nondifferentiable region. We find that the stability of a piecewise differentiable system aligns with the behavior of its subsystems as long as the “distance” between these subsystems is sufficiently small. The second method is to examine the eigenvalues of the symmetric part of the Jacobian matrix in the vicinity of the equilibrium. This method applies to functions with even weaker regularity conditions, and does not require the eigenvalues to have a negative upper bound (or positive lower bound) over the domain. The third method establishes a connection between nondifferentiable systems and their approximate counterparts, revealing that their stability can be consistent under certain conditions. Additionally, we reaffirm the first two results via the approximation method. Examples are provided to illustrate the applications of our main results, including piecewise differentiable systems, general nondifferentiable systems, and realistic scenarios.

A Hydrolytically Stable Metal-Organic Framework for Simultaneous Desulfurization and Dehydration of Wet Flue Gas.

Metal-organic frameworks (MOFs) have great prospects as adsorbents for industrial gas purification, but often suffer from issues of water stability and competitive water adsorption. Herein, we present a hydrolytically stable MOF that could selectively capture and recover trace SO2 from flue gas, and exhibits remarkable recyclability in the breakthrough experiments under wet flue-gas conditions, due to its excellent resistance to the corrosion of SO2 and the water-derived capillary forces. More strikingly, its SO2 capture efficiency is barely influenced by the increasing humidity, even if the pore filling with water is reached. Mechanistic studies demonstrate that the delicate pore structure with diverse pore dimensions and chemistry leads to different adsorption kinetics and thermodynamics as well as segregated adsorption domains of SO2 and H2O. Significantly, this non-competitive adsorption mechanism enables simultaneous desulfurization and dehydration by a single adsorbent, opening an avenue toward cost-effective and simplified processing flowcharts for flue gas purification.

Automated steering control for improved path tracking and stability of articulated heavy goods vehicles

In the context of automated driving, articulated HGVs, such as tractor-semitrailers are popularly used for goods transportation. They are advantageous due to their larger capacity, but their increased mass and size pose lateral instability issues which may lead to safety-critical situations. Automated steering controllers capable of precise path-tracking and improved lateral stability may help avoid such problems. Here, we present two lateral controllers: Front Axle Reference (FAR) and Adaptive Reference (AR). FAR provides precise path tracking at the front of the vehicle, while AR drives more like a human driver, reducing the overall offtracking of the vehicle while ensuring stability. Both controllers are designed using Artificial Flow Guidance (AFG), which provides a motion reference based on path geometry. Simulations carried out for a broad range of speeds show centimetre-level path-tracking precision and improved lateral stability compared to the simple and familiar Pure Pursuit method. Controller performance is also seen to be robust to changes in trailer mass. Preliminary experimental results, conducted at low-speeds, tend to support these findings.

Ion Migration at Metal Halide Perovskite Grain Boundaries Elucidated with a Machine Learning Force Field.

Metal halide perovskites are promising optoelectronic materials with excellent defect tolerance in carrier recombination, believed to arise largely from their unique soft lattices. However, weak lattice interactions also promote ion migration, leading to serious stability issues. Grain boundaries (GBs) have been experimentally identified as the primary migration channels, but the relevant mechanism remains elusive. Using molecular dynamics with a machine learning force field, we directly model ion migration at a common CsPbBr3 GB. We demonstrate that the as-built GB model, containing 6400 atoms, experiences structural reconstruction over several nanoseconds, and only Br atoms diffuse after that. A fraction of Br atoms near the GB either migrate toward the GB center or along the GB through different migration channels. Increasing the temperature not only accelerates the ion migration via the Arrhenius activation but also allows more Br atoms to migrate. The activation energies are much lower at the GB than in the bulk due to large-scale structural distortions and favorable non-stoichiometric local environments available at GBs. Making the local GB composition more stoichiometric by doping or annealing can suppress the ion migration. The reported results provide valuable atomistic insights into the GB properties and ion migration in metal halide perovskites.

Significant differences in knee kinematics of healthy subjects with high and low anterior tibial laxity

BackgroundAnterior tibial laxity is considered to be a risk factor for knee injuries, including anterior cruciate ligament ruptures. The anterior cruciate ligament reconstruction also aims to restore anterior tibial laxity. While anterior tibial laxity is considered to be linked to dynamic knee stability, the mechanisms connecting anterior tibial laxity to these stability issues are not fully understood. The purpose of this study was to investigate the kinematic alterations between different anterior tibial laxity in healthy subjects. We hypothesized that anterior tibial laxity affects the anteroposterior tibial displacement during dynamic movements.MethodsThis study involved thirty-five healthy subjects. There were twenty males and fifteen females with an average age of 18.91 ± 0.78 years. Their knees were categorized into “Tight” (the smallest 50%) and “Lax” (the largest 50%) groups based on anterior tibial laxity measurements using a Kneelax3 arthrometer. Kinematic data were collected using a three-dimensional motion capture system when they performed level walking, upslope walking, and vertical jumping. The knee kinematics were recorded for statistical analysis. We used independent sample t-tests to analyze key kinematic differences between groups.ResultsThe “Lax” group exhibited increased posterior tibial translation during upslope walking (5.4 ± 2.22 mm at swing max flexion, p = 0.018) and vertical jumping (8.5 ± 2.78 mm at propulsion max flexion, p = 0.003; 7.6 ± 3.17 mm at landing max flexion, p = 0.019) than the “Tight” group. Significant differences in tibial internal rotation were observed during initial contact of the gait cycle of level walking (1.9° ± 0.95°, p = 0.049) and upslope walking (2.1° ± 1.03°, p = 0.041) in the “Lax” group compared to the “Tight” group. No significant differences in adduction/abduction or medial/lateral tibial translation were found between groups.ConclusionThe study revealed that high anterior tibial laxity resulted in increased posterior tibial translation and tibial internal rotation. High anterior tibial laxity resulted in dynamic instability of knees during motions, especially in high-demanding activities like upslope or vertical jumping. However, further research is needed to explore the clinical functional effects of knee laxity.

Weakly Solvating Cyclic Ether-Based Deep Eutectic Electrolytes for Stable High-Temperature Lithium Metal Batteries.

Deep eutectic electrolytes (DEE) have emerged as an innovative approach to address the instability and safety issues of lithium metal batteries at elevated temperatures. However, in practice, there is often an undesirable incompatibility between the eutectic mixture and electrodes, and also an insufficient reduction stability of DEE due to the increased Li+ concentration. Herein, we designed a new DEE by utilizing weakly solvating tetrahydropyran (THP) solvent. Due to the high reduction resistance of THP and concentrated lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), this DEE demonstrates enhanced compatibility with Li metal anode and high temperature tolerance with LiMn2O4 cathode. The Li||LiMn2O4 cell (1.6 mAh cm-2) shows a high capacity retention of 96.02 % after 600 cycles at room temperature. More importantly, this Li||LiMn2O4 cell achieves a remarkable high-temperature performance with a high capacity retention of 91.72 % after 120 cycles and low self-discharge after storage for 240 hours at a high temperature of 55 °C, which is critical for LiMn2O4 cathode. Overall, this electrolyte design provides an alternative pathway for the development of DEEs for high-temperature and high-voltage lithium metal batteries, which can also be expanded to other batteries.

Probabilistic Robust Damping Controller Optimization for Mitigating Subsynchronous Control Interaction in DFIG and PMSG‐Based Wind Farms

ABSTRACTAdvanced control and mitigation solutions are required due to the enormous challenges posed by sub‐synchronous control interaction in wind farms. These concerns include system instability, potential damage to turbines, and grid stability issues. This research presents the probabilistic robust damping controller, an adaptive control approach, to address the issues in grid‐connected wind farms. The innovation employs the balanced remora optimization algorithm to optimize controller parameters, ensuring system stability under various conditions. For permanent magnet synchronous generator‐based wind farms with weak grid circumstances, critical elements such as the DC‐link voltage, the d‐q axis current reference, and the actual values in the grid‐side converter are essential for problem mitigation. The controller generates controlled output using these input signals. The MATLAB‐based implementation demonstrates the controller effectiveness in damping issues within a series‐compensated doubly fed induction generator. Comparative analysis with conventional controllers under different grid conditions and disturbances validates its superior performance. Time‐domain simulations, both with and without time delay, further confirm the controller's ability to enhance system stability and dampen the issues. Four schemes are used to evaluate the doubly fed induction generator‐based wind farms: wind speed at 13 m/s with 75% series compensation, 7 m/s with 75% compensation, 9 m/s with 45% compensation, and 9 m/s with 60% compensation. Under short circuit ratio, the wind farms based on permanent magnet synchronous generators are analyzed in three scenarios: normal, strong, and weak cases.

Control strategy of the novel stator free speed regulating wind turbine generation system.

Building a high-proportion renewable energy power system is a key measure to address the challenges of the energy revolution and climate change. However, current high-proportion renewable energy systems face issues of frequency instability and voltage fluctuations. To address these challenges, this paper proposes a novel topology for a stator free speed regulating wind turbine generation system. The stator free speed regulating machine connects a gearbox and a synchronous generator, forming a flexible drive chain that increases system inertia and enhances frequency stability in high-proportion renewable energy power systems. The synchronous generator at the end of the drive chain can be directly connected to the grid without the converter, thanks to the speed regulation provided by the stator free speed regulating machine, thus avoiding harmonic pollution caused by power electronic devices in traditional wind turbines, enhancing the reactive power support capability, and improving voltage stability in high-proportion renewable energy systems. Given that the proposed stator free speed regulating machine consists solely of a rotating inner and outer rotor without a stator, traditional motor control strategies are not applicable. Therefore, this paper focuses on developing control strategies for the stator free speed regulating machine, employing a dual closed-loop PI control strategy with an outer loop for speed and an inner loop for current, based on flux orientation of the outer rotor. Simulation experiments will validate the feasibility of the proposed stator free speed regulating wind turbine generation system topology and the effectiveness of the control strategy.

Managing singular kernels and logarithmic corrections in the staggered six-vertex model

In this paper, we investigate the spectral properties of the staggered six-vertex model with Z2 symmetry for arbitrary system sizes L using non-linear integral equations (NLIEs). Our study is motivated by two key questions: what is the accuracy of results based on the ODE/IQFT correspondence in the asymptotic regime of large system sizes, and what is the optimal approach based on NLIE for analyzing the staggered six-vertex model?We demonstrate that the quantization conditions for low-lying primary and descendant states, derived from the ODE/IQFT approach in the scaling limit, are impressively accurate even for relatively small system sizes. Specifically, in the anisotropy parameter range π/4 < γ < π/2, the difference between NLIE and ODE/IQFT results for energy and quasi-momentum eigenvalues is of order OL−2.Furthermore, we present a unifying framework for NLIEs, distinguishing between versions with singular and regular kernels. We provide a compact derivation of NLIE with a singular kernel, followed by an equivalent set with a regular kernel. We address the stability issues in numerical treatments and offer solutions to achieve high-accuracy results, validating our approach for system sizes ranging from L = 2 to L = 1024.Our findings not only validate the ODE/IQFT approach for finite system sizes but also enhance the understanding of NLIEs in the context of the staggered six-vertex model. We hope the insights gained from this study have significant implications for resolving the spectral problem of other lattice systems with emergent non-compact degrees of freedom and provide a foundation for future research in this domain.

Study on Instability Mechanism and Compensation Strategy for Distributed Energy Storage Systems

Distributed energy storage systems (DESSs), which would become key components in a new power system, can flexibly deliver peak load shaving and demand management. With the popularization of distributed renewable energy generation in a distribution network, the grid impedance varies and DESSs thus have to face stability issues. In order to enhance the system’s stability, a compensation strategy is proposed for the inverter in a DESS. First, a stability analysis model is developed to show the main factors that affect system stability. Then, an improved compensation strategy is proposed for the phase-locked loop (PLL) in a DESS, in which control parameters are adaptively tuned on-line according to real-time conditions to improve the stability of a grid-tied DESS. Simulation and hardware-in-the-loop (HIL) experimental results are given to validate the effectiveness of the proposed strategy. Simulation and experimental results show that the proposed strategy significantly increases the system’s tolerance to grid impedance variations, maintains total harmonic distortion (THD) below 5% during normal operation, and effectively reduces low-order harmonic content caused by impedance fluctuations. Moreover, the strategy is demonstrated to enhance system stability under low state-of-charge (SOC) conditions, showcasing its robustness and adaptability across various operating scenarios.

Stabilization Strategies of Buried Interface for Efficient SAM‐Based Inverted Perovskite Solar Cells

AbstractIn recent years, self‐assembled monolayers (SAMs) anchored on metal oxides (MO) have greatly boosted the performance of inverted (p‐i‐n) perovskite solar cells (PVSCs) by serving as hole‐selective contacts due to their distinct advantages in transparency, hole‐selectivity, passivation, cost‐effectiveness, and processing efficiency. While the intrinsic monolayer nature of SAMs provides unique advantages, it also makes them highly sensitive to external pressure, posing a significant challenge for long‐term device stability. At present, the stability issue of SAM‐based PVSCs is gradually attracting attention. In this minireview, we discuss the fundamental stability issues arising from the structural characteristics, operating mechanisms, and roles of SAMs, and highlight representative works on improving their stability. We identify the buried interface stability concerns in three key aspects: 1) SAM/MO interface, 2) SAM inner layer, and 3) SAM/perovskite interface, corresponding to the anchoring group, linker group, and terminal group in the SAMs, respectively. Finally, we have proposed potential strategies for achieving excellent stability in SAM‐based buried interfaces, particularly for large‐scale and flexible applications. We believe this review will deepen understanding of the relationship between SAM structure and their device performance, thereby facilitating the design of novel SAMs and advancing their eventual commercialization in high‐efficiency and stable inverted PVSCs.

Coordinated optimization of control parameters for suppressing transient overvoltage in wind power DC transmission systems

With the increasing proportion of new energy in power systems, the instability issues of novel power systems become more prominent. This paper addresses the transient overvoltage problem in wind power DC transmission systems by proposing a method for transient overvoltage suppression based on doubly-fed wind turbines, high-voltage DC transmission systems, and SVC control parameter optimization. The electromagnetic transient model of the wind power DC transmission system is combined with intelligent optimization algorithms through joint invocation to achieve coordinated optimization of control parameters. Case studies validate the effectiveness of the proposed model and method. The results indicate that the improved genetic algorithm, SEGA, proposed in this paper, effectively suppresses overvoltage at the grid connection point of wind turbines. Furthermore, by simultaneously applying coordinated control strategies based on DFIG and SVC and optimizing parameters of HVDC, DFIG, and SVC, transient overvoltage phenomena can be effectively eliminated.

Robust MG control considering uncertain constant power load

The destabilization of Microgrids (MGs) is attributed to the negative incremental resistance of constant power loads (CPLs). Furthermore, the inadequately damped modes of the droop control, typically employed for distributed generation (DG) power sharing, contribute to disturbances in MG dynamic performance. This paper introduces a novel control strategy aimed at mitigating instability issues associated with both CPL and droop controllers in MGs. The proposed approach utilizes an optimized H∞ control scheme, incorporating the Whale Optimization Algorithm (WOA), to enhance stability on both the CPL and distributed generation (DG) sides of the MG. The proposed controller is modeled and validated through comprehensive simulations in MATLAB, demonstrating its effectiveness under various uncertainty scenarios and disturbance conditions. These simulations demonstrate the controller's capability to effectively mitigate disturbances, optimize DG power sharing, and regulate the DC voltage of the CPL, thereby enhancing overall microgrid stability and performance. Additionally, a comparison between the proposed robust H∞ and conventional droop control schemes highlights the superiority of the proposed approach, with results confirming improved MG dynamic performance. The proposed controller exhibits a notable enhancement in Minimum Voltage Deviation (MVD), showing a substantial improvement of 96.19%. Additionally, both the Critical Response Time (CRT) and Settling Response Time (SRT) witness significant improvements of 95.33% and 97.69%, respectively, when subjected to system disturbances. Finally, the implemented MG is validated on a Real-Time Digital Simulator (RTDS), affirming the practicality of the proposed compensation technique.

Adaptive Fixed‐Time Prescribed Performance Synchronization Control for Multi‐Motor Driving Systems

ABSTRACTIn this article, the fixed‐time synchronization control problem is developed for multi‐motor driving systems. Initially, the issue of multi‐motor tracking and synchronization is converted into a stability issue through the introduction of coupling synchronization errors. Subsequently, based on the prescribed performance control (PPC) scheme, an adaptive fixed‐time PPC is proposed to ensure that the synchronization error and tracking error converge to the prescribed boundary. Additionally, the radial basis function (RBF) neural networks are employed for estimating uncertain nonlinearities. Finally, the simulation results showcase the effectiveness of the proposed method.

Building Bridges to European Integration: Albania and Kosovo's Joint Efforts in the Balkans

This study aims to look at the joint efforts of Albania and Kosovo in enhancing European integration within the Balkans. It tries to figure out, through an analysis of the joint programs and strategic partnerships, the extent to which these initiatives help them realize their shared goal of EU membership and regional stability. Prior Work: Previous scholarship has looked mostly into individual tracks on how to integrate into Europe by analyzing the political, economic, and social reforms undertaken by Albania and Kosovo separately. Other studies have tried to identify challenges and opportunities for the Western Balkans in this regard of EU integration. Yet little is known about cooperative work between Albania and Kosovo, and what it means for the wider regional context represents a gap in this literature. Key Findings: The two countries have managed, as shown by these findings, to build such a framework of cooperation together with dimensions being diplomatic, economic, and even cultural. Cross-border infrastructure projects, policy reforms, and joint diplomacy as well as collaboration in regional and international initiatives have played a bigger part in lifting up their prospects for integration. The paper shows how important it is for these two countries to ally strategically in tackling common challenges, like issues of political instability within their territories, fostering economic development programs, and social cohesion that make up the key tenets upon which EU membership is anchored.Value: This paper is therefore important in providing an insightful analysis into how synergistic cooperation between Albania and Kosovo can be used to enhance European integration prospects. It underscores the role bilateral cooperation can play in ensuring regional stability on the path to EU membership. The paper provides insight into how other aspiring member states from the Balkans can use cooperative strategies to inform the broader European integration agenda from a disadvantaged region. Future Longitudinal studies should be done to assess the impact that such joint initiatives by Albania and Kosovo could have on their EU integration trajectories over time. Comparative analyses with other regional Balkan partnerships could give a more nuanced knowledge of best practices and lessons learned. Moreover, investigating how international organizations and external stakeholders support these bilateral agreements will further make a lot of sense in the academic discussion on European integration in the region. Received: 2 August 2024 / Accepted: 12 November 2024 / Published: 3 December 2024

A Cd‐Free Electron Transport Layer Simultaneously Enhances Charge Carrier Separation and Transfer in Sb2Se3 Photocathodes for Efficient Solar Hydrogen Production

AbstractEfficient photoelectrochemical (PEC) water splitting is a pivotal technique to achieve sustainable hydrogen production, driving the exploration for high‐performance photoelectrodes. Antimony selenide (Sb2Se3) semiconductor has received significant attention due to its cost‐effectiveness, eco‐friendly nature, and favorable photoelectric properties. However, traditional Sb2Se3‐based photocathodes typically employ cadmium sulfide (CdS) as an electron transport layer (ETL), which introduces toxicity and stability issues, hindering their commercial application potential. This study develops a versatile method to improve the PEC performance of Sb2Se3‐based photocathodes by incorporating Cd‐free (Zn,Sn)O ETL. Comprehensive investigations demonstrate remarkable improvement in surface and heterojunction interface properties, leading to charge carrier dynamics optimization with highly interesting carrier separation efficiency of 96.5% and transfer efficiency of 93.6%. As a result, the champion Mo/Sb2Se3/(Zn,Sn)O/TiO2/Pt photocathode delivers a notable photocurrent density (Jph) of 31.8 mA cm−2 (close to its theoretical value), and a half‐cell solar‐to‐hydrogen (HC‐STH) conversion efficiency of 4.32%. This advancement highlights a promising pathway toward large‐scale and environmentally friendly solar hydrogen production applications.

Weakly Solvating Cyclic Ether‐Based Deep Eutectic Electrolytes for Stable High‐Temperature Lithium Metal Batteries

Deep eutectic electrolytes (DEE) have emerged as an innovative approach to address the instability and safety issues of lithium metal batteries at elevated temperatures. However, in practice, there is often an undesirable incompatibility between the eutectic mixture and electrodes, and also an insufficient reduction stability of DEE due to the increased Li+ concentration. Herein, we designed a new DEE by utilizing weakly solvating tetrahydropyran (THP) solvent. Due to the high reduction resistance of THP and concentrated lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), this DEE demonstrates enhanced compatibility with Li metal anode and high temperature tolerance with LiMn2O4 cathode. The Li||LiMn2O4 cell (1.6 mAh cm−2) shows a high capacity retention of 96.02% after 600 cycles at room temperature. More importantly, this Li||LiMn2O4 cell achieves a remarkable high‐temperature performance with a high capacity retention of 91.72% after 120 cycles and low self‐discharge after storage for 240 hours at a high temperature of 55 °C, which is critical for LiMn2O4 cathode. Overall, this electrolyte design provides an alternative pathway for the development of DEEs for high‐temperature and high‐voltage lithium metal batteries, which can also be expanded to other batteries.

Optimized operation of AC–DC microgrid cluster with modified PLL and socket protocol

AbstractMicrogrids integrating inverter based resources face challenges like stability issues during voltage fluctuations and reliance on diesel generators in islanded mode. This paper presents a novel control strategy for photovoltaic and wind‐integrated microgrids to enhance reliability and efficiency. The strategy utilizes a modified phase‐locked loop with droop control for seamless synchronization in grid‐connected and islanded modes. Central to this approach is the localized autonomous controller with a socket protocol interfaced communication layer, dynamically managing operations based on real‐time conditions such as generation, load, and battery state of charge. By integrating battery storage systems, the strategy reduces diesel generator dependency during grid outages. Comprehensive simulations and controller hardware‐in‐the‐loop testing validate its effectiveness, demonstrating improved stability and decreased reliance on diesel generators. The socket protocol enhances real‐time communication, monitoring, and optimization of microgrid operations, ensuring optimal battery storage system utilization and minimal diesel usage. The proposed strategy addresses critical microgrid challenges, offering significant advancements in enhancing system resilience.

Multifunctional nanocomposites based on kaolinite/titania/iron applied to hydrogen peroxide production and bisphenol–A removal

The rising global demand for hydrogen peroxide, recognized for its eco–friendly properties, underscores the need for greener synthesis methods. Traditional production processes pose environmental risks, while direct synthesis faces challenges like water formation, explosion hazards, and stability issues, limiting industrial application. On the other hand, Bisphenol A (BPA), an endocrine disruptor widely used in plastics, presents significant environmental and health concerns due to its potential leaching into food and water. The present work introduces efficient and selective photocatalysts aimed at sustainable hydrogen peroxide synthesis and BPA degradation. Both processes were enhanced by the synergistic properties of Fe2O3–TiO2 nanoparticles dispersed within a kaolinite matrix. The Fe2O3–TiO2 photocatalysts, characterized by photoluminescence spectroscopy and X–ray diffraction, showed reduced emission upon iron incorporation and anatase presence on the kaolinite surface. The photocatalytic activity was evaluated through hydroxylation of terephthalic acid, revealing a 127 μmol/L min hydroxylation rate for the KaFeTi400 sample. BPA degradation studies indicated optimal performance in acidic conditions, achieving 96 % removal in 2 h and 98 % in 4 h, with the addition of H2O2 enhancing efficiency. Further, the photocatalyst facilitated benzyl alcohol oxidation to benzaldehyde, demonstrating a H2O2 production rate of 120 μmol. These findings highlight the multifunctional capabilities and environmental benefits of the photocatalyst, underscoring its potential for sustainable hydrogen peroxide synthesis and broader applications in environmental remediation. The catalysts address the pressing challenges associated with hydrogen peroxide synthesis and pollutant removal, particularly in the context of sustainability and environmental impact.

Surface engineering-based S, N co-doped biochar for improved anaerobic digestion: Enhancing microbial-pollutant and inter-microbial electron transfer synergistic EPS protection

Enhancing extracellular electron transfer (EET) efficiency is crucial for improving the anaerobic digestion (AD) system's capability to treat recalcitrant wastewater. In this study, a novel S, N co-doped biochar (S-N-BC) was prepared through surface engineering to optimize EET within AD systems. The addition of S-N-BC significantly enhanced the performance of a mesophilic AD system treating Congo red wastewater, increasing the decolorization rate by 78%, COD degradation rate by 82%, and methane yield by 87% compared to the control. Additionally, the shock resistance of anaerobic granular sludge was improved, as evidenced by the formation of the protective extracellular polymeric substances (EPS) barrier and the enhanced activities of the electron transport system. Mechanistic analysis revealed that adding S-N-BC did not alter the Congo red decolorization pathway but significantly enriched various electrochemically active bacteria and established EET pathways between microbial-pollutant and inter-microbial. This significantly accelerated EET efficiency within the AD system, ensuring stable and efficient operation under challenging conditions. This study proposed a novel approach using S-N-BC to simultaneously enhance "dual-pathway EET" between microbial-pollutant and inter-microbial while constructing an EPS protective barrier, addressing the issues of low efficiency and fragile stability of AD systems for treating recalcitrant wastewater.