CN103218755A - Micro-grid evaluating method with inverse non-extensive entropy adopted - Google Patents

Micro-grid evaluating method with inverse non-extensive entropy adopted Download PDF

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CN103218755A
CN103218755A CN2013101450951A CN201310145095A CN103218755A CN 103218755 A CN103218755 A CN 103218755A CN 2013101450951 A CN2013101450951 A CN 2013101450951A CN 201310145095 A CN201310145095 A CN 201310145095A CN 103218755 A CN103218755 A CN 103218755A
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entropy
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electrical network
little electrical
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CN103218755B (en
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陈继开
徐冰亮
李浩茹
于海洋
武国良
陈晓光
张明江
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Heilongjiang Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Heilongjiang Electric Power Co Ltd
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Abstract

The invention discloses a micro-grid evaluating method with inverse non-extensive entropy adopted, and relates to the field of micro-grid evaluation. The invention provides an index weight computing method based on the inverse non-extensive entropy and provides the micro-grid evaluating method with the inverse non-extensive entropy adopted in order to solve the problems that in index weight computing of a Shannon entropy weight method, computed index weight is not accurate, and the fact that an evaluating result is not just is caused. Firstly, a mathematical expression of the inverse non-extensive entropy is determined; secondary, a q value of the inverse non-extensive entropy is determined; and thirdly, a micro-grid is evaluated by the adoption of the micro-grid evaluating method with the inverse non-extensive entropy adopted. The micro-grid evaluating method is applied to the field of micro-grid evaluation.

Description

Adopt little electrical network assessment method of anti-non-extension entropy
Technical field
The present invention relates to little electrical network test and appraisal field.
Background technology
Because little electrical network not only can solve distributed power source and insert problem on a large scale, give full play to every advantage of distributed power source, but also can bring many-sided benefit, so a large amount of scientific researches and engineering trial have been carried out at little electrical network both at home and abroad in recent years for the user.China is wideling popularize green novel energy source generating and intelligent grid construction at present, little electrical network encircles the research focus that has become power domain as key one wherein, and national grid subordinate's Utilities Electric Co. of how tame provinces and cities has set up little electrical network demonstration project and done many correlative studys.In order to understand little power grid construction in each department and development, State Grid Corporation of China need test and assess to the little electrical network in each department according to little electrical network assessment indicator as the supvr of domestic electrical network, thereby grasp the little power network development situation of China, further encourage outstanding little power grid construction also to promote its successful experience, this to future Chinese little power network development have directive significance.Yet current little power network development also is in initial stage, has more uncertain factor, and index system does not form as yet, and assessment method waits discussion, simultaneously, also is faced with huge dominance investment and long-term problems such as stealthy benefit coexistence.At this situation, how making up the assessment indicator system of science and proposing rational assessment method is a problem demanding prompt solution.
At present, existing scholar has done Primary Study to the test and appraisal problem of little electrical network, and little Electric Power Network Planning assessment indicator is made up and should be used as preliminary discussion.Think that little electrical network quality of power supply standard should be higher than major network, and be foundation with isolated system in the external electric system and interacted system relevant criterion, discussed little electrical network under isolated island is incorporated into the power networks state transition condition to the requirement aspect the quality of power supply and the capability of overload.Characteristic, the intermittent DG that also has the scholar to embody as equivalent power supply/load from the little electrical network aspects such as situation, energy storage configuration, islet operation state and on-road efficiency of exerting oneself propose little operation of power networks reliability assessment index and computing method, for little electric network reliability index system foundation is benefited our pursuits.Yet, mostly assessment method at little electrical network is to utilize analytical hierarchy process (AHP) to carry out the calculating of assessment indicator weight at present, AHP is applicable to the calculating of subjective weight, but we wish that the index weight should be the comprehensive of subjective weight and objective weight during actual the test and appraisal, so need a kind of new index weighing computation method that index objective weight accurately is provided.Though there is the scholar to propose a kind of index weighing computation method at present based on anti-Shannon entropy power method, and apply it in the intelligent grid test and appraisal, but discover, anti-Shannon entropy power method also is not suitable for the index weight calculation that comprises outstanding " not exclusive small probability event ", if use the method will cause the inaccurate of parameter weight without distinction, finally cause the inequity of evaluating result.
Summary of the invention
The present invention will solve anti-Shannon entropy power method to exist the parameter weight inaccurate in the index weight calculation, the iniquitous problem that causes evaluating result, and proposed index weighing computation method, and provide the little electrical network assessment method that adopts anti-non-extension entropy based on this algorithm based on anti-non-extension entropy.
One, determines the mathematic(al) representation of anti-non-extension entropy
Anti-non-extension entropy discrete form S qAs follows:
S q = k q - 1 [ 1 - Σ i = 1 n p ( i ) q ] , q ∈ R - - - ( 1 )
In the formula, 0≤p (i)≤1 and q are non-extensive parameter, and k is the Boltzmann constant;
By formula (1) as can be known, when q immobilizes, along with the increase of p (i) complexity of being investigated system, S qAlso with non-linear increase thereupon;
The mathematical expression that proposes anti-non-extension entropy according to formula (1) is as follows:
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) - - - ( 2 )
Two, determine the q value of anti-non-extension entropy
1) at first construct an index matrix:
Figure BDA00003093163100023
For same index, there is this index diversity factor K of l little electrical network between 1~m, to change in this matrix representation: n little electrical network, l represents that the little electrical network quantity that changes appears in diversity factor;
2) susceptibility of the anti-non-extension entropy of definition:
δ = 1 K max
In the following formula, K MaxExpression S ' q(l=1)=S ' q(l=2) the index diversity factor K value of correspondence the time;
3), set the susceptibility δ (0<δ≤0.5) of anti-non-extension entropy according to the assessment accuracy requirement
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) S q ′ ( l = 1 ) = S q ′ ( l = 2 )
Obtain the mapping table of n and q, when setting δ=0.33, corresponding relation such as the table 1 of obtain participating in evaluation and electing regional little electrical network quantity n and q:
The q value of the anti-non-extension entropy of table 1
Figure BDA00003093163100031
Three, adopt little electrical network assessment method of anti-non-extension entropy that little electrical network is tested and assessed
1) establish total n little electrical network and participate in assessment, evaluation index quantity is m, x IjFor the index i corresponding parameters of little electrical network j (1≤i≤m, 1≤j≤n), carry out index parameter normalization according to following principle:
Carry out normalization for the corresponding parameter of income type index i according to formula:
d ij = x ij - min ( x ij ) max ( x ij ) - min ( x ij ) - - - ( 3 )
Carry out normalization for the corresponding parameter of profit and loss type index i according to formula:
d ij = max ( x ij ) - x ij max ( x ij ) - min ( x ij ) - - - ( 4 )
Then form standard index matrix HD=[D 1D 2D m] T, phasor D wherein I=1 ..., m={ d Ij| 1≤j≤n};
2) to D I=1 ..., mCarry out the probability of occurrence statistics, if D I=IComprise outstanding " not exclusive small probability event " and event number l=L, then at first select the q value, utilize the anti-non-extension entropy S ' of formula (2) parameter I according to table 1 q(i=I l=L), then makes l=1, once more the anti-non-extension entropy S ' of parameter I q(i=I, l=1);
Otherwise jump to step 4);
3) (i=I l=1), and goes out the anti-entropy of correct index I according to formula (6) vertebra to utilize the anti-Shannon entropy of formula formula (5) to calculate anti-Shannon entropy h ';
h ′ = - Σ i n p ( i ) ln ( 1 - p ( i ) ) - - - ( 5 )
In the formula, 0≤p (i)≤1 and
Figure BDA00003093163100035
h ′ ( i = I , l = L ) = S q ′ ( i = I , l = L ) × h ′ ( i = I , l = 1 ) S q ′ ( i = I , l = 1 ) - - - ( 6 )
4) except that index I, utilize formula (5) to calculate the anti-Shannon entropy of all the other indexs, and release the anti-entropy power of all indexs according to formula (7);
w E ( i ) = h ′ ( i ) Σ i = 1 m h ′ ( i ) - - - ( 7 )
5) determine comprehensive weight according to formula (8):
IP(i)=w ak×w E(i) (8)
In the formula, w AkThe subjective weight of representing different little electrical networks realization targets;
6) adopt the linear weighted function method, with index comprehensive weight IP (i) and each index parameter x of each little electrical network IjCarry out linear weighted function, release the decision value line ordering of going forward side by side, finally obtain n little electrical network test and appraisal synthesis result.
The invention effect:
The present invention compares with anti-Shannon entropy power method, not only keep the advantage of original assessment method but also index that can outstanding to comprising " not exclusive small probability event " and carried out the reasonable weight value computing, thereby improved the accuracy of little electrical network test and appraisal, compared with anti-Shannon entropy power method and improved 25% at least.
Utilize anti-Shannon entropy power method to calculate the weight of the index that comprises outstanding " not exclusive small probability event " all greater than actual expectation value (even weight of outstanding greater than comprising " unique small probability event " index), and adopt the index weighing computation method based on anti-non-extension entropy of the present invention to remedy this shortcoming, so the evaluating result that obtains is more rationally just.
Description of drawings
Fig. 1 is a process flow diagram of the present invention;
Fig. 2 be under the q=0.5 index anti-non-extension entropy with probability distribution variation relation figure;
Fig. 3 be under the q=0.99 index anti-non-extension entropy with probability distribution variation relation figure;
Fig. 4 be under the q=2 index anti-non-extension entropy with probability distribution variation relation figure;
Fig. 5 is that anti-Shannon entropy is with index diversity factor change curve; Wherein,
Figure BDA00003093163100042
Expression l=1, Expression l=2,
Figure BDA00003093163100044
Expression l=3,
Figure BDA00003093163100045
Expression l=4;
Fig. 6 is that anti-non-extension entropy is with index diversity factor change curve; Wherein,
Figure BDA00003093163100046
Expression l=1,
Figure BDA00003093163100047
Expression l=2,
Figure BDA00003093163100048
Expression l=3,
Figure BDA00003093163100049
Expression l=4;
Fig. 7 is two kinds of anti-entropy power curves;----expression w SE(i, l=1),
Figure BDA000030931631000411
Expression w SE(i, l=4), Expression w TE(i, l=4)
Fig. 8 is based on little electrical network evaluating result of two kinds of anti-entropy power methods; Wherein,---represent anti-Shanon entropy power method,
Figure BDA000030931631000413
Represent anti-non-extension entropy power method, A is an evaluating result difference.
Embodiment
Embodiment one: little electrical network assessment method of the anti-non-extension entropy of the employing of present embodiment is realized according to the following steps:
One, determines the mathematic(al) representation of anti-non-extension entropy
Anti-non-extension entropy discrete form S qAs follows:
S q = k q - 1 [ 1 - Σ i = 1 n p ( i ) q ] , q ∈ R - - - ( 1 )
In the formula, 0≤p (i)≤1 and q are non-extensive parameter, and k is the Boltzmann constant;
By formula (1) as can be known, when q immobilizes, along with the increase of p (i) complexity of being investigated system, S qAlso with non-linear increase thereupon;
The mathematical expression that proposes anti-non-extension entropy according to formula (1) is as follows:
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) - - - ( 2 )
Two, determine the q value of anti-non-extension entropy
1) at first construct an index matrix:
Figure BDA00003093163100053
For same index, there is this index diversity factor K of l little electrical network between 1~m, to change in this matrix representation: n little electrical network, l represents that the little electrical network quantity that changes appears in diversity factor;
2) susceptibility of the anti-non-extension entropy of definition:
δ = 1 K max
In the following formula, K MaxExpression S ' q(l=1)=S ' q(l=2) the index diversity factor K value of correspondence the time;
3), set the susceptibility δ (0<δ≤0.5) of anti-non-extension entropy according to the assessment accuracy requirement
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) S q ′ ( l = 1 ) = S q ′ ( l = 2 )
Obtain the mapping table of n and q, when setting δ=0.33, corresponding relation such as the table 1 of obtain participating in evaluation and electing regional little electrical network quantity n and q:
The q value of the anti-non-extension entropy of table 1
Three, adopt little electrical network assessment method of anti-non-extension entropy that little electrical network is tested and assessed
1) establish total n little electrical network and participate in assessment, evaluation index quantity is m, x IjFor the index i corresponding parameters of little electrical network j (1≤i≤m, 1≤j≤n), carry out index parameter normalization according to following principle:
Carry out normalization for the corresponding parameter of income type index i according to formula:
d ij = x ij - min ( x ij ) max ( x ij ) - min ( x ij ) - - - ( 3 )
Carry out normalization for the corresponding parameter of profit and loss type index i according to formula:
d ij = max ( x ij ) - x ij max ( x ij ) - min ( x ij ) - - - ( 4 )
Then form standard index matrix HD=[D 1D 2D m] T, phasor D wherein I=1 ..., m={ d Ij| 1≤j≤n};
2) to D I=1 ..., mCarry out the probability of occurrence statistics, if D I=IComprise outstanding " not exclusive small probability event " and event number l=L, then at first select the q value, utilize the anti-non-extension entropy S ' of formula (2) parameter I according to table 1 q(i=I l=L), then makes l=1, once more the anti-non-extension entropy S ' of parameter I q(i=I, l=1);
Otherwise jump to step 4);
3) (i=I l=1), and goes out the anti-entropy of correct index I according to formula (6) vertebra to utilize the anti-Shannon entropy of formula formula (5) to calculate anti-Shannon entropy h ';
h ′ = - Σ i n p ( i ) ln ( 1 - p ( i ) ) - - - ( 5 )
In the formula, 0≤p (i)≤1 and
Figure BDA00003093163100065
h ′ ( i = I , l = L ) = S q ′ ( i = I , l = L ) × h ′ ( i = I , l = 1 ) S q ′ ( i = I , l = 1 ) - - - ( 6 )
4) except that index I, utilize formula (5) to calculate the anti-Shannon entropy of all the other indexs, and release the anti-entropy power of all indexs according to formula (7);
w E ( i ) = h ′ ( i ) Σ i = 1 m h ′ ( i ) - - - ( 7 )
5) determine comprehensive weight according to formula (8):
IP(i)=w ak×w E(i) (8)
In the formula, w AkThe subjective weight of representing different little electrical networks realization targets;
6) adopt the linear weighted function method, with index comprehensive weight IP (i) and each index parameter x of each little electrical network IjCarry out linear weighted function, release the decision value line ordering of going forward side by side, finally obtain n little electrical network test and appraisal synthesis result.
In the present embodiment, by formula (2) as can be known, anti-non-extension entropy is a kind of distortion of Tsallis entropy, raising along with the system complex degree, the value of anti-non-extension entropy will be non-linear reducing, and this means when carrying out system evaluation with a plurality of assessment indicators as foundation, along with the increase of the diversity factor of numerical value in each index, corresponding anti-non-extension entropy is Nonlinear Monotone and increases progressively, the basic demand of during these compliance with system test and appraisal each index entropy being weighed.
In the present embodiment, little electrical network assessment indicator construction step is as follows:
13 little electrical network assessment indicators are numbered in order, and set the corresponding parameter of No. 1 little electrical network index in area, as shown in table 2:
The little electrical network index parameter in table 2 somewhere
Figure BDA00003093163100072
The little electrical network index value in No. 1 area that makes table 2 provide is X I, 1={ x Ij| j=1,1≤i≤13} (i is the index sequence number) is satisfying under the condition of standardized normal distribution, obtains the corresponding index parameter of all the other 14 little electrical networks at random according to formula (9), forms index matrix X 13 * 15(l=1).
μ ( i ) = α × X i , 1 σ = β × μ ( i ) - - - ( 9 )
In the formula, μ (i)---the mathematical expectation of index i;
σ---standard deviation.
Here work as index i=2,3,4,5,11,, establish α=0.24 and β=0.12 at 12 o'clock; Work as i=6,7,8,9,10,, establish α=1 and β=0.46 at 13 o'clock.
In the present embodiment, as follows based on the evaluating result of two kinds of anti-entropy power:
At first according to formula
Figure BDA00003093163100081
With
Figure BDA00003093163100082
Calculate anti-Shannon entropy power w SE(i l=1), then adjusts index matrix, makes the index i=2 of 2~No. 4 little electrical network correspondences in area, and 3,4,5,11,12 is consistent with No. 1 area, obtains New Set matrix X 13 * 15(l=4), utilize anti-non-extension entropy to weigh the anti-entropy power w that little electrical network assessment method and anti-Shannon entropy power method is calculated little each index of electrical network once more respectively TE(i, l=1) and w SE(i, l=4), 3 anti-entropy power curves As Fig. 7 instituteShow:
Observe Fig. 7 as can be known, as microgrid assessment indicator i=2,3,4,5,11,, w is arranged at 12 o'clock SE(i, l=1)<w SE(i, l=4), this has run counter to the development of encouragement developed regions and has had the original intention of little electrical network of outstanding " unique small probability event " index.And in fact, we wish to comprise index weight and w that the index weight of outstanding " unique small probability event " should outstanding greater than comprising " not exclusive small probability event " SE(i, l=1)>w SE(i, l=4).Just can obtain correct anti-entropy power w as a result and utilize non-extension entropy to weigh little electrical network assessment method SE(i, l=1)>w TE(i, l=4), this illustrates that anti-non-extension entropy powers and functions characterize the index weight that comprises outstanding " not exclusive small probability event " enough exactly, it is as shown in table 3 to establish subjective weights:
The subjective weighted value of each target of table 3
Figure BDA00003093163100083
Based on anti-non-extension entropy power method and anti-Shannon entropy power method 15 little electrical networks are tested and assessed respectively, evaluating result as shown in Figure 8:
Analysis chart 8 is found, because every index value of 5~No. 15 little electrical networks in area is followed standardized normal distribution, so weigh the appraisal result basically identical of methods based on two kinds of anti-entropys.On the contrary, for 1~No. 4 little electrical network in area, appraisal result based on anti-non-extension entropy power method is all weighed method less than anti-Shannon entropy, this is owing to have the index (index i=1~5 and 11~12) that comprises outstanding " not exclusive small probability event " in 1~No. 4 little electrical network in area, but utilize anti-Shannon entropy power method to calculate the weight of this type of index all greater than actual expectation value (even weight of outstanding greater than comprising " unique small probability event " index), so anti-relatively Shannon entropy power method, the evaluating result that utilizes anti-non-extension entropy power method to obtain is more reasonable.
The present embodiment effect:
Present embodiment is compared with anti-Shannon entropy power method, not only can keep the advantage of original assessment method but also index that can outstanding to comprising " not exclusive small probability event " and carry out the reasonable weight value computing, thereby improved the accuracy of little electrical network test and appraisal, accuracy is compared with anti-Shannon entropy power method and has been improved 25% at least.
Utilize weight that anti-Shannon entropy power method calculates this type of index all greater than actual expectation value (even weight of outstanding greater than comprising " unique small probability event " index), and the evaluating result that adopts the index weighing computation method based on anti-non-extension entropy of present embodiment to obtain is more rationally just.

Claims (1)

1. adopt little electrical network assessment method of anti-non-extension entropy, it is characterized in that adopting little electrical network assessment method of anti-non-extension entropy to realize according to the following steps:
One, determines the mathematic(al) representation of anti-non-extension entropy
Non-extension entropy discrete form S qAs follows:
S q = k q - 1 [ 1 - Σ i = 1 n p ( i ) q ] , q ∈ R - - - ( 1 )
In the formula, 0≤p (i)≤1 and q are non-extensive parameter, and k is the Boltzmann constant;
By formula (1) as can be known, when q immobilizes, along with the increase of p (i) complexity of being investigated system, S qAlso with non-linear increase thereupon;
The mathematical expression that proposes anti-non-extension entropy based on formula (1) is as follows:
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) - - - ( 2 )
Two, determine the q value of anti-non-extension entropy
1) at first construct an index matrix:
Figure FDA00003093163000013
For same index, there is this index diversity factor K of l little electrical network between 1~m, to change in this matrix representation: n little electrical network, l represents that the little electrical network quantity that changes appears in diversity factor;
2) susceptibility of the anti-non-extension entropy of definition:
δ = 1 K max
In the following formula, K MaxExpression S ' q(l=1)=S ' q(l=2) the index diversity factor K value of correspondence the time;
3), set the susceptibility δ (0<δ≤0.5) of anti-non-extension entropy according to the assessment accuracy requirement
S q ′ = 1 - 1 - Σ i = 1 n p ( i ) q 1 - n ( 1 - q ) S q ′ ( l = 1 ) = S q ′ ( l = 2 )
Obtain the mapping table of n and q, when setting δ=0.33, corresponding relation such as the table 1 of obtain participating in evaluation and electing regional little electrical network quantity n and q:
The q value of the anti-non-extension entropy of table 1
Figure FDA00003093163000021
Three, adopt little electrical network assessment method of anti-non-extension entropy that little electrical network is tested and assessed
1) establish total n little electrical network and participate in assessment, evaluation index quantity is m, x IjFor the index i corresponding parameters of little electrical network j (1≤i≤m, 1≤j≤n), carry out index parameter normalization according to following principle:
Carry out normalization for the corresponding parameter of income type index i according to formula:
d ij = x ij - min ( x ij ) max ( x ij ) - min ( x ij ) - - - ( 3 )
Carry out normalization for the corresponding parameter of profit and loss type index i according to formula:
d ij = max ( x ij ) - x ij max ( x ij ) - min ( x ij ) - - - ( 4 )
Then form standard index matrix HD=[D 1D 2D m] T, phasor D wherein I=1 ..., m={ d Ij| 1≤j≤n};
2) to D I=1 ..., mCarry out the probability of occurrence statistics, if D I=IComprise outstanding " not exclusive small probability event " and event number l=L, then at first select the q value, utilize the anti-non-extension entropy S ' of formula (2) parameter I according to table 1 q(i=I l=L), then makes l=1, once more the anti-non-extension entropy S ' of parameter I q(i=I, l=1);
Otherwise jump to step 4);
3) (i=I l=1), and releases the anti-entropy of correct index I according to formula (6) to utilize the anti-Shannon entropy of formula formula (5) to calculate anti-Shannon entropy h ';
h ′ = - Σ i n p ( i ) ln ( 1 - p ( i ) ) - - - ( 5 )
In the formula, 0≤p (i)≤1 and
Figure FDA00003093163000025
h ′ ( i = I , l = L ) = S q ′ ( i = I , l = L ) × h ′ ( i = I , l = 1 ) S q ′ ( i = I , l = 1 ) - - - ( 6 )
4) except that index I, utilize formula (5) to calculate the anti-Shannon entropy of all the other indexs, and release the anti-entropy power of all indexs according to formula (7);
w E ( i ) = h ′ ( i ) Σ i = 1 m h ′ ( i ) - - - ( 7 )
5) determine comprehensive weight according to formula (8):
IP(i)=w ak×w E(i) (8)
In the formula, w AkThe subjective weight of representing different little electrical networks realization targets;
6) adopt the linear weighted function method, with index comprehensive weight IP (i) and each index parameter x of each little electrical network IjCarry out linear weighted function, release the decision value line ordering of going forward side by side, finally obtain n little electrical network test and appraisal synthesis result.
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CN110740558A (en) * 2019-10-18 2020-01-31 南昌大学 method for measuring plasma electron non- time delay parameter
CN112888128A (en) * 2021-01-18 2021-06-01 南昌大学 Method for measuring plasma ion non-extensive parameter
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