A novel cascaded H-bridge photovoltaic inverter with flexible arc suppression function

0 Introduction

With the continuous development and utilization of new energy sources,a large amount of photovoltaic (PV)power generation equipment has been connected to lowand medium-voltage distribution systems,significantly enhancing their power transmission capacity.Inverters one of the core devices in such PV power generation systems,and they have undergone significant development in recent years.In terms of device topology,early PV inverters mostly used three-phase full-bridge structures.With the continuous advancement of technology,new generation PV inverters gradually adopted cascaded topologies [1].Traditional photovoltaic inverters generally need to be connected to a medium-voltage grid through a step-up transformer,whereas high-voltage direct-coupled inverters can be directly connected to a distribution grid without the need for a step-up transformer.This increases the efficiency of the power conversion.In terms of functional applications,the multifunctional integration of PV inverters and further expansion of the application value of the equipment have gradually become major focuses of inverter technology research.Zhu et al.[2] proposed a photovoltaic inverter capable of compensating for grid harmonics.This inverter calculates the compensation current commands in real-time by analyzing the amplitude and phase of the higher-order harmonics of a grid,thereby achieving precise tracking.In addition,they introduced a phase-cutting strategy on the direct current (DC) side of the inverter,which enhanced the efficiency of the boost converter.Li et al.[3] established an inverter control model to analyze the variation in the grid reactive power of PV inverters in standalone and gridconnected modes.They adopted an algorithm that combines reactive power compensation with harmonic compensation,to effectively improve the power quality.You et al.[4]incorporated a negative-sequence current compensation strategy in an inverter.By using power flow control to simultaneously adjust the three-phase voltages,they reduced the imbalance between adjacent feeders and mitigated the impact of load voltage imbalance caused by power outages.Zhao et al.[5] introduced a third-harmonic compensation strategy for cascaded PV inverters.This strategy addresses overmodulation issues caused by uneven interphase and intraphase illumination,thereby reducing the total harmonic distortion of the output current waveform.Darshni et al.[6] integrated low-voltage ride-through and anti-islanding control strategies in an inverter.This effectively enhanced the stability of the inverter during grid faults.Li et al.[7]investigated a special third-harmonic injection strategy for an inverter that reduced the second-harmonic ripples in DC buses.Research on the multifunctionality of photovoltaic inverters has made significant progress,especially in the management of grid imbalance.Jitendra et al.[8] developed a voltage optimization algorithm aimed at achieving power balance by balancing the three-phase output voltage,while significantly reducing the harmonic content of the output current.However,this study did not consider the ability to suppress harmonics while providing reactive compensation.Lago et al.[9] employed the instantaneous power theory and third-order generalized integrals to design a three-phase imbalance suppression strategy.By estimating the amplitude of orthogonal signals using third-order generalized integrals and calculating the negative-sequence compensation current based on instantaneous power theory,the imbalance component in the output current was effectively suppressed.However,this study did not consider the compensation for zero-sequence components.Sen et al.[10] proposed a boosttype multilevel inverter circuit based on switch capacitors for photovoltaic inverter control.This technology generated a seven-level voltage output through a single circuit,thereby reducing equipment costs and output harmonics.However,this study did not discuss the theoretical limits of the compensation capability.Khlifi et al.[11] proposed a control method for PV inverters based on multilevel fast capacitors,which not only reduced the fluctuation of the output power,but also significantly reduced the total harmonic distortion in the grid current by using a Kalmanbased high-gain observer to estimate the capacitor voltage.However,this study did not address the voltage-stabilization issue on the DC side.

The above studies integrated functions such as reactive power compensation,harmonic compensation,interphase and intraphase balance,and anti-islanding control into gridconnected inverters and thereby broadened the application depth of the equipment.However,in addition to the aforementioned issues,frequent single-phase grounding faults also affect the stable power generation of the system.Currently,research on fault current suppression in PV inverters is limited.Therefore,it is necessary to rely on arc-suppression devices to compensate for the fault current.Zhang et al.[12] proposed a cascaded arcsuppression device that integrated flexible arc suppression by regulating zero-sequence currents.This device regulates the zero-sequence current during normal operation to reduce the impact of faults on distribution networks.Fan et al.[13] developed a flexible arc-suppression device based on the joint operation of multiple transformers.The device effectively suppresses the grounding fault current by precisely adjusting the zero-sequence voltage of the secondary-side voltage control system of a grounding transformer.Wang et al.[14] designed a cascaded flexible arc-suppression device that combined overvoltage and arc suppression.This device achieved a lower residual current and effectively compensated for fault currents in systems with a high three-phase imbalance.You et al.[15,16] adopted a hybrid arc suppression method for cascaded H-bridge arc suppression devices.This method achieved adaptive arc suppression for both high-and low-impedance faults.Its effectiveness surpassed that of conventional current-and voltage-based arc-suppression methods.However,the existing flexible arc-suppression devices mentioned above suffer from disadvantages such as high cost and single functionality.These devices activate only when a single-phase grounding fault occurs in the distribution network,resulting in low utilization.In addition,the energy source used by the devices to compensate for the active component of the grounding fault current was not discussed in the aforementioned studies.Therefore,research on the multifunctional integration of flexible arc-suppression devices has become a key development direction.

Cascaded PV inverters and fully powered electronic flexible arc-suppression devices share a similar topology.This study combines the functions of a cascaded PV inverter and flexible arc-suppression device and proposes a method to integrate power transmission and flexible arc suppression in a novel cascaded H-bridge PV inverter(NCHPI).Simultaneous control of the power transmission and flexible arc suppression was achieved by using the zero axis of a reverse Park transformation as the input for the compensation current.Additionally,based on the characteristics of neutral-point grounding in the proposed inverter topology,the zero-sequence current is suppressed during normal operation,reducing the total harmonic distortion (THD) of the output current.The innovations of this study are as follows:

1) An integral sliding-mode controller based on an adaptive fuzzy neural network is proposed for flexible arcsuppression control.This reduces the adverse effects of external interference on sliding mode control and effectively improves the response speed and control accuracy of the control system.

2) An adaptive update law was designed for the neural network parameters to enhance the adaptability of the sliding mode control under different distribution network mathematical models.This further improved the robustness of the proposed controller and simplified the debugging process.

3) An arc-suppression exit strategy based on nonlinear current ramp-down was designed to reduce the amplitude fluctuation of the zero-sequence voltage during the exit process.This decreases the likelihood of misjudgment and shortens exit time.

The remainder of this paper is organized as follows:Section 1 introduces the principle of the proposed NCHPI.Section 2 discusses a sliding-mode controller based on an adaptive fuzzy neural network and the exit strategy for flexible arc suppression.Section 3 presents a simulation of the proposed NCHPI in a MATLAB/Simulink model of a neutral-point unearthed 10 kV distribution network.Finally,Section 4 concludes the study.

1 Working principle of NCHPI

A cascaded high-voltage direct hanging inverter bridge arm was formed by connecting the midpoint of the far DC power source bridge arm of each H-bridge unit to that of the near DC power source bridge arm of the next unit (Fig.1).Subsequently,a near DC power source of the first stage was linked to a power distribution network via a connecting inductor,and the midpoint of the far DC power source of the final stage was grounded.The PV array shown in module①of Fig.1 was used as the DC power source;it was connected to a grid without grounding at the neutral point to achieve efficient energy conversion.If the above module is replaced with the energy storage element shown in module② of Fig.1 and neutral point is grounded to ensure the formation of a reverse zero-sequence current-feeding loop,it constitutes the topology of a flexible arc-suppression device [12].However,flexible arc-suppression devices function only when a grounding fault occurs,resulting in low efficiency and a large space requirement.Traditional cascaded photovoltaic inverters can be divided into Y-type[1] and delta-type connections [5] with no grounded neutral point;hence,there is no zero-sequence current loop at the 10 kV side.To achieve flexible arc suppression in a PV inverter,the end of it should be connected in Y-type and the neutral point should be grounded.However,grounding creates a zero-sequence current loop,which leads to an increase in the zero-sequence current.Therefore,it is necessary to implement power output and zero-sequence current suppression during normal operation at the control algorithm level,along with fault arc suppression in the event of single-phase grounding faults.The parameters in Fig.1 are as follows: eX (X =A,B,and C) represents the electromotive force of phase X of the power supply in the distribution network,iZX represents the output current of phase X in the NCHPI,uHX represents the output voltage of phase X in the NCHPI,Ln represents the output-side connecting inductor of the NCHPI,and Rn represents the parasitic resistance of the connecting inductor.CA,CB,and CC represent the sum of the capacitances to the ground of all the branches in the three phases.RA,RB,and RC represent the sum of the leakage resistance to the ground of all branches in the three phases.To simplify the analysis,we assumed that CA= CB= CC= C0 and that RA= RB= RC= R0.

Using the current arc suppression method and considering the fault current as the suppression target [17,18],it can be theoretically compensated directly to zero.If a single-phase grounding fault occurs on the A-phase of the 10 kV line,combined with Kirchhoff’s current law from Fig.1,we can obtain

During the normal operation of the distribution network,the electromotive force of the three-phase power source is symmetrical.Therefore,Eq.(1) can be rearranged as follows.

If if=0,u0=-eA.The compensating current iNi injected by the NCHPI at this point is given by

Eq.(2) holds true at any moment during the fault occurrence phase.Hence,the compensation current iNi in Eq.(3) is a transient quantity.Therefore,ensuring that the reference current accurately tracks iNi can compensate the fault current to zero at any time.

Traditional PV inverters often apply a dq-axis to decouple the control of active and reactive powers with less utilization of the zero axis.However,the zero-axis can naturally achieve a balanced three-phase output.Therefore,Eq.(3) can be adopted as the reference current for the zeroaxis.After a reverse Park transformation,the target of compensating current is generated to accomplish flexible arc suppression.

During the normal operation of a distribution network,there is a certain magnitude of unbalanced current within the system [12].After grounding the neutral point of the NCHPI,the system generates a zero-sequence current flowing through the NCHPI,which affects the quality of the output current.However,the unbalanced current in the three phases can be suppressed by setting a compensating current at the zero-axis during the reverse Park transformation and implementing the necessary controls.In the remain of this paper,this is referred to as “unbalanced current suppression.”

During a single-phase grounding fault,the fault current reaches its maximum value within a single power frequency cycle [19],resulting in a short-circuit impact current.The suppression of the unbalanced current can also suppress the short-circuit transient current.If the unbalanced current is not suppressed,the distribution network is equivalent to a neutral-point effectively grounded system.When a singlephase grounding fault occurs,the impact current surges,potentially damaging electrical equipment.However,if an unbalanced current suppression function is added,the distribution network remains equivalent to a neutral-point non-effectively grounded system,significantly reducing the fault impact current [12].

2 Controlling method of NCHPI

The control structure of the NCHPI is shown in Fig.2.It consists of three main parts: active power and reactive power transmission control,flexible arc and unbalanced current suppression,and grounding fault detection and exit strategies.

Similar to traditional PV inverters,the front part of the power transmission control employs a maximum power point tracking (MPPT) [20,21] algorithm to calculate the reference value of the d-axis current,whereas the back part utilizes a voltage-current dual-loop control and the reference value of the q-axis current to calculate the dq-axis control voltage.The specific implementation process can be found in [22].

A nonlinear controller can be applied for both unbalanced current and flexible arc suppression.When there is no fault,the controller acts on the unbalanced current,and the control goal is to make the zero-sequence current of the NCHPI output zero.Therefore,the reference value of the zero-sequence current was switched to zero.When a fault occurs,the controller acts on the latter,and it is necessary to model the injected compensating current iNi to achieve precise control.The zero-sequence injected voltage is given by

where vcon represents the zero-sequence control voltage,and KPWM is the modulation coefficient.The state equation of the injected compensating current iNi can be expressed as in [23].

Applying Kirchhoff’s voltage law to Ln,we obtain

Rearranging Eq.(5),

Set iNi as the state variable x and vcon as the control variable u;considering the modeling inaccuracies due to different fault locations in the system,different inverter connection locations,and other unknown disturbances dv(t)and fluctuations in the system parameters,Eq.(6) can be rewritten as

Here, g (t )=u0 .State-equation coefficients,.An and Bn represent the rated values of A and B,respectively,and ΔA and ΔB represent the parameters of the filtering inductor and fluctuations of the DC voltage,respectively.φ(t) represents the aggregated uncertainty term of the system.φ(t) can be represented as

Owing to the existence of the aggregated uncertainty term φ(t),the stability of the control variable u decreases,making it challenging for the injected compensating current iNi to stably track the given reference current.Therefore,it is necessary to design a suitable controller to improve the asymptotic stability of the control variable u.

This enables the injected compensating current to stably track the given reference current.

2.1 Integral sliding mode controller

Under the influence of harmonics,conventional proportional-integral (PI) controllers cannot achieve satisfactory results for arc and unbalanced current suppression [23,24].

To address this issue,an integral sliding mode control method is proposed to achieve stable tracking of the reference current.Based on the compensating current system state equation (Eq.6),the integral sliding mode controller is designed as follows.

Define the current tracking error as

where,ir represents the reference value of the injected current,which is a transient quantity determined by Eq.(3).i represents the actual value of the injected compensation current.

The integral sliding surface is defined as

where ki is the sliding mode gain to be designed,which is positive.

The integral sliding mode control law is given by

where sgn(·) is the symbol function.ks is the controller gain,which is a positive value.The switching gain ρ is a design parameter that is positive.

Define a Lyapunov function The derivative of this function can be expressed as follows:

Here,represents an absolute-value operation.Only the design of the switching gain must be determined by ρ ≥This ensures that d V1 /d t≤ 0.According to the Lyapunov stability and Barbalat’s theorems [25],the designed integral sliding mode control law (Eq.11) ensures the asymptotic stability of the system,even in the presence of external disturbances and uncertainties,such as parameter fluctuations.

2.2 Design of adaptive fuzzy neural network

Eq.(3) does not consider the influence of line voltage drops when calculating the reference current.However,owing to the difference in fault location and NCHPI installation position,there are also differences in the line impedance between them,resulting in different line voltage drops.When considering the voltage drops caused by line impedance,the voltage reference value in Eq.(3) is no longer electromotive force [15].However,obtaining an accurate voltage reference value is difficult,and using eX instead of the exact value renders the injected current unable to achieve full compensation.

The aggregated uncertainty in the system is challenging to determine in practical applications,and a larger switching gain can lead to the “chattering”phenomenon [26].However,changes in the fault or inverter access location can directly impact the control accuracy when the model of the injecting current is imprecise or when unmodeled dynamics are present.Therefore,we propose an adaptive fuzzy neural network imitating a sliding-mode controller (AFNNISMC)to enhance the reliability of arc suppression.

The adaptive fuzzy neural network (AFNN) structure designed in this study is illustrated in Fig.3.The network comprises four layers,and the signal transmission and functional relationships in each layer are as follows:

1) Input layer: This is represented by the input variableUnlike traditional neural-network-based control methods,this study chooses the sliding mode surface of Eq.(10) as the input variable,to significantly reduce the complexity and computational burden of the network.

2) Membership layer: This maps the input variables to fuzzy sets using Gaussian membership functions.The mapping relationship is defined as follows.

where NPi represents the number of Gaussian membership functions for the i-th input variable qi,and exp() is an exponential function.mij and cij represent the mean and standard deviation,respectively,of the j-th Gaussian membership function for the i-th input.The parameter vectors m and c represent the mean and standard deviation,respectively.m=[m1…mi…mn]T∈RNr.represents the number of neurons in the membership layer.The parameter vector c is defined as c=[c1…ci…cn]T∈RNr,where

3) Ruler layer: The output of the h-th neuron in this layer (denoted as lh) is defined as the weighted product of n input signals,where n is the number of input variables.The input signals to this layer were the output signals of each Gaussian membership function of the previous layer.Here,lh is expressed as

where Ni denotes the number of neurons in the ruler layer.lh is the h-th parameter of l=[l1 l2 … lNi]∈represents the connection weights between ruler and membership layers.

4) Output layer: The output layer sums the weighted outputs of all the neurons in the ruler layer and uses them as the output.The relationship between the input and output signals of the output layer can be expressed as

whererepresents the connection weights between the output and ruler layers.

Thus,the control law of AFNNISMC is represented as

2.3 Design of adaptive updating law for network parameters

Changes in the fault occurrence and device access locations affect the mathematical model of the distribution network.For fixed network parameters,adapting to a modified mathematical model is challenging.Therefore,following the Lyapunov stability theorem,we designed an adaptive updating law for network parameters to achieve real-time online updating of the parameters and simplify the debugging process.The adaptive law is defined as follows:

where m*,and c* are the ideal values of the three parameters.ηws,ηms,and ηcs are learning rates with positive values.Reference [27] shows the convergence of the aforementioned adaptive law and proof of stability of the AFNNISMC control system,which has not been reiterated here.

According to Barbalat’s theorem,as time progresses,the sliding surface s will tend to zero.Therefore,the stability of the control system based on the AFNNISMC(Fig.3) can be guaranteed.The network parameters of the control algorithm designed in this study can achieve online self-adjustment [27],effectively solving the problem of reduced control performance owing to inappropriate initial connection weights and selection of Gaussian function parameters.This,reduces the burden of network parameter design and debugging.The designed AFNNISMC system is illustrated in Fig.4.

Additionally,if unbalanced current suppression is not implemented,the AFNNISMC will undergo a period of rapid parameter adaptation to quickly track and compensate for the large fault impact current,resulting in a prolonged transient process.However,with the addition of unbalanced current suppression,the duration of the transient process was comparable to that of a typical neutral-point ineffectively grounded system.Therefore,to minimize the duration of the transient process,the AFNNISMC should be used in conjunction with unbalanced current suppression.

2.4 Exit strategy of arc suppression based on nonlinear variable-speed descent of current

For a transient arc grounding fault,selecting an opportune moment is necessary to exit after arc suppression.The traditional exit strategy involves reducing the compensation current reference value by a certain proportion after a period of arc suppression and then checking whether the zero-sequence voltage amplitude changes proportionally to determine whether the fault has disappeared [16].However,this adjustment method causes oscillations in the amplitude of the zero-sequence voltage,requiring longer stabilization and detection times.Therefore,we propose a strategy based on the nonlinear variable-speed descent of the current,which reduces the rate of voltage decline with time,decreases the adjustment time,and suppresses the amplitude of voltage oscillation.

We assume that the zero-sequence current changes according to the trend of a first-order linear differential equation.Letrepresent the reference value of the zeroaxis current.Then,its rate of change is given by

where β is the variable-speed coefficient,and it is positive.

The solution to this equation is

Let the final value of the reference current be half of the initial value Iref.So,Eq.(18) becomes

To avoid the zero-sequence voltage oscillations caused by sudden changes in the reference value,this function is continuous during the initial period.Therefore,its particular solution is

It is assumed that the device starts reducing the reference current at time T1 and aims to reach the vicinity of the target value at time T2.The expression forbased on Eq.(20) is

Eq.(22) allows for the implementation of a nonlinear variable-speed descent of the reference current.Differentiating the domain [T1,T2] yields

The initial and final values of its rate of change are

By appropriately setting the variable-speed coefficient β,the rate of change at the beginning can be increased.As Eq.(23) monotonically increases within its domain,the descent rate gradually decreases,maintaining a lower value near the final value to reduce the adjustment time of the zero-sequence voltage amplitude and mitigate the oscillations.Subsequently,the ratio of the zero-sequence voltage amplitudes before and after the reference current reduction is obtained to determine whether the fault has disappeared.

2.5 Control process of NCHPI

The specific control process for the NCHPI is illustrated in Fig.5.First,the voltage,current,and other parameters of the distribution network are collected,and power transmission control is performed to generate the d-and q-axis reference voltages.Next,we determine whether a grounding fault has occurred.If not,unbalanced current suppression is performed.Otherwise,the control strategy is changed,and based on the previously calculated parameters,the reverse inductive current is outputted to suppress the grounding current and reduce the fault point current to zero.After 0.5 s of control,the proposed exit strategy is applied to gradually reduce the inductive current.If the fault disappears,it is identified as an intermittent fault.If the fault persists,it is identified as a permanent fault,and arc suppression continues while notifying the staff for handling.

There are many studies on grounding fault detection algorithms.For example,[28-30] used semantic segmentation,Bayesian network optimization,and adaptive transient calibration methods for high-resistance grounding fault detection [31],and all these achieved good detection results.Because fault-detection algorithms are not the focus of this study,they will not be discussed in detail.

In the signal generation part,the dq0-axis reference voltage is calculated in parallel to generate a three-phase control voltage,which is then modulated using carrier phase-shift pulse width modulation (CPSPWM) to generate drive signals for H-bridge insulate-gate bipolar transistors(IGBTs).

Furthermore,the modulation wave will only experience overmodulation at limited moments of fault occurrence and at the moment of arc suppression exit.Therefore,imposing an amplitude limitation on the modulation wave is sufficient to prevent overmodulation.

Current high-performance digital signal processors(DSPs) have a clock frequency of up to 150 MHz,enabling them to rapidly complete the computational process of neural networks.Consequently,the instantaneous value of the zero-axis reference voltage in each control cycle can be computed using a neural network without significant computational lag [22].Furthermore,the high-performance clock frequency ensures real-time computation of other control processes.By appropriately setting the sampling period,complete control parameters can be computed within this timeframe to achieve high-precision,real-time control.

3 Verification of simulation examples

In practical applications,when there are multiple energy resources in a distribution grid,the proposed algorithm can be incorporated into a PV inverter with a direct-coupled topology.The device proposed in this study can be constructed by directly grounding a neutral point to form a ground loop.Thus,once an arc-ground fault occurs in the distribution grid,the photovoltaic inverter automatically outputs a reverse inductive current to achieve arc suppression at the grounding point.

MATLAB/Simulink was used to construct the distribution network model illustrated in Fig.6,where the NCHPI was installed at the busbar,and five lines were connected to loads of varying sizes at their terminals.

To bring the simulation results closer to the actual operating conditions,certain parameters of the NCHPI must be tuned.The most important parameters include the number of cascades,connection inductance (Ln),and DC-side capacitance (C).These parameters are subject to limitations such as the voltage level,ripple magnitude,voltage tolerance,and filtering effect.The parameters are tuned based on the formula which is relative to parameters tuning described in [32,33].Finally,the parameters of the simulation model are set as shown in Tables 1 and 2.The parameters in Table 2 are set for 1000 W/m2 and 25 ℃.N is the cascaded number.VOC is the opencircuit voltage.Vm is the maximum power-point voltage.ISC is the short-circuit current.Pm is the maximum power,and C is the capacitance on the DC side.

The simulation solver was set to automatic a variable step size,with a minimum step size of 5 μs.The sampling period was also set to 5 μs.

3.1 Suppression of unbalanced current

In reality,most loads are low-voltage;however,there are some high-voltage loads.These high-voltage loads are mostly large-power three-phase asynchronous motors,such as industrial dust removal and oil pump motors.These motors are connected in Yg,Y,and delta configurations and are prone to unbalanced currents owing to the influence of the production conditions.Therefore,an additional unbalanced load is set on the 10 kV side in Fig.6.The magnitudes of the three-phase loads were 1 MW/500 var,1.1 MW/600 var,and 1.2 MW/700 var.Different connection modes were set simultaneously.The zero-sequence currents before and after unbalanced current suppression are shown in Fig.7.In all three connection modes,there was a short-term oscillation after unbalanced current suppression,followed by a new equilibrium.In the Yg configuration,the amplitude of the zero-sequence current was 6.84 A,which decreased to 0.65 A after suppression.For the Y and delta configurations,the zero-sequence current fluctuated less after an unbalanced load was applied because of the absence of a grounding path on the load side.However,after suppression,the currents decreased to 0.25 and 0.24 A,respectively.This reduction was due to the proposed unbalanced current suppression,which effectively suppressed the zero-sequence current caused by the ground parameters.

To verify the improvement effect of unbalanced current suppression on the quality of the NCHPI output current,waveform segments were taken at 2.2 and 3.7 for fast Fourier transform analysis,and the THD was calculated as shown in Table 3.Because the third harmonics contained in the output current exhibited zero-sequence characteristics,the reduction in the THD after the suppression of the unbalanced current was mainly due to the decrease in the third harmonics and unbalanced current.This demonstrates that the proposed method effectively reduces the THD of the output current.

3.2 Suppression of grounding arc

3.2.1 Flexible suppression of impact current and arc

At 0.1 s,a metal-to-ground single-phase fault occurs at point A in the A-phase (Fig.6).The fault currents are shown in Fig.8.After injecting the compensation current,the maximum residual current was 0.54 A,which satisfied the arc suppression condition of less than 5 A.The impact current (Fig.8) was 107.29 A during the fault transient before the NCHPI installation,with the maximum fault current reaching 29.03 A after transitioning to a steady state.However,when the NCHPI was connected,unbalanced current suppression was inactive,and the increased impact current during the transient phase was due to the NCHPI providing a grounding point.This effectively turned the distribution network into a neutral point effectively grounded system [12].Upon the activation of unbalanced current suppression,the neutral point had minimal current flow,resulting in the equivalent neutral-toground impedance approaching infinity.Consequently,the distribution network returned to a state of ineffective neutral grounding,and the fault current became similar to that when the NCHPI was not installed.

The fault impact current in an ungrounded neutral system (107.92 A) (pink dash-dotted line in Fig.8) was almost equal to the fault impact current with unbalanced current suppression (104.12 A) (red dashed line in Fig.8).Both were significantly lower than the fault impact current without unbalanced current suppression (blue solid line in Fig.8),which was 906.31 A.Additionally,in both the non-effectively grounded neutral system and system with unbalanced current suppression,the transient duration was only 10 ms.Without unbalanced current suppression,owing to the larger fault impact current,the rapid adaptive adjustment of AFNNISMC parameters caused significant fluctuations in the zero-axis reference voltage,resulting in a longer transient duration of about 20 ms.Therefore,combining AFNNISMC with the unbalanced current suppression function achieved a shorter transient duration.

The impact currents for different transition resistances are listed in Table 4.As the transition resistance increased,the impact current decreased gradually.The impact current without unbalanced current suppression was approximately five to six times higher than that with suppression,demonstrating the effective reduction of the impact current during the occurrence of a single-phase grounding fault.

The fault cleared at 0.5 s,and arc suppression initiated at 0.7 s.The zero-sequence voltage amplitudes are shown in Fig.9.With the fixed ratio descent method,the adjustment time was 0.1 s,and there were fluctuations of～100 V after the set value was reached.However,with the nonlinear variable-speed descent method proposed in this paper,the adjustment time was only 0.07 s,and there was almost no fluctuation in the zero-sequence voltage amplitude when the set value was reached.In Fig.9,although the proposed exit strategy in this paper only advances the adjustment time by 0.03 s compared to the traditional exit strategy,the amplitude fluctuation of the zero-sequence voltage after stabilization is significantly reduced.Compared to the traditional exit strategy,it reduces the likelihood of misjudgments.Compared with the fixed-ratio descent method,the method proposed in this paper has a shorter adjustment time and more stable zero-sequence voltage.

3.2.2 Arc suppression result with random installation position and fault location

The NCHPI installation position and ground fault location were changed,and the fault current was recorded.The waveform when the equipment was installed at location G and fault occurred at location A is shown in Fig.10.The amplitude of the residual current was 0.51 A,and no reignition occurred during the arc-suppression control period.The remaining scenarios are presented in Table 5.Changes in the installation position and fault location caused the longitudinal impedance between them to change,and this had a certain impact on the control method proposed in this study.Therefore,the residual current amplitude fluctuated between 0.5 and 2 A.However,the proposed control method does not rely on precise mathematical models.Hence,the residual current meets the technical requirements of less than 5 A.Therefore,even when the fault location or equipment installation position changes,effective arc suppression can be achieved.In other words,the NCHPI can be installed at any position on the 10 kV side,with similar arc-suppression effects at all locations.

3.3 Transmission control of active and reactive powers

Assume that the PV array is operating at 25 ℃ with an irradiance of 1000 W/m2.At 1 s,a grounding fault occurs in the A-phase and lasts until 1.5 s.Flexible arc suppression control is initiated at 1.4 s.According to the scheduling command,the reactive power needs to be adjusted from 0 to 0.1 Mvar at 1.3 s,and the exit strategy begins at 1.7 s.At 1.8 s,the status of the fault is assessed to determine whether it has been cleared.At 1.9 s,the reactive power is adjusted to 0.These moments are sequentially designated as T1 to T7.

The active and reactive powers are presented in Fig.11 and 12,respectively.The active power initially maintained a maximum output of 1.69 MW.During the T1 to T3 period,the single-phase grounding fault caused the DC voltage of the PV array at the A-phase to rise to the open-circuit voltage,while those at the B-and C-phases decreased,resulting in a decrease in the output power as all three-phase DC voltages deviated from the voltage corresponding to the maximum power point.During the T3 to T4 period,the start of the flexible arc-suppression control caused the voltage at the non-fault phases of the PV array to rise slightly,leading to a slight increase in the active power output.Owing to changes in the zero-sequence reference current,the active power fluctuated between 0.91 and 1.25 MW during this time period.During the T4 to T5 period,the fault disappeared.However,the equipment continued to maintain arc-suppression control at this time.Hence,the three-phase AC-side voltage remained unbalanced.Consequently,the average active power remained almost unchanged,averaging at 1.15 MW and maintaining fluctuations within±0.006 MW.From T5 to T6,the zero-sequence reference current decreased,and the DC voltage of the PV array began to recover,gradually increasing the output power to 1.42 MW.At T6,it was determined that the fault had disappeared,and the zero-sequence reference current decreased to 0.Consequently,the output power continued to recover to the pre-fault value and gradually stabilized at approximately 1.69 MW over time.

Reactive power: From T1 to T2,the unbalanced voltage caused by the single-phase grounding fault resulted in significant fluctuations in the reactive power output.However,the reactive power reference value remained at 0.Hence,the reactive power fluctuated around 0.From T2 to T3,the scheduling command caused the reactive power output to rise to 0.1 Mvar,and the oscillations gradually decreased over time.From T3 to T5,the device entered arcsuppression control,accompanied by a large amount of reactive power output.This caused the total reactive power output of the device to exceed the capacity limit,thus exacerbating the oscillations.During the T5 to T6 period,the zero-sequence reference current decreased,reducing the total reactive power output of the device.This decrease in zero-sequence reference current caused fluctuations in reactive power,with maximum and minimum values reaching～0.26 and 0.01 Mvar,respectively.During T6 to T7,the zero-sequence reference current decreased to zero,and the total reactive power output continued to decrease.The zero-sequence reference current instantaneously switched to zero,resulting in a maximum impact at T6.The maximum reactive power output at this time was 0.26 Mvar.Prior to T6,the minimum reactive power output was 0.01 Mvar,but it still maintained a state of reactive power output.The average reactive power decreased to zero.After T7,the amplitude gradually decreased over time.

3.4 Comparison with other algorithms

To verify the performance of the proposed method,a comparison was made between the backstepping control in [23] and quasi-PR control in [34].The NCHPI was installed at the busbar.The comparison results for a fault at location A are shown in Fig.13.The residual current for back-stepping control in [23] and quasi-PR control in [34]were 3.69 and 4.11 A respectively,but the proposed method suppressed the residual current to around 0.52 A.Further details are provided in Table 6.Because the backstepping control in [23] relies on precise mathematical models with fixed parameters,the residual current fluctuates more when the fault location or installation position changes.However,the quasi-PR control in [34] is model-independent but unable to adaptively adjust the parameters,resulting in a higher residual current.The AFNNISMC control strategy enables online updating of arc-suppression parameters without relying on precise mathematical models,thereby achieving lower residual currents regardless of the fixed installation or fault location.

Existing quasi-PR and backstepping controls have a wide range of applications and relatively low programming complexity.In contrast,the AFNNISMC presents a challenge owing to its complex programming requirements.Additionally,the AFNNISMC is currently less commonly applied and requires careful consideration of the learning rate selection.

However,the AFNNISMC leverages the intelligent sliding-mode control capabilities of neural networks and adaptive laws.Compared to traditional algorithms such as quasi-PR and backstepping controls,it can adapt to modeling inaccuracies caused by the changes in the actual mathematical model and adjust the control parameters accordingly without altering the original control objectives.This allows for the computation of a more precise zero-axis control voltage to achieve flexible arc suppression.

A comparison of the functionalities of devices in different studies is presented in Table 7.Compared to the devices proposed in other studies,the device proposed in this study integrates power transmission,harmonic compensation,unbalanced current suppression,and flexible arc-suppression functions,thereby expanding the capabilities of flexible arc-suppression devices.However,it has the following drawbacks:

1) The NCHPI requires a photovoltaic battery power supply;thus,it only achieves the above functions during the daytime.Furthermore,it cannot transmit power to the distribution grid at night,and the voltage on the DC side is almost zero,rendering the flexible arc-suppression function ineffective.

2) During parallel control execution,output power of the NCHPI still exhibited certain fluctuations,and the upper limit of the reactive power supplied to the distribution grid was relatively low.

4 Conclusion

This study proposed a novel cascaded H-bridge PV inverter with flexible arc-suppression capability,enabling the parallel control of power transmission and flexible arc suppression.The simulation studies yielded the following conclusions.

1) Simulation of single-phase grounding fault scenarios at different locations for different transition resistances showed that the proposed devices could achieve flexible arc suppression and suppress residual currents to below 1.5 A.Compared to similar control algorithms,the proposed control method can achieve a lower residual current,reducing the possibility of arc re-ignition.

2) During the exit phase,the proposed current nonlinear variable-speed descent strategy stabilized the zero-sequence voltage to the target value within three to four cycles,reducing the fluctuation of the zero-sequence voltage amplitude and avoiding misjudgment.

3) The proposed device can control flexible arc suppression,active power,and reactive power transmission.Under constant illumination,the output active power can be maintained at over 60% of the rated value,and the reactive power output can be increased.When the fault disappears and exits arc suppression,active and reactive power transmissions can automatically recover to the rated value,ensuring the power supply capability of the equipment.

In the future,energy storage devices will be integrated into NCHPIs to enable their operation even under nighttime conditions.Further studies will involve building a physical prototype with low-voltage ride-through control to experimentally validate the contents proposed in this study.

Acknowledgments

The authors would like to thank the Natural Science Foundation of Fujian,China (No.2021J01633).

Declaration of Competing Interest

We declare that we have no conflict of interest.