最新刊期

    卷 47 , 期 11 , 2023

      Basic Research

    • ZHAO Zexin, CHEN Weijiang, ZHAO Guoliang, XU Yunfei, LU Zhengang, HAN Bin
      Vol. 47, Issue 11, Pages: 1-8(2023) DOI: 10.7500/AEPS20221025004
      摘要:Flexible low-frequency AC transmission systems have technological and economic advantages when applied to medium- and long-distance offshore wind power transmission. The study of power transmission capacity is an important reference for determining system parameters and schemes. In this paper, the voltage and current constraints of the flexible low-frequency AC transmission system for offshore wind power are analyzed. A transmission capacity calculation method described by the maximum transmission power and the longest transmission distance is derived. The transmission capacities of 220 kV and 330 kV systems are calculated, and the influences of the transmission frequency and submarine cable cross section are analyzed. The results show that selecting 12.5~30 Hz transmission frequency and maximum 1 200 mm2 submarine cable cross section, the maximum capacity of wind farms delivered by 220 kV and 330 kV systems are 200~400 MW and 200~570 MW, respectively, for the offshore distance of 250 km. The actual parameters of the flexible low-frequency AC transmission system for offshore wind power are determined specifically on the basis of economic analysis.  
      关键词:offshore wind power transmission;flexible low-frequency AC transmission;power transmission capacity;transmission frequency;system parameter   
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    • LI Jiarong, LIN Jin, CHEN Kaixuan, SONG Yonghua, XU Yanhui
      Vol. 47, Issue 11, Pages: 9-17(2023) DOI: 10.7500/AEPS20221102003
      摘要:Offshore wind power-to-hydrogen is an important way to utilize medium- and far-offshore wind resources. Distributed wind power-to-hydrogen units have become the focus of academic research and industry practice because they does not need centralized confluence and large-scale platform construction. However, affected by the wake effect of the wind farm, the operating states of different units in the distributed wind power-to-hydrogen clusters couple each other, resulting in differences in hydrogen production ability. This paper proposes the optimal capacity model of the distributed wind power-to-hydrogen considering the wake effect. Optimal configuration of electrolytic cell capacity space distribution is carried out based on unit collaborative control. The realistic wind resource data of the waters of Jiangsu Province in China are adopted for case studies. First, the collaborative control of wind power-to-hydrogen units considering the wake effect can effectively increase the annual expected hydrogen production by about 3.05%. Furthermore, compared with the uniform distribution scheme of electrolytic cell capacity space, the optimal configuration scheme of capacity space with large margin and small interior can reduce the levelized cost of hydrogen for offshore wind power-to-hydrogen, which verifies the effectiveness of the proposed optimal model.  
      关键词:offshore wind power-to-hydrogen;distributed wind power-to-hydrogen unit;wake effect;optimal capacity configuration   
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    • XU Siying, WANG Han, CAO Yunfeng, WANG Wei, YANG Dongmei, CAI Xu
      Vol. 47, Issue 11, Pages: 18-28(2023) DOI: 10.7500/AEPS20221027002
      摘要:The self-synchronous voltage source doubly-fed wind turbines adopt the control method of “inertia transmission on the rotor side-inertia synchronization on the grid side”, which has the ability of autonomously synchronous grid-connection and inertia response. There is currently a lack of research and analysis on the grid-connected stability of this control method and optimal parameter design with multi-objective constraint. In view of this, a state-space model considering the dynamics of the grid-side converter and the rotor-side converter for the self-synchronous voltage source doubly-fed wind power system is constructed. Under different power grid intensities, the influence law of the control parameters of the inertia transfer link and the stabilization link on the small-signal stability in the middle and high frequency bands is analyzed. A multi-objective optimization model of control parameters considering different operation points and dynamic performances of the unit is given, and a global optimization of the control parameters is performed by using the particle swarm optimization algorithm. The simulation model of a 2 MW doubly-fed wind turbine is constructed in PSCAD/EMTDC, and the simulation results verify the correctness of the theoretical analysis and parameter design.  
      关键词:doubly-fed wind turbine;inertia synchronization;stability;state-space model;multi-objective optimization   
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    • XIE Zhen, GAO Xiang, ZHANG Xuanguang, ZHANG Xing
      Vol. 47, Issue 11, Pages: 29-38(2023) DOI: 10.7500/AEPS20220809008
      摘要:With the increasing proportion of wind power, the stability problem of the power synchronized grid-forming doubly-fed induction generator (PS-DFIG) connected to the weak grid has received extensive attention. Compared with the power response characteristics of phase-locked synchronized grid-following control, the interaction between the active power loop and the rotor speed loop in PS-DFIG based on grid-forming control is more likely to cause low-frequency torque oscillation. First, the small-signal model of active power and generator speed of the PS-DFIG system is established, and the coupling characteristics of active power and rotor speed responses are analyzed. On this basis, the influence of the loop characteristics of the PS-DFIG system on the low-frequency oscillation of the drivetrain is studied by means of the electrical damping analysis method. Then, based on the multi-loop bandwidth design criterion, the differential feedforward method is introduced into the active power loop to improve the active power bandwidth. At the same time, the torque compensation is added to the output of the rotor speed loop, which improves the electrical damping characteristics of the electromagnetic torque, relatively improves the parameter robustness of the power loop, and effectively reduces the risk of low-frequency oscillation of the drivetrain system of PS-DFIG system. Finally, the experimental verification is carried out on the hardware-in-loop platform of RT-LAB.  
      关键词:weak grid;grid-forming doubly-fed wind turbine;power synchronization;small-signal model;low-frequency oscillation;electrical damping analysis   
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    • SHEN Danfeng, WANG Guanzhong, WU Hao, GAN Deqiang
      Vol. 47, Issue 11, Pages: 39-49(2023) DOI: 10.7500/AEPS20221006003
      摘要:Power systems with high penetration of renewable energy oscillate in a wide range of frequencies, and the damping and oscillation frequencies are notably affected by system parameters. To avoid the system instability caused by the change of operation parameters and the improper setting of controller parameters, it is urgent to quantify the relationship between the system oscillation modes and parameters and analyze the hidden mechanism behind them. A method for calculating the all eigenvalue trajectories based on polynomial approximation is proposed. Through a series of linear combinations of polynomial basis functions, the complex implicit functional relationship between all eigenvalues and multiple parameters of the system is accurately described, and the explicit expression of the changing eigenvalue trajectories is obtained. The detailed electromagnetic transient modeling of the doubly-fed induction generator (DFIG)-based wind turbine grid-connection system is carried out, and the accuracy of the proposed method is verified by taking the single-machine infinite system and the wind-thermal-bundled system as examples. The influence of the important parameters, such as series-compensated capacitor, rotor-side controller proportion and integral coefficient, on the key modes of the DFIG-based wind turbine grid-connection system, such as sub-synchronous oscillation and low-frequency oscillation, is analyzed by using the explicit expression of eigenvaluetrajectories.  
      关键词:DFIG-based wind turbine;grid-connection;eigenvalue trajectory;wide-band oscillation;polynomial approximation;small-signal stability   
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    • LI Guanqun, YE Hua, BIN Zijun
      Vol. 47, Issue 11, Pages: 50-59(2023) DOI: 10.7500/AEPS20220815003
      摘要:In the flexible DC transmission system for wind farm integration, high-frequency oscillation may occur when V/f controlled modular multilevel converter (MMC) charges with the converter transformer under the no-load condition. The dynamics of the converter transformer and the MMC control links have significant influences on the high-frequency oscillation of the system. This paper studies the high-frequency oscillation mechanism when V/f controlled MMC charges with the converter transformer under the no-load condition, and analyzes the influences of parameters of the AC circuit and MMC control on the high-frequency small-signal stability of the system. First, the harmonic state space (HSS) model of a sending-end MMC station considering converter transformer stray capacitance is established. By analyzing the eigenvalue locus with varying converter transformer stray capacitance and comparing it with the time-domain simulation results, the necessity to consider the stray capacitance in the high-frequency small-signal stability analysis is revealed. Then, the participation factor analysis is carried out for the high-frequency oscillation modes when MMC charges with the converter transformer under the no-load condition. The state variables with high- degree participation and corresponding key links are determined. A reduced-order model suitable for the high-frequency small-signal stability analysis is also established. Besides, the mechanism of the high-frequency oscillation is revealed by the impedance characteristic analysis. Finally, the influences of parameters of the AC circuit and MMC control on the high-frequency small-signal stability are analyzed by calculating the eigenvalue locus of the system. The analysis results are validated by the electromagnetic transient simulation.  
      关键词:flexible DC transmission;high-frequency oscillation;modular multilevel converter (MMC);stability analysis;harmonic state space (HSS);eigenvalue analysis;impedance analysis   
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    • ZHANG Zhe, QIN Boyu, GAO Xin, DING Tao
      Vol. 47, Issue 11, Pages: 60-68(2023) DOI: 10.7500/AEPS20220712005
      摘要:The complexity and variability of operation mode, uncertainty of disturbance fault and weak immunity of power electronics equipment bring great challenges to the safe and stable operation of hybrid AC/DC power grids. To ensure the power grid voltage stability after the large-disturbance fault, a response-driven emergency control strategy is proposed based on convolutional neural network (CNN) and long short-term memory (LSTM) network. First, the mapping relationship between voltage time sequence value of key bus nodes and the voltage stability level is analyzed, and the large-disturbance voltage stability evaluation model based on CNN-LSTM network is established offline. Secondly, the evaluation model is used to predict the enhancement of power grid voltage stability level after the operation of alternative generator tripping and load shedding spot control measures and to determine the sensitivity of response-driven emergency control measures. Finally, considering the sensitivity of emergency control measures, an emergency control optimization problem is established with the actual operation constraints of the power grid, and the optimal emergency control strategy is obtained. For the actual scenario of hybrid AC/DC power grid with the voltage instability problem, the simulation results verify the accuracy of the proposed response-driven control sensitivity prediction method. The optimal coordination strategy of emergency control measures for voltage stability can ensure the safe and stable operation of power grid after large-disturbance faults.  
      关键词:voltage stability;emergency control;convolutional neural network (CNN);long short-term memory (LSTM) network;control sensitivity   
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    • WANG Wenbo, LIU Xuan, LIN Hai, DU Pengcheng, JIANG Jinliang
      Vol. 47, Issue 11, Pages: 69-76(2023) DOI: 10.7500/AEPS20220817001
      摘要:An accurate and reliable anomaly detection method for power industrial control communication traffic is a key means to identify network attacks and achieve active defense, which is of great significance to ensure the safe and stable operation of power grids. This paper proposes a method for detecting application-layer message anomalies in power industrial control communication traffic based on the moth-flame optimization (MFO) algorithm and one-dimensional convolutional neural network (1D-CNN) to address the problems of insufficient detection depth, few attack classifications, and weak recognition of unknown anomalies in existing anomaly detection methods for power industrial control communication traffic. First, the depth protocol parsing is used to extract multi-dimensional features of application-layer message of traffic data. Secondly, redundant features are eliminated by calculating the feature importance through the random forest algorithm. Then, the built 1D-CNN anomaly detection model is trained and combined with the MFO algorithm to optimize the hyperparameters for improving the model performance. Finally, the Softmax classifier is employed to output the anomaly detection results of the message. The simulation results verify the effectiveness of the proposed method  
      关键词:power industrial control communication traffic;anomaly detection;cyber security;artificial intelligence;deep learning;application-layer message   
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    • PAN Dihan, DONG Lianxin, FAN Shuai, HUANG Yixuan, YANG Shihai, HE Guangyu
      Vol. 47, Issue 11, Pages: 77-87(2023) DOI: 10.7500/AEPS20220624001
      摘要:Modeling of air-conditioning-building electrothermal coupling system is the basis of tapping the potential of air-conditioning (AC) regulation. In order to solve the problems of limited fitting accuracy and insufficient consideration of electrothermal coupling characteristics in the current research of second-order equivalent thermal parameter (ETP) modeling, the analytical recursive form of second-order ETP model is first derived. It has the advantages of high fitting accuracy, bounded recursive values and flexible and adjustable step size, which can improve the accuracy, reliability and adaptability of the model to diversified data acquisition technologies. Then, the average energy efficiency ratio is used to describe the electrothermal conversion process of AC, and the parameter identification method for the air-conditioning-building electrothermal coupling analytical model considering the average energy efficiency ratio is proposed. The indoor air temperature fitting mechanism and heating capacity fitting mechanism are comprehensively used to optimize the parameters. Finally, an actual test environment is built to verify the performance of the proposed method. The results show that this method can significantly improve the accuracy of parameter identification on the existing basis, so as to provide a more accurate and reliable model basis for the energy system simulation, AC load control and other applications.  
      关键词:electrothermal coupling system;air-conditioning;second-order equivalent thermal parameter model;analytical solution;parameter identification;average energy efficiency ratio   
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    • FU Hao, LI Peng, FU Xiaopeng, WANG Zhiying, CAI Xipeng, WANG Chengshan
      Vol. 47, Issue 11, Pages: 88-100(2023) DOI: 10.7500/AEPS20221031016
      摘要:The integration of high proportion of renewable energy and power electronics equipment under “carbon emission peak and carbon neutrality” goals brings challenges to the real-time (RT) simulation of power systems. To realize an efficient and accurate RT simulation of the new power system with limited computing resources and RT constraints, the partitioning and resource allocation method for RT simulation computing tasks based on field programmable gate array (FPGA) is studied. First, from the two dimensions of computing resource demand and actual computing time, the solution units and functional modules under different simulation architectures of the RT simulator are finely modeled, and then the spatial-temporal demand model of the simulation task is established. On this basis, the optimal allocation model of the multiple FPGA RT simulator is established. With the goal of giving full play to the optimal solution performance of the RT simulator, the large-scale complex simulation tasks are reasonably divided, and the logical resources, memory and other computing resources are optimally configured. Finally, the correctness of the proposed spatial-temporal demand model and effectiveness of the optimal resource allocation method are verified using the IEEE 123-node test feeder and a practical distribution system in China.  
      关键词:real-time simulator;field programmable gate array (FPGA);spatial-temporal demand modeling;optimal resource allocation   
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    • DAI Zhihui, QIN Haoyu, LI Hangze, QIU Hongyi, QIU Xiaoxuan
      Vol. 47, Issue 11, Pages: 101-109(2023) DOI: 10.7500/AEPS20220826008
      摘要:A single-end line protection based on reflection coefficient and model matching is proposed to address the issues of internal remote high-resistance fault rejection and lightning interference misoperation of line protection in flexible DC power grid. First, based on the reflection coefficient of voltage traveling waves, a directional criterion is constructed to avoid protection misoperation under backward faults or lightning stroke. Secondly, using the voltage traveling wave transfer function to analyze internal short-circuit faults, as well as the function model satisfied by the initial traveling wave of fault voltage at the protection point under forward external faults or forward lightning strikes, a recognition criterion based on model matching is designed according to the different matching degrees between the first traveling wave of fault and the reference function model. Then, a complete single-end line protection scheme is constructed by combining the starting criterion and pole-selection criterion. Finally, the PSCAD simulation results verify that the proposed protection scheme has high reliability and can withstand 500 Ω transition resistance and 20 dB noise  
      关键词:flexible DC power grid;single-end line protection;traveling wave;reflection coefficient;model matching   
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      Application Research

    • CHEN Sheng, ZHANG Jingchun, HAN Haiteng, WEI Zhinong, SUN Guoqiang, ZHOU Yizhou
      Vol. 47, Issue 11, Pages: 110-120(2023) DOI: 10.7500/AEPS20221031009
      摘要:Hydrogen energy can provide important support for the low-carbon transformation of China’s energy industry. The power-to-hydrogen technology can convert the renewable energy that is difficult to be accommodated by the power grid into green hydrogen and inject it into the natural gas pipelines, which enables the long-distance transmission and utilization of green hydrogen. This paper proposes an optimal dispatch model of the electricity-gas integrated energy system with green hydrogen injection, in which the grid auxiliary services are taken into account to accommodate high proportion of renewable energy. First, the quasi-dynamic operation model of the natural-gas system that considers green hydrogen injections and pipeline line-pack is established. Then, a flexible operation model of the integrated energy system considering auxiliary services of peak regulation and flexible reserve is constructed. Finally, numerical examples quantify and evaluate the value of power-to-hydrogen and multi-energy coordination on accommodating renewable energy and improving system operation flexibility. The impact mechanism of penetration ratio of renewable energy and ratio limit of pipeline injected hydrogen on dispatch results of integrated energy system is analyzed.  
      关键词:integrated energy system;optimal dispatch;electricity-gas-hydrogen hybrid;quasi-dynamic model;auxiliary service;flexible operation   
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    • ZHOU Yibin, XIAO Hao, PEI Wei, WANG Xiaojun
      Vol. 47, Issue 11, Pages: 121-132(2023) DOI: 10.7500/AEPS20220704006
      摘要:Aiming at the collaborative optimization operation problem of the microgrid cluster composed of microgrids belonging to different stakeholders under privacy protection, this paper proposes a multi-agent collaborative optimization operation and strategy evolution method of microgrid cluster based on federated learning. First, each microgrid trains its own equivalent package model locally and uploads it to the cloud. Then, the cloud collects the equivalent package model of each microgrid, performs scenario deduction and global strategy search, and issues strategies to each microgrid. Finally, each microgrid learns new strategies through the distributed joint training of vertical federated neural networks to realize the collaborative optimization operation and strategy evolution of microgrid clusters under privacy protection. The simulation results of the collaborative operation of microgrid clusters with different scales show that this method realizes the collaborative optimization operation of multi-agent microgrid cluster under privacy protection. Compared with autonomous control, non-cooperative game as well as the multi-agent deep reinforcement learning method, the proposed method improves the overall economic benefits of the microgrid cluster and ensures the reasonable distribution of the interests of each participant.  
      关键词:microgrid cluster;multi-agent;federated learning;collaborative optimization   
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    • LIAO Zhixian, LI Binbin, SUO Zhiwen, HAN Linjie, ZHAO Xiaodong, XU Dianguo
      Vol. 47, Issue 11, Pages: 133-143(2023) DOI: 10.7500/AEPS20220927004
      摘要:Aiming at the problems of large magnetic component volume, multiple power conversion units and high cost of the existing multi-port power electronic transformer (PET), this paper proposes a three-port topology and its control strategy based on magnetic integration. To reduce the volume of the magnetic component, six arm inductors and multiple high-frequency (HF) transformers in the traditional topology are simplified into three integrated transformers. The low-voltage direct current (LVDC) port can be obtained by connecting a three-phase bridge to the secondary winding of the transformer, thus saving a great number of power conversion units. To achieve multi-port power control, the DC, line-frequency and HF components of the arm voltage are used to control the power at medium-voltage DC (MVDC), medium-voltage AC (MVAC) and LVDC ports, respectively. To improve the power quality of the MVDC port, the HF component of the arm voltage is designed as a three-phase symmetrical six-step waveform, so that the current components excited by it could cancel each other in the three-phase circuit, thus the HF current ripple of the MVDC port can be eliminated. Finally, a 4 MW simulation model is established to verify the effectiveness of the proposed topology and its control strategy.  
      关键词:AC/DC hybrid distribution network;power electronic transformer (PET);three-port topology;magnetic integration;modular multilevel converter (MMC)   
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    • ZHU Lin, LI Chushan, LU Yiping, YANG Huan, LI Wuhua
      Vol. 47, Issue 11, Pages: 144-154(2023) DOI: 10.7500/AEPS20221031021
      摘要:The power electronic transformer (PET) based on the three-level cell has the advantages of few power modules and high power density, which has broad application prospects in the scenarios of uninterruptible power supplies in data centers, railway power distribution systems and super-charging stations. However, there are many switching devices in PET, and the faulty module removal action triggered by the device fault will lead to the loss of system capacity, which can easily lead to system instability, fault expansion and other problems. To address this problem, this paper proposes a fault-tolerant operation technology based on cooperation among faulty modules, faulty phase and non-fault phase. First, the common fault results of three-level cell H-bridge with different fault types are analyzed by using the switch combination enumeration method, and faulty module reconfiguration and fault-tolerant operation are realized based on partial device bypass. Secondly, the in-phase coordinated control strategy is proposed to realize the capacitor voltage stability and equalization of the faulty module, and the line voltage balance is achieved through the inter-phase coordinated control, which ensures the normal operation of the circuit. Finally, specific fault-tolerant control methods are proposed for different fault results and the effectiveness of the proposed fault-tolerant methods is verified by simulation. The simulation results prove that the PET can operate stably with fault-tolerant control.  
      关键词:power electronic transformer (PET);three-level converter;cascaded H-bridge;fault-tolerant control;coordinated control;faulty module reconfiguration   
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    • ZHOU Hanbin, YANG Jian, HUANG Liansheng, SONG Dongran, CHEN Xiaojiao, DONG Mi
      Vol. 47, Issue 11, Pages: 155-164(2023) DOI: 10.7500/AEPS20221102009
      摘要:When the finite control set model predictive control strategy is applied to the three-level inverter, there are several problems such as large current harmonics, high requirement for the microcontroller computing ability, complex multi-objective optimization and limited output vector switching. In this regard, this paper proposes a double-vector model predictive control strategy based on the finite state machine. First, the finite state machine is adopted to describe the finite control set and the restricted vector switching, which is regarded as the basis for the operation of the three-level inverter to avoid excessive phase voltage and line-to-line voltage jumps. Then, a simplified control set method suitable for the finite state machine is proposed, so that the number of candidate vectors does not exceed five. Next, combined with the DC-side capacitor voltage balance control, the optimal double-vector combination is determined, and multi-objective optimization is not required. Finally, the duty cycle of the double vectors is calculated, and the harmonics of the output current are further reduced. Simulation and experimental results verify the good performance of the proposed strategy.  
      关键词:three-level inverter;model predictive control (MPC);finite state machine (FMS);voltage jump suppression;capacitor voltage balance   
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    • LIU Qihui, YAN Jiaying, WU Yong, WU Linlin
      Vol. 47, Issue 11, Pages: 165-173(2023) DOI: 10.7500/AEPS20221019002
      摘要:When an AC short circuit fault occurs in the wind power grid-connected system, the phase locking error of the phase locked loop (PLL) leads to the power coupling of the wind turbine, which will generate a transient overvoltage at the time of fault clearing. It is urgent to study the transient overvoltage mechanism, characteristics and suppression strategy considering the phase locking error. First, the influence of PLL parameters, fault locations and fault types on transient overvoltage is analyzed. Then, taking the three-phase fault as an example, the characteristics of phase angle jumping and the mechanism of transient overvoltage caused by phase locking error are revealed, and the control strategy of the rotor-side converter (RSC) and the grid-side converter (GSC) based on the improved PLL structure and phase locking error compensation is proposed to realize the active suppression of doubly-fed induction generator (DFIG) transient overvoltage. Finally, simulation verifies that the proposed strategy can not only achieve fault ride-through of DFIG, but also suppress the transient overvoltage.  
      关键词:wind power grid-connected system;phase angle jumping;phase locked loop (PLL);transient overvoltage;suppression strategy   
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    • ZHOU Kai, HU Hao, BI Ruyu, HU Zhijian, DENG Ke, LI Xudong
      Vol. 47, Issue 11, Pages: 174-184(2023) DOI: 10.7500/AEPS20211022005
      摘要:The master station-centralized control-substation operation ticket system can effectively prevent misoperation and achieve sequential control. This paper proposes a reasoning method for multi-station cooperative operation tickets at master station based on the substation state matrix. A bay model based on sequential control operations is constructed and a node state matrix based on the bay model is also constructed to generate a substation state matrix. A two-level operation ticket reasoning model based on the substation state matrix is then constructed. The lower-level model is a station-side operation ticket reasoning model based on the substation state matrix. The upper-level model is a multi-station operation ticket reasoning model based on the inter station correlation vector-substation state matrix. By constructing a multi-layer finite state machine model under rule constraints, the solution of the two-level model is achieved, and the generation of multi-station operation ticket reasoning is achieved. This method can achieve the reasoning generation of operation tickets for multi-bay and multi-substation equipment from operation to maintenance states, and is suitable for various wiring forms. The simulation test results show that the proposed method has high invoicing efficiency and quality.  
      关键词:substation;operation ticket;bay state;multi-station cooperation;finite state machine   
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      Review

    • YONG Weizhen, WANG Jianxue, XUE Lin, BIE Zhaohong
      Vol. 47, Issue 11, Pages: 185-199(2023) DOI: 10.7500/AEPS20220726003
      摘要:With the development of economy and society, the link between water and energy is getting closer, and the water-energy collaborative optimization for regional Energy Internet has become one of the research hotspots in the future. In view of this, this paper summarizes the basic concepts, nexus characteristics, important fields and key technologies of the water-energy nexus system. Firstly, this paper introduces the links and structures of the water supply and drainage system, and compares the similarities and differences between water supply and drainage system and energy systems. Secondly, the general nexus relationship of water-energy system is discussed, and the water-energy nexus morphology in typical application scenarios and at physical levels is further explained. Then, the important fields of water-energy collaborative optimization, i.e. model construction, planning and design, operation management and market interaction are combed and expounded from the perspective of mathematical modeling and research ideas. Finally, the key technologies of water-energy collaborative optimization are analyzed and prospected from the aspects of uncertainty handling, multi-agent management, flexibility exploitation and resilience enhancement.  
      关键词:water-energy nexus system;Energy Internet;multi-energy system;collaborative optimization   
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