CN113947444A - Electricity selling package recommending method considering multi-granularity hesitation fuzzy set and incomplete weight - Google Patents

Electricity selling package recommending method considering multi-granularity hesitation fuzzy set and incomplete weight Download PDF

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CN113947444A
CN113947444A CN202111359084.4A CN202111359084A CN113947444A CN 113947444 A CN113947444 A CN 113947444A CN 202111359084 A CN202111359084 A CN 202111359084A CN 113947444 A CN113947444 A CN 113947444A
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马愿谦
李启源
陈汉忠
尹宇晨
刘宇杭
马晓龙
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Zhejiang Sci Tech University ZSTU
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Abstract

The invention discloses an electricity selling package recommending method considering multi-granularity hesitation fuzzy set and incomplete weight, which comprises the steps of establishing a user load information database based on a user electricity utilization characteristic index, and clustering users based on an improved K-means clustering algorithm to determine the category of a target user; considering incomplete weight information and a multi-granularity hesitation fuzzy language evaluation set provided by a user, and constructing an evaluation matrix of the user on the electric power selling package; respectively calculating the satisfaction degrees of the historical user and the target user to the electricity selling package; and obtaining the full-sequencing electricity selling package recommendation and the Top-M electricity selling package recommendation based on the user satisfaction quantification result. The method adopts the multi-granularity hesitation fuzzy language evaluation set to represent the evaluation information of the user, considers the incompleteness of the attribute weight information provided by the user for selling the electric package, not only can reflect the hesitation fuzziness of the user when evaluating the electric package, but also can enable the user to provide the evaluation information more flexibly, and more truly reflect the satisfaction degree of the user.

Description

Electricity selling package recommending method considering multi-granularity hesitation fuzzy set and incomplete weight
Technical Field
The invention relates to the technical field of power information, in particular to an electric sales package recommendation method considering multi-granularity hesitation fuzzy set and incomplete weight.
Background
On 15 days 3 and 15 months 2015, the public center and the state department issue a plurality of opinions about further advanced power system reform, which marks that the power selling side is opened, and the single buying-single selling vertical integrated control mode of the traditional power market is converted into a multi-buying-multi-selling customized and marketized mode; in 2019, in 6 months, the national development and reform committee issues 'notice on fully releasing the power generation and utilization plan of the operational power users', the user coverage range of the retail market is further expanded, and the user develops from the original passive power supply receiving mode to the mode of automatically selecting power selling companies. Meanwhile, with the implementation of the concept of high-quality development, for power consumers, the power consumers are required to obtain diversified and convenient value-added services as well as reliability and safety of power supply; for the electricity selling companies, it is also expected to enhance the viscosity of existing users and attract a large number of new users through value-added services such as electricity selling packages, comprehensive energy services, energy-saving services, and the like. The electricity selling package is a necessary means for an electricity selling company to improve the income and obtain market competitiveness as service and operation mode innovation in a competitive electricity selling market environment. The foreign electric power markets of Germany, America, UK and the like provide thousands of electricity selling packages for users, and China also designs various forms of electricity price packages for the users to decide, such as: the method is characterized in that a power package which considers the peak clipping and valley filling effects of user behavior changes and influences on the power package is designed for industrial and commercial users; based on the user reference price decision and the user viscosity, the electricity selling package is optimally designed; and (4) respectively designing customized time-of-use electricity price packages and peak-valley combined power packages by considering the limited selection behaviors of users. However, in the face of a lot of electricity selling packages in the electricity selling market, how to accurately and scientifically recommend electricity packages meeting the needs of users to the users is a key point for improving the satisfaction of the users and increasing the market share of the users. In addition, in the conventional documents [1] and [2], a customized time-of-use electricity price package and a peak-valley combined power package are also designed in consideration of the limited selection behavior of the user.
The existing domestic and foreign recommendations for the electricity sales packages can be roughly divided into a direct recommendation method and an indirect recommendation method. Most of direct recommending methods for electricity selling packages are applied to an online recommending platform, and the basic idea is to compare the cost of each electricity selling package based on the electricity utilization condition of a user and recommend the electricity selling package with the lowest cost to the corresponding user, for example: platform iSelect, Power to Choose, Energy Made Easy, Check24, etc. The online recommendation method is simple and easy to implement, but the electricity selling package recommendation method only based on the cost of the electricity charge of the user ignores the diversity of user evaluation information, such as: green electricity, loyalty. Besides the direct cost-based recommendation method, the hierarchical clustering is carried out on the users based on the electricity utilization diversity characteristic quantity of the users, and stepped electricity price packages and stepped time-of-use electricity price packages are recommended for users with changeable electricity utilization behaviors and users with regular electricity utilization behaviors respectively. Although the recommendation method considers the electricity consumption behavior characteristics and the preference of the user, the hesitation fuzzy characteristics shown when the user evaluates the electricity selling package and the heterogeneity of evaluation information caused by the difference of knowledge and culture background of different users are still ignored, and a large error is brought to the accurate recommendation of the electricity selling package. In addition, considering that the user has limited knowledge of the property of the electricity selling package, the provided weight information has incomplete conditions, such as: the problem that how to process the diversified attribute weight language information and convert the incomplete weight information provided by the user into the determined attribute weight information is necessary to be solved by an electric power selling company for accurately recommending the electric power selling package for the user is that the attribute weight information possibly provided by the user is 'the attribute A is more important than the attribute B' or 'the attribute A is more important than the attribute B by 2 times'.
[1] Xiaobai, Zuianqi, Jianzhuo, etc. customized electricity price package design based on limited user selection behavior [ J ] power grid technology, 2021,45(3): 1050-.
Xiao Bai,Cui Hanqi,Jiang Zhuo,et al.Customized electricity price package design based on limited rational user selection behavior[J].Power System Technology,2021,45(3):1050-1058.
[2] Zhang Zhi, Lufeng, forest Intelligence, etc. consider the peak-valley combined power package design of the power selling company with limited user [ J ] power system automation, 2021,45(16): 114-.
Zhang Zhi,Lu Feng,Lin Zhenzhi,et al.Peak-valley combination electricity package design for electricity retailer considering bounded rationality of consumers[J].Automation of Electric Power Systems,2021,45(16):114-123.
Disclosure of Invention
The technical problem to be solved by the invention is to provide the method for recommending the electricity selling package considering the multi-granularity hesitation fuzzy set and the incomplete weight, so as to provide the recommendation of the electricity selling package for the user based on the user satisfaction quantization result.
In order to solve the technical problem, the invention provides an electricity selling package recommending method considering multi-granularity hesitation fuzzy set and incomplete weight, which comprises the following specific processes:
s1, establishing a user load information database based on the user electricity utilization characteristic indexes, clustering the users based on an improved K-means clustering algorithm, and determining the category of the target user;
step S2, considering the incomplete weight information and the multi-granularity hesitation fuzzy language evaluation set provided by the user, and constructing an evaluation matrix of the user for the electric sales package;
step S3, calculating the satisfaction of the historical user and the target user to the electric power selling package;
and step S4, obtaining the complete-sequence electricity selling package recommendation and the Top-M electricity selling package recommendation based on the user satisfaction quantification result.
The invention is an improvement of the method for recommending the electricity selling package considering the multi-granularity hesitation fuzzy set and the incomplete weight:
the specific process of step S1 is as follows:
step S1.1, building user load information database
Based on user A ═ { A1,A2,…,Ai,…,AIThe daily load data for a month is:
Figure BDA0003358361720000021
wherein the content of the first and second substances,
Figure BDA0003358361720000022
k is the total hours of a month; based on the monthly load rate
Figure BDA0003358361720000023
Number of hours of maximum utilization
Figure BDA0003358361720000024
Mean value of peak-to-valley rate of working day
Figure BDA0003358361720000025
Mean peak-to-valley rate of off-day
Figure BDA0003358361720000026
Peak load mean
Figure BDA0003358361720000027
Mean average of load rate in flat phase
Figure BDA0003358361720000028
Mean value of load rate at valley period
Figure BDA0003358361720000029
Obtain user AiLoad characteristic index vector of
Figure BDA00033583617200000210
And a user load information database corresponding to the user and the load characteristic index vector thereof is established;
(1) the monthly load rate:
Figure BDA00033583617200000211
wherein the content of the first and second substances,
Figure BDA00033583617200000212
and
Figure BDA00033583617200000213
are respectively user AiThe average load per month and the maximum load,
Figure BDA00033583617200000214
for user AiDaily load data for the kth hour of the total hours of a month;
(2) number of hours of maximum utilization
Figure BDA00033583617200000215
Wherein the content of the first and second substances,
Figure BDA00033583617200000216
for user AiElectricity consumption in whole month;
(3) mean value of peak-to-valley rate of working day
Figure BDA00033583617200000217
Wherein, KWIs the total number of days of the working day,
Figure BDA00033583617200000218
the day maximum load on day i of the working day,
Figure BDA00033583617200000219
the day minimum load for day i of the non-workday;
(4) mean peak-to-valley rate of off-day
Figure BDA0003358361720000031
Wherein, KNWIs the total number of days on the non-working day,
Figure BDA0003358361720000032
the day maximum load on day j of the non-workday,
Figure BDA0003358361720000033
the daily minimum load on day j of the non-workday;
(5) peak load mean
Figure BDA0003358361720000034
Wherein peak periods are defined as 08:00-11:00 and 18:00-21:00, T is the total number of days, and T is KW+KNW，
Figure BDA0003358361720000035
For user A in the peak period of the t dayiThe average value of the loads of (a),
Figure BDA0003358361720000036
is the user A on the t dayiThe load mean value of (1);
(6) mean average of load rate in flat phase
Figure BDA0003358361720000037
Wherein, the ordinary period is defined as 06:00-08:00, 11:00-18:00 and 21:00-22:00,
Figure BDA0003358361720000038
for the tth balance period user AiThe load mean value of (1);
(7) mean load factor at off-peak
Figure BDA0003358361720000039
Wherein the valley time periods are defined as 22:00-24:00 and 00:00-06:00,
Figure BDA00033583617200000310
for the user A in the trough period of the t dayiThe load mean value of (1);
step S1.2, clustering based on historical user load information database
Based on the user load information database established in the step S1.1, clustering historical users by adopting an improved K-means clustering algorithm, and specifically comprising the following steps:
step S1.2.1, making the clustering number C equal to 2, randomly selecting C users, and marking as C1,C2,…,Cj,…,CcUsing the load characteristic index vector as the clustering center
Figure BDA00033583617200000311
Step S1.2.2, calculate user A separatelyi(I-1, 2, …, I) and each cluster center
Figure BDA00033583617200000312
European distance of
Figure BDA00033583617200000313
Step S1.2.3 for user AiAre compared and obtained
Figure BDA00033583617200000314
And will be user AiClassified as j, and the number of users belonging to the j is set as IjThe corresponding user is represented as
Figure BDA0003358361720000041
Step S1.2.4, calculating the square error J based on the classification result of step S1.2.3 as equation (8)c(t):
Figure BDA0003358361720000042
Wherein, t is the iteration number,
Figure BDA0003358361720000043
is corresponding to Ai,jClass j user AiA load characteristic index vector of (a);
step S1.2.5, recalculating the cluster centers
Calculating the average distance D between the load characteristic index vectors of all users in each class and the clustering center, selecting the users with the distance to the clustering center being less than 2D in the class, and then recalculating the mean value of the load characteristic indexes of the selected users as a new clustering center;
step S1.2.6, determine whether formula (9) is satisfied:
Jc(t+1)-Jc(t)≥0 (9)
if not, t is t +1, and then the step S1.2.1 is returned to continue the iteration;
if the formula (9) is satisfied, the iteration is ended, and the clustering quality index I is calculated based on the clustering result of the t iterationqc.av：
Figure BDA0003358361720000044
Wherein, Iqc(i) When the number of clusters is c, the closeness degree of the ith user to the cluster center of the class to which the ith user belongs is represented as follows:
Figure BDA0003358361720000045
wherein the content of the first and second substances,
Figure BDA0003358361720000046
represents the average distance between classes as user AiAverage value of the distance between the user load characteristic index phasor and other user load characteristic indexes except the category to which the user belongs;
Figure BDA0003358361720000047
representing the average distance within a class, as user AiAverage of the phasor distances from the other user load characteristic indexes in the category to which the user belongs;
step S1.2.7, making the cluster number c ═ c +1, returning and executing step s 1.2.1-step S1.2.6 until the cluster number reaches the maximum value
Figure BDA0003358361720000048
Step S1.2.8, comparing the clustering quality index I under different clustering numbersqc.av，Iqc.avThe corresponding cluster number at the maximum is the optimal cluster number c;
step S1.3, calculating the similarity between the target user and the historical user based on Pearson correlation coefficient
The target user is a user needing to recommend the electricity selling package and is represented as W ═ W1,W2,…,Wn,…,WMAnd obtaining load characteristic index vectors of each target user based on daily load data of each user in a certain month by combining the formula (1) with the formula (7)
Figure BDA0003358361720000049
Calculating the center of each cluster under the optimal cluster number c
Figure BDA00033583617200000410
The class corresponding to the minimum distance is the target user WnThe category to which it belongs;
set target user WnBelonging to the p-th class of historical users, wherein the number of the class of users is NpIs shown as
Figure BDA00033583617200000411
The similarity between the target user and the historical user is described by using the Pearson correlation coefficient:
Figure BDA0003358361720000051
wherein the content of the first and second substances,
Figure BDA0003358361720000052
represents a target user WnAnd historical users
Figure BDA0003358361720000053
The similarity of (2);
Figure BDA0003358361720000054
and
Figure BDA0003358361720000055
respectively represent users WnAnd historical users
Figure BDA0003358361720000056
The d-th load characteristic index of (1),
Figure BDA0003358361720000057
and
Figure BDA0003358361720000058
respectively represent users WnAnd historical users
Figure BDA0003358361720000059
Average value of load characteristic index.
The invention is further improved by taking the multi-granularity hesitation fuzzy set and incomplete weight into consideration as a recommendation method of the power selling package:
the specific process of the step 2 is as follows:
step S2.1, building an evaluation matrix of the user for the electricity sales package based on the hesitation fuzzy language set
The set of electricity selling set is T ═ T1,T2,…Tj,…,TJUser a ═ a }1,A2,…,Ai,…,AIThe evaluation attribute set for the electricity sales package is
Figure BDA00033583617200000510
Describing the evaluation information of the user on the electricity selling package by adopting hesitation fuzzy language:
let user AiLanguage ofSaid evaluation set is
Figure BDA00033583617200000511
Wherein g (A)i) Represents the granularity of the language evaluation set and is odd,
Figure BDA00033583617200000512
represents the evaluation amount of the p-th language, p is 0,1, …, g (A)i) -1 symbolic corner marks for language evaluation quantities; language evaluation set
Figure BDA00033583617200000513
The elements are arranged in sequence:
if p is>q, then:
Figure BDA00033583617200000514
user AiSelf-language-based evaluation set
Figure BDA00033583617200000515
And evaluating the electricity selling package, wherein an evaluation matrix is as follows:
Figure BDA00033583617200000516
wherein the content of the first and second substances,
Figure BDA00033583617200000517
represents user AiPair electric sales package TjProperty (2) of
Figure BDA00033583617200000518
Given the hesitation fuzzy language evaluation information, J and K are respectively the J-th package and the K-th attribute;
step S2.2, determining the attribute weight of the electricity selling package considering the incomplete weight
Determining each attribute weight by using dispersion maximization method
Figure BDA00033583617200000519
Figure BDA0003358361720000061
Wherein "other" represents user AiThe incomplete weight information is provided in the form of,
Figure BDA0003358361720000062
representation for the kth attribute
Figure BDA0003358361720000063
User A ofiThe degree of deviation between language evaluations given to each electricity sales package:
Figure BDA0003358361720000064
wherein the content of the first and second substances,
Figure BDA0003358361720000065
p＝0,1,…,g(Ai)-1，
Figure BDA0003358361720000066
for user AiEvaluating the kth attribute in the qth package;
integrating the evaluation information of each user by adopting an Hesitation Fuzzy Language Weighted Average Operator (HFLWAO) to obtain the evaluation matrix of each user on the electric sales package
Figure BDA0003358361720000067
Figure BDA0003358361720000068
Wherein the content of the first and second substances,
Figure BDA0003358361720000069
represents user AiPair electric sales package TjThe evaluation results of (1);
the HFLWAO is calculated as follows:
(1) based on electricity selling set meal TjThe K attributes of (a) are set as follows:
Figure BDA00033583617200000610
akthe evaluation result of the kth attribute;
(2) respectively make
Figure BDA00033583617200000611
The following iterations are performed:
Figure BDA0003358361720000071
wherein trunc (·) is an integer function; delta (-) represents a mapping between symbolic logo of language evaluation quantity and hesitation fuzzy language set, mhAs a result of the evaluation of the package by the user,
Figure BDA0003358361720000072
in order to evaluate the degree of progress,
Figure BDA0003358361720000073
to evaluate the degree of membership;
let beta be [0, g (A) ]i)-1]The equivalent information of beta is described by a binary group:
Figure BDA0003358361720000074
presence of a transformation function Δ-1(. h), converting the binary equivalent information into equivalent values:
Figure BDA0003358361720000075
(3) obtaining by calculation of a distributed language evaluation operator DAA
Figure BDA0003358361720000076
Figure BDA0003358361720000077
Wherein the content of the first and second substances,
Figure BDA0003358361720000081
for a two-tuple of language evaluation,
Figure BDA0003358361720000082
ratio representing linguistic evaluation variables:
Figure BDA0003358361720000083
step S2.3, unification of multi-granularity hesitation fuzzy language evaluation information of the user on the electric power selling package
Converting language evaluation sets under different granularities used by a user for evaluating the power selling package into language evaluation sets under the same granularity, and determining the granularity as g (A)i) Evaluation set
Figure BDA0003358361720000084
Evaluation information of (2)
Figure BDA0003358361720000085
Conversion to g (A) on the basis of particle sizef) Evaluation set
Figure BDA0003358361720000086
Evaluation information of (2)
Figure BDA0003358361720000087
The process is as follows:
step S2.3.1, let g (×) -LCM (g (a)i)-1,g(Af) -1) +1, where LCM (·) represents the minimum common multiple;
step S2.3.2, creating a set of virtual languages
Figure BDA0003358361720000088
Let thetae＝0，e＝0,1,…,g(*)-1；
Step S2.3.3, if
Figure BDA00033583617200000815
zh＝0,1,…,g(Ai) -1, calculating
Figure BDA0003358361720000089
Obtaining:
Figure BDA00033583617200000810
step S2.3.4, order
Figure BDA00033583617200000811
z h0,1, …, g (×) -1, if
Figure BDA00033583617200000812
Computing
Figure BDA00033583617200000813
Step S2.3.5 based on
Figure BDA00033583617200000814
Calculating the normalized language evaluation variable ratio, as shown in formula (22):
Figure BDA0003358361720000091
step S2.3.6, obtaining the unified language evaluation information based on the formula (22)
Figure BDA0003358361720000092
Based on the steps S2.3.1-S2.3.6, an evaluation matrix of the user for the electricity sales package under uniform granularity is obtained
Figure BDA0003358361720000093
Wherein the content of the first and second substances,
Figure BDA00033583617200000912
representing user A at a uniform granularityiPair electric sales package TjEvaluation information of (2):
Figure BDA0003358361720000094
Figure BDA0003358361720000095
is at AfThe language evaluation at the granularity of the language,
Figure BDA0003358361720000096
in order to evaluate the degree of membership newly,
Figure BDA0003358361720000097
the evaluation degree is new.
The invention is further improved by taking the multi-granularity hesitation fuzzy set and incomplete weight into consideration as a recommendation method of the power selling package:
the specific process of the step 3 is as follows:
user A at uniform granularity based on formula (23)iPair electric sales package TjEvaluation information of (2)
Figure BDA0003358361720000098
The expectation of the evaluation information of the user is obtained, and the satisfaction matrix of the user to the electric sales package is obtained
Figure BDA0003358361720000099
Wherein the content of the first and second substances,
Figure BDA00033583617200000910
for user AiPair electric sales package TjSatisfaction of (2):
Figure BDA00033583617200000911
target user WnPair electric sales package TjSatisfaction degree SCnjComprises the following steps:
Figure BDA0003358361720000101
the invention is further improved by taking the multi-granularity hesitation fuzzy set and incomplete weight into consideration as a recommendation method of the power selling package:
the full-sequencing electricity selling package recommendation specifically comprises the following steps:
calculating a root mean square error epsilon based on satisfaction results of the target users for each electricity selling package1nThen according to the root mean square error epsilon1nRecommending to the target user according to the order of the electricity selling packages corresponding from small to large for the target user to decide:
Figure BDA0003358361720000102
wherein J is the total number of the electricity sales packages and OnjAnd
Figure BDA0003358361720000103
respectively represent for the target user WnAnd sell electric set meal TjThe actual sorting result of (a) and the sorting result obtained by the algorithm of the formula (25);
the Top-M electricity selling package recommendation specifically comprises the following steps:
based on the satisfaction result of the target user for each electricity selling package, the electricity selling company only recommends the packages ranked in the top M to the target user, and does not provide the ranking result;
recommend to target user WnThe first M sets of electricity sales packages
Figure BDA0003358361720000104
Set of packages with actual ranking as top M
Figure BDA0003358361720000105
Accuracy of recommendation e2nComprises the following steps:
Figure BDA0003358361720000106
Figure BDA0003358361720000107
is a target user WnThe set of packages actually ranked top M,
Figure BDA0003358361720000108
obtaining a target user W for an algorithmnThe packages with the top M are ranked, and M is the total number of recommended packages.
The invention has the following beneficial effects:
1. the invention provides an electricity selling package recommending method considering multi-granularity hesitation fuzzy sets and incomplete weights, and clusters users by utilizing an improved K-means clustering algorithm, so that the influence of noise points can be effectively reduced, and the clustering result can more effectively reflect the load characteristics of various users;
2. the invention provides an electric sales package recommendation method considering a multi-granularity hesitation fuzzy set and an incomplete weight, which adopts a multi-granularity hesitation fuzzy language evaluation set to represent evaluation information of a user, and considers the incompleteness of attribute weight information of an electric sales package provided by the user, so that the hesitation fuzzy performance of the user in the electric sales package evaluation can be reflected, users with different culture backgrounds can more flexibly and elastically provide evaluation information, the satisfaction degree of the user on the electric sales package can be more truly reflected, and a new thought is provided for an electric sales company to recommend the electric sales package;
3. the invention provides the electricity selling package recommending method considering the multi-granularity hesitation fuzzy set and the incomplete weight, which can ensure higher recommending accuracy and better recommending performance.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of a process for building and clustering a user load information database according to the present invention;
FIG. 2 is a schematic diagram of an electricity selling package recommending process considering multi-granularity hesitation fuzzy sets and incomplete weight information according to the present invention;
FIG. 3 is a histogram showing the average daily load frequency distribution of each user in the park of experiment 1;
FIG. 4 is a schematic diagram of the average daily load rate, average daily peak-to-valley rate and language evaluation set granularity of each user in the campus of experiment 1;
FIG. 5 is a schematic diagram of cluster quality index values corresponding to different cluster numbers in experiment 1;
fig. 6 is a schematic diagram of the clustering results of the various types of users and the number of the various types of users in experiment 1;
FIG. 7 is a graph illustrating the satisfaction of the late-peak historical user with selling an electricity package in experiment 1;
FIG. 8 is a graph showing the similarity between the target user and the late peak type historical user in experiment 1;
fig. 9 is a schematic diagram of a result of quantifying satisfaction of the target user W1 for each electricity sales package in experiment 1;
FIG. 10 is a schematic diagram of the clustering centers obtained by the improved K-means clustering algorithm and the original K-means clustering algorithm in experiment 1;
FIG. 11 is a diagram of the optimal cluster number and cluster quality index for different noise ratios in experiment 1;
fig. 12 is a schematic diagram of the evaluation result of the satisfaction of various target users with the electricity sales package in experiment 1;
fig. 13 is a schematic diagram showing comparison of recommended ordering results of the electricity sales packages obtained by different methods in experiment 1.
Detailed Description
The invention will be further described with reference to specific examples, but the scope of the invention is not limited thereto:
embodiment 1, consider a multi-granularity hesitation fuzzy set and incomplete weight electricity-selling package recommendation method, as shown in fig. 1-2, first, based on a user electricity characteristic index, establish a user load information database, and based on an improved K-means clustering algorithm, cluster users, determine a category to which a target user belongs; then, considering incomplete weight information and a multi-granularity hesitation fuzzy language evaluation set provided by the user, and constructing an evaluation matrix of the user on the electric sales package; then, the satisfaction degrees of the historical user and the target user for selling the electric package are calculated respectively; and finally, based on the user satisfaction quantification result, a full-sequencing recommendation method and a Top-M recommendation method are provided.
1. User load information database building and clustering
1.1 building user load information database
The power utilization characteristics of different types of users have difference, the difference is reflected in the difference of user load characteristic indexes, and the power utilization characteristics are based on that a is equal to { A } A1,A2,…,Ai,…,AIDaily load data of a month
Figure BDA0003358361720000111
Wherein the content of the first and second substances,
Figure BDA0003358361720000112
k is the total hours of a certain month, and the electricity utilization characteristics of each user are described by taking the monthly load rate, the maximum utilization hours, the peak-to-valley difference rate mean value of working days and non-working days and the peak-to-valley period load rate mean value as characteristic indexes. With user AiFor example, the physical meanings and definitions of the characteristic indexes are as follows.
(1) Rate of load of the moon
The monthly load rate is used for reflecting the load change fluctuation condition of the user in the whole month, is the ratio of the average load of the month to the maximum load, and the calculation formula is shown as a formula (1).
Figure BDA0003358361720000113
Wherein the content of the first and second substances,
Figure BDA0003358361720000114
and
Figure BDA0003358361720000115
are respectively user AiThe average load per month and the maximum load,
Figure BDA0003358361720000116
for user AiDaily load data for the kth hour of the total hours of a month;
rate of load of the moon
Figure BDA0003358361720000117
The larger, user AiThe greater the load fluctuations over the month.
(2) Number of hours of maximum utilization
The maximum utilization hours are used for reflecting the time utilization efficiency of the user load, and the calculation formula is shown in formula (2) as the ratio of the total monthly electricity consumption to the maximum monthly load:
Figure BDA0003358361720000121
wherein the content of the first and second substances,
Figure BDA0003358361720000122
for user AiElectricity consumption in whole month, maximum utilization hours
Figure BDA0003358361720000123
The larger; user AiThe more efficient the utilization of the load time of the whole month.
(3) Mean value of peak-to-valley rate of working day
The working day peak-valley difference rate mean value is used for reflecting the stability of the power utilization of the user in working days, is the mean value of the ratio of the difference value between the maximum load and the minimum load in working days and the ratio of the maximum load in working days, and the calculation formula is shown as a formula (3).
Figure BDA0003358361720000124
Wherein, KWIs the total number of days of the working day,
Figure BDA0003358361720000125
the day maximum load on day i of the working day,
Figure BDA0003358361720000126
the day minimum load for day i of the non-workday;
mean value of peak-to-valley rate of working day
Figure BDA0003358361720000127
The larger the user's workload fluctuates.
(4) Mean peak-to-valley rate of off-day
The non-working day peak-valley difference rate mean value is used for reflecting the stability of the non-working day power utilization of the user, is the mean value of the ratio of the maximum load and the minimum load of the non-working day to the maximum load of the non-working day, and has a calculation formula shown in a formula (4):
Figure BDA0003358361720000128
wherein, KNWIs the total number of days on the non-working day,
Figure BDA0003358361720000129
the day maximum load on day j of the non-workday,
Figure BDA00033583617200001210
the daily minimum load on day j of the non-workday;
mean peak-to-valley rate of off-day
Figure BDA00033583617200001211
The larger, user AiThe greater the non-workday load fluctuations.
(5) Peak load mean
The peak period load rate mean value is used for reflecting the variation fluctuation condition of the load of the user in the peak period, the peak period is defined as 08:00-11:00 and 18:00-21:00, and is the mean value of the ratio of the peak period load mean value to the current day load mean value, and the calculation formula is shown as the formula (5):
Figure BDA00033583617200001212
wherein T is the total number of days, and satisfies that T is KW+KNW，
Figure BDA00033583617200001213
For user A in the peak period of the t dayiThe average value of the loads of (a),
Figure BDA00033583617200001214
is the user A on the t dayiThe load mean value of (1);
peak load mean
Figure BDA00033583617200001215
The larger, user AiThe more pronounced the fluctuation of the load during the peak period.
(6) Mean average of load rate in flat phase
The average value of the average period load rate is used for reflecting the variation fluctuation condition of the load of the user in the average period, the average period is defined as 06:00-08:00, 11:00-18:00 and 21:00-22:00, and is the average value of the ratio of the average value of the load of the average period to the average value of the load of the current day, and the calculation formula is shown as the formula (6):
Figure BDA0003358361720000131
wherein the content of the first and second substances,
Figure BDA0003358361720000132
for the tth balance period user AiThe load mean value of (1);
mean average of load rate in flat phase
Figure BDA0003358361720000133
The larger, user AiThe more pronounced the fluctuation of the load during the flat period.
(7) Mean load factor at off-peak
The mean value of the valley period load rate is used for reflecting the variation fluctuation condition of the load of the user in the valley period, the valley period is defined as 22:00-24:00 and 00:00-06:00, and is the mean value of the ratio of the mean value of the load of the valley period to the mean value of the load of the current day, and the calculation formula is shown as the formula (7):
Figure BDA0003358361720000134
wherein the content of the first and second substances,
Figure BDA0003358361720000135
for the user A in the trough period of the t dayiLoad average of (2). Mean load factor at off-peak
Figure BDA0003358361720000136
The larger, user AiThe more pronounced the fluctuation of the load during the valley period.
Based on the user load characteristic index, the user A can be obtainediLoad characteristic index vector of
Figure BDA0003358361720000137
And a user load information database corresponding to the user and the load characteristic index vector thereof is established, so that support is provided for historical user clustering and calculation of similarity between the target user and the historical user.
1.2 clustering based on historical user load information database
Considering that the number of existing historical users is large, in order to reduce the calculation amount, users with similar load characteristics need to be clustered. Based on the built user load information database, clustering historical users by adopting an improved K-means clustering algorithm, and specifically comprising the following steps:
1) making the clustering number C equal to 2, randomly selecting C users, and marking as C1,C2,…,Cj,…,CcUsing the load characteristic index vector as the clustering center
Figure BDA0003358361720000138
2) Calculate user A separatelyi(I-1, 2, …, I) and each cluster center
Figure BDA0003358361720000139
European distance of
Figure BDA00033583617200001310
3) For AiAre compared and obtained
Figure BDA00033583617200001311
And will be user AiClassified as j, and the number of users belonging to the j is set as IjThe corresponding user is represented as
Figure BDA00033583617200001312
4) Calculating a square error J based on the classification result of the step 3)c(t) as shown in formula (8), wherein t is the number of iterations;
Figure BDA00033583617200001313
wherein the content of the first and second substances,
Figure BDA00033583617200001314
is corresponding to Ai,jClass j user AiLoad characteristic index vector of
5) Recalculating cluster centers
The original K-means clustering algorithm directly takes the mean value of each class as a new clustering center, and needs to be improved in order to reduce the influence of noise points. Firstly, calculating the average distance D between all user load characteristic index vectors and a cluster center in each class; then, selecting users in the category, wherein the distance between the users and the cluster center is less than 2D; and finally, recalculating the mean value of the load characteristic indexes of the selected users as a new clustering center. The operation can eliminate the influence of noise points, so that the clustering center can better reflect the characteristic of normal user load;
6) judging whether formula (9) is satisfied:
Jc(t+1)-Jc(t)≥0 (9)
if not, t is t +1, and then the step 1) is returned to continue the iteration;
if the formula (9) is satisfied, the iteration is ended, and the clustering quality index I is calculated based on the clustering result of the t iterationqc.avAs shown in formula (10);
Figure BDA0003358361720000141
wherein, Iqc(i) When the number of clusters is c, the closeness degree of the ith user to the cluster center of the class to which the ith user belongs depends on the intra-class distance and the inter-class distance, as shown in formula (11).
Figure BDA0003358361720000142
Wherein the content of the first and second substances,
Figure BDA0003358361720000143
represents the average distance between classes as user AiAverage value of the distance between the user load characteristic index phasor and other user load characteristic indexes except the category to which the user belongs;
Figure BDA0003358361720000144
representing the average distance within a class, as user AiAverage of the phasor distances from other user load characteristic indicators within the category to which they belong. Therefore, the larger the average distance between classes is, the smaller the average distance in the classes is, and the better the clustering quality is;
7) making the clustering number c equal to c +1, returning to the step 1), executing the steps 1) to 6) until the clustering number reaches the maximum value
Figure BDA0003358361720000145
8) Comparing clustering quality index I under different clustering numbersqc.av，Iqc.avMaximum time pairThe number of clusters is the optimal number of clusters c.
1.3 Pearson correlation coefficient-based calculation of similarity between target user and historical user
The target user is a user needing to recommend the electricity selling package and is represented as W ═ W1,W2,…,Wn,…,WMAnd (6) based on daily load data of each user in a certain month, combining the formula (1) and the formula (7), obtaining load characteristic index vectors of each target user
Figure BDA0003358361720000146
Calculating the center of each cluster under the optimal cluster number c
Figure BDA0003358361720000147
The class corresponding to the minimum distance is the target user WnThe category to which it belongs.
Set target user WnBelonging to the p-th class of historical users, wherein the number of the class of users is NpIs shown as
Figure BDA0003358361720000148
Considering that the Pearson correlation coefficient can effectively measure the correlation and the closeness degree between the load characteristics of each user, the similarity between the target user and the historical user is described by using the coefficient, as shown in formula (12).
Figure BDA0003358361720000149
Wherein the content of the first and second substances,
Figure BDA00033583617200001410
represents a target user WnAnd historical users
Figure BDA00033583617200001411
The greater the similarity, the more similar the load characteristics of the two users are, and the more likely it is to select the same electricity sales package.
Figure BDA0003358361720000151
And
Figure BDA0003358361720000152
respectively represent users WnAnd historical users
Figure BDA0003358361720000153
The d-th load characteristic index of (1),
Figure BDA0003358361720000154
and
Figure BDA0003358361720000155
respectively represent users WnAnd historical users
Figure BDA0003358361720000156
Average value of load characteristic index.
2 evaluation of selling electric combo by user considering multi-granularity hesitation fuzzy set and incomplete weight
2.1 construction of evaluation matrix of user for selling electric package based on hesitation fuzzy language set
Setting the set of electricity selling packages as T ═ T1,T2,…Tj,…,TJUser a ═ a }1,A2,…,Ai,…,AIThe evaluation attribute set for the electricity sales package is
Figure BDA0003358361720000157
Considering that quantitative information is difficult to give when a user evaluates the property of the electric power selling package and certain hesitation ambiguity is shown, a hesitation ambiguity language is adopted to describe the evaluation information of the user on the electric power selling package.
Let user AiIs a language evaluation set of
Figure BDA0003358361720000158
Wherein g (A)i) Represents the granularity of the language evaluation set and is odd,
Figure BDA0003358361720000159
represents the evaluation amount of the p-th language, p is 0,1, …, g (A)i) -1 symbolic corner mark for language evaluation quantity. Language evaluation set
Figure BDA00033583617200001510
The elements are arranged in sequence, namely: if p is>q, then:
Figure BDA00033583617200001511
user AiSelf-language-based evaluation set
Figure BDA00033583617200001512
The electricity sales package is evaluated according to the evaluation matrix of
Figure BDA00033583617200001513
Wherein the content of the first and second substances,
Figure BDA00033583617200001514
represents user AiPair electric sales package TjProperty (2) of
Figure BDA00033583617200001515
And giving hesitation fuzzy language evaluation information. It is to be noted that it is preferable that,
Figure BDA00033583617200001516
may comprise a plurality of
Figure BDA00033583617200001517
The language evaluation amount in (1), J and K are respectively the J-th package and the K-th attribute.
2.2 Electricity sales package Attribute weight determination with consideration of incomplete weight
The electricity selling package attribute weight reflects the importance degree of the attribute in the electricity selling package evaluation. Given that the user has limited knowledge of the importance of the properties of the electricity sales package, and that the weight information that may be provided is incomplete, such as: user AiThe weight information provided is: attribute 1 is more important than Attribute 2
Figure BDA00033583617200001518
Attribute 1 weight not exceeding
Figure BDA00033583617200001519
The difference between the importance of the attribute 3 and the importance of the attribute 4 is not less than
Figure BDA00033583617200001520
The information is called incomplete weight information, and in order to ensure that the obtained weights can comprehensively reflect the importance degree of each attribute, the weight of each attribute is determined by adopting a dispersion maximization method
Figure BDA00033583617200001521
The model is shown in formula (13).
Figure BDA0003358361720000161
Wherein "other" represents user AiIncomplete weight information is provided.
Figure BDA0003358361720000162
Representation for the kth attribute
Figure BDA0003358361720000163
User A ofiThe degree of deviation between the language evaluations given to each electricity sales package is shown in equation (14).
Figure BDA0003358361720000164
Wherein the content of the first and second substances,
Figure BDA0003358361720000165
p＝0,1,…,g(Ai)-1，
Figure BDA0003358361720000166
for user AiEvaluation of the kth Attribute for the qth package
Solution formula(13) The single-target optimization model can obtain the weight of each attribute of the electricity selling package
Figure BDA0003358361720000167
In order to ensure the integrity and the interpretability of user evaluation information, a Hesitation Fuzzy Language Weighted Average Operator (HFLWAO) is adopted to integrate the evaluation information of each user, and an evaluation matrix of each user for selling the electric package is obtained
Figure BDA0003358361720000168
Wherein the content of the first and second substances,
Figure BDA0003358361720000169
represents user AiPair electric sales package TjThe method of determining (2) is represented by the following formula (15):
Figure BDA00033583617200001610
the calculation method of HFLWAO is as follows:
1) based on sell electric meal TjThe K attributes of (a) are set as follows:
Figure BDA00033583617200001611
akthe evaluation result of the kth attribute;
2) respectively order
Figure BDA0003358361720000171
The following iterations are performed:
Figure BDA0003358361720000172
wherein, trunc (·) is an integer function, and a decimal part is directly removed; and delta (-) represents a mapping relation between the symbolic corner mark of the language evaluation quantity and the hesitation fuzzy language set.
mhAs a result of the evaluation of the package by the user,
Figure BDA0003358361720000173
in order to evaluate the degree of progress,
Figure BDA0003358361720000174
to evaluate the degree of membership;
with user AiLanguage evaluation set of
Figure BDA0003358361720000175
For example, let β ∈ [0, g (A)i)-1]The equivalent information of β can be described by a binary, namely:
Figure BDA0003358361720000176
similarly, there is a transformation function Δ-1(. the binary equivalent information is converted into equivalent values, namely:
Figure BDA0003358361720000177
3) based on the result obtained in step 2), calculating by using a distributed language evaluation operator DAA
Figure BDA0003358361720000178
Namely:
Figure BDA0003358361720000181
wherein the content of the first and second substances,
Figure BDA0003358361720000182
for a two-tuple of language evaluation,
Figure BDA0003358361720000183
ratio representing linguistic evaluation variableFor example, the calculation formula is shown in formula (21).
Figure BDA0003358361720000184
2.3 unification of multiple-granularity hesitation fuzzy language evaluation information of users for selling electric packages
Considering the difference of culture and knowledge background of each user in the user load information database, the granularity of the language evaluation set used when different users evaluate the electric sales packages is different, namely: the user presents the characteristic of multi-granularity hesitation ambiguity on the evaluation information of the electric power selling package. Without loss of generality, in order to ensure the accuracy and fairness of the evaluation result, the language evaluation sets under different granularities need to be converted into the language evaluation sets under the same granularity. It is assumed that the particle size is g (A)i) Evaluation set
Figure BDA0003358361720000185
Evaluation information of (2)
Figure BDA0003358361720000186
Conversion to g (A) on the basis of particle sizef) Evaluation set
Figure BDA0003358361720000187
Evaluation information of (2)
Figure BDA0003358361720000188
The method comprises the following specific steps:
1) let g (═ LCM (g (A)) bei)-1,g(Af) -1) +1, where LCM (·) represents the minimum common multiple;
2) creating a virtual language set
Figure BDA0003358361720000189
Let thetae＝0，e＝0,1,…,g(*)-1；
3) If it is
Figure BDA0003358361720000191
zh＝0,1,…,g(Ai) -1, calculating
Figure BDA0003358361720000192
Obtaining:
Figure BDA0003358361720000193
4) order to
Figure BDA0003358361720000194
z h0,1, …, g (×) -1, if
Figure BDA0003358361720000195
Computing
Figure BDA0003358361720000196
5) Based on
Figure BDA0003358361720000197
Calculating the normalized language evaluation variable ratio, as shown in formula (22):
Figure BDA0003358361720000198
6) the unified language evaluation information is obtained based on the formula (22)
Figure BDA0003358361720000199
Based on steps 1) -6), an evaluation matrix of the user for the electricity sales package under uniform granularity can be obtained
Figure BDA00033583617200001910
Wherein the content of the first and second substances,
Figure BDA00033583617200001911
representing user A at a uniform granularityiPair electric sales package TjThe evaluation information of (2) is presented in the form of a binary group, namely:
Figure BDA00033583617200001912
Figure BDA00033583617200001913
is at AfThe language evaluation at the granularity of the language,
Figure BDA00033583617200001914
in order to evaluate the degree of membership newly,
Figure BDA00033583617200001915
to a new degree of evaluation
3. Electricity selling package recommendation and effect evaluation based on user satisfaction
The recommendation of the power selling company to the power selling package needs to consider the satisfaction degree of the user to the power selling package, and the higher the satisfaction degree is, the higher the recommendation success probability is. The satisfaction degree of the target user to the electric package selling can be obtained by firstly calculating the satisfaction degree of the user to the electric package selling in the historical user information database and then combining the similarity degree of the target user and the affiliated user.
Based on the obtained evaluation information of the users to the electricity selling package in the information database (namely, the users A under the unified granularity of the Chinese style (23) in the step 2.3)iPair electric sales package TjEvaluation information of (2)
Figure BDA0003358361720000201
) The expectation of the evaluation information of the user is obtained, and a satisfaction matrix of the user to the electric sales package in the database can be obtained
Figure BDA0003358361720000202
Wherein the content of the first and second substances,
Figure BDA0003358361720000203
for user AiPair electric sales package TjSatisfaction of, calculating methods such asAnd (3) formula (24).
Figure BDA0003358361720000204
The satisfaction degree of the target user on the electric sales package depends on the satisfaction degree of the user on the electric sales package in the historical user library and the similarity degree of the target user and the historical user. With target user Wn and the pth type history user
Figure BDA0003358361720000205
For example, target user WnPair electric sales package TjSatisfaction degree SCnjAs in formula (25):
Figure BDA0003358361720000206
based on the calculation result of the satisfaction degree of the target user for each electricity selling package, two recommendation methods are provided: and (4) performing full-sequencing recommendation and Top-M recommendation, and respectively comparing and evaluating the recommendation effect of the electricity selling package through the root mean square error and the intersection.
(1) Full-rank recommendation
Based on the satisfaction result of the target user on each electricity selling package, the electricity selling company sorts the electricity selling packages, and recommends all the electricity selling packages and the corresponding sorting result to the target user for the target user to choose.
To measure the performance of the proposed full-rank recommendation method, the root mean square error is calculated based on the ranking results. With a target user WnFor example, the root mean square error ε1nThis can be calculated by equation (26).
Figure BDA0003358361720000207
Wherein J is the total number of the electricity sales packages and OnjAnd
Figure BDA0003358361720000208
are respectively provided withRepresenting a target user WnAnd sell electric set meal TjThe actual ranking result of (i.e., the user's own provided ranking result) and the ranking result of the algorithm (i.e., the ranking result of equation (25)). Root mean square error epsilon1nThe smaller the better the performance of the proposed electric sales package recommendation algorithm.
(2) Top-M recommendation
Based on the satisfaction result of the target user for each electricity selling package, the electricity selling company only recommends the packages ranked in the top M to the target user, and does not provide the ranking result.
To measure the performance of the proposed Top-M recommendation method, the first M sets of electricity sales packages obtained by the proposed algorithm are compared
Figure BDA0003358361720000211
Set of packages with actual ranking as top M
Figure BDA0003358361720000212
And calculating the recommendation accuracy. With a target user WnFor example, the accuracy ε2nCan be calculated using equation (27):
Figure BDA0003358361720000213
Figure BDA0003358361720000214
is a target user WnThe set of packages actually ranked top M,
Figure BDA0003358361720000215
obtaining a target user W for an algorithmnThe packages with the top M are ranked, and M is the total number of recommended packages.
Experiment 1:
1. case background
The method for recommending the electricity sales package considering the multi-granularity hesitation fuzzy set and the incomplete weight, which is described in the embodiment 1, takes a certain large park in the east of China as an analysis trial object, and users in the park comprise residents, industries and businessesWaiting for various types of users, based on 2020/1/1-2020/1/31 load data collected by the smart meter, and taking 700 bits of user A as { A ═ A }1,A2,…,A700Verification is performed on the basis of a total of 21700 load curve data for that month. Wherein, 600 users are randomly selected as history users, and 100 users are selected as target users. The histogram of the load frequency distribution of each user per day is averaged, as shown in fig. 3. The electricity selling company provides the park users with an electricity selling set of T ═ T1,T2,…,T10As shown in table 1:
table 1 electricity selling package provided by electricity selling company for park user
Figure BDA0003358361720000216
During the trial period, the electricity selling company carries out questionnaire survey on each user in the park and evaluates the attribute set based on the electricity selling package
Figure BDA0003358361720000217
As shown in table 2:
TABLE 2 evaluation Attribute set for electricity sales packages
Figure BDA0003358361720000218
Figure BDA0003358361720000221
And collecting the evaluation information of the power selling package of the user based on the language evaluation set of each user. According to statistics, the language evaluation set granularity of the users in the park for the electricity sales packages can be divided into 3, 5, 7 and 9, as shown in formulas (28) to (31), and the average daily load rate and the average daily peak-valley difference rate of each user and the corresponding language evaluation set granularity are shown in fig. 4.
Figure BDA0003358361720000222
Figure BDA0003358361720000223
Figure BDA0003358361720000224
Figure BDA0003358361720000225
2. Historical user cluster analysis
Based on the expressions (1) - (7), calculating the load characteristic indexes of 600 historical users in the park, and clustering the historical users according to the improved K-means clustering algorithm, wherein the clustering quality indexes corresponding to different clustering numbers are shown in FIG. 5.
As shown in fig. 5, when the cluster number is 5, that is: when c is 5, the clustering quality index value is the largest, the clustering effect is the best, and the clustering result and the number of various users are respectively a late peak type, a peak flat type, a peak avoidance type, a heavy industry type and a double peak type as shown in fig. 6. Wherein, the late peak type is a working group which mainly uses the electricity load of residents, works in the daytime and goes home after leaving work at 19:00 night; the peak-flat type is mainly used by office users, businesses, office buildings and other work places, and users who get on work in the morning at about 9:00 and get off work at night at about 19: 00-20: 00; the peak avoiding type aims at night places such as bars, KTVs, bread factories, traffic lighting and the like or peak-shifting electricity users; heavy industrial types are in the steel industry, the metallurgical industry, etc. which are constantly maintained at a high level for loads; the user who uses electricity continuously in the morning and reduces the power consumption moderately after lunch is mainly the users in agriculture, textile industry and the like who work for a fixed and regular time.
Then, based on the historical user clustering result, the distance between each target user characteristic index phasor and each clustering center is calculated, and the category to which each target user belongs is determined, as shown in fig. 8.
3. Evaluation of historical users on electricity sales packages
A certain user A1 in the late peak pattern isExample, its language evaluation set is L5The user gives an evaluation matrix according to the attributes of each electricity selling package
Figure BDA0003358361720000226
Comprises the following steps:
Figure BDA0003358361720000231
by
Figure BDA0003358361720000232
It can be known that the user shows a certain hesitation fuzzy characteristic when evaluating the electricity sales package, and the evaluation information shows that the state is also the same, and the evaluation behavior of the user can be reflected more truly.
Binding evaluation matrix
Figure BDA0003358361720000233
With user A1The provided electricity selling package attribute weight information is shown as a formula (32), and based on a formula (13), the established dispersion maximization model is shown as a formula (33).
Figure BDA0003358361720000234
Figure BDA0003358361720000235
Using the link () of MATLAB to obtain the weight of each attribute as
Figure BDA0003358361720000241
Evaluating information for users on the basis of the above
Figure BDA0003358361720000242
Carry out integration to obtain user A1The evaluation results of the electricity sales package are shown in table 3:
table 3 user a1Self-language-based evaluation setEvaluation result of electricity sales package
Figure BDA0003358361720000243
Further, the language evaluation information under different granularities is converted into the evaluation information under the same granularity. Herein with L7As the unified evaluation granularity, based on section 2.3, the evaluation result of the user on the electricity sales package under the unified granularity is obtained, as shown in table 4:
table 4 user a at unified language evaluation granularity1Evaluation result of electricity sales package
Figure BDA0003358361720000244
4. User satisfaction evaluation for electricity sales package
Based on the obtained uniform granularity, the user A1The evaluation result of the electricity selling package is expected to obtain the user A1The satisfaction with each electricity sales package is shown in table 5.
TABLE 5 user A1Satisfaction degree of each electricity selling package
Figure BDA0003358361720000251
Similarly, the satisfaction evaluation results of other historical users for the electricity selling packages can be obtained, and as shown in fig. 7, the satisfaction of the target user for each electricity selling package is calculated and obtained based on the formula (25) by combining the similarity between the target user and the historical user belonging to the category. With target users W of late peak type1For example, the similarity result with the history user of the late peak type is shown in fig. 8, and the satisfaction quantification result for each electricity sales package is shown in fig. 9.
As can be seen from fig. 7, for the same electricity selling package, the satisfaction evaluation results of different historical users in the late peak type are different, and the satisfaction of the same historical user for different electricity selling packages is also different. From FIG. 8, the eye isTarget user W1The similarity between the users and the late peak historical users is more than 97.5%, and it can be seen that the improved K-means clustering algorithm provided by the embodiment 1 can effectively classify the users with the same load characteristics into one class.
Based on the obtained historical user satisfaction, and the target user W1The similarity with the historical user is further obtained1Satisfaction degree for each electricity selling package. As can be seen from FIG. 9, target user W1Pair electric sales package T7The most satisfactory level of (c) is 587.4434. And in practice, target user W1The electricity consumption period is mainly concentrated on 19:00-22:00, and the electricity consumption period is advocated by low-carbon action and electricity sales package T7The properties of (1) are identical. Therefore, the obtained result is consistent with the reality, and the correctness of the provided user satisfaction quantification method is demonstrated.
5. Recommendation and performance evaluation of electricity selling package
Based on the satisfaction quantitative result of the target user to each electricity selling package, a full-sequencing recommendation method and a Top-M recommendation method can be respectively adopted to recommend the electricity selling packages, wherein M is 5. Still taking the target user W1 as an example, the electricity selling package and the sorting result provided by the electricity selling company to the target user W1 are shown in table 6 by adopting the full sorting recommendation method. The actual ordering results for each electricity sales package are also shown in Table 6.
TABLE 6 result of electric power selling company adopting full-sorting recommendation method for target user W1 recommendation
Figure BDA0003358361720000252
As shown in Table 6, the ordering results of the electricity sales packages obtained by the method provided by the invention are mostly consistent with the actual ordering results, except for electricity sales packages T9And T10The sorting results are consistent except the differences. The root mean square error ε can be calculated from equation (26)110.447. Electricity selling set meal T9And T10The reason why the sorting results are different is that the user W uses electricity at a cost equivalent to the electricity consumption cost of the user W1More concern about the environmental protection degree and increment of the packageService type, which is higher in maintenance demand than in failure diagnosis prediction demand for equipment for residential users, for home appliances, and thus, for electricity sales package T10Is higher than T9It is demonstrated that the ordering result obtained by the method of example 1 is in fact.
Similarly, by adopting the Top-5 recommendation method, the electricity selling company directly serves as the user W1Recommended electricity selling package set
Figure BDA0003358361720000253
The recommendation accuracy ε can be calculated from equation (27)21100%. It can be seen that the accuracy of the recommendation method of example 1.
6. Improved K-means clustering result comparison
To demonstrate the effectiveness of the improved K-means clustering algorithm herein, 5% random noise was superimposed on the collected campus user load data to obtain improved K-means clustering results and clustering centers at the optimal clustering number (c ═ 5), as shown in fig. 10. And calculating the load data after the random noise is superimposed by using an original K-means clustering algorithm to obtain a clustering center of each calculation result, as shown in FIG. 10. As can be seen from fig. 10, the result obtained by using the original K-means clustering algorithm is greatly affected by random noise, and the clustering centers except (a) and (c) are all shifted, however, the improved K-means clustering algorithm can effectively reduce the influence of noise points, and better reflect the load distribution characteristics of users.
In order to further explain the robustness of the improved K-means clustering algorithm to noise, random noise with different proportions is respectively superposed on the collected user load data to obtain the corresponding optimal clustering number c and clustering quality index Iqc.avAs shown in fig. 11. As shown in fig. 11, when the superimposed noise ratio is less than 30%, the optimal clustering numbers obtained by the improved K-means clustering algorithm are all 5, and the optimal clustering numbers start to deviate when the noise ratio reaches 10% in the original K-means clustering algorithm. In addition, as the proportion of the superimposed noise increases, the corresponding clustering quality indexes under the two clustering algorithms are reduced, but the clustering quality index corresponding to the improved K-means clustering algorithm is higher than that of the original K-means clustering algorithmAlgorithm and the descending speed is slower. It can be seen that the improved K-means clustering algorithm of embodiment 1 is robust to noise.
7. Comparing recommended sorting results of electricity selling packages of various target users
By using the method for recommending the electricity sales packages provided in embodiment 1, the satisfaction evaluation results of various target users for the electricity sales packages are calculated, as shown in fig. 12. As can be seen from fig. 12, for the same type of target users, the satisfaction trends of the users for the electricity sales packages are the same, and the ordering results of the electricity sales packages are approximately consistent. The satisfaction degree of different types of target users to the same electric sales package is greatly different. Therefore, the method for recommending the electricity selling packages provided by the embodiment 1 can meet the requirements of different types of users on the electricity selling packages. Wherein, the late peak type user mainly using the residential electricity load and the peak-flat type user mainly using the commercial and office buildings pay attention to the electricity cost, therefore, the electricity selling set meal T with lower cost and more rewarding electricity quantity7And T3Is more satisfactory. For peak avoiding users, the power consumption time is more special than that of other users, the peak avoiding users are typical peak-off users, the peak-valley time setting of the power selling package is relatively concerned, and the power selling package T9Compared with T10The electricity charge is more saved, therefore, the electric-power selling package T is more favored9. In addition, heavy industrial users mainly in the steel and iron and metallurgical industries are very sensitive to power quality disturbance, and the loss caused by disturbance is far greater than the electricity cost, so that the attention degree of the heavy industrial users on power quality value-added service is greater than other attributes of the electricity sales package, and the heavy industrial users on the electricity sales package T4The satisfaction degree of the method is the maximum and is in line with the reality. Similarly, a bimodal customer production facility, mainly in the textile industry, is sensitive to voltage sags, improving the immunity of the facility effectively reduces the risk of customer losses, and therefore, it is suitable for selling a package of electricity T8The satisfaction of (2) is greater.
8. Comparison of recommended sorting results of electricity selling packages
To further prove the effectiveness of the method for recommending the electric sales packages provided in embodiment 1 of embodiment 1, the actual ordering results of the electric sales packages of various target users are combined with the ordering obtained by the method for recommending the electric sales packages provided in embodiment 1Comparing the results of the sorting results obtained by only considering the cost, the sorting results obtained by clustering by using the original K-means and the results obtained by directly adopting the electric sales package recommendation method provided by the embodiment 1 without clustering, and respectively calculating the mean values epsilon of the root mean square errors of various target users under the full-sorting recommendation and the Top-5 recommendation1And the average value of accuracy ∈2As shown in fig. 13.
As can be seen from fig. 13, the sorting result obtained by the method for recommending an electric package sold in embodiment 1 is not much different from the actual sorting result, although the sorting of 2 to 4 packages is different, the maximum root mean square error is 0.6325, the electric packages sold in the top 5 are consistent with the actual package, and the accuracy reaches 100%, thereby illustrating the accuracy of the method for recommending an electric package sold in embodiment 1.
Compared with the actual sequencing result, the root mean square error of the recommendation result considering only the cost of the electricity selling package is larger, the maximum is 4.8374, the recommendation accuracy is not higher than 60%, therefore, the evaluation of the electricity selling package by the user has diversity, and under the condition that the cost is not greatly different, the value-added service, the reward policy and the like contained in the electricity selling package are also the attention points of the user.
In addition, if the original K-means clustering algorithm is used to cluster the historical users, as shown in fig. 10, except for the late peak users and the peak avoidance users, the clustering centers of other types of users are shifted, as shown in fig. 13, the root mean square errors of the late peak users and the peak avoidance users are 0.4472 and 0.7746 respectively, and the accuracy is 100%, while the root mean square errors of the other types of users are 1.7321, 3.1623 and 0.8944 respectively, which are higher than the root mean square error of the result obtained by the method for recommending the electric package sold in embodiment 1, and the recommendation accuracies are 80%, 60% and 80%, respectively, and are lower than 100%. And if the clustering of the historical users is not considered, the electricity sales packages are recommended directly according to the similarity between the target user and all the historical users, the root mean square error corresponding to the recommendation result is large, the minimum is 1, the maximum is 3.3466, the recommendation accuracy is not more than 80%, and the recommendation performance is poor.
To sum up, the improved K-means clustering algorithm provided by the method for recommending an electricity sales package in embodiment 1 clusters users, can more accurately cluster users with similar load characteristics into one category, and considers the multiple attributes of an electricity sales package, the multi-granularity hesitation fuzzy characteristic of user evaluation information and incomplete weight information, so that the root mean square error of the recommendation result obtained by the method for recommending an electricity sales package is smaller, the recommendation accuracy is higher, and the recommendation performance is better.
Finally, it is also noted that the above-mentioned lists merely illustrate a few specific embodiments of the invention. It is obvious that the invention is not limited to the above embodiments, but that many variations are possible. All modifications which can be derived or suggested by a person skilled in the art from the disclosure of the present invention are to be considered within the scope of the invention.

Claims (5)

1. The method for recommending the electricity selling package considering the multi-granularity hesitation fuzzy set and the incomplete weight is characterized by comprising the following steps of: the specific process is as follows:
s1, establishing a user load information database based on the user electricity utilization characteristic indexes, clustering the users based on an improved K-means clustering algorithm, and determining the category of the target user;
step S2, considering the incomplete weight information and the multi-granularity hesitation fuzzy language evaluation set provided by the user, and constructing an evaluation matrix of the user for the electric sales package;
step S3, calculating the satisfaction of the historical user and the target user to the electric power selling package;
and step S4, obtaining the complete-sequence electricity selling package recommendation and the Top-M electricity selling package recommendation based on the user satisfaction quantification result.
2. The method of claim 1, wherein the method further comprises:
the specific process of step S1 is as follows:
step S1.1, building user load information database
Based on user A ═ { A1,A2,…,Ai,…,AIThe daily load data for a month is:
Figure FDA0003358361710000011
wherein the content of the first and second substances,
Figure FDA0003358361710000012
k is the total hours of a month; based on the monthly load rate
Figure FDA0003358361710000013
Number of hours of maximum utilization
Figure FDA0003358361710000014
Mean value of peak-to-valley rate of working day
Figure FDA0003358361710000015
Mean peak-to-valley rate of off-day
Figure FDA0003358361710000016
Peak load mean
Figure FDA0003358361710000017
Mean average of load rate in flat phase
Figure FDA0003358361710000018
Mean value of load rate at valley period
Figure FDA0003358361710000019
Obtain user AiLoad characteristic index vector of
Figure FDA00033583617100000110
And a user load information database corresponding to the user and the load characteristic index vector thereof is established;
(1) the monthly load rate:
Figure FDA00033583617100000111
wherein the content of the first and second substances,
Figure FDA00033583617100000112
and
Figure FDA00033583617100000113
are respectively user AiThe average load per month and the maximum load,
Figure FDA00033583617100000114
for user AiDaily load data for the kth hour of the total hours of a month;
(2) number of hours of maximum utilization
Figure FDA00033583617100000115
Wherein the content of the first and second substances,
Figure FDA00033583617100000116
for user AiElectricity consumption in whole month;
(3) mean value of peak-to-valley rate of working day
Figure FDA0003358361710000021
Wherein, KWIs the total number of days of the working day,
Figure FDA0003358361710000022
the day maximum load on day i of the working day,
Figure FDA0003358361710000023
the day minimum load for day i of the non-workday;
(4) mean peak-to-valley rate of off-day
Figure FDA0003358361710000024
Wherein, KNWIs the total number of days on the non-working day,
Figure FDA0003358361710000025
the day maximum load on day j of the non-workday,
Figure FDA0003358361710000026
the daily minimum load on day j of the non-workday;
(5) peak load mean
Figure FDA0003358361710000027
Wherein peak periods are defined as 08:00-11:00 and 18:00-21:00, T is the total number of days, and T is KW+KNW，
Figure FDA0003358361710000028
For user A in the peak period of the t dayiThe average value of the loads of (a),
Figure FDA0003358361710000029
is the user A on the t dayiThe load mean value of (1);
(6) mean average of load rate in flat phase
Figure FDA00033583617100000210
Wherein, the ordinary period is defined as 06:00-08:00, 11:00-18:00 and 21:00-22:00,
Figure FDA00033583617100000211
for the tth balance period user AiThe load mean value of (1);
(7) mean load factor at off-peak
Figure FDA00033583617100000212
Wherein the valley time periods are defined as 22:00-24:00 and 00:00-06:00,
Figure FDA00033583617100000213
for the user A in the trough period of the t dayiThe load mean value of (1);
step S1.2, clustering based on historical user load information database
Based on the user load information database established in the step S1.1, clustering historical users by adopting an improved K-means clustering algorithm, and specifically comprising the following steps:
step S1.2.1, making the clustering number C equal to 2, randomly selecting C users, and marking as C1,C2,…,Cj,…,CcUsing the load characteristic index vector as the clustering center
Figure FDA0003358361710000031
Step S1.2.2, calculate user A separatelyi(I-1, 2, …, I) and each cluster center
Figure FDA0003358361710000032
European distance of
Figure FDA0003358361710000033
Step S1.2.3 for user AiAre compared and obtained
Figure FDA0003358361710000034
And will be user AiClassified as j, and the number of users belonging to the j is set as IjThe corresponding user is represented as
Figure FDA0003358361710000035
Step S1.2.4, calculating the square error J based on the classification result of step S1.2.3 as equation (8)c(t):
Figure FDA0003358361710000036
Wherein, t is the iteration number,
Figure FDA0003358361710000037
is corresponding to Ai,jClass j user AiA load characteristic index vector of (a);
step S1.2.5, recalculating the cluster centers
Calculating the average distance D between the load characteristic index vectors of all users in each class and the clustering center, selecting the users with the distance to the clustering center being less than 2D in the class, and then recalculating the mean value of the load characteristic indexes of the selected users as a new clustering center;
step S1.2.6, determine whether formula (9) is satisfied:
Jc(t+1)-Jc(t)≥0 (9)
if not, t is t +1, and then the step S1.2.1 is returned to continue the iteration;
if the formula (9) is satisfied, the iteration is ended, and the clustering quality index I is calculated based on the clustering result of the t iterationqc.av：
Figure FDA0003358361710000038
Wherein, Iqc(i) When the number of clusters is c, the closeness degree of the ith user to the cluster center of the class to which the ith user belongs is represented as follows:
Figure FDA0003358361710000039
wherein the content of the first and second substances,
Figure FDA00033583617100000310
represents the average distance between classes as user AiAverage value of the distance between the user load characteristic index phasor and other user load characteristic indexes except the category to which the user belongs;
Figure FDA0003358361710000041
representing the average distance within a class, as user AiAverage of the phasor distances from the other user load characteristic indexes in the category to which the user belongs;
step S1.2.7, making the cluster number c ═ c +1, returning and executing step s 1.2.1-step S1.2.6 until the cluster number reaches the maximum value
Figure FDA0003358361710000042
Step S1.2.8, comparing the clustering quality index I under different clustering numbersqc.av，Iqc.avThe corresponding cluster number at the maximum is the optimal cluster number c;
step S1.3, calculating the similarity between the target user and the historical user based on Pearson correlation coefficient
The target user is a user needing to recommend the electricity selling package and is represented as W ═ W1,W2,…,Wn,…,WMAnd obtaining load characteristic index vectors of each target user based on daily load data of each user in a certain month by combining the formula (1) with the formula (7)
Figure FDA0003358361710000043
Calculating the center of each cluster under the optimal cluster number c
Figure FDA0003358361710000044
The class corresponding to the minimum distance is the target user WnThe category to which it belongs;
set target user WnBelonging to the p-th class of historical users, wherein the number of the class of users is NpIs shown as
Figure FDA0003358361710000045
The similarity between the target user and the historical user is described by using the Pearson correlation coefficient:
Figure FDA0003358361710000046
wherein the content of the first and second substances,
Figure FDA0003358361710000047
represents a target user WnAnd historical users
Figure FDA0003358361710000048
The similarity of (2);
Figure FDA0003358361710000049
and
Figure FDA00033583617100000410
respectively represent users WnAnd historical users
Figure FDA00033583617100000411
The d-th load characteristic index of (1),
Figure FDA00033583617100000412
and
Figure FDA00033583617100000413
respectively represent users WnAnd historical users
Figure FDA00033583617100000414
Average value of load characteristic index.
3. The method of claim 2, wherein the method further comprises:
the specific process of the step 2 is as follows:
step S2.1, building an evaluation matrix of the user for the electricity sales package based on the hesitation fuzzy language set
The set of electricity selling set is T ═ T1,T2,…Tj,…,TJUser a ═ a }1,A2,…,Ai,…,AIThe evaluation attribute set for the electricity sales package is
Figure FDA0003358361710000051
Describing the evaluation information of the user on the electricity selling package by adopting hesitation fuzzy language:
let user AiIs a language evaluation set of
Figure FDA0003358361710000052
Wherein g (A)i) Represents the granularity of the language evaluation set and is odd,
Figure FDA0003358361710000053
represents the evaluation amount of the p-th language, p is 0,1, …, g (A)i) -1 symbolic corner marks for language evaluation quantities; language evaluation set
Figure FDA0003358361710000054
The elements are arranged in sequence:
if p is>q, then:
Figure FDA0003358361710000055
user AiSelf-language-based evaluation set
Figure FDA0003358361710000056
And evaluating the electricity selling package, wherein an evaluation matrix is as follows:
Figure FDA0003358361710000057
wherein the content of the first and second substances,
Figure FDA0003358361710000058
represents user AiPair electric sales package TjProperty (2) of
Figure FDA0003358361710000059
Given the hesitation fuzzy language evaluation information, J and K are respectively the J-th package and the K-th attribute;
step S2.2, determining the attribute weight of the electricity selling package considering the incomplete weight
Determining each attribute weight by using dispersion maximization method
Figure FDA00033583617100000510
Figure FDA00033583617100000511
Wherein "other" represents user AiThe incomplete weight information is provided in the form of,
Figure FDA00033583617100000512
representation for the kth attribute
Figure FDA00033583617100000513
User A ofiThe degree of deviation between language evaluations given to each electricity sales package:
Figure FDA0003358361710000061
wherein the content of the first and second substances,
Figure FDA0003358361710000062
Figure FDA0003358361710000063
for user AiEvaluating the kth attribute in the qth package;
integrating the evaluation information of each user by adopting an Hesitation Fuzzy Language Weighted Average Operator (HFLWAO) to obtain the evaluation matrix of each user on the electric sales package
Figure FDA0003358361710000064
Figure FDA0003358361710000065
Wherein the content of the first and second substances,
Figure FDA0003358361710000066
represents user AiPair electric sales package TjThe evaluation results of (1);
the HFLWAO is calculated as follows:
(1) based on electricity selling set meal TjThe K attributes of (a) are set as follows:
Figure FDA0003358361710000067
akthe evaluation result of the kth attribute;
(2) respectively make
Figure FDA0003358361710000068
The following iterations are performed:
Figure FDA0003358361710000071
wherein trunc (·) is an integer function; delta (-) represents a mapping between symbolic logo of language evaluation quantity and hesitation fuzzy language set, mhAs a result of the evaluation of the package by the user,
Figure FDA0003358361710000072
in order to evaluate the degree of progress,
Figure FDA0003358361710000073
to evaluate the degree of membership;
let beta be [0, g (A) ]i)-1]The equivalent information of beta is described by a binary group:
Figure FDA0003358361710000074
presence of a transformation function Δ-1(. h), converting the binary equivalent information into equivalent values:
Figure FDA0003358361710000075
(3) obtaining by calculation of a distributed language evaluation operator DAA
Figure FDA0003358361710000076
Figure FDA0003358361710000077
Wherein the content of the first and second substances,
Figure FDA0003358361710000081
for a two-tuple of language evaluation,
Figure FDA0003358361710000082
ratio representing linguistic evaluation variables:
Figure FDA0003358361710000083
step S2.3, unification of multi-granularity hesitation fuzzy language evaluation information of the user on the electric power selling package
Converting language evaluation sets under different granularities used by a user for evaluating the power selling package into language evaluation sets under the same granularity, and determining the granularity as g (A)i) Evaluation set
Figure FDA0003358361710000084
Evaluation information of (2)
Figure FDA0003358361710000085
Conversion to g (A) on the basis of particle sizef) Evaluation set
Figure FDA0003358361710000086
Evaluation information of (2)
Figure FDA0003358361710000087
The process is as follows:
step S2.3.1, let g (×) -LCM (g (a)i)-1,g(Af) -1) +1, where LCM (·) represents the minimum common multiple;
step S2.3.2, creating a set of virtual languages
Figure FDA0003358361710000088
Let thetae＝0，e＝0,1,…,g(*)-1；
Step S2.3.3, if
Figure FDA0003358361710000089
Computing
Figure FDA00033583617100000810
Obtaining:
Figure FDA00033583617100000811
step S2.3.4, order
Figure FDA00033583617100000812
If it is
Figure FDA00033583617100000813
Computing
Figure FDA00033583617100000814
Step S2.3.5 based on
Figure FDA0003358361710000091
Calculating the normalized language evaluation variable ratio, as shown in formula (22):
Figure FDA0003358361710000092
step S2.3.6, obtaining the unified language evaluation information based on the formula (22)
Figure FDA0003358361710000093
Based on the steps S2.3.1-S2.3.6, an evaluation matrix of the user for the electricity sales package under uniform granularity is obtained
Figure FDA0003358361710000094
Wherein the content of the first and second substances,
Figure FDA0003358361710000095
representing user A at a uniform granularityiPair electric sales package TjEvaluation information of (2):
Figure FDA0003358361710000096
Figure FDA0003358361710000097
is at AfThe language evaluation at the granularity of the language,
Figure FDA0003358361710000098
in order to evaluate the degree of membership newly,
Figure FDA0003358361710000099
the evaluation degree is new.
4. The method of claim 3, wherein the method further comprises:
the specific process of the step 3 is as follows:
user A at uniform granularity based on formula (23)iPair electric sales package TjEvaluation information of (2)
Figure FDA00033583617100000910
The expectation of the evaluation information of the user is obtained, and the satisfaction matrix of the user to the electric sales package is obtained
Figure FDA00033583617100000911
Wherein the content of the first and second substances,
Figure FDA00033583617100000912
for user AiPair electric sales package TjSatisfaction of (2):
Figure FDA0003358361710000101
target user WnPair electric sales package TjSatisfaction degree SCnjComprises the following steps:
Figure FDA0003358361710000102
5. the method of claim 4, wherein the method further comprises:
the full-sequencing electricity selling package recommendation specifically comprises the following steps:
calculating a root mean square error epsilon based on satisfaction results of the target users for each electricity selling package1nThen according to the root mean square error epsilon1nSell electricity according to the correspondence from small to largeAnd recommending the package ordering to the target user for the target user to decide:
Figure FDA0003358361710000103
wherein J is the total number of the electricity sales packages and OnjAnd
Figure FDA0003358361710000104
respectively represent for the target user WnAnd sell electric set meal TjThe actual sorting result of (a) and the sorting result obtained by the algorithm of the formula (25);
the Top-M electricity selling package recommendation specifically comprises the following steps:
based on the satisfaction result of the target user for each electricity selling package, the electricity selling company only recommends the packages ranked in the top M to the target user, and does not provide the ranking result;
recommend to target user WnThe first M sets of electricity sales packages
Figure FDA0003358361710000105
Set of packages with actual ranking as top M
Figure FDA0003358361710000106
Accuracy of recommendation e2nComprises the following steps:
Figure FDA0003358361710000107
Figure FDA0003358361710000108
is a target user WnThe set of packages actually ranked top M,
Figure FDA0003358361710000109
obtaining a target user W for an algorithmnSet of packages ranked M top, M being recommended packagesAnd (4) total number.
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CN116596640A (en) * 2023-07-19 2023-08-15 国网山东省电力公司营销服务中心(计量中心) Recommendation method, system, equipment and storage medium for electric power retail electric charge package
CN116596640B (en) * 2023-07-19 2024-06-21 国网山东省电力公司营销服务中心(计量中心) Recommendation method, system, equipment and storage medium for electric power retail electric charge package

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CN116562990A (en) * 2023-07-03 2023-08-08 湖北国网华中科技开发有限责任公司 Electricity selling transaction service recommendation method and device
CN116562990B (en) * 2023-07-03 2023-10-27 湖北国网华中科技开发有限责任公司 Electricity selling transaction service recommendation method and device
CN116596640A (en) * 2023-07-19 2023-08-15 国网山东省电力公司营销服务中心(计量中心) Recommendation method, system, equipment and storage medium for electric power retail electric charge package
CN116596640B (en) * 2023-07-19 2024-06-21 国网山东省电力公司营销服务中心(计量中心) Recommendation method, system, equipment and storage medium for electric power retail electric charge package

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