A Method of Power Supply Mode Selection for Urban Distribution Network Planning Based on Association Rules

2.1 Support

The support of rule R is the proportion of the tuples which contain A and Β to total tuples, represents probability that A and Β simultaneously exist in database, denoted by

where D_A∪B represents the number of tuples which contain A and B, D represents the number of total tuples.

2.2 Confidence

The confidence of ruler is the proportion of the tuples contain A and B to the tuples contain A, represents the probability of occurrence B in items in which A has occurred, denoted by

where D_A∪B represents the number of tuples contain A and B, D_a represents the number of tuples contain A.

The implementation for mining association rules consist of two phases. In the 1st phase, frequent itemsets are mined from the dataset namely finding the sets of items that satisfies constraints which their support is greater than minimum support thresholds. In the 2nd phase, is to mine the sets of strong association rules namely finding all sets of association rules that their confidence is greater than minimum confidence thresholds from frequent itemsets.

Where, frequent itemsets can be defined as the items with constraints which their support is greater than minimum support thresholds in the case of given dataset and minimum support thresholds namely sup(A) ≥ min Sup; In the case of given dataset and minimum support thresholds as well as minimum confidence thresholds, strong association rules can be defined as the rules in the association rules A ⇒ B that satisfy following constraints

3.1 Correlative Factors Selecting

There are many correlative factors which influence power supply modes, this article referred to correlative factors in literature [32], as shown in Table 1. Correlative factors information are obtained by real planning data, which usually includes historical data of regional load, population, industrial proportion, developmental level of GDP, climatic conditions, forecasting period, city centrality, city function, and so on. It is crucial to keep the continuity of them and can’t be disconnected when selecting the correlative factors, and supplement of correlative factors should be done when necessary. For different existing schemes, the given correlation factors are different, however, there are always some general characters among them. In the analysis of actual correlative factors, correlative factors which were employed usually are population, industrial proportion, developmental level of GDP, climatic conditions, forecasting period. This article employed factor analysis method of literature ^[33] for preliminary selection of correlative factors data.

3.2 Applicability Evaluation of Power Supply Modes

The other part of history database of power supply mode in urban distribution network is applicable level of the models. The modes of actual use in planning are results of preferential choices which experts have selected according to characteristic of designed area, and which have reflected the expert’s preferences. These results can be used as candidate items for choosing fit modes. But not all candidate modes used in the past have good effectiveness in the new task, and the case that the mode was not adopted in the past can be the best choice in present can’t be excluded from. Therefore, it is necessary to conduct applicability evaluation of power supply modes when building history database for forecasting models. This article employed the methods of literature [34] and literature [35] for applicability evaluation of power supply mode. Applicability evaluation of power supply mode needs starting from demands of the mode itself, such as certain modes must depend on correlative factors to select. In this article, the applicability of power distribution district and each of power supply mode is classified as quantitatively different levels, which is as a kind of correlative factors to be considered. Value range of applicability of power supply mode is 0~1. Where, 0 represents the mode can’t fit demands under the given conditions, 1 represents the mode is fit. When the number is greater than 0 and less than 1, represents applicable level of the mode which is chose to use and the designed areas, which can be set with reference to practical experience.

Based on the above two parts in Section 3, raw database of power supply modes in urban distribution network with correlative factors is built. The parts of database of power supply modes are shown in Table 2. In Table 2, the transverse and longitudinal items can be extended. On the basis of raw database, association rules mining are conducted in order to obtain objective rulebase.

4.1 The Whole Process of Mode Selecting

For mode selection, the first is to establish the historical database, which contains the data of all the correlative factors and modes applicability after the evaluation, taking a mode as the target mode with all the historical correlative factors to conduct data generalization; after that association rules mining between correlative factors and the mode applicability is conducted to get the association rules which meet the conditions; at last, in allusion to target mode to conduct rules matching. Putting the given conditions into the historical database, data generalization of the given conditions is conducted according to reference standard which is the same as historical data, applicable conclusion of target mode can be obtained after rules matching between known ranked data and the mined rules. Where, data generalization, association rule mining and rules matching are all to take one mode as study objective in application of mode selection, the applicability of each mode under given conditions can be obtained by conducting the same study process for other modes. Whole process for mode selecting is shown in Figure 1.

Figure 1

Flow chart of the whole process

4.2 Data Analysis and Data Generalization

By consulting a source, correlative factors with no need for quantization already have a certain partition basis; quantitative data analysis and data generalization mainly use k-means clustering algorithm literature [36] employed, which the outside does not need to set clustering center, but need to set the number of cluster centers. This article set number of cluster center is 5, dynamic computing each of the cluster centers according to the historical data so as to grade the existing data in order to obtain generalized database which can be used directly in association rule mining algorithm. In database every correlative factor is represented by different letters, as shown in Table 3.

4.3 Association Rules Mining

Essence of association rule mining is to find out the relationship between the correlative factors and power supply mode in urban distribution with the generalized data, and to construct the database of association rules with constrains of minimum support and minimum confidence and the effectiveness is larger than 1. The core computation of association rule mining widely uses the FP-Growth algorithm which basic idea is to highly compress the data of historical database into a frequent pattern tree structure, where the compressed data still has kept the original information, then by using method of pattern-growth to generate frequent item sets, and then to mine association rules. The FP-Growth algorithm includes 2 stages, the first stage is to search for all frequent itemsets and to form a tree structure; the second stage is to set minimum support and minimum confidence so as to generate association rules that satisfy the itemsets constraints. At present, there are 2 methods of threshold setting. One is to set different thresholds in each layer of the rules mining, another is to set the only value in the whole algorithm. In this article, the only threshold standard is set for simplicity. Because of all the rules have upper and lower limits of support and confidence, which is the direct basis which user conduct setting. If want to get more rules, the lower limit of support and confidence are as the main reference for setting, whereas reference to the upper limit. The first stage is the core of the algorithm. At last, association rules are obtained which rules format is such as R0&E2:T4, which represents that if corresponding correlative factors satisfy R0 and E2 conditions, applicable level of the target model is T4.

4.4 Rules Matching

For the new task, the result that each correlative factor was graded can be obtained after data generalization of the known data according to each the clustering center in history database, such as the result is R1 and P4 respectively, can be represented as R1&P4. Such, status quo of correlative factors in this area can be obtained and serve as known conditions to match with rules of association rulesbase which by above data mining obtained. At last, the conclusion of the applicability of the mode can be obtained by Case Based Reasoning (CBR) method. CBR is an analogy reasoning method which is by accessing solutions of past similar problems in knowledge base to obtain solution of the current problem. That is, by using the old cases and experience to solve new problems and evaluate new problem, and to explain the abnormal conditions or to understand the new situation.

Rules matching have the following 3 kinds of circumstances^[32].

1. If there is only one matched result in the rule base, applicable level of the supply mode in distribution network corresponding to the matching conditions will be recommended out.

2. If there are multiple matching results corresponding to known conditions in the rule base, ranking them in accordance with the support degree and association degree from high to low, the rule with the highest support will be directly as the final conclusion.

3. If there is no relevant rule in the rule database to match with the known conditions, reminder of “current history database without the matching result” is given directly. At this point you can try to use other mechanisms to select power supply mode in distribution network. The matching process is shown in Figure 2.

Figure 2

Flow chart of rules matching with CBR

5.1 History Database Building

This article chose initial data of 42 representative domestic urban areas as source of historical database, selected correlative factors are the city population, the development level of GDP, the proportion of second industry, the applicable level of power supply modes in distribution network is also considered as correlative factor. After the applicability evaluation of modes, generated initial historical database is shown in Table 4.

It is observed from Table 4 that, for the target mode, under given known conditions, only the area which is corresponding to scheme 9 did not adopt target mode, its applicable level is 0. The areas which are corresponding to other schemes all adopted the target mode, but degree of dependence to target mode is different. Where, scheme 6~8 fully adopted target mode, setting their quantization data is 1; degree of dependence of scheme 1~3 to target model is 0.75, the degree of dependence of the remaining schemes is set to 0.25. The raw data is used as a basis of the follow-up association rules mining.

5.2 Cluster Analysis and Data Generalization

Original data is divided into definite grade after data generalization and is represented by different letters. After data generalization for the data in Table 4, database which association rules mining can use directly was obtained. Part of the data is as shown in Table 5.

5.3 Database for Association Rules

Association rules mining is conducted by taking the generalized data as the mining object. In the example, 132 efficiently strong association can be get by setting constrains of minimum confidence is 0.1, the minimum support degree is 0.02, and the effectiveness is more than 1, as shown in Table 6.

5.4 Matching Results and Mode Selection

The above analysis is only to contrapose hand in hand wiring of T way. At present, there are more than 30 kinds of load forecasting algorithms, for each kind of power supply modes in distribution network, changing its applicability and repeating the above process of data generalization and association rules mining, corresponding association rules can be obtained for each mode. For hand in hand wiring of T way, obtained association rules is E2&P1&R1: T0

Putting the known correlative factors of the area in this example into the historical database to participate in data generalization, the obtained generalization condition is E2&P1&R1. Matching the conditions in association rule results of each mode, the applicability of each mode of the area is obtained. Part of result is shown in Table 7.