The Bell Inequality Is Satisfied by Quantum Correlations Computed Consistently with Quantum Non-Commutation

In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.

Studies of commutation failures in hybrid LCC/MMC HVDC systems

A hybrid of line commutated converters(LCCs)and modular multi-level converters(MMCs)can provide the advantages of both the technologies.However,the commutation failure still exists if the LCC operates as an inverter in a hybrid LCC/MMC system.In this paper,the system behavior during a commutation failure is investigated.Both halfbridge and full-bridge MMCs are considered.Control strategies are examined through simulations conducted in PSCAD/EMTDC.Additionally,commutation failure protection strategies for multi-terminal hybrid LCC/MMC systems with AC and DC circuit breakers are studied.This paper can contribute to the protection design of future hybrid LCC/MMC systems against commutation failures.

Research of Three-Phase Unbalanced Treatment in Low-Voltage Distribution Network Based on New Commutation Switch

Low-voltage distribution systems in our country are mostly used in agricultural loads and household loads. The value and using time of these kinds of loads are uncontrollable, which lead to the three-phase imbalance in low-voltage distribution system, and seriously affect the quality of power supply. A new type of the commutation system and an improved quantum genetic algorithm (IQGA) are proposed in the paper. At last, the rationality and the efficiency of the method are verified by a practical example.

Analysis of Commutation Failure in Multi-Infeed HVDC System under Different Load Models

HVDC technology has been widely used in modern power system. On one hand, HVDC has the advantages of economy, high efficiency and strong controllability. While on the other hand, it makes the dynamic characteristics of the power system becoming more and more complex. That puts forward a new challenge to system stability and raises new questions for power system simulation. This paper focuses on the interaction between AC and DC systems, especially the problem of commutation failure caused by AC system fault. Based on the data of China Southern Power Grid, this paper calculates the fault regions that may cause commutation failure and calculates the system critical clearance time under different load models, analyzes the impacts of different load models on commutation failure and the stability of AC/DC hybrid system.

New two chamber transfer switch for 6500 A commutation current

HVDC transfer switches are used in different locations in electrode lines of HVDC transmission systems for their reconfigurations. They have to carry and commutate currents to the overload currents of HVDC transmission systems, which increased to 6,400 A in the past years. Common designs of transfer switches use combinations of several switching units connected in series and parallel. This paper describes the design and development of a new DC commutation switch with two switching units only, but it is able to carry currents up to 10,000 A and has an actual tested commutation capability of 6,500 A.

Calculation Method for Commutation Failure Fault Level in LCC-HVDC System Under Single-line-to-ground Faults Considering DC Current Variation

Earlier studies have reported some calculation methods for commutation failure fault level(CFFL) in line-commutated-converter based high-voltage direct current(LCCHVDC) system under single-line-to-ground(SLG) faults. The accuracy of earlier methods is limited because they only consider the commutating voltage drop and phase shift, while neglecting the DC current variation. Hence, this paper proposes a CFFL calculation method under SLG faults considering DC current variation, for better planning and designing of LCC-HVDC systems. First, the fault commutating voltage magnitude and phase shift are calculated. Then, the fault DC voltage during different commutation processes is deduced. Based on the commutating voltage magnitude and phase shift, and DC voltage during different commutation processes under SLG faults, the characteristics of CFFL with different fault time are demonstrated and analyzed. Next, the transient time-domain response of the DC current after the fault is obtained based on the DC transmission line model. Discrete commutation processes are constructed based on the commutation voltage-time area rule to solve the extinction angle under different fault levels and fault time. Finally, the CFFL is calculated considering the fault time, commutating voltage drop, phase shift, and DC current variation. The accuracy of the proposed method compared with the traditional method is validated based on the CIGRE benchmark model in PSCAD/EMTDC.

A Continuous Fault Ride-through Scheme for DFIGs Under Commutation Failures in LCC-HVDC Transmission Systems

Experimental and theoretical studies have confirmed that,relative to a one-shot voltage fault,a doubly-fed induction generator(DFIG)will suffer a greater transient impact during continuous voltage faults.This paper presents the design and application of an effective scheme for DFIGs when a commutation failure(CF)occurs in a line-commutated converter based high-voltage direct current(LCC-HVDC)transmission system.First,transient demagnetization control without filters is proposed to offset the electromotive force(EMF)induced by the natural flux and other low-frequency flux components.Then,a rotor-side integrated impedance circuit is designed to limit the rotor overcurrent to ensure that the rotor-side converter(RSC)is controllable.Furthermore,coordinated control of the demagnetization and segmented reactive currents is implemented in the RSC.Comparative studies have shown that the proposed scheme can limit rotor fault currents and effectively improve the continuous fault ride-through capability of DFIGs.

Commutation of Geometry-Grids and Fast Discrete PDE Eigen-Solver GPA

A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<<dim(G).A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain.In this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so on.They give the general form of pre-processing matrix,theory and numerical test of GPA.The conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.

Improved Identification Method and Fault Current Limiting Strategy for Commutation Failure in LCC-HVDC

Line-commutated converter based high-voltage direct-current(LCC-HVDC)transmission systems are prone to subsequent commutation failure(SCF),which consequently leads to the forced blocking of HVDC links,affecting the operation of the power system.An accurate commutation failure(CF)identification is fairly vital to the prevention of SCF.However,the existing CF identification methods cause CF misjudge or detection lag,which can limit the effect of SCF mitigation strategy.In addition,earlier approaches to suppress SCF do not clarify the key factor that determines the evolution of extinction angle during system recovery and neglect the influence.Hence,this paper firstly analyzes the normal commutation process and CF feature based on the evolution topology of converter valve conduction in detail.Secondly,the energy in the leakage inductance of converter transformer is presented to characterize the commutation state of the valves.Then a CF identification method is proposed utilizing the leakage inductance energy.Thirdly,taking the key variable which is crucial to the tendency of extinction angle during the recovery process into account,a fault current limiting strategy for SCF mitigation is put forward.Compared with the original methods,the proposed methods have a better performance in CF identification and mitigation in terms of detection accuracy and mitigation effect.Finally,case study on PSCAD/EMTDC validates the proposed methods.

A Commutation Failure Prediction and Mitigation Method

The mitigation of commutation failure(CF)depends on the accuracy of CF prediction.In terms of the large error of the existing extinction angle(EA)calculation during the fault transient period,a method for CF prediction and mitigation is proposed.Variations in both DC current and overlap angle(OA)are considered in the proposed method to predict the EA rapidly.In addition,variations in critical EA and the effect of firing angle(FA)on both DC current and OA are considered in the proposed method to obtain the accurate FA order for the control system.The proposed method can achieve good performance in terms of CF mitigation and reduce reactive consumption at the inverter side when a fault occurs.Simulation results based on the PSCAD/EMTDC show that the proposed method predicts CF rapidly and exhibits good performance in terms of CF mitigation.

Quantitative Assessment for Commutation Security Based on Extinction Angle Trajectory

In order to reduce the risk of commutation failure(CF)in the AC/DC hybrid power system,the quantitative analysis on CF is required for on-line assessment and optimal control.This paper presents an accurate and reliable method to quantify the commutation security based on the trajectory due to the complexity of the high-voltage direct current(HVDC)model.Firstly,the characteristics of the extinction angle trajectory are analyzed under both commutation success and failure conditions.The commutation security margin index(CSMI)is then proposed for the HVDC systems.Moreover,a search strategy for parameter limits is put forward based on the sensitivity analysis of CSMI to accelerate the search speed with a guaranteed accuracy level.A modified IEEE 39-bus power system and an actual large-scale power system with 46 generators and 821 buses are utilized to verify the validity and robustness of the proposed index and strategy.

Commutation Failure Mitigation Method Based on Imaginary Commutation Process

The commutation failure(CF) mitigation effectiveness is normally restricted by the delay of extinction angle(EA)measurement or the errors of existing prediction methods for EA or firing angle(FA). For this purpose, this paper proposes a CF mitigation method based on the imaginary commutation process. For each sample point, an imaginary commutation process is constructed to simulate the actual commutation process.Then, the imaginary EA is calculated by comparing the imaginary supply voltage-time area and the imaginary demand voltage-time area, which can update the imaginary EA earlier than the measured EA. In addition, the proposed method considers the impacts of commutation voltage variation, DC current variation, and phase angle shift of commutation voltage on the commutation process, which can ensure a more accurate EA calculation. Moreover, the DC current prediction is proposed to improve the CF mitigation performance under the single-phase AC faults. Finally, the simulation results based on CIGRE model prove that the proposed method has a good performance in CF mitigation.

Analysis on Local and Concurrent Commutation Failure of Multi-infeed HVDC Considering Inter-converter Interaction

This paper provides a comprehensive analysis of local and concurrent commutation failure(CF)of multi-infeed high-voltage direct current(HVDC)system considering multi-infeed interaction factor(MIIF).The literature indicates that the local CF is not influenced by MIIF,whereas this paper concludes that both the local CF and concurrent CF are influenced by MIIF.The ability of remote converter to work under reduced reactive power enables its feature to support local converter via inter-connection link.The MIIF measures the strength of electrical connectivity between converters.Higher MIIF gives a clearer path to remote converter to support local converter,but at the same time,it provides an easy path to local converter to disturb remote converter under local fault.The presence of nearby converter increases the local commutation failure immunity index(CFII)while reducing concurrent CFII.Higher MIIF causes reactive power support to flow from remote converter to local converter,which reduces the chances of CF.A mathematical approximation to calculate the increase in local CFII for multi-infeed HVDC configurations is also proposed.A power flow approach is used to model the relation between MIIF and reactive power support from remote end.The local and concurrent CFIIs are found to be inverse to each other over MIIF;therefore,it is recommended that there is an optimal value of MIIF for all converters in close electric proximity to maintain CFII at a certain level.The numerical results of established model are compared with PSCAD/EMTDC simulations.The simulation results show the details of the influence of MIIF on local CF and concurrent CF of multi-infeed HVDC,which validates the analysis presented.

Analysis of the Sending-Side System Instability Caused by Multiple HVDC Commutation Failure

As high-voltage direct current(HVDC)lines with large capacity are being commissioned with higher frequency,the characteristics of“strong”DC and“weak”AC transmission in the power grid are topics of interest.In particular,the coupling and interaction between the sending-side and receivingside AC systems interconnected by large-scale DC links is gaining importance.In this paper,the impact of the multiple HVDC commutation failure on the stability of the sending system under different power flow directions is analyzed based on the threearea AC/DC equivalent model.The main influencing factors and the counter-measures are discussed,and the single HVDC line blocking is taken as a comparison.Finally,the results are verified using the North China-Central China-East China power grid case system.The study provides a basis and reference to ensure security and stability of the ultra-high-voltage(UHV)AC/DC hybrid power grid.

A DC Chopper Topology to Mitigate Commutation Failure of Line Commutated Converter Based High Voltage Direct Current Transmission

To reduce the probability of commutation failure(CF)of a line commutated converter based high-voltage direct current(LCC-HVDC)transmission,a DC chopper topology composed of power consumption sub-modules based on thyristor full-bridge module(TFB-PCSM)is proposed.Firstly,the mechanism of the proposed topology to mitigate CF is analyzed,and the working modes of TFB-PCSM in different operation states are introduced.Secondly,the coordinated control strategy between the proposed DC chopper and LCC-HVDC is designed,and the voltage-current stresses of the TFB-PCSMs are investigated.Finally,the ability to mitigate the CF issues and the fault recovery performance of LCC-HVDC system are studied in PSCAD/EMTDC.The results show that the probability of CF of LCC-HVDC is significantly reduced,and the performances of fault recovery are effectively improved by the proposed DC chopper.

Assessment of commutation failure in HVDC systems considering spatial-temporal discreteness of AC system faults

This paper presents a novel commutation failure(CF) assessment method considering the influences of voltage magnitude drop, phase shift, and spatial-temporal discreteness of AC system faults. The commutating voltage-time area is employed to analyze the spatial-temporal discreteness of AC system faults causing CF in high-voltage direct current systems, and the influences of fault position and fault time on CF are revealed. Based on this, a novel CF criterion is proposed, further considering the influence of voltage phase shift and the spatial-temporal discreteness. Then this research develops a new CF assessment method, which does not rely on electromagnetic transient simulations. A real case from the China Southern Power Grid is used to verify the practicability of the proposed method by comparing with simulation results obtained using PSCAD/EMTDC.

Improved Coordinated Control Approach for Evolved CCC-HVDC System to Enhance Mitigation Effect of Commutation Failure

The evolved capacitor commutated converter(ECCC),embedded with anti-parallel thyristors based dual-directional full-bridge modules(APT-DFBMs),can effectively reduce commutation failure(CF)risks of line-commutated converter-based high voltage direct current(HVDC)and improve the dynamic responses of capacitor-commutated converterbased HVDC.This paper proposes an improved coordinated control strategy for ECCC with the following improvements:(1)under normal operation state,series-connected capacitors can accelerate the commutation process,thereby reducing the overlap angle and increasing the successful commutation margin;(2)under AC fault conditions,the ability of ECCC to mitigate the CF issue no longer relies on the fast fault detection,since the capacitors inside the APT-DFBMs can consistently contribute to the commutation process and further reduce the CF probability;(3)the inserted capacitors can output certain amount of reactive power,increase the power factor,and reduce the required reactive power compensation capacity.Firstly,the proposed coordinated control approach is presented in detail,and the extra commutation voltage to mitigate the CFs provided by the proposed control approach and an existing approach is compared.Secondly,the mechanism of the improved control approach to accelerate commutation process and improve the power factor is analyzed theoretically.Finally,the detailed electromagnetic transient(EMT)simulation in PSCAD/EMTDC is conducted to validate the effectiveness of the proposed coordinated control.The results show that the proposed approach can present a further substantial improvement for ECCC,especially enhancing the CF mitigation effect.

Commuting Space of Primary and Secondary Schools in the Context of Child Friendly Cities:A Case Study of Bajiao Street of Shijingshan District

With the continuous promotion of the construction of child friendly cities,the school commuting space is an important component of the construction of child friendly roads.Based on the background of child friendly cities,the commuting space of 11 primary and secondary schools in Bajiao Street is analyzed through literature analysis and field research methods.Firstly,the relevant literature on school commuting space is sorted out,and the characteristics of school commuting space are summarized,including transportation,landscape,culture,leisure,and security.Secondly,the characteristics of commuting space of primary and secondary schools in Bajiao Street are analyzed from three aspects:in front of the school gate,path space,and node space.This paper aims to provide reference and guidance for the future construction of children’s walking school commuting and promote the construction of a child friendly city.

A NOTE WITH REGARD TO A FORMULA OF COMMUTATION RELATIONS OF THE MASTER SYMMETRIES FOR KP EQUATIONS

there are infinite symmetries and infinite conserved constants, and they form Lie algebras respectively. Under the commutation relation :

COMMUTATIONAL REPRESENTATIONS OF YANG HIERARCHY OF INTEGRABLE EVOLUTION EQUATIONS

Let u =（u1, u2, … , up）T be a potential vector of dimension p, and λ denote a spectral parameter. Assume that a series of zero curvature