CN109741091B - User load classification method based on basic load reduction strategy - Google Patents
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Abstract
本发明公开基于基础负荷削减策略的用户负荷分类方法,包括:步骤1,提取用户负荷数据,对负荷数据进行预处理;步骤2,选取削减负荷基准值,以聚合度为评价参数,采用削减基准负荷数值的方法区分负荷类型;步骤3,根据负荷类型区分结果,采用模糊C均值算法对负荷数据进行聚类。本发明针对当前负荷聚类方法中因为用户规模而错误识别用户类型的问题,提出了改进的负荷聚类算法处理技巧,利用模糊算法,验证本发明所提出的算法的精确性。本发明采用的方法能有效地排除用户规模对用户类型的干扰。
The invention discloses a user load classification method based on a basic load reduction strategy, comprising: step 1, extracting user load data, and preprocessing the load data; step 2, selecting a load reduction reference value, taking the aggregation degree as an evaluation parameter, and using the reduction reference value The method of load numerical value distinguishes the load type; step 3, according to the load type distinction result, the load data is clustered by the fuzzy C-means algorithm. Aiming at the problem of wrong identification of user types due to user scale in the current load clustering method, the invention proposes an improved load clustering algorithm processing skill, and uses a fuzzy algorithm to verify the accuracy of the algorithm proposed by the invention. The method adopted in the present invention can effectively eliminate the interference of the user scale on the user type.
Description
技术领域technical field
本发明属于电力系统负荷分类领域,具体为基于基础负荷削减策略的用户负荷分类方法。The invention belongs to the field of power system load classification, in particular to a user load classification method based on a basic load reduction strategy.
背景技术Background technique
负荷聚类是通过一定的数学手段,将大量的用户整合为一个个不同的聚合体。针对电网实时运营的情况,合理引导不同类别的聚合体有序用电,能够产生巨大的经济效益。而现有的聚类方法一般都是通过对负荷的走向和数值进行聚类。但是不同地区由于规模和用户数目不一致,导致同一类型或用电规律的用户不能被识别出来,造成分类结果不够精良。本发明针对上述问题,提出了基于负荷削减的一种聚类方法,通过模糊算法验证本发明聚类的结果。Load clustering is to integrate a large number of users into different aggregates through certain mathematical means. According to the real-time operation of the power grid, rationally guiding different types of aggregates to use electricity in an orderly manner can generate huge economic benefits. The existing clustering methods generally cluster the trend and value of the load. However, due to the inconsistent scale and number of users in different regions, users of the same type or electricity consumption pattern cannot be identified, resulting in insufficient classification results. In view of the above problems, the present invention proposes a clustering method based on load reduction, and verifies the clustering result of the present invention through a fuzzy algorithm.
现有技术中,也有通过其他方式实现负荷分类的方法。例如,申请号201810382946.7 的中国专利公开了一种基于决策树的模糊C聚类的负荷分类方法,其先通过凝聚型层次聚类算法确定最优分类数目,然后采用模糊C均值聚类算法对负荷数据进行聚类,从而实现负荷分类。In the prior art, there are also other methods for implementing load classification. For example, the Chinese Patent Application No. 201810382946.7 discloses a load classification method based on decision tree fuzzy C clustering, which first determines the optimal number of classifications through agglomerative hierarchical clustering algorithm, and then adopts the fuzzy C-means clustering algorithm to classify the load. The data is clustered to achieve load classification.
发明内容SUMMARY OF THE INVENTION
本发明的目的是针对现有技术存在的问题,提供基于基础负荷削减策略的用户负荷分类方法,以解决当前负荷聚类方法中因为用户规模而错误识别用户类型的问题。The purpose of the present invention is to provide a user load classification method based on a basic load reduction strategy to solve the problem of wrong identification of user types due to user scale in the current load clustering method.
为实现上述目的,本发明采用的技术方案是:For achieving the above object, the technical scheme adopted in the present invention is:
基于基础负荷削减策略的用户负荷分类方法,包括以下步骤:The user load classification method based on the basic load reduction strategy includes the following steps:
步骤1,提取用户负荷数据,对负荷数据进行预处理;
步骤2,选取削减负荷基准值,以聚合度为评价参数,采用削减基准负荷数值的方法区分负荷类型;
步骤3,根据负荷类型区分结果,采用模糊C均值算法对负荷数据进行聚类。Step 3: Clustering the load data by using the fuzzy C-means algorithm according to the load type discrimination result.
优选地,步骤1中的预处理步骤包括:定义偏差率η,Preferably, the preprocessing step in
其中,yi表示某一点的负荷数据,表示负荷数据在一时间周期内的平均值。Among them, yi represents the load data of a certain point, Indicates the average value of load data over a period of time.
优选地,当η>500%时,需要查验数据是否为不良数据点,若当前负荷曲线绝大多数负荷点均超标,则认定为正常测量数据;若仅为个别点超标,则判定为不良数据点。Preferably, when η>500%, it is necessary to check whether the data is a bad data point. If most of the load points in the current load curve exceed the standard, it will be regarded as normal measurement data; if only a few points exceed the standard, it will be judged as bad data. point.
优选地,步骤2的具体过程为:Preferably, the specific process of
2.1,选取削减负荷基准值;2.1, select the reference value for reducing the load;
2.2,数据标准化;2.2, data standardization;
2.3,计算数据梯度;2.3, calculate the data gradient;
2.4,判断聚合度是否满足要求,若满足,则输出区分的负荷类型,若不满足,则重新选取削减负荷基准值,转至2.2。2.4. Determine whether the degree of aggregation meets the requirements. If so, output the differentiated load types. If not, reselect the load reduction reference value and go to 2.2.
优选地,步骤3进一步包括:Preferably,
3.1,确定分类个数、幂指数、隶属度矩阵;3.1, determine the number of classifications, power exponent, and membership matrix;
3.2,计算聚类中心度;3.2, calculate the cluster centrality;
3.3,修正隶属度函数和目标函数;3.3, modify the membership function and objective function;
3.4,当隶属度函数满足终止限度或满足最大步长时,停止迭代,否则转至3.2。3.4, when the membership function satisfies the termination limit or satisfies the maximum step size, stop the iteration, otherwise go to 3.2.
优选地,对于隶属度函数,给定终止限度εJ>0或定义最大步长l,当满足时或满足最大步长时,停止迭代。Preferably, for the membership function, the termination limit ε J > 0 is given or the maximum step size l is defined, when the The iteration stops when the maximum step size is met.
优选地,隶属度和聚类中心度的迭代公式如下所示:Preferably, the iterative formulas for membership and cluster centrality are as follows:
Ij={1≤i≤c,dij=0}I j ={1≤i≤c,d ij =0}
当时,when hour,
当时,时,when hour, hour,
优选地,步骤3进一步包括:设样本取自p元样本总体,把样本X1,X2,L Xn总体划为c类,其中c的值不小于2,vi表示第i个聚类中心,设变量uij表示第i个样本对第j个样本的隶属度,则设定目标函数如下:Preferably,
约束条件:Restrictions:
uij∈[0,1]1≤j≤n,1≤i≤cu ij ∈[0,1]1≤j≤n,1≤i≤c
根据拉格朗日乘数法计算最优解:Calculate the optimal solution according to the Lagrange multiplier method:
并根据给定的约束条件,在MATLAB中进行优化。And according to the given constraints, it is optimized in MATLAB.
与现有技术相比,本发明的有益效果是:本发明针对当前负荷聚类方法中因为用户规模而错误识别用户类型的问题,提出了改进的负荷聚类算法处理技巧,利用模糊算法,验证本发明所提出的算法的精确性;本发明提出的算法具有更优良的聚类效果,可以根据工程或公司的实际需求,对负荷进行更有效的聚类。Compared with the prior art, the beneficial effects of the present invention are: the present invention proposes an improved load clustering algorithm processing skill for the problem of wrongly identifying user types due to the user scale in the current load clustering method, and uses a fuzzy algorithm to verify the results. The accuracy of the algorithm proposed by the present invention; the algorithm proposed by the present invention has better clustering effect, and can perform more effective clustering of loads according to the actual needs of the project or the company.
附图说明Description of drawings
图1为本发明基于基础负荷削减策略的用户负荷分类方法的流程示意图;1 is a schematic flowchart of a user load classification method based on a basic load reduction strategy of the present invention;
图2(a)-(e)为传统模糊聚类结果示意图;Figure 2(a)-(e) are schematic diagrams of traditional fuzzy clustering results;
图3(a)-(c )为本发明方法得到的聚类结果示意图;3(a)-(c) are schematic diagrams of clustering results obtained by the method of the present invention;
图4为c=3时聚类中心与轮廓值的关系示意图;4 is a schematic diagram of the relationship between the cluster center and the contour value when c=3;
图5为c=5时聚类中心与轮廓值的关系示意图;5 is a schematic diagram of the relationship between the cluster center and the contour value when c=5;
图中:Q-负荷;t-时间;T-聚类中心;S(i)-轮廓值。In the figure: Q-load; t-time; T-cluster center; S(i)-contour value.
具体实施方式Detailed ways
下面将结合本发明中的附图,对本发明的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动条件下所获得的所有其它实施例,都属于本发明保护的范围。The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
如图1所示,本发明提供基于基础负荷削减策略的用户负荷分类方法,包括以下步骤:As shown in FIG. 1, the present invention provides a user load classification method based on a basic load reduction strategy, including the following steps:
步骤1,提取用户负荷数据,对负荷数据进行预处理;
步骤2,选取削减负荷基准值,以聚合度为评价参数,采用削减基准负荷数值的方法区分负荷类型。为了排除同一类型的负荷,因为地区规模和用户数目的差异,导致聚类结果不同的,本发明采用削减基准负荷数值的方法,放大负荷曲线的差异,使负荷曲线的梯度变大,从而区分负荷类型。Step 2: Select the reference load reduction value, take the degree of aggregation as the evaluation parameter, and use the method of reducing the reference load value to distinguish the load types. In order to exclude the same type of load, if the clustering results are different due to the difference in the regional scale and the number of users, the present invention adopts the method of reducing the reference load value, amplifies the difference of the load curve, and makes the gradient of the load curve larger, so as to distinguish the load type.
步骤2的具体过程为:The specific process of
2.1,选取削减负荷基准值;2.1, select the reference value for reducing the load;
2.2,数据标准化;2.2, data standardization;
2.3,计算数据梯度;2.3, calculate the data gradient;
2.4,判断聚合度是否满足要求,若满足,则输出区分的负荷类型,若不满足,则重新选取削减负荷基准值,转至2.2。2.4. Determine whether the degree of aggregation meets the requirements. If so, output the differentiated load types. If not, reselect the load reduction reference value and go to 2.2.
步骤3,根据负荷类型区分结果,采用模糊C均值算法对负荷数据进行聚类。本发明借助于L.A.Zadeh(20世纪60年代)提出的模糊集的理论和Ruspini和Bezdek提出的模糊聚类算法,结合用户的用电习惯与用电特征,对负荷曲线进行直接聚类。Step 3: Clustering the load data by using the fuzzy C-means algorithm according to the load type discrimination result. With the help of the fuzzy set theory proposed by L.A. Zadeh (1960s) and the fuzzy clustering algorithm proposed by Ruspini and Bezdek, the present invention performs direct clustering on the load curve in combination with the user's electricity usage habits and electricity usage characteristics.
步骤3进一步包括:
3.1,确定分类个数、幂指数、隶属度矩阵;3.1, determine the number of classifications, power exponent, and membership matrix;
3.2,计算聚类中心度;3.2, calculate the cluster centrality;
3.3,修正隶属度函数和目标函数;3.3, modify the membership function and objective function;
3.4,当隶属度函数满足终止限度或满足最大步长时,停止迭代,否则转至3.2。3.4, when the membership function satisfies the termination limit or satisfies the maximum step size, stop the iteration, otherwise go to 3.2.
经过上步骤以后,可以确定最终的隶属度函数矩阵中的元素和聚类中心,使得目标函数的值达到最小。After the above steps, the elements and cluster centers in the final membership function matrix can be determined, so that the value of the objective function can be minimized.
本发明在开始算法之初,对负荷数据进行预处理,排除地区规模与用户数目对聚类结果的影响,具有重要的现实意义。再针对不同类型用户的特点去进行聚类,效果更加优良。At the beginning of the algorithm, the present invention preprocesses the load data and excludes the influence of the regional scale and the number of users on the clustering result, which has important practical significance. Then clustering is performed according to the characteristics of different types of users, and the effect is better.
实施例Example
本发明数据采用美国PJM电力市场的数据,选取24小时的负荷数据,对其进行算例分析演示。本实施例选取美国PJM电力市场不同地区的负荷数据,为了排除其他因素干扰,选取了113组统一工作日不同地区的负荷数据进行聚类分析。The data of the present invention adopts the data of the PJM power market in the United States, selects the load data of 24 hours, and analyzes and demonstrates the calculation example. In this embodiment, the load data of different regions of the PJM electricity market in the United States is selected. In order to exclude the interference of other factors, 113 groups of load data of different regions on a unified working day are selected for cluster analysis.
(1)本发明首先针对数据进行预处理,剔除偏差过于剧烈的数据,防止极端数值对分类产生干扰。定义偏差率η:(1) The present invention first preprocesses the data, and eliminates the data with too severe deviation, so as to prevent the extreme value from interfering with the classification. Define the deviation rate η:
式中yi表示某一点的负荷数据,表示负荷数据在24h内的平均值。where y i represents the load data at a certain point, Indicates the average value of load data within 24 hours.
当η>500%时,需要查验数据是否为不良数据点,若该负荷曲线绝大多数负荷点均超标,认定为正常测量数据;若仅为个别点超标,判定为不良数据点。When η>500%, it is necessary to check whether the data is a bad data point. If most of the load points in the load curve exceed the standard, it is regarded as normal measurement data; if only a few points exceed the standard, it is judged as a bad data point.
(2)基准负荷削减值得选取。(2) The base load reduction is worth selecting.
为了排除同一类型的负荷,因为地区规模和用户数目的差异,导致聚类结果不同的,本发明采用削减基准负荷数值的方法,放大负荷曲线的差异,使负荷曲线的梯度变大,从而区分负荷类型。In order to exclude the same type of load, if the clustering results are different due to the difference in the regional scale and the number of users, the present invention adopts the method of reducing the reference load value, amplifies the difference of the load curve, and makes the gradient of the load curve larger, so as to distinguish the load type.
(3)模糊算法(3) Fuzzy algorithm
本实施例借助于L.A.Zadeh(20世纪60年代)提出的模糊集的理论和Ruspini和Bezdek 提出的模糊聚类算法,结合用户的用电习惯与用电特征,对负荷曲线进行直接聚类。设样本取自p元样本总体。把样本X1,X2,L Xn总体划为c类,其中c的值不小于2。vi表示第i个聚类中心。设变量uij表示第i个样本对第j个样本的隶属度。In this embodiment, the load curve is directly clustered by means of the fuzzy set theory proposed by LAZadeh (1960s) and the fuzzy clustering algorithm proposed by Ruspini and Bezdek, combined with the user's electricity usage habits and electricity usage characteristics. Suppose the sample is taken from the p-element sample population. The samples X 1 , X 2 , LX n are generally classified as class c, where the value of c is not less than 2. v i represents the i-th cluster center. Let the variable u ij represent the membership degree of the ith sample to the jth sample.
目标函数如下:The objective function is as follows:
约束条件:Restrictions:
uij∈[0,1]1≤j≤n,1≤i≤cu ij ∈[0,1]1≤j≤n,1≤i≤c
根据拉格朗日乘数法计算最优解:Calculate the optimal solution according to the Lagrange multiplier method:
并根据系统给定的约束条件,在MATLAB中进行优化。And according to the constraints given by the system, it is optimized in MATLAB.
进一步地,根据拉格朗日乘数法,可以得到J(u,c)的最优解。隶属度和聚类中心度的迭代公式如下所示:Further, according to the Lagrange multiplier method, the optimal solution of J(u,c) can be obtained. The iterative formulas for membership and cluster centrality are as follows:
Ij={1≤i≤c,dij=0}I j ={1≤i≤c,d ij =0}
当时,when hour,
当时,时,when hour, hour,
模糊算法步骤如下:The fuzzy algorithm steps are as follows:
1)确定分类个数c和幂指数m>1和隶属度矩阵同时处理方式是去除[0,1] 上的随机数作为矩阵初始数据。l=1作为第1步迭代。1) Determine the number of classifications c and the power exponent m>1 and the membership matrix At the same time, the processing method is to remove the random numbers on [0,1] as the initial data of the matrix. l=1 as the first iteration.
2)根据上述公式计算聚类中心度。2) Calculate the cluster centrality according to the above formula.
3)修正隶属度函数U(l)和目标函数J(l)。3) Modify the membership function U (l) and the objective function J (l) .
其中, in,
4)对给定的隶属度函数终止限度εJ>0或定义最大步长l。当满足时或满足最大步长时,停止迭代。否则跳转步骤2)。4) For a given membership function termination limit ε J > 0 or define the maximum step size l. when satisfied The iteration stops when the maximum step size is met. Otherwise, skip to step 2).
经过上步骤以后,可以确定最终的隶属度函数矩阵U中的元素和聚类中心V,使得目标函数的J(U,V)的值达到最小。After the above steps, the elements in the final membership function matrix U and the cluster center V can be determined, so that the value of J(U, V) of the objective function is minimized.
本发明针对当前负荷聚类方法中因为用户规模而错误识别用户类型的问题,提出改进的负荷聚类算法处理技巧,利用模糊算法,验证本发明所提出的算法的精确性。Aiming at the problem of wrong identification of user types due to user scale in the current load clustering method, the invention proposes an improved load clustering algorithm processing skill, and uses a fuzzy algorithm to verify the accuracy of the algorithm proposed by the invention.
对传统的负荷聚类算法与本发明的改进的负荷聚类算法进行比较,如附图所示。图2 (a)-(e)为传统模糊聚类结果示意图。图3(a)-(c )为本发明方法得到的聚类结果示意图。对比传统方法的聚类效果,能够验证得到本发明采用的方法能有效地排除用户规模对用户类型的干扰。The traditional load clustering algorithm is compared with the improved load clustering algorithm of the present invention, as shown in the accompanying drawings. Figure 2 (a)-(e) are schematic diagrams of traditional fuzzy clustering results. 3(a)-(c) are schematic diagrams of clustering results obtained by the method of the present invention. Comparing the clustering effect of the traditional method, it can be verified that the method adopted in the present invention can effectively eliminate the interference of the user scale on the user type.
对于传统方法,根据模糊算法结果可知,负荷大致可以分为5类,类别之间有如下区分:For the traditional method, according to the results of the fuzzy algorithm, the load can be roughly divided into five categories, and the categories are distinguished as follows:
(1)负荷峰谷值出现的时间点不同。第二类和第五类负荷与第四类负荷比较,峰值分别出现在9:00和8:00,存在明显时差。(1) The time points at which the load peak and valley values appear are different. Comparing the second and fifth types of loads with the fourth type of loads, the peaks appear at 9:00 and 8:00, respectively, and there is a significant time difference.
(2)负荷曲线走向不一致。第二类、第四类和第五类负荷出现了双峰,而第一类与第三类在9:00至21:00时一直处于高负荷状态。(2) The direction of the load curve is inconsistent. The second, fourth, and fifth types of loads have double peaks, while the first and third types have been in a high load state from 9:00 to 21:00.
(3)峰谷值数存在值差异。第二类负荷和第四类峰值在4×104MW,谷值略小于 3×104MW。对比第一三五类负荷,峰谷值降低5×103MW左右。(3) There are differences in the number of peaks and valleys. The peak value of the second type of load and the fourth type of load is 4×10 4 MW, and the valley value is slightly less than 3×10 4 MW. Compared with the first, third and fifth types of loads, the peak-to-valley value is reduced by about 5×10 3 MW.
传统方法中,由于算法存在边界不清晰的问题,所以类别之间的交叉现象比较严重。针对电力系统而言,区分点(3)不利于负荷聚类。因为有些地区由于地区规模造成的峰谷值不一致时,不应单独区分开来。In traditional methods, due to the problem of unclear boundaries in the algorithm, the phenomenon of crossover between categories is serious. For the power system, the distinguishing point (3) is not conducive to load clustering. Because some regions have inconsistent peak-to-valley values due to regional scale, they should not be separately distinguished.
而本发明采用负荷削减的方法,拉高了负荷变化梯度,可以解决由于用户规模不同而造成的误识别。其结果如图3(a)-(c )所示。On the other hand, the present invention adopts the method of load reduction, which increases the load change gradient, and can solve the misidentification caused by different user scales. The results are shown in Figures 3(a)-(c).
对比图2与图3,可知当分类结果变为3类以后,曲线的规律性明显加强,聚类依据中按照变化趋势的权重加大,有利于识别用户用电规律。根据图3,可以将负荷明显地分为平稳型负荷、双峰型负荷以及单峰型负荷。为针对不用地区、不用用电习惯的用户更好的制定需求侧响应的策略提供了良好的实验基础。Comparing Fig. 2 and Fig. 3, it can be seen that when the classification result becomes three types, the regularity of the curve is obviously strengthened, and the weight according to the change trend in the clustering basis is increased, which is conducive to identifying the electricity consumption law of users. According to Fig. 3, the load can be clearly divided into the steady load, the bimodal load and the unimodal load. It provides a good experimental basis for better formulating demand-side response strategies for users who do not use regions and electricity habits.
本发明采用轮廓值作为算法的一个指标。The present invention uses the contour value as an index of the algorithm.
具体地,采用轮廓值S(i)进行对比分析,Specifically, the contour value S(i) is used for comparative analysis,
其中a表示第i个点的与同类别点标准化距离;b表示与不同类别点的标准化距离。轮廓值S(i)的取值范围为[-1,1],S(i)越大说明分类越合理。当S(i)<0时,说明该点分类不合理,还有更合理的分类方法。where a represents the normalized distance between the i-th point and points of the same category; b represents the normalized distance from points of different categories. The value range of the contour value S(i) is [-1, 1], and the larger S(i) is, the more reasonable the classification is. When S(i)<0, it means that the classification of this point is unreasonable, and there is a more reasonable classification method.
如附图所示,图4为c=3时聚类中心与轮廓值的关系示意图。图5为c=5时聚类中心与轮廓值的关系示意图。As shown in the accompanying drawings, FIG. 4 is a schematic diagram of the relationship between the cluster center and the contour value when c=3. FIG. 5 is a schematic diagram of the relationship between the cluster center and the contour value when c=5.
根据本发明提出的处理技巧,将负荷值削减一定的基准值之后,负荷之间的变化梯度被拉大,负荷重新划分聚类标准。根据图4可知,当聚类标准划分为5类时,第1类和第 2类中有样本的隶属度出现负值,表明该点样本对聚类中心从属度低,存在更优的聚类方式。根据图5可知,当划分样本为3类时,样本轮廓值均为正且对于绝大部分样本,隶属度较高,是较为合理的分类方式。且该分类方式避免了因为电力负荷数据规模而造成误分类的现象。According to the processing technique proposed by the present invention, after the load value is reduced by a certain reference value, the change gradient between the loads is enlarged, and the load is re-divided into clustering criteria. According to Figure 4, when the clustering standard is divided into 5 categories, the membership degree of the samples in the first and second categories has a negative value, indicating that the sample at this point has a low degree of membership to the cluster center, and there is a better clustering Way. According to Figure 5, when the samples are divided into three categories, the contour values of the samples are all positive, and for most of the samples, the degree of membership is high, which is a more reasonable classification method. And this classification method avoids the phenomenon of misclassification caused by the scale of power load data.
对比传统方法的聚类效果可见,在分类数目从5类减少至3类时,从图4、图5对比发现,本发明算法的分类结果更加精确。Comparing the clustering effect of the traditional method, it can be seen that when the number of classifications is reduced from 5 to 3, it is found from the comparison of Fig. 4 and Fig. 5 that the classification result of the algorithm of the present invention is more accurate.
尽管已经示出和描述了本发明的实施例,对于本领域的普通技术人员而言,可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型,本发明的范围由所附权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.
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