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Review

A Review of Key Technologies for Active Midpoint Clamping (ANPC) Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization

1
China Southern Power Grid Technology Co., Ltd., Guangzhou 510080, China
2
Guangdong Provincial Key Laboratory of New Technology for Smart Grid, China Southern Power Grid Technology Co., Ltd., Guangzhou 510080, China
3
School of Automation, Wuhan University of Technology, Wuhan 430070, China
*
Author to whom correspondence should be addressed.
Energies 2025, 18(23), 6169; https://doi.org/10.3390/en18236169
Submission received: 2 September 2025 / Revised: 17 November 2025 / Accepted: 21 November 2025 / Published: 25 November 2025
(This article belongs to the Special Issue Advancements in Power Electronics for Power System Applications)

Abstract

To enhance the operational efficiency of energy storage converters in grid-connected systems with high renewable penetration, this study systematically investigates key technologies of active neutral-point clamped (ANPC) topology under “electrical–thermal–mechanical” multi-physical field coupling. The study reviews recent progress in structural design, modulation strategies, and fault-tolerant control, highlighting their impact on efficiency, reliability, and power density. At the structural stage, a hybrid SiC/IGBT device configuration combined with a three-dimensional stacked bus reduces conduction loss and achieves parasitic inductance. In the modulation stage, improved finite-set model predictive control and adaptive space vector modulation shorten computation time to 20 µs and keep total harmonic distortion (THD) within 2.8%. System-level evaluations demonstrate that a 250 kW ANPC converter attains a peak efficiency of 99.1%, a power density of 4.5 kW/kg, and a mean time between failure exceeding 150,000 h. These findings reveal a clear transition from single-objective performance improvement toward integrated multi-physics co-design. By unifying advanced modulation, intelligent fault-tolerant control, and multi-field coupling optimization, ANPC-based converters advance converters to a new stage of higher efficiency, reliability, and stability. The results provide essential technical support for next-generation power conversion systems in renewable-rich grids.

1. Introduction

Driven by the global push toward deep decarbonization, the share of renewables in electricity generation continues to rise [1]. According to the latest statistics from the International Renewable Energy Agency (IRENA), global installed renewable capacity reached 3870 GW in 2023, exceeding 40% of total installed power generation capacity. At the same time, the intrinsic intermittency and volatility of wind and photovoltaic resources pose persistent challenges to the secure and stable operation of power systems [2,3]. In this context, energy storage systems (ESSs) have become a pivotal buffer for power smoothing and frequency regulation. The Global Energy Storage Market Outlook 2023 projects a 28% compound annual growth rate for storage from 2022 to 2030, with cumulative installations expected to reach 1200 GW/3600 GWh by 2030. Figure 1 depicts the global distribution of installed power generation capacity in 2023, and Figure 2 compares projected storage capacity growth between 2022 and 2030.
As the core conversion interface between storage media and the grid, the PCS largely determines the ESS efficiency, reliability, and techno-economic performance [2,3,4,5]. Emerging “new-type” power systems impose stringent requirements on modern storage converters: ≥99% full-load efficiency in 1500 V high-voltage applications; robust operation from −40 °C to +70 °C; <10 ms power-regulation response for fast dynamics; and stable operation under ±15% grid-voltage deviation with strong grid adaptability [3,6,7,8]. Meeting these specifications with conventional topologies is increasingly difficult. Although the two-level converter is structurally simple and control-friendly, silicon IGBTs incur high switching losses—escalating sharply above 10 kHz—while devices endure the full DC-bus voltage stress; the output THD typically exceeds 5% [9,10,11,12,13]. The three-level neutral-point clamped (NPC) topology alleviates some of these issues by increasing voltage levels, but two fundamental bottlenecks remain: (i) neutral-point potential imbalance, leading to DC-link capacitor voltage drift and waveform distortion; and (ii) uneven switching-loss distribution, which concentrates heat in specific devices and risks localized overheating [6,12].
Against this backdrop, the ANPC topology has emerged as a compelling evolutionary form of the three-level NPC converter [14]. By adding two active switches and anti-parallel diodes to each phase leg, ANPC achieves three salient breakthroughs: (1) active midpoint-potential control, enabling dynamic, bidirectional midpoint-current regulation that suppresses capacitor voltage deviation and improves output waveforms; (2) flexible loss allocation, wherein alternative zero-state current paths (P-O-N and P-N-O) allow active, algorithm-guided partitioning of conduction and switching losses across devices to mitigate thermal hotspots; and (3) superior harmonic performance, whereby optimized modulation reduces THD by ~30% at a given switching frequency relative to conventional NPC, supporting compliance with IEEE 1547-2018 [6,7,11,12,15,16]. In practical settings, ANPC thereby expands the feasible operating envelope for high-voltage, high-power storage converters that must reconcile efficiency, dynamic performance, and long-term reliability.
The technical requirements for ANPC-based converters vary across application scenarios. Grid-scale storage at 1500 V typically targets > 99% efficiency and >20-year cycle life with THD < 3%; commercial and industrial systems at 1000 V emphasize > 98% efficiency and a high power density over ~15 years; EV-related storage near 800 V prioritizes > 97% efficiency, compactness, and vibration/shock resilience over ~10 years [13,14]. Relative to NPC, ANPC introduces added circuit states and active clamping that enhance midpoint control, device-stress sharing, high-frequency efficiency, and reliability—albeit at higher cost and control complexity (e.g., advanced digital platforms), leading to differentiated positioning: ANPC for performance-critical, high-reliability use cases (grid nodes, data centers, fast charging), and NPC for cost-sensitive, standardized deployments (Table 1) [17,18,19,20,21].
While ANPC’s structural advantages provide the performance ceiling, realizing those benefits in the field depends critically on (i) modulation strategy design; (ii) redundant/fault-tolerant control; and (iii) multi-physics co-optimization that couples the electrical, thermal, and mechanical domains. Recent progress includes improved model predictive control (MPC), with ~60% computational-complexity reduction and adaptive space vector modulation (SVM), achieving THD < 3%; multi-layer redundancy combining fault prediction (accuracy > 95%), hierarchical fault tolerance (recovery < 100 μs), and health management; and electro-thermal–mechanical co-design that integrates SiC/IGBT hybridization with 3D packaging, enabling 4.5 kW/kg power density at the system level [19]. These advances point to a transition from single-objective tuning toward co-designed, system-aware ANPC converters that align with the reliability and lifetime expectations of utility-scale assets.
This paper provides a structured, state-of-the-art review titled “A Review of Key Technologies for ANPC Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization.” The main contributions are threefold:
  • Modulation strategies: This paper synthesizes and compares improved MPC and adaptive SVM methods—covering realization mechanisms, complexity reduction (~60%), THD control (<3%), and a hybrid, condition-aware modulation scheme suited to wide-range operating points.
  • Redundant/fault-tolerant control: This paper summarizes a three-layer protection architecture (prediction–tolerance–health) with demonstrated metrics (prediction accuracy > 95%, recovery time < 100 μs), highlighting implementation pathways on modern digital platforms and the trade-offs among response speed, device stress, and availability.
  • Multi-physics field co-optimization: This paper reviews coupled electro-thermal–mechanical modeling and design, emphasizing SiC/IGBT hybrid integration and 3D interconnect/packaging that raise power density to 4.5 kW/kg, and we discuss comprehensive evaluation frameworks that consider lifecycle cost and reliability.
The remainder of the paper is organized as follows. Section 2 reviews modulation strategy innovations for ANPC, including improved MPC, adaptive SVM, and hybrid schemes with quantitative comparisons. Section 3 presents redundant and fault-tolerant control technologies, covering fault prediction, hierarchical tolerance, and health management. Section 4 details multi-physics co-optimization methods and design flows that link device choices, packaging, thermal paths, and mechanical robustness to converter-level metrics. Section 5 analyzes the synergistic interactions among the three pillars and distills the design guidelines across application scenarios. Section 6 summarizes open challenges and outlines future research trends—such as AI-assisted control, digital twins, and wide-temperature reliability qualification—for next-generation, high-power-density, high-reliability ANPC energy storage converters.

2. Modulation Strategy of ANPC Topology in Energy Storage Converter

2.1. Current Status of Modulation Strategy Development

The three main stages in the evolution of modulation strategies are shown in Table 1 [7,8,11,12]. The basic SVPWM phase (2010–2015) was a direct transplantation of the NPC topological modulation method, with a single zero-vector selection problem. The loss equalization modulation phase (2015–2018) introduced dynamic zero-vector allocation and achieved a breakthrough in reducing loss imbalance by 40%. The intelligent modulation phase (2018–present) focuses on the convergence of MPC with AI and improvements in the approaches, with recent advances including neural network prediction of switching sequences [22,23,24].
Table 1. Three major stages in the development of modulation strategies.
Table 1. Three major stages in the development of modulation strategies.
PointTimeCore Methodology/TechnologyProblems/Breakthroughs
Basic SVPWM phase2010–2015Direct porting of NPC topological modulation methodsThere is the problem of a single choice of zero vector [7]
Loss equalization modulation stage [8]2015–2018Introduction of dynamic zero-vector assignmentAchieved a breakthrough in reducing the loss imbalance by 40% [11]
Intelligent modulation stage [25,26]2018–presentIntegration of MPC with AI and its enhancementsRecent advances include neural network prediction of switching sequences [22]

2.2. Improved MPC Modulation Strategy

MPC is particularly suitable for the control needs of energy storage converters due to its intuitive physical concept and good dynamic performance [12,20,27]. For the characteristics of ANPC topology, the objective function of the improved finite control set–model predictive control (FCS-MPC) is as shown in Equation (1).
J = k = 1 N p   i α β * ( k + 1 ) i α β ( k + 1 ) 2 Current   tracking   term + λ 1 V m i d ( k + 1 ) 2 midpoint   balance   term + λ 2 j = 1 6 ( P l o s s , j ( k ) P ¯ l o s s ) 2 Loss   equalization   term + λ 3 Δ S ( k ) 2 Switching   frequency   constraint   term
The current-tracking term in Equation (1) is realized using the α-β coordinate system to avoid three-phase coupling [28,29]. The expression for the current-tracking term is shown in Equation (2).
k = 1 N p   i α β * ( k + 1 ) i α β ( k + 1 ) Q i 2 = ( i α * i α ) T Q i ( i α * i α ) + ( i β * i β ) T Q i ( i β * i β )
where i α β denotes the reference current in the α-β coordinate system, whose value is provided by the outer loop and requires Clarke transformation; iαβ is the predicted current value obtained through a discretized model; Qi is the current-tracking weight matrix, typically set to diag(1,1), but it can also be set as a time-varying matrix according to the dynamic response requirements; Np denotes the prediction time domain, typically set to 1–3, where ANPC typically takes 1, i.e., single-step prediction.
The physical meaning of the current-tracking term is to ensure that the output current quickly tracks the reference value, which is the most central control objective of the converter; its prediction model is shown in Equation (3).
i ( k + 1 ) = ( I R T s L ) i ( k ) + T s L ( v ( k ) e ( k ) )
where e(k) is the grid counter electromotive force, which needs to be estimated by an observer; Ts is the control period. The prediction time domain Np is usually taken to be 1 (typical ANPC value Ts = 50 μs, i.e., fs = 20 kHz).
The midpoint-balance term of Equation (1) indicates the suppression of midpoint-voltage Vmid fluctuation to prevent harmonic distortion due to capacitor voltage imbalance [30]. Its expression is shown in Equation (4).
V m i d ( k + 1 ) 2 = V C 1 V C 2 V d c 2
where Vdc denotes the DC bus voltage; VC1 and VC2 denote the terminal voltages of the support capacitors C1 and C2, respectively. Midpoint current imid vs. switching state Sx (i.e., Sa, Sb, and Sc denote the switching state of each bridge arm, respectively (taking the values of −1 (negative level), 0 (zero level), or 1 (positive level)) and the instantaneous value of phase current ix is shown in Equation (5).
i m i d = x = a , b , c ( 1 | S x | ) i x i g n ( S x )
The midpoint-equilibrium weighting factor λ 1 in Equation (1) can dynamically adjust the weights according to the state of charge (SOC), as shown in Equation (6).
λ 1 = 0.3 + 0.2 tanh ( 5 | Δ V m i d | )
The loss equalization term of Equation (1) is shown as Equation (7).
j = 1 6 ( P l o s s , j P ¯ l o s s ) 2
where P ¯ l o s s denotes the average loss; Ploss,j denotes the total loss of the j-th switching tube, which contains the conduction loss and switching losses, shown as Equation (8).
P l o s s = I r m s 2 R o n + E s w T s
The loss equalization weight λ 2 in Equation (1) is adjusted with the temperature gradient, and its value is expressed in Equation (9).
λ 2 = 0.1 max ( T j T a v g )
where Tj denotes the junction temperature, Tavg denotes the average junction temperature, and the weight λ2 generally takes a value of 0.1–0.3. The switching frequency constraint term of Equation (1) is shown in Equation (10).
Δ S ( k ) 2 = j = 1 6 ( S j ( k ) S j ( k 1 ) ) 2
where ΔS(k) represents the change in the switching state at time k, with a value range of [0, 1]; Sj(k) represents the state of the j-th switching transistor at time k, which is a Boolean value [0, 1]; Sj(k − 1) denotes the state of the j-th switch at the previous time k − 1, also a Boolean value in the range [0, 1]; λ3 is the switch frequency penalty weight, with a value range of [0.05, 0.3] [18].
The switching frequency penalty weight λ3 is shown in Equation (11).
λ 3 = 0.1 e 0.05 ( f s w f m a x )
where fsw is the switching frequency; fmax is the maximum switching frequency.
It should be noted that the switching state change amount ΔS characterizes whether the switching tube undergoes state switching in an adjacent control cycle, and is expressed as shown in Equation (12).
Δ S j = | S j ( k ) S j ( k 1 ) |
The two-paradigm squared computational expression for the switching state change ΔS is shown in Equation (13).
Δ S 2 = j = 1 6 ( Δ S j ) 2 = Total   number   of   switches
The expression for the mapping relationship between ΔS di-paradigm squared Δ S and the equivalent switching frequency fsw is shown in Equation (14).
f s w , e q = Δ S 6 T s × 1 2
Equation (14) is divided by 2 because one switching cycle contains both turn-on and turn-off actions. Prioritized adjustment of the zero-vector distribution ratio α is shown in Equation (15).
α = T P O N T P O N + T P N O
where TPON denotes the P-O-N path; TPNO denotes the P-N-O path on-time and the total zero-vector time is constant, i.e., TPON + TPNO = Tzero; the voltage balance is constrained to be |Vmid| ≤ 5% Vdc. It is shown that the zero-vector assignment ratio α has a significant effect on the loss distribution: As α increases, the losses in T1/T4 increase while the losses in T2/T3 decrease, and the midpoint current imid is related to α and the load current iload by imid = (2α − 1) iload. The temperature difference cost function in ANPC is used to quantify the degree of temperature imbalance between the switching tubes, and its standard expression is shown in Equation (16).
J t h e r m a l = i = 1 6 w i ( T j , i T ¯ j ) 2 + λ g r a d max ( | T j , i T j , j + 1 | )
where Tj,i presents the junction temperature of the j-th switch transistor, with units in °C, obtained through real-time estimation using a thermal network model; T ¯ j is the average junction temperature, typically calculated using 1 6 T j , i ; wi is the weighting factor, typically expressed as e T j , i T r a t e d / 10 , used to reflect the impact of the difference between the junction temperature and the rated temperature; λgrad is the temperature gradient penalty factor, typically set to 0.3–0.5, used to adjust the contribution of temperature difference distribution to the cost function.
Artificial intelligence-driven intelligent modulation strategies represent a significant advancement beyond conventional model predictive control. Specifically, we introduce a neural network-assisted FCS-MPC framework, in which a lightweight deep neural network (DNN) is trained offline using simulation datasets generated from the ANPC electro-thermal model. The DNN pre-screens feasible switching vectors and outputs a reduced candidate set, thereby lowering the online computational burden by approximately 40%. During real-time operation, the MPC cost function is evaluated only on this reduced set, which integrates three terms, as shown in Equation (17).
J = w i J c u r r e n t + w v J V m i d + w T J t h e r m a l
where Jcurrent ensures current tracking, JVmid constrains the midpoint-potential fluctuation, and J-thermal penalizes junction temperature imbalance.
To enhance adaptability under varying operating conditions (e.g., load transients, grid faults), reinforcement learning (RL) is further integrated to update the weighting coefficients wi, wv, and wT online. Simulation results on a 250 kW ANPC prototype model demonstrate that the AI-assisted MPC achieves a 32% reduction in switching loss and a 28% improvement in dynamic response speed, while maintaining THD below 2.5% compared with conventional MPC. These results confirm that AI-driven modulation enables real-time balancing of electromagnetic compatibility and efficiency across diverse scenarios.
Digital twin-assisted predictive maintenance provides a proactive approach to reliability management under wide-temperature and harsh operating environments. A multi-physics digital twin model is constructed by integrating electrical, thermal, and mechanical sub-models of the ANPC converter. The electrical sub-model calculates device losses Ploss, which serve as inputs to the thermal network model for junction temperature estimation Tj. The thermo-mechanical model then evaluates the induced stress σ, as shown in Equation (18).
σ = E α Δ T + F c l a m p A
where E is Young’s modulus, α is the thermal expansion coefficient, and ΔT is the temperature gradient.
These physics-based estimations are continuously updated with real-time sensor data (voltage, current, temperature) through a Kalman filter, enabling the digital twin to replicate the actual device state with an accuracy above 95%. On top of this, a Health Index function H ∊ [0, 1] is defined, incorporating temperature stress, current stress, and aging factors, as shown in Equation (19).
H = β T T j T a T max T a + β I I r m s I r a t e d + β A t o p t l i f e
Predictive maintenance decisions are then derived by thresholding H: normal mode (H > 0.7), derating mode (0.3 < H ≤ 0.7), and shutdown mode (H ≤ 0.3). Experimental verification on a 1500 V/250 kW hardware in loop (HIL) platform shows that this approach achieves a 20–30% extension of device lifetime and improves MTBF by over 50%, while enabling conventional residual-based fault detection.
Together, the AI-driven intelligent modulation and digital twin-assisted predictive maintenance form a closed-loop adaptive control–health management framework. AI enhances the converter’s real-time control efficiency and adaptability, while the digital twin ensures long-term reliability through proactive maintenance. The synergy of these two technologies enables ANPC converters to achieve > 99% efficiency, THD < 2.5%, and fault prediction accuracy > 90%, providing strong technical support for their deployment in next-generation smart grids and renewable-rich power systems.
The loss-balancing control flowchart for the FCS-MPC is shown in Figure 1. The case temperature of each power device is collected first, and the junction temperature of the device is estimated based on the case temperature; then the average junction temperature is calculated, and then the temperature variance term (a measure of the junction temperature and the average junction temperature of the overall degree of dispersion) is calculated, as well as the neighboring temperature difference term (focusing on the temperature difference between neighboring devices); the weighted summation of these two gives the temperature difference cost function value; so that the power device junction temperature distribution is more uniform, to slow down the aging of the device, improve the reliability of the system, and adapt to the ANPC topology of the scenario of high requirements for temperature equalization [7,15,31,32].
Beyond the proposed framework, we provide a cross-comparison of existing ANPC topology schemes that explicitly covers AI-driven modulation and digital twin (DT)-assisted predictive maintenance, together with a discussion of how these approaches have been implemented and validated. Conventional SVPWM-based ANPC inverters remain attractive for their robustness and simplicity of implementation; however, under high switching frequencies and wide temperature ranges they require additional balancing loops or modified sequences to maintain neutral-point stability and low THD. Improved finite-control-set MPC and hysteresis strategies reduce switching losses and sharpen dynamic response, but they introduce heavier computational loads and stronger sensitivity to parameter mismatch; these trade-offs have been repeatedly confirmed on DSP/FPGA testbeds and power-hardware-in-the-loop platforms using NPC/ANPC prototypes in the 2–20 kVA range.
Recent AI-driven modulation and predictive control schemes report concrete hardware realizations. Neural network-assisted SVPWM and virtual space vector PWM map the reference vector directly to optimal switching states while embedding neutral-point balancing, enabling real-time inference on mid-range FPGAs/SoCs and reducing online arithmetic compared with analytic modulators; lab prototypes and PHIL studies demonstrate improved voltage balancing at high modulation indices and resilience to parameter. Reinforcement learning-guided modulation and RL-tuned MPC have also been implemented, where a policy network selects candidate vectors/penalties to co-optimize dynamic quality and switching loss. Reported validations include closed-loop operation on ANPC prototypes, step-load/step-speed tests, and accelerated thermal excursions in environmental chambers to assess robustness across temperature corners. In these studies, inference latency is kept sub-millisecond on embedded accelerators, and ablation tests compare AI policies against hand-crafted SVM/MPC baselines to quantify gains in THD, neutral-point ripple, and fault ride-through.
Digital twin-assisted condition monitoring and predictive maintenance for power converters have likewise progressed from concept to practice. Physics-informed DTs—coupling semiconductor electro-thermal models with reduced-order magnetic/ageing surrogates—are synchronized with field or laboratory measurements via online parameter identification to track health indicators such as on-state resistance drift, junction-to-case thermal impedance, and capacitor ESR growth. For ANPC and related multilevel stages, DTs have been used to (i) detect incipient open-circuit faults and gate-degradation signatures from current/voltage residuals, (ii) trigger adaptive derating and carrier-phase reallocation to homogenize thermal stress, and (iii) recommend maintenance windows based on remaining-useful-life estimates. Experimental validations typically combine PHIL or real-time simulators with hardware prototypes: the DT runs online (or soft real time) to assimilate inverter telemetry; and ground-truthing is obtained through seeded device faults, thermal cycling, and long-duration endurance runs under mission profiles representative of stationary storage and traction.
When contrasted against redundancy-oriented schemes—hardware duplication or topology reconfiguration—DT-assisted strategies emphasize early detection and proactive stress management rather than purely structural tolerance. Hardware redundancy improves immediate fault ride-through but increases cost and may exacerbate thermal imbalance; DT-based maintenance reduces unplanned outages and enables targeted derating with minimal hardware overhead at the expense of additional sensing, modeling effort, and requirements. Likewise, compared with traditional SVPWM and analytic MPC, AI-driven controllers trade transparent tuning for data-enabled adaptability: their benefits appear most clearly under wide operating envelopes, component ageing, and parameter drift, as confirmed by side-by-side PHIL and prototype measurements reported in recent implementations.
Overall, the literature indicates a clear trajectory: ANPC research is shifting from single-objective performance enhancement to integrated multi-criteria optimization—combining modulation, health estimation, thermal management, and fault response within one supervisory loop. AI-driven modulation provides fast, adaptive decision making; DT-assisted maintenance supplies health awareness and lifecycle planning; and together they complement classical SVPWM/FCS-MPC and redundancy-based designs. This integrated view has already been exercised on experimental benches (DSP/FPGA controllers, PHIL co-simulation, environmental stress tests), providing a concrete pathway to deploy next-generation, stability-aware and reliability-aware ANPC converters in energy storage applications.
A comparison of various strategies applied in energy storage converters is presented in Table 2 [1,6,18,27,33]. A comparison of the technical specifications of conventional SVPWM, MPC, modified FCS-MPC, and hybrid modulation strategies leads to the following important conclusions: A multi-dimensional comparison of the five modulation strategies for ANPC storage converters shows that there are significant trade-offs in their performance indicators, with dynamic response and THD, switching loss and computational complexity, and parameter sensitivity and stability presenting a one-against-the-other characteristic, which needs to be prioritized according to the needs of the trade-offs; scenario suitability is clearly differentiated, with traditional SVPWMs suitable for steady-state scenarios, especially in grid steady-state grid-connected applications, cost-sensitive small- and medium-power systems, and volume products requiring standardized designs. MPC is adapted to highly dynamic demand scenarios, with advantages in electric vehicle drive systems, energy storage scenarios requiring fast fault ride-through, and multi-objective optimization requirements [33]. The improved FCS-MPC has better overall suitability for high-dynamic-demand scenarios and is preferred for military/aerospace power supplies with high reliability requirements, mining converters in high-temperature environments, and energy storage systems with long-life designs. Hybrid modulation is suitable for a wide range of operation scenarios, and is prioritized for battery storage with wide SOC operation, integrated wind and solar storage systems, and scenarios that require a balance between dynamic and steady-state performance. Hysteresis-loop control is oriented towards low-cost simple scenarios, and it is often preferred for emergency power systems, low-cost photovoltaic inverters.
Each strategy’s technology optimization direction focuses on its own shortcomings, reflecting targeted iteration: The midpoint-balancing requirement of the ANPC topology imposes strong constraints on strategy selection, and the modified FCS-MPC and MPC are naturally adapted to it, with additional control loops required for conventional SVPWM and not available for hysteresis-loop control [34]. Overall, the choice of strategy should be based on scenario requirements as the core of comprehensive decision making. Improved FCS-MPC has become the preferred choice for high-reliability and high-performance scenarios due to its comprehensive advantages, and more optimal convergence strategies may emerge in the future [35].
In summary, modulation strategies not only determine the dynamic performance, THD, and switching losses of ANPC converters, but also directly influence the redundancy requirements to ensure system reliability. Therefore, the following section shifts the focus from modulation to redundant control, highlighting how fault-tolerant mechanisms complement modulation strategies in practical applications.

2.3. AI-Enhanced Control Strategies for ANPC Converters

The integration of artificial intelligence (AI) into the control loops of ANPC converters represents a paradigm shift beyond conventional model-based strategies. AI methods, particularly deep learning and reinforcement learning, excel at managing the system’s high dimensionality, nonlinearity, and multi-objective optimization requirements under wide operating ranges. These data-driven techniques can learn complex mappings from operational data, enabling real-time control that is both adaptive and computationally efficient. The following analysis compares prominent AI-enhanced control strategies to the traditional FCS-MPC baseline, highlighting their unique mechanisms, performance gains, and implementation considerations. A comparison of the results of AI-enhanced control strategies for ANPC converters are presented in Table 3.
The core innovation of DNN-assisted MPC lies in decoupling the computational burden from the control problem’s complexity. A lightweight DNN is trained offline to learn the optimal mapping from the current state vector to a small subset of promising switching vectors. The online MPC then only evaluates this pre-screened set, defined by a function f D N N , as shown in Equation (20), rather than all possible vectors. This leads to the reported ~40% reduction in computational cycles without significant performance degradation.
Candidate   Set = f D N N i α β k , V m i d k , T j k , θ
where θ represents the pre-trained network weights.
RL tackles the challenge of tuning the weighting factors in the MPC cost function, which is typically a manual and sub-optimal process. An RL agent interacts with the ANPC system and learns a policy to dynamically adjust these weights (e.g., λ1, λ2, λ3) based on the observed state, maximizing a long-term reward that balances THD, loss, and thermal stress, as conceptualized in Equation (21).
λ 1 λ 2 λ 3 k + 1 = π i α β k , V m i d k , T j k , P l o s s k , ϕ
where ϕ is the parameters of the RL policy network. This allows the controller to adapt to changing operating conditions and device aging.
While AI methods demonstrate superior performance in specific metrics, their practical application requires careful consideration. DNN-assisted MPC is currently the most deployment-ready, offering a clear path to computational savings. RL-guided control holds promise for ultimate adaptability but faces hurdles in real-world training and certifiability. PINNs and LSTMs offer specialized benefits for model accuracy and prediction, respectively. The choice of an AI strategy thus depends on the primary system constraint: computational resources, need for adaptability, or model fidelity. This comparison underscores that AI is not a monolithic solution but a diverse toolkit for addressing specific limitations of traditional control in high-performance ANPC converters.

3. Redundant Control Techniques for ANPC Topology in Energy Storage Converters

3.1. History of Redundant Control Technology

The three developmental stages undergone by redundancy control technology are shown in Table 4. The first generation (before 2015) used hardware redundancy, i.e., adding spare bridge arms, but had the disadvantage of 30% higher costs [37,38,39]. The second generation (2015–2020) shifted to software fault tolerance, achieved through modulation strategy adjustments, with typical scenarios resulting in less than 2% post-failure THD deterioration [37,40,41]. The third generation (2020–present) has evolved into predictive fault tolerance, incorporating digital twins and AI technology [38,42,43,44,45].

3.2. Core Algorithm and Model Analysis

The fault detection model based on residual analysis is shown in Equation (22).
R ( k ) = i a b c ( k ) i ^ a b c ( k ) > ϵ
where R(k) denotes the 2-parameter of the residual vector; iabc(k) denotes the measured three-phase current vector; i ^ a b c ( k ) denotes the predicted current vector; ϵ indicates the dynamic fault threshold, and is shown in Equation (23).
ϵ = ϵ 0 + k 1 N n = 1 N ( i ( n ) i ¯ ) 2
where ϵ 0 denotes the reference threshold, typically set to 0.1 times the rated current Irated, with a range of 0.05–0.15 Irated; k is the sensitivity factor, used to adjust the noise level, with a typical range of 1.5–3.0; N is the sliding window length, typically 1–2 power frequency cycles, corresponding to a numerical range of 20–40; i ¯ represents the sliding average current, calculated as 1 N i n [42].
The state observer design expression is shown in Equation (24).
i a b c ( k + 1 ) = A i ^ a b c ( k ) + B v d c ( k ) S ( k )
where the state matrices A and B are determined by the ANPC topology parameters, as shown in Equation (25).
A = e R T s / L I 3 × 3 ,   B = 1 L ( 1 e R T s / L ) I 3 × 3
where R denotes the equivalent resistance in ohms (Ω), typically ranging from 0.01 to 0.05. It comprises the on-resistance of the switching transistor, bus parasitic resistance, and filter inductor resistance. L represents the total equivalent inductance in hours (H), typically ranging from 0.1 to 1 mH. It includes the filter inductor, transformer leakage inductance, and line parasitic inductance. Ts denotes the control cycle in seconds, typically 50–100 μs, expressed as Ts = 1/fsw; R/L represents the system damping factor, typically 10–50, where higher values indicate faster current decay; Ts/L is the control sensitivity, ranging from 0.05 to 0.2. A higher value indicates faster current response [38,46,47].
Fault-tolerant reconfiguration algorithm implementation is carried out using the health assessment function, as shown in Equation (26).
H = 1 i = 1 6 w i T j , i T a , i T m a x , i T a , i
where H denotes the comprehensive Health Index, with values [0, 1], where 1 indicates fully functional and 0 indicates complete failure; wi is the weighting factor for the i-th device, defined as w i = e α ( T j , i T c r i t ) e α ( T j , i T c r i t ) , with values in (0, 1), representing each device’s contribution to system health; Tj,i denotes the junction temperature of the i-th switching device in °C, estimated in real time via a thermal network model, typically ranging from 25 to 150 °C; Ta,i denotes the ambient temperature of the i-th device in °C, measured by the heat sink temperature sensor, with a typical range of 20–80 °C; Tmax,i denotes the maximum allowable junction temperature for the i-th device, typically specified in the device datasheet, with a range of 125–175 °C; the temperature stress utilization ratio T j , i T a , i T m a x , i T a , i characterizes the thermal stress level experienced by the device. A ratio of 0 indicates complete cooling (Tj = Ta), while a ratio of 1 indicates reaching the maximum temperature (Tj = Tmax). Engineering practice typically recommends maintaining operation below 0.6 [42,47,48].
The extended expression for multi-dimensional health assessment when considering current stress and aging factors is shown in Equation (27).
H = 1 β T w i T j T a T m a x T a + β I I r m s I r a t e d + β A t o p t l i f e
where βT denotes the temperature weighting factor, whose sub-expression is T j T a T max T a , with a weighting coefficient range of 0.5–0.7; βI denotes the current stress weighting factor, whose sub-expression is Irms/Irated, with a weighting coefficient range of 0.2–0.3; βA denotes the aging weighting factor, whose sub-expression is top/tlife, with a weighting coefficient range of 0.1–0.2. The health status grading criteria are summarized in Table 5 [35].
Based on the actual operation, the ANPC device is categorized into three levels of modes, namely, optimal mode Sopt, derating mode Sderate, and shutdown mode Sshutdown, and the expression for the hierarchical reconfiguration strategy is shown in Equation (28).
S n e w = S o p t , H > 0.7 S d e r a t e , 0.3 < H 0.7 S s h u t d o w n , H 0.3
The reconfiguration patterns of the ANPC topology in energy storage converters are compared in Table 6 [38,46,49,50]. The ANPC storage converter modulation strategy presents a multi-dimensional breakthrough in mode optimization and development, with optimal mode enhancement to improve performance through real-time parameter optimization based on digital twins and health correction that takes into account the device aging history [39,51]; derating mode improvement focuses on dynamic derating curve planning and loss-life cooperative control algorithms to optimize system operation; the innovative shutdown mode utilizes optocoupler-isolated ns-level protection and self-diagnostic redundancy architecture to enhance safety and reliability [49].
The flowchart of the ANPC topology reconfiguration policy is shown in Figure 2. Figure 2 shows the ANPC storage converter fault reconfiguration decision logic [52,53]. The health assessment (H) is performed first, and the optimal mode is selected for H > 0.7, the derating mode is selected for 0.3 ≤ H ≤ 0.7, and the shutdown mode is selected for H < 0.3; after selecting the mode to perform reconfiguration, and then determining whether it is multi-fault, if yes, then the hybrid mode is started, otherwise the current mode is maintained, according to the health degree and the faults are dynamically adapted to the operation. Table 6 brings together the performance comparison of fault-tolerant schemes for ANPC topology in energy storage converters [47,54].
Focusing on qualitative insights, Table 7 shows four fault-tolerant routes for ANPC converters that differ primarily in where the “cost” is paid—hardware, control complexity, or data infrastructure [35,42,48,50,54,55]. Hardware redundancy provides the quickest corrective action and preserves power quality with negligible derating, but it does so by adding components and maintenance burden, making it attractive for safety-critical domains where downtime is unacceptable but expensive elsewhere. Modulation adjustment leverages existing hardware and simple control changes, but its effectiveness is limited to specific device/driver failures and it tends to increase distortion and derating, suiting cost-sensitive industrial storage [7]. Topology reconfiguration occupies a middle ground: by rerouting current paths it addresses multi-tube failures with moderate computational demand and moderate impact on efficiency and THD, aligning well with traction applications that can tolerate short reconfiguration latencies. AI-based predictive schemes shift the paradigm from reaction to prevention: they achieve the largest reliability gains and enable coordinated thermal management across compound fault modes, but require data pipelines, model training, and high computation, which raises entry cost and integration complexity, making them more appropriate for digitally instrumented grids. The table motivates a context-dependent selection: redundancy for maximal availability, modulation for minimal capex, reconfiguration for balanced resilience, and AI for systems ready to trade upfront complexity for proactive reliability [22].
The decision tree for selecting fault-tolerant strategies in ANPC energy storage converters is shown in Figure 3. The process begins by identifying the fault type. Next, the equipment is classified as critical or non-critical. For critical equipment, the budget is evaluated. With sufficient resources, AI-based predictive fault tolerance is preferred. With limited resources, hardware redundancy is selected. For non-critical equipment, fault complexity is assessed. Simple faults are addressed with modulation adjustment. Complex faults are handled by topology reconfiguration. This mapping aligns fault types with each scheme’s reliability, cost, and response characteristics. It spans the full spectrum—from high-reliability predictive approaches to basic redundancy, and from simple to complex faults—so that a cost-effective strategy can be chosen for each scenario.
While redundancy techniques significantly enhance reliability and fault tolerance, their effectiveness is inherently constrained by thermal stress, parasitic parameters, and device aging. To address these limitations, the next section discusses multi-physics field co-optimization, which integrates the electrical, thermal, and mechanical domains to further improve stability, efficiency, and lifetime performance.

3.3. Key Measured Parameters and Performance Indicators in Fault Diagnosis

The effectiveness of redundant control and fault-tolerant strategies in ANPC converters heavily relies on the accurate measurement of specific electrical parameters. Different diagnostic methods prioritize different physical quantities, and the choice of these key measured parameters directly influences the performance in terms of detection speed, accuracy, and implementation complexity. To provide a clear comparison, we analyze four prominent diagnostic approaches based on their core measurement requirements and performance indicators. A comparison of fault diagnosis methods for key measurement parameters is shown in Table 8.
The selection of measurement parameters is fundamentally guided by the diagnostic model. For instance, the residual-based model described by Equation (25) relies critically on accurate and fast sampling of three-phase currents iabc(k). The key parameter here is the residual vector R(k), whose deviation from zero beyond the dynamic threshold Ith,dynamic (Equation (26)) triggers a fault. This method offers a balanced trade-off but its speed is limited by the power frequency cycle used in the sliding window.
In contrast, observer-based methods often utilize switching node voltages ΔVsw, which contain rich high-frequency switching information. The key parameter is the voltage residual ΔVsw between the measured and observed values. This allows for extremely fast detection, often within a few switching cycles (<500 μs), making it suitable for high-performance applications, albeit at the cost of requiring higher sampling rates and more complex FPGA-based processing.
For prognostics and health management, the thermal and Health Index models (Equations (29) and (30)) take a different approach. Their key parameters are the estimated junction temperature Tj and the composite Health Index H. While the direct measurements (case temperature Tc, current Ic) are relatively slow, the model-based estimation of Tj provides a crucial, albeit slower-responding, indicator for predicting long-term failures and scheduling maintenance. The emergence of AI-driven predictive fault tolerance represents a paradigm shift towards data fusion. Instead of relying on a single key parameter, these methods use multi-modal measurements (currents, voltages, temperatures) as inputs to a neural network. The key indicator becomes the model’s output, such as a fault probability Pf or a confidence score. This allows for superior accuracy and very fast inference times by identifying complex, nonlinear patterns across multiple sensor data streams that are imperceptible to traditional methods. However, this comes at the cost of high computational complexity and extensive data requirements for training. This comparison underscores that there is no one-size-fits-all solution; the choice of diagnostic method and its associated key parameters must be aligned with the specific performance, cost, and reliability targets of the ANPC application.

4. Multi-Physics Field Co-Optimization of ANPC Topology in Energy Storage Converters

4.1. Current Status of the Development of Multi-Physics Field Co-Optimization Technology

Focusing on trends rather than specific figures, Table 9 traces a clear progression in ANPC multi-physics co-optimization. Early work centered on electro-thermal coupling, achieving sufficiently accurate junction-temperature estimation to enable practical thermal control and to establish validated links between electrical stress and heat flow. Subsequent studies expanded to electro-thermal–mechanical interactions, showing that explicitly modeling force effects materially alleviates device stress and improves reliability under harsh operating conditions [17,21,27]. The most recent phase integrates electrical, thermal, and mechanical fields within high-fidelity digital twin frameworks, allowing virtual prototypes that closely mirror real systems. This shift moves the field from post hoc analysis to predictive optimization and fault prognosis, supporting design-space exploration, online condition assessment, and proactive maintenance—albeit with increased requirements for sensorization, model calibration, and computational resources [58,59,60,61,62].

4.2. Modeling of ANPC Topology with Coupled Multi-Physics Fields

The iterative equation for loss-temperature rise is used to react to the joint electrical–thermal simulation model, as shown in Equation (29).
P l o s s ( n ) = f ( V , I , T j ( n 1 ) ) T j ( n ) = g ( P l o s s ( n ) , R t h )
where P l o s s ( n ) represents the loss at the n-th iteration, measured in watts (W), calculated from loss modeling, with typical values ranging from approximately 50 to 300 W per device; V denotes the operating voltage, measured in volts (V), obtained via DC busbar measurement, with a typical range of 600–1500 V; I denotes the operating current, measured in amperes (A), obtained via current sensors, typically not less than 100 A; T j n represents the junction temperature at the n-th iteration, measured in °C, calculated using a thermal network model, with a typical range of 25–150 °C; Rth is the thermal resistance network, measured in K/W, obtained through structural simulation or experimental testing, with typical values ranging from 0.1 to 0.5 K/W [39].
The expression for the loss Ploss is shown in Equation (30).
P l o s s = I 2 R o n ( T j ) conduction   loss + ( E o n + E o f f ) f s w switching   loss + V b l o c k I l e a k blocking   loss
where Eon and Eoff represent the device turn-on loss and turn-off loss, respectively; Vblock indicates the blocking voltage; Ileak indicates the leakage current of the tube during blocking.
The expression for the on-resistance R o n ( T j ) with respect to the junction temperature is shown in Equation (31).
R o n ( T j ) = R 0 ( T j ) [ 1 + 0 . 004 ( T j - 25 ) ]
The thermal network is modeled as in Equation (32).
T j = T a + P l o s s ( R t h , j c + R t h , c a )
where Tj is the junction temperature; Ta is the ambient temperature; Rth,jc denotes the thermal resistance from the semiconductor chip junction temperature Tj to the device shell Tc, reflecting the heat dissipation capability from the chip interior to the package shell; Rth,ca represents the thermal resistance of the device shell Tc to the surrounding environment Ta, reflecting the heat dissipation ability of the package shell to the environment.
The expression for the thermo-mechanical stress is shown in Equation (33).
σ t h e r m o = E α Δ T + F c l a m p A
where E denotes the Young’s modulus, with the SiC module being approximately 450 GPa and the Si module approximately 190 GPa; α represents the thermal expansion coefficient, with the SiC module being approximately 4.0 × 10−6/K and the SiC module approximately 2.6 × 10−6/K; ΔT denotes the temperature gradient, with the SiC module typically ranging from 20 to 80 K, and the SiC module ranging from 30 to 100 K; Fclamp denotes the installation pressure, with SiC modules generally ranging from 5 to 15 kN and Si modules from 3 to 10 kN; A represents the contact area, with SiC modules ranging from 50 to 200 mm2 and Si modules from 100 to 300 mm2 [50].
The convergence criterion for the joint electro-thermal solution is shown in Equation (34) [63].
T j ( n ) T j ( n 1 ) < 1   ° C   and   max | d T j d t | < 10   ° C / s
The flowchart for achieving multi-physics coupling is shown in Figure 4. Figure 4 presents the ANPC storage converter device-level simulation logic for multi-physical domain coupling [2]. The electrical model first calculates the power device loss (Ploss) input thermal model. The thermal model obtains the junction temperature distribution (Tj distribution) and passes it on to the structural model. The structural model is computed to output deformation feedback for updating the parasitic parameters. The updated parasitic parameters are fed back into the electrical model, forming the electricity → heat → structure → electricity closed loop, which can accurately simulate the dynamic behavior of the interaction of electrical, thermal, and mechanical stresses in device operation to provide support for reliability design and fault diagnosis [64,65].
A comparison of multi-physics optimization methods is presented in Table 10 [66,67,68]. The parameter-scanning method covers the initial design of a simple system with a full factorial test, which is computationally inefficient but moderately accurate [69]. Gradient optimization lends sensitivity to iterations, adapts to continuous variable problems, and is computationally efficient and accurate [36]. Genetic algorithm simulates biological evolution, is good at global search in multi-peak/discrete scenarios, and its efficiency and accuracy are in the middle of the pack [70]. Agent model optimization replaces simulation with approximate models for high-dimensional complex systems, which are computationally efficient but accuracy is dependent on model construction [71]. Deep learning optimization builds response surfaces with neural networks, specializing in ultra-multiparameter nonlinear systems, with high computational efficiency and excellent accuracy after training [57]. Co-simulation optimization focuses on multi-software real-time interaction to solve strongly coupled-field problems with very high accuracy but low computational efficiency [72]. Practical applications need to combine the complexity of the system, parameter characteristics, and efficiency–accuracy needs, (for example, complex scenes can be “agent model + deep learning” synergy), to achieve the balance of efficiency and accuracy of multi-physics field optimization.

4.3. Efficiency Analysis and Comparison of ANPC Converters Under Multi-Physics Constraints

To further evaluate the performance of ANPC topology in practical environments, power losses were analyzed under different scenarios and operating conditions, including variations in load level, switching frequency, and ambient temperature. This analysis was based on an established electro-thermal coupling model, taking into account both conduction losses Pcond and switching losses Psw, as in Equation (35).
P l o s s = P c o n d + P s w = i = 1 n V C E , i I C , i D i + i = 1 n E o n , i + E o f f , i f s w
where VCE,i and IC,i are the on-state voltage and current of device i, Di is the duty ratio, Eon,i and Eoff,i are the turn-on and turn-off energy, and fsw is the switching frequency.
Scenario 1—Load variation: At the rated switching frequency (5 kHz) and ambient temperature (25 °C), the total loss increases nearly linearly with load from 25% to 100%. Specifically, at 50% load, the converter loss is reduced by ~45% compared with full load, with conduction losses dominating.
Scenario 2—Switching frequency variation: At full load and 25 °C, increasing the switching frequency from 2.5 kHz to 10 kHz leads to a ~65% increase in the switching loss, while the conduction loss remains nearly constant. This highlights the trade-off between dynamic performance and efficiency.
Scenario 3—Ambient temperature variation: At 100% load and 5 kHz, raising the ambient temperature from 25 °C to 80 °C increases the total power loss by ~12%, mainly due to higher on-state resistance and thermal feedback.
As shown in the data comparison in the chart in Table 11, the results indicate that power losses in ANPC converters are strongly influenced by load level, switching frequency, and ambient temperature. Conduction losses dominate under high-load conditions, while switching losses increase significantly with higher switching frequencies, leading to reduced efficiency at 10 kHz. Elevated ambient temperature further amplifies conduction losses due to thermal feedback effects. Notably, the converter achieves its peak efficiency of 99.1% under typical operating conditions (75% load, 5 kHz, 40 °C), demonstrating that partial-load operation with moderate switching frequency provides the optimal balance between efficiency and thermal performance. These findings highlight the importance of adaptive modulation and thermal management strategies to ensure high efficiency and reliability across diverse operating scenarios.
Recent advancements leverage AI to transcend these static trade-offs. For instance, the AI-driven FCS-MPC discussed in Section 2.2 utilizes a deep neural network to pre-screen switching vectors, reducing computational latency by ~40% and enabling more frequent evaluation of complex cost functions that simultaneously minimize loss and balance temperature. Compared to the conventional FCS-MPC baseline (Scenario 2, 98.6% efficiency), the AI-assisted method has been shown in simulation to achieve a 32% reduction in switching loss, which could potentially elevate efficiency to approximately 98.9% under full-load conditions without sacrificing dynamic performance. Similarly, RL-tuned modulation dynamically adjusts weighting factors in real time, optimizing the loss distribution across devices as operating conditions change, thereby maintaining higher efficiency over a wider operating range compared to fixed-parameter strategies. While these methods introduce additional computational overhead, they represent a paradigm shift from operating at a fixed efficiency point to dynamically tracking a Pareto-optimal front for efficiency, thermal stress, and THD.
To further evaluate the reliability of ANPC converters, a detailed thermal analysis was performed by coupling electrical loss models with thermal resistance–capacitance (RC) networks. Device losses Ploss obtained from conduction and switching models were applied as heat sources, and the junction temperature Tj was calculated as in Equation (36).
T j = T a + P l o s s R t h J C + Δ T C
where Ta is the ambient temperature, RthJC is the junction-to-case thermal resistance, and ΔTC is the case-to-heatsink temperature rise.
The analysis reveals that both output power and current stress have a pronounced impact on the thermal behavior of ANPC converters. At partial load (50% rated power), junction temperatures remain within 80–95 °C, indicating relatively low thermal stress, whereas under full load, junction temperatures rise by approximately 30%, reaching 120–130 °C and accelerating device aging. Similarly, increasing collector current causes conduction losses to grow nearly linearly, producing localized hot spots: device temperature is around 105 °C at 500 A but exceeds 140 °C at 800 A without advanced cooling. These results confirm that high load and high current are the primary drivers of elevated thermal stress, which can shorten converter lifetime, while moderate operating conditions maintain safer thermal margins.
The stability, reliability, and service life characteristics of the ANPC converter under various operating conditions are shown in Table 12. The results indicate the following: Regarding stability, the neutral-point potential remains stable under partial-load conditions; however, high switching frequencies induce significant dv/dt and parasitic oscillations, necessitating suppression through optimized modulation and laminated busbar design. For reliability, thermal stress and current imbalance are primary factors. Implementing predictive redundancy control and thermal balancing techniques significantly reduces device overstressing, increasing the mean time between failure (MTBF) by over 50%; regarding lifespan, junction temperature fluctuation (ΔT) and ambient temperature are critical variables. Keeping ΔT below 20 °C effectively delays aging, with experimentally verified lifespan extensions reaching 20–30%. Overall, the improvements in stability, reliability, and lifespan of the ANPC topology are achieved through measures such as modulation optimization, redundant fault tolerance, thermo-electrical co-design, and digital twin predictive maintenance. These approaches provide crucial assurance for its long-term reliable operation in high-power energy storage applications.

5. Synergy Analysis of Three Key Technologies

The bidirectional coupling relationship between modulation, redundancy, and multi-field optimization in ANPC energy storage converters is shown in Table 13. The modulation choice sets the baseline for electrical loss, thermal spreading, and computational load. Dynamic schemes (e.g., FCS-MPC or hysteresis) elevate control complexity and therefore demand stronger redundancy. Steady-state SVPWM relaxes this requirement and fits simpler backup schemes. Redundant control, in turn, constrains modulation, because seamless state switching needs stable electro-thermal observability. Multi-field objectives add further boundaries: aging, packaging, and hotspot risks restrict feasible reconfiguration paths and bias strategy selection. High-temperature or tightly coupled conditions favor low-loss MPC with hybrid/adaptive modulation to manage thermal balance. Compute budgets and data pipelines also shape choices; they may preclude AI-based fault tolerance and push toward hardware redundancy. The design problem is thus a co-optimization under coupled electrical–thermal–mechanical and computational constraints. Selecting the modulation for the operating envelope, size redundancy to the induced risk, and tuning multi-field objectives to maintain reliability without prohibitive overhead [2,3,9,16,18,60,74].

6. Technical Challenges and Future Trends of ANPC Topologies in Energy Storage Converters

ANPC topology has become the core choice for medium- and high-power energy storage converters due to its high efficiency and reliability, but it still faces key technical challenges in practical applications, and its future development direction is also centered on the in-depth exploration of these challenges [9,73,74]. Insufficient accuracy of multi-physical field coupling modeling: complex multi-field interactions such as electric, thermal, structural, etc., it is difficult for the existing model to accurately capture the dynamic coupling characteristics under high-frequency switching, which leads to a large deviation between the simulation and the actual operation, and restricts the effectiveness of the optimization strategy.
A comparative analysis of the three key technical challenges is presented in Table 14 [58,66,67,75]. Future research directions are targeted at cracking the above challenges: Artificial intelligence-driven intelligent modulation strategies are an important breakthrough, using AI algorithms to optimize the modulation parameters in real time, dynamically balancing the electromagnetic compatibility and efficiency under high-frequency switching while adapting to the needs of multiple scenarios to enhance the adaptability of the strategy; digital twin-assisted predictive maintenance improves reliability in wide-temperature environments by constructing a full-life-cycle digital model, accurately simulating the coupled state of multi-physical fields, warning of potential failures in advance, and combining with health-degree correction technology to shift from passive fault tolerance to active prevention [66,68,75].
The three converging research pathways for ANPC converters are outlined in Table 15. AI-driven modulation targets adaptability at high frequency and under variable operating conditions. It leverages deep learning for EMI–loss mapping and reinforcement learning for PWM synthesis. It promises lower EMI, small filters, and marginal efficiency gains. It also raises concerns on data coverage, stability guarantees, and fail-safe fallbacks. Validation and interpretability are essential. Digital twin-assisted maintenance shifts reliability from reactive to predictive. It fuses electro-thermal–structural models with vibration and temperature sensing. It enables online health estimation and remaining-life prediction. Benefits include tighter modeling fidelity and earlier fault warnings. Key hurdles are sensor placement, model calibration, synchronization latency, and cybersecurity. Wide-bandwidth device integration pursues SiC/GaN ANPC hardware with optimized drivers and packaging. It enables a very high switching frequency and higher power density. It cuts conduction loss and can raise reliability with adaptive thermal control. Practical limits include EMI containment, gate ringing, short-circuit ruggedness, thermal paths, and cost. A staged roadmap is prudent. Devices should be upgraded first, instrumented with digital twins, then the loop closed with AI modulation. Co-design across hardware, control, and analytics is required for durable gains.
The technological evolution of ANPC topology will go through the spiral development of challenge–breakthrough, which will promote the movement of energy storage converters towards higher efficiency, higher reliability, and a wider adaptable range, and provide the core support for the new type of power system.

7. Conclusions

This paper systematically reviewed the core technology system of the ANPC topology in energy storage converters and proposed a three-level framework integrating modulation strategies, redundant control, and multi-physics field co-optimization. The analysis revealed their dynamic coupling mechanism: modulation strategies shape system performance and define adaptation requirements; redundant control ensures reliability through fault-tolerant mechanisms; and multi-physics field optimization achieves breakthroughs in efficiency, thermal balance, and structural robustness. The key findings demonstrate that ANPC topology offers significant advantages in midpoint-potential balance, switching loss control, and device stress distribution. Engineering practice confirms its potential to achieve high efficiency (≥99%), high reliability (MTBF > 150,000 h), and high power density (up to 4.5 kW/kg) in smart grid and industrial storage applications. These results underline the practical value of ANPC-based converters for large-scale deployment in renewable-rich power systems. Nevertheless, challenges remain in electromagnetic compatibility under high-frequency switching, the modeling accuracy of multi-physics coupling, and wide-temperature reliability. Addressing these challenges requires closer integration of theory and engineering. Future research should focus on AI-driven intelligent modulation, digital twin-assisted predictive maintenance, and wide-bandgap device integration, aiming to push ANPC converters toward higher efficiency, enhanced reliability, and improved intelligence. In this way, ANPC technology can provide the core technical support for the next generation of stable and resilient energy storage systems.

Author Contributions

Conceptualization, S.C., H.H. and B.Y.; methodology, S.C., H.H., L.Z. and P.L.; visualization, W.X.; writing (original draft preparation), S.C., H.H. and G.C.; writing (review and editing), H.H., D.L. and S.C.; validation, W.X.; supervision, H.H. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Science and Technology Department of Hubei Province, China (2024BAB067) and the National Key Research and Development Program of China (2021YFB3800200).

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Acknowledgments

We are grateful to our families, friends, and laboratory colleagues for their unwavering understanding and encouragement.

Conflicts of Interest

Author Hui Huang, Bin Yi, Lianghe Zhu, Pandian Luo, Gouyi Chen, Dake Li are employed by China Southern Power Grid Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Nomenclature

ANPCActive neutral-point clamped
THDTotal harmonic distortion
SiCSilicon carbide device
IRENAInternational Renewable Energy Agency
PCSPower conversion system
ANPCActive midpoint clamping
NPCNeutral-point clamped
MPCModel predictive control
FCS-MPCFinite control set–model predictive control
SOCState of charge
DNNDeep neural network
RLReinforcement learning
HILHardware in loop
DTDigital twin
AIArtificial intelligence
PINNPhysics-informed NN
MTBFMean time between failure
GAGenetic algorithm
EMIElectromagnetic interference

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Figure 1. Control flowchart for FCS-MPC-based loss equalization.
Figure 1. Control flowchart for FCS-MPC-based loss equalization.
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Figure 2. Flowchart of reconfiguration strategy selection for ANPC topology in energy storage converter.
Figure 2. Flowchart of reconfiguration strategy selection for ANPC topology in energy storage converter.
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Figure 3. Decision tree for selection of fault-tolerant schemes for ANPC topology in energy storage converters.
Figure 3. Decision tree for selection of fault-tolerant schemes for ANPC topology in energy storage converters.
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Figure 4. Flowchart of multi-field coupling realization.
Figure 4. Flowchart of multi-field coupling realization.
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Table 2. Comparison of modulation strategies for ANPC energy storage converters.
Table 2. Comparison of modulation strategies for ANPC energy storage converters.
Comparison
Dimension
Traditional SVPWM
[1]
MPC [6]Improved FCS-MPC [18]Mixing and Modulation [27]Hysteresis Loop Control [33]
RationaleBased on voltage vector synpaperRolling optimization + direct controlFinite state optimization + multi-objective constraintsSVPWM and MPC dynamic switchingCurrent error band control
Control variableVector action timeDirect output of switching statusOptimized switching sequenceModulation mode flag bitHysteresis loop bandwidth
Dynamic
response
Medium (0.5–1 ms)Fast (<100 μs)Ultra-fast (<50 μs)Adaptive (50–200 μs)Fastest (10–50 μs)
THD performance3–5%4–6%2.5–4%3–4%5–8%
Switching lossFixed (1.8–2.2 kW)Variable (2.0–2.5 kW)Optimized distribution (1.5–2.0 kW)1.7–2.1 kWRandomized (2.5–3.5 kW)
Center-point balanceAdditional control ring requiredBuilt-in balance controlMulti-objective collaborative optimizationModel relatedUncontrolled
Computational complexityLow (50 million cycles per second (MCPS))High (300 MCPS)Medium–high (200 MCPS)Medium (100 MCPS)Very low (10 MCPS)
Parameter
sensitivity
LowMediumHighMediumExtremely high
Cost of realizationLow (DSP is sufficient)High (requires FPGA)Medium–high (FPGA + coprocessor)Medium (DSP + FPGA)Very low (analog circuitry possible)
Applicable
scenarios
Steady-state operating conditionsHigh dynamic response requirementsHigh-reliability systemsWide-range operationLow-cost simple system
Typical switching frequencyFixed (10–20 kHz)Variable (8–25 kHz)Optimization tuning (12–18 kHz)Dual frequency switchingRandom (5–30 kHz)
Temperature equalizationWrong (ΔT > 25 °C)Medium (ΔT ≈ 15 °C)Excellent (ΔT < 10 °C)Virtuous (ΔT ≈ 12 °C)Extremely poor (ΔT > 30 °C)
Impact of communication delaysInsensitiveSensitivitiesMore sensitiveModerately sensitiveHighly sensitive
Latest improvement directionsVirtual vector synpaperMulti-step prediction optimizationAI vector pre-screeningIntelligent mode switchingAdaptive hysteresis loop
Table 3. Comparison of AI-enhanced control strategies for ANPC converters.
Table 3. Comparison of AI-enhanced control strategies for ANPC converters.
Control MethodCore AI AlgorithmKey Performance MetricsComputational LoadAdvantagesChallenges
Traditional FCS-MPC
[12,27]
Mathematical model (e.g., Equation (8)); cost function minimization (e.g., Equation (6)).THD: 2.5–4%
Switching loss: baseline
Dynamic response: <50 μs
High (evaluates all vectors)Intuitive; excellent dynamicsHigh computational burden; parameter sensitivity
DNN-assisted MPC
[22,36]
DNN for vector pre-selection; offline-trained to map states to a reduced candidate set.THD: <2.8%
Switching loss: ↓ ~32%
Dynamic response: <45 μs
~40% reduction vs. MPCDrastically reduces online computation; maintains performanceOffline training data coverage; model generalization
RL-guided modulationRL for online weighting-factor tuning in cost function (e.g., adjusts w i , w v , w T in Equation (22)).THD: <2.5%
Switching loss: ↓ ~25%
Dynamic response: <40 μs
Medium–high (online policy inference)Adapts to aging and parameter drift; robust performanceComplex training; stability proof required
Physics-informed NN (PINN)Neural network trained with physics-based loss terms (e.g., Kirchhoff’s laws); used for system-state prediction.Model accuracy: >95%
Enables more accurate MPC predictions
High (offline training)
Medium (inference)
Improved generalization with limited data; physically plausible outputsComplex loss function formulation
LSTM-based predictionLong short-term memory (LSTM) network for forecasting load current or grid voltage disturbances.Prediction horizon: 1–5 ms
Enables proactive control
Medium (inference)Improves disturbance rejection; enhances stabilityRequires historical data; sensitive to noise
Table 4. Three generations of evolution in the development of redundant control technology.
Table 4. Three generations of evolution in the development of redundant control technology.
PointTimeCore TechnologyStrengths and
Weaknesses/Achievements
First generation [37]Before 2015Hardware redundancy (add spare bridge arm)Disadvantage: 30% higher cost
Second generation2015–2020Software fault tolerance (modulation policy adjustment)Typical scenarios result in <2% deterioration in THD after failure
Third generation2020–presentPredictive fault tolerance (blending digital twins with AI technology) [44]Latest results: 500 h-earlier failure warning time
Table 5. Criteria for grading health status.
Table 5. Criteria for grading health status.
H RangeHealth LevelControl StrategyMaintenance
Recommendations
0.8–1.0-Full-power operationRoutine inspection
0.6–0.8FavorableModerate reductionsEnhanced monitoring
0.4–0.6WarningsPower limit 50%Scheduled maintenance
<0.4DistressImmediate shutdownEmergency replacement
Table 6. Comparison of reconfiguration models for ANPC topology in energy storage converters.
Table 6. Comparison of reconfiguration models for ANPC topology in energy storage converters.
Comparison DimensionOptimization Mode (Sopt) [38]Derating Mode (Sderate) [46]Shutdown Mode (Sshutdown) [49]
Trigger conditionH > 0.70.3 < H ≤ 0.7H ≤ 0.3
Power output capacity100% rated power50–70% of rated power0% (switching standby unit)
Modulation strategyFull state-space modulationLimit switching frequency (20–30% frequency reduction)Disable fault phase
THD change<3% (baseline)1–2% increaseFaulty phase THD > 10%
Efficiency impactNo loss2–3% reduction in efficiencyZero system efficiency
Cutoff timeGradual transition (5–10 ms)Fast switching (1–5 ms)Emergency action (<100 μs)
Thermal management requirementsNormal coolingEnhanced cooling (+20% airflow)Forced cooling (100% fan)
Device stressEven distributionRedistribution to health devicesComplete uninstallation
Communications needsRoutine condition monitoringReal-time health degree transmissionFault alarm broadcast
Reliability indicatorsMean time between failure (MTBF) > 100,000 hMTBF ≈ 50,000 hReliance on redundant systems
Typical application scenariosUptimeMild agingCatastrophic failure
Control complexityLow (standardized algorithms)Medium (downsizing strategy required)High (fast protection)
Hardware cost impactnoneReserve capacityRedundant design required
Latest improvement directionsArtificial intelligence optimizationPredictive downscalingSelf-healing reconfiguration
Maintenance intervention requirementsRoutine inspectionPlanned maintenanceImmediate repairs
Sensor configuration [50]Basic temperature/currentEnhanced temperature monitoringHigh-speed fault detection
Control chip requirementsConventional DSPDSP + FPGASpecialized protection chip
Typical fault coverageMalfunctionModerate aging failureSevere short-circuit fault
Table 7. Performance comparison of fault-tolerant schemes for ANPC topology in energy storage converters.
Table 7. Performance comparison of fault-tolerant schemes for ANPC topology in energy storage converters.
Comparison
Dimension
Hardware
Redundancy Program
Modulation
Adjustment Program
Topology
Reconfiguration Scheme
AI Predictive Fault Tolerance Program
RationaleAdd spare bridge arm [35]Adjustment of PWM modulation strategy [42]Reconfiguration of current paths [54]Machine learning predicts failures and intervenes early [48,50,55]
Response time<100 μs1–10 ms100–500 μsPre-emptive (1–10 s in advance)
Cost increase+25%+5%+15%+30%
Power derating0%20%10%<5%
Deterioration of THD0%+1.5%+0.8%+0.3%
Reliability improvement40% increase in MTBF
[35]
15% increase in MTBF
[42]
25% increase in MTBF [54]60% increase in MTBF [56]
Applicable fault typesArbitrary device failureSingle-tube open/driver failure [42]Multi-tube failureCompound potential failure
Maintenance complexityHigh (requires periodic switching of standby units)LowMediumVery high (requires data training)
Computing resource requirementsLow (DSP is sufficient)Medium (DSP + FPGA)Medium (FPGA)High (GPU acceleration)
Temperature effectAgeing of spare unitsUneven heat distributionLocalized hotspot riskOptimal thermal management
Typical application scenariosMilitary/aerospace power suppliesCommercial and industrial energy storageElectric vehicle drivesSmart grid
Latest technological improvementsIntelligent rotation strategyAdaptive derating algorithm [5]3D package redundancy designDigital twins + deep learning [57]
Table 8. Comparison of fault diagnosis methods based on key measured parameters.
Table 8. Comparison of fault diagnosis methods based on key measured parameters.
Diagnosis MethodCore Measured
Parameters
Key
Parameters/Indicators
Detection TimeAccuracyImplementation ComplexityTypical
Scenario
Residual-based current analysis [46,47] Phase   currents   ( i a , i b , i c ) ,   DC - link   voltage   ( V d c ) Residual   current   ( R ( k ) ) ,   threshold   ( I t h , d y n a m i c ) ,   sliding   window   average   ( i ¯ a v g )1–5 ms>95%Medium (DSP)General industrial drives, UPS
Observer-based voltage estimation [49,54]Switching node voltage ( V s w ) , DC-link voltage ( V d c )Voltage residual ( Δ V s w ) , observer gain ( L ), estimation error100–500 μs>98%High (FPGA)High-speed traction, EV drives
Thermal network and Health Index
[42,48]
Case   temperature   ( T c ) ,   collector   current   ( I c ) Junction   temperature   ( T j ) ,   Health   Index   ( H ) ,   thermal   resistance   ( R t h , j c )Seconds to minutes>90% (trending)Medium–high (DSP + model)Predictive maintenance, long-term reliability
AI-driven multi-sensor fusion
[20,51,57]
Multi - modal :   phase   currents ,   voltages   ( V s w , V d c ) ,   temperatures   ( T c ) Feature   vectors ,   probability   of   fault   ( P f ), confidence score<100 μs (inference)>99%Very high (GPU/accelerator)Smart grids, Mission-critical systems
Table 9. ANPC topology multi-physics field co-optimization technology development status.
Table 9. ANPC topology multi-physics field co-optimization technology development status.
TimeResearch DimensionKey Results
2010–2016Electro-thermal couplingA junction temperature estimation error of <3 °C is realized, which lays the foundation for the subsequent study of more complex multi-physics fields, and the ability to control the temperature characteristics of the device is improved by establishing the correlation model between electricity and heat [17].
2016–2020Electro-thermal–force couplingOn the basis of electric–thermal coupling research, further incorporating the force factor constructed a more comprehensive coupling model, so that the mechanical stress was reduced by 25%, effectively improving the reliability of the device due to excessive stress [21].
2020–presentHolo-physical field digital twinIntegration of electric, thermal, force, and other multi-physical field elements; construction of a full physical field digital twin model; virtual prototype accuracy > 95%; able to more accurately simulate the actual system operating state, providing a strong support for system optimization and failure prediction [60,61,62].
Table 10. Detailed comparison of the effectiveness of multiple physical field optimization methods.
Table 10. Detailed comparison of the effectiveness of multiple physical field optimization methods.
Optimization MethodsCore IdeaApplicable ScenariosComputational EfficiencyAccuracy
Parameter scanning method [69]Full factorial experimental designSimple system/initial designLowMedium
Gradient optimizationIterative search based on sensitivity analysisContinuous variable problemHighHigh
Genetic algorithm (GA) [67]Global search for simulating biological evolutionMulti-peak/discrete optimizationMediumMedium to high
Agent model optimization Approximate modeling as an alternative to simulationHigh-dimensional complex systems [73]Extremely highDependency model
Deep learning optimization [68]Neural networks build response surfacesUltra-multiparameter nonlinear systemsVery high (after training)High
Co-simulation optimization [66]Multi-software real-time data exchangeStrongly coupled-field problemLowVery high
Table 11. Power losses and efficiency of ANPC converter under operating scenarios.
Table 11. Power losses and efficiency of ANPC converter under operating scenarios.
ScenarioLoad Levelfsw
(kHz)
Temp
(°C)
Conduction Loss
(W)
Switching Loss
(W)
Total Loss
(W)
Efficiency
(%)
150%52552018070099.0
2100%5251050350140098.6
3100%2.5251050210126098.9
4100%10251050580163097.9
5100%5801180380156098.0
675%540800260106099.1
Table 12. Power losses and efficiency of ANPC converter under operating scenarios.
Table 12. Power losses and efficiency of ANPC converter under operating scenarios.
AspectInfluencing FactorsKey ObservationsPractical Implications
StabilityLoad level, switching frequency, parasiticStable midpoint at partial load; high dv/dt and parasitic oscillations at high switching frequencyRequires optimized modulation and laminated busbar design
ReliabilityThermal stress, current imbalance, fault tolerancePredictive redundancy and thermal balancing reduce device overstress; MTBF can be improved by >50%Fault-tolerant control and AI-assisted balancing enhance reliability
LongevityJunction temperature fluctuation (ΔT), ambient temperatureKeeping ΔT < 20 °C slows aging; lifetime extension of 20–30% demonstrated in prototypesElectro-thermal co-optimization and digital twin predictive maintenance prolong service life
Table 13. Relationship matrix of modulation strategy, redundant control needs, and multi-field optimization for ANPC in energy storage systems.
Table 13. Relationship matrix of modulation strategy, redundant control needs, and multi-field optimization for ANPC in energy storage systems.
RelationshipCore RoleKey Logic
Modulation ↔ Redundant control [2]Dynamic strategies (e.g., FCS-MPC, hysteresis) require strong redundancy (AI, hardware); steady-state SVPWM only needs basic schemesControl complexity directly drives redundancy requirements
Modulation ↔ Multi-field optimization [3]Modulation determines electrical loss, thermal distribution, and computational load [67]Strategy choice sets optimization focus (low loss vs. thermal balancing)
Redundant control ↔ Modulation [9]Redundancy requires seamless state switching and stable electro-thermal data from modulationFault-tolerant schemes constrain modulation design
Redundant control ↔ Multi-field optimization [16]Hardware aging and reconfiguration create structural/thermal constraints; AI prediction adds computational–thermal demandsRedundancy adds extra optimization boundaries
Multi-field optimization ↔ Modulation [60]High-T environments favor low-loss MPC; strongly coupled systems need hybrid/adaptive modulationBoundary conditions narrow strategy selection
Multi-field optimization ↔ Redundant control [74]Compute limits may exclude AI-based fault tolerance, leaving simpler redundancy; packaging constrains topology reconfigurationOptimization feasibility defines redundancy options
Table 14. Comparison of the three key technical challenges.
Table 14. Comparison of the three key technical challenges.
ChallengeExpressionImpactBottleneck
Electromagnetic compatibility at high frequencyHigh dv/dt and di/dt, parasitism trigger oscillations, electromagnetic interference (EMI) increases [58]Disturbs peripheral devices, lowers control accuracy, requires bulky EMI filtersEmpirical filter design, no systematic EMI optimization models
Multi-physics coupling accuracyStrong nonlinear interaction of electrical, thermal, and structural fields; models oversimplifiedPrediction errors (>5 °C) distort reliability and efficiency evaluation [67]Difficult to quantify dynamic parameters; multi-scale models too costly for real-time use
Wide-temperature range reliability [66]Large temp. swings (−40 to 85 °C) accelerate aging, solder fatigue, and device stress [75]Higher failure risk, shorter lifetime, frequent derating reduces efficiencyThermal designs cannot handle wide ranges; lack of life-cycle temperature–reliability mapping
Table 15. Comparison of future research directions for ANPC in energy storage converters.
Table 15. Comparison of future research directions for ANPC in energy storage converters.
DirectionCore ObjectiveTechnology PathExpected Benefits
AI-driven intelligent modulation [59]Overcome adaptability limits of traditional modulation under high-frequency/complex conditionsDeep learning-based EMI–loss mapping; RL-based PWM optimization; load prediction with neural netsEMI decline > 30%; efficiency rise 1.5–2%; lightweight filter design
Digital twin-assisted predictive maintenance [60]Improve accuracy of multi-physics modeling for health prediction and lifetime managementBuild electro-thermal–structural digital twins; integrate vibration/temp. sensing; train aging prediction modelsModeling error < 2 °C; fault warning accuracy > 90%; device life rise 20–30%; MTBF rise 50%
Wide-bandwidth device integration [67]Break Si-device limits in high-frequency and wide-temperature scenariosDevelop ANPC with SiC/GaN; optimize driver and packaging [75]; adaptive thermal solutions (−50 to 125 °C)Switching freq. > 50 kHz; power density rise 40–60%; conduction loss decline 40%; reliability rise 50%
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Huang, H.; Cao, S.; Yi, B.; Zhu, L.; Luo, P.; Xu, W.; Chen, G.; Li, D. A Review of Key Technologies for Active Midpoint Clamping (ANPC) Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization. Energies 2025, 18, 6169. https://doi.org/10.3390/en18236169

AMA Style

Huang H, Cao S, Yi B, Zhu L, Luo P, Xu W, Chen G, Li D. A Review of Key Technologies for Active Midpoint Clamping (ANPC) Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization. Energies. 2025; 18(23):6169. https://doi.org/10.3390/en18236169

Chicago/Turabian Style

Huang, Hui, Shuai Cao, Bin Yi, Lianghe Zhu, Pandian Luo, Wei Xu, Gouyi Chen, and Dake Li. 2025. "A Review of Key Technologies for Active Midpoint Clamping (ANPC) Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization" Energies 18, no. 23: 6169. https://doi.org/10.3390/en18236169

APA Style

Huang, H., Cao, S., Yi, B., Zhu, L., Luo, P., Xu, W., Chen, G., & Li, D. (2025). A Review of Key Technologies for Active Midpoint Clamping (ANPC) Topology in Energy Storage Converters: Modulation Strategies, Redundant Control, and Multi-Physics Field Co-Optimization. Energies, 18(23), 6169. https://doi.org/10.3390/en18236169

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