Optimal Clustering Equivalent Method for Wind Farms Using Gaussian Mixture Model

Abstract

The present invention discloses an optimal clustering equivalent method for a wind farm using a Gaussian mixture model, which includes the following steps: obtaining different wind speeds of wind turbines at different positions in the farm through the overall control of the wind farm; building a wind farm model containing physical parameters such as multiple wind turbines, transformers, and collector lines to obtain the steady-state active power and the reactive power under the voltage dip caused by a fault; calculating the probability generated by each corresponding cluster for each sample point data, and iterating multiple steps to obtain the probability of the updated cluster until Gaussian convergence. Divide each sample into the cluster with the maximum probability respectively to obtain N types of clustering results; calculate the likelihood function value and select the clustering center for the clustering results of the previous step to obtain the optimal n types of clustering results; simplify and equivalentize the wind turbines, transformers, and collector lines within the group respectively, and finally obtain the simplified equivalent result of the wind farm with the optimal number of clusters. The present invention is relatively simple in principle and easy to implement, and has certain engineering practical value.

Description

Technical Field

[0001] The present invention belongs to the technical field of new energy grid connection in power systems, and particularly relates to an optimal clustering equivalent method for wind farms using Gaussian mixture models. Background Art

[0002] With the continuous increase in the proportion of wind power penetration in the power system, the construction and real-time simulation technology of doubly-fed wind farms have become increasingly important. Due to the excessive number of wind turbines in actual wind farms, using a detailed wind farm model for simulation not only consumes a large amount of time but may even cause the occurrence of the curse of dimensionality. Therefore, considering both the real-time simulation accuracy and simulation time of wind farms, it is necessary to establish a suitable equivalent model for doubly-fed wind farms.

[0003] Since the equivalent research of wind farms mainly includes single-machine equivalence and multi-machine equivalence. Due to the long distances between the units in the wind farm and the different line parameters, single-machine equivalence cannot accurately describe the dynamic characteristics of the entire wind farm. The usual multi-machine equivalence can be divided into the following three steps: 1) Select the real-time parameters of the wind turbines or the characteristic information of certain time-series electrical quantities to obtain different cluster division indicators; 2) Secondly, select a suitable clustering method to divide the clusters; 3) Calculate the equivalent parameters in different clustering groups respectively to obtain the final clustering result.

[0004] The mechanical characteristic variables, state variables, and disturbed curves of rotor currents of wind turbines during fault excision have been used for wind turbine grouping. Many literatures have studied the index of DFIG output active power and used the fuzzy C-means algorithm to perform clustering analysis on the characteristic vectors related to the units. Improve the traditional K-means algorithm from the aspect of avoiding the deviation of the clustering center to realize the dynamic equivalent multi-machine representation of the wind farm. The AIC criterion and the BIC criterion are widely used in index evaluation and can be considered in combination with wind farm clustering. In summary, an equivalent method with good equivalent effect and achieving the optimal equivalent clustering number is urgently needed. Studying the equivalent method of wind farms is of great significance for the economic and stable operation of new energy systems and has certain engineering and scientific research significance. Summary of the Invention

[0005] The purpose of the present invention is to provide an optimal clustering equivalent method for wind farms using Gaussian mixture models, which solves the problem in the prior art that it is difficult to obtain the optimal equivalent clustering number for large-scale wind farms.

[0006] The technical solution adopted by the present invention is: an optimal clustering equivalent method for wind farms using Gaussian mixture models, which specifically includes the following steps:

[0007] Step 1, obtain the wind speeds of the wind turbines at different positions in the wind farm through the wind farm master control;

[0008] Step 2: Build a wind farm model with physical parameters of multiple wind turbines, transformers, and collector lines through MATLAB / Simulink, and obtain the steady-state active power and reactive power under the voltage dip caused by faults respectively;

[0009] Step 3: Select the wind speed, steady-state active power, and reactive power under the voltage dip caused by the fault in Step 2 for Gaussian distribution clustering. Calculate the probability generated by each sample point data from its corresponding cluster, and perform multi-step iteration to obtain the probability of the updated cluster until Gaussian convergence; Divide each sample into the cluster with the maximum probability respectively, and finally obtain the N-class clustering results;

[0010] Step 4: Calculate the likelihood function value according to the clustering results in Step 3, and then use the Akaike Information Criterion AIC and Bayesian Information Criterion BIC to evaluate and select the clustering centers. The wind speed corresponding to the clustering centers is the equivalent wind speed within the group, and thus N clustering groups are obtained;

[0011] Step 5: Utilize the clustering results in Step 4. In the equivalent calculation of the wind farm, based on the principle of equal power and current before and after equivalence, simplify and equivalent the wind turbines, transformers, and collector lines within the N clustering groups respectively, and finally obtain the simplified equivalent result of the wind farm with the optimal number of clustering groups.

[0012] The characteristics of the present invention also lie in that

[0013] The wind farm model built in Step 2 includes multiple 1.5MW doubly-fed wind turbines with low voltage ride-through capabilities, which are collected to the collector line by 0.69kV / 35kV box-type transformers and connected to the large power grid system through 35kV / 110kV step-up transformers.

[0014] The parameters of the collector lines in the wind farm in Step 2 are complex. When the voltage at the connection point changes due to a fault, the voltage changes reflected on each single wind turbine are different. Due to the different wind speeds of each wind turbine, there are also differences in the pitch angles of the wind turbine pitch control systems and the states of the wind turbines operating in the starting area and the constant speed and constant power area. In the fault caused by the voltage dip of the doubly-fed wind turbine, since the changes in the stator and rotor currents will cause changes in the electromagnetic torque, it will further affect the rotor speed and the output active power and reactive power of the wind turbine.

[0015] Gaussian mixture model clustering is a method based on probability models. It is assumed that the input samples follow k Gaussian distributions with unknown parameters, and each Gaussian distribution corresponds to different means and covariance matrices (1 ≤ j ≤ k). Then the samples that follow the same distribution are clustered into one class. Take the wind speed, steady-state active power, and reactive power in Step 2 as the sample set , and initialize the parameter mixing coefficient of the Gaussian mixture distribution , mean vector and covariance matrix , and reasonably assume that each mixture element has a diagonal matrix. Secondly, calculate each sample point x i ( i = 1, 2, 3, … m) belonging to the probability of the j-th Gaussian distribution:

[0016]

[0017] Calculate the updated iterative model parameter values of the mean vector , covariance matrix and mixing coefficient .

[0018]

[0019] According to Divide each sample into the cluster with the highest probability, and perform three-dimensional clustering based on the three-dimensional sample set of wind speed, steady-state active power, and reactive power . Obtain the final cluster division , and finally obtain N clustering results.

[0020] In step 4, use the AIC and BIC criteria to determine whether the optimal number of clusters is obtained: The definitions of AIC and BIC are as follows:

[0021] AIC = -2ln(L) + 2k (5)

[0022]

[0023] In the formula, k is the number of model parameters, m is the number of samples, is the likelihood function; among them is the j-th different sample point, is the mean corresponding to different Gaussian distributions, is the covariance matrix corresponding to different Gaussian distributions; combined with the three-dimensional clustering data of the fan, different AIC values and BIC values correspond to different numbers of clusters. When both are the smallest, the number of clusters of the wind farm reaches the optimal solution.

[0024] The calculation process of step 5 is as follows:

[0025] The equivalent power and equivalent current of the A-th group of fans after equal value can be expressed as:

[0026]

[0027] The impedance of the A-th group of wind turbines after equivalence can be expressed as:

[0028]

[0029] In formulas (7) and (8) is the equivalent power of the wind farms within the group, is the equivalent current at the outlet of the wind farms within the group, is the equivalent impedance of the wind farms within the group, is the power corresponding to each individual wind turbine, is the current at the outlet corresponding to each individual wind turbine, is the voltage at the outlet corresponding to each individual wind turbine, is the voltage at the outlet of the wind farms within the group, is the voltage at the grid connection point of the wind farm, is the equivalent capacitive current to the ground of the wind farms within the group.

[0030] Considering the capacitance of each wind turbine within the group, the capacitance of the wind turbines in Group A to the ground can be approximately expressed as the sum of the capacitances of individual wind turbines to the ground.

[0031]

[0032] Formula (9) is the capacitance to the ground of all the wind turbines in Group A.

[0033] The capacity of the transformer parameters is multiplied by the capacity of a single unit within the group, and the internal parameters and impedance of the generator are in parallel according to the parallel principle with the impedance of a single unit within the group. The capacity and impedance of the equivalent step-up transformer in Group A can be expressed as:

[0034]

[0035] In formulas (10) and (11), a is the number of wind turbines in Group A, is the capacity of a single transformer, is the impedance value of a single transformer.

[0036] Finally, according to the clustering results of the wind turbines, the equivalent wind speed of the equivalent machine is calculated, and the equivalent wind speed is used as the wind speed of each equivalent machine within the group, and finally various parameters of the equivalent machine are obtained.

[0037] The beneficial effects of the present invention are that the optimal clustering equivalent method for wind farms using the Gaussian mixture model in the present invention uses the Gaussian mixture model clustering method and the AIC criterion and BIC criterion for discrimination to obtain the optimal number of clusters, solves the shortcomings of the traditional K-means algorithm that requires given initial clustering centers and the number of clusters, and proposes a new evaluation index for the research of wind farm equivalent methods. The calculation principle is simple and easy to implement, making the equivalent clustering results of the wind farm more in line with the actual situation and having a certain engineering practical value. Description of the Drawings

[0038] Figure 1 It is a schematic diagram of the detailed model of the wind farm for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0039] Figure 2(a) is the active power clustering index for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0040] Figure 2(b) is the reactive power clustering index for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0041] Figure 3 It is the flow chart of the equivalent effect for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0042] Figure 4 It is the clustering effect diagram for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention; the xyz coordinates represent wind speed, active power, and reactive power respectively, and different clustering effect diagrams are represented by different graphs;

[0043] Figure 5(a) is the AIC criterion discrimination diagram for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0044] Figure 5(b) is the BIC criterion discrimination diagram for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention;

[0045] Figure 6(a) is the active power waveform for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention under different voltage dips;

[0046] Figure 6(b) is the reactive power waveform for the optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention under different voltage dips. Detailed implementation manners

[0047] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0048] Step 1, obtain the wind speeds of the wind turbines at different positions in the wind farm through the total control of the wind farm;

[0049] Step 2, build a wind farm model with multiple wind turbine sets, transformers, and physical parameters of the collector lines through MATLAB / Simulink, and respectively obtain the steady-state active power and the reactive power under the voltage dip caused by the fault;

[0050] In the wind farm in Step 2, the parameters of the collector line are complex. When the voltage at the grid connection point changes due to a fault, the voltage changes reflected on each individual wind turbine are different. Due to the different wind speeds of each wind turbine, there are also differences in the pitch angles of the wind turbine pitch control systems and the states of the wind turbines operating in the starting area and the constant speed and constant power area. In the fault caused by voltage dip of the doubly-fed wind turbine, since the changes in the stator and rotor currents will cause changes in the electromagnetic torque, it will further affect the rotor speed of the wind turbine and the active and reactive powers output

[0051] Step 3: Select the wind speed, steady-state active power used for Gaussian distribution clustering and grouping, and the reactive power under the voltage dip caused by the fault in Step 2. Calculate the probability generated by each sample point data from its corresponding cluster, and perform multi-step iteration to obtain the probability of the updated cluster until Gaussian convergence; divide each sample into the cluster with the maximum probability respectively, and finally obtain the clustering and grouping results of N classes

[0052] The three-dimensional Gaussian mixture model clustering method is adopted in Step 3

[0053] Gaussian mixture model clustering is a method based on the probability model. It is assumed that the input samples follow k Gaussian distributions with unknown parameters, and each Gaussian distribution corresponds to a different mean and covariance matrix (1 ≤ j ≤ k). Then the samples belonging to the same distribution are clustered into one class. Take the wind speed, steady-state active power and reactive power in Step 2 as the sample set , and initialize the parameters of the Gaussian mixture distribution, the mixing coefficient , mean vector and covariance matrix , and reasonably assume that each mixing element has a diagonal matrix. Secondly, calculate the probability that each sample point x i ( i = 1, 2, 3, … m) belongs to the j-th Gaussian distribution:

[0054]

[0055] Calculate the updated iterative model parameter values, the mean vector , covariance matrix and mixing coefficient according to formulas (2), (3) and (4).

[0056]

[0057] According to , divide each sample into the cluster with the maximum probability, and perform three-dimensional clustering based on the three-dimensional sample set of wind speed, steady-state active power and reactive power to obtain the final cluster division , Finally, N types of clustering results are obtained.

[0058] Step 4: Calculate the likelihood function value according to the clustering and grouping results in Step 3, and then use the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to judge and select the clustering centers. The wind speed corresponding to the clustering center is the equivalent wind speed within the group, and thus N clustering groups are obtained;

[0059] In Step 4, the AIC and BIC criteria are used to determine whether the optimal number of grouping is obtained. The definitions of AIC and BIC are as follows:

[0060] AIC = -2ln(L) + 2 k (5)

[0061]

[0062] In the formula, k is the number of model parameters, m is the number of samples, is the likelihood function; where is the j-th different sample point, is the mean value corresponding to different Gaussian distributions, is the covariance matrix corresponding to different Gaussian distributions; Combining the three-dimensional clustering data of the wind turbines, different AIC values and BIC values correspond to different numbers of clusters. When both take the minimum value, the number of clusters of the wind farm reaches the optimal solution.

[0063] Step 5: Using the clustering results in Step 4, in the equivalent calculation of the wind farm, based on the principle that the power and current before and after equivalence are equal, simplify and equivalent the wind turbines, transformers, and collector lines within the N clustering groups respectively, and finally obtain the simplified equivalent result of the wind farm with the optimal number of grouping.

[0064] The calculation process of Step 5 is as follows:

[0065] The equivalent power and equivalent current of the wind turbines in the A-th group after equivalence can be expressed as:

[0066]

[0067] The impedance of the wind turbines in the A-th group after equivalence can be expressed as:

[0068]

[0069] In formulas (7) and (8), is the equivalent power of the wind farm within the group, is the equivalent current at the outlet of the wind farm within the group, is the equivalent impedance of the wind farm within the group, is the power corresponding to each individual wind turbine, is the outlet current corresponding to each individual fan, is the outlet voltage corresponding to each individual fan, is the voltage at the wind farm outlet within the cluster, is the voltage at the wind farm grid connection point, is the equivalent capacitance current of the wind farm in the group to the ground.

[0070] Considering the capacitance of each wind turbine in the group, the ground capacitance of the wind turbines in group A can be approximately expressed as the sum of the ground capacitance of a single wind turbine.

[0071]

[0072] Formula (9) is the ground capacitance of all wind turbines in group A.

[0073] The transformer parameter capacity is multiplied by the capacity of a single unit in the group, and the internal parameters and impedance of the generator are connected in parallel with the impedance of a single unit in the group according to the parallel principle. The capacity and impedance of the equivalent step-up transformer in group A can be expressed as:

[0074]

[0075] In formula (10) and formula (11), a is the number of fans in group A, is the capacity of a single transformer, is the impedance value of a single transformer.

[0076] Finally, according to the clustering results of wind turbines, the equivalent wind speed of the equivalent machine is calculated, and the equivalent wind speed is used as the wind speed of each equivalent machine in the group, and finally various parameters of the equivalent machine are obtained.

[0077] The optimal clustering equivalent method of the wind farm using the Gaussian mixture model in the present invention is based on the principle of: Figure 1 The detailed model of a doubly-fed wind farm is taken as an example.

[0078] The doubly-fed wind farm consists of multiple wind turbines, transformers, and complex collection lines. The wind turbines generate electricity that is output through a 690V / 35Kv transformer and collected on a 35Kv busbar, and then boosted through a 35Kv / 110kv transformer and connected to the large power grid. If a detailed wind farm model is used for simulation, it will not only take a lot of time, but may even cause the occurrence of dimensionality disaster. Therefore, the real-time simulation accuracy and simulation time of the wind farm are comprehensively considered, and then a suitable doubly-fed wind farm equivalent model is established.

[0079] (1) The wind speed, active power during steady state, and reactive power during fault period are clustered in three dimensions using Gaussian mixture model clustering algorithm to obtain the clustering result graph;

[0080] (2)For the obtained clustering groups, the AIC criterion and the BIC criterion are used for discrimination. Observe whether the discrimination results correspond to the clustering results to obtain the final clustering results;

[0081] (3)The equivalent calculation of the transformer and the collector parameters is carried out by adopting the principle that the power and current before and after equivalence are equal, and the final equivalent model of the wind farm is obtained. According to the clustering results of the wind turbines, the equivalent wind speed of the equivalent machine is calculated, and the equivalent wind speed is used as the wind speed of each equivalent machine in the group, and finally various parameters of the equivalent machine are obtained.

[0082] Example 1

[0083] Take Figure 1 the detailed model of the doubly-fed wind farm described above as an example. To verify the performance of the proposed clustering equivalent method using the Gaussian mixture model, a detailed model of 30 wind turbines is established in MATLAB / Simulink. In this model, the 690V voltage at the outlet of the wind turbine is stepped up to 35Kv by a transformer, collected on the 35Kv AC bus, and then sent to the large power grid through a 35Kv / 110Kv transformer to complete the grid connection of the new energy wind farm. The detailed model refers to the physical parameters of the transformer line of a wind farm with 30 wind turbines and is reasonably modified to meet the simulation requirements.

[0084] The equivalent steps of the doubly-fed wind farm are as follows:

[0085] 1) Obtain the different wind speeds of the wind turbines at different positions in the field through the wind farm total control;

[0086] 2) Build a wind farm model with the physical parameters of multiple wind turbines, transformers, and collector lines through MATLAB / Simulink, and obtain the steady-state active power and the reactive power under the voltage dip caused by faults respectively;

[0087] 3) Select the wind speed, steady-state active power, and reactive power under the voltage dip caused by the fault in step 2 for Gaussian distribution clustering. Calculate the probability that each sample point data is generated by its corresponding cluster, and perform multi-step iteration to obtain the probability of the updated cluster until Gaussian convergence; divide each sample into the cluster with the maximum probability respectively, and finally obtain the N-class clustering group results;

[0088] 4) Calculate the likelihood function value according to the clustering group results in step 3, and then use the Akaike information criterion AIC and the Bayesian information criterion BIC to judge and select the clustering centers. The wind speed corresponding to the clustering centers is the equivalent wind speed in the group, and thus N clustering groups are obtained;

[0089] 5) Using the clustering results in step 4, in the equivalent calculation of the wind farm, adopt the principle of equal power and current before and after equivalence, and simplify and equivalent the wind turbines, transformers, and collector lines in the N clustering groups respectively, and finally obtain the simplified equivalent result of the wind farm with the optimal number of clustering groups.

[0090] Use MATLAB / Simulink for simulation tests and verify the equivalent accuracy for different voltage sag degrees.

[0091] Figure 6 (a) shows the comparison of active power and reactive power among the detailed model, single-machine equivalent model and the equivalent model proposed in the present invention under the voltage sag degree of 0.5 pu. Figure 6 (b) shows the comparison of active power and reactive power among the detailed model, single-machine equivalent model and the equivalent model proposed in the present invention under the voltage sag degree of 0.85 pu.

[0092] The above simulation results all prove that the simulation accuracy proposed in the present invention is high.

Claims

1. The optimal clustering equivalent method for a wind farm using a Gaussian mixture model, characterized in that, Specifically, it includes the following steps: Step 1: Obtain the wind speeds of the wind turbines at different positions in the wind farm through the overall control of the wind farm; Step 2: Build a wind farm model with multiple wind turbine sets, transformers, and physical parameters of the collector lines through MATLAB / Simulink, and respectively obtain the steady-state active power and the reactive power under the voltage dip caused by faults; Step 3: Select the wind speed, steady-state active power, and the reactive power under the voltage dip caused by the fault in Step 2 for Gaussian distribution clustering. Calculate the probability generated by each sample point data from its corresponding cluster, and perform multiple-step iterations to obtain the probability of the updated cluster until Gaussian convergence; respectively divide each sample into the cluster with the maximum probability, and finally obtain the N-class clustering results; Step 4: Calculate the likelihood function value according to the clustering results in Step 3, and then use the Akaike Information Criterion AIC and Bayesian Information Criterion BIC to judge and select the clustering center. The wind speed corresponding to the clustering center is the equivalent wind speed within the group, and thus N clustering groups are obtained; Step 5: Utilize the clustering results in Step 4. In the equivalent calculation of the wind farm, based on the principle of equal power and current before and after equivalence, simplify and equivalent the wind turbines, transformers, and collector lines within the N clustering groups respectively, and finally obtain the simplified equivalent result of the wind farm with the optimal number of clustering groups.

2. The optimal clustering equivalent method for a wind farm using a Gaussian mixture model according to claim 1, characterized in that, The wind farm model built in Step 2 includes multiple 1.5MW doubly-fed wind turbines with low voltage ride-through capabilities, which are collected to the collector line by 0.69kV / 35kV box transformers and connected to the large power grid system through 35kV / 110kV step-up transformers.

3. The optimal clustering equivalent method for a wind farm using a Gaussian mixture model according to claim 1, characterized in that, The specific method of using the three-dimensional Gaussian mixture model clustering method in Step 3 is as follows: Suppose the input samples follow k Gaussian distributions with unknown parameters, and each Gaussian distribution corresponds to a different mean and covariance matrix , where 1 ≤ j ≤ k. Then the samples belonging to the same distribution are clustered into one class; Take the wind speed, steady-state active power, and reactive power in step 2 as the sample set , and initialize the parameters of the Gaussian mixture distribution, namely the mixing coefficients , the mean vectors , and the covariance matrices . Assume that each mixture element has a diagonal matrix, and then calculate the probability that each sample point x i belongs to the j-th Gaussian distribution , where i = 1, 2, 3, … m ; wherein, is the j-th sample point, is the mean value corresponding to different Gaussian distributions; is the covariance matrix corresponding to different Gaussian distributions; Calculate the mean vector of the updated iterative model parameter values according to equations (2), (3) and (4). , covariance matrix and mixing coefficients ; According to Each sample is assigned to the cluster with the highest probability, based on the three-dimensional sample set of wind speed, steady-state active power, and reactive power Three-dimensional clustering is performed to obtain the final cluster partition , and finally N types of clustering results are obtained.

4. The optimal clustering equivalent method for a wind farm using a Gaussian mixture model according to claim 1, characterized in that, In Step 4, use the AIC and BIC criteria to determine whether the optimal number of clustering groups is obtained: The definitions of AIC and BIC are as follows: AIC = -2ln(L) + 2 k (5) In the formula, k is the number of model parameters, m is the number of samples, is the likelihood function; where is the j-th different sample point, is the mean corresponding to different Gaussian distributions, is the covariance matrix corresponding to different Gaussian distributions; Combining the three-dimensional clustering data of the fan, different AIC values and BIC values correspond to different numbers of clusters. When both are minimized, the number of clusters of the wind farm at this time reaches the optimal solution.

5. The optimal clustering equivalent method for a wind farm using a Gaussian mixture model according to claim 1, characterized in that, The calculation process of Step 5 is as follows: The equivalent power of the fans in Group A after equivalence and the equivalent current can be expressed as: The impedance of the wind turbines in the A-th group after equivalence can be expressed as: In Equations (7) and (8) is the equivalent power of the wind farms within the group, is the equivalent current at the outlet of the wind farms within the group, is the equivalent impedance of the wind farms within the group, is the power corresponding to each individual wind turbine, is the current at the outlet corresponding to each individual wind turbine, is the voltage at the outlet corresponding to each individual wind turbine, is the voltage at the outlet of the wind farms within the group, is the grid connection point voltage of the wind farm, is the equivalent capacitive current to the ground of the wind farms within the group; Considering the capacitance of each wind turbine within the group, the capacitance of the wind turbines in the A-th group to the ground can be approximately expressed as the sum of the capacitances of single wind turbines to the ground; Equation (9) is the capacitance to ground of all the fans in Group A; The capacity of the transformer parameters is multiplied by the capacity of a single unit within the group, and the internal parameters and impedance of the generator are connected in parallel according to the parallel principle with the impedance of a single unit within the group; the capacity and impedance of the equivalent step-up transformer within the A-th group can be expressed as: In Formula (10) and Formula (11), is the number of internal fans in Group A, is the capacity of a single transformer, is the impedance value of a single transformer.

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