CN105046574A - Black-start scheme evaluation method - Google Patents

Abstract

The invention discloses a black-start scheme evaluation method, which comprises the steps of asking L experts to give a ranking vector for all evaluation indexes used for black-start scheme evaluation and figuring out a subjective based on the weight ordered binary comparison method; figuring out an objective weight based on the method of variation coefficient, according to an initial decision matrix formed by the values of all evaluation indexes; figuring out a comprehensive weight based on the vector similarity theory; converting the initial decision matrix in the form of real values into a decision matrix in the form of a Vague set, and converting a weight vector into a vector in the same form with the obtained decision matrix; and ranking all schemes based on the PROMTTHEE method of the Vague set to obtain a ranking sequence. According to the technical scheme of the invention, the objective difference of data and the subjective preference of experts are well combined, and then a more reasonable index weight is given. Meanwhile, the priority relationship of quantization schemes can be quantized more accurately based on the PROMTTHEE method, so that the schemes can be completely ranked.

Description

A kind of method of black-start scheme assessment

Technical field

The invention belongs to field of power, particularly relate to the method for a kind of black-start scheme assessment.

Background technology

Power system blackstart refers to that whole network system is because of after fault stoppage in transit, by there is self-startup ability also referred to as the startup with black start-up ability unit in system, drive the unit of non self starting, and expand system power supply scope gradually, finally realize the recovery of whole system.Black-start scheme is generally made in advance by dispatcher, uses when occurring that the whole network has a power failure in order to system.For specific system, may there is numerous feasible programs, and may there is huge difference for the combined action of system recovery procedure in different schemes, how to assess numerous schemes, thus the sequence of implementation is with preferred, it is one of important topic of black starting-up research always.

" China Power " 02 phase in 2013 puts into collection submission-build the purple person of outstanding talent of young tiger Ai Xinlan Chinese blue-propose choose reasonable black-start scheme based on the black-start scheme assessment Sha Fengyang improving DEA Model, powers, reduces loss of outage and have vital meaning smooth recovery system.To the deficiency of schemes ranking, a kind of black-start scheme appraisal procedure based on improving DEA Model can not be proposed for traditional data envelope analytical model.On the basis of analysis conventional DEA Model, introduce optimum and differ from 2 virtual schemes most, setting up the DEA Model after improving, obtain one group of common weight, calculate the efficiency index of each scheme according to this, realize the sequence of black-start scheme.For the case of actual electric network black starting-up, adopt institute's extracting method and additive method to compare analysis, result shows that institute's extracting method can provide correct black-start scheme sequence, improves the ga s safety degree of assessment result simultaneously.

Electrics and electronics engineering institute of North China Electric Power University--Chinese Higher school Power System and its Automation specialty the 27 Annual Conference collection of thesis, black starting-up after Chinese Higher school Power System and its Automation specialty the 27 Annual Conference proposes electric system full cut-off electricity recovers to be a very important problem, black-start scheme assessment works out black-start scheme to auxiliary dispatching personnel, realize the fast quick-recovery after system full cut-off and there is vital role, propose a kind of black-start scheme appraisal procedure combined based on group decision and analytical hierarchy process (AHP), Analytic Hierarchy Process Model is set up by extracting the important indicator affecting black starting-up, and carry out group decision in conjunction with Weight of Expert and obtain comprehensive evaluation value.The method makes full use of the feature of group decision and AHP method, reduces the impact of individual preference on evaluation result better.The application example of Southern Hebei Network demonstrates the deficiency that the method compensate for black starting-up individual decision making method to a certain extent, can be management and running personnel and works out the decision references that black-start scheme provides science more.

The assessment of black-start scheme is a Multi-attribute synthetic evaluation problem, and researchist conducts in-depth research this problem from different perspectives, proposes numerous Efficient Evaluation method.About black-start scheme appraisal procedure roughly can be divided into Deterministic Methods and the large class of fuzzy class methods two in existing document.Conventional Deterministic Methods has levels analytic approach AHP, DEA DEA and TOPSIS etc.; The thought of fuzzy class methods data obfuscation is then combined with methods such as deterministic AHP or DEA by use blur tool.

Summary of the invention

A kind of method that the object of the present invention is to provide black-start scheme to assess, is intended to solve black-start scheme when there is more feasible program, cannot confirms the priority of scheme, reduce network system and recover efficiency, affect the technical matters of user's use.

The present invention realizes like this, use orderly binary comparison method supervisor's weight of trying to achieve and the objective weight utilizing VC Method to try to achieve are combined by vectorial similarity theory and obtain comprehensive weight by a kind of method of black-start scheme assessment, then, carry out scheme evaluation by the PROMETHEE method based on Vague collection, make full use of subjective and objective information and Vague collection treats the characteristic of things from the pros and cons; Because the desired value in original scheme can be processed into fuzzy data by PROMETHEE method, do not need to check that the validity of data is so can realize the sequence completely of any scheme, in addition the objective difference of data and the subjective preferences of expert combine by the present invention well, than single use objective weight or subjective weight more reasonable; Utilizing Vague collection to consider a problem from the pros and cons makes ranking results have more cogency.

Concrete steps comprise:

Step one, L position expert please provide the ordering vector of each evaluation index of black starting-up assessment, utilize orderly binary comparison method to obtain subjective weight;

The initial decision matrix that step 2, basis are made up of the value of each evaluation index utilizes VC Method to ask for objective weight;

Step 3, vector similarity theory is utilized to try to achieve comprehensive weight;

Step 4, the initial decision matrix conversion of real number form is become the decision matrix of Vague collection form, and weight vectors is also changed into this form;

Step 5, utilize the PROMETHEE method based on Vague collection to sort to each scheme, obtain collating sequence.

Further, described subjective weight is tried to achieve by orderly binary comparison method, and overcome and may run into consistency check unpassable situation when AHP class methods determine subjective weight and the shortcoming having to repeatedly revise comparator matrix, concrete grammar is:

Step one, determine evaluation object and expert collection: set X as investigate entire objects collection, be designated as X={x ₁, x ₂... x _nbe that the expert participating in agriculture products weight integrates as P={p ₁, p ₂... p _l;

Step 2, application set value process of iteration are the sequence of each index: the L position expert chosen, giving every Weight of Expert is { λ ₁, λ ₂... λ _l, allow every expert sort to index according to significance level in index set, the index ordered set of kth (1≤k≤L) position selection of specialists is X _k=(x ₃, x ₅, x ₁, x _n..., x _n-1), x in formula ₃be positioned at X _kfirst position, namely represent x ₃think most important at expert k, according to each index at X _kin position give this index score respectively, at X _kmiddle x ₃corresponding must be divided into N, x ₅corresponding must be divided into N-1, by that analogy, and x _n-1corresponding must be divided into 1;

If μ _i,kthe score that (1≤i≤N, 1≤k≤L) obtains at expert k place for index i, order as comprehensive grading, 1≤i≤N in formula, according to g _idescending new sequence is carried out to evaluation index, $X^{*}=\{x_1^{*},x_2^{*},...,x_N^{*}\};$

Step 3, respectively acquisition comparator matrix is compared to adjacent evaluation index by L position expert;

By the significance level of L position expert by the relatively rear index of last index in the adjacent index of contrast, the two no less important value is 1.0; The former is important a little, value 1.2; The former is obviously important, value 1.4; The former is strongly important, value 1.6; The former is extremely important, value 1.8; Provide evaluation interval, interval endpoint value gets adjacent r _knumerical value, its relative importance is between both two r _kbetween the significance level that numerical value is corresponding;

Step 4, interval is converted into point value by following formula:

$r_i=\frac{\frac{1}{2}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_i(r_{\mathrm{ij}}^{\′\′2}-r_{\mathrm{ij}}^{\′2})}{\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_i(r_{\mathrm{ij}}^{\′\′}-r_{\mathrm{ij}}^{\′})}$

In formula, r _ij' for expert i is to the lower bound in the Evaluations matrix of index j, r _ij" be the upper bound in Evaluations matrix, j=1,2 ..., n-1;

Step 5, determine the weight of evaluation index: compare because N number of index is adjacent, N-1 fiducial value can be obtained:

In formula: r ₁the implication of representative be first index after rearrangement relative to the significance level of second index, can with the ratio of the absolute importance degree of first index and second index set forth,

$\begin{array}{c}{r}_1=\frac{x_1^{**}}{x_2^{**}},r_2=\frac{x_2^{**}}{x_3^{**}},\\ r_3=\frac{x_3^{**}}{x_4^{**}},...,r_{N-1}=\frac{x_{N-1}^{**}}{x_N^{**}}\end{array}$

comprehensive weight be:

$w_N^{*}={(1+\underset{k=1}{\overset{N-1}{\mathrm{\Σ}}}\underset{i=k}{\overset{N-1}{\mathrm{\Π}}}{r}_i)}^{-1}$

The weight of other indexs is:

$w_i^{*}=r_i{w}_{i+1}^{*}.$

Further, described objective weight is tried to achieve by VC Method, and make use of the more succinct and feature that accuracy is higher of VC Method computation process, concrete grammar is:

Step one, establish certain assessment indicator system to have m evaluation index, carried out system evaluation and data sampling to n evaluation object, so raw data Evaluations matrix can be expressed as matrix X:

$X={\left(x_{\mathrm{ij}}\right)}_{n\×m}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{21}& ...& x_{2m}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n1}& ...& x_{\mathrm{nm}}\end{array}\right]$

Step 2, according to the average of each index of calculated with actual values of each object of classification index and standard deviation:

Wherein the average of a jth index and standard deviation are respectively

$\begin{array}{c}{\stackrel{\‾}{x}}_j=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}\\ S_j=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_{\mathrm{ij}}-\stackrel{\‾}{x_j})}\end{array}$

J=1 in formula, 2 ... m;

Step 3, calculate the coefficient of variation of each index:

$B_j=S_j/\stackrel{\‾}{x_j};$

Step 4, determine the weight of each index:

First the index coefficient of variation is normalized, then the weight sets V of index is obtained _j={ ν ₁, ν ₂... ν _m, wherein

Further, vector similarity theory is utilized to try to achieve comprehensive weight; If a kind of vector of enabling legislation gained and the vectorial similarity degree of other enabling legislation gained large, then illustrate majority decision person hold close subjective preferences or the weight ratio that obtained by former data processing more reliable and more stable, these weight vectors should obtain larger proportion in right vector; Therefore, can by meeting being principle to the maximum with the similarity of subjective and objective weight and asking for comprehensive weight of comprehensive weight:

(1) calculating of vector similarity

For any two N dimensional vector X=(x ₁, x ₂..., x _n), Y=(y ₁, y ₂... y _n), its inner product is expressed as:

[X,Y]＝x ₁y ₁+x ₂y ₂+…x _ny _n

The norm of vector is expressed as:

$\left|\right|X\left|\right|=\sqrt{[X,X]}=\sqrt{x_1^2+x_2^2+...+x_n^2}$

The angle of vector is expressed as:

Then two vectorial length similarity α are:

$\mathrm{\α}(X,Y)=\left\{\begin{array}{cc}1-\left|\frac{\left|\right|X\left|\right|-\left|\right|Y\left|\right|}{\left|\right|X\left|\right|}\right|& \left|\right|Y\left|\right|\≤2\left|\right|X\left|\right|\\ 0& \left|\right|Y\left|\right|>2\left|\right|X\left|\right|\end{array}\right.$

Two vectorial direction similarity similarity β are:

Two vectorial similarity similarity γ are:

γ(X，Y)＝αβ

(2) based on vector similarity Evaluation formula

Suppose total N number of evaluation index, it is that then wherein a kth weight vectors is that decision maker obtains L group weight vectors altogether by objective and subjective synthetic approach:

W _k＝(w _k1,w _k2,…,w _kN),k＝1,2,…,L

Subjective and objective weight employing combination coefficient is tried to achieve summation weight is:

W ^C＝θ ₁W ₁+θ ₂W ₂+…θ _LW _L

W in formula ^cfor comprehensive weight vector, θ ₁, θ ₂... θ _lfor combination coefficient;

Arbitrary weight vectors W _kwith the total similarity of other vectors be:

γ＝(γ ₁,γ ₂,…,γ _L)

Wherein ${\mathrm{\γ}}_k=\underset{i=1,i\≠k}{\overset{L}{\mathrm{\Σ}}}\mathrm{\γ}(W_i,W_k),$ Because set weight coefficient vector as:

θ＝(θ ₁,θ ₂,…θ _L)，

Wherein, ${\mathrm{\θ}}_k=\frac{\underset{i=1,i\≠k}{\overset{L}{\mathrm{\Σ}}}\mathrm{\γ}(W_i,W_k)}{\underset{k=1}{\overset{L}{\mathrm{\Σ}}}\underset{i=1,i\≠k}{\overset{L}{\mathrm{\Σ}}}\mathrm{\γ}(W_i,W_k)}.$

Further, obtain the comprehensive weight of Vague collection form, this kind of weight describes the importance relation between each index from the pros and cons, concrete grammar be:

Suppose have the ordering vector of L position expert to 6 indexs to be respectively:

γ _i(…x ₁…x ₆…)i＝(1,2,…L)

Subjective weight vectors is:

ω′＝(ω ₁′,ω ₂′,ω ₃′,ω ₄′,ω ₅′,ω ₆′)

Utilize initial decision matrix D and try to achieve objective weight based on the objective weight acquiring method of VC Method and be:

ω″＝(ω ₁″,ω ₂″,ω ₃″,ω ₄″,ω ₅″,ω ₆″)

Ask and make vectorial ω ' and ω " the maximum combining coefficient vector θ of similarity=(θ ', θ "), wherein:

$\left\{\begin{array}{c}{\mathrm{\θ}}^{\′}=\frac{\mathrm{\γ}({\mathrm{\ω}}^{\′\′},{\mathrm{\ω}}^{\′})}{\mathrm{\γ}({\mathrm{\ω}}^{\′\′},{\mathrm{\ω}}^{\′})+\mathrm{\γ}({\mathrm{\ω}}^{\′},{\mathrm{\ω}}^{\′\′})}\\ {\mathrm{\θ}}^{\′\′}=\frac{\mathrm{\γ}({\mathrm{\ω}}^{\′},{\mathrm{\ω}}^{\′\′})}{\mathrm{\γ}({\mathrm{\ω}}^{\′\′},{\mathrm{\ω}}^{\′})+\mathrm{\γ}({\mathrm{\ω}}^{\′},{\mathrm{\ω}}^{\′\′})}\end{array}\right.$

Comprehensive weight is:

w＝θ′ω′+θ″ω″＝(ω ₁,ω ₂,ω ₃,ω ₄,ω ₅,ω ₆)

ω _j＝(w _j,1-w _j)

Wherein, j=1,2 ... 6.

Further, in m alternatives, the evaluation indice of i-th scheme is made to be U _i={ u _i1, u _i2..., u _i6, wherein u _ij(j=1,2 ..., 6) and represent the jth evaluation index value of i-th scheme;

The initial decision matrix of m scheme to be evaluated can be obtained by evaluation indice:

$D=\left[\begin{array}{c}{u}_1\\ u_2\\ .\\ .\\ .\\ u_m\end{array}\right]=\left[\begin{array}{cccc}{d}_{11}& d_{12}& ...& d_{16}\\ d_{21}& d_{22}& ...& d_{26}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ d_{m1}& d_{m2}& ...& d_{m6}\end{array}\right]$

Ask the decision matrix of Vague form according to the following steps:

$R=\left[\begin{array}{cccc}({\_}_{11},v_{11})& ({\_}_{12},v_{12})& ...& ({\_}_{16},v_{16})\\ ({\_}_{21},v_{21})& ({\_}_{22},v_{22})& ...& ({\_}_{26},v_{26})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ ({\_}_{m1},v_{m1})& ({\_}_{m2},v_{m2})& ...& ({\_}_{m6},v_{m6})\end{array}\right]$

The property value of Vague form (_ _ij, ν _ij) represent that a jth attribute is to the property value of i-th scheme, _ _ijbe the degree that i-th scheme is under the jurisdiction of attribute j, ν _ijfor the degree do not belonged to;

(1) for asking for option A _ithe degree of membership index of relative priority j _ _ijwith non-affiliated degree index ν _ij, first definition scheme A _ic is collected about being subordinate to of attribute j _iwith non-affiliated collection D _i.

C _i＝{k|d _ij≥d _kj}

D _i＝{k|d _ij＜d _kj}

Try to achieve intermediary outcomes:

$\begin{array}{c}{c}_{\mathrm{ij}}=\frac{\underset{k\∈C_i,k\≠i}{\mathrm{\Σ}}(d_{\mathrm{ij}}-d_{\mathrm{kj}})}{d_{\mathrm{ij}}}\\ e_{\mathrm{ij}}=\frac{\underset{k\∈D_i,k\≠i}{\mathrm{\Σ}}(d_{\mathrm{kj}}-d_{\mathrm{ij}})}{d_{\mathrm{ij}}}\end{array}$

Intermediary outcomes is utilized to try to achieve degree of membership index and non-affiliated degree index is:

${\_}_{\mathrm{ij}}=\frac{c_{\mathrm{ij}}}{c_{\mathrm{ij}}+e_{\mathrm{ij}}},v_{\mathrm{ij}}=\frac{e_{\mathrm{ij}}}{c_{\mathrm{ij}}+e_{\mathrm{ij}}}.$

Further, the step assessed each scheme is as follows, first this appraisal procedure utilizes the relation that is dominant between preference function determination attribute, more accurate than simple scale-of-two comparative approach, utilize PROMETHEE method to assess simultaneously, take full advantage of the mode of thinking of the mankind from the pros and cons evaluation of programme:

Step one, select different preference functions according to the feature of each attribute: suppose that all properties is all profit evaluation model, the size of preference function value represents the size of the relation that to be dominant between scheme, the property value f of the attribute j of the Vague form of scheme a and scheme b _j(a), f _jb () is respectively:

$\left\{\begin{array}{c}{f}_j\left(a\right)=\{<x,{\_}_A\left(x\right),v_A\left(x\right)>|x\&Element;E_1\}\\ f_j\left(b\right)=\{<y,{\_}_B\left(y\right),v_B\left(y\right)>|y\&Element;E_2\}\end{array}\right.$

j＝1,2,…n

The value of step 2, calculating preference function:

$\left\{\begin{array}{c}{P}_j(a,b)=P(f_j\left(a\right)-f_j\left(b\right))=P({\_}_A\left(x\right)+v_B\left(y\right)-{\_}_A\left(x\right)\\ \&times;v_B\left(y\right),v_A\left(x\right)\&times;{\_}_B\left(y\right))=P(\_\left(r_j\right),g\left(r_j\right))\\ \_\left(r_j\right)={\_}_A\left(x\right)+v_B\left(y\right)-{\_}_A\left(x\right)\&times;v_B\left(y\right)\\ g\left(r_j\right)=v_A\left(x\right)\&times;{\_}_B\left(y\right)\end{array}\right.$

Step 3, calculating preference index Π (a, b):

$\left\{\begin{array}{c}\mathrm{\&Pi;}(a,b)=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{P}_j(a,b)=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(\_\left(p_j\right),g\left(p_j\right))\\ \_\left(p_j\right)={\mathrm{\&omega;}}_{\mathrm{ja}}\&times;\_\left(r_j\right)\\ g\left(p_j\right)={\mathrm{\&omega;}}_{\mathrm{jb}}+g\left(r_j\right)-{\mathrm{\&omega;}}_{\mathrm{jb}}\&times;g\left(r_j\right)\end{array}\right.$

Step 4, calculate the Π (a, b) of any two schemes, calculate inflow accordingly, flow out, and net flow index;

Flow out:

${\mathrm{\&Phi;}}^{+}\left(a\right)=\underset{b\&NotEqual;a}{\mathrm{\&Sigma;}}\mathrm{\&Pi;}(a,b)$

Flow into:

${\mathrm{\&Phi;}}^{-}\left(a\right)=\underset{b\&NotEqual;a}{\mathrm{\&Sigma;}}\mathrm{\&Pi;}(b,a)$

Net flow:

Φ(a)＝Φ ⁺(a)-Φ ^-(a)＝(_(a),g(a))

Wherein, what _ (a) represented scheme agrees with value, and g (a) represents the opposition value of scheme;

The preferential index S (a) of step 5, numerical procedure:

S(a)＝_(a)-g(a)。

The present invention based on PROMETHE comprehensive evaluation model for power system blackstart path evaluation, and contrast with the method adopted in document " the power system blackstart effective scheme based on DEA/AHP model is assessed " and document " weighing the power system blackstart scheme evaluation of model of fuzzy synthetic evaluation based on entropy ", find that ranking results of the present invention is consistent with the ranking results of above two kinds of methods, and computation process clear thinking of the present invention

Accompanying drawing explanation

Fig. 1 is the method flow diagram of the black-start scheme assessment that the embodiment of the present invention provides.

Embodiment

For summary of the invention of the present invention, Characteristic can be understood further, hereby exemplify following examples, and coordinate accompanying drawing to be described in detail as follows.

Refer to Fig. 1:

The present invention is achieved in that a kind of method that black-start scheme is assessed comprises:

S101, L position expert please provide the ordering vector of each evaluation index of black starting-up assessment, utilize orderly binary comparison method to obtain subjective weight;

The initial decision matrix that S102, basis are made up of the value of each evaluation index utilizes VC Method to ask for objective weight;

S103, vector similarity theory is utilized to try to achieve comprehensive weight;

S104, the initial decision matrix conversion of real number form is become the decision matrix of Vague collection form, and weight vectors is also changed into this form;

S105, utilize the PROMETHEE method based on Vague collection to sort to each scheme, obtain collating sequence.

Further, described subjective weight is tried to achieve by orderly binary comparison method, and concrete grammar is:

Step one, determine evaluation object and expert collection: set X as investigate entire objects collection, be designated as X={x ₁, x ₂... x _nbe that the expert participating in agriculture products weight integrates as P={p ₁, p ₂... p _l;

Step 2, application set value process of iteration are the sequence of each index: the L position expert chosen, giving every Weight of Expert is { λ ₁, λ ₂... λ _l, allow every expert sort to index according to significance level in index set, the index ordered set of kth (1≤k≤L) position selection of specialists is X _k=(x ₃, x ₅, x ₁, x _n..., x _n-1), x in formula ₃be positioned at X _kfirst position, namely represent x ₃think most important at expert k, according to each index at X _kin position give this index score respectively, at X _kmiddle x ₃corresponding must be divided into N, x ₅corresponding must be divided into N-1, by that analogy, and x _n-1corresponding must be divided into 1;

If μ _i,kthe score that (1≤i≤N, 1≤k≤L) obtains at expert k place for index i, order as comprehensive grading, 1≤i≤N in formula, according to g _idescending new sequence is carried out to evaluation index, $X^{*}=\{x_1^{*},x_2^{*},...,x_N^{*}\};$

Step 3, respectively acquisition comparator matrix is compared to adjacent evaluation index by L position expert;

By the significance level of L position expert by the relatively rear index of last index in the adjacent index of contrast, the two no less important value is 1.0; The former is important a little, value 1.2; The former is obviously important, value 1.4; The former is strongly important, value 1.6; The former is extremely important, value 1.8; Provide evaluation interval, interval endpoint value gets adjacent r _knumerical value, its relative importance is between both two r _kbetween the significance level that numerical value is corresponding;

Step 4, interval is converted into point value by following formula:

$r_i=\frac{\frac{1}{2}\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i(r_{\mathrm{ij}}^{\&prime;\&prime;2}-r_{\mathrm{ij}}^{\&prime;2})}{\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i(r_{\mathrm{ij}}^{\&prime;\&prime;}-r_{\mathrm{ij}}^{\&prime;})}$

In formula, r _ij' for expert i is to the lower bound in the Evaluations matrix of index j, r _ij" be the upper bound in Evaluations matrix, j=1,2 ..., n-1;

Step 5, determine the weight of evaluation index: compare because N number of index is adjacent, N-1 fiducial value can be obtained:

In formula: r ₁the implication of representative be first index after rearrangement relative to the significance level of second index, can with the ratio of the absolute importance degree of first index and second index set forth,

$\begin{array}{c}{r}_1=\frac{x_1^{**}}{x_2^{**}},r_2=\frac{x_2^{**}}{x_3^{**}},\\ r_3=\frac{x_3^{**}}{x_4^{**}},...,r_{N-1}=\frac{x_{N-1}^{**}}{x_N^{**}}\end{array}$

comprehensive weight be:

$w_N^{*}={(1+\underset{k=1}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{i=k}{\overset{N-1}{\mathrm{\&Pi;}}}{r}_i)}^{-1}$

The weight of other indexs is:

$w_i^{*}=r_i{w}_{i+1}^{*}.$

Further, described objective weight is tried to achieve by VC Method, and concrete grammar is:

Step one, establish certain assessment indicator system to have m evaluation index, carried out system evaluation and data sampling to n evaluation object, so raw data Evaluations matrix can be expressed as matrix X:

$X={\left(x_{\mathrm{ij}}\right)}_{n\&times;m}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{21}& ...& x_{2m}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n1}& ...& x_{\mathrm{nm}}\end{array}\right]$

Step 2, according to the average of each index of calculated with actual values of each object of classification index and standard deviation:

Wherein the average of a jth index and standard deviation are respectively

$\begin{array}{c}{\stackrel{\&OverBar;}{x}}_j=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ij}}\\ S_j=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(x_{\mathrm{ij}}-\stackrel{\&OverBar;}{x_j})}\end{array}$

J=1 in formula, 2 ... m;

Step 3, calculate the coefficient of variation of each index:

$B_j=S_j/\stackrel{\&OverBar;}{x_j};$

Step 4, determine the weight of each index:

First the index coefficient of variation is normalized, then the weight sets V of index is obtained _j={ ν ₁, ν ₂... ν _m, wherein

Further, the method utilizing vector similarity theory to try to achieve comprehensive weight comprises:

(1) calculating of vector similarity

For any two N dimensional vector X=(x ₁, x ₂..., x _n), Y=(y ₁, y ₂... y _n), its inner product is expressed as:

[X,Y]＝x ₁y ₁+x ₂y ₂+…x _ny _n

The norm of vector is expressed as:

$\left|\right|X\left|\right|=\sqrt{[X,X]}=\sqrt{x_1^2+x_2^2+...+x_n^2}$

The angle of vector is expressed as:

Then two vectorial length similarity α are:

$\mathrm{\&alpha;}(X,Y)=\left\{\begin{array}{cc}1-\left|\frac{\left|\right|X\left|\right|-\left|\right|Y\left|\right|}{\left|\right|X\left|\right|}\right|& \left|\right|Y\left|\right|\&le;2\left|\right|X\left|\right|\\ 0& \left|\right|Y\left|\right|>2\left|\right|X\left|\right|\end{array}\right.$

Two vectorial direction similarity similarity β are:

Two vectorial similarity similarity γ are:

γ(X,Y)＝αβ

(2) based on vector similarity Evaluation formula

Suppose total N number of evaluation index, it is that then wherein a kth weight vectors is that decision maker obtains L group weight vectors altogether by objective and subjective synthetic approach:

W _k＝(w _k1,w _k2,…,w _kN),k＝1,2,…,L

Subjective and objective weight employing combination coefficient is tried to achieve summation weight is:

W ^C＝θ ₁W ₁+θ ₂W ₂+…θ _LW _L

W in formula ^cfor comprehensive weight vector, θ ₁, θ ₂... θ _lfor combination coefficient;

Arbitrary weight vectors W _kwith the total similarity of other vectors be:

γ＝(γ ₁,γ ₂,…,γ _L)

Wherein ${\mathrm{\&gamma;}}_k=\underset{i=1,i\&NotEqual;k}{\overset{L}{\mathrm{\&Sigma;}}}\mathrm{\&gamma;}(W_i,W_k),$ Because set weight coefficient vector as:

θ＝(θ ₁,θ ₂,…θ _L)，

Wherein, ${\mathrm{\&theta;}}_k=\frac{\underset{i=1,i\&NotEqual;k}{\overset{L}{\mathrm{\&Sigma;}}}\mathrm{\&gamma;}(W_i,W_k)}{\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1,i\&NotEqual;k}{\overset{L}{\mathrm{\&Sigma;}}}\mathrm{\&gamma;}(W_i,W_k)}.$

Further, the concrete grammar obtaining the comprehensive weight of Vague collection form is:

Suppose have the ordering vector of L position expert to 6 indexs to be respectively:

γ _i(…x ₁…x ₆…)i＝(1,2,…L)

Subjective weight vectors is:

ω′＝(ω ₁′,ω ₂′,ω ₃′,ω ₄′,ω ₅′,ω ₆′)

Utilize initial decision matrix D and try to achieve objective weight based on the objective weight acquiring method of VC Method and be:

ω″＝(ω ₁″,ω ₂″,ω ₃″,ω ₄″,ω ₅″,ω ₆″)

Ask and make vectorial ω ' and ω " the maximum combining coefficient vector θ of similarity=(θ ', θ "), wherein:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}^{\&prime;}=\frac{\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;\&prime;},{\mathrm{\&omega;}}^{\&prime;})}{\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;\&prime;},{\mathrm{\&omega;}}^{\&prime;})+\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;},{\mathrm{\&omega;}}^{\&prime;\&prime;})}\\ {\mathrm{\&theta;}}^{\&prime;\&prime;}=\frac{\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;},{\mathrm{\&omega;}}^{\&prime;\&prime;})}{\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;\&prime;},{\mathrm{\&omega;}}^{\&prime;})+\mathrm{\&gamma;}({\mathrm{\&omega;}}^{\&prime;},{\mathrm{\&omega;}}^{\&prime;\&prime;})}\end{array}\right.$

Comprehensive weight is:

w＝θ′ω′+θ″ω″＝(ω ₁,ω ₂,ω ₃,ω ₄,ω ₅,ω ₆)

ω _j＝(w _j,1-w _j)

Wherein, j=1,2 ... 6.

Further, in m alternatives, the evaluation indice of i-th scheme is made to be U _i={ u _i1, u _i2..., u _i6, wherein u _ij(j=1,2 ..., 6) and represent the jth evaluation index value of i-th scheme;

The initial decision matrix of m scheme to be evaluated can be obtained by evaluation indice:

$D=\left[\begin{array}{c}{u}_1\\ u_2\\ .\\ .\\ .\\ u_m\end{array}\right]=\left[\begin{array}{cccc}{d}_{11}& d_{12}& ...& d_{16}\\ d_{21}& d_{22}& ...& d_{26}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ d_{m1}& d_{m2}& ...& d_{m6}\end{array}\right]$

Ask the decision matrix of Vague form according to the following steps:

$R=\left[\begin{array}{cccc}({\_}_{11},v_{11})& ({\_}_{12},v_{12})& ...& ({\_}_{16},v_{16})\\ ({\_}_{21},v_{21})& ({\_}_{22},v_{22})& ...& ({\_}_{26},v_{26})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ ({\_}_{m1},v_{m1})& ({\_}_{m2},v_{m2})& ...& ({\_}_{m6},v_{m6})\end{array}\right]$

The property value of Vague form (_ _ij, ν _ij) represent that a jth attribute is to the property value of i-th scheme, _ _ijbe the degree that i-th scheme is under the jurisdiction of attribute j, ν _ijfor the degree do not belonged to;

(1) for asking for option A _ithe degree of membership index of relative priority j _ _ijwith non-affiliated degree index ν _ij, first definition scheme A _ic is collected about being subordinate to of attribute j _iwith non-affiliated collection D _i.

C _i＝{k|d _ij≥d _kj}

D _i＝{k|d _ij＜d _kj}

Try to achieve intermediary outcomes:

$\begin{array}{c}{c}_{\mathrm{ij}}=\frac{\underset{k\&Element;C_i,k\&NotEqual;i}{\mathrm{\&Sigma;}}(d_{\mathrm{ij}}-d_{\mathrm{kj}})}{d_{\mathrm{ij}}}\\ e_{\mathrm{ij}}=\frac{\underset{k\&Element;D_i,k\&NotEqual;i}{\mathrm{\&Sigma;}}(d_{\mathrm{kj}}-d_{\mathrm{ij}})}{d_{\mathrm{ij}}}\end{array}$

Intermediary outcomes is utilized to try to achieve degree of membership index and non-affiliated degree index is:

${\_}_{\mathrm{ij}}=\frac{c_{\mathrm{ij}}}{c_{\mathrm{ij}}+e_{\mathrm{ij}}},v_{\mathrm{ij}}=\frac{e_{\mathrm{ij}}}{c_{\mathrm{ij}}+e_{\mathrm{ij}}}.$

Further, the step assessed each scheme is as follows:

Step one, select different preference functions according to the feature of each attribute: suppose that all properties is all profit evaluation model, the size of preference function value represents the size of the relation that to be dominant between scheme, the property value f of the attribute j of the Vague form of scheme a and scheme b _j(a), f _jb () is respectively:

$\left\{\begin{array}{c}{f}_j\left(a\right)=\{<x,{\_}_A\left(x\right),v_A\left(x\right)>|x\&Element;E_1\}\\ f_j\left(b\right)=\{<y,{\_}_B\left(y\right),v_B\left(y\right)>|y\&Element;E_2\}\end{array}\right.$

j＝1,2,…n

The value of step 2, calculating preference function:

$\left\{\begin{array}{c}{P}_j(a,b)=P(f_j\left(a\right)-f_j\left(b\right))=P({\_}_A\left(x\right)+v_B\left(y\right)-{\_}_A\left(x\right)\\ \&times;v_B\left(y\right),v_A\left(x\right)\&times;{\_}_B\left(y\right))=P(\_\left(r_j\right),g\left(r_j\right))\\ \_\left(r_j\right)={\_}_A\left(x\right)+v_B\left(y\right)-{\_}_A\left(x\right)\&times;v_B\left(y\right)\\ g\left(r_j\right)=v_A\left(x\right)\&times;{\_}_B\left(y\right)\end{array}\right.$

Step 3, calculating preference index Π (a, b):

$\left\{\begin{array}{c}\mathrm{\&Pi;}(a,b)=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{P}_j(a,b)=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(\_\left(p_j\right),g\left(p_j\right))\\ \_\left(p_j\right)={\mathrm{\&omega;}}_{\mathrm{ja}}\&times;\_\left(r_j\right)\\ g\left(p_j\right)={\mathrm{\&omega;}}_{\mathrm{jb}}+g\left(r_j\right)-{\mathrm{\&omega;}}_{\mathrm{jb}}\&times;g\left(r_j\right)\end{array}\right.$

Step 4, calculate the Π (a, b) of any two schemes, calculate inflow accordingly, flow out, and net flow index;

Flow out:

${\mathrm{\&Phi;}}^{+}\left(a\right)=\underset{b\&NotEqual;a}{\mathrm{\&Sigma;}}\mathrm{\&Pi;}(a,b)$

Flow into:

${\mathrm{\&Phi;}}^{-}\left(a\right)=\underset{b\&NotEqual;a}{\mathrm{\&Sigma;}}\mathrm{\&Pi;}(b,a)$

Net flow:

Φ(a)＝Φ ⁺(a)-Φ ^-(a)＝(_(a),g(a))

Wherein, what _ (a) represented scheme agrees with value, and g (a) represents the opposition value of scheme;

The preferential index S (a) of step 5, numerical procedure:

S(a)＝_(a)-g(a)。

The present invention based on PROMETHE comprehensive evaluation model for power system blackstart path evaluation, the objective difference of data and the subjective preferences of expert are combined well, give more rational index weights; By PROMTTHEE method by scheme between two between the relation of being dominant carry out comprehensive evaluation, can sort completely by implementation, utilize Vague collection to consider a problem from the pros and cons and make ranking results have more cogency.

The above is only to preferred embodiment of the present invention, not any pro forma restriction is done to the present invention, every according to technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all belong in the scope of technical solution of the present invention.

Claims (9)

1. the method for the assessment of the black-start scheme based on combining weights PROMETHEE evaluation model, it is characterized in that, the initial decision matrix conversion of real number form is become the decision matrix of Vague collection form by the method for this black-start scheme assessment, and weight vectors is also changed into the decision matrix of Vague collection form; Utilize the PROMETHEE method based on Vague collection form to sort to scheme, obtain collating sequence.

2. as claimed in claim 1 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, the initial decision matrix conversion of real number form is being become the decision matrix of Vague collection form, and is needing before weight vectors also being changed into the decision matrix of Vague collection form:

Provide the ordering vector of each evaluation index of black starting-up assessment, utilize orderly binary comparison method to obtain subjective weight;

VC Method is utilized to ask for objective weight according to the initial decision matrix that the value by each evaluation index forms;

Vector similarity theory is utilized to try to achieve comprehensive weight.

3., as claimed in claim 2 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, described subjective weight is tried to achieve concrete grammar by orderly binary comparison method and is:

Step one, determine evaluation object and expert collection: X be investigate entire objects collection, be designated as X={x ₁, x ₂... x _nbe that the expert participating in agriculture products weight integrates as P={p ₁, p ₂... p _l;

Step 2, application set value process of iteration are the sequence of each index: weight is { λ ₁, λ ₂... λ _l, sort to index according to significance level in index set, the index ordered set that k (1≤k≤L) chooses is X _k=(x ₃, x ₅, x ₁, x _n..., x _n-1), x in formula ₃be positioned at X _kfirst position, namely represent x ₃think most important at k, according to each index at X _kin position give index score respectively, at X _kmiddle x ₃corresponding must be divided into N, x ₅corresponding must be divided into N-1, x _n-1corresponding must be divided into 1;

μ _i,kthe score that (1≤i≤N, 1≤k≤L) obtains at k place for index i, order as comprehensive grading, 1≤i≤N in formula, according to g _idescending new sequence is carried out to evaluation index,

Step 3, respectively acquisition comparator matrix is compared to adjacent evaluation index;

By contrasting the significance level of the relatively rear index of last index in adjacent index, provide evaluation interval, interval endpoint value gets adjacent r _knumerical value, relative importance is between both two r _kbetween the significance level that numerical value is corresponding;

Step 4, interval is converted into point value by following formula:

In formula, r _ij' for expert i is to the lower bound in the Evaluations matrix of index j, r _ij" be the upper bound in Evaluations matrix, j=1,2 ..., n-1;

Step 5, determine the weight of evaluation index: compare because N number of index is adjacent, obtain N-1 fiducial value:

In formula: r ₁the implication of representative be first index after rearrangement relative to the significance level of second index, with the ratio of the absolute importance degree of first index and second index set forth,

comprehensive weight be:

The weight of other indexs is:

4., as claimed in claim 2 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, described objective weight is tried to achieve concrete grammar by VC Method and is:

Step one, assessment indicator system have m evaluation index, and carried out system evaluation and data sampling to n evaluation object, raw data Evaluations matrix is expressed as matrix X:

Step 2, according to the average of each index of calculated with actual values of each object of classification index and standard deviation:

Wherein the average of a jth index and standard deviation are respectively:

J=1 in formula, 2 ... m;

Step 3, calculate the coefficient of variation of each index:

Step 4, determine the weight of each index:

First the index coefficient of variation is normalized, then the weight sets V of index is obtained _j={ ν ₁, ν ₂... ν _m, wherein

5. as claimed in claim 2 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, the described method utilizing vector similarity theory to try to achieve comprehensive weight comprises:

Step one, the calculating of vector similarity:

For any two N dimensional vector X=(x ₁, x ₂..., x _n), Y=(y ₁, y ₂... y _n), inner product is expressed as:

[X,Y]＝x ₁y ₁+x ₂y ₂+…x _ny _n；

The norm of vector is expressed as:

The angle of vector is expressed as:

Then two vectorial length similarity α are:

Two vectorial direction similarity similarity β are:

Two vectorial similarity similarity γ are:

γ(X,Y)＝αβ；

Step 2, based on vector similarity Evaluation formula:

Total N number of evaluation index, obtaining L group weight vectors altogether by objective and subjective synthetic approach is that then wherein a kth weight vectors is:

W _k＝(w _k1,w _k2,…,w _kN),k＝1,2,…,L；

Subjective and objective weight employing combination coefficient is tried to achieve summation weight is:

W ^C＝θ ₁W ₁+θ ₂W ₂+…θ _LW _L；

W in formula ^cfor comprehensive weight vector, θ ₁, θ ₂... θ _lfor combination coefficient;

Arbitrary weight vectors W _kwith the total similarity of other vectors be:

γ＝(γ ₁,γ ₂,…,γ _L)；

Wherein because set weight coefficient vector as:

θ＝(θ ₁,θ ₂,…θ _L)；

Wherein,

6. as claimed in claim 1 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, the concrete grammar obtaining the comprehensive weight of Vague collection form is:

The ordering vector of 6 indexs is respectively:

γ _i(…x ₁…x ₆…)i＝(1,2,…L)；

Subjective weight vectors is:

ω′＝(ω ₁′,ω ₂′,ω ₃′,ω ₄′,ω ₅′,ω ₆′)；

Utilize initial decision matrix D and try to achieve objective weight based on the objective weight acquiring method of VC Method and be:

ω″＝(ω ₁″,ω ₂″,ω ₃″,ω ₄″,ω ₅″,ω ₆″)；

Ask and make vectorial ω ' and ω " the maximum combining coefficient vector θ of similarity=(θ ', θ "), wherein:

Comprehensive weight is:

w＝θ′ω′+θ″ω″＝(ω ₁,ω ₂,ω ₃,ω ₄,ω ₅,ω ₆)；

ω _j＝(w _j,1-w _j)；

Wherein, j=1,2 ... 6.

7., as claimed in claim 1 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, in m alternatives, make the evaluation indice of i-th scheme be U _i={ u _i1, u _i2..., u _i6, wherein u _ij(j=1,2 ..., 6) and represent the jth evaluation index value of i-th scheme;

The initial decision matrix of m scheme to be evaluated is obtained by evaluation indice:

8., as claimed in claim 7 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, the method for solving of described Vague form decision matrix:

The property value of Vague form (_ _ij, ν _ij) represent that a jth attribute is to the property value of i-th scheme, _ _ijbe the degree that i-th scheme is under the jurisdiction of attribute j, ν _ijfor the degree do not belonged to;

Step one, for asking for option A _ithe degree of membership index of relative priority j _ _ijwith non-affiliated degree index ν _ij, first definition scheme A _ic is collected about being subordinate to of attribute j _iwith non-affiliated collection D _i;

C _i＝{k|d _ij≥d _kj}；

D _i＝{k|d _ij<d _kj}；

Try to achieve intermediary outcomes:

Intermediary outcomes is utilized to try to achieve degree of membership index and non-affiliated degree index is:

9. as claimed in claim 7 based on the method that the black-start scheme of combining weights PROMETHEE evaluation model is assessed, it is characterized in that, the step assessed each scheme is further as follows:

Step one, select different preference functions according to the feature of each attribute, all properties is all profit evaluation model, and the size of preference function value represents the size of the relation that to be dominant between scheme, the property value f of the attribute j of the Vague form of scheme a and scheme b _j(a), f _jb () is respectively:

j＝1,2,…n

The value of step 2, calculating preference function:

Step 3, calculating preference index Π (a, b):

Step 4, calculate the Π (a, b) of any two schemes, calculate inflow accordingly, flow out, and net flow index; Flow out:

Flow into:

Net flow:

Φ(a)＝Φ ⁺(a)-Φ ^-(a)＝(_(a),g(a))；

Wherein, what _ (a) represented scheme agrees with value, and g (a) represents the opposition value of scheme;

The preferential index S (a) of step 5, numerical procedure:

S(a)＝_(a)-g(a)。