The multilevel coordinated optimal control method of a photovoltaic distribution network based on an improved FPA algorithm

The control method of the photovoltaic distribution network has problems of low control accuracy and high line loss of the photovoltaic distribution network. Therefore, this paper proposes a multilevel coordinated optimization control method of a photovoltaic distribution network based on an improved FPA algorithm. First, we analyze the FCM algorithm, use the Euclidean distance to calculate the number of clusters, analyze the basic principle of the flower pollination algorithm, build the coordinated optimization control model of the photovoltaic distribution network, calculate the power flow result of the photovoltaic distribution network by improving the FPA algorithm, determine the global pollination behavior according to the flower pollination algorithm, and use the greedy strategy to obtain the optimal candidate solution. At this time, the obtained solution is the multi-level coordinated optimization control result of the photovoltaic distribution network. The experimental results show that this method can effectively improve the multi-level coordination and optimization control effect of the photovoltaic distribution network and reduce the line loss of the photovoltaic distribution network.


Introduction
Since China's reform and opening up, the economy and technology have developed rapidly.With the changes in foreign energy markets and the support of China's policies, China's photovoltaic industry has gradually begun to develop and catch up [1] .China has unique advantages in developing photovoltaic power generation.Due to its vast land area and sufficient illumination, with the world's attention to environmental protection and the country's attention to energy security, the development of photovoltaic power generation in China has accelerated.From "bright project" to "power transmission to rural areas" and other projects, from 2011 to 2019, photovoltaic power generation has become a trend to be integrated into the power grid.Under various supporting policies issued by China, China has gradually become a global photovoltaic power generation country in terms of solar radiation [2] .The traditional distribution network voltage regulation is relatively simple, while the access of distributed photovoltaic brings more uncertainty and randomness, which makes it difficult for the traditional distribution network voltage regulation strategy and equipment to effectively regulate the voltage in the high proportion photovoltaic distribution network [3,4] .In the distribution network, the distribution of the power flow in the distribution network is changed by changing the tap of the on-load voltage regulating transformer, the number of capacitor banks with parallel compensation, and other reactive power compensation equipment, and then the voltage regulation is carried out.Therefore, relevant scholars have studied this issue and made some progress.
Tang et al. proposed a coordinated control method of a photovoltaic distribution network based on a discrete consistency algorithm [5] , mining the load data of a photovoltaic distribution network, designing adjacent photovoltaic controllers according to the discrete consistency algorithm, and conducting multi-photovoltaic coordinated control of DC distribution network data according to the decision tree algorithm.This method can effectively improve the control accuracy of the distribution network, but the line loss rate of this method is too high.Zhang et al. proposed the distributed Newton method for coordinated control of the photovoltaic distribution network [6] , analyzed the hierarchical relationship between the load data of the photovoltaic distribution network, used the analytic hierarchy process to realize the voltage data classification of the photovoltaic distribution network power generation cluster, and used the distributed Newton method to design photovoltaic inverter to realize voltage optimization control.This method can improve the convergence speed, but the control accuracy of the photovoltaic distribution network is low.
In view of the above problems, this paper proposes a multi-level coordinated optimization control method for a photovoltaic distribution network based on an improved FPA algorithm, which can effectively improve the multi-level coordinated optimization control effect of photovoltaic distribution network and shorten the line loss of photovoltaic distribution network.

Multilevel Coordinated Optimal Control Method Of Photovoltaic Distribution Network
Based On Improved Fpa Algorithm

FCM algorithm analysis
The previous clustering anomaly detection model has the disadvantage of slow response and incorrect detection of unknown attacks.In view of this disadvantage, this paper adds an improved common flower pollination algorithm with strong global search ability to the FCM anomaly detection model, replaces the Euclidean distance in the FCM algorithm with Markov distance to deal with high-dimensional data, and then designs an anomaly detection algorithm based on the improved flower pollination FCM, to make full use of the advantages of both, and further enhance the performance of anomaly detection algorithm.
A traditional FCM algorithm has the disadvantage of highly relying on the initial value.For this disadvantage, this section proposes a solution algorithm to solve this problem, and then applies a new objective function to the clustering algorithm, so that the algorithm can deal with high-dimensional data well [7,8] .At the same time, the improved flower pollination algorithm is used to calculate the initial cluster center of FCM.IFPA algorithm can adaptively change the switching probability and Cauchy mutation of the iterating individuals, which may lead to the optimal cluster center; After having the optimal initial clustering center, cluster analysis is carried out to divide the data into normal and abnormal, which is completed in this way.

Method for determining the number of clusters
In the classification, the traditional FCM algorithm uses the Euclidean distance to calculate, assuming that c is used to represent a reasonable number of clusters.If the algorithm has an unreasonable initial clustering center, the following situations will occur: (1) If the number of cluster categories given by the algorithm is greater than c , then the algorithm clustering will cluster out empty categories, or a category has been repeatedly divided.
(2) If the initial cluster center is smaller than c , then there will be a merger, which refers to the merger of two reasonable categories.
The normal number in the target set should be more than the abnormal number so that the anomaly detection system can play a normal role.In actual anomaly detection, if there is an isolated point, it may be an attack to a large extent.For this reason, it is necessary to distinguish between noise and non-noise when doing anomaly detection.In this paper, the improved FPA algorithm is used to divide classes to effectively improve the coordination effect of the photovoltaic distribution network: the specific process is as follows: We separate noisy and non-noisy data and then calculate the noise and non-noise data sets respectively to determine the number of clusters contained in the two data sets.
The way to find the outliers or noise points in the set x , and calculate the sum of the distance between i x and other data , which is expressed as i S ; Then we calculate the average value ' S of i S .If i S is greater than ' S , then we take i x as noise or outlier.The number of data sets is expressed as n , and S is the dimension.The calculation equation is as follows. ' We find the outliers of photovoltaic distribution network data according to the following algorithm: First, we traverse the data set X , calculate the sum of the distances between the data point i x and other tertiary data points, which is expressed as i S , and then calculate the corresponding ' S .
We carry out the second traversal of i S .If ' i S S > , then this data should be regarded as noise or outliers, so as to find the outlier set ' X .
We extract the set ' X of outliers in the target set, so that the remaining set '' X can be obtained.
The following algorithm can determine the number of initial clustering centers.
(1) First, we traverse the data sample set, so that you can find out that the distance between the two data is the smallest.Then the first cluster center 1 v is one of the above two data with a small distance.At the same time, delete this data in the sample set.The threshold radius d is given.
(2) We make the distance from the data to i v be i dis , and traverse with this distance.When i dis d > , this data is regarded as the 1 i + th cluster center, which is expressed as 1 i v + .The traversed data in the sample set should be removed.
(3) We repeat Step (2) until the data sample no longer contains data.This sample can clarify the number of initial clustering centers.
The aggregation of ' X and '' X has been separated above, so the algorithm of determining the initial cluster center by carrying out ' X and '' X respectively can get the cluster number and initial value of the cluster center of photovoltaic distribution network data through calculation.

Building a mathematical model of the photovoltaic distribution network
Among the biological groups in nature on earth, angiosperms cover most of all plant species, and the range of plant growth and distribution is the most extensive.Flower pollination is an important part of angiosperm reproduction and growth.Biologically speaking, the process of pollen transfer from anther to stigma is called pollination.From the perspective of biological evolution, flower pollination can be understood as an optimization process in the process of plant reproduction.The best individual is the plant individual produced by pollination and reproduction and finally survived.It is from this process that the proponent of the flower pollination algorithm gets the inspiration of the flower pollination algorithm and further abstracts the generally applicable rules of the algorithm.
Pollen transmission needs to be carried out with the help of certain conditions.If it is divided according to the media it uses, it can be summarized as the following two kinds: one is biological pollination, and the other is abiotic pollination.The former refers to the process of pollen transmission with the help of natural biological populations, such as bees, butterflies, birds, and other different kinds of animals as the media of pollen transmission.This process is the most important way of flower pollination, accounting for about 90%; Non-biological pollination refers to the use of natural non-biological media such as wind and water media for the transmission and diffusion of their pollen.In the process of pollination, it can be divided into self-pollination and cross-pollination according to different pollination objects.Self-pollination is often due to the lack of transmission media, and pollen can only be sent to the stigma of the same flower for pollination and reproduction; Cross-pollination refers to the process of transferring pollen from one flower to the stigma of another plant.This process basically requires a transmission medium.According to the basic phenomena of nature, biological pollination, and cross-pollination mostly occur between plants far away, while the limitations of non-biological pollination and self-pollination show that this kind of pollination usually occurs only between plants close to each other.Therefore, this paper calculates the power flow of the photovoltaic distribution network by improving the FPA algorithm.The schematic diagram of the photovoltaic distribution network with one feeder is shown in Figure 1. ,2 ,2 .Some nodes are also connected to the PV power station, and the active power of the PV power station connected to node i is , PV i P .In addition, the complex impedance and complex power of the branch between node i and 1 i + are expressed as i i r jx + and i i P jQ + , respectively.In this paper, Equations (4)~( 6) are used to calculate the power flow of photovoltaic distribution network shown in Figure 1, as follows: In order to simplify the power flow analysis of the photovoltaic distribution network and speed up the solution of the power flow equation, the power flow equation shown in Equations ( 4) ~ ( 6) can be simplified according to the following assumptions.The terms containing 4) and ( 5) represent the active and reactive power losses of the branch, but the values of these two terms are much smaller than the other terms in the equation, so the terms containing where 1 V is the voltage of node 1 at the head end of the feeder.According to the voltage obtained in the previous section, the flower pollination function is brought in to solve the optimal parameters of multi-level coordination of the photovoltaic distribution network.

Multilevel coordinated optimal control of photovoltaic distribution network based on the improved FPA algorithm
Inspired by the biological reproduction process of flower pollination in nature, relevant scholars proposed a flower pollination algorithm.Through an in-depth study of the flower pollination process, the basic function of the flower pollination optimization algorithm was proposed.From the previous research experience of various experts and scholars, the complexity of an algorithm directly affects the applicability of the algorithm in practical problems.If we simulate the real complex flower pollination process, the algorithm will be too complex, and the huge amount of calculation will greatly reduce the efficiency of the algorithm.Then even if we develop such an algorithm, its practical application value will be reduced or even ignored.Therefore, in order to carry out simple calculations in the algorithm and the rationality of the algorithm, the following assumptions are put forward in the process of research: a plant has only one flower, a multi-flower and only one gamete.Therefore, each gamete at this time can be understood as a candidate solution in the solution space of the algorithm.The global pollination behavior of a photovoltaic distribution network with an improved FPA algorithm is realized by Equation (9): where x + and t i x are the i th candidate solutions of generation 1 t + and generation t in the solution space of flower pollination algorithm respectively; * g is the global optimal solution of the current photovoltaic distribution network of the algorithm; γ is a scale factor, which is used to control the moving step size; ( ) L λ is the moving step, which can be understood as the transmission intensity of pollen.The calculation equation of is shown in Equation (10): in the improved FPA algorithm λ , generally, the value is 3/2, namely,1.5; ( )λ Γ is a standard gamma function.
Abiotic self pollination of flower pollination is called local pollination, which is realized by Equation (11):  ) where ε is a random number that obeys uniform distribution on (0,1).In the improved FPA algorithm, when a new candidate solution is generated by using the above Equation (9) or Equation (11), the greedy strategy is used to decide whether to accept the new candidate solution.If the new solution is better than the original solution, the new solution will be used to replace the original optimal solution, otherwise the new solution will be abandoned and the original optimal solution will still be retained.At this time, the multilevel coordinated optimal control of the photovoltaic distribution network based on an improved FPA algorithm is realized.

Experimental Design
In order to verify the multi-level coordinated optimal control effect of this method on the photovoltaic distribution network, an actual feeder is used as the analysis object to verify the effectiveness of the proposed method.The feeder is a 10 KV radiant three-phase balance system with a total of 30 nodes.The total load of the line is 14.45 mw+j1.48mvar.The photovoltaic system in the line is connected to the feeder through the step-up transformer.Since the feeder only contains a voltage-regulating element of the photovoltaic inverter, the cooperation between the photovoltaic inverter and other voltage-regulating devices is not involved in the voltage control process of the distribution network, and only the photovoltaic inverter is used as a voltage regulating device to regulate the voltage of distribution network.

Comparison of line loss control effect after photovoltaic multi-level coordination and optimization
In order to verify the optimization control effect of this method on multi-level coordination of a photovoltaic distribution network, methods in [5] and [6] and this method are used to carry out the line loss control effect after multi-level coordination optimization of photovoltaic distribution network.The results are shown in Figure 2. According to the analysis of Figure 2, for the line with serial number 1, the line loss after multilevel coordination and optimization of the photovoltaic distribution network in [5] method is 37.2 kw, the line loss after multilevel coordination and optimization of the photovoltaic distribution network in [6]  method is 42.5 kw, and the line loss after multilevel coordination and optimization of the photovoltaic distribution network in this method is 12.5 kw.For the line with serial number 8, the line loss after multilevel coordination and optimization of the photovoltaic distribution network in [5] method is 43.5 kw, the line loss after multilevel coordination and optimization of the photovoltaic distribution network in [6] method is 22.1 kw, and the line loss after multilevel coordination and optimization of photovoltaic distribution network in this method is 13.0 kw.After the coordination of this method, the line loss of the photovoltaic distribution network is far lower than that of other methods, which shows that this method can effectively reduce the line loss of the photovoltaic distribution network and that the multi-level coordination and optimization control effect of a photovoltaic distribution network based on this method is better.

Multi-level coordination and optimization control effect of photovoltaic distribution network
In order to verify the effect of multi-level coordinated optimization control of photovoltaic distribution network based on this method, methods in [5] and [6] and this method are used to verify the accuracy of multi-level coordinated optimization control of photovoltaic distribution network.The results are shown in Figure 3.
Figure 3 Multi-level coordination and optimization control effect of photovoltaic distribution network According to the analysis of Figure 3, when the number of experimental iterations is 50, the precision of multi-level coordination and optimization control of the photovoltaic distribution network of [5] method is 58.2%, the precision of multi-level coordination and optimization control of the photovoltaic distribution network of [6] method is 55.1%, and the precision of multi-level coordination and optimization control of photovoltaic distribution network of this method is 92.6%.When the number of experimental iterations is 200, the accuracy of the multi-level coordinated optimization control of photovoltaic distribution network of [5] method is 57.0%, the accuracy of the multi-level coordinated optimization control of the photovoltaic distribution network of [6] method is 66.5%, and the accuracy of multi-level coordinated optimization control of photovoltaic distribution network of this method is 93.9%.This method always has high precision of multi-level coordination and optimization control of photovoltaic distribution network, which shows that this method can effectively improve the effect of multi-level coordination and optimization control of photovoltaic distribution network.

Conclusion
This paper presents a multi-level coordinated optimal control method for a photovoltaic distribution network based on an improved FPA algorithm.We analyze the basic principle of the flower pollination algorithm, use the Euclidean distance to calculate the number of clusters, build the coordinated optimization control model of the photovoltaic distribution network, improve the FPA algorithm to calculate the power flow results of the photovoltaic distribution network, and use the greedy strategy to obtain the optimal candidate solution to realize the multi-level coordinated optimization control of photovoltaic distribution network.The experimental results show that the multi-level coordinated optimal control accuracy of the photovoltaic distribution network based on this method can reach 99.2%, which shows that this method can effectively improve the multi-level coordinated optimization control effect of the photovoltaic distribution network.

Figure 1
Figure 1 Model of the photovoltaic distribution network Among them, the head end of the feeder is connected to the large power grid through OLTC.There are n nodes on the feeder, and i is the number of the node, : {1,..., } bus i n ∈Ω = , , , L i Li P jQ + represents the effective value of the voltage of node i .Each node has a local load, and the complex power of the load of node i is , , L i Li P jQ +.Some nodes are also connected to the PV power

Figure 2
Figure 2 Line loss control effect after photovoltaic multi-level coordination and optimization