CN115940267A - Distributed photovoltaic cluster division method for regional power distribution network - Google Patents
Distributed photovoltaic cluster division method for regional power distribution network Download PDFInfo
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Abstract
The invention belongs to the technical field of photovoltaic power generation control, and discloses a distributed photovoltaic cluster division method for a regional power distribution network, which is characterized in that the electrical distance between nodes is calculated based on a frequency-active sensitivity matrix, and an electrical distance matrix is obtained; obtaining an optimized initial centroid through a PSO algorithm, and performing node clustering analysis on the power distribution network by using a K-means algorithm according to the initial centroid to finish cluster division on the energy storage nodes; carrying out cluster division on the remaining photovoltaic nodes without energy storage and the load nodes by taking the energy storage nodes as the mass center; carrying out weighted calculation on three indexes of the active balance degree, the energy storage balance degree and the modularity degree to obtain a comprehensive performance index; and taking the partition scheme with the highest comprehensive performance index as the optimal cluster partition. According to the invention, the distribution area containing the distributed photovoltaic is subjected to cluster division by taking the distribution area energy storage as a center, and necessary inertia and frequency support is provided for a power grid.
Description
Technical Field
The invention belongs to the technical field of photovoltaic power generation control, and relates to a distributed photovoltaic cluster division method for a regional power distribution network.
Background
With the continuous development of distributed photovoltaics, a distribution area with a high distributed photovoltaic ratio in a power grid generally selects and configures distributed energy storage. The access of the distributed energy storage of the transformer area increases the consumption capability of renewable energy sources for configuring the energy storage transformer area, and meanwhile, the system has the advantages of quickly adjusting the inertia and frequency of the system, improving the system trend and reducing the network loss. The mass distributed photovoltaic large-scale application also has some technical problems, such as the requirement on secondary equipment and a communication system is high due to the fact that a distribution network side energy management system needs to be constructed.
When the permeability of the mass distributed photovoltaic in the regional power distribution network reaches a certain proportion and is widely accessed, the distributed power supply under the transformer area and the configured energy storage need to provide more support for the power grid, including inertia and frequency support and voltage support. Meanwhile, in order to facilitate the dispatching and management of the power distribution network on a mass of distributed power sources, the distribution area containing distributed photovoltaic is subjected to cluster division in the power distribution network by taking the distribution area energy storage as a center, so that the balance between network-source-load-storage is realized in a cluster, and necessary inertia and frequency support can be provided for the power grid.
Disclosure of Invention
In order to improve inertia-frequency support capability, the invention provides a distributed photovoltaic cluster division method for a regional power distribution network.
The technical scheme adopted by the invention is as follows: a distributed photovoltaic cluster division method for a regional distribution network comprises the following processes:
the method comprises the following steps: calculating the electrical distance between the nodes based on the frequency-active sensitivity matrix, and obtaining an electrical distance matrix;
step two: obtaining an optimized initial centroid through a PSO algorithm, and performing cluster analysis on nodes of the power distribution network by applying a K-means algorithm according to the initial centroid to perform cluster division on the energy storage nodes;
step three: the energy storage nodes are used as centroids to perform cluster division on the remaining photovoltaic nodes without energy storage and the load nodes;
step four: carrying out weighted calculation on three indexes of the active balance degree, the energy storage balance degree and the modularity degree to obtain a comprehensive performance index, and evaluating a cluster division result according to the comprehensive performance index;
step five: repeating the second step and the fourth step to complete the traversal of different numbers of cluster partitions; and taking the partition scheme with the highest comprehensive performance index as the optimal cluster partition.
Further preferably, in step one, the distance between two nodes is defined according to the frequency-active sensitivity matrix:
in the formula, S δP A frequency-active sensitivity matrix between a node j and a node i;
is the maximum element of all the j-th column in the frequency-active sensitivity matrix between the node j and the node i; d is a radical of ij Is the distance between node j and node i; />
And defining the electrical distance between the node i and the node j by adopting the Euclidean distance:
in the formula, d i1 ,d i2 …d in Respectively representing the distance between the node i and the node 1,2 \8230n; d j1 ,d j2 …d jn Respectively representing the distance between the node j and the nodes 1,2 \8230n, wherein n is the number of the nodes;
edge weight A of connection between node i and node j ij Comprises the following steps:
in the formula: and e is an electrical distance matrix consisting of electrical distances between any two nodes in the power distribution network.
Further preferably, in the second step, the PSO algorithm generates z particles according to the z energy storage nodes, gives each particle an initial position and speed, and then starts iteration; recording individual extreme value P of each particle while continuously and iteratively updating self speed and position of the particle best And global extreme G of population best (ii) a The updating of the speed and the position of the particles is influenced by two extreme values, the optimal solution is searched in the continuous iteration process, and the formula is as follows:
in the formula: k is the number of iterations;
is the position of node i at the kth iteration; v i k The speed of the node i at the kth iteration; omega is the inertial weight; c. C 1 、c 2 The first and the second learning factors are respectively; r is 1 、r 2 Is a parameter randomly generated between 0 and 1;
optimizing a K-means clustering algorithm according to a PSO algorithm, and defining a deviation function F of the particles as follows:
in the formula: k is the number of clusters; a is i Is the data vector of node i; c q Is the centroid of cluster q; k is a radical of q Is a subset of cluster q; d is the distance of the node to the centroid.
Preferably, in the second step, the modularity is used as a fitness function for particle optimization, and a PSO algorithm is applied to optimize and improve a K-means clustering algorithm to divide the energy storage clusters.
Further preferably, the specific process of step two is as follows:
s11, inputting node parameters and PSO algorithm parameters of the power distribution network;
s12, initializing the speed and the position of the particles according to the electrical distance matrix between the nodes;
s13, calculating to obtain a cluster to which each node belongs, selecting a node with the minimum sum of the electrical distances from the cluster to other energy storage nodes as the centroid of a new cluster, dividing the cluster again, and solving the fitness of the particles and the extreme value of the particles;
s14, updating the local optimal solution, the global optimal solution and the position corresponding to the optimal solution according to the extreme values of all the particles;
s15, recalculating the speed of the particles, and determining the positions of the particles through a relation formula of the positions and the speeds;
s16, judging whether an iteration ending condition is met, if so, obtaining the position of the optimal particle, otherwise, continuing the iteration, and obtaining the optimal particle which is the initial centroid;
and S17, clustering the energy storage nodes by applying a K-means algorithm according to the optimized initial centroid obtained by the PSO, and finishing cluster division of the energy storage nodes.
Further preferably, the specific process of step three is as follows:
s21, in all n nodes, the number of the energy storage nodes is z, and the energy storage node set is as follows:
B＝{ξ s }
b denotes the set of all energy storage nodes, ξ s Represents the s-th energy storage node, s =1,2, \ 8230;, z;
and S22, according to the energy storage nodes, determining that the node set without the residual energy storage is as follows:
H＝{ξ s′ }
h represents the remaining set of non-storage nodes, ξ s′ Represents the s 'th node without energy storage, s' =1,2, \ 8230, n-z;
respectively calculating the electrical distance from the energy storage node to the energy storage node:
D(ξ s ,ξ s′ )＝||ξ s -ξ s′ || 2
D(ξ s ,ξ s′ ) Representing the electrical distance from the s 'th non-energy-storage node to the s' th energy-storage node;
s23, forming an electrical distance matrix D without the energy storage nodes according to the electrical distance from the energy storage nodes to the energy storage nodes, classifying the rest energy storage nodes to the cluster where the energy storage node with the closest distance is located, and finally expressing the clustering result as follows by using a set:
C＝{C x }
wherein, C represents the set of all clusters, namely the final cluster division result; c x Representing the x-th cluster, including energy storage nodes and no energy storage nodes, and the number of the clusters after division is still N c Wherein x =1,2, \8230, N c ；
S24, a centroid calculation method: the xth cluster C x The total number of the nodes is m, wherein g energy storage nodes exist, m-g energy storage nodes do not exist, and the electrical distance sum D between the r-th energy storage node and other nodes in the cluster is calculated Tr ：
ξ r Representing the r-th energy storage node, ξ r′ Representing the r' th node without energy storage, wherein r is less than or equal to g; r' =1,2, \ 8230;, m-g;
selecting the minimum D of the sum of the electrical distances from other nodes Tk ＝min(D Tr ) Node xi of k Determining the new centroid; steps S22 and S23 are repeated until the iteration ends.
Further preferably, the calculation process of the energy storage balance degree is as follows:
the xth cluster C x M nodes, wherein g nodes are configured with an energy storage system, and the x-th cluster C x The total discharge power of the energy storage devices of the middle g energy storage nodes is as follows:
wherein the content of the first and second substances,
representing the discharge rated power of the energy storage device on the r energy storage node in the x cluster;
the xth cluster C x The h-th period net power is:
wherein, P r_load,h 、P r_pv,h Respectively representing the instantaneous power of the load or photovoltaic of the nth node during the h period
The xth cluster C x The average net power of (d) is:
t is the duration of the selected typical scene;
obtaining the energy storage configuration coefficient y in the xth cluster x ；
In the formula: n is a radical of hydrogen c A number indicating cluster division, and according to the number of cluster division,
configuring a coefficient predicted value for the integral energy storage, S is a standard deviation of the integral energy storage configuration of the power distribution network, and->
Indicating the degree of energy storage balance of the energy storage configuration.
Further preferably, the active balance degree is calculated as follows:
in the formula: n is a radical of hydrogen c A number representing a cluster division; c represents the set of all clusters;
represents the xth cluster C x The active power balance degree of (2); p is x_TTL,h Denotes the x-th cluster C x Net power over h time period; t is the duration of the selected typical scene; />
Representing the active balance that is exhibited by considering all clusters as a whole.
Further preferably, the modularity of all clusters
Is defined as:
in all n nodes, A ij Representing the edge weight of the connection between the node i and the node j, and taking 1 when the node i is directly connected with the node j, and taking 0 when the node i is not connected with the node j; k is a radical of i Represents the sum of the weights, k, of all edges connected to node i j Represents the sum of the weights of all edges connected to node j; w represents the sum of the weights of the entire network; δ is a matrix of 0 to 1, δ (i, j) =1 if node i and node j are located in the same cluster, and δ (i, j) =0 if they are not located in the same cluster.
Further preferably, the comprehensive performance index rho is as follows:
in the formula w 1 ，w 2 And w 3 The weight of the modularity, the active balance and the energy storage balance are respectively; determining the weight of the modularity, the active power balance and the energy storage balance through an analytic hierarchy process.
The invention is based on the electrical distance between the nodes defined by the sensitivity, and compared with the common impedance method for calculating the electrical distance, the sensitivity method can embody the dynamic characteristic of the network. The optimized initial clustering mass center is obtained through the PSO algorithm, the defect that local optimization is easily caused by only adopting a K-means algorithm is overcome, and the global property and the accuracy of the clustering process are improved. The energy storage nodes are used as the mass centers to carry out cluster division on the remaining photovoltaic nodes without energy storage and the load nodes, so that the balance degree between the network-source-load-storage in the cluster can be increased, the inertia-frequency support effect is improved, and the energy storage utilization rate is improved. The cluster division result is evaluated by the indexes of the energy storage balance degree, the active balance degree and the modularity degree, so that the requirements on cluster network configuration and dynamic response can be considered more comprehensively, and the optimal division result is obtained.
The distributed photovoltaic cluster division method for the regional power distribution network, provided by the invention, is used for carrying out cluster division on a distribution area containing distributed photovoltaic by taking the area energy storage as a center in the power distribution network so as to facilitate the scheduling and management of the power distribution network on a mass distributed power supply, so that the balance between network-source-load-storage can be realized in a cluster, and necessary inertia and frequency support can be provided for a power grid.
According to the distributed energy storage method, the distribution area with high distributed photovoltaic ratio in the power distribution network is considered to be possible to select and configure distributed energy storage, nodes configured with the energy storage are clustered firstly, and each cluster is guaranteed to have certain inertia and frequency support capability on the power distribution network.
The invention has universality. The photovoltaic power distribution network is suitable for power distribution networks with different distributed photovoltaic ratios.
The method provides practical effective reference for the distributed photovoltaic cluster division method of the regional distribution network.
Drawings
Figure 1 is a flow chart of the overall scheme of the present invention.
FIG. 2 is a schematic diagram of cluster partitioning of nodes.
Detailed Description
The invention is explained in more detail below with reference to the figures and examples.
As shown in fig. 1 and fig. 2, a method for dividing a distributed photovoltaic cluster of a regional distribution network includes the following steps:
the method comprises the following steps: calculating the electrical distance between the nodes based on the frequency-active sensitivity matrix, and obtaining an electrical distance matrix;
step two: obtaining an optimized initial centroid through a PSO algorithm, and performing cluster analysis on nodes of the power distribution network by applying a K-means algorithm according to the initial centroid to perform cluster division on the energy storage nodes;
step three: the energy storage nodes are used as centroids to perform cluster division on the remaining photovoltaic nodes without energy storage and the load nodes;
step four: carrying out weighted calculation on three indexes of the active balance degree, the energy storage balance degree and the modularity degree to obtain a comprehensive performance index, and evaluating a cluster division result according to the comprehensive performance index;
step five: repeating the second step to the fourth step to complete the traversal of different numbers of cluster partitions; and taking the partition scheme with the highest comprehensive performance index as the optimal cluster partition. When the number of the divided clusters is different, the clustering result is influenced, and the optimal cluster division can be obtained by comparing the difference of different cluster numbers and the difference of the comprehensive performance indexes.
In the first step of this embodiment, the electrical distance between nodes is calculated based on the frequency-active sensitivity matrix, and the principle and process of obtaining the electrical distance matrix are as follows;
in the load flow calculation, the polar coordinate form of the load flow equation is as follows:
in the formula: delta P i Is the active power variation of node i, P i Active power, Δ Q, for node i i Amount of reactive power change, Q, for node i i Is the reactive power of node i, delta j Is the power angle of the node j; delta delta i The power angle variation of the node i is obtained; u shape j Is the voltage at node j; u shape i Is the voltage of node i; delta U i Is the voltage variation of node i.
The elements of the Jacobian matrix may represent the frequency-power sensitivity relationship of any injected power node. Distributed photovoltaic power generation is in grid-connected operation in a power distribution network, the existing power distribution network is connected in a grid in a state that the power factor is 1 when the power distribution network receives new energy, therefore, the influence of the distributed photovoltaic injected active power on the node frequency is the main influence factor of the power system analysis, and a tidal current equation is expressed in a Jacobian matrix form as follows:
the jacobian matrix is represented by a block matrix as:
wherein | U | = Δ U |) j /ΔU i (ii) a J is a Jacobian matrix, J Pδ Is a block matrix of active power versus power angle partial derivatives, J Qδ Is a block matrix of reactive power to partial derivatives of power angle, J PV Is a block matrix of active power versus voltage partial derivatives, J QV The voltage partial derivative is a block matrix of reactive power to voltage partial derivative, wherein delta P is active power variation, and delta Q is reactive power variation.
For a massive distributed photovoltaic grid-connected power distribution system, grid-connected node frequency change after photovoltaic power generation active power injection is taken as a research object, photovoltaic power generation active power injection is taken as a control variable, grid-connected node frequency is taken as a controlled variable, a frequency-active sensitivity matrix needs to be obtained through quantitative calculation of active power and reactive power of a feeder line branch through node frequency change after power distribution network power flow calculation, and a jacobian matrix is obtained through Newton-Raphson iterative power flow calculation. Since the coupling degree of the power angle and the reactive power is high and the coupling degree of the power angle and the reactive power is low, the value of delta Q =0 is obtained
Δδ＝(J Pδ -J PV J QV -1 J Qδ ) -1 ΔP
The resulting frequency-active sensitivity matrix is:
S δP ＝(J Pδ -J PV J QV -1 J Qδ ) -1
in the formula: delta is the power angle variation; j is a unit of QV -1 The inverse matrix of the blocking matrix of the reactive power to the voltage partial derivative is used; s. the δP Is a frequency-active sensitivity matrix;
the frequency-active sensitivity matrix describes the relation between the injected active power change and the node frequency change, and the value of the frequency-active sensitivity matrix represents the close relation between the node and the node active frequency. According to the frequency-active sensitivity matrix, the distance between two nodes is defined:
in the formula, S δP A frequency-active sensitivity matrix between a node j and a node i;
is the maximum element of all the j-th column in the frequency-active sensitivity matrix between the node j and the node i; d is a radical of ij The distance between the node j and the node i represents the ratio of the change amount of the frequency of the node j and the node i when the active change of the node j in the frequency-active sensitivity matrix is represented. A smaller ratio indicates a greater influence, i.e., a closer distance, of node j on node i.
In practical situations, the relation between the nodes in the power distribution network and all the nodes in the power distribution network are related to assume that the power distribution network has n nodes, and the Euclidean distance is adopted to define the electrical distance between the node i and the node j:
in the formula (d) i1 ,d i2 …d in Respectively representing the distance between the node i and the node 1,2 \8230n; d j1 ,d j2 …d jn Respectively representing the distance between the node j and the node 1,2 \8230n;
thus, the edge weights A for node i and node j ij Comprises the following steps:
in the formula: and e is an electrical distance matrix formed by electrical distances between any two nodes in the power distribution network.
In the power distribution network, the energy storage device can store peak electric quantity generated by photovoltaic to offset load peak, thereby reducing light rejection rate and increasing asset utilization rate; the distribution-type energy storage of the transformer area also has the characteristics of quickly adjusting inertia and frequency of a power system, improving system tide and reducing network loss, and especially when a distributed power source occupies a certain proportion of the capacity of a power distribution network. Therefore, according to the role of energy storage in inertia and frequency support, nodes are divided into two categories according to whether the nodes are provided with energy storage devices or not: the method comprises the steps that energy storage nodes (nodes containing distributed photovoltaic and energy storage) and energy-storage-free nodes (nodes containing distributed photovoltaic and load nodes, the photovoltaic proportion is small) are subjected to cluster division through a clustering method.
The K-means algorithm is simple to implement and high in convergence speed, but if an improper initial clustering centroid is selected, the local optimum is trapped. In the second step of this embodiment, an improved K-means algorithm is adopted, the initial centroid is optimized through a Particle Swarm Optimization (PSO), and according to the obtained optimized initial centroid, the partitioning cluster uses the K-means algorithm to cluster nodes of the power distribution network, and performs cluster partitioning on energy storage nodes, so that the accuracy of the conventional K-means algorithm is improved.
The PSO algorithm first generates z particles from the z energy storage nodes, assigns an initial position and velocity to each particle, and then starts iteration. Recording individual extreme value P of each particle while continuously and iteratively updating self speed and position of the particle best And global extreme G of population best . On the other hand, the updating of the speed and position of the particle is influenced by two extreme values, and the optimal solution is searched in the continuous iteration process, wherein the formula is as follows:
in the formula: k is the number of iterations;
is the position of node i at the kth iteration; v i k The speed of the node i at the kth iteration; omega is the inertial weight; c. C 1 、c 2 The first and the second learning factors are respectively; r is 1 、r 2 Are randomly generated parameters between 0-1.
Optimizing a K-means clustering algorithm according to a PSO algorithm, and defining a deviation function F of the particles as follows:
in the formula: k is the number of clusters; a is i A data vector for node i; c q Is the centroid of cluster q; k is a radical of q Is a subset of cluster q; d is the distance of the node to the centroid. And (3) taking the modularity as a fitness function of particle optimization, and dividing the energy storage clusters by applying a PSO algorithm to optimize and improve a K-means clustering algorithm.
Obtaining an optimized initial clustering center of mass through a PSO algorithm, and performing node clustering analysis on the power distribution network by applying a K-means algorithm according to the initial center of mass, wherein the specific process of cluster division is as follows:
and S11, inputting node parameters and PSO algorithm parameters of the power distribution network.
And S12, initializing the speed and the position of the particles according to the electrical distance matrix between the nodes.
And S13, calculating to obtain a cluster to which each node belongs, selecting the node with the minimum sum of the electrical distances from the cluster to the rest energy storage nodes as the mass center of a new cluster, dividing the cluster again, and solving the fitness of the particles and the extreme value of the particles.
And S14, updating the local optimal solution, the global optimal solution and the position corresponding to the optimal solution according to the extreme values of all the particles.
S15, recalculating the velocity of the particles (not less than the minimum value V of the velocity of the particles) min And cannot exceed the maximum value V of the velocity of the particles max ) And determining the position of the particle (the position of the particle cannot be exceeded) by a relational formula of the position and the speedUpper and lower limits of interval) of (2).
And S16, judging whether the iteration end condition is met, if so, obtaining the position of the optimal particle, otherwise, continuing the iteration, and obtaining the optimal particle which is the initial centroid.
And S17, clustering the energy storage nodes by applying a K-means algorithm according to the optimized initial centroid obtained by the PSO, and finishing cluster division of the energy storage nodes. The energy storage node dividing cluster result is expressed by a set as:
B＝{B x }
wherein B represents the set of all energy storage nodes, B x Denotes the x-th energy storage cluster, x =1,2, \ 8230;, N c ，N c The number of cluster partitions.
In step three of this embodiment, a specific process of performing cluster division on the remaining nodes without energy storage by using the energy storage node as a centroid is as follows:
s21, in all n nodes, the number of the energy storage nodes is z, and the energy storage node set is as follows:
B＝{ξ s }
b represents the set of all storage nodes, ξ s Represents the s-th energy storage node, s =1,2, \8230;, z;
and S22, according to the energy storage nodes, determining that the node set without the residual energy storage is as follows:
H＝{ξ s′ }
h represents the remaining set of non-storage nodes, ξ s′ Represents the s 'th node without energy storage, s' =1,2, \ 8230, n-z;
respectively calculating the electrical distance from the energy storage node to the energy storage node:
D(ξ s ,ξ s′ )＝||ξ s -ξ s′ || 2
D(ξ s ,ξ s′ ) Denotes the s th ′ Electrical distance from the no energy storage node to the s-th energy storage node;
s23, forming an electrical distance matrix D without the energy storage nodes according to the electrical distance from the energy storage nodes to the energy storage nodes, classifying the rest energy storage nodes to the cluster where the energy storage node with the closest distance is located, and finally expressing the clustering result as follows by using a set:
C＝{C x }
wherein, C represents the set of all clusters, namely the final cluster division result; c x Representing the x-th cluster, including energy storage nodes and no energy storage nodes, and the number of the clusters after division is still N c Where x =1,2, \ 8230;, N c 。
S24, a centroid calculation method:
suppose the xth cluster C x The total number of the nodes is m, wherein g energy storage nodes exist, m-g energy storage nodes exist when no energy storage node exists, and the sum D of the electrical distances between the r-th energy storage node and other nodes in the cluster is calculated Tr ：
ξ r Representing the r-th energy storage node, ξ r′ The r' th node without energy storage is represented, and r is less than or equal to g; r' =1,2, \ 8230;, m-g;
selecting the minimum D of the sum of the electrical distances from other nodes Tk ＝min(D Tr ) Node xi of k Determining the new centroid; steps S22 and S23 are repeated until the iteration ends.
The embodiment also evaluates the cluster division result by using the three indexes of the energy storage balance degree, the active balance degree and the modularity degree to obtain an optimal cluster division mode.
(1) Degree of balance of stored energy
Suppose the x-th cluster C x There are m nodes, where g nodes are configured with an energy storage system ESS (energy storage system), the energy storage of the cluster is expressed as:
in the formula, P 1 ESS 、P 2 ESS 、
Respectively representing rated power of 1 st, 2 nd and g th energy storage nodes in the x-th cluster; the energy storage configuration converter has certain loss in the actual working process, and the power in the actual charging and discharging process can be expressed as:
in the formula:
respectively representing the charging power and the discharging power of the ith energy storage node in the xth cluster in the h period;
respectively representing charging and discharging reference power of an ith energy storage node in an xth cluster in an h period; />
Respectively the charging and discharging efficiency of the energy storage system.
Considering the supporting capability of the energy storage device to the grid frequency, the power requirements of the energy storage device are as follows:
in the formula:
respectively represents the charging and discharging rated power, P, of the energy storage device on the r-th energy storage node in the x-th cluster r_load,h 、P r_pv,h Respectively representing the load or the instantaneous power of the photovoltaic of the nth node during the h period.
Then the xth cluster C x Energy storage device for medium-g energy storage nodesThe total power of the power placement is as follows:
in practical situations, the load and photovoltaic power characteristics of all nodes of a cluster often show the external characteristics of the load, and the x-th cluster C containing m nodes x The h-th period net power is:
the xth cluster C x The average net power of (d) is:
t is the duration of the selected typical scene;
thereby obtaining the energy storage configuration coefficient y in the xth cluster x ；
In the formula: n is a radical of c A number indicating cluster division, and according to the number of cluster division,
configuring a coefficient predicted value for the integral energy storage, S is a standard deviation of the integral energy storage configuration of the distribution network, and>
the energy storage balance degree is measured by the standard deviation rate of the energy storage configuration, and the larger the value is, the higher the integral energy storage balance degree is.
(2) Degree of active balance
In the aspect of network-source-load-storage balance, in order to reduce active power transmission among clusters and show the self-absorption capacity of the clusters to the maximum extent so as to reduce the light rejection rate, the active balance degree is used as an index for cluster division, the high active balance degree of the clusters represents that the matching degree of the intra-cluster network-source-load-storage of the clusters is high, the uncertainty and the volatility of photovoltaic output can be effectively relieved, and the active balance degree of the xth cluster is defined as:
in the formula: n is a radical of c A number representing a cluster division; c represents the set of all clusters;
represents a cluster C x The active power balance degree of (2); p is x_TTL,h Represents the xth cluster C x Net power over h time period; t is the duration of the selected typical scene; />
Representing the active balance exhibited by treating all clusters as a whole.
(3) Degree of modularity
The modularity is a method for measuring the structural strength of the network community, which is provided by MarkNewman, the size of the modularity can be used for measuring the quality of the network community division result, and the larger the value is, the more compact the connection between nodes in each community is, the less the connection between communities is, and the smaller the value is, otherwise, the network community division result is.The power distribution network accessed by the mass distributed photovoltaic has a similar structure with the network community, and the cluster division of each node in the power distribution network and the structural analysis of the network community have similar targets, so that the modularity can be used for measuring whether the cluster division result of the distributed photovoltaic in the power distribution network is reasonable or not, and the modularity of all clusters
Is defined as:
of all n nodes, A ij Representing the edge weight of the connection between the node i and the node j, and taking 1 when the node i is directly connected with the node j, and taking 0 when the node i is not connected with the node j; the edge rights reflect the connection strength relationship between the nodes. k is a radical of i Represents the sum of the weights, k, of all edges connected to node i j Represents the sum of the weights of all edges connected to node j; w represents the sum of the weights of the entire network; δ is a matrix of 0 to 1, δ (i, j) =1 if node i and node j are located in the same cluster, and δ (i, j) =0 if they are not located in the same cluster.
In summary, the three set indexes for evaluating the cluster division result are respectively:
(1) Energy storage balance degree: the relative size of the maximum difference between the maximum power which can be provided by stored energy and the maximum equivalent source-load instantaneous power is represented, and each cluster is ensured to have certain inertia-frequency support capability in a short time when the power balance exceeds or is deficient.
(2) Active power balance degree: the method embodies the network-source-load-storage balance in the cluster, namely, the active power transmission among the clusters is reduced as much as possible, and the local consumption of the distributed photovoltaic energy is realized to the maximum extent.
(3) Modularity: the closeness of the connection between the centroid and each node within the cluster can be measured. The value of the modularity and the value of the active balance degree are not more than 1, and for a cluster, the higher the internal link degree is, the closer the modularity approaches to 1; the cluster shows that the smaller the external net power is, the stronger the self-absorption capacity is, and the closer the active balance degree is to 1; the 3 indexes have the same order of magnitude, so the comprehensive performance index rho is set as follows:
in the formula w 1 ，w 2 And w 3 The weight of the modularity, the active balance and the energy storage balance are respectively.
The Analytic Hierarchy Process (AHP) is a multi-target comprehensive evaluation method, which is suitable for the problem that the target value is difficult to describe quantitatively, and is used for determining the index weights of the three evaluation cluster division results from different aspects. The basic steps for determining the weight of each index are as follows:
(1) Using natural numbers between 1-9 as scale to indicate relative importance degree between two indexes
| Scale | Means of |
| 1 | Two indexes are of |
| 3 | One index is slightly more important than the |
| 5 | One index is significantly more important than the other |
| 7 | One index is more important than the other |
| 9 | One index is extremely important than the other |
| 2，4，6，8 | The median value of the above two adjacent judgments |
| Reciprocal of the | If the scale of A and B is 3, then B and A are 1/3 of each other |
(2) Obtaining a 3 x 3 matrix of relative importance of the three indexes in pairs
| Degree of balance of stored energy | Degree of active balance | Modularity degree | |
| Degree of balance of stored |
1 | ||
| Degree of |
1 | ||
| |
1 |
(3) Calculating the weight of each index
Normalizing each column of the matrix to obtain a judgment matrix, adding each row to obtain a 3 x 1 vector, and normalizing the vector to obtain a characteristic vector of the judgment matrix, namely the weight vector of the three indexes.
(4) The results are subjected to consistency test
a. Calculating the maximum value a of the characteristic root of the judgment matrix max ；
b. Calculating a consistency index CR:
where p is the number of indices, where 3,RI is taken as the average random uniformity, the value of which is related to the matrix order n p And (4) correlating. In general, the larger the matrix order, the greater the probability of occurrence of consistent random deviation, and the corresponding relationship is as follows:
the table lookup can obtain the value of 0.58, generally, if CR is less than 0.1, the judgment matrix is considered to pass the consistency check, and the weight of each index is finally determined.
The foregoing description is of the preferred embodiment of the invention only, and is not intended to limit the invention in any way, so that any person skilled in the art, having the benefit of the foregoing disclosure, may modify or modify the invention to practice equivalent embodiments with equivalent variations. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention will still fall within the protection scope of the technical solution of the present invention.
Claims (10)
1. A distributed photovoltaic cluster division method for a regional distribution network is characterized by comprising the following steps:
the method comprises the following steps: calculating the electrical distance between the nodes based on the frequency-active sensitivity matrix, and obtaining an electrical distance matrix;
step two: obtaining an optimized initial centroid through a PSO algorithm, and performing cluster analysis on nodes of the power distribution network by applying a K-means algorithm according to the initial centroid to perform cluster division on the energy storage nodes;
step three: carrying out cluster division on the remaining photovoltaic nodes without energy storage and the load nodes by taking the energy storage nodes as the mass center;
step four: performing weighted calculation by using three indexes of the active balance degree, the energy storage balance degree and the modularity degree to obtain a comprehensive performance index, and evaluating a cluster division result by using the comprehensive performance index;
step five: repeating the second step and the fourth step to complete the traversal of different numbers of cluster partitions; and taking the partition scheme with the highest comprehensive performance index as the optimal cluster partition.
2. The method for dividing distributed photovoltaic clusters of a regional distribution network according to claim 1, wherein in the first step, the distance between two nodes is defined according to the frequency-active sensitivity matrix:
in the formula, S δP Is a frequency-active sensitivity matrix between node j and node i;
is the maximum element of all the j-th column in the frequency-active sensitivity matrix between the node j and the node i; d ij Is the distance between node j and node i;
and defining the electrical distance between the node i and the node j by adopting the Euclidean distance:
in the formula, d i1 ,d i2 …d in Respectively representing the distance between the node i and the node 1,2 \8230n; d is a radical of j1 ,d j2 …d jn Respectively representing the distance between the node j and the nodes 1,2 \8230n, wherein n is the number of the nodes;
edge weight A of connection between node i and node j ij Comprises the following steps:
in the formula: and e is an electrical distance matrix formed by electrical distances between any two nodes in the power distribution network.
3. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 1, wherein in the second step, a PSO algorithm generates z particles according to z energy storage nodes, gives each particle an initial position and speed, and then starts iteration; continuously iterating the particlesRecording the individual extreme value P of each particle while updating the speed and position of the particle best And global extreme G of population best (ii) a The updating of the speed and the position of the particles is influenced by two extreme values, the optimal solution is searched in the continuous iteration process, and the formula is as follows:
in the formula: k is the number of iterations;
is the position of node i at the kth iteration; v i k The speed of the node i at the kth iteration; omega is the inertial weight; c. C 1 、c 2 The first learning factor and the second learning factor are respectively; r is a radical of hydrogen 1 、r 2 Is a parameter randomly generated between 0 and 1;
optimizing a K-means clustering algorithm according to a PSO algorithm, and defining a deviation function F of the particles as follows:
in the formula: k is the number of clusters; a is i A data vector for node i; c q Is the centroid of cluster q; k is a radical of q Is a subset of cluster q; d is the distance of the node to the centroid.
4. The method for dividing the distributed photovoltaic clusters of the regional power distribution network according to claim 3, wherein in the second step, the modularity is used as a fitness function for particle optimization, and a PSO algorithm is used for optimizing and improving a K-means clustering algorithm to divide the energy storage clusters.
5. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 1, wherein the specific process of the second step is as follows:
s11, inputting node parameters and PSO algorithm parameters of the power distribution network;
s12, initializing the speed and the position of the particles according to the electrical distance matrix between the nodes;
s13, calculating to obtain a cluster to which each node belongs, selecting a node with the minimum sum of the electrical distances from the cluster to other energy storage nodes as the centroid of a new cluster, dividing the cluster again, and solving the fitness of the particles and the extreme value of the particles;
s14, updating the local optimal solution, the global optimal solution and the position corresponding to the optimal solution according to the extreme values of all the particles;
s15, recalculating the speed of the particles, and determining the positions of the particles through a relation formula of the positions and the speeds;
s16, judging whether an iteration ending condition is met, if so, obtaining the position of the optimal particle, otherwise, continuing the iteration, and obtaining the optimal particle which is the initial centroid;
and S17, clustering the energy storage nodes by applying a K-means algorithm according to the optimized initial centroid obtained by the PSO, and finishing cluster division of the energy storage nodes.
6. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 1, wherein the specific process of the third step is as follows:
s21, in all n nodes, the number of the energy storage nodes is z, and the energy storage node set is as follows:
B＝{ξ s }
b denotes the set of all energy storage nodes, ξ s Represents the s-th energy storage node, s =1,2, \ 8230;, z;
s22, according to the energy storage nodes, determining the node set without the residual energy storage as follows:
H＝{ξ s′ }
h represents the remaining set of non-storage nodes, ξ s′ Represents the s 'th node without energy storage, s' =1,2, \ 8230, n-z;
respectively calculating the electrical distance from the energy-storage-free node to the energy-storage node:
D(ξ s ,ξ s′ )＝||ξ s -ξ s′ || 2
D(ξ s ,ξ s′ ) Representing the electrical distance from the s 'th non-energy-storage node to the s' th energy-storage node;
s23, forming an electrical distance matrix D without the energy storage nodes according to the electrical distance from the energy storage nodes to the energy storage nodes, classifying the rest energy storage nodes to the cluster where the energy storage node with the closest distance is located, and finally expressing the clustering result as follows by using a set:
C＝{C x }
wherein, C represents the set of all clusters, namely the final cluster division result; c x The xth cluster is represented and comprises energy storage nodes and no energy storage nodes, and the number of the divided clusters is still N c Where x =1,2, \ 8230;, N c ；
S24, a centroid calculation method: the xth cluster C x The total number of the nodes is m, wherein g energy storage nodes exist, m-g energy storage nodes do not exist, and the electrical distance sum D between the r-th energy storage node and other nodes in the cluster is calculated Tr ：
ξ r Representing the r-th energy storage node, ξ r′ The r' th node without energy storage is represented, and r is less than or equal to g; r' =1,2, \ 8230;, m-g;
selecting the minimum D of the sum of the electrical distances from other nodes Tk ＝min(D Tr ) Node xi of k Determining the new centroid; steps S22 and S23 are repeated until the iteration ends.
7. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 1, wherein the calculation process of the energy storage balance degree is as follows:
the xth cluster C x M nodes, wherein there are g nodesWith energy-storage system, x-th cluster C x The total discharge power of the energy storage devices of the middle g energy storage nodes is as follows:
wherein the content of the first and second substances,
representing the discharge rated power of the energy storage device on the r-th energy storage node in the x-th cluster;
the xth cluster C x The h-th period net power is:
wherein, P r_load,h 、P r_pv,h Respectively representing the load or the instantaneous power of the photovoltaic of the nth node during the h period
The xth cluster C x The average net power of (d) is:
t is the duration of the selected typical scene;
obtaining the energy storage configuration coefficient y in the xth cluster x ；
In the formula: n is a radical of c Indicating the number of cluster divisions, and, according to the number of cluster divisions,
configuring a coefficient predicted value for the integral energy storage, S is a standard deviation of the integral energy storage configuration of the power distribution network, and->
Indicating the degree of energy storage balance of the energy storage configuration.
8. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 7, wherein the active balance degree is calculated in the following way:
in the formula: n is a radical of c A number representing a cluster division; c represents the set of all clusters;
represents the xth cluster C x The active power balance degree of (2); p x_TTL,h Represents the xth cluster C x Net power over h time period; t is the duration of the selected typical scene; />
Representing the active balance exhibited by treating all clusters as a whole.
9. The method for dividing distributed photovoltaic clusters of a regional distribution network according to claim 8, wherein the method is characterized in thatModularity of all clusters
Is defined as:
of all n nodes, A ij Representing the edge weight of the connection between the node i and the node j, and taking 1 when the node i is directly connected with the node j, and taking 0 when the node i is not connected with the node j; k is a radical of i Represents the sum of the weights, k, of all edges connected to node i j Represents the sum of the weights of all edges connected to node j; w represents the sum of the weights of the entire network; δ is a matrix of 0 to 1, δ (i, j) =1 if node i and node j are located in the same cluster, and δ (i, j) =0 if they are not located in the same cluster.
10. The method for dividing the distributed photovoltaic clusters of the regional distribution network according to claim 9, wherein the comprehensive performance index p is:
in the formula w 1 ，w 2 And w 3 The weight of the modularity, the active balance and the energy storage balance are respectively; determining the weight of the modularity, the active power balance and the energy storage balance through an analytic hierarchy process.
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| CN117879047A (en) * | 2024-03-13 | 2024-04-12 | 国网山西省电力公司经济技术研究院 | Optimization method and system for distributed photovoltaic access distribution network |
| CN117879047B (en) * | 2024-03-13 | 2024-05-24 | 国网山西省电力公司经济技术研究院 | Optimization method and system for distributed photovoltaic access distribution network |
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| CN117217504A (en) * | 2023-11-09 | 2023-12-12 | 国网山东省电力公司日照供电公司 | Distributed photovoltaic and adjustable resource characteristic analysis management system and method |
| CN117879047A (en) * | 2024-03-13 | 2024-04-12 | 国网山西省电力公司经济技术研究院 | Optimization method and system for distributed photovoltaic access distribution network |
| CN117879047B (en) * | 2024-03-13 | 2024-05-24 | 国网山西省电力公司经济技术研究院 | Optimization method and system for distributed photovoltaic access distribution network |
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