The main objective of this research work is to develop a simple state estimation calculator in LabView for three phase power system network. LabView based state estimation calculator has been chosen as the main platfo...The main objective of this research work is to develop a simple state estimation calculator in LabView for three phase power system network. LabView based state estimation calculator has been chosen as the main platform because it is a user friendly and easy to apply in power systems. This research work is intended to simultaneously acclimate the power system engineers with the utilization of LabView with electrical power systems. This proposed work will discuss about the configuration and the improvement of the intelligent instructional VI （virtual instrument） modules in power systems for state estimation solutions. In the proposed model state estimation has been carried out and model has been developed such that it can accommodate the latest versions of state estimation algorithm.展开更多
This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypa...This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypass topology error processing can generate an incorrect power system network topology, subsequently distorting the results of the state estimation and economic dispatch.The main goal of this paper is to assess the economic impact of this misconfigured network topology on realtime LMP in an entire power system with network congestion. To this end, we start with our prior result, a simple and analytical congestion price equation, which can be applied to any single line congestion scenario. This equation can be extended to better understand the degree to which the LMP at any bus changes due to any line status error. Furthermore, it enables a rigorous analysis of the relationship between the change in LMP at any bus with respect to any line error and various physical/economical grid conditions such as the bidding prices for marginal generators and the locations of the congested/erroneous lines. Numerical examples on the impact analysis of this topology error are illustrated in IEEE 14-bus and 118-bus systems.展开更多
A new type of ANN (Artificial Neural Network) structure is introduced, and a nonlinear transformation of the original features is proposed so as to improve the learning covergence of the neural network. This kind of i...A new type of ANN (Artificial Neural Network) structure is introduced, and a nonlinear transformation of the original features is proposed so as to improve the learning covergence of the neural network. This kind of improved ANN is then used to analyse the transient stability of two real power systems. The results show that this method possesses better effectiveness and high convergence speed.展开更多
This paper proposes a new Initial CCT (Critical Clearing Time) estimation method using a hybrid neural network composed of iRprop (Improving the Resilient back PROPation Algorithm) and RAN (Resource Allocation Network...This paper proposes a new Initial CCT (Critical Clearing Time) estimation method using a hybrid neural network composed of iRprop (Improving the Resilient back PROPation Algorithm) and RAN (Resource Allocation Network). In transient stability study, CCT evaluation is very important but time consuming due to the fact it needs many iteration of time domain simulations gradually increasing the fault clearing time. The key to reduce the required computing time in this process is to find accurate initial estimation of CCT by a certain handy method before going to the iterative stage. As one of the strongest candidates of this handy method is the utilization of the pattern recognition ability of neural networks, which enable us to jump to a close estimation of the real CCT without any heavy computing burden. This paper proposes a new hybrid neural network which is a combination of the well-known iRprop and RAN. In the proposed method, the outputs of the hidden units of RAN are modified by multiplying the contribution factors calculated by an additional iRprop network. Numerical studies are done using two different test systems for the purpose of confirming the validity of the proposal. The result of the proposed method is the best. Properly evaluating the contribution of each input to the hidden units, the estimation error obtained by the proposed method is improved further than the original RAN based estimation.展开更多
The employment of maximum power point tracking techniques in the photovoltaic power systems is well known and even of immense importance. There are various techniques to track the maximum power point reported in sever...The employment of maximum power point tracking techniques in the photovoltaic power systems is well known and even of immense importance. There are various techniques to track the maximum power point reported in several literatures. In such context, there is an increasing interest in developing a more appropriate and effective maximum power point tracking control methodology to ensure that the photovoltaic arrays guarantee as much of their available output power as possible to the load for any temperature and solar radiation levels. In this paper, theoretical details of the work, carried out to develop and implement a maximum power point tracking controller using neural networks for a stand-alone photovoltaic system, are presented. Attention has been also paid to the command of the power converter to achieve maximum power point tracking. Simulations results, using Matlab/Simulink software, presented for this approach under rapid variation of insolation and temperature conditions, confirm the effectiveness of the proposed method both in terms of efficiency and fast response time. Negligible oscillations around the maximum power point and easy implementation are the main advantages of the proposed maximum power point tracking (MPPT) control method.展开更多
This paper addresses a terminal sliding mode control(T-SMC) method for load frequency control(LFC) in renewable power systems with generation rate constraints(GRC).A two-area interconnected power system with wind turb...This paper addresses a terminal sliding mode control(T-SMC) method for load frequency control(LFC) in renewable power systems with generation rate constraints(GRC).A two-area interconnected power system with wind turbines is taken into account for simulation studies. The terminal sliding mode controllers are assigned in each area to achieve the LFC goal. The increasing complexity of the nonlinear power system aggravates the effects of system uncertainties. Radial basis function neural networks(RBF NNs) are designed to approximate the entire uncertainties. The terminal sliding mode controllers and the RBF NNs work in parallel to solve the LFC problem for the renewable power system. Some simulation results illustrate the feasibility and validity of the presented scheme.展开更多
This paper presents a novel adaptive scheme for energy management in stand-alone hybrid power systems. The proposed management system is designed to manage the power flow between the hybrid power system and energy sto...This paper presents a novel adaptive scheme for energy management in stand-alone hybrid power systems. The proposed management system is designed to manage the power flow between the hybrid power system and energy storage elements in order to satisfy the load requirements based on artificial neural network (ANN) and fuzzy logic controllers. The neural network controller is employed to achieve the maximum power point (MPP) for different types of photovoltaic (PV) panels. The advance fuzzy logic controller is developed to distribute the power among the hybrid system and to manage the charge and discharge current flow for performance optimization. The developed management system performance was assessed using a hybrid system comprised PV panels, wind turbine (WT), battery storage, and proton exchange membrane fuel cell (PEMFC). To improve the generating performance of the PEMFC and prolong its life, stack temperature is controlled by a fuzzy logic controller. The dynamic behavior of the proposed model is examined under different operating conditions. Real-time measured parameters are used as inputs for the developed system. The proposed model and its control strategy offer a proper tool for optimizing hybrid power system performance, such as that used in smart-house applications.展开更多
In recent years, introduction of a renewable energy source such as solar energy is expected. However, solar radiation is not constant and power output of photovoltaic (PV) system is influenced by weather conditions. I...In recent years, introduction of a renewable energy source such as solar energy is expected. However, solar radiation is not constant and power output of photovoltaic (PV) system is influenced by weather conditions. It is difficult for getting to know accurate power output of PV system. In order to forecast the power output of PV system as accurate as possible, this paper proposes a decision technique of forecasting model for short-term-ahead power output of PV system based on solar radiation prediction. Application of Recurrent Neural Network (RNN) is shown for solar radiation prediction in this paper. The proposed method in this paper does not require complicated calculation, but mathematical model with only useful weather data. The validity of the proposed RNN is confirmed by comparing simulation results of solar radiation forecasting with that obtained from other展开更多
This paper considers the use of the inherent structural characteristics of power system networks for improving the reactive power reserve margins for both topologically weak and strong networks. The inherent structura...This paper considers the use of the inherent structural characteristics of power system networks for improving the reactive power reserve margins for both topologically weak and strong networks. The inherent structural characteristics of the network are derived from the Schur complement of the partitioned Y-admittance matrix using circuit theory representations. Results show that topologically strong networks, operating close to the upper voltage limit could be made to increase their loadability margin by locating reactive power compensators close to generator sources, whereas topologically weak (ill conditioned) networks could be made to operate within the feasible operating limits by locating reactive power compensators on buses farther from generator sources.展开更多
In this paper, a new method has been introduced to find the most vulnerable lines in the system dynamically in an interconnected power system to help with the security and load flow analysis in these networks. Using t...In this paper, a new method has been introduced to find the most vulnerable lines in the system dynamically in an interconnected power system to help with the security and load flow analysis in these networks. Using the localization of power networks, the power grid can be divided into several divisions of sub-networks in which, the connection of the elements is stronger than the elements outside of that division. By using our proposed method, the probable important lines in the network can be identified to do the placement of the protection apparatus and planning for the extra extensions in the system. In this paper, we have studied the pathfinding strategies in most vulnerable line detection in a partitioned network. The method has been tested on IEEE39-bus system which is partitioned using hierarchical spectral clustering to show the feasibility of the proposed method.展开更多
In this paper, a relay selection strategy and distributed power control algorithm are proposed for the underlay spectrum sharing mode based cooperative cognitive ad hoc network with energy-limited users. The study aim...In this paper, a relay selection strategy and distributed power control algorithm are proposed for the underlay spectrum sharing mode based cooperative cognitive ad hoc network with energy-limited users. The study aims to minimize the total power consumption of cooperative cognitive ad hoc network while ensuring the quality of service(QoS) requirement of cognitive user and keeping the interference to primary user below interference tolerance. The power control problem is transformed into a convex optimization problem. Based on Lagrange dual decomposition theory, a gradient iterative algorithm is constructed to search for the optimal solution and complete distributed power optimization. Simulation results show that the algorithm converges fast and reduces transmit power of cognitive users effectively while guaranteeing the QoS requirement.展开更多
The huge amount of electrical power of many countries is consumed in lighting the streets. However, vehicles pass with very low rate in specific periods of time and parts of the streets are not occupied by vehicles ov...The huge amount of electrical power of many countries is consumed in lighting the streets. However, vehicles pass with very low rate in specific periods of time and parts of the streets are not occupied by vehicles over time. In this paper, we propose a system that automatically switches off the light for the parts of the streets having no vehicles and turns on the light for these parts once there are some vehicles that are going to come. Logically, this system may save a large amount of the electrical power. In addition, it may increase the lifetime of the lamps and reduce the pollutions. This system automatically controls and monitors the light of the streets. It can light only the parts that have vehicles and help on the maintenance of the lighting equipments. Vehicular Ad-Hoc Networks (VANET) make it possible to propose such system. VANET enables the possibility to know the presence of vehicles, their locations, their directions and their speeds in real time. These quantities are what are needed to develop this system. An advantage of using VANET is that there is no need to use specific network and equipments to design the system, but VANET infrastructure will be used. This decreases the cost and speed up the deployment of such system. This paper focuses on the proposal of different possible architectures of this system. Results show that the saved energy may reach up to 65% and an increase of the lifetime of the lamps of 53%.展开更多
This paper presents an proportional integral (PI) based voltage-reactive power control for wind diesel based decentralized hybrid power system with wide range of disturbances to demonstrate the compensation effect on ...This paper presents an proportional integral (PI) based voltage-reactive power control for wind diesel based decentralized hybrid power system with wide range of disturbances to demonstrate the compensation effect on system with intelligent tuning methods such as genetic algorithm (GA), artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS). The effect of probabilistic load and/or input power pattern is introduced which is incorporated in MATLAB simulink model developed for the study of decentralized hybrid power system. Results show how tuning method becomes important with high percentage of probabilistic pattern in system. Testing of all tuning methods shows that GA, ANN and ANFIS can preserve optimal performances over wide range of disturbances with superiority to GA in terms of settling time using Integral of Square of Errors (ISE) criterion as fitness function.展开更多
The paper dwells on the unified power quality indexes characterizing the phenomenon of voltage unbalance in three-phase systems. Voltage unbalance is one of the commonest occurrences in the town mains of 0.38 kV volta...The paper dwells on the unified power quality indexes characterizing the phenomenon of voltage unbalance in three-phase systems. Voltage unbalance is one of the commonest occurrences in the town mains of 0.38 kV voltage. The phenomenon describes as inequality of vector magnitude of phase voltage and shearing angle between them. Causes and consequences of the voltage unbalance in distribution networks have been considered. The algorithm, which allows switching one-phase load, has been developed as one of the methods of reducing the unbalance level. The algorithm is written in the function block diagram programming language. For determining the duration and magnitude of the unbalance level it is proposed to introduce the forecasting algorithm. The necessary data for forecasting are accumulated in the course of the algorithm based on the Function Block Diagram. The algorithm example is given for transforming substation of the urban electrical power supply system. The results of the economic efficiency assessment of the algorithm implementation are shown in conclusion. The use of automatic switching of the one-phase load for explored substation allows reducing energy losses (active electric energy by 7.63%;reactive energy by 8.37%). It also allows improving supply quality to a consumer. For explored substation the average zero-sequence unbalance factor has dropped from 3.59% to 2.13%, and the negative-sequence unbalance factor has dropped from 0.61% to 0.36%.展开更多
针对新型电力系统协同调控对传输网络提出了超大带宽、多业务感知承载、确定性传输、绿色低碳的要求,围绕细粒度光传送网(fine-grained Optical Transport Network,fgOTN)组网策略展开研究,通过对比分析,明确了fgOTN传输网中多类业务的...针对新型电力系统协同调控对传输网络提出了超大带宽、多业务感知承载、确定性传输、绿色低碳的要求,围绕细粒度光传送网(fine-grained Optical Transport Network,fgOTN)组网策略展开研究,通过对比分析,明确了fgOTN传输网中多类业务的承载平面,并分别提出了从同步数字体系传输网和光传送网向fgOTN传输网平滑演进的可行性方案,并对fgOTN传输网的建设方案及光路子系统配置提出了推荐性建议,对电力系统骨干传输网向fgOTN的演进具有一定的指导意义。展开更多
文摘The main objective of this research work is to develop a simple state estimation calculator in LabView for three phase power system network. LabView based state estimation calculator has been chosen as the main platform because it is a user friendly and easy to apply in power systems. This research work is intended to simultaneously acclimate the power system engineers with the utilization of LabView with electrical power systems. This proposed work will discuss about the configuration and the improvement of the intelligent instructional VI （virtual instrument） modules in power systems for state estimation solutions. In the proposed model state estimation has been carried out and model has been developed such that it can accommodate the latest versions of state estimation algorithm.
基金supported in part by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIP)(No.2015R1C1A1A01051890)part by the National Science Foundation DGE-1303378
文摘This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypass topology error processing can generate an incorrect power system network topology, subsequently distorting the results of the state estimation and economic dispatch.The main goal of this paper is to assess the economic impact of this misconfigured network topology on realtime LMP in an entire power system with network congestion. To this end, we start with our prior result, a simple and analytical congestion price equation, which can be applied to any single line congestion scenario. This equation can be extended to better understand the degree to which the LMP at any bus changes due to any line status error. Furthermore, it enables a rigorous analysis of the relationship between the change in LMP at any bus with respect to any line error and various physical/economical grid conditions such as the bidding prices for marginal generators and the locations of the congested/erroneous lines. Numerical examples on the impact analysis of this topology error are illustrated in IEEE 14-bus and 118-bus systems.
文摘A new type of ANN (Artificial Neural Network) structure is introduced, and a nonlinear transformation of the original features is proposed so as to improve the learning covergence of the neural network. This kind of improved ANN is then used to analyse the transient stability of two real power systems. The results show that this method possesses better effectiveness and high convergence speed.
文摘This paper proposes a new Initial CCT (Critical Clearing Time) estimation method using a hybrid neural network composed of iRprop (Improving the Resilient back PROPation Algorithm) and RAN (Resource Allocation Network). In transient stability study, CCT evaluation is very important but time consuming due to the fact it needs many iteration of time domain simulations gradually increasing the fault clearing time. The key to reduce the required computing time in this process is to find accurate initial estimation of CCT by a certain handy method before going to the iterative stage. As one of the strongest candidates of this handy method is the utilization of the pattern recognition ability of neural networks, which enable us to jump to a close estimation of the real CCT without any heavy computing burden. This paper proposes a new hybrid neural network which is a combination of the well-known iRprop and RAN. In the proposed method, the outputs of the hidden units of RAN are modified by multiplying the contribution factors calculated by an additional iRprop network. Numerical studies are done using two different test systems for the purpose of confirming the validity of the proposal. The result of the proposed method is the best. Properly evaluating the contribution of each input to the hidden units, the estimation error obtained by the proposed method is improved further than the original RAN based estimation.
文摘The employment of maximum power point tracking techniques in the photovoltaic power systems is well known and even of immense importance. There are various techniques to track the maximum power point reported in several literatures. In such context, there is an increasing interest in developing a more appropriate and effective maximum power point tracking control methodology to ensure that the photovoltaic arrays guarantee as much of their available output power as possible to the load for any temperature and solar radiation levels. In this paper, theoretical details of the work, carried out to develop and implement a maximum power point tracking controller using neural networks for a stand-alone photovoltaic system, are presented. Attention has been also paid to the command of the power converter to achieve maximum power point tracking. Simulations results, using Matlab/Simulink software, presented for this approach under rapid variation of insolation and temperature conditions, confirm the effectiveness of the proposed method both in terms of efficiency and fast response time. Negligible oscillations around the maximum power point and easy implementation are the main advantages of the proposed maximum power point tracking (MPPT) control method.
基金supported by National Natural Science Foundation of China(60904008,61273336)the Fundamental Research Funds for the Central Universities(2018MS025)the National Basic Research Program of China(973 Program)(B1320133020)
文摘This paper addresses a terminal sliding mode control(T-SMC) method for load frequency control(LFC) in renewable power systems with generation rate constraints(GRC).A two-area interconnected power system with wind turbines is taken into account for simulation studies. The terminal sliding mode controllers are assigned in each area to achieve the LFC goal. The increasing complexity of the nonlinear power system aggravates the effects of system uncertainties. Radial basis function neural networks(RBF NNs) are designed to approximate the entire uncertainties. The terminal sliding mode controllers and the RBF NNs work in parallel to solve the LFC problem for the renewable power system. Some simulation results illustrate the feasibility and validity of the presented scheme.
文摘This paper presents a novel adaptive scheme for energy management in stand-alone hybrid power systems. The proposed management system is designed to manage the power flow between the hybrid power system and energy storage elements in order to satisfy the load requirements based on artificial neural network (ANN) and fuzzy logic controllers. The neural network controller is employed to achieve the maximum power point (MPP) for different types of photovoltaic (PV) panels. The advance fuzzy logic controller is developed to distribute the power among the hybrid system and to manage the charge and discharge current flow for performance optimization. The developed management system performance was assessed using a hybrid system comprised PV panels, wind turbine (WT), battery storage, and proton exchange membrane fuel cell (PEMFC). To improve the generating performance of the PEMFC and prolong its life, stack temperature is controlled by a fuzzy logic controller. The dynamic behavior of the proposed model is examined under different operating conditions. Real-time measured parameters are used as inputs for the developed system. The proposed model and its control strategy offer a proper tool for optimizing hybrid power system performance, such as that used in smart-house applications.
文摘In recent years, introduction of a renewable energy source such as solar energy is expected. However, solar radiation is not constant and power output of photovoltaic (PV) system is influenced by weather conditions. It is difficult for getting to know accurate power output of PV system. In order to forecast the power output of PV system as accurate as possible, this paper proposes a decision technique of forecasting model for short-term-ahead power output of PV system based on solar radiation prediction. Application of Recurrent Neural Network (RNN) is shown for solar radiation prediction in this paper. The proposed method in this paper does not require complicated calculation, but mathematical model with only useful weather data. The validity of the proposed RNN is confirmed by comparing simulation results of solar radiation forecasting with that obtained from other
文摘This paper considers the use of the inherent structural characteristics of power system networks for improving the reactive power reserve margins for both topologically weak and strong networks. The inherent structural characteristics of the network are derived from the Schur complement of the partitioned Y-admittance matrix using circuit theory representations. Results show that topologically strong networks, operating close to the upper voltage limit could be made to increase their loadability margin by locating reactive power compensators close to generator sources, whereas topologically weak (ill conditioned) networks could be made to operate within the feasible operating limits by locating reactive power compensators on buses farther from generator sources.
文摘In this paper, a new method has been introduced to find the most vulnerable lines in the system dynamically in an interconnected power system to help with the security and load flow analysis in these networks. Using the localization of power networks, the power grid can be divided into several divisions of sub-networks in which, the connection of the elements is stronger than the elements outside of that division. By using our proposed method, the probable important lines in the network can be identified to do the placement of the protection apparatus and planning for the extra extensions in the system. In this paper, we have studied the pathfinding strategies in most vulnerable line detection in a partitioned network. The method has been tested on IEEE39-bus system which is partitioned using hierarchical spectral clustering to show the feasibility of the proposed method.
基金supported by Natural Science Foundation ofChongqing(No.CSTC2009BA2064)Fundamental Research Fundsfor Central Universities(No.CDJZR12160004)PostgraduateScience and Technology Innovation Fund(No.CDJXS12161109)
文摘In this paper, a relay selection strategy and distributed power control algorithm are proposed for the underlay spectrum sharing mode based cooperative cognitive ad hoc network with energy-limited users. The study aims to minimize the total power consumption of cooperative cognitive ad hoc network while ensuring the quality of service(QoS) requirement of cognitive user and keeping the interference to primary user below interference tolerance. The power control problem is transformed into a convex optimization problem. Based on Lagrange dual decomposition theory, a gradient iterative algorithm is constructed to search for the optimal solution and complete distributed power optimization. Simulation results show that the algorithm converges fast and reduces transmit power of cognitive users effectively while guaranteeing the QoS requirement.
文摘The huge amount of electrical power of many countries is consumed in lighting the streets. However, vehicles pass with very low rate in specific periods of time and parts of the streets are not occupied by vehicles over time. In this paper, we propose a system that automatically switches off the light for the parts of the streets having no vehicles and turns on the light for these parts once there are some vehicles that are going to come. Logically, this system may save a large amount of the electrical power. In addition, it may increase the lifetime of the lamps and reduce the pollutions. This system automatically controls and monitors the light of the streets. It can light only the parts that have vehicles and help on the maintenance of the lighting equipments. Vehicular Ad-Hoc Networks (VANET) make it possible to propose such system. VANET enables the possibility to know the presence of vehicles, their locations, their directions and their speeds in real time. These quantities are what are needed to develop this system. An advantage of using VANET is that there is no need to use specific network and equipments to design the system, but VANET infrastructure will be used. This decreases the cost and speed up the deployment of such system. This paper focuses on the proposal of different possible architectures of this system. Results show that the saved energy may reach up to 65% and an increase of the lifetime of the lamps of 53%.
文摘This paper presents an proportional integral (PI) based voltage-reactive power control for wind diesel based decentralized hybrid power system with wide range of disturbances to demonstrate the compensation effect on system with intelligent tuning methods such as genetic algorithm (GA), artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS). The effect of probabilistic load and/or input power pattern is introduced which is incorporated in MATLAB simulink model developed for the study of decentralized hybrid power system. Results show how tuning method becomes important with high percentage of probabilistic pattern in system. Testing of all tuning methods shows that GA, ANN and ANFIS can preserve optimal performances over wide range of disturbances with superiority to GA in terms of settling time using Integral of Square of Errors (ISE) criterion as fitness function.
文摘The paper dwells on the unified power quality indexes characterizing the phenomenon of voltage unbalance in three-phase systems. Voltage unbalance is one of the commonest occurrences in the town mains of 0.38 kV voltage. The phenomenon describes as inequality of vector magnitude of phase voltage and shearing angle between them. Causes and consequences of the voltage unbalance in distribution networks have been considered. The algorithm, which allows switching one-phase load, has been developed as one of the methods of reducing the unbalance level. The algorithm is written in the function block diagram programming language. For determining the duration and magnitude of the unbalance level it is proposed to introduce the forecasting algorithm. The necessary data for forecasting are accumulated in the course of the algorithm based on the Function Block Diagram. The algorithm example is given for transforming substation of the urban electrical power supply system. The results of the economic efficiency assessment of the algorithm implementation are shown in conclusion. The use of automatic switching of the one-phase load for explored substation allows reducing energy losses (active electric energy by 7.63%;reactive energy by 8.37%). It also allows improving supply quality to a consumer. For explored substation the average zero-sequence unbalance factor has dropped from 3.59% to 2.13%, and the negative-sequence unbalance factor has dropped from 0.61% to 0.36%.
文摘针对新型电力系统协同调控对传输网络提出了超大带宽、多业务感知承载、确定性传输、绿色低碳的要求,围绕细粒度光传送网(fine-grained Optical Transport Network,fgOTN)组网策略展开研究,通过对比分析,明确了fgOTN传输网中多类业务的承载平面,并分别提出了从同步数字体系传输网和光传送网向fgOTN传输网平滑演进的可行性方案,并对fgOTN传输网的建设方案及光路子系统配置提出了推荐性建议,对电力系统骨干传输网向fgOTN的演进具有一定的指导意义。
