The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-di...The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.展开更多
To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Cons...To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Considering that several different PSFs can get joint invertibility to make restoration wellposed,we proposed a motion-blurred image restoration method based on joint invertibility of PSFs by means of computational photography.Firstly,we designed a set of observation device which composed by multiple cameras with the same parameters to shoot the moving target in the same field of view continuously to obtain the target images with the same background.The target images have the same brightness,but different exposure time and different motion blur length.It is easy to estimate the blur PSFs of the target images make use of the sequence frames obtained by one camera.According to the motion blur superposition feature of the target and its background,the complete blurred target images can be extracted from the observed images respectively.Finally,for the same target images with different PSFs,the iterative restoration is solved by joint solution of multiple images in spatial domain.The experiments showed that the moving target observation device designed by this method had lower requirements on hardware conditions,and the observed images are more convenient to use joint-PSF solution for image restoration,and the restoration results maintained details well and had lower signal noise ratio(SNR).展开更多
From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single...From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single input single output systems. Then it analyzes the feasibility of inverse system control method, and yields some conclusions on feasibility.展开更多
In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop...In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.展开更多
Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various ...We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.展开更多
In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by...In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are invertible.Moreover,the ideal created by a given rational univariate representation is defined.Some results on invertible rational univariate representations and created ideals are established.Based on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.展开更多
Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to ...Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.展开更多
We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective ...We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.展开更多
The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosyst...The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosystems. Given a finite commutative ring (?) with identity, it is known, that the weak invertibility of a linear finite automaton(LFA) over (?) depends only on its transfer function matrix. Let H be the set of all possible transfer function matrices which weakly invertible LFAs over (?) can have. Our展开更多
We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand ...We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand the proposed models better,we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants,which can also be used for identification purpose.A sufficient condition for invertibility is also provided.展开更多
In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the...In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the Drazin spectrum and the Aluthge transform of an operator M ∈ B(H), respectively.展开更多
This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper cons...This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper constructs an internal model to learn the information of the states and input of the grid-connected inverter under steady state.Second,by utilizing the internal model principle,the paper turns the tracking control problem into the robust stabilization control problem based on some appropriate coordinate transformations.Then,The paper designs a dynamics state feedback control law to deal with this robust stabilization problem,and thus the solution of the robust current tracking control problem of three-phase grid-connected inverters can be obtained.This control method can ensure the asymptotic stability of the closedloop system.Finally,the paper illustrates the effectiveness of the proposed control approach through several groups of simulations,and compares it with the feedforward control method to verify the robustness of the proposed control method to uncertain parameters.展开更多
This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating...This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating RaRb transformation sequence is also established.展开更多
Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numb...Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numbers.Furthermore,we establish several necessary and sufficient,easy-to-check conditions for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when some coefficients of p are complex numbers.展开更多
Despite the intrinsic durability of polymeric hole transport materials,poly-triarylamines(PTAA)-based inverted perovskite solar cells(PSCs)have lagged behind their counterparts in efficiency,primarily due to poor surf...Despite the intrinsic durability of polymeric hole transport materials,poly-triarylamines(PTAA)-based inverted perovskite solar cells(PSCs)have lagged behind their counterparts in efficiency,primarily due to poor surface wettability,insufficient interfacial contact,and unfavorable energy level alignment at the PTAA/perovskite interface.Here,we report a highly effective interfacial engineering strategy employing the ionic liquid 1,3-dimethylimidazolium dimethyl phosphate(DMIMPH)as a multifunctional interfacial modifier.The incorporation of DMIMPH improves PTAA wettability,promoting the growth of high-quality perovskite films with enhanced interfacial contact.Concurrently,DMIMPH effectively tunes the energy levels of PTAA,enhances its electrical conductivity,and passivates interfacial defects with more efficient hole extraction and charge transport.Moreover,its interaction with residual PbI_(2) modulates perovskite crystallization kinetics,yielding highly crystalline perovskite films with enlarged grain sizes,reduced PbI_(2) residue,and suppressed trap densities.As a result,PTAA-based p-i-n PSCs employing this approach achieve a record certified power conversion efficiency(PCE)of 24.52%,with a champion efficiency of 25.12%—the highest certified value for PTAA-based perovskite devices to date.Impressively,the DMIMPH-modified PSCs without encapsulation maintained 87.48%of their initial efficiency after 1600 h in air.This strategy offers an effective pathway for advancing the performance and stability of polymer-based inverted PSCs.展开更多
Organic electrochemical transistors(OECTs)are promising for next-generation bioelectronics due to their high performance and biocompatibility.Nevertheless,they still face tremendous operational stability challenges du...Organic electrochemical transistors(OECTs)are promising for next-generation bioelectronics due to their high performance and biocompatibility.Nevertheless,they still face tremendous operational stability challenges due to the limited robustness of the organic mixed ionic-electronic conductor(OMIEC)channel.Here,by modulating the molecular weight(MW)of OMiEC,enhanced OECT and relevant circuit operation stabilities are demonstrated,showing more than 3,000,0o0 full cycles(~42 h)with less than 15%current variation in an OECT,and 150,000 cycles(~4 h)with less than 5%voltage variation in an OECT-based inverter,which are among the highest of reported OECT-based electronics.Specifically,p(g2T-T),a typical p-type OMIEC,with varying MW(7-43 kDa),is synthesized,where lower-MW p(g2T-T)(~9 kDa)exhibits superior device performance and cycling stability in OECTs,outperforming those in high-MW counterparts(>30 kDa).It is indicated that low-MW p(g2T-T)maintains higher volumetric capacitance,ordered orientation,and reduced swelling.Therefore,irreversible microstructural degradation is effectively avoided,along with better performance yield.Furthermore,MW regulation enables physiological signal sensing with high tolerance to body fluid environments for 7 days.These findings highlight MW modulation as a versatile approach to suppress excessive swelling,advancing the design of durable OECT-based electronics.展开更多
The hybrid series-parallel microgrid attracts more attention by combining the advantages of both the series-stacked voltage and parallel-expanded capacity.Low-voltage distributed generations(DGs)are connected in serie...The hybrid series-parallel microgrid attracts more attention by combining the advantages of both the series-stacked voltage and parallel-expanded capacity.Low-voltage distributed generations(DGs)are connected in series to form the intra-string,and then multiple strings are interconnected in parallel.For the existing control strategies,both intra-string and inter-string depend on the centralized or distributed control with high communication reliance.It has limited scalability and redundancy under abnormal conditions.Alternatively,in this study,an intra-string distributed and inter-string decentralized control framework is proposed.Within the string,a few DGs close to the AC bus are the leaders to get the string power information and the rest DGs are the followers to acquire the synchronization information through the droop-based distributed consistency.Specifically,the output of the entire string has the active power−angular frequency(ω-P)droop characteristic,and the decentralized control among strings can be autonomously guaranteed.Moreover,the secondary control is designed to realize multi-mode objectives,including on/off-grid mode switching,grid-connected power interactive management,and off-grid voltage quality regulation.As a result,the proposed method has the ability of plug-and-play capabilities,single-point failure redundancy,and seamless mode-switching.Experimental results are provided to verify the effectiveness of the proposed practical solution.展开更多
基金supported by National Natural Science Foundation of China under Grant No.10562002Natural Science Foundation of Inner Mongolia under Grant Nos.200508010103 and 200711020106
文摘The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.
基金funding of Natural Science Foundation of Shandong Province(ZR2013F0025),www.sdnsf.gov.cn.
文摘To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Considering that several different PSFs can get joint invertibility to make restoration wellposed,we proposed a motion-blurred image restoration method based on joint invertibility of PSFs by means of computational photography.Firstly,we designed a set of observation device which composed by multiple cameras with the same parameters to shoot the moving target in the same field of view continuously to obtain the target images with the same background.The target images have the same brightness,but different exposure time and different motion blur length.It is easy to estimate the blur PSFs of the target images make use of the sequence frames obtained by one camera.According to the motion blur superposition feature of the target and its background,the complete blurred target images can be extracted from the observed images respectively.Finally,for the same target images with different PSFs,the iterative restoration is solved by joint solution of multiple images in spatial domain.The experiments showed that the moving target observation device designed by this method had lower requirements on hardware conditions,and the observed images are more convenient to use joint-PSF solution for image restoration,and the restoration results maintained details well and had lower signal noise ratio(SNR).
文摘From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single input single output systems. Then it analyzes the feasibility of inverse system control method, and yields some conclusions on feasibility.
文摘In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
基金supported by the National Natural Science Foundation of China.
文摘Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
文摘We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.
基金the National Natural Science Foundation of China under Grant No.12161057。
文摘In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are invertible.Moreover,the ideal created by a given rational univariate representation is defined.Some results on invertible rational univariate representations and created ideals are established.Based on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.
文摘Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.
基金supported in part by a grant from the Ministry of Science of Slovenia
文摘We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.
文摘The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosystems. Given a finite commutative ring (?) with identity, it is known, that the weak invertibility of a linear finite automaton(LFA) over (?) depends only on its transfer function matrix. Let H be the set of all possible transfer function matrices which weakly invertible LFAs over (?) can have. Our
基金supported by the Fundamental Research Funds for the Central Universities of China(Grant No.2010121005)supported by the Scientific Research and Development Funds for Youth of Fujian University of Technology of China(Grant No.GY-Z09081)
文摘We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand the proposed models better,we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants,which can also be used for identification purpose.A sufficient condition for invertibility is also provided.
基金the National Natural Science Foundation of China (No.10571113)
文摘In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the Drazin spectrum and the Aluthge transform of an operator M ∈ B(H), respectively.
基金Supported by the Fundamental Research Funds for the Central Universities(2024ZYGXZR047)the National Natural Science Foundation of China(62373156)the Guangdong Basic and Applied Basic Research Foundation(2024A1515011736)。
文摘This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper constructs an internal model to learn the information of the states and input of the grid-connected inverter under steady state.Second,by utilizing the internal model principle,the paper turns the tracking control problem into the robust stabilization control problem based on some appropriate coordinate transformations.Then,The paper designs a dynamics state feedback control law to deal with this robust stabilization problem,and thus the solution of the robust current tracking control problem of three-phase grid-connected inverters can be obtained.This control method can ensure the asymptotic stability of the closedloop system.Finally,the paper illustrates the effectiveness of the proposed control approach through several groups of simulations,and compares it with the feedforward control method to verify the robustness of the proposed control method to uncertain parameters.
基金Project supported by the National Natural Science Foundation of China.
文摘This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating RaRb transformation sequence is also established.
基金supported by the Yunnan Natural Science Foundation(Grant No.201601YA00004)supported by National Natural Science Foundation of China(Grant No.11701052)+1 种基金Chongqing Natural Science Foundation(Grant No.cstc2017jcyjAX0373)the Fundamental Research Funds for the Central Universities(Grant Nos.106112016CDJRC000080 and 106112017CDJXY100007)。
文摘Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numbers.Furthermore,we establish several necessary and sufficient,easy-to-check conditions for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when some coefficients of p are complex numbers.
基金supported by the Research Projects of the Department of Education of Guangdong Province 2024ZDZX3079The financial support from the Guangdong Basic and Applied Basic Research Foundation(No.2023A1515011677)+4 种基金the Scientific and Technical Innovation Council of Shenzhen(20220812165832002)the Research Projects of Department of Education of Guangdong Province-2023GCZX015the Innovation Team Project of Guangdong(2022KCXTD055)the China Postdoctoral Science Foundation(Certificate Number:2024M763441)is gratefully acknowledgedsupported by the Postdoctoral Fellowship Program of CPSF under Grant Number GZB20250031 and Research Projects of the Department of Education of Guangdong Province 2023GCZX015。
文摘Despite the intrinsic durability of polymeric hole transport materials,poly-triarylamines(PTAA)-based inverted perovskite solar cells(PSCs)have lagged behind their counterparts in efficiency,primarily due to poor surface wettability,insufficient interfacial contact,and unfavorable energy level alignment at the PTAA/perovskite interface.Here,we report a highly effective interfacial engineering strategy employing the ionic liquid 1,3-dimethylimidazolium dimethyl phosphate(DMIMPH)as a multifunctional interfacial modifier.The incorporation of DMIMPH improves PTAA wettability,promoting the growth of high-quality perovskite films with enhanced interfacial contact.Concurrently,DMIMPH effectively tunes the energy levels of PTAA,enhances its electrical conductivity,and passivates interfacial defects with more efficient hole extraction and charge transport.Moreover,its interaction with residual PbI_(2) modulates perovskite crystallization kinetics,yielding highly crystalline perovskite films with enlarged grain sizes,reduced PbI_(2) residue,and suppressed trap densities.As a result,PTAA-based p-i-n PSCs employing this approach achieve a record certified power conversion efficiency(PCE)of 24.52%,with a champion efficiency of 25.12%—the highest certified value for PTAA-based perovskite devices to date.Impressively,the DMIMPH-modified PSCs without encapsulation maintained 87.48%of their initial efficiency after 1600 h in air.This strategy offers an effective pathway for advancing the performance and stability of polymer-based inverted PSCs.
基金supported by the National Key R&D Program of China(2024YFB3211600)the National Natural Science Foundation of China(Nos.62273073,52273316)+4 种基金the National Key R&D Program of China(2023YFC2411800,2022YFE0134800)the Natural Science Foundation of Sichuan(2025ZNSFSC0515)Chengdu Science Technology Bureau(2023-YF06-00028-HZ)and the Fundamental Research Funds for the Central Universities(ZYGX2025TS009,ZYGX2024XJ029,ZYGX2024XJ031)Sci-entific Research Innovation Capability Support Project for Young Faculty(ZYGXQNJSKYCXNLZCXM-M1P).
文摘Organic electrochemical transistors(OECTs)are promising for next-generation bioelectronics due to their high performance and biocompatibility.Nevertheless,they still face tremendous operational stability challenges due to the limited robustness of the organic mixed ionic-electronic conductor(OMIEC)channel.Here,by modulating the molecular weight(MW)of OMiEC,enhanced OECT and relevant circuit operation stabilities are demonstrated,showing more than 3,000,0o0 full cycles(~42 h)with less than 15%current variation in an OECT,and 150,000 cycles(~4 h)with less than 5%voltage variation in an OECT-based inverter,which are among the highest of reported OECT-based electronics.Specifically,p(g2T-T),a typical p-type OMIEC,with varying MW(7-43 kDa),is synthesized,where lower-MW p(g2T-T)(~9 kDa)exhibits superior device performance and cycling stability in OECTs,outperforming those in high-MW counterparts(>30 kDa).It is indicated that low-MW p(g2T-T)maintains higher volumetric capacitance,ordered orientation,and reduced swelling.Therefore,irreversible microstructural degradation is effectively avoided,along with better performance yield.Furthermore,MW regulation enables physiological signal sensing with high tolerance to body fluid environments for 7 days.These findings highlight MW modulation as a versatile approach to suppress excessive swelling,advancing the design of durable OECT-based electronics.
基金supported by the Smart Grid-National Science and Technology Major Project(2025ZD0804500)the National Natural Science Foundation of China under Grant 52307232the Hunan Provincial Natural Science Foundation of China under Grant 2024JJ4055.
文摘The hybrid series-parallel microgrid attracts more attention by combining the advantages of both the series-stacked voltage and parallel-expanded capacity.Low-voltage distributed generations(DGs)are connected in series to form the intra-string,and then multiple strings are interconnected in parallel.For the existing control strategies,both intra-string and inter-string depend on the centralized or distributed control with high communication reliance.It has limited scalability and redundancy under abnormal conditions.Alternatively,in this study,an intra-string distributed and inter-string decentralized control framework is proposed.Within the string,a few DGs close to the AC bus are the leaders to get the string power information and the rest DGs are the followers to acquire the synchronization information through the droop-based distributed consistency.Specifically,the output of the entire string has the active power−angular frequency(ω-P)droop characteristic,and the decentralized control among strings can be autonomously guaranteed.Moreover,the secondary control is designed to realize multi-mode objectives,including on/off-grid mode switching,grid-connected power interactive management,and off-grid voltage quality regulation.As a result,the proposed method has the ability of plug-and-play capabilities,single-point failure redundancy,and seamless mode-switching.Experimental results are provided to verify the effectiveness of the proposed practical solution.
