CN106910141B - Complex active power distribution network decomposition scheme optimization method and device - Google Patents
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Abstract
The invention relates to a method and a device for optimizing a decomposition scheme of a complex active power distribution network, wherein the method comprises the following steps: acquiring a decomposition scheme set of a complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set; determining a merit and disadvantage ordering sequence of each decomposition scheme by a set pair analysis method according to the decomposition scheme set and evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set; performing stability analysis on the superiority and inferiority sorting sequence, updating the superiority and inferiority sorting sequence, and selecting a decomposition scheme corresponding to a top-ranked element in the superiority and inferiority sorting sequence as an optimal decomposition scheme; according to the technical scheme provided by the invention, the decision model of the decomposition scheme of the complex active power distribution network can simultaneously consider the identity and the opposites of the influence factors, and a new thought is provided for processing the optimal decision problem of the decomposition scheme of the complex active power distribution network.
Description
Technical Field
The invention relates to the field of power distribution networks, in particular to a method and a device for optimizing a decomposition scheme of a complex active power distribution network.
Background
Set Pair Analysis (SPA) is an uncertain theory, and is a systematic Analysis method for definite, uncertain system-same, different and inverse quantitative Analysis, which is proposed by Chinese scholars Zhao Keqin in 1989. The core idea is that the deterministic information and the uncertain information are contained in the same system, and the determinacy and the uncertainty of objects are researched from the same aspect, the different aspect and the opposite aspect, so that the connection and the conversion among the objects are comprehensively described.
The basic concept of set pair analysis is set pair and its degree of association. The set pair is a pair formed by two sets with certain relation, and the analysis is developed according to a certain characteristic of the set pair, and the classification and the quantitative description are carried out on the relation of the set pair on the characteristic, so as to obtain a relation expression of the set pair under a certain problem background, wherein the relation expression comprises the following steps:
μ＝a+bi+cj
in the formula: mu is called contact, and contact for a particular problem is generally only a structural function, and is a numerical value only in special cases. a represents the degree of identity of the two sets, called identity; b represents the uncertainty degree of the difference of the two sets, which is called the difference degree; c represents the degree of opposition of the two sets, called opposition; i is the coefficient of the difference degree, and the value is [ -1,1 ]. i varies between-1 and 1, which reflects the interconversion between certainty and uncertainty, with i → 0, the uncertainty is obviously increased, and when i takes on-1 and 1, the problem is deterministic; j is an opposite sign or a corresponding coefficient, and the specified value is-1.
The contact degree can uniformly process uncertainties caused by fuzzy, random, incomplete information and the like. This scoring is a quantitative description of certainty and uncertainty, where a, c are relatively deterministic and b is relatively non-deterministic, a, b, c satisfying the following normalization condition:
a+b+c＝1
this relativity is due to the complexity and variability of the objective subject, as well as uncertainty caused by subjectivity and ambiguity of the recognition and characterization of the objective subject. Therefore, in the formula (1), the determinism, uncertainty, identity and oppositivity have relativity and ambiguity in recognition, and the depicted result is also relative and non-unique. The set pair analysis effectively describes the opposite unified relationship between the determined and uncertain systems, conforms to the natural dialectics and human thinking modes, and has methodology significance.
The power distribution network has numerous devices, complex structure, large scale and complex analysis and calculation. Particularly, with the development of the smart power grid, a large number of distributed power sources are connected to the power distribution network, the traditional power distribution network gradually develops into a complex active power distribution network, and the calculation scale of network analysis and calculation is further increased. The calculation scale of the problem can be greatly reduced through network decomposition, and a large amount of calculation time is saved. For a complex active power distribution network, a plurality of network decomposition schemes often exist, how to select an optimal scheme from a plurality of feasible network decomposition schemes preferably needs to consider the calculation speed and also needs to consider the limitation of a plurality of factors such as calculation precision, resource utilization rate and the like. In practical decision making, the factors to be considered are often opposite and uniform, and how to make the factors well uniform in a network decomposition scheme decision model is a problem worthy of research.
Disclosure of Invention
The invention provides a method and a device for optimizing a decomposition scheme of a complex active power distribution network, and aims to enable a decision model of the decomposition scheme of the complex active power distribution network to simultaneously consider the identity and the oppositiveness of influence factors and provide a new idea for processing the optimization decision problem of the decomposition scheme of the complex active power distribution network.
The purpose of the invention is realized by adopting the following technical scheme:
in a preferred method of a decomposition scheme for a complex active power distribution network, the improvement comprising:
acquiring a decomposition scheme set of a complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
determining a priority ranking sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
and performing stability analysis on the high-low ranking sequence, updating the high-low ranking sequence and selecting a decomposition scheme corresponding to the top ranking element in the high-low ranking sequence as an optimal decomposition scheme.
Preferably, the acquiring a decomposition scheme set of the complex active power distribution network and evaluation indexes corresponding to the decomposition schemes in the decomposition scheme set includes:
and respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
Further, determining a resource utilization index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 1 ：
In the above formula, n is the number of network partitions, P i 2 For the calculation size of the ith partition in the network, i ∈ [1,n ∈ ]]；
Determining the parallel computation complexity index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 2 ：
In the above formula, O min In order to theoretically minimize the complexity of parallel computing,
the calculation complexity of the ith partition in the network, l is the number of the coordination level servers, M is a calculation cost coefficient, i belongs to [1,n ]]，M∈[2,5]N is the number of partitions of the network;
determining the parallel computation accuracy index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U i ' is the voltage value of node i after network decomposition, U i For the voltage value of node i before network decomposition, i belongs to [1,m ∈ ]]M is the total number of nodes in the network;
determining a parallel computing acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required for solving the problem serially, T P The time required to solve the problem in parallel;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers required for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computation.
Preferably, the determining, according to the decomposition scheme set and the evaluation index corresponding to each decomposition scheme in the decomposition scheme set, a merit and disadvantage ranking sequence of each decomposition scheme by using a set pair analysis method includes:
converting non-profit type indexes in the evaluation indexes corresponding to the decomposition schemes into profit type indexes;
carrying out dimensionless processing on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme;
selecting an optimal normalized index value set U = (U) in normalized index values corresponding to the decomposition schemes 1 ,u 2 ,...u n ) And worst normalized index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
Determining the relative closeness of each decomposition scheme and the optimal normalized index value set U in a comparison space [ V, U ] of each decomposition scheme;
and sequencing the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring the priority sequencing sequence of the decomposition schemes.
Further, the converting a non-profit type index in the evaluation indexes corresponding to each decomposition scheme into a profit type index includes:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-revenue type indicator, will &>
Conversion to revenue-type metrics:
in the above formula, the first and second carbon atoms are,
is->
The profit-type index value of (1), device for selecting or keeping>
For the maximum index value of the kth decomposition scheme with respect to the r-th index,k∈[1,m]，r∈[1,n]m is the total number of decomposition schemes, and n is the total number of evaluation indexes.
Further, the performing non-dimensionalization on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme includes:
carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
Further, the determining, in the comparison space [ V, U ] of each decomposition scheme, the relative closeness of each decomposition scheme to the optimal normalized index value set U includes:
let decomposition scheme set S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Recording the normalized index value of the kth decomposition scheme relative to the r index as d kr The optimal normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is epsilon [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k The degree of opposition of the kth decomposition scheme and the optimal normalized index value set U is represented by i as a difference coefficient and j as an opposition marker symbol;
wherein i ∈ [ -1,1]，j＝1，
Determining the relative closeness gamma of the kth decomposition scheme and the optimal normalization index value set U according to the following formula k ：
Preferably, the performing stability analysis on the priority ranking sequence, updating the priority ranking sequence, and selecting a decomposition scheme corresponding to a top-ranked element in the priority ranking sequence as an optimal decomposition scheme includes:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Sorting the top elements in the priority sorting sequence;
the difference coefficient i of the decomposition schemes corresponding to each element in the high-low ranking sequence is equal, and gamma in the high-low ranking sequence is selected k Corresponding decomposition scheme and gamma p Corresponding decomposition scheme, when i is greater than or equal to 0 and less than or equal to 1 and c k b p -c p b k When the value is less than or equal to 0, i is required to satisfy the requirement of i epsilon [0,1]If yes, then gamma in said merit-ranking sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k When > 0, i is satisfied
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when i is more than or equal to-1 and less than 0 and a k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when-1 is more than or equal to i and less than 0 and a k b p -a p b k When < 0, i is satisfied
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme to the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U is obtained.
In a preferred apparatus for a complex active power distribution grid decomposition scheme, the improvement comprising:
the system comprises an acquisition module, a judgment module and a processing module, wherein the acquisition module is used for acquiring a decomposition scheme set of the complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
the determining module is used for determining the priority ordering sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and the evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
and the analysis module is used for carrying out stability analysis on the priority sequence, updating the priority sequence and selecting a decomposition scheme corresponding to the top-ranked element in the priority sequence as an optimal decomposition scheme.
Preferably, the obtaining module includes:
the first determining unit is used for respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
Further, determining a resource utilization index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 1 ：
In the above formula, n is the number of partitions in the network, P i 2 For the calculation size of the ith partition in the network, i ∈ [1,n ∈ ]]；
Determining the parallel computation complexity index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 2 ：
In the above formula, O min In order to theoretically minimize the complexity of parallel computing,
the calculation complexity of the ith partition in the network, l is the number of the coordination level servers, M is a calculation cost coefficient, i belongs to [ 1],n]，M∈[2,5]N is the number of partitions of the network;
determining the parallel computation accuracy index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U i ' is the voltage value of node i after network decomposition, U i For the voltage value of node i before network decomposition, i belongs to [1,m ∈ ]]M is the total number of nodes in the network;
determining a parallel computing acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required for solving the problem serially, T P The time required to solve the problem in parallel;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers required for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computing.
Preferably, the determining module includes:
the conversion unit is used for converting non-profit type indexes in the evaluation indexes corresponding to the decomposition schemes into profit type indexes;
a normalization unit, configured to perform dimensionless processing on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme;
a selection unit for selectingAn optimal normalized index value set U = (U) of normalized index values corresponding to each decomposition scheme 1 ,u 2 ,...u n ) And worst normalized index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
A second determining unit, configured to determine, in the comparison space [ V, U ] of each decomposition scheme, a relative closeness of each decomposition scheme to the optimal normalized index value set U;
and the sorting unit is used for sorting the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring the priority sorting sequence of the decomposition schemes.
Further, the conversion unit includes:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-profit type indicator, then pressing the following formula will->
Conversion to revenue-type metrics:
in the above-mentioned formula, the compound has the following structure,
is->
The profit-type index value of (a), device for selecting or keeping>
For the maximum index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
Further, the specification unit includes:
carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
Further, the second determining unit includes:
let decomposition scheme set S = { S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Let the normalized index value of the kth decomposition scheme with respect to the r index be d kr The optimal normalized index value among the normalized index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is epsilon [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, i, of the kth decomposition scheme to the optimal normalized index value set UIs the coefficient of the degree of difference, j is the opposite sign;
wherein i ∈ [ -1,1]，j＝1，
Determining the relative closeness gamma of the kth decomposition scheme and the optimal normalization index value set U according to the following formula k ：
Preferably, the analysis module includes:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Sorting the top elements in the priority sorting sequence;
the difference coefficient i of the decomposition schemes corresponding to each element in the high-low ranking sequence is equal, and gamma in the high-low ranking sequence is selected k Corresponding decomposition scheme and gamma p A corresponding decomposition scheme;
a first judgment unit for judging when i is more than or equal to 0 and less than or equal to 1 and c is k b p -c p b k When the value is less than or equal to 0, i is required to satisfy the requirement of i epsilon [0,1]If yes, then gamma in said merit-ranking sequence k And gamma p Does not change, if not, then gamma is determined to be the same in the said sequence k And gamma p The sequencing positions of the two groups are interchanged;
a second judgment unit for when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k When > 0, i is satisfied
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p Does not change, if not, then gamma is determined to be the same in the said sequence k And gamma p Exchange of sequencing position；
A third judgment unit for a when-1 is not less than i < 0 k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p Does not change, if not, then gamma is determined to be the same in the said sequence k And gamma p The sequencing positions of the two groups are interchanged;
a fourth judgment unit for a when-1 is not less than i < 0 k b p -a p b k When i is less than 0, i is satisfied
If yes, then gamma in said sequence of merit-least-squares is determined k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme to the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme to the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And (4) determining the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U.
The invention has the beneficial effects that:
according to the technical scheme provided by the invention, the optimization decision of the complex active power distribution network decomposition scheme is carried out by adopting pair analysis, the concept of the method for evaluating the quality degree of the scheme by using relative closeness is clear, the calculation is simple, and the programming is convenient to realize; a complex active power distribution network decomposition decision scheme with better credibility is obtained through pair-gathering analysis, and the actual requirement for achieving the optimal comprehensive factors such as resource utilization rate, parallel computation complexity and parallel computation precision is met; and when the quality of the scheme is judged under a relatively determined condition, analyzing the stability of the sequencing result by using the relative uncertainty information, giving an i stable region, searching other sequencing results, and judging relatively stable sequencing from unstable sequencing.
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FIG. 1 is a flow chart of a preferred method of a complex active power distribution network decomposition scheme of the present invention;
fig. 2 is a schematic structural diagram of a preferred device of a complex active power distribution network decomposition scheme of the invention.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention provides a preferred method for a complex active power distribution network decomposition scheme, which comprises the following steps of:
101. acquiring a decomposition scheme set of a complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
102. determining a priority ranking sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
103. and performing stability analysis on the high-low ranking sequence, updating the high-low ranking sequence and selecting a decomposition scheme corresponding to the top ranking element in the high-low ranking sequence as an optimal decomposition scheme.
Specifically, the step 101 includes:
and respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
Determining a resource utilization index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 1 ：
In the above formula, n is the number of partitions of the network,
for the calculation size of the ith partition in the network, i ∈ [1,n ∈ ]]；
The resource utilization rate represents the overall utilization efficiency of the server, and after the respective calculation of each partition is completed, the coordination server needs to calculate the coordination amount by utilizing the calculation data of each sub-partition server. If the calculation scales of the sub-partitions are too different, the sub-partitions wait for each other, and resources are wasted. y is 1 The closer to 1 indicates that the calculation scale of each partition is closer, and the resource utilization efficiency is higher. The index is a revenue-type index.
The steps of parallel computation can be briefly described as three steps: firstly, each sub server carries out calculation of each region, and sends the data result related to the coordination quantity to the coordination server, then the coordination server calculates the correction value of each coordination quantity through the data transmitted by each sub server, and finally sends the data of the coordination quantity value to each sub server, and each sub server carries out parallel calculation on each sub partition. The calculation in a general power system needs to be iterated for multiple times, the steps are repeated until the required precision is met, and the parallel calculation complexity index y corresponding to each decomposition scheme in the decomposition scheme set is determined according to the following formula 2 ：
In the above formula, O min In order to theoretically minimize the complexity of parallel computing,
the calculation complexity of the ith partition in the network, l is the number of the coordination level servers, M is a calculation cost coefficient, i belongs to [1,n ]]，M∈[2,5]N is the number of partitions of the network;
the coordination level server is mainly used for being responsible for communication with each sub-partition, the calculation scale is much smaller than that of each sub-partition calculation server, a coefficient M (2-5) is multiplied by a second term of a denominator in equation (4) to represent the calculation cost of the coordination level server higher than each sub-server, and the smaller value of equation (4) represents the larger parallel calculation scale of the used partition method. When y is 2 And when the speed is not less than 1, the parallel computation complexity reaches the theoretical minimum parallel computation complexity, and the maximum acceleration ratio can be obtained by parallel computation at the moment. The index is a revenue-type index.
And calculating the known network to obtain the voltage value of each node in the network, thereby obtaining the voltage level of the research system. And decomposing the voltage change conditions of the nodes before and after partitioning through a voltage level comparison network, and determining the influence of parallel calculation on the overall calculation precision after partitioning. Determining the parallel computation accuracy index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U i ' is the voltage value of node i after the network decomposition, U i For the voltage value of node i before network decomposition, i belongs to [1,m ∈ ]]M is the total number of nodes in the network;
the speed-up ratio is the degree of the parallel capability of the system when the parallel system runs a parallel program, and is related to the characteristics of hardware, software and application. Determining a parallel computation acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required to solve the problem serially, T P For parallel solvingThe time required to solve the problem;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers required for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computing.
After obtaining the decomposition scheme set and the evaluation index corresponding to each decomposition scheme in the decomposition scheme set, the step 102 includes:
converting non-income type indexes in the evaluation indexes corresponding to the decomposition schemes into income type indexes;
carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes to obtain normalized index values corresponding to the decomposition schemes;
selecting an optimal normalized index value set U = (U) in normalized index values corresponding to the decomposition schemes 1 ,u 2 ,...u n ) And worst normalization index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
Wherein, for analysis in the same range, the optimal solution and the worst solution are determined, and both can be generated in the solution set or come from the outside of the solution set, and can be determined according to the system target and objective conditions.
Determining the relative closeness of each decomposition scheme and the optimal normalized index value set U in the comparison space [ V, U ] of each decomposition scheme;
and sequencing the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring the priority sequencing sequence of the decomposition schemes.
Specifically, the converting a non-profit type index in the evaluation indexes corresponding to each decomposition scheme into a profit type index includes:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-profit type indicator, then pressing the following formula will->
Conversion to revenue-type metrics:
in the above formula, the first and second carbon atoms are,
is->
Get-type index value of>
For the maximum index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
The non-dimensionalizing the evaluation index corresponding to each decomposition scheme to obtain the normalized index value corresponding to each decomposition scheme includes:
carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
Said determining, in the comparison space [ V, U ] of each decomposition scheme, the relative closeness of each decomposition scheme to the optimal normalized index value set U includes:
let decomposition scheme set S = { S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Let the normalized index value of the kth decomposition scheme with respect to the r index be d kr The optimal normalized index value among the normalized index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is the [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k The degree of opposition of the kth decomposition scheme and the optimal normalized index value set U is represented by i as a difference coefficient and j as an opposition marker symbol;
wherein i ∈ [ -1,1]，j＝1，
Is as followsDetermining a relative closeness γ of the kth decomposition scheme to the optimal normalized index value set U k ：
Before determining the relative closeness of each decomposition scheme and the optimal normalized index value set U, the method needs to determine the relative closeness progress of a single optimal index in each decomposition scheme and the optimal normalized index value set, and comprises the following steps:
recording the evaluation scheme as s k ＝(d k1 ,d k2 ,...,d kn ) (k =1,2,.. Multidot., m), at e r Comparison interval [ v ] r ,u r ]Determine set pair { d } kr ,u r A degree of association.
At d kr ∈[v r ,u r ]Discussion of the time
The numerical value of (c): when +>
Taking the minimum value at a time>
When d is kr ＝v r Or u r Taking the maximum value at a time>
To make it possible to
Is normalized, i.e. is ready to be used>
Remove->
And &>
Get respectively->
Both can be regarded as pair d kr And u r The positive and negative proximity, respectively, can be defined as a set pair d kr ,u r Like and opposite ones of the.
From a + b + c =1, set pair { d is calculated kr ,u r The difference degree of the } is:
thus { d } kr ,u r The degree of association is:
according to the above formula, when d kr ＝u r Or v r Then, the difference is zero at the minimum; when in use
When the degree of difference is at most
Complexity hereinIn the decision method of the decomposition scheme of the active power distribution network, mu is adopted k ＝a k +b k i+c k Relatively stable a in j k And c k Form a relative degree of closeness gamma k To evaluate the quality of the scheme. But b k Is relatively uncertain, its value size marks the size of the uncertainty, and the sign and value of i can be considered as b k To a k Or c k The correction direction and the correction degree of (2) will have an influence on the evaluation result of the recipe. Therefore, it is necessary to perform ranking stability analysis on the evaluation results of the complex active power distribution network decomposition scheme, and to search for ranking results other than the basic ranking as much as possible, i.e., to obtain an extended ranking.
Analytical mu k ＝a k +b k i+c k j is available when i>0 is defined as a pair k Is corrected in the forward direction, marks the pair S k The positive attitude of the ideal optimal solution U is approached and the stronger the i is to 1, the stronger this correction is. On the contrary, when i < 0, it is regarded as the pair c k Is corrected in the forward direction, marks the pair S k This correction is stronger the closer to the negative attitude of U, and the closer i is to-1. For this purpose, i is [ -1,1]In the above, a stability analysis of the recipe sequence may be performed, and thus, the step 103 includes:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Sorting the top elements in the priority sorting sequence;
the difference coefficient i of the decomposition schemes corresponding to the elements in the superiority and inferiority sorting sequence is equal, and gamma in the superiority and inferiority sorting sequence is selected k Corresponding decomposition scheme and gamma p Corresponding decomposition scheme, when i is greater than or equal to 0 and less than or equal to 1 and c k b p -c p b k When the value is less than or equal to 0, i is required to satisfy the requirement of i epsilon [0,1]If yes, then gamma in said merit-ranking sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k When greater than 0, i is fullFoot
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged; />
When i is more than or equal to-1 and less than 0 and a k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when i is more than or equal to-1 and less than 0 and a k b p -a p b k When < 0, i is satisfied
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme to the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme to the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U is obtained.
The invention also provides a preferred device for the decomposition scheme of the complex active power distribution network, as shown in fig. 2, the device comprises:
the system comprises an acquisition module, a judgment module and a processing module, wherein the acquisition module is used for acquiring a decomposition scheme set of the complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
the determining module is used for determining the priority ordering sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and the evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
and the analysis module is used for carrying out stability analysis on the superiority and inferiority sorting sequence, updating the superiority and inferiority sorting sequence and selecting a decomposition scheme corresponding to the top-ranking element in the superiority and inferiority sorting sequence as an optimal decomposition scheme.
The acquisition module includes:
the first determining unit is used for respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
Determining a resource utilization index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 1 ：
In the above formula, n is the number of partitions of the network,
for the calculation size of the ith partition in the network, i E [1,n]；
Determining the parallel computation complexity index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 2 ：
In the above formula, O min In order to theoretically minimize the complexity of parallel computing,
the calculation complexity of the ith partition in the network, l is the number of the coordination level servers, and M is the calculation cost coefficient，i∈[1,n]，M∈[2,5]N is the number of partitions of the network;
determining the parallel computing precision index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U i ' is the voltage value of node i after the network decomposition, U i For the voltage value of node i before network decomposition, i belongs to [1,m ]]M is the total number of nodes in the network;
determining a parallel computing acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required for solving the problem serially, T P The time required to solve the problem in parallel;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers required for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computing.
The determining module includes:
the conversion unit is used for converting non-profit type indexes in the evaluation indexes corresponding to the decomposition schemes into profit type indexes;
a normalization unit, configured to perform dimensionless processing on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme;
a selection unit for selectingAn optimal normalized index value set U = (U) in the normalized index values corresponding to the decomposition schemes 1 ,u 2 ,...u n ) And worst normalization index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
A second determining unit, configured to determine, in the comparison space [ V, U ] of each decomposition scheme, a relative closeness of each decomposition scheme to the optimal normalized index value set U;
and the sorting unit is used for sorting the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring the priority sorting sequence of the decomposition schemes.
The conversion unit includes:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-profit type indicator, then pressing the following formula will->
Conversion to revenue-type indicators:
in the above formula, the first and second carbon atoms are,
is->
The profit-type index value of (a), device for selecting or keeping>
For the maximum index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
The specification unit includes:
carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
The second determination unit includes:
let decomposition scheme set S = { S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Recording the normalized index value of the kth decomposition scheme relative to the r index as d kr The optimal normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is epsilon [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k The degree of opposition of the kth decomposition scheme and the optimal normalized index value set U is represented by i, i is a difference coefficient, and j is an opposition marker symbol;
wherein i ∈ [ -1,1]，j＝1，
Determining a relative closeness γ of the kth decomposition scheme to the optimal normalized index value set U as follows k ：
The analysis module comprises:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Ordering the top elements in the priority ordering sequence;
the difference coefficient i of the decomposition schemes corresponding to the elements in the superiority and inferiority sorting sequence is equal, and gamma in the superiority and inferiority sorting sequence is selected k Corresponding decomposition scheme and gamma p A corresponding decomposition scheme;
a first judgment unit for judging when i is more than or equal to 0 and less than or equal to 1 and c is k b p -c p b k When the value is less than or equal to 0, i needs to satisfy the requirement of i epsilon [0,1]If yes, then γ in said merit-least ordered sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
a second judgment unit for when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k When > 0, i must satisfy
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
a third judging unit for judging whether the first and second judgment units are correct,for when-1. Ltoreq. I < 0 and a k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
a fourth judgment unit for a when i is more than or equal to-1 and less than 0 k b p -a p b k When < 0, i is satisfied
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme and the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U is obtained.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (14)
1. A method for optimizing a decomposition scheme of a complex active power distribution network is characterized by comprising the following steps:
acquiring a decomposition scheme set of a complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
determining a priority ranking sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
performing stability analysis on the superiority and inferiority sorting sequence, updating the superiority and inferiority sorting sequence, and selecting a decomposition scheme corresponding to the top-ranked element in the superiority and inferiority sorting sequence as an optimal decomposition scheme;
the performing stability analysis on the priority ranking sequence, updating the priority ranking sequence, and selecting a decomposition scheme corresponding to a top-ranked element in the priority ranking sequence as an optimal decomposition scheme includes:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Sorting the top elements in the priority sorting sequence;
the difference coefficient i of the decomposition schemes corresponding to each element in the high-low ranking sequence is equal, and gamma in the high-low ranking sequence is selected k Corresponding decomposition scheme and gamma p Corresponding decomposition scheme, when i is greater than or equal to 0 and less than or equal to 1 and c k b p -c p b k When the value is less than or equal to 0, i is required to satisfy the requirement of i epsilon [0,1]If yes, then gamma in said merit-ranking sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k >At 0, i must satisfy
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p Does not change, if not, then gamma is determined to be the same in the said sequence k And gamma p The sequencing positions of the two groups are interchanged;
when-1 is less than or equal to i<At 0 and a k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p Does not change, if not, then gamma is determined to be the same in the said sequence k And gamma p The sequencing positions of the two groups are interchanged;
when-1 is not more than i<0 and a k b p -a p b k <At 0, i must satisfy
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme and the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U is obtained.
2. The method according to claim 1, wherein the obtaining of the decomposition scheme set of the complex active power distribution network and the evaluation index corresponding to each decomposition scheme in the decomposition scheme set comprises:
and respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
3. The method of claim 2, wherein the resource utilization indicator y corresponding to each decomposition scheme in the set of decomposition schemes is determined according to the following formula 1 ：
In the above formula, n is the number of network partitions, P i 2 For the calculation size of the ith partition in the network, i ∈ [1,n ∈ ]]；
Determining the parallel computation complexity index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 2 ：
In the above formula, O min For theoretical minimum parallel computational complexity, P i 2 The calculation complexity of the ith partition in the network, l is the number of the coordination level servers, M is a calculation cost coefficient, i belongs to [1,n ]]，M∈[2,5]N is the number of partitions of the network;
determining the parallel computing precision index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U' i For the voltage value of node i, U after network decomposition i For the voltage value of node i before network decomposition, i belongs to [1,m ]]M is the total number of nodes in the network;
determining a parallel computation acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required for solving the problem serially, T P The time required to solve the problem in parallel;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers needed for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computing.
4. The method according to claim 1, wherein the determining, by using a set pair analysis method, a sequence of rank order of merits of each decomposition scheme according to the set of decomposition schemes and an evaluation index corresponding to each decomposition scheme in the set of decomposition schemes comprises:
converting non-income type indexes in the evaluation indexes corresponding to the decomposition schemes into income type indexes;
carrying out dimensionless processing on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme;
selecting an optimal normalized index value set U = (U) in normalized index values corresponding to the decomposition schemes 1 ,u 2 ,...u n ) And worst normalization index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
Determining the relative closeness of each decomposition scheme and the optimal normalized index value set U in a comparison space [ V, U ] of each decomposition scheme;
and sequencing the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring a merit and disadvantage sequencing sequence of the decomposition schemes.
5. The method of claim 4, wherein converting the non-profit-type indicators in the evaluation indicators corresponding to each decomposition scheme into profit-type indicators comprises:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-profit type indicator, then pressing the following formula will->
Conversion to revenue-type indicators:
in the above formula, the first and second carbon atoms are,
is->
The profit-type index value of (a), device for selecting or keeping>
For the maximum index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
6. The method according to claim 4, wherein the performing non-dimensionalization on the evaluation index corresponding to each decomposition scheme to obtain a normalized index value corresponding to each decomposition scheme comprises:
carrying out dimensionless treatment on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
7. The method of claim 4, wherein said determining a relative proximity of said each decomposition scheme to said optimal normalized index value set U in a comparison space [ V, U ] of said each decomposition scheme comprises:
let decomposition scheme set S = { S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Let the normalized index value of the kth decomposition scheme with respect to the r index be d kr The optimal normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is the [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k The degree of opposition of the kth decomposition scheme and the optimal normalized index value set U is represented by i as a difference coefficient and j as an opposition marker symbol;
wherein i ∈ [ -1,1]，j＝1，
Determining a relative closeness γ of the kth decomposition scheme to the optimal normalized index value set U as follows k ：
8. A device for optimizing a decomposition scheme of a complex active power distribution network is characterized by comprising:
the system comprises an acquisition module, a judgment module and a processing module, wherein the acquisition module is used for acquiring a decomposition scheme set of the complex active power distribution network and evaluation indexes corresponding to all decomposition schemes in the decomposition scheme set;
the determining module is used for determining the priority ordering sequence of each decomposition scheme by adopting a set pair analysis method according to the decomposition scheme set and the evaluation indexes corresponding to each decomposition scheme in the decomposition scheme set;
the analysis module is used for carrying out stability analysis on the priority sequence, updating the priority sequence and selecting a decomposition scheme corresponding to the top-ranked element in the priority sequence as an optimal decomposition scheme;
the analysis module comprises:
let gamma be k ＞γ p Then is equal to gamma p In contrast, γ k Sorting the top elements in the priority sorting sequence;
the difference coefficient i of the decomposition schemes corresponding to each element in the high-low ranking sequence is equal, and gamma in the high-low ranking sequence is selected k Corresponding decomposition scheme and gamma p A corresponding decomposition scheme;
a first judgment unit for judging when i is more than or equal to 0 and less than or equal to 1 and c is k b p -c p b k When the value is less than or equal to 0, i is required to satisfy the requirement of i epsilon [0,1]If yes, then γ in said merit-least ordered sequence k And gamma p The sorting position of (1) is not changed, if notSatisfy, then gamma in the sequence of rank order of superiority and inferiority k And gamma p The sequencing positions of the two groups are interchanged;
a second judgment unit for when i is more than or equal to 0 and less than or equal to 1 and c k b p -c p b k >At 0, i must satisfy
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
a third judgment unit for when-1 is not more than i<At 0 and a k b p -a p b k When the value is more than or equal to 0, i needs to satisfy i e [ -1,0), if yes, gamma in the sequence of the high-low order sequence k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
a fourth judgment unit for when-1 is not more than i<At 0 and a k b p -a p b k <At 0, i must satisfy
If yes, then gamma is in the sequence of the superiority and inferiority ranking k And gamma p If the rank position of (2) is not changed, then gamma in the high-low ranking sequence is determined k And gamma p The sequencing positions of the two groups are interchanged;
in the above process, a k For the identity of the kth decomposition scheme with the optimal normalized index value set U, b k Is the difference degree between the kth decomposition scheme and the optimal normalized index value set U, c k Is the degree of opposition, a, of the kth decomposition scheme to the optimal normalized index value set U p For the identity of the p-th decomposition scheme and the optimal normalized index value set U, b p The difference degree of the p decomposition scheme and the optimal normalized index value set U, c p And (4) determining the degree of opposition of the p-th decomposition scheme and the optimal normalized index value set U.
9. The apparatus of claim 8, wherein the acquisition module comprises:
the first determining unit is used for respectively determining a resource utilization rate index, a parallel computing complexity index, a parallel computing precision index, a parallel computing acceleration ratio index, a parallel computing efficiency index and a parallel computing cost index corresponding to each decomposition scheme in the decomposition scheme set.
10. The apparatus of claim 9, wherein the resource utilization indicator y corresponding to each decomposition scheme in the set of decomposition schemes is determined according to the following formula 1 ：
In the above formula, n is the number of network partitions, P i 2 For the calculation size of the ith partition in the network, i ∈ [1,n ∈ ]]；
Determining the parallel computation complexity index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 2 ：
In the above formula, O min For theoretical minimum parallel computational complexity, P i 2 The calculation complexity of the ith partition in the network, l is the number of the coordination level servers, M is a calculation cost coefficient, i belongs to [1,n ]]，M∈[2,5]N is the number of partitions of the network;
determining the parallel computing precision index y corresponding to each decomposition scheme in the decomposition scheme set according to the following formula 3 ：
In the above formula, U i ' is the voltage value of node i after network decomposition, U i For the voltage value of node i before network decomposition, i belongs to [1,m ∈ ]]M is the total number of nodes in the network;
determining a parallel computation acceleration ratio index S corresponding to each decomposition scheme in the decomposition scheme set according to the following formula P ：
S P ＝T S /T P
In the above formula, T S Time required to solve the problem serially, T P The time required to solve the problem in parallel;
determining a parallel computing efficiency index E corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
E＝S P /P
in the above formula, S P For parallel computing of the acceleration ratio, P is the number of servers needed for parallel computing;
determining a parallel computing cost index C corresponding to each decomposition scheme in the decomposition scheme set according to the following formula:
C＝T P *P
in the above formula, T P The time required to solve the problem in parallel, P is the number of servers required for parallel computing.
11. The apparatus of claim 8, wherein the determining module comprises:
the conversion unit is used for converting non-profit type indexes in the evaluation indexes corresponding to the decomposition schemes into profit type indexes;
the normalizing unit is used for carrying out non-dimensionalization processing on the evaluation indexes corresponding to the decomposition schemes to obtain normalized index values corresponding to the decomposition schemes;
a selection unit, configured to select an optimal normalization index value set U = (U) from the normalization index values corresponding to the decomposition schemes 1 ,u 2 ,...u n ) And worst normalized index value set V = (V) 1 ,v 2 ,...v n ) Constructing a comparison space [ V, U ] of the decomposition schemes]；
A second determining unit, configured to determine, in the comparison space [ V, U ] of each decomposition scheme, a relative closeness of each decomposition scheme to the optimal normalized index value set U;
and the sorting unit is used for sorting the decomposition schemes from large to small according to the relative closeness of the decomposition schemes and the optimal normalized index value set U, and acquiring the priority sorting sequence of the decomposition schemes.
12. The apparatus of claim 11, wherein the conversion unit comprises:
assume that the k-th decomposition scheme has an index value with respect to the r-th index
Is a non-revenue type indicator, will &>
Conversion to revenue-type indicators:
in the above formula, the first and second carbon atoms are,
is->
The profit-type index value of (a), device for selecting or keeping>
For the maximum index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
13. The apparatus of claim 11, wherein the specification unit comprises:
carrying out dimensionless treatment on the evaluation indexes corresponding to the decomposition schemes according to the following formula:
in the above formula, d kr For the k-th decomposition scheme with respect to the normalized index value of the r-th index,
for the index value of the kth decomposition scheme with respect to the r index, k ∈ [1,m ]]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes.
14. The apparatus of claim 11, wherein the second determining unit comprises:
let decomposition scheme set S = { S = } 1 ,s 2 ,...,s m }, evaluation index set E = { E = 1 ,e 2 ,...,e n Let the normalized index value of the kth decomposition scheme with respect to the r index be d kr The optimal normalized index value among the normalized index values of the respective decomposition schemes with respect to the r-th index is u r The worst normalization index value among the normalization index values of the respective decomposition schemes with respect to the r-th index is v r Wherein k is epsilon [1,m]，r∈[1,n]M is the total number of decomposition schemes, and n is the total number of evaluation indexes;
in the comparison space [ V, U ] of the decomposition schemes]Determining the degree of connection between the kth decomposition scheme and the optimal normalized index value set U according to the formula, namely set pair { s k Degree of association U { s } of U k ,U}：
u{s k ,U}＝a k +b k i+c k j
In the above formula, s k For the kth decomposition scheme in the set of decomposition schemes, a k For the identity of the kth decomposition scheme to the optimal normalized index value set U, b k The degree of difference between the kth decomposition scheme and the optimal normalized index value set U, c k For the kth decomposition scheme and the optimal specificationConverting the oppositivity of the index value set U, wherein i is a difference coefficient, and j is an oppositional mark symbol;
wherein i ∈ [ -1,1]，j＝1，
Determining a relative closeness γ of the kth decomposition scheme to the optimal normalized index value set U as follows k ：
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