CN103020729A - Comprehensive evaluation method for short-circuit current limitation of Gansu power grid - Google Patents

Abstract

According to the operation characteristics of Gansu power grid, the present invention provides a comprehensive evaluation method for limiting short-circuit current based on a three-layer fuzzy comprehensive evaluation model. Combined with the three-layer fuzzy comprehensive evaluation model, the comprehensive evaluation of the short-circuit current limit in Gansu power grid is carried out, which makes the fuzzy comprehensive evaluation process more comprehensive and accurate.

Description

The integrated evaluating method of Gansu Power Grid short-circuit current limitation

Technical field

The invention belongs to power system security defense technique field, be specifically related to security of system, stability, short-circuit current limitation effect and performance driving economy thereof, the limiting short-circuit current allocation plan is made evaluation method comprehensive and that optimize.

Background technology

Compare with the development research of the current limiting measures such as the exploration of short circuit current limitation technology and short circuit current limiter, the problem that affects of the safety of distributing and on electric system may bringing of the comprehensive current limiting measures of Short Circuit Current in electric system, economical operation is at present also less to be discussed by people.And can these be major issues of studying current limiting measures and being applied in electric system, do not analyze these problems and just may make current limiting measures can't obtain appropriate application and performance optimum efficiency, even bring new problem for the normal operation of electric system.

Traditional limiting short-circuit current way is normally calculated comparison one by one to various current limiting measures, therefore has the problems such as computing method are loaded down with trivial details, counting yield is low, and can't consider simultaneously safety, economic problems.Finding the solution also often in the situation that single current limiting measures can't meet the demands of aggregate measures, comprehensive limited several current limiting measures realize by rule of thumb, can not effectively realize the integrated evaluating method of measures for limiting short-circuit current, therefore be difficult for forming the current limiting measures allocation plan of optimizing.The research of the problem of distributing rationally for various current limiting measures still is in the starting stage.

Model of fuzzy synthetic evaluation is that the analytical hierarchy process in fuzzy set theory develops, and is all well used in many-sides such as power plant's addressing, multiple goal power source plannings at present.It uses the Fuzzy Linear shift theory take fuzzy mathematics as the basis, considers the various factors relevant with being evaluated things, makes the evaluation of Comprehensive to being evaluated things.According to the complexity that is evaluated things, can be divided into individual layer and multi-layer Fuzzy comprehensive evaluation.

The integrated evaluating method of measures for limiting short-circuit current need to be considered to take Multiobjective Decision Making Method in the operational research, sets up mathematical model, draws the optimum solution of the short-circuit current under the multi-constraint condition; Study theoretically the relation curve between short-circuit current and the system reliability, seek equilibrium point or system's best operating point; Set up comprehensive current limiting measures cost function, the limiting short-circuit current allocation plan of research economy, security, reliability multiple-objection optimization.

Summary of the invention

The object of the invention is to, the deficiency for above-mentioned limiting short-circuit current Optimal Configuration Method exists proposes a kind of limiting short-circuit current integrated evaluating method based on three layers of model of fuzzy synthetic evaluation.

The objective of the invention is to realize by following technological means:

Set up three layers of model of fuzzy synthetic evaluation

Determine set of factors

U=(U ₁，U ₂，…，U _m)

Wherein, set of factors U is for estimating the index system of things.Set of factors U can be divided into the m class, and each class is a subset of factors U _r(r=1,2 ..., m), each subset of factors has again n factor, i.e. U _r=(C _R1, C _R2..., C _Rn).

Determine weight sets

Weight sets is by set of factors U or subset of factors U _rIn the set that forms of the weight of each factor relative importance, determine that the method for weight sets has expert evaluation method, expert survey and judgement matrix analysis method.Preferably, adopt judgement matrix analysis method, by veteran expert the relative importance between each factor of set of factors is made in twos relatively rear Judgement Matricies, the eigenvalue of maximum characteristic of correspondence vector of judgment matrix is weight sets corresponding to this set of factors after normalization.

With subset of factors U _r=(C _R1, C _R2..., C _Rn) be example, as follows Judgement Matricies:

At subset of factors U _rIn get two factor C at every turn _RiAnd C _Rj(i, j=1,2 ..., n), c _IjExpression C _RiWith C _RjTo the ratio of the influence degree of target, wherein, preferably, c _IjValue determine according to 1～9 value method of Saaty, as shown in table 1.

1～9 value method table of table 1Saaty

All comparative result may be configured as judgment matrix is compared on the n rank

Represent, then consisted of the precedence relationship judgment matrix of all factors under this rule layer

$\widetilde{B_i}=\left[\begin{array}{cccc}{c}_{11}& c_{12}& ...& c_{1n}\\ c_{21}& c_{22}& ...& c_{2n}\\ ...& ...& ...& ...\\ c_{n1}& c_{n2}& ...& c_{\mathrm{nn}}\end{array}\right]$

C in the formula _IjImportance for the relative factor j of factor i.Its element satisfies:

(1)c _ij>0(i，j＝1，2，…，n)；

(2)c _ii=1(i=1，2，…，n)；

(3)c _ij=1/c _ji(i，j＝1，2，…，n)。

Matrix is referred to as just reciprocal type matrix at mathematics.Also should carry out consistency desired result for the judgment matrix that is consisted of by the mutual important relationship of many factors, rationally effective to guarantee the judgment matrix that is consisted of.

According to matrix theory, when just reciprocal type matrix satisfied consistance, its maximum characteristic root equaled the order of matrix number, so represent to estimate the coincident indicator of judgment matrix with CI:

$\mathrm{CI}=\frac{{\mathrm{\λ}}_{\max }-n}{n-1}$

λ in the following formula _MaxBe matrix

Eigenvalue of maximum.

When the CI value was 0, judgment matrix had crash consistency, and the CI value is larger, illustrated that the consistance of judgment matrix is poorer, and check consistency also needs to introduce the mean random coincident indicator RI value of judgment matrix, saw Table 2 for the RI value on 1-10 rank:

The RI value of table 21～10 rank judgment matrixs

Exponent number	1	2	3	4	5	6	7	8	9	10
											RI	0.00	0.00	0.58	0.90	1.12	1.24	1.36	1.41	1.45	1.49

For 1,2 rank judgment matrixs, RI is pro forma, because 1,2 rank judgment matrixs always have crash consistency.When exponent number〉2 the time, the ratio of the coincident indicator CI of judgment matrix and same order mean random coincident indicator RI is called at random Consistency Ratio CR:

$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}$

When CR≤0.1, think that judgment matrix has satisfied consistance, otherwise need to adjust the scale between the various factors of the element that consists of judgment matrix.

After having verified that judgment matrix satisfies consistency desired result, according to the eigenvalue of maximum that calculates, obtain its corresponding maximal eigenvector Q=[q ₁, q ₂..., q _n], then have:

$\widetilde{B_r}Q={\mathrm{\λ}}_{\max }Q$

Proper vector Q is carried out normalization, obtain Q=[w ₁, w ₂..., w _n], wherein:

$w_i=\frac{q_i}{{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00002396074400012.png"\; state="\{\{state\}\}">q</figure-callout>}}_1+q_2+\&CenterDot;\&CenterDot;\&CenterDot;+q_n}$

W then _i(i=1 ... n) be the weight coefficient of corresponding element.

Determine the comment collection

Estimate the set of collection for forming being evaluated comments at different levels that things makes.If total p of comment is then estimated collection V and can be expressed as V=(v ₁, v ₂..., v _p).

V in the formula _k(k=1,2 ..., p) representative comments at different levels from high to low, i.e. opinion rating.

To estimating each concentrated comment v _kCan provide corresponding mark, then can obtain minute manifold that the comment set pair answers is E=(e ₁, e ₂..., e _p).General 5 grades of comments are namely thought and can be made comparatively accurately description, i.e. p=5 to evaluation object.

Carry out the one-level fuzzy overall evaluation

The one-level fuzzy overall evaluation is to subset of factors U _rIn each factor carry out fuzzy overall evaluation.B _rThe single factor evaluation matrix of one-level fuzzy overall evaluation, i.e. B _rFuzzy relationship matrix r to V _rFor:

$R_r={\left({\mathrm{\&mu;}}_{\mathrm{rjk}}\right)}_{n\&times;p}=\left[\begin{array}{ccc}{\mathrm{\&mu;}}_{r11}& ...& {\mathrm{\&mu;}}_{r1p}\\ ...& ...& ...\\ {\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="1"\; label="rn"\; filenames="HDA00002396074400012.png"\; state="\{\{state\}\}">rn</figure-callout>}1}& ...& {\mathrm{\&mu;}}_{\mathrm{rnp}}\end{array}\right]$

μ in the formula _Rjk(r=1,2 ..., m; J=1,2 ..., n; K=1,2 ..., p) be U _rJ factor C _RjBe under the jurisdiction of comment and concentrate the degree of membership of k comment.

By the compose operation of fuzzy matrix, can get U _rThe fuzzy overall evaluation collection

That describe is U _rIn all factors be under the jurisdiction of the weighted sum that comment is concentrated each comment.

Get weighted mean The type operator, then

$S_{\mathrm{rk}}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}{\mathrm{\&mu;}}_{\mathrm{rjk}}$

Carry out Secondary Fuzzy Comprehensive Evaluation

Secondary Fuzzy Comprehensive Evaluation namely carries out fuzzy overall evaluation to each factor among the set of factors U.By the result of a fuzzy overall evaluation, can get the Secondary Fuzzy Comprehensive Evaluation matrix and be:

Then the Secondary Fuzzy Comprehensive Evaluation collection is

S _k(k=1,2 ..., when p) referring to consider the affecting of all factors, be evaluated things is concentrated k comment to comment degree of membership.

Calculate the relative importance value of fuzzy overall evaluation

Element S with Secondary Fuzzy Comprehensive Evaluation collection S _kBe weight, k element among minute manifold E be weighted on average, as the relative importance value N of fuzzy overall evaluation.

$N=\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_k{e}_k/\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_k$

Introduce fuzzy behavioral indicator

Improvement for multi-level fuzzy gross assessment model mainly is to introduce fuzzy behavioral indicator, each factor that is about in the subset of factors quantizes, seek concrete mathematic(al) representation, with actual numerical value the expressed physical significance of each factor in each subset of factors is characterized.

Confirm membership function

Membership function is described each behavioral indicator and is under the jurisdiction of the degree that comment is concentrated each comment, is optimized in conjunction with multi-level fuzzy gross assessment model, thereby makes evaluation procedure have more objectivity.

This method considers the scope of application, current limitation effect, financial cost of various measures for limiting short-circuit current and on the factors such as impact of electrical network, carry out short-circuit current limiting measure comprehensive evaluation in conjunction with multi-level fuzzy gross assessment model, make the multi-layer fuzzy comprehensive process have more objectivity.

Description of drawings

Below in conjunction with accompanying drawing the present invention is elaborated:

Fig. 1 is fuzzy Evaluation Model Recurison order hierarchy structural relation figure;

Fig. 2 is the membership function of behavioral indicator.

Embodiment

The below, is described further summary of the invention of the present invention as one embodiment of the present of invention with Gansu Power Grid 750/330kV rack short-circuit current limiting measure configuration scheme.

With static security, transient security, four constraints such as short-circuit current limitation effect and performance driving economy are as set of factors U, in the subset of factors static security, consider circuit or transformer overload and out-of-limit two the sub-factors of busbar voltage, in the subset of factors transient security, consider sub-factor of maximum generation machine merit angular difference, in subset of factors short-circuit current limitation effect, consider the 3300kV three-phase, single-phase short circuit current and 750kV three-phase, four sub-factors of single-phase short circuit current are considered switchgear investment and two sub-factors of system losses in the subset of factors performance driving economy.

Above-mentioned set of factors and subset of factors are divided into three layers, are defined as respectively solution layer, rule layer and indicator layer.Specifically fuzzy Evaluation Model Recurison order hierarchy structural relation is as shown in Figure 1:

Comprehensively to the specificity analysis of each current limiting measures, propose North China Power Telecommunication Network short-circuit current current limiting measures allocation plan, for described Limited Current measure scheme, 330kV and above electricity grid substation take the current limiting measures situation to be expressed as follows table:

Table 3 embodiment transformer station takes the current limiting measures situation

Determine current limitation effect, make such scheme will exceed standard the website short-circuit current limitation at below 95% of switch rated capacity, the below considers static security, transient security, short-circuit current current limitation effect, four aspects of performance driving economy and carries out comprehensive evaluation, draws schemes synthesis evaluation and optimization degree.

Step 1: the weight coefficient collection that calculates set of factors and each sub-set of factors

Precedence relationship judgment matrix according to all factors under the rule layer

Formula

$\widetilde{B_r}=\left[\begin{array}{cccc}{c}_{11}& c_{12}& ...& c_{1n}\\ c_{21}& c_{22}& ...& c_{2n}\\ ...& ...& ...& ...\\ c_{n1}& c_{n2}& ...& c_{\mathrm{nn}}\end{array}\right]$

And c in the formula _IjThe element formula that satisfies condition:

c _ij>0(i，j＝1，2，…，n)；

c _ii=1(i=1，2，…，n)；

c _ij=1/c _ji (i，j＝1，2，…，n)。

Can calculate the weight coefficient collection w of set of factors and each sub-set of factors.

At first determine diagonal of a matrix right side element according to the rule layer set of factors

(1) four rule layer factor static security (B ₁), transient security (B ₂), short-circuit current current limitation effect (B ₃), performance driving economy (B ₄) the judgment matrix element that consists of is b ₁₂=1/3, b ₁₃=1/5, b ₁₄=3, b ₂₃=1/2, b ₂₄=1, b ₃₄=2;

(2) single criterion layer static security (B ₁) two sub-factor circuit or transformer overload (C ₁₁) and the out-of-limit (C of busbar voltage ₁₂) the judgment matrix element that consists of is c ₁₂=5;

(3) single criterion layer transient security (B ₂) only having a sub-factor generator maximum work angular difference, the judgment matrix element of its formation is c ₁₂=1;

(4) single criterion layer short-circuit current current limitation effect (B ₃) four sub-set of factors 500kV three-phase shortcircuit electric current (C are arranged ₃₁), 500kV single-phase short circuit current (C ₃₂), 220kV three-phase shortcircuit electric current (C ₃₃), 220kV single-phase short circuit current (C ₃₄) the judgment matrix element that consists of is c ₁₂=1, c ₁₃=3, c ₁₄=3, c ₂₃=3, c ₂₄=3, c ₃₄=1;

(5) single criterion layer performance driving economy (B ₄) two sub-factor switchgear investment (C ₄₁) and system losses (C ₄₂) the judgment matrix element that consists of is c ₁₂=1/2;

List the precedence relationship judgment matrix of all factors under the rule layer

Formula, compute matrix

Eigenvalue of maximum λ _Max, the coincident indicator CI computing formula of judgment matrix is estimated in substitution:

$\mathrm{CI}=\frac{{\mathrm{\&lambda;}}_{\max }-n}{n-1}$

After calculating the CI value, introduce the mean random coincident indicator RI value of judgment matrix, for the RI value reference table 2 on 1-10 rank:

When exponent number〉2 the time, calculate the coincident indicator CI of judgment matrix and the ratio of same order mean random coincident indicator RI and be called at random Consistency Ratio CR:

$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}$

Result of calculation CR≤0.1 o'clock thinks that judgment matrix has satisfied consistance, otherwise adjusts the scale between the various factors of the element that consists of judgment matrix.

After having verified that judgment matrix satisfies consistency desired result, according to the eigenvalue of maximum that calculates, the following formula of substitution:

$\widetilde{B_r}Q={\mathrm{\&lambda;}}_{\max }Q$

Calculate its corresponding maximal eigenvector Q=[q ₁, q ₂..., q _n].

Proper vector Q is carried out normalization, obtain Q=[w ₁, w ₂..., w _n], wherein:

$w_i=\frac{{\mathrm{<figure-callout\; id="1"\; label="q\; i\; q"\; filenames="HDA00002396074400012.png"\; state="\{\{state\}\}">q</figure-callout>}}_i}{q_{}}$

w _i(i=1 ... n) be the weight coefficient of corresponding element.

Calculate respectively w of set of factors weight coefficient w and sub-set of factors weight coefficient ₁, w ₂, w ₃, w ₄

Step 2: determine to estimate collection

The opinion rating standard is divided into: " best ", and " better ", " good ", " generally ", " poor ", five grades, i.e. evaluation integrates the { v as V= ₁, v ₂, v ₃, v ₄, v ₅, fractional value corresponding to each grade is respectively { 9,7,5,3,1}.

Step 3: confirm fuzzy behavioral indicator

Introduce following fuzzy behavioral indicator in the embodiments of the invention:

1. circuit or transformer overload index λ _L

${\mathrm{\&lambda;}}_L=\underset{\mathrm{\&alpha;}}{\mathrm{\&Sigma;}}{(S_l/S_l^{\max })}^2$

α is transmission line of electricity or transformer set of fingers in the formula; S _lPower for branch road l;

Be its upper limit.

2. line voltage out-of-limit index λ _U

${\mathrm{\&lambda;}}_U=\underset{\mathrm{\&beta;}}{\mathrm{\&Sigma;}}{\left(\frac{U_i-U_i^{\mathrm{SP}}}{\mathrm{\&Delta;}{U}_i^{\lim }}\right)}^2$

$U_i^{\mathrm{sp}}=(U_i^H+U_i^L)/2,{\mathrm{\&Delta;U}}_i^{\lim }=(U_i^H-U_i^L)/2$

β is the bus set in the formula; U _iBe the voltage magnitude of bus i,

With

Be respectively its upper and lower bound.

3. maximum generation machine merit angular difference δ _Max

δ _max＝MAX|δ _i-δ _j|

δ in the formula _i, δ _jBe the merit angle between any two generators in the transient state process behind the failure removal.

4. short-circuit current current limitation effect index λ _SC:

${\mathrm{\&lambda;}}_{\mathrm{SC}}=\underset{\mathrm{\&gamma;}}{\mathrm{\&Sigma;}}{({\mathrm{\&Delta;I}}_{\mathrm{SC}}/I_0)}^2$

γ is the set of bus isolating switch in the formula; Δ I _SCBe the short-circuit current value that reduces Ex post, I ₀Be the specified cut-off current of isolating switch.

5. switchgear investment target λ _e

In the formula, Mi refers to the cost of switchgear, unit: ten million yuan.Switchgear investment total price is calculated gained according to every current limiting measures unit price, and transformer station takes current limiting measures m according to table 3 embodiment _i, d _iSituation can calculate the Mi value,

M _i＝m _i·d _i。

6. system losses index λ _Loss

λ _loss＝ΔP _loss

Δ P in the formula _LossThat the active power loss that system increases under certain scheme is weighed.

Wherein, switchgear investment total price is calculated gained according to every current limiting measures unit price.

Step 4: confirm the parameter of each behavioral indicator membership function, with circuit or transformer overload index analysis, as shown in table 4:

Table 4 behavioral indicator membership function parameter

Index	λ 1	λ 2	λ 3	λ 4	λ 5
						λ L	λ L1	λ L2	λ L3	λ L4	λ L5

Behavioral indicator is under the jurisdiction of and estimates degree that language concentrates each comment and trapezoidally described with Triangleshape grade of membership function with half in the embodiments of the invention, as shown in Figure 2, and μ (v among the upper figure _k, λ _P) (k=1,2 ..., 5) and represent that namely behavior index is to comment v _kDegree of membership, λ wherein ₁～λ ₅Being constant parameter, characterizing the micro-judgment value of corresponding index, is the parameter of each behavioral indicator membership function.

According to circuit or transformer overload index λ _L, determine desired value λ _L∈ (λ _Ln-1, λ _Ln) the substitution formula:

$e_k=n-\frac{{\mathrm{\&lambda;}}_{\mathrm{Ln}}-{\mathrm{\&lambda;}}_L}{{\mathrm{\&lambda;}}_{\mathrm{Ln}}-{\mathrm{\&lambda;}}_{\mathrm{Ln}-1}}$

Can calculate circuit or transformer overload index minute manifold e that the comment set pair is answered _k, calculate successively index minute manifold corresponding to comment collection E.

Step 5: the comprehensive evaluation result of measures for limiting short-circuit current

Calculate the relative importance value of fuzzy overall evaluation

Element S with Secondary Fuzzy Comprehensive Evaluation collection S _kBe weight, k element among minute manifold E be weighted on average the computing formula of the relative importance value N of substitution fuzzy overall evaluation:

$N=\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_k{e}_k/\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_k$

Calculate the comprehensive evaluation relative importance value of this measures for limiting short-circuit current.

Claims (10)

1. a comprehensive evaluation method for limiting short-circuit current, is characterized in that, described method is based on three-layer fuzzy comprehensive evaluation model, comprises the following steps: -Determine the current limiting plan according to the effect of various current limiting measures; -Determine the criterion level and index level factor sets related to the evaluated scheme; -Determine the weight set composed of the weights of the relative importance of each factor in the criterion layer and the index layer; - Determine the level of the evaluated program and the corresponding comment set; -Through the simulation calculation and analysis of Gansu power grid, the quantified value of each fuzzy evaluation index in the index layer is obtained, and the fuzzy comprehensive evaluation is carried out in combination with the membership functions and weights of each factor mentioned in the index layer, and then according to the evaluation results of the index layer and the criterion layer The weight of each factor is again fuzzy comprehensive evaluation, and the priority of the fuzzy comprehensive evaluation of the current limiting scheme is obtained. the 2. The method according to claim 1, characterized in that, the determination of the current limiting scheme is based on the effects of various short-circuit current limitations, and the current limiting effect is simulated and calculated for the Gansu power grid to form a preliminary scheme, and then check the constraints , optimize the current limiting scheme, and determine the current limiting measures adopted in the current limiting scheme. the 3. The method according to claim 1, characterized in that, for the grid structure and actual operation of Gansu power grid, the set of factors includes 750/330kV power grid static security, transient stability, short-circuit current limiting effect and Four sub-factor sets of operating economy. the 4. The method according to claim 2, characterized in that, by analyzing the actual impact on the grid power flow distribution and bus voltage in Gansu after various current-limiting measures are implemented, the static safety sub-factor set further includes line or transformer overvoltage. There are two sub-factors: load and bus voltage over-limit. the 5. The method according to claim 2, characterized in that, by analyzing the actual impact on the transient stability of Gansu power grid after various current-limiting measures are implemented, the transient stability sub-factor set further includes the maximum generator power angle Poor factor. the 6. The method according to claim 2, characterized in that, for the actual short-circuit current level and distribution of Gansu power grid, said short-circuit current limiting effect sub-factor set further includes 750kV three-phase, 750kV single-phase short-circuit current and 330kV three-phase , 330kV single-phase short-circuit current four sub-factors. the 7. The method according to claim 2, wherein the set of operating economy sub-factors further includes two sub-factors of switchgear investment and system network loss. the 8. The method according to claim 1, wherein the weight set is determined by a judgment matrix analysis method. the 9. The method according to claim 1, wherein the fuzzy comprehensive evaluation performs a fuzzy comprehensive evaluation on each factor in the index layer. the 10 . The method according to claim 1 , wherein the fuzzy comprehensive evaluation is performed on each factor in the criterion layer in combination with the results of the fuzzy comprehensive evaluation of the indicators. 11 . the

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