CN110969347B

CN110969347B - Power transmission network structure morphology assessment method

Info

Publication number: CN110969347B
Application number: CN201911156696.6A
Authority: CN
Inventors: 崔国柱; 汪湲; 王砥凡; 王飞; 魏飞; 牟宏; 张成相; 王春义; 蒋德玉; 孙伟; 顾洁; 卢兆军; 王东阳; 张�杰; 谢红涛
Original assignee: Linyi Power Supply Co of State Grid Shandong Electric Power Co Ltd
Current assignee: Linyi Power Supply Co of State Grid Shandong Electric Power Co Ltd
Priority date: 2019-11-22
Filing date: 2019-11-22
Publication date: 2023-08-18
Anticipated expiration: 2039-11-22
Also published as: CN110969347A

Abstract

The invention discloses a method for evaluating the structural morphology of a power transmission network, which comprises the following steps: determining a basic principle of selecting comprehensive evaluation indexes of the power system, establishing a simplified principle for describing the topological structure of an actual power grid, and carrying out comprehensive evaluation methods on the power grid structure indexes, other indexes and the power system based on a complex network theory; the invention further learns and researches the theoretical basis of a complex network and the complex network characteristics of the power grid, judges the system relevance of nodes and the network from the power grid structure by utilizing the complex network theory, analyzes the power grid characteristics by utilizing the element characteristics of the power system, explores the relation between the power grid structure and the performance, realizes the combination of the whole and the individual, constructs a comprehensive evaluation index system of a comprehensive and effective power grid planning scheme, defines the calculation method and the specification requirement of each evaluation index, and objectively gives each index weight value and evaluates the power grid by combining a multi-objective decision method of the power grid planning scheme evaluation.

Description

Power transmission network structure morphology assessment method

Technical Field

The invention relates to the technical field of power grid evaluation, in particular to a power transmission grid structure morphology evaluation method.

Background

With the continuous increase of energy demand and the reinforcement of strategic reserve situations worldwide, energy has become a fundamental factor affecting the sustainable development of future society; in the face of various factors such as gradual shortage of fossil energy, continuously-increased environmental pressure and the like, under the condition of comprehensively considering various conditions such as economic development, energy storage, energy consumption level, demand prediction, environmental constraint and the like, the great development and reasonable utilization of renewable energy sources become an important way facing energy crisis and environmental deterioration at the present stage; in order to adapt to the large environment of sustainable development of energy, the power grid is taken as the most important energy transmission network, and the current development form of the power grid is required to be changed and improved; under the background of full-ball new energy transformation, the future electric power energy is gradually changed from traditional fossil energy to renewable energy, and the high-proportion renewable energy is absorbed to become the necessary development trend and important capability of the future electric power system;

because the power system in the future scene does not have a definite and clear structure for research, the future power system can be planned only through the development of the power grid scale level, the prediction and development trend of the energy load distribution, the growth condition of each industry on the electric energy demand and the like; therefore, the comprehensive evaluation of the future power system development form can be characterized as the comprehensive evaluation of the future power system planning to a certain extent; under the condition of comprehensively considering all characteristics of a future power system, a power system which is safe, reliable, flexible, stable, environment-friendly and economical to construct and can consume high-proportion renewable energy sources is taken as a target, and a power system planning scheme which is most in line with the future development form of the power system is selected, so that the method has a vital significance for the development of the power system;

The investment cost of the power grid construction is huge, a large amount of time and manpower and material resources are needed to be invested, and meanwhile, a large amount of projects to be built, which are generated by power grid planning, cannot be realized as much as possible, and are often limited by investment budget or the actual construction environment of the power grid, so that the evaluation decision of the power system planning scheme is very important; in the process of continuously developing the power grid, a comprehensive evaluation system of the power system is proposed and widely researched, and an evaluation method with good applicability and practicality is provided, so that the comprehensive evaluation result of the power grid is influenced significantly; in the process of comprehensively deciding the power grid planning scheme, various problems need to be considered, such as large investment and large manpower and material resources, and the planning scheme is changed once being put into construction so as to solve the larger problem; therefore, if the decision implementation of the power grid planning project is poor or an unreasonable place exists, not only a great amount of unnecessary waste of funds, manpower and material resources can be brought, but also the society, the environment and the like can be negatively influenced;

the comprehensive evaluation work of the traditional power system mainly comprises evaluation on the aspects of vulnerability, reliability, safety, economy and the like of the current power grid, and the future power system is different from the traditional power grid in the aspects of power grid structure, power transmission technology, management mode, power flow control and the like, particularly, under the condition that the current wind power, photoelectricity and other distributed power sources with nonlinearity and uncertainty are accessed into the power grid in a high proportion, the AC-DC connection mode of the future power grid is more complex, and the running mode of the power system is more diversified; therefore, in the future strong uncertainty environment, the evaluation index system for more complex power grid structures and more diversified system operation modes is more complex, and the future power system structures and operation modes need to be comprehensively evaluated to clearly and comprehensively recognize the economy, the safety, the reliability, the environmental protection, the adaptability and the sustainability of the power grid planning scheme, so that the invention provides a power transmission grid structure form evaluation method to solve the problems in the prior art.

Disclosure of Invention

Aiming at the problems, the invention provides a power transmission network structure morphology assessment method, which is used for deeply studying and researching a complex network theoretical basis and complex network characteristics of a power grid, judging the system relevance of nodes and the network from the power grid structure by using the complex network theory, analyzing the power grid characteristics by using element characteristics of a power system, exploring the relation between the power grid structure and the performance, realizing the combination of the whole and an individual, and constructing a comprehensive and effective power grid planning scheme comprehensive evaluation index system.

In order to solve the above problems, the present invention provides a method for evaluating the structural morphology of a power transmission network, comprising the following steps:

step one: basic principle for determining comprehensive evaluation index selection of power system

The basic principle of comprehensive evaluation index selection of the power system is determined, on one hand, each characteristic of the power grid is to be truly reflected comprehensively and objectively, including topological characteristics and operation characteristics of the power grid structure, the practicability and operability of an evaluation index system are ensured, and any important index is not omitted; on the other hand, the actual condition of the power grid, the problems of difficulty in acquisition, difficulty in calculation and the like of index data are considered, the authenticity of measurement is ensured, the problem of repeated index calculation is avoided, and the indexes are required to have internal connection and are consistent with the evaluation purpose so as to jointly reflect the characteristics of the power grid;

Step two: establishing a simplified principle in describing the topology of an actual power grid

The method comprises the steps of analyzing a power grid structure by applying a complex network theory, simplifying and analyzing the power grid structure when describing the topological structure of an actual power grid, and making a simplification principle:

(1) The research object is mainly a power transmission network and a power distribution network, and meanwhile, the main wiring structures of a power plant and a power transformation station are not considered, and the power supply and the load connected to the generator and the low-voltage side bus are all imaged as injecting a certain active power into the corresponding bus;

(2) Nodes in the power grid topology model only comprise power points, load nodes and intermediate nodes, the ground zero point is ignored, and all the nodes are defaults to be identical indiscriminate nodes;

(3) Ignoring differences in transmission line voltage levels, differences in physical structural characteristics and electrical parameter characteristics of different transmission lines, namely considering that the topological characteristics of all transmission lines are the same, and not considering the weights of all sides;

(4) In a power grid topology model, all power transmission lines and transformer branches are abstracted into edges, and all edges do not consider the directions;

(5) The parallel capacitor branches are not considered, and the transmission lines which are combined with the same rod are combined, so that multiple edges and self loops in a power grid topological model are avoided, and a simple diagram is formed;

Step three: power grid structure index based on complex network theory

According to the simplified rule of the second step, a specific network can be abstracted into an undirected and unauthorized network g= (V, E), wherein V represents a set of all nodes in the network, E represents a set of all edges, the number of nodes is n, the number of edges is l, and the following important parameters are selected according to the definition in the classical complex network theory to describe the structural characteristics of the network:

(1) Node degree k

In a complex network, the degree is a simple and important attribute for individual nodes, and is also a parameter which is most widely researched in a complex network structure, and the degree number k of the node i _i Defined as the number of all edges/connected to the node,

wherein ：k_i Degree of node i, l _ij For the edge of node i that is connected to node j,

the greater the degree of a node indicates the greater the importance of that node in the overall network, the networkEach node of the plurality has a degree of each, and the degree k of each node i is equal to the degree k of each node i _i Summing and averaging to obtain the node average degree of the whole network, and recording as<k>，

wherein ：k_i The degree for node i, n is the total node number,

(2) Node degree distribution P (k)

The distribution of the node degrees in the network may be represented by a distribution function P (k), i.e. the proportion of all nodes with a degree k in the network to the nodes of the entire network,

wherein ：n_k Is the number of nodes with a node number k, n is the total number of nodes,

the degree of each node in the network is generally described by using the concept of degree distribution when the degree of the network connectivity is expressed, different types of networks usually show quite different degree distribution characteristics, and on the contrary, different types of networks can be distinguished according to the difference of degree distribution, for example, the degree distribution of a regular network is delta distribution, and the distribution function is in a single peak shape; the degree distribution of the random network is similar to poisson distribution, the distribution function of the random network shows an exponentially decreasing trend at a place far away from the peak value of the function, the degree distribution of the scale-free network is a power law distribution, which is also called scale-free distribution, in practical application, the node degree distribution is generally represented in a cumulative distribution form,

wherein: a P (k) node degree distribution function, k being node degree, gamma being a degree distribution index,

(3) Node degree correlation k _nn

The degree distribution completely determinesThe statistical nature of uncorrelated networks, however, a large number of real network networks are correlated, there is interdependence between nodes of different degrees, in the sense that the probability that a node of degree k is connected to another node of degree k' is related to k, in which case a conditional probability P is introduced _c (k '|k), defined as the probability of pointing from a node of degree k to a node of degree k',

P _c (k'|k)＝P _c (k')≈k'P(k') (2-5)

wherein: k ' is the degree of a node, P (k ') represents the probability that the degree of a node is k ',

the degree correlation is obtained by measuring the average nearest neighbor connectivity of the nodes with degree k, and judging whether the connected nodes have the same attribute, such as similarity,

wherein: k' is the degree of the node, condition P _C (k '|k) represents the probability that a node of degree k points to a node of degree k',

(4) Network diameter D

Distance d between nodes i and j in the network _ij Is defined as the number of edges traversed by the shortest path connecting the two nodes, the diameter D of the network is defined as the maximum value of the distance between any two nodes in the network,

D＝max d _ij (2-7)

wherein ：d_ij For the number of edges traversed by the shortest path between node i and node j,

(5) Characteristic path length L

In the topology of a network, the characteristic path length, also called the average path length of the network, is defined as the average value of the distance between any two nodes in the network, which is a measure of the quality or information transmission efficiency in a network,

wherein: n is the total node number, d _ij For the number of edges traversed by the shortest path between node i and node j,

From the global perspective, the characteristic path length shows the degree of tightness of the linkage between each node in the network, so that the overall structural characteristics of the network can be clearly known, the specific calculation of the characteristic path length can be widely applied to the field of graph theory, and the main idea is to calculate the shortest distance between every two paired nodes in the complex network, including Dijkstra, floyd algorithm;

(6) Medium number b

The betweenness is a standard index for measuring the centrality of a node in a network, importance information of the node in path planning is given by calculating the shortest path number passing through the node, the energy or information between two nodes in the network is assumed to be along the shortest path between the nodes in the propagation process, the role played by the node or the edge in the network propagation process is characterized according to the shortest path number passing through the node or the edge, the contribution is larger as the number is larger, and the importance is correspondingly larger:

wherein ：n_jk N, the shortest path number connecting nodes j and k _jk (i) To connect nodes j and k and pass through the shortest path number of node i,

(7) Clustering coefficient C

The clustering coefficient is a parameter describing the aggregation of a network, and is used for measuring the aggregation and discrete degree of network nodes, and the assumption is made that nodes i and k _i The nodes are directly connected, then for an undirected network, this k _i The maximum number of edges that may exist between adjacent nodes isAnd the number of the actually existing edges is E _i The clustering coefficient of the node i is defined as the actual edge number E _i And the number of total edges which may be present +.>Ratio of (3):

wherein ：k_i For the number of nodes adjacent to node i, E _i For the actual number of edges that node i connects to neighboring nodes,

from a geometric perspective, it can be defined as:

clustering coefficient C for all nodes of whole network _i And obtaining a clustering coefficient C of the network by averaging:

wherein ：C_i For the clustering coefficient of the node i, n is the total node number, C is more than or equal to 0 and less than or equal to 1, if C=0, all the points of the whole network are isolated and are not connected with each other, if C=1, all the nodes in the network are connected with each other by edges, and the larger the C of the network is, the higher the aggregation degree of the whole network is;

(8) Efficiency E

Limiting the summation in equations (2-8) to only the node pair belonging to the largest connection, taking into account the harmonic mean of the geodesic (i.e., the simple path that experiences the least number of edges between two points), and introducing a definition of network efficiency:

wherein: n is the total node number, and the edge number d of the ground wire is measured _ij The reciprocal of the distance between two nodes i and j is the efficiency between the two nodes, and the efficiency of all node pairs in the network is averaged to obtain the global of the whole network Efficiency, measuring information transmission speed between nodes, and d when no path is communicated between nodes i and j _ij = infinity, and e=0, so efficiency is suitable for measuring non-all-pass networks;

(9) Fault tolerance probability f _c

In studying the tolerance of the grid to large cascading errors and attacks, the usual method is to find the relation between node deletion (without reassigning the network) and global connectivity (presence and relative size of the connection after deleting the nodes), the traditional analysis method is based on a penetration theory, in the sense that the network penetration below a critical probability is related to the presence or absence of a certain number of edges, its study is mapped to the standard penetration problem of the network to errors and attacks, according to the complex network theory, the condition that there is a large connection in the network is:

wherein: k is the degree of the node, P (k) is the node degree distribution function,

for a randomly deleted node, its fault tolerance probability is defined as:

taking the index distribution of each node of the power grid into consideration to obtain<k>=γ sum<k ² >＝2γ ² Therefore:

wherein: gamma is the node degree distribution index;

step four: other indexes

The problems of safety and reliability during operation of the power grid and the problems of uncertainty of the power grid in the operation process are considered due to the access of high-proportion clean energy and a distributed generation technology, and the following indexes are selected to realize comprehensive evaluation of the power grid in all aspects:

a. Reliability class index: the power system transmits power from a power supply end to a power receiving end according to quality and quantity standards under specified conditions so as to meet the power supply load power and electric quantity requirements, and the power system measures through quantitative reliability indexes;

(1) Line load factor

The index reflects the utilization rate of 220kV lines of a power transmission network and is specifically divided into a maximum load rate, a minimum load rate and an average load rate of the lines:

220kv line maximum load rate = line annual maximum active power/line thermal stability limit (2-17)

220kv line minimum load rate = line annual minimum active power/line thermal stability limit (2-18)

220kv line average load rate = line annual average active power/line thermal stability limit (2-19);

(2) Ratio of capacitance Rs

Referring to the ratio of the total capacity (kVA) of the power transformation equipment to the corresponding total load (kW) in a specified power supply area, the capacity-to-load ratio is estimated by the following method:

wherein Sei is the main transformer capacity (kVA) of the voltage class transformer station i, pmax is the full network maximum predicted load (kW) at the voltage class,

(3) System power supply reliability I _ASA

The definition of the system power supply reliability is the ratio of the total number of hours of the system without power failure in a certain set time to the total number of power supply hours required to be satisfied:

Wherein: g is a load node; omega shape _F The method comprises the steps of integrating the positions of all types of load nodes in a system;the number of users for node g; u (u) _g For the average outage duration (h/year) at load point g,

(4) Average power outage duration I of system _SAID

The average power outage duration of the system is the total power outage time experienced by each user in the system on average over a specified period of time:

wherein ：u_g Average outage duration (h/year) for load point g;the number of users for node g;

b. security class index: refers to the safety of the power system in the event of an accident and the ability to avoid cascading failures without causing system crashes and large-area power outages,

(1) Average power failure frequency I of system _SAIF

The average power outage frequency of the system is the number of continuous power outages which are averagely experienced by the power grid in a certain set time:

wherein ：λ_g Annual fault outage frequency (times/year) for load point g;the number of users who are the node g,

(2) System overall security index I _IS

The power supply safety refers to the capability of a system for transferring loads under fault conditions, and the integral safety coefficient I of the system is proposed according to the definition of an N-1 safety criterion in the guidance of a planning design technology of a power distribution network _IS The system quantitatively evaluates the active power distribution by calculating the transfer rate of loads with different importance degrees under the condition of 'N-1' of the system The overall power security level of the network:

wherein: m is the mth element in the power system which may fail (the branch line to which the load point is connected and the switch on the branch line are not counted); omega shape _m A set of load nodes that are affected by the failure of the mth element; EN is the total number of elements in the power system that may fail; w (w) _g Indicating the importance level of the load, w _g E {1,2,3,5}, three-level load, two-level load, one-level load and extra-level load respectively; τ _mg To characterize the probability of successful transfer of load g in the event of failure of the mth element τ _mg ∈[0,1]，τ _mg The larger the value is, the larger the success rate of transfer is represented;

(3) System outage risk index I _ENSR

The risk resistance of the power grid is taken into consideration of power supply safety, the risk resistance refers to the capability of the power grid to resist accident occurrence within a set time, the economic loss of a power grid operator is reduced, and the system outage risk index IENSR is provided for representing the risk resistance of the system due to different severity of consequences caused by load loss of different types of users in the system:

in the formula ：u_m Average outage duration (h/year) for element m in the system; f (F) _m Is the component unreliability, whereinw _g Indicating the importance of the load; τ _mg To characterize the probability of successful transfer of load g at the failure of the mth element; s is S _g The off-stream capacity for load point g;

c. economic class index: when the power grid runs, the power supply cost is low, the consumption of power generation energy is low, and the loss rate of the power grid is low;

(4) Grid loss rate L _n

Taking the line loss rate as the network loss condition of the evaluation power grid:

L _n = (amount of power supply-amount of electricity sold)/amount of power supply x 100% (2-26)

(5) Cost of system investment f _inv

The investment cost of the power system mainly considers the construction cost of the power transmission line:

wherein ,f_inv Representing investment costs c _i-j Price for single transmission line between nodes i and j, n _i-j The number of the transmission lines is newly built between the nodes i and j;

(6) Unit power network investment increasing sales electric quantity

The sales-increasing electric quantity corresponding to the unit power grid investment is represented, and the economic benefit of the power grid investment is reflected:

unit power grid investment increase sales power= (current year sales power-last year sales power)/last year power grid investment

(2-27)；

d. Environmental protection type index: environmental effects caused by a power grid connected with a distributed power supply and a high proportion of renewable energy sources include low carbon effects caused by saved carbon emission, renewable energy permeability and saved land;

(2) Permeability of renewable energy source

(2) Low carbon yield E _c

Under future-oriented power grid planning, the large-scale access of renewable energy sources changes the inherent energy structure of the regional power system, thereby generating low-carbon benefits E on the power generation side _C1 The method is calculated according to the following formula:

wherein ,ε_c,coal Carbon emission coefficient (kg/gce) for the main network; c _coal Coal consumption (gce/h) corresponding to unit electricity of the main network; p (P) _w,g,t Injecting power (MW) into a power grid to be planned for an external power grid within a period t; Δt is the duration of the period t,

while generating low carbon benefits E in terminal power utilization link _C2 ：

wherein ,the coal consumption of the coal-fired unit is reduced by 1 percentage point for each increase of the whole network load rate; Δζ _t For the proportion of the t-th stage load rate exceeding the expected level,

thus, there are:

E _C ＝E _C1 +E _C2 (2-31)；

step five: comprehensive evaluation method for electric power system

According to the evaluation index established in the third and fourth steps, two methods are selected to be applied to comprehensive decision and compared, one is the combination of the entropy weight method and the TOPSIS method, the other is the rank sum ratio method,

a. the entropy weight method is combined with the TOPSIS method

(1) Entropy weight method

In the comprehensive evaluation index system, since the effect, meaning and influence of each evaluation index are different, in order to put them in the same evaluation system model for evaluation, a reasonable weight ratio must be given to each index according to the importance degree of the index, the weight of each index directly relates to the contribution degree of the index to the overall evaluation target, therefore, the core and the key of the comprehensive evaluation are the weights for determining each comprehensive evaluation index,

The entropy weight method is an objective weight method, the weight value of the index is determined according to the information quantity transmitted by each evaluation index, the calculated values of different indexes are respectively processed according to the entropy weight method, and then the weight of each index is determined according to the entropy value calculation condition of different indexes, wherein the specific calculation process is as follows:

1) Establishing an evaluation index sample matrix

There are currently 3 grid planning schemes S to be evaluated ₁ ,S ₂ ,S ₃ The method comprises the steps of carrying out a first treatment on the surface of the The evaluation was performed using 23 evaluation indexes, A respectively ₁ ,A ₂ ,...A ₂₃ Setting the ith planning scheme S _i In the evaluation index A _j The value below is p _ij Establishing a 3×23-order index sample matrix P:

2) Establishing normalized dimensionless index

Because of the difference in order magnitude and dimension of each evaluation index in the sample matrix P, in order to facilitate evaluation, the evaluation needs to be normalized, namely, the types of index data are consistent, so that the evaluation is comparable, and the normalization processing method is as follows:

order the

Benefit index normalization formula:

a normalized formula of the cost index:

3) Determining weights of various indexes

The entropy of the evaluation index is obtained according to the definition of the entropy:

in the formula The entropy weight of the j-th index is:

the weight vector of each index is taken as follows: w= (w) ₁ ,w ₂ ,...,w ₂₃ ) ^T ；

(2) TOPSIS method

The evaluation was performed using the TOPSIS method, and the main steps were as follows:

1) Forming a decision matrix

The planning scheme set of the existing multi-index system participating in comprehensive evaluation is S= (S) ₁ ,S ₂ ,S ₃ ) The index set is a= (a) ₁ ,A ₂ ,...A ₂₃ ) Scheme S _i Lower index A _i Has a value of p _ij The decision matrix P formed is:

2) Normalizing decision matrix

Because each index has different dimensions, in order to eliminate the influence of the different dimensions on the comprehensive decision, the decision matrix is normalized to obtain a normalized decision matrix B= (B) _ij ) _m×n ：

Forming a weighted canonical matrix C= (C) according to the index weights _ij ) _m×n Each index weight vector is w:

c _ij ＝w _j ·b _ij (3-8)

3) Determination of the orthoideal solution C ⁺ And negative ideal solution C ^-

Let the ideal solution C ⁺ The j-th index value of (2)The j index value of the negative ideal solution +.>

For a positive ideal solution:

for negative ideal solutions:

4) Calculating the distance degree of each evaluation object from the positive ideal solution and the negative ideal solution

Scheme S _i Distance to ideal solutionThe method comprises the following steps:

scheme S _i Distance to negative ideal solutionThe method comprises the following steps:

5) Calculating comprehensive evaluation index of each scheme

According to f _i ⁺ Ranking the order of the quality of each evaluation scheme；

b. Entropy weight method and rank sum ratio method

The specific calculation process of the rank sum ratio method is as follows:

1) Rank of coding

Constructing n rows and m columns of matrixes according to m evaluation indexes of n evaluation objects to obtain the rank of each index evaluation object, and aiming at A ₁ ,A ₂ ,...A ₂₃ Index sample whose order statistic is A ₍₁₎ ,A ₍₂₎ ,...A ₍₂₃₎ If A _i ＝A _(k) Then k is called A _i Rank in the samples, denoted R _i For each i=1,..23, R _i Is the ith statistic, R ₁ ，...,R _n The method is characterized by comprising the steps of (1) summarizing rank statistics, ranking benefit indexes in order from small to large, ranking cost indexes in order from large to small, and averaging ranks when the same index data are the same, wherein the obtained rank matrix is recorded as R= (R) _ij ) _n×m ；

2) Calculating Rank Sum Ratio (RSR)

According to the mathematical expression of the rank and the ratio, combining the characteristics of comprehensive evaluation of a power grid planning scheme, and calculating RSR of the rank and the ratio method

The expression is:

wherein: n is the number of planning schemes to be evaluated, m is the number of evaluation indexes, R is the rank order of each group of indexes obtained according to the sorting of evaluation objects,

when the weights of the evaluation indexes are different, a Weighted Rank Sum Ratio (WRSR) is calculated, and the calculation formula is as follows:

wherein w_j As the weight of the j-th evaluation index,

3) Calculating probability units

The obtained WRSR values are arranged from small to large, and each group of frequency f is listed _i Calculating cumulative frequency Σfof each group _i Then calculate the cumulative frequency p _i ：

p _i ＝∑f _i /n (3-16)

Then p is _i Conversion to probability units Probit _i ，Probit _i P being normally distributed as standard _i The quantile u is added with 5;

4) Calculating a linear regression equation

Probability units Probit corresponding to cumulative frequency _i As an independent variable, in WRSR _i As a function variable, a linear regression equation is calculated:

WRSR＝a+b×Probit (3-17)

5) Step ordering

And calculating a corresponding WRSR estimated value according to the regression equation, and grading and sequencing the evaluation objects.

The further improvement is that: in the first step, the following principles are mainly used for constructing an evaluation index system: data measurability and comparability, evaluation index independence, practicality, pertinence, combination of quantitative analysis and qualitative analysis, objectivity and comprehensiveness principles.

The further improvement is that: in the second step, the basis for simplifying analysis is as follows: because the topological characteristic of the complex network of the power system is not reflected by the position of the node in the network and the condition of the connecting edge, the specific position, the size and the shape of the actual node are not needed to be considered, meanwhile, the curve and the straight of the actual edge and the actual geographic distance are ignored, a topological structure model of the power grid is built based on the curve and straight and the actual geographic distance, parameters describing the topological structure of the power grid are selected as indexes, and the current small world model is defined as an undirected, unauthorized, simple and sparse connected graph and the actual condition of data acquisition is considered.

The further improvement is that: in the fourth step, the following indexes are selected to reflect the reliability, vulnerability, safety, economical efficiency and environmental protection of the operation of the power grid.

The further improvement is that: in the fifth step, the basis for selecting two methods to be applied to the comprehensive decision and comparing the two methods is as follows: since the significance and importance of the respective indices are different, the weights of the respective indices are also different in the evaluation process.

The beneficial effects of the invention are as follows: the invention further learns and researches the theoretical basis of a complex network and the complex network characteristics of the power grid, judges the system association of nodes and the network from the power grid structure by utilizing the complex network theory, analyzes the power grid characteristics by utilizing the element characteristics of the power system, explores the relation between the power grid structure and the performance, realizes the combination of the whole and the individual, constructs a comprehensive evaluation index system of a comprehensive and effective power grid planning scheme, determines the calculation method and the specification requirement of each evaluation index, objectively gives each index weight value and evaluates the power grid by combining a multi-objective decision method of the power grid planning scheme evaluation;

the method selects two comprehensive evaluation methods of combining the entropy weight method with the TOPSIS method and combining the entropy weight method with the rank and ratio method to evaluate the power grid planning schemes, and the obtained schemes have consistent relative advantages and disadvantages, but the comprehensive evaluation advantages and disadvantages of the schemes have differences due to the difference of the calculation emphasis points of the TOPSIS method and the rank and ratio method, and meanwhile, the comprehensive evaluation method combining the entropy weight method with the rank and ratio method is more applicable and has more statistical significance.

Drawings

FIG. 1 is a schematic diagram of a comprehensive evaluation index system of a power system according to the present invention;

FIG. 2 is a schematic diagram of a multi-index system comprehensive evaluation model of the invention;

FIG. 3 is a schematic diagram of application scheme 1 of the present invention;

FIG. 4 is a schematic diagram of application 1 of the present invention;

fig. 5 is a schematic diagram of application scheme 2 of the present invention.

FIG. 6 is a schematic diagram of application scheme 2 of the present invention

FIG. 7 is a schematic diagram of application scheme 3 of the present invention

Fig. 8 is a schematic diagram of application scheme 3 of the present invention.

Detailed Description

The present invention will be further described with reference to the following embodiments in order to make the technical means, the achievement of the objects and the effects of the present invention easy to understand.

According to fig. 1 and 2, the embodiment provides a method for evaluating the structural form of a power transmission network, which specifically comprises the following steps:

The basic principle of comprehensive evaluation index selection of the power system is determined, on one hand, each characteristic of the power grid is to be truly reflected comprehensively and objectively, including topological characteristics and operation characteristics of the power grid structure, the practicability and operability of an evaluation index system are ensured, and any important index is not omitted; on the other hand, the actual condition of the power grid, the problems of difficulty in acquisition, calculation difficulty and the like of index data are considered, the authenticity of measurement is ensured, the problem of repeated index calculation is avoided, and the indexes are required to have internal connection and are consistent with the evaluation purpose so as to jointly reflect the characteristics of the power grid;

The method is characterized in that a complex network theory is applied to analyze the structure of a power grid, because the topological characteristic of the complex network of the power system is not represented by the position of a node in the network and the condition of a connecting edge, the specific position, the size and the shape of an actual node are not needed to be considered, the curve and the straight of the actual edge and the actual geographic distance are ignored, a topological structure model of the power grid is built based on the curve and the straight and the actual geographic distance, parameters describing the topological structure of the power grid are selected as indexes, the current small world model is defined as an undirected, unauthorized, simple and sparse connected graph, and the actual condition of data acquisition is considered, so that the simplified analysis is carried out when the topological structure of the actual power grid is described, and a simplification principle is made;

step three: power grid structure index based on complex network theory

(1) Node degree k

(2) Node degree distribution P (k)

(3) Node degree correlation k _nn

The degree distribution completely determines the statistical properties of the uncorrelated network, whereas a large number of real network networks are correlated, there is interdependence between nodes of different degrees, in the sense that the probability that a node of degree k is connected to another node of degree k' is related to k, in which case a conditional probability P is introduced _c (k '|k), defined as the probability of pointing from a node of degree k to a node of degree k',

(4) Network diameter D

(5) Characteristic path length L

In the topology of a network, the characteristic path length is also called as the average path length of the network, which is defined as the average value of the distance between any two nodes in the network, and is a method for measuring the quality or information transmission efficiency in a network;

(6) Medium number b

The betweenness is a standard index for measuring the centrality of a node in a network, the importance information of the node in path planning is given by calculating the shortest path number passing through one node, the energy or information between two nodes in the network is assumed to be along the shortest path between the nodes in the propagation process, the role played by the node or the edge in the network propagation process is characterized according to the shortest path number passing through the node or the edge, the contribution is larger when the number is larger, the importance is correspondingly larger,

(7) Clustering coefficient C

The clustering coefficient is a parameter describing the aggregation of a network, and is used for measuring the aggregation and discrete degree of network nodes, and the assumption is made that nodes i and k _i The nodes are directly connected, then for an undirected network, this k _i The maximum number of edges that may exist between adjacent nodes isAnd the number of the actually existing edges is E _i The clustering coefficient of the node i is defined as the actual edge number E _i And the number of total edges which may be present +.>Is a ratio of (2);

(8) Efficiency E

The summation in the formula (2-8) is limited to the node pair belonging to the maximum connection, taking into account the harmonic average value of the geodesic (i.e. the simple path with the least number of edges between two points) and introducing the definition of network efficiency;

(9) Fault tolerance probability f _c

In studying the tolerance of the grid to large cascading errors and attacks, the common approach is to find the relation between node deletion (without reassigning the network) and global connectivity (the existence and relative size of the connection after deleting the nodes), the traditional analysis method is based on a penetration theory, in the sense that the network penetration below a critical probability is related to the existence or non-existence of a certain number of edges, its study is mapped to the standard penetration problem of the network facing errors and attacks, and according to the complex network theory, there is one large connection in the network on condition that;

step four: other indexes

The safety and reliability problems during the operation of the power grid and the access of high-proportion clean energy and a distributed generation technology are considered, so that the power grid faces the problem of uncertainty in the operation process, and the following indexes are selected to reflect the reliability, vulnerability, safety, economy and environmental protection of the operation of the power grid so as to realize comprehensive evaluation of the whole aspects of the power grid:

(1) Line load factor

The index reflects the utilization rate of 220kV lines of a power transmission network and is specifically divided into a maximum load rate, a minimum load rate and an average load rate of the lines;

(2) Ratio of capacitance Rs

Refers to the ratio of the total capacity (kVA) of the power transformation equipment to the corresponding total load (kW) in a specified power supply area, the capacity-to-load ratio is estimated by the following method,

(3) System power supply reliability I _ASA

The system power supply reliability is defined as the ratio of the total number of hours of the system without power failure to the total number of power supply hours required to be satisfied within a certain prescribed time,

(4) Average power outage duration I of system _SAID

The average power outage duration of the system is the total power outage time suffered by each user in the system in a certain set time;

(1) Average power failure frequency I of system _SAIF

The average power outage frequency of the system is the number of continuous power outages which the power grid is averagely subjected to in a certain set time,

(2) System overall security index I _IS

The power supply safety refers to the capability of a system for transferring loads under fault conditions, and the integral safety coefficient I of the system is proposed according to the definition of an N-1 safety criterion in the guidance of a planning design technology of a power distribution network _IS The system quantitatively evaluates the overall power supply safety level of the active power distribution network by calculating the transfer rates of loads with different importance degrees under the condition of 'N-1' of the system;

(3) System outage risk index I _ENSR

The risk resistance of the power grid is brought into the consideration range of power supply safety, the risk resistance refers to the capability of the power grid for resisting accident occurrence within a set time, the economic loss of a power grid operator is reduced, and the severity of the consequences caused by the loss of load of different types of users in the system is different, so that a system outage risk index IENSR is provided for representing the risk resistance of the system;

(7) Loss rate of power grid network

(8) Cost of system investment f _inv ；

(9) Unit power network investment increasing sales electric quantity

(2-27)；

(3) Permeability of renewable energy source

(2) Low carbon yield E _c

Under future-oriented power grid planning, the large-scale access of renewable energy sources changes the inherent energy structure of the regional power system, thereby generating low-carbon benefits E on the power generation side _C1 ；

Step five: comprehensive evaluation method for electric power system

According to the evaluation indexes established in the third step and the fourth step, because the significance and the importance degree of each index are different, the weights of each index are different in the evaluation process, two methods are selected to be applied to comprehensive decision and are compared, one method is the combination of an entropy weight method and a TOPSIS method, the other method is a rank sum ratio method,

a. the entropy weight method is combined with the TOPSIS method

(1) Entropy weight method

1) Establishing an evaluation index sample matrix

2) Establishing normalized dimensionless index

Because of the difference in order magnitude and dimension of each evaluation index in the sample matrix P, in order to facilitate evaluation, the evaluation needs to be normalized, namely the types of index data are consistent, so that the evaluation is comparable;

3) Determining the weight of each index;

(2) TOPSIS method

1) Forming a decision matrix

The planning scheme set of the existing multi-index system participating in comprehensive evaluation is S= (S) ₁ ,S ₂ ,S ₃ ) The index set is a= (a) ₁ ,A ₂ ,...A ₂₃ ) Scheme S _i Lower index A _i Has a value of p _ij The decision matrix P is formed;

2) Normalizing decision matrix

Because each index has different dimensions, in order to eliminate the influence of the different dimensions on the comprehensive decision, the decision matrix is normalized to obtain a normalized decision matrix B= (B) _ij ) _m×n ；

Let the ideal solution C ⁺ The j-th index value of (2)The j index value of the negative ideal solution +.>/>

4) Calculating the distance degree between each evaluation object and the positive ideal solution and the negative ideal solution;

5) Calculating the comprehensive evaluation index of each scheme;

b. entropy weight method and rank sum ratio method

The specific calculation process of the rank sum ratio method is as follows:

1) Rank of coding

According to n scoresConstructing n rows and m columns of matrixes by using m evaluation indexes of the price object to obtain the rank of each index evaluation object, wherein the rank of each index evaluation object is equal to that of A ₁ ,A ₂ ,...A ₂₃ Index sample whose order statistic is A ₍₁₎ ,A ₍₂₎ ,...A ₍₂₃₎ If A _i ＝A _(k) Then k is called A _i Rank in the samples, denoted R _i For each i=1,..23, R _i Is the ith statistic, R ₁ ，...,R _n The method is characterized by comprising the steps of (1) summarizing rank statistics, ranking benefit indexes in order from small to large, ranking cost indexes in order from large to small, and averaging ranks when the same index data are the same, wherein the obtained rank matrix is recorded as R= (R) _ij ) _n×m ；

2) Calculating Rank Sum Ratio (RSR)

According to the mathematical expression of the rank and ratio, combining the characteristic of comprehensive evaluation of a power grid planning scheme, and calculating RSR of a rank and ratio method;

3) Calculating probability units

The obtained WRSR values are arranged from small to large, and each group of frequency f is listed _i Calculating cumulative frequency Σfof each group _i Then calculate the cumulative frequency p _i ；

4) Calculating a linear regression equation

Probability units Probit corresponding to cumulative frequency _i As an independent variable, in WRSR _i Is a dependent variable;

5) Step ordering

Evaluation application

Evaluation index system and evaluation for verifying power system planning scheme established in advance

Basic data and parameters

The research area is a new urban area, mainly comprises industrial and commercial users, is expected to plan the annual maximum load of 120MW and the annual power consumption of 1.27 multiplied by 108MWh, and comprises 1 substation of 220/110kV, 92 planned lines to be selected and 22 load nodes.

Aiming at the electricity utilization characteristics and the demands of the region, 3 power grid planning and construction schemes are planned by a planning department according to early-stage technical and economic analysis. Each programming scheme has 22 load points, several circuit breakers, fuses and disconnectors. The parameter information of each plan is shown in table 1.

Table 1 parameter information for each plan

The reliability parameters of each element of the planned power grid are shown in table 2.

TABLE 2 element reliability parameters

Evaluation index calculation

Power grid structure index

1. Node degree, degree distribution, degree correlation

1) Grid planning scheme 1, see figures 3, 4

2) Grid planning scheme 2, see fig. 5, 6

3) Grid planning scheme 3, see FIGS. 7, 8

The node degree, the degree distribution map and the degree accumulation distribution map of each scheme are respectively obtained through calculation and analysis of node degree and degree distribution of three schemes, the calculation result can show that the scale-free network degree distribution based on the small world model is unbalanced, most of the node degrees are concentrated near 1 and 2, only the degree of a few nodes reaches 5, the structure is unstable, and the result accords with the characteristics of the scale-free network. The average degree of each scheme is close to 2, that is, each node is directly connected with other 2 nodes. In a single logarithmic coordinate, the node degree cumulative distribution of each scheme presents a linear characteristic, which can be fitted by adopting an exponential function and calculated according to the formula (2-4). For an exponential distribution function, it is its scale index. The smaller it is, the more uneven it is its distribution. From the above results, it can be seen that the node average degree is highest in scheme 1, the node degree distribution is relatively most uniform, scheme 3 times, and scheme 2 finally. From the analysis of the degree correlations of each plan, the network of plans is degree-degree negative correlated, and nodes with large degree values are more prone to be connected with nodes with relatively smaller degree values.

The invention further learns and researches the theoretical basis of a complex network and the complex network characteristics of the power grid, judges the system relevance of nodes and the network from the power grid structure by utilizing the complex network theory, analyzes the power grid characteristics by utilizing the element characteristics of the power system, explores the relation between the power grid structure and the performance, realizes the combination of the whole and the individual, constructs a comprehensive evaluation index system of a comprehensive and effective power grid planning scheme, defines the calculation method and the specification requirement of each evaluation index, objectively gives each index weight value and evaluates the power grid by combining a multi-objective decision method of the power grid planning scheme evaluation;

The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims

1. A power transmission network structure form evaluation method is characterized in that: the method comprises the following steps:

The characteristics of the power grid are reflected by utilizing the topological characteristics and the operation characteristics of the power grid and the availability and calculation difficulty of index data;

(1) The main wiring structures of the power plant and the transformer substation are not considered, and the power supply and the load connected to the generator and the low-voltage side bus are abstracted to be a certain active power injected into the corresponding bus;

(5) The parallel capacitor branches are not considered, and the transmission lines which are combined with the same rod and are combined to form a simple diagram;

step three: power grid structure index based on complex network theory

According to the simplified rule of the second step, a specific network is abstracted into an undirected and unauthorized network g= (V, E), wherein V represents a set of all nodes in the network, E represents a set of all edges, the number of nodes is n, the number of edges is l, and the network structure characteristics are described according to the definition in the classical complex network theory:

(1) Node degree k

In a complex network, the degree k of node i _i Is defined as being connected with the nodeThe number of all edges i that are connected,

the greater the degree of a node indicates the greater the importance of the node in the overall network, each node in the network having its own degree, the degree k for all nodes i _i Summing and averaging to obtain the node average degree of the whole network, and recording as<k>，

wherein ：k_i The degree for node i, n is the total node number,

(2) Node degree distribution P (k)

and carrying out form characterization of cumulative distribution on the distribution condition of the node degree, wherein the formula is as follows:

(3) Node degree correlation k _nn

One degree isThe probability that the node of k is connected to another node with the degree of k' is related to k, and the conditional probability P is introduced _c (k '|k), defined as the probability of pointing from a node of degree k to a node of degree k',

P _c (k'|k)＝P _c (k')≈k'P(k') (2-5)

(4) Network diameter D

D＝max d _ij (2-7)

(5) Characteristic path length L

In the topology of a network, the characteristic path length is used to define an average value of the distance between any two nodes in the network, said average value being used to measure the quality or information transmission efficiency in a network,

wherein: n is the total node number, d _ij For the number of edges traversed by the shortest path between node i and node j, fromFrom the global perspective, the characteristic path length is used for calculating the shortest distance between every two paired nodes in the complex network;

(6) Medium number b

The betweenness is a standard index for measuring the centrality of the nodes in the network, importance information of the nodes in path planning is given by calculating the shortest path number passing through one node, the energy or information between two nodes in the network is assumed to be along the shortest path between the nodes in the propagation process, the role played by the nodes or edges in the network propagation process is characterized according to the shortest path number passing through the nodes or edges, the contribution is larger as the number is larger, and the importance is correspondingly larger:

(7) Clustering coefficient C

The clustering coefficient is a parameter describing the aggregation of a network and is used for measuring the aggregation and discrete degree of network nodes, and the nodes i and k are assumed to be _i The nodes are directly connected, then for an undirected network, this k _i The maximum number of edges that may exist between adjacent nodes isAnd the number of the actually existing edges is E _i The clustering coefficient of the node i is defined as the actual edge number E _i And the number of total edges which may be present +.>Ratio of (3):

wherein ：k_i For the number of nodes adjacent to node i, E _i For the actual number of edges that node i connects with neighboring nodes, from a geometric perspective it can be defined as:

(8) Efficiency E

Limiting the summation in equations (2-8) to only the node pair belonging to the largest connection, taking into account the harmonic mean of the geodesic, and introducing a definition of the network efficiency:

Wherein: n is the total node number, and the edge number d of the ground wire is measured _ij The reciprocal of the distance between two nodes i and j is the efficiency between the two nodes, and the efficiency of all node pairs in the network is averaged to obtain the global efficiency of the whole network;

(9) Fault tolerance probability f _c

According to the complex network theory, the conditions of the network connection part are as follows:

for a randomly deleted node, its fault tolerance probability is defined as:

wherein: gamma is the node degree distribution index;

step four: other indexes

a. reliability class index: the capacity of the power system for transmitting power from a power source end to a power receiving end according to quality and quantity standards under specified conditions so as to meet power supply load power and electric quantity requirements is measured through quantitative reliability indexes;

(1) Line load factor

220kv line maximum load rate = line annual maximum active power/line thermal stability limit (2-17);

220kv line minimum load rate = line annual minimum active power/line thermal stability limit (2-18);

(2) Ratio of capacitance Rs

The ratio of the total capacity of the power transformation equipment in a specified power supply area to the corresponding total load is estimated by adopting the following method:

wherein Sei is the main transformer capacity of the voltage class transformer station i, pmax is the full-network maximum predicted load at the voltage class,

(3) System power supply reliability I _ASA

wherein: g is a load node; omega shape _F A set of locations for all types of load nodes in the system;the number of users for node g; u (u) _g For the average outage duration at load point g,

(4) Average power outage duration I of system _SAID

wherein ：u_g Average outage duration for load point g;the number of users for node g;

(1) Average power failure frequency I of system _SAIF

wherein ：λ_g Annual fault outage frequency for load point g;the number of users who are the node g,

(2) System overall security index I _IS

The power supply safety refers to the capability of the system for transferring load under the fault condition, and the integral safety coefficient I of the system is provided _IS The system quantitatively evaluates the overall power supply safety level of the active power distribution network by calculating the transfer rates of loads with different importance degrees under the condition of the system N-1:

wherein: m is an mth element in the power system which may fail; omega shape _m A set of load nodes that are affected by the failure of the mth element; EN is the total number of elements in the power system that may fail; w (w) _g Indicating the importance level of the load, w _g E {1,2,3,5}, three-level load, two-level load, one-level load and extra-level load respectively; τ _mg To characterize the probability of successful transfer of load g in the event of failure of the mth element τ _mg ∈[0,1]，τ _mg The larger the value is, the larger the success rate of transfer is represented;

(3) System outage risk index I _ENSR

System outage risk index IENSR to characterize the anti-risk capability of the system:

in the formula ：u_m Average outage duration for element m in the system; f (F) _m Is the component unreliability, whereinw _g Indicating the importance of the load; τ _mg To characterize the probability of successful transfer of load g at the failure of the mth element; s is S _g The off-stream capacity for load point g;

c. economic class index: when the power grid operates, the power supply cost is low, the power generation energy consumption is low, and the grid loss rate is low;

(1) Grid loss rate L _n

(2) Cost of system investment f _inv

wherein ,f_inv Representing investment costs c _i-j For the cost of a single transmission line between the nodes i and j, n _i-j The number of the transmission lines is newly built between the nodes i and j;

(3) Unit power network investment increasing sales electric quantity

Unit power grid investment increase sales power= (current year sales power-last year sales power)/last year power grid investment (2-27);

d. environmental protection type index: environmental effects caused by a power grid connected with a distributed power supply and a high proportion of renewable energy sources include low carbon effects caused by saved carbon emission, renewable energy source permeability and saved land;

(1) Permeability of renewable energy source

(2) Low carbon yield E _c

The method is characterized by comprising the following steps:

wherein ,ε_c,coal Carbon emission coefficient of the main network; c _coal Coal consumption corresponding to the unit electric quantity of the main network; p (P) _w,g,t Injecting power to a power grid to be planned for an external power grid in a period t; delta t is the duration of time t, and low carbon benefits E are generated in the terminal power utilization link _C2 ：

wherein ,the coal consumption of the coal-fired unit is reduced by 1 percentage point for each increase of the whole network load rate; Δζ _t The ratio of the load rate in the t-th stage to exceed the expected level;

thus, there are:

E _C ＝E _C1 +E _C2 (2-31)；

step five: comprehensive evaluation method for electric power system

a. the entropy weight method is combined with the TOPSIS method

(1) Entropy weight method

Reasonable weight duty ratio is given to each index according to the importance degree of each index, the contribution degree of the overall evaluation target is obtained based on the weight of each index, the core and the key of the comprehensive evaluation are the weights for determining each comprehensive evaluation index,

the specific calculation process is as follows:

1) Establishing an evaluation index sample matrix

2) Establishing normalized dimensionless index

The normalization processing method comprises the following steps:

order the

Benefit index normalization formula:

a normalized formula of the cost index:

3) Determining weights of various indexes

in the formula The entropy weight of the j-th index is:

(2) TOPSIS method

1) Forming a decision matrix

2) Normalizing decision matrix

Normalized decision matrix b= (B) _ij ) _m×n ：

Forming a weighted canonical matrix according to each index weightC＝(c _ij ) _m×n Each index weight vector is w:

c _ij ＝w _j ·b _ij (3-8)

For a positive ideal solution:

for negative ideal solutions:

4) Calculating the distance degree scheme S of each evaluation object from positive ideal solution and negative ideal solution _i Distance to ideal solutionThe method comprises the following steps:

5) Calculating comprehensive evaluation index of each scheme

According to f _i ⁺ The size of each evaluation scheme is arranged in order of quality;

b. entropy weight method and rank sum ratio method

The specific calculation process of the rank sum ratio method is as follows:

1) Rank of coding

2) Calculating rank sum ratio

According to the mathematical expression of the rank and the ratio, and combining the characteristics of comprehensive evaluation of a power grid planning scheme, the calculation expression of the rank and the ratio method is as follows:

wherein: n is the number of planning schemes to be evaluated, m is the number of evaluation indexes, R is the rank order of each group of indexes obtained according to the sorting of the evaluation objects,

when the weights of the evaluation indexes are different, calculating a weighted rank sum ratio WRSR, wherein the calculation formula is as follows:

wherein w_j As the weight of the j-th evaluation index,

3) Calculating probability units

The obtained WRSR values are arranged from small to large, and each group of frequency f is listed _i Calculating cumulative frequency Σf of each group _i Then calculate the cumulative frequency p _i ：

p _i ＝Σf _i /n (3-16)

4) Calculating a linear regression equation

WRSR＝a+b×Probit (3-17)

5) Step ordering

And calculating a corresponding WRSR estimated value based on the obtained regression equation, and grading and sequencing the evaluation objects.