Model aggregation and low-pass control parameter optimization method considering distributed photovoltaic

Abstract

The invention discloses a model aggregation and low-pass control parameter optimization method considering distributed photovoltaic, belongs to the technical field of new energy, and aims to solve the problem that a traditional distributed photovoltaic model only considers the condition of grid connection with a single control strategy. The method comprises the following steps: establishing a distributed photovoltaic access power distribution network detailed model, and simulating and analyzing different low-voltage fault working conditions; generating sample data based on transient characteristics and equivalent impedance of a photovoltaic inverter machine end, and clustering and aggregating distributed photovoltaic cells by adopting a K-means method; a simplified power distribution network distributed photovoltaic aggregation model is established, provincial power grid simulation data are accessed, and the parameters of the power distribution network aggregation model are optimized by adopting a gradient descent method with the purpose of maximizing the transient voltage increase of a power distribution network collection point during a fault period. The photovoltaic low-pass control parameters optimized by the method are obviously changed, the transient voltage of the collection point of the power distribution network during the fault period is improved, and the supporting capacity of the power distribution network for the transient voltage is improved.

Description

Technical Field

[0001] The present invention relates to the field of new energy technologies, and in particular to a model aggregation and low-throughput control parameter optimization method considering distributed photovoltaics. Background Art

[0002] Distributed photovoltaic power generation is one of the main ways to utilize new energy. my country strongly supports the development of distributed photovoltaic power generation in the central and eastern regions. In recent years, distributed photovoltaic power generation in the central and eastern regions has developed rapidly. By the end of 2019, the installed capacity of distributed photovoltaic power generation exceeded 60 million kilowatts, and the installed capacity increased year by year. At the same time, the voltage levels of distributed photovoltaic access to the grid are complex and diverse, ranging from 380V to 110kV, and the total access capacity is large and there are many distributed nodes. The traditional centralized access photovoltaic analysis method cannot meet the needs of distributed photovoltaic analysis. Distributed photovoltaics themselves do not have the ability to regulate peak, frequency and voltage, which has a great impact on the operation of the grid.

[0003] At present, many scholars at home and abroad have conducted extensive research on distributed photovoltaic modeling and simulation, mainly based on the distributed photovoltaic active-voltage grid-connected characteristics to carry out equivalent modeling and analysis of distributed photovoltaic, but did not discuss the impact of reactive characteristics, and could not reflect the supporting role of distributed photovoltaic on grid voltage when transient voltage stability problems occur in the actual grid. Distributed photovoltaic models often only consider the situation of grid connection with a single control strategy, while the actual distributed photovoltaic is grid-connected with multiple control strategies.

[0004] In the scenario where distributed photovoltaics are connected to the distribution network, there may be a problem of insufficient reactive power support when a collection point fails. According to the technical requirements of reactive power support at the collection point, control strategies for distributed photovoltaics at different access locations can be proposed to improve the distribution network's support capacity for transient voltages. Summary of the invention

[0005] The present invention solves the problem that traditional distributed photovoltaic models often only consider the situation of grid-connected with a single control strategy, and proposes a model aggregation and low-throughput control parameter optimization method considering distributed photovoltaics. The photovoltaic low-throughput control parameters optimized by this method have obvious changes, which significantly improves the transient voltage at the distribution network collection point during the fault period and enhances the distribution network's support capacity for transient voltage.

[0006] In order to achieve the above object, the present invention adopts the following technical solution: a model aggregation and low penetration control parameter optimization method considering distributed photovoltaics, comprising the following steps: S1, establish a detailed model of distributed photovoltaic access to the distribution network, and simulate and analyze different low voltage fault conditions; S2, based on the transient characteristics and equivalent impedance of the photovoltaic inverter, generates sample data and uses the K-means method to group and aggregate distributed photovoltaics; S3, establish a simplified distributed photovoltaic aggregation model for the distribution network, and access the provincial power grid simulation data. The photovoltaic aggregation model parameters are weighted by capacity and averaged. S4, based on the established distributed photovoltaic aggregation model of the distribution network, the parameters of the distribution network aggregation model are optimized by using the gradient descent method with the goal of maximizing the transient voltage increase at the distribution network collection point during the fault period.

[0007] In this technical solution, firstly, a detailed model of distributed photovoltaic access to the distribution network is established to simulate and analyze the low-voltage fault condition; then, sample data is generated, and the K-means method is used to determine the differences between the characteristic data of different distribution network collection points and other clusters, and then the sample data is clustered and aggregated by analyzing the extraction results of these features; then a simplified distribution network distributed photovoltaic aggregation model is established, and finally the stochastic gradient descent method is used to optimize the photovoltaic model parameters of the aggregation model.

[0008] The present invention is further configured as follows: Step S1 comprises: The simulation analyzes the voltage, current and power change characteristics of distributed photovoltaic grid-connected points and distribution network collection points under various low-voltage faults at the distribution network collection points, and classifies various low-voltage states to form multiple simulation working conditions.

[0009] In this technical solution, simulation and analysis are performed under various low-voltage fault operating conditions. A three-phase short-circuit fault occurs at the distribution network collection point, causing the voltage at the distribution network collection point to drop to different voltage values. There are a total of 30 simulation conditions.

[0010] The present invention is further configured as follows: Step S2 comprises: S21, obtain samples, set the number of clusters and cluster centers, calculate the distance from the sample to each cluster center, plan the sample to the nearest cluster center, and use the sample mean as the new cluster center; S22, determine whether the SSE criterion function converges, if so, output the clustering aggregation, if not, return to step S22.

[0011] In this technical solution, the voltage, active power, reactive power, and equivalent impedance from the grid connection point to the collection point of the distributed photovoltaic power generation during a fault under various simulation conditions are used as sample data, and a corresponding sample set is defined.

[0012] The present invention is further configured as follows: the optimization target of maximizing the transient voltage increase at the distribution network collection point during a fault is expressed as: X( k) ={K 1_Iq_LV ,K 2_Iq_LV ,Iq set_LV ,K1_Ip_LV ,K 2_Ip_LV ,Ip set_LV} in, is the transient voltage level at the sink point, X (k) K is the optimization variable. 1_Iq_LV ,K 2_Iq_LV ,Iq set_LV They are low voltage ride through active control parameters respectively.

[0013] In this technical solution, the goal is to achieve the highest transient voltage at the distribution network collection point during a low voltage fault.

[0014] The present invention is further configured as follows: the optimization of the parameters of the distribution network aggregation model by using the gradient descent method includes: S41, data initialization, and judging whether the variables meet the constraints; S42, calculated gradient function g k =g(X (k) ), if there is |g k |≤δ, δ is the calculation accuracy, stop iteration, and let the distributed photovoltaic inverter optimize the variable X opt =X (k) .

[0015] In this technical solution, the gradient function is specifically:

[0016] The present invention is further configured as follows: if there is no |g k |≤δ, let the search direction t k =g(X (k) ) is equal to the gradient direction, let X (k+1) =X (k) +λt k , λ is the search step length, we get When |f(X (k+1) )-f(X (k) )|≤δor|X (k +1) -X (k) When |≤δ, stop iteration, X opt =X (k+1) , and let t k =g(X (k+1) ), otherwise go to step S32.

[0017] In this technical solution, when X (k+1) =X (k) +λt k At the same time, check whether the optimization variables meet the constraints.

[0018] The present invention is further configured as follows: the SSE criterion function is specifically: Among them, dis(x i ,c j ) is the Euclidean distance, Φ j represents the jth cluster, x i and c j are the sample data and the center point of the j-th cluster respectively.

[0019] In this technical solution, when the SSE criterion function converges, the result is output.

[0020] The present invention is further configured as follows: the Euclidean distance is specifically: Among them, x i and c j All are four-bit vectors, l represents x i and c j Contains four different attributes.

[0021] In this technical solution, according to the above formula, the i and c j The Euclidean distance of .

[0022] The present invention has the following beneficial effects: The present invention relates to a model aggregation and low-voltage control parameter optimization method considering distributed photovoltaics. After optimization by the method, the photovoltaic low-voltage control parameters are significantly changed, which significantly improves the transient voltage at the distribution network collection point during the fault period and enhances the distribution network's support capacity for transient voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 1 is a flow chart of a method for optimizing model aggregation and low penetration control parameters considering distributed photovoltaics in Embodiment 1; Figure 2 This is a flow chart of a method for optimizing model aggregation and low-throughput control parameters considering distributed photovoltaics in Embodiment 1, which uses a K-means method to group distributed photovoltaics; Figure 3 This is a flow chart of optimizing photovoltaic model parameters of a distribution network aggregation model by a method for optimizing model aggregation and low-throughput control parameters taking into account distributed photovoltaics in this embodiment 1; Figure 4 This is a topological diagram of a detailed model of distributed photovoltaic access to a distribution network in accordance with a model aggregation and low penetration control parameter optimization method considering distributed photovoltaics in this embodiment 1; Figure 5This is a voltage comparison curve before and after parameter optimization under typical line faults after the distribution network aggregation model is connected to the provincial power grid, showing a model aggregation and low-throughput control parameter optimization method considering distributed photovoltaics in this embodiment 2. DETAILED DESCRIPTION

[0024] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation method described herein is only an optimal embodiment of the present invention, which is only used to explain the present invention and does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0025] Embodiment 1: This embodiment proposes a model aggregation and low-through control parameter optimization method considering distributed photovoltaics, referring to Figure 1 , mainly including the following steps.

[0026] Step S1, reference Figure 4 , establish a detailed model of distributed photovoltaic access to the distribution network, and simulate and analyze different low-voltage fault conditions; wherein, this step specifically includes: creating a detailed model of distributed photovoltaic access to the distribution network, specifically including distributed photovoltaic power stations, loads, transformers and transmission lines, simulating and analyzing the voltage, current and power change characteristics of distributed photovoltaic grid-connected points and distribution network collection points under various low-voltage faults at the distribution network collection points, and classifying various low-voltage states to form a variety of simulation conditions; the distributed photovoltaic model adopts a control strategy that keeps reactive and active power unchanged during fault ride-through, and the voltage level grid above the collection point is replaced by an infinite power source.

[0027] In this embodiment, the simulation analysis of various low-voltage faults is that when the distributed photovoltaic output is at five operating conditions of 10%, 40%, 60%, 80% and 100%, a three-phase short circuit fault occurs at the distribution network collection point, and the voltage at the distribution network collection point drops by 0%, 20%, 40%, 50%, 60% and 80% respectively, for a total of 30 simulation conditions.

[0028] Step S2, based on the transient characteristics and equivalent impedance of the photovoltaic inverter machine end, generate sample data, and use the K-means method to cluster the distributed photovoltaics; specifically, use the K-means method to cluster the distributed photovoltaics, judge the differences between the characteristic data of different distribution network collection points and other clusters, and then complete the clustering and aggregation of the sample data by analyzing the extraction results of these features.

[0029] For the specific steps of K-means method to cluster distributed photovoltaics, refer to Figure 2 , mainly includes the following processes.

[0030] Step S21, obtain samples, set the number of clusters and cluster centers, calculate the distance from the sample to each cluster center, plan the sample to the nearest cluster center, and use the sample mean as the new cluster center. Among them, the voltage, active power, reactive power, and equivalent impedance from the grid connection point to the collection point of the distributed photovoltaic during the fault period under the above 30 simulation conditions are used as samples.

[0031] For the convenience of description, the above sample data is defined as a sample set containing n data Ω, which is specifically expressed as: Ω={x i ∣x i =(x i1 ,x i2 ,x i3 ,x i4 ),i=1,2,…,n} Among them, x i =(x i1 ,x i2 ,x i3 ,x i4 ) is a four-dimensional vector, which represents the four different attributes of the i-th data, including the grid connection point voltage, active power, reactive power, and the equivalent impedance from the grid connection point to the collection point; n is the sample size.

[0032] Then, m centers are randomly selected from the above sample set data object, denoted as c j ; as the initial cluster center; and for the remaining data objects, they are assigned to the clusters represented by the cluster centers that are most similar to them according to their similarity (Euclidean distance) with these cluster centers.

[0033] The cluster center of the cluster is expressed as: C={c j ∣c j =(c j1 ,c j2 ,c j3 ,c j4 ),j=1,2,...,m} Among them, c j =(c j1 ,c j2 ,c j3 ,c j4 ) is the center point of the jth cluster, and each center point c j They all contain 4 different attributes, and m is the number of clusters.

[0034] Two data x i and c j The Euclidean distance betweeni ,c j ), which is expressed as follows: Among them, x i and c j Are four-dimensional vectors, l represents x i and c j Contains four different attributes; x i =(x i1 ,x i2 ,…x id ), c j =(c j1 ,c j2 ,c j3 ,c j4 ).

[0035] Among them, dis(x i ,c j ) is smaller, indicating that x i and c j The more similar, the x i With different cluster centers c j Between dis(x i ,c j ) for comparison, the clustered data should satisfy: dis(x i ,c j )<dis(x i ,c q ),q∈[1,m],j≠q Where q∈[1,m], q is an integer, m is the number of clusters, Take the data x that satisfies the above operation i Put it into the corresponding cluster class φ j middle.

[0036] The updated center point of the same cluster is c j It is expressed as follows: Among them, N(φ j ) are of the same cluster class φ j The number of data in .

[0037] Step S22, determine whether the SSE criterion function converges, if so, output the cluster aggregation, if not, return to step S22; specifically, calculate the distance of each updated new cluster center to the mean of all data objects in the cluster, and repeat this process until the criterion function converges.

[0038] The SSE criterion function is as follows: Among them, dis(x i ,c j ) is the Euclidean distance, Φ j represents the jth cluster, x i and c j are the sample data and the center point of the jth cluster, respectively, i =(x i1 ,x i2 ,x i3 ,x i4 ), c j =(c j1 ,c j2 ,c j3 ,c j4 ), m is the number of clusters.

[0039] Step S3, establish a simplified distributed photovoltaic aggregation model of the distribution network, and connect it to the provincial power grid simulation data, and take the average value of the photovoltaic aggregation model parameters according to the capacity weighted; wherein, the simplified distributed photovoltaic aggregation model of the distribution network includes establishing a distributed photovoltaic distribution network composed of photovoltaic power stations, loads, transformers and transmission lines, and connecting to the main distribution network to form a distributed photovoltaic access distribution network model, so as to realize the access of the aggregated distribution network model to the provincial power grid simulation data.

[0040] Step S4, reference Figure 3 ,On the established distributed photovoltaic aggregation model of the distribution network, the ,target is to maximize the transient voltage increase at the distribution network ,aggregation point during the fault period, and the parameters of the distribution ,network aggregation model are optimized by adopting the gradient descent ,method.

[0041] In step S4, firstly, the corresponding optimization variables, optimization objectives and constraints are determined, which specifically includes the following process.

[0042] In the photovoltaic control system, the reactive current control parameter used in the low voltage ride-through control strategy is K 1_Iq_LV , K 2_Iq_LV , Iq set_LV , the reactive current provided during a low voltage fault is as follows: Iq LVRT =K 1_Iq_LV *(VL in -Vt)+K 2_Iq_LV *Iq0+Iq set_LV Among them, all parameters are taken as per unit value, VL in is the low voltage ride-through voltage limit, generally 0.9, Vt is the terminal voltage of the photovoltaic inverter, Iq0 is the initial reactive current value of the photovoltaic inverter, Iq LVRT Reactive current provided to PV inverter stations during low voltage faults.

[0043] The low voltage ride through active control parameter is K 1_Ip_LV , K 2_Ip_LV 、Ip set_LV , the active current provided during a low voltage fault is shown in the following equation.

[0044] Ip LVRT =K 1_Ip_LV *Vt+K 2_Ip_LV *Ip0+Ip set_LV Among them, all parameters are taken as per unit value, Ip0 is the initial reactive current value of the photovoltaic inverter, Ip LVRT Reactive current provided to PV inverter stations during low voltage faults.

[0045] Therefore, the optimization variable is determined as the low voltage ride-through control parameter set of the large-scale distributed photovoltaic inverter connected to the distribution network as X (k) ={K 1_Iq_LV ,K 2_Iq_LV ,Iq set_LV ,K 1_Ip_LV ,K 2_Ip_LV ,Ip set_LV}.

[0046] Determine the variable X (k) When the photovoltaic access distribution network is connected to the distribution network in the optimized mode, the transient voltage level of the distribution network collection point under the typical line low voltage fault occurs, which is recorded as Determine the optimization goal as The maximum value means that during the low voltage fault period, the transient voltage at the distribution network collection point is the highest; that is, the optimization goal is to maximize the transient voltage increase at the distribution network collection point during the fault period.

[0047] Determine the corresponding constraints: Due to the safety and stability constraints of the photovoltaic inverter equipment, the set of variables to be optimized has limit requirements, as shown in Table 1: Table 1 Constraints of variables to be optimized Optimize variable names Constraint requirements <![CDATA[K 1_Iq_LV ]]> <![CDATA[1.5≤K 1_Iq_LV ≤5]]> <![CDATA[K 2_Iq_LV ]]> <![CDATA[0≤K 2_Iq_LV ≤1 <!-- 5 -->]]> <![CDATA[Iq set_LV ]]> <![CDATA[-1≤Iq set_LV ≤1]]> <![CDATA[K 1_Ip_LV ]]> <![CDATA[0≤K 1_Ip_LV ≤1]]> <![CDATA[K 2_Ip_LV ]]> <![CDATA[0≤K 2_Ip_LV ≤1]]> <![CDATA[Ip set_LV ]]> <![CDATA[0≤Ip set_LV ≤1]]> .

[0048] The steps to optimize the parameters of the distribution network aggregation model by using the gradient descent method continue to refer to Figure 3 , first set the search step size λ = 0.1 and the calculation accuracy δ = 0.002.

[0049] In this technical solution, the gradient function is

[0050] Step S41, data initialization, and judging whether the variables meet the constraint conditions.

[0051] More specifically, the data initialization process is as follows: based on the distributed photovoltaic system not providing reactive current control during low voltage ride-through, that is, K 1_Iq_LV =0, K 2_Iq_LV =0, Iq set_LV =0, K 1_Ip_LV =0, K 2_Ip_LV =0, Ip set_LV =0, simulation analysis of the transient voltage level of the distribution network collection point when a typical line low voltage fault occurs in the vicinity of large-scale distributed photovoltaic access distribution network, the initial value is

[0052] Step S42, calculate the gradient g under the current parameter combination k =g(X (k) ), if there is |g k |≤δ, δ is the calculation accuracy, stop iteration, and let the distributed photovoltaic inverter optimize the variable X opt =X (k) .

[0053] If not present |g k |≤δ, let the search direction t k =g(X (k) ) is equal to the gradient direction, let X (k+1) =X (k) +λt k , λ is the search step size, and checks whether the optimization variables meet the constraints.

[0054] Step S43, setting the low voltage ride-through control parameter of the distributed photovoltaic inverter to X (k) The transient voltage level of the distribution network collection point under the typical line low voltage fault in the vicinity of the photovoltaic access distribution network under this mode is simulated and analyzed, and the results are

[0055] Step S44, when |f(X (k+1) )-f(X (k) )|≤δor|X (k+1) -X (k) When |≤δ, stop iteration, X opt =X (k+1) , and let t k =g(X (k+1) ), otherwise k=k+1, and return to step S42.

[0056] Step S45, finally output the optimized variable X opt .

[0057] In an embodiment of the scheme of the present invention, firstly, a detailed model of distributed photovoltaic access to the distribution network is established to simulate and analyze the low-voltage fault condition; then, sample data is generated, and the K-means method is used to determine the differences between the characteristic data of different distribution network collection points and other clusters, and then the sample data is clustered and aggregated by analyzing the extraction results of these features; then a simplified distribution network distributed photovoltaic aggregation model is established, and finally the stochastic gradient descent method is used to optimize the photovoltaic model parameters of the aggregation model.

[0058] Example 2 Based on the model aggregation and low penetration control parameter optimization method considering distributed photovoltaics in Example 1, refer to Figure 4 This embodiment takes the typical distribution network structure connected to the provincial power grid model as an example to complete the distributed photovoltaic model parameter optimization, and shows the influence of the photovoltaic low-through control parameters before and after optimization on the actual transient voltage of the distribution network collection point during the fault period. The simulation results are as follows Figure 5 shown.

[0059] Depend on Figure 5 It can be seen that the photovoltaic low-breakdown control parameters after optimization by this method have obvious changes, which can significantly improve the transient voltage at the distribution network collection point during the fault period, thereby improving the grid support capacity of distributed photovoltaic power generation equipment and improving the overall stability of the distributed photovoltaic distribution network.

[0060] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

Claims

1. A model aggregation and low penetration control parameter optimization method considering distributed photovoltaics, characterized in that: The following steps are involved: S1, establish a detailed model of distributed photovoltaic access to the distribution network, and simulate and analyze different low voltage fault conditions; S2, based on the transient characteristics and equivalent impedance of the photovoltaic inverter, generates sample data and uses the K-means method to group and aggregate distributed photovoltaics; S3, establish a simplified distributed photovoltaic aggregation model for the distribution network, and access the provincial power grid simulation data. The photovoltaic aggregation model parameters are weighted by capacity and averaged. S4, based on the established distributed photovoltaic aggregation model of the distribution network, the parameters of the distribution network aggregation model are optimized by using the gradient descent method with the goal of maximizing the transient voltage increase at the distribution network collection point during the fault period.

2. According to claim 1, a method for optimizing model aggregation and low-throughput control parameters considering distributed photovoltaics is characterized in that: The step S1 comprises: The simulation analyzes the voltage, current and power change characteristics of distributed photovoltaic grid-connected points and distribution network collection points under various low-voltage faults at the distribution network collection points, and classifies various low-voltage states to form multiple simulation working conditions.

3. A method for optimizing model aggregation and low penetration control parameters considering distributed photovoltaics according to claim 1 or 2, characterized in that: The step S2 comprises: S21, obtain samples, set the number of clusters and cluster centers, calculate the distance from the sample to each cluster center, plan the sample to the nearest cluster center, and use the sample mean as the new cluster center; S22, determine whether the SSE criterion function converges, if so, output the clustering aggregation, if not, return to step S22.

4. A method for optimizing model aggregation and low penetration control parameters considering distributed photovoltaics according to claim 3, characterized in that: The optimization objective of maximizing the transient voltage increase at the distribution network collection point during a fault is expressed as: X (k) ={K 1_Iq_LV ,K 2_Iq_LV ,Iq set_LV ,K 1_Ip_LV ,K 2_Ip_LV ,Ip set_LV } in, is the transient voltage level at the sink point, X (k) K is the optimization variable. 1_Iq_LV ,K 2_Iq_LV ,Iq set_LV They are low voltage ride through active control parameters respectively.

5. A method for optimizing model aggregation and low penetration control parameters considering distributed photovoltaics according to claim 1, 2 or 4, characterized in that: The parameters of the distribution network aggregation model optimized by using the gradient descent method include: S41, data initialization, and judging whether the variables meet the constraints; S42, calculated gradient function g k =g(X (k) ), if there is |g k |≤δ, δ is the calculation accuracy, stop iteration, and let the distributed photovoltaic inverter optimize the variable X opt =X (k) .

6. A method for model aggregation and low penetration control parameter optimization considering distributed photovoltaics according to claim 5, characterized in that: If not present |g k |≤δ, let the search direction t k =g(X (k) ) is equal to the gradient direction, let X (k+1) =X (k) +λt k , λ is the search step length, we get When |f(X (k+1) )-f(X (k) )|≤δor|X (k+1) -X (k) When |≤δ, stop iteration, X opt =X (k+1) , and let t k =g(X (k+1) ), otherwise go to step S32.

7. The method for optimizing model aggregation and low-throughput control parameters considering distributed photovoltaics according to claim 3, characterized in that: The SSE criterion function is as follows: Among them, dis(x i ,c j ) is the Euclidean distance, Φ j represents the jth cluster, x i and c j are the sample data and the center point of the j-th cluster respectively, and m is the number of clusters.

8. A method for model aggregation and low penetration control parameter optimization considering distributed photovoltaics according to claim 7, characterized in that: The Euclidean distance is specifically: Among them, x i and c j Are four-dimensional vectors, l represents x i and c j Contains four different attributes.

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