Boost PFC converter is commonly utilized in rectifier circuits due to its ability to achieve a high power factor and low input current distortion. For the single-phase boost PFC converter, large-capacity and low-priced aluminum electrolytic capacitors (AECs) are typically employed to balance the instantaneous power deviation between the input and the output. However, the failure-prone nature of electrolytic capacitors may result in system instability or even collapse. Therefore, the real-time detection of electrolytic capacitor status information, assessment of its service life, and timely replacement of the soon-to-be-failed electrolytic capacitor can provide an important technical guarantee for the reliability of PFC power supply operation. This paper proposes an improved "zero-crossing removal interval" harmonic injection method for online detection of capacitance parameters to solve current zero-crossing distortion caused by harmonic injection. Additionally, based on the harmonic response of the bus voltage, the harmonic capacitor current reconstruction is achieved, and a model for calculating the C_R and R_E parameters without capacitor current sampling is constructed.

Firstly, the AC and DC input-output power action characteristics of the Boost PFC converter are fully utilized, i.e., the high harmonic current injection of the current control loop produces a high harmonic voltage splitting phenomenon on the output voltage. The two split harmonic voltage signals are employed to reconstruct the capacitor current; the capacitor's low-frequency impedance model is used to estimate C_R; a mid-frequency domain harmonic capacitor parameter computation model is established to estimate the R_E. In addition, the high harmonic current injection in the current loop inevitably results in an asymmetric zero-crossing distortion of the input current, directly affecting the accuracy of the capacitance parameter computation model. Consequently, the zero-crossing removal interval harmonic current injection method is employed to solve zero-crossing distortion caused by inter-area injection. The improved “zero-crossing removal interval” method avoids the reconstructed high-order capacitor current calculation error, enhancing C_R and R_E accuracy.

Eighteen types of capacitor conditions are selected for simulation calculation, and 48 W/72 W/144 W Boost PFC experimental prototypes are established. The proposed detection method is verified under an input voltage of 60 V, a switching frequency of 100 kHz, and an output voltage of 120 V. The results demonstrated that the method exhibits high detection accuracy under symmetrical injection conditions with a 10% zero-crossing removal interval, a 10 V injection amplitude, and a 650 Hz frequency. Furthermore, the improved “zero-crossing removal interval” method can achieve parameter detection error within 5% under different loads (100 Ω, 200 Ω, and 300 Ω) and capacitor conditions (196 mΩ/412 μF and 216 mΩ/617 μF), regardless of light or heavy loads.

This paper presents the following conclusions. (1) The proposed method considers the impact of current on distortion caused by harmonic injection. A “zero-crossing removal interval” harmonic injection method improves the accuracy of capacitance parameter detection. (2) In the “zero-crossing removal interval” method, the capacitor current is obtained through algorithmic reconstruction, which avoids high-precision capacitor current sampling. The harmonic injection is achieved by the control algorithm without additional hardware equipment. (3) The proposed capacitance parameter calculation model is derived based on the AC-DC power balance, making it straightforward to extend to similar AC-DC converters.

The rotating rectifier is the key part of multiphase annular brushless excitation systems. Nevertheless, the rectifiers often experience faults caused by diode failures, which brings security risks in practice. Accurately diagnosing faults in the rotating rectifier is pivotal for ensuring the safe operation of multiphase annular brushless excitation systems. However, the types of rotating rectifier faults are diverse, and the characteristics of different faults are inherently weak. Traditional mechanism-driven diagnostic schemes offer interpretability but often struggle with precise fault diagnosis. New data-driven diagnostic schemes exhibit speed and accuracy but encounter challenges in training and debugging in practical applications. This paper proposes a hybrid mechanism-data-driven diagnostic scheme for rotating rectifier faults.

Based on the fault mechanism, the frequency domain characteristics of the excitation current after the fault are derived, and the fault characteristic patterns are summarized. Then, thresholds of the mechanism diagnosis model are calculated using finite element simulation data. Extracting the frequency domain characteristics of the excitation current allows the fault mechanism to be clearly described, thus providing a solid foundation for subsequent fault diagnosis. The current waveform under normal operation and different fault conditions can be simulated by adjusting the models, which allows for determining thresholds for various operating conditions.

Then, the fast dynamic time warping (Fast-DTW) algorithm is introduced to calculate the similarity of excitation current time-domain waveforms, subsequently forming a data-driven model combined with the k-nearest neighbors (kNN) classifier. The fast-DTW algorithm can align waveforms of different time lengths and start points to capture subtle differences between waveforms. By combining the fast-DTW algorithm with the kNN classifier, the data-driven model can realize the diagnosis of rotating rectifier faults.

Mechanism-driven and data-driven diagnostic schemes are integrated based on ensemble learning principles. Ensemble learning significantly enhances the overall performance of the model by combining the results of multiple learners. Five mechanism-driven and five data-driven models are established to obtain a final diagnostic result based on the absolute majority voting method. The hybrid diagnostic scheme exhibits the advantages of mechanism-driven and data-driven models, effectively overcoming the limitations of a single-driven model.

Finally, the verification of prototype experiments indicates that the hybrid scheme’s diagnostic accuracy reaches 100%, significantly surpassing single-driven models. Establishing diagnostic models requires offline simulation data, reducing training difficulty and improving practicality on-site. The hybrid scheme maintains a reasonable diagnostic speed while ensuring high accuracy.

In conclusion, the proposed hybrid mechanism-data-driven fault diagnosis scheme combines mechanism analysis and data-driven methods to enhance the accuracy and robustness of fault diagnosis, demonstrating excellent test performance in prototype experiments. The diagnostic approach based on the time-frequency characteristics of the excitation current demonstrates excellent interpretability, achieving accurate fault diagnosis solely through training with simulation data.

Due to the existence of important loads, the new distribution network needs to be supplied with power when the equipment of the original distribution network is overhauled. Two closing types exist when accessing the new distribution network: loop and ring-closing. The distribution network is cut off for loop closing, leading to power supply interruption, or the ring of the distribution network is directly closed, producing a large impulse current due to the large voltage difference between the two distribution networks. As a result, the relay protection malfunction occurs, which affects the reliability and stability of the power grid. Two ways are adopted to avoid the above issues. One is to provide the loop closing condition through theoretical calculation, and the voltage of the loop closing point is similar by controlling the whole distribution network. The loop is directly closed after meeting the ring closing conditions. However, the control process is more complex, and the loop closing current is still large. The second is to use the voltage regulating device to change the voltage of one side of the ring closing point and carry out the ring-closing. Although the control effect of the ring-closing device is better, the price and maintenance costs are high.

This paper proposes an improved phase shifter (IPST) with an amplitude modulation winding (ETm) based on the amplitude modulation winding (ETp) of the traditional phase shifter. It can flexibly change the voltage amplitude and phase by adjusting the gears of ETp and ETm, thereby changing the voltage at the closing point. The voltage between the two distribution networks is similar, and the loop closure is realized. In addition, the voltage quality on the load side is degraded because of the internal impedance of the IPST after the load transfer. An IPST equivalence model is established based on the multi-port network theory. The impedance characteristics of the IPST port are converted into the equivalent analytical formula. The functional expressions of the regulation voltage on the amplitude modulation gear T_m and phase modulation gear T_p are derived. Thus, the target gear of the IPST is predicted, and the voltage quality is improved. Thirdly, to address the problem of the inrush current generated when the IPST exits bypass closing, the functional relationship of the inrush current on the IPST gear is derived. The IPST target gear is predicted by combining the current regulation target and the voltage quality constraint. The voltage quality can be ensured, and the impulse current can drop and safely exit the IPST. Finally, the impedance expression’s correctness and the control strategy’s effectiveness are verified through PSCAD/ EMTDC.

As a typical multilevel inverter, a neutral point clamped (NPC) three-level inverter is suitable for large-capacity and high-voltage converters, which can effectively reduce current harmonic content. However, the NPC three-level inverter has the problem of neutral point voltage imbalance due to the structural characteristics of capacitive voltage division. The traditional virtual space-vector pulse width modulation (VSVPWM) has limited ability to suppress neutral point voltage fluctuation. Correcting its offset is challenging, especially in the medium and high modulation depths. Therefore, this paper proposes a sector reconfiguration VSVPWM. By introducing equivalent medium vectors and reconstructing sectors in medium and high modulation depths, small and medium vectors can fully participate in neutral point balance adjustment while retaining fixed sector division. This method can effectively suppress the neutral point voltage fluctuation and accelerate the recovery of the neutral point offset. There is only one balance coefficient for each fixed sector, which is easy to implement.

Firstly, the equivalent relationship between a large vector and a medium vector is analyzed. An equivalent medium vector with constant amplitude is then constructed. The equivalent medium vector can participate in the neutral point balance by adjusting the proportion of medium and large vectors. After that, a virtual vector group, including equivalent medium vectors, is constructed. Furthermore, an equivalent medium vector VSVPWM (EMV-VSVPWM) is proposed, which improves the neutral point adjustment ability in the sector with a medium vector. Secondly, the level of modulation depth is divided based on the operational sector position, and the neutral point margin of the EMV-VSVPWM strategy depths is analyzed in one modulation period. It is found that the regions with weaker capacity of neutral point balance exist in high modulation depth. Therefore, a sector reconstruction VSVPWM (SR-VSVPWM) is then designed. The sector boundary and vector selection boundary in the medium and high modulation depths are separated to increase the proportion of small and medium vectors in such regions, which can enhance the neutral point adjustment margin. Furthermore, the neutral point balance coefficient of small and medium vectors is unified to reduce the computational complexity. Meanwhile, the vector sequence is optimized according to the principle of constant switching state, and the switching loss is reduced.

The initial neutral point voltage offset and modulation depth experiments are carried out on a hardware experimental platform in the loop. The results indicate that the SR-VSVPWM strategy can achieve the fast balance of the middle point in pure resistor load and resistor-inductance load conditions. Compared with the traditional VSVPWM single small vector adjustment, the neutral point voltage offset is eliminated, and the balance time in the high modulation depth is reduced by about 46%. In addition, the current harmonics are also reduced. When the experiment on variable modulation depth is considered, SR-VSVPWM still exhibits strong suppression of neutral point fluctuations and good current quality in high modulation depth. After the switching frequency is reduced to 5 kHz, the neutral point fluctuation level of SR-VSVPWM is 79.1% of the traditional VSVPWM.

In the inverter-driven permanent magnet synchronous machine (PMSM) control system, high-frequency current harmonics near the switching frequency and its multiples are generated using space vector pulse width modulation (SVPWM), which brings high-frequency electromagnetic vibration. Therefore, a double random SVPWM control method combining random switching frequency and random zero vector is applied to the high-frequency current harmonic spectrum expansion. Meanwhile, the random number is generated by the improved Mersenne twister (MT) algorithm, which enhances the random performance of the random sequences and ensures the spreading effect of the double random SVPWM control method.

Firstly, random zero vector control can be achieved by changing the action time of the zero vector and reassigning the randomized zero vectors into the space vectors. Secondly, the switching frequency of the traditional SVPWM control method is fixed, and the random switching frequency control can be achieved by changing the fixed switching frequency of the inverter and dispersing the harmonics at the switching frequency and its multiples into the specified frequency domain. Thirdly, the random number is generated by the improved MT algorithm, which is applied to the double random SVPWM control of the permanent magnet synchronous machine to enhance the degree of freedom and spatial traversal of the random sequence. The new control method proposed is named LKMT-DRC.

Experimental verifications are conducted on a 4.4 kW fractional-slot permanent magnet synchronous machine. The PMSM phase current harmonics and vibration acceleration under the conventional SVPWM control and LKMT-DRC control are compared, and the vibration suppression effect of the LKMT-DRC control is analyzed using different spreading ranges. Under the inverter power supply mode, the harmonic frequencies introduced by the SVPWM control mode are mainly f_k±2f₀ and f_k±4f₀, and the frequency of the introduced high-frequency radial electromagnetic force wave is mainly f_k±f₀. Compared with the traditional SVPWM control mode, the high-frequency harmonics concentrated on the switching frequency. Its integer multiples can be effectively dispersed using LKMT-DRC control mode, and the vibration suppression effect caused by the high-frequency electromagnetic force wave can be significantly reduced. Meanwhile, the random numbers generated by the proposed LKMT algorithm can improve the randomness and spatial traversability of the random sequences, which ensures the effectiveness of the double-random SVPWM control method.

The contributions of the proposed double random SVPWM control method based on the improved MT algorithm are as follows. (1) A mathematical model of the high-frequency radial electromagnetic force introduced by PMSM under inverter power supply conditions is derived, and the effect of the high-frequency electromagnetic force under inverter power supply mode on motor vibration is analyzed. (2) The LKMT-DRC control method is proposed, which effectively reduces high-frequency harmonic content and suppresses high-frequency electromagnetic vibration. (3) The effects of different spreading ranges on the final damping under the LKMT-DRC control mode are analyzed, and the appropriate ranges are indicated.

The LLC converter plays a pivotal role in the infrastructure supporting electric vehicles, where efficiency and reliability are paramount. Its ability to efficiently transfer energy between different voltage levels makes it particularly suitable for EV charging stations, where power conversion efficiency directly impacts operational costs and environmental sustainability.

Synchronous rectification has emerged as a promising strategy for optimizing LLC converter performance. By replacing traditional diode rectifiers with active switches that operate synchronously with the converter's switching frequency, synchronous rectification minimizes energy losses and improves overall efficiency. However, existing synchronous rectification methods have faced challenges, such as complex control algorithms, sensitivity to load variations, and the need for high-frequency sampling.

Unlike conventional approaches that rely on high-frequency sampling for precise timing control, the novel synchronous rectification scheme utilizes a streamlined time-domain analysis. This approach dynamically adjusts the timing of the synchronous rectifier based on real-time feedback from the LLC converter's operating modes, ensuring optimal efficiency across a wide range of operating conditions with high-frequency sampling and alleviating the computational burden.

By reducing the complexity of control algorithms and eliminating the need for high-frequency sampling circuits, the scheme not only lowers manufacturing costs but also enhances reliability by reducing potential points of failure. This simplification is particularly advantageous in high-power applications like EV charging stations, where robustness and operational uptime are essential.

Simulation studies have validated the effectiveness of the proposed scheme under different load conditions and frequencies. Simulations have shown significant efficiency improvements compared to traditional methods, highlighting the scheme's potential to reduce energy losses and improve overall system performance.

Furthermore, experimental validation using a 6.6 kW prototype shows that the proposed scheme delivers consistent and efficient operation under steady-state and dynamic conditions, further supporting its potential for commercial EV charging infrastructure integration.

The adoption of the proposed synchronous rectification scheme promises to enhance the efficiency and reliability of LLC converters and accelerate the transition to electric mobility. As governments and industries worldwide prioritize sustainability goals and seek to reduce carbon footprints, improvements in energy conversion technologies play a crucial role in supporting the widespread adoption of electric vehicles.

In conclusion, the synchronous rectification scheme represents a significant step in evolving LLC converters for electric vehicle charging infrastructure. By overcoming traditional limitations and leveraging streamlined control strategies, the scheme enhances performance and contributes to the sustainability of transportation systems. As research continues to refine and optimize power conversion technologies, the ongoing advancements in LLC converter designs underscore their pivotal role in shaping a cleaner, greener future for global transportation.

In servo systems, the bandwidth of the current loop is increased by raising the switching frequency. However, the dead-time nonlinearity of the voltage source inverter (VSI) intensifies with the increase of switching frequency, causing the deviation between the actual and the theoretical output voltage, resulting in serious distortion of the inverter output current waveform.

The requirement of computational power constrains the implementation of high switching frequency control. Consequently, the dead-time nonlinearity compensation strategy should be more straightforward to decrease computational time, especially for high switching frequency applications. The amplitude increase is relatively modest at a low switching frequency but significantly surges at a high one, bringing on a severe degradation of the linear modulation region. It is an imperfect solution to compensate after the occurrence of dead-time, which unavoidably introduces compensation errors. Furthermore, the accurate solution of inverter nonlinear voltage error (INVE) under different currents represents a crucial aspect of achieving exact INVE compensation. Nevertheless, the existing methods are complex.

This paper proposes a novel strategy that combines no-dead-time double modulation wave pulse-width modulation (PWM) and inverter nonlinearity compensation for analyzing the dead-time nonlinearity and the nonideal characteristics of the inverter on the output voltage error. Firstly, according to the continuous current characteristics of the anti-parallel diode, the drive vacancy area is added between the complementary drive pulses to avoid the introduction of dead time. Compared with the ideal space vector pulse width modulation (SVPWM), an auxiliary modulating wave is added. Depending on the current polarity, its amplitude is adjusted up or down from the original modulating waveform. The underlap periods are generated between the complementary drive pulse by contrasting the double-modulating and the triangular carrier waves. It is practical to avoid both the bridge arm shoot-through and the introduction of dead time. Most importantly, the actual output voltage of this method is identical to the optimal voltage, which directly eliminates the dead-time nonlinearity and removes the limitation of dead time on the output duty cycle at a high switching frequency. Moreover, the control signals of each switching device are obtained based on the comparison between the double-modulating and the carrier wave. No additional control loop calculations are required, while the generated PWM signals are symmetric about the carrier midpoint.

Secondly, the inverter nonlinearity is equated to the INVE, which varies with the current. When the motor is at a standstill of ${{\theta }_{\text{e}}}={{0}^{\circ }}$, by injecting the ramp current signal into the direct axis and applying Kirchhoff's voltage law, the sum of INVE containing the nonlinear factor of the two-phase VSI is obtained. Finally, the relationship between the INVE and the current amplitude is calculated using the linear iterative interpolation approach, and the online compensation of the INVE is achieved.

The results show that the proposed strategy can increase the linear modulation region of the output voltage, eliminate the output duty cycle limitation derived from the dead-time, and effectively suppress the current harmonic distortion phenomenon caused by the dead-time nonlinearity of high switching frequency inverters. In addition, the strategy is easy to implement without additional control loop calculations, which can be applied to servo drive control systems requiring high switching frequencies.

A Bi-stable permanent magnet actuator (BPMA) shares the same magnetic circuit as the breaking and closing coils, and the magnetic flux generated by any coil passes through the breaking and closing air gaps. The permanent magnet automatically distributes the permanent magnetic flux according to the dynamic reluctance of the air gaps. The electromagnetic flux and permanent magnetic flux in the upper and lower air gaps always cause the moving iron core to be coupled by two opposite magnetic forces. As the motion of the moving iron core and the change of coil current, the magnetic circuit quickly saturates, and the electromagnetic flux and permanent magnetic flux interact, exacerbating the complexity of nonlinear coupling in the breaking and closing air gaps. To flexibly control the action characteristics of permanent magnet switches, it is necessary to simultaneously control the air gap flux and the magnetic force pointing to the breaking and closing positions. Therefore, this paper proposes an air gap flux decoupling control method based on finite control set-model predictive control (FCS-MPC). Decoupling control can be achieved by rapidly weakening the magnetic force pointing to the non-excited coil and rapidly increasing the magnetic force pointing to the excited coil.

Firstly, according to the operating principle of BPMA, the vector magnetic force acting on the moving iron core depends on the “magnetic flux squared difference” of the breaking and closing air gaps. Therefore, only controlling this vector magnetic flux square difference in real-time can dynamically control BPMA. Secondly, a predictive model of the breaking and closing air gap magnetic flux is designed through discretization of the voltage balance equation, which can predict the magnetic flux at the next moment based on the voltage and current values collected at the current moment. Thirdly, the breaking and closing air gap magnetic flux and the mechanism drive circuit are regarded as a whole. A set of switching states is constructed through the excitation intensity analysis under different switching states. Predictive magnetic flux is obtained by traversing all switching state combinations. Finally, a decoupling control cost function is designed, the predictive magnetic flux under different switching combinations is input into the cost function, and the optimal control is selected for the next control period. In rolling optimization over multiple control periods, the breaking and closing air gap magnetic flux quickly approaches their respective reference values, achieving decoupling control.

A co-simulation platform for intelligent control is designed based on LabVIEW and Multisim, and hardware testing circuits are constructed. The simulation and experimental waveforms show that this proposed scheme can effectively control the breaking and closing air gap flux. As a result, the non-excited air gap flux to zero is quickly reduced, approaching the set reference value of the excited air gap flux and effectively weakening the coupling between the air gaps. Compared with the traditional current closed-loop control scheme, the proposed control scheme reduces the energy loss during the entire action process and improves the response and action time of the core action.

The doubly salient electric-excited motor has many advantages such as a simple structure, low manufacturing cost and high reliability, making it a good candidate for applications in electric vehicles, aerospace, and other fields. However, its large torque ripple and low torque density limit its development and applications. This paper proposes a new topology structure for the doubly salient electromagnetic machine (DSEM).

The topology structure and working mechanism of the proposed DSEM are analyzed in detail. The combination of stator poles and rotor poles is elaborated, and the winding method of armature windings is described with the influence on the harmonics of EMF. The relationship between the pole-combination and harmonics of the magnetic field, together with the output torque, is investigated according to the magnetic field modulation mechanism, and the air-gap flux density harmonics of 18/10 and 18/11 DSEMs are obtained by finite element analysis. The influence of pole combination on motor characteristics is analyzed by finite element analysis, including the no-load electromagnetic performance, the torque features, and the loss characters, which shows the superiority of the DSEM with odd-number rotor poles. Finally, a prototype of the new 18/11 DSEM is manufactured and tested.

The results show that due to the new winding method, the flux in armature windings changes bipolar, resulting in high sinusoidal flux linkages and, thus, a high sinusoidal EMF. The DSEM with odd-number rotor poles has more effective space magnetic harmonics than that with even-number rotor poles, almost with odd orders, resulting in higher output torque. Besides, due to the offset of even-order time-harmonics, the DSEM with odd-number rotor poles has higher sinusoidal EMFs and lower torque ripples. In addition, different rotor poles show different characteristics, as seen from the simulation results.

The following conclusions can be drawn. (1) By adjusting the winding method of the field winding and the armature winding, the new type of DSEM realizes the bipolar change of the armature flux, and the back EMF has a high sinusoidal degree. (2) As can be seen from equations (21) and (26), the effective harmonics’ frequency of air-gap flux density in the odd-rotor pole motor is different from that in the even-rotor pole motor, resulting in different torque harmonics. (3) If the number of rotor poles is even, there are more even order harmonics in the motor back EMF, and the cogging torque and torque ripple are also large; if odd, the armature coils with opposite polarity are connected in series, and the even harmonics in the motor back EMF cancel each other, resulting in smaller harmonic content, cogging torque, and torque ripples. (4) The motor performance is optimal for the proposed DSEM with 18 stator poles when the rotor pole number is 11 or 13.

Power electronic transformer with cascaded H-bridge (CHB-PET) can realize the flexible interconnection of AC/DC microgrid and renewable energy sources such as energy storage devices and DC loads. In a practical project, CHB-PET is connected to different bus segments through two short leads that are standby for each other. Considering the fault occurring AC side of CHB-PET, the spare short lead needs to be put into operation quickly to realize the rapid recovery of power supply. However, the conventional scheme cannot distinguish whether there is a fault before the spare short lead is put into operation, and there is a risk of connecting the faulty short lead. To solve this problem, this paper proposes a scheme based on the cooperative control of CHB-PET and DC microgrid, which achieves safe input of short leads by actively injecting characteristic voltage.

Firstly, CHB is blocked to achieve fault isolation after fault occurring. The energy storage device is switched to DC voltage control mode, maintaining the DC bus voltage and ensuring the normal operation of DC microgrid load and other equipment. Secondly, CHB is unlocked and switched to the U/f control. CHB-PET can inject characteristic voltage into the spare line to detect whether there is a fault point in the line. Furthermore, a fault detection method considering the current imbalance factor is proposed to reduce the time required for fault detection, so as to realize the rapid and safe investment of spare short lead.

The verification results on PSCAD/EMTDC simulation platform show that the scheme based on characteristic voltage injection can give accurate detection results when the spare line is fault-free. When three-phase fault, phase-phase fault, double-phase to ground fault and single-phase to ground fault occur in the spare line, the transition resistance of the phase-to-phase fault is 200 Ω, and the transition resistance of the ground fault is 300 Ω. The proposed scheme can also give accurate detection results. Through the simulation verification and experimental verification of the proposed scheme in different scenarios, the consistent results are obtained, which confirms the accuracy of the simulation model and the feasibility of the proposed scheme.

Through the simulation analysis, the following conclusions can be drawn: (1) The scheme uses the CHB-PET ontology to inject characteristic voltage with controlled amplitude and frequency into the standby line. According to the difference of electrical characteristics of the standby line in different scenarios, proposed scheme can accurately detect whether there is a fault in the standby line. (2) In three stages of the proposed scheme, the collaborative control of CHB-PET and DC microgrid energy storage device is used to ensure the normal operation of each equipment in the DC microgrid after the AC short lead fault, which is conducive to the rapid recovery after the fault. (3) In the fault detection stage of spare short lead, the fault detection criterion is constructed by using the product of the characteristic current imbalance factor and the current integral value. Compared with the direct use of the current integral value, the fault detection time under high resistance fault is reduced and the protection action speed is improved.