With the increasing complication, compaction, and automation of distribution network equipment, a small failure will cause an outbreak chain reaction and lead to operational risk in the power distribution system, even in the whole power system. Therefore, scientific assessment of power distribution equipment operation risk is significant to the security of power distribution system. In order to get the satisfactory assessment conclusions from the complete and incomplete information and improve the assessment level, an operational risk assessment model of distribution network equipment based on rough set and DS evidence theory was built. In this model, the rough set theory was used to simplify and optimize the operation risk assessment indexes of distribution network equipment and the evidence DS theory was adopted to combine the optimal indexes. At last, the equipment operational risk level was obtained from the basic probability distribution decision. Taking the transformer as an example, this paper compared the assessment result obtained from the method proposed in this paper with that from the ordinary Rogers ratio method and discussed the application of the proposed method. It proved that the method proposed in this paper is feasible, efficient, and provides a new way to assess the distribution network equipment operational risk.
As the basis part of the power system, the distribution network has direct contact with the power user. The task of distribution network is to assign the electrical energy to users, and the safe and stable operation of the distribution network equipment is closely related to the reliability of power supply. The construction of smart grid leads to a wider application of new distribution network equipment such as transformers, SF6 circuit breakers, vacuum circuit breakers, and boxtype substations. With the increasing complication, compaction, and automation of distribution network equipment, a small fault somewhere in the equipment may outbreak chain reaction, causing catastrophic damages to the distribution network system, even in the entire power system, namely, operational risk [
In the basic theory of equipment risk assessment, a variety of mathematical methods such as risk matrix method, Monte Carlo method [
In summary, most studies on equipment risk apply the risk assessment theory to construct evaluation index system and carried out corresponding assessment, and transformer works were the main object to study the distribution network equipment. Though these studies have solved the problem of equipment risk assessment to some extent, there are still some problems for further study. For example, there are multiple indexes to describe the operational risk of a distribution network device, but they play different roles in the operational risk assessment. It is a critical issue to exclude the indexes that are irrelevant or unimportant from the risk assessment index system and get the accurate risk state of the equipment. So, applying the attribute reduction function of rough set and DS evidence theory, this paper proposed an operational risk assessment model of distribution network equipment based on rough set and DS evidence theory to further study the operational risk management of distribution network equipment. The rest of the paper is arranged as follows. Part two introduced the rough set theory and DS evidence theory firstly and built an operational risk assessment model of distribution network equipment. Taking the transformer as an instance, part three makes a detailed description of equipment operational risk assessment methods based on rough set and DS evidence theory and carries out an example to discuss the assessment results and their application. Part four gives the conclusion of this paper.
As a theory of data analysis and processing, rough set theory was founded by Polish scientist Z. Pawlak in 1982. It is a theoretical method to study the representation, learning, and induction of incomplete and uncertain knowledge and data [
The discernibility matrix proposed by a Polish mathematician, A. Skowron, is one of the efficient algorithms for information system reduction, and it can calculate the reduction easily [
Let
If
All the conjunctive expressions in the minimal disjunctive form of function
DS evidence theory is a powerful tool to deal with uncertain problems brought by cognition limitations. DS evidence theory was formally founded by Shafer in 1976 [
Then the function
If all the conditions of (
Combined with rough set theory and DS evidence theory, this paper built an operational risk assessment model of distribution network equipment operational risk assessment model, and the detailed steps are as follows.
Apply reduction function of rough set to the index reduction of distribution network equipment operational risk (the selection of original indexes depends on the specific equipment). After index reduction, one or multiple indexes may be left.
For the reduction of multiple indexes, use the collection rule of DS evidence theory to combine the reduced indexes and get the basic probability assignment of various index combination results.
After the basic probability assignment of each reduction is obtained, there is no need to assess the operational risk of distribution network equipment by a single reduction. Use the collection rule of DS evidence theory to combine the reductions and get the results of all the combinations. Then by adopting the decisionmaking method based on basic belief assignment and the combination results above, the operational risk level of distribution network can be evaluated.
As one of the main equipment in distribution network, the operational risk of transformer is an important part of distribution network operational risk. So, the transformer is chosen to make an analysis of the numerical example in this paper. The basic data of transformer operation came from article [
Operational risk assessment data of a transformer in a certain working condition.
ID 







Risk level 

1  1.231  0.765  0.596  2.192  0.561  0.941  0.355  1 
2  0.055  6.455  1.100  0.141  0.390  0.355  0.065  1 
3  0.074  0.257  2.763  1.407  0.053  0.019  0.461  2 
4  0.000  0.588  0.642  2.650  0.000  0.000  0.837  2 
5  1.141  1.873  0.245  2.179  0.524  2.136  0.580  2 
6  0.348  12.760  0.183  0.428  0.813  4.444  0.269  3 
7  1.189  7.944  0.269  0.469  2.537  9.444  0.457  3 
8  1.455  14.000  0.103  0.695  2.093  0.364  0.204  3 
9  0.000  1.059  0.611  1.544  0.000  0.000  0.010  4 
10  0.007  2.545  0.266  1.476  0.005  0.018  0.332  4 
11  0.003  1.500  0.467  1.429  0.002  0.005  0.122  4 
12  0.017  18.218  0.146  0.375  0.045  0.309  0.159  5 
13  0.000  5.739  0.110  1.500  0.000  0.000  0.303  5 
14  0.029  11.429  0.124  0.708  0.041  0.333  0.201  5 
15  0.049  4.727  0.515  0.411  0.113  0.219  0.113  5 
The index reduction based on rough set theory is built on the basis of discrete data, so the continuous attributes should be discretized firstly. The discretization of continuous attribute is usually determined by the intervals given by experts’ experience or the system’s automatic division of the input data according to a certain principle. For the data in Table
Discretization rules of the transformer operational risk assessment data.
Item  Original data scope  Discretized data  Original data scope  Discretized data  Original data scope  Discretized data 


0.000~0.500  0  0.501~1.000  1  1.001~1.500  2 

0.000~5.000  0  5.001~10.000  1  10.001~20.000  2 

0.000~0.500  0  0.501~1.000  1  1.001~3.000  2 

0.000~0.900  0  0.901~1.800  1  1.001~2.700  2 

0.000~0.500  0  0.501~1.500  1  1.501~3.000  2 

0.000~0.500  0  0.501~1.000  1  1.001~10.000  2 

0.000~0.300  0  0.301~0.600  1  0.601~0.900  2 
In order to facilitate the operation process, we use symbols
Discernibility matrix of the transformer.
Order  1  2  3  4  5 

1 


2 



3 




4 





5 





According to (
It can be concluded that there are two reductions, namely,
The two attribute reductions to assess the operational risk status of the transformer are
Let the operational risk status of the transformer be 5 categories, namely, Class 1, Class 2, Class 3, Class 4, and Class 5. Use
Assume the transformer’s values of
Basic probability assignment of risk status.
Class 1  Class 2  Class 3  Class 4  Class 5 
 


0.32  0.14  0.24  0  0.20  0.1 

0.24  0.34  0.15  0  0.17  0.1 

0.12  0.25  0.20  0  0.33  0.1 
According to the combination rule of DS evidence theory, the combination results of
Combination results of
Class 1  Class 2  Class 3  Class 4  Class 5 
 


0.1083  0.6278  0.1093  0  0.1188  0.0358 
Combine the combination results of
Combination results of
Class 1  Class 2  Class 3  Class 4  Class 5 
 


0.0234  0.9013  0.0323  0  0.04111  0.00189 
It can be obtained from the combination results in Table
As the gases produced by oil and solid insulation materials under different temperatures and discharge modes differ in type and volume, the ratios among gas volume can be used to judge the operational fault properties of a device. In general, Rogers ratio method is widely used to judge the operational status of a transformer (shown in Tables
Correspondence between gas ratio range and code using Rogers ratio method.

Ratio range  >0.1, <1.0  ≥1.0, <3.0  ≥3.0  ≤0.1 
Code  0  1  2  3  
 

Ratio range  <1.0  ≥1.0  
Code  0  1  
 

Ratio range  <1.0  ≥1.0, <3.0  ≥3.0  
Code  0  1  2  
 

Ratio range  <0.5  ≥0.5, <3.0  ≥3  
Code  0  1  2 
Fault diagnosis using Rogers ratio method.




Diagnosis 

0  0  0  0  Normal aging 
3  0  0  0  Partial discharge (corona) 
1~2  0  0  0  Overheating (≤150°C) 
1~2  1  0  0  Overheating (150°C~200°C) 
0  1  0  0  Overheating (200°C~300°C) 
0  0  1  0  Metal superheating 
1  0  1  0  Circular current in coil 
1  0  2  0  Circular current in iron core and shell or joint overload 
0  0  0  1  Arc dischargeno perfoliate discharge 
0  0  1~2  1  Arc dischargeperfoliate discharge 
0  0  2  2  Continuous discharge breakdowns 
3  0  0  1~2  Partial dischargecorona (sign of creepage) 
As assumed above,
Using the method proposed in this paper, the key operational risk measurement indexes are
Correspondence between operational risk level and status.
Risk level of the transformer  Corresponding status 

1  Normal 
2  Lowenergy discharge 
3  Highenergy discharge 
4  Lowtemperature overheating 
5  Hightemperature overheating 
As the corresponding relationships in Tables
As the equipment of distribution network becomes more complex, compact, and automated, a small fault inside the equipment may lead to the operational risk of the distribution network or even the whole power system as a result of chain reaction. So it is of great theoretical and practical significance to evaluate the operational risk of the distribution network scientifically. Based on the study of rough set theory and DS evidence theory, this paper proposed an operational risk assessment method of distribution network equipment. Taking the transformer as an instance, and obtaining its’ operational monitoring data, this paper used the reduction function of the rough set to reduce the operational risk indexes of the transformer. Then the DS evidence theory was adopted to combine the optimized indexes and further improve the accuracy of transformer’s risk assessment. With method comparasion and application discussion, results showed that the method proposed in this paper is not only able to get the risk assessment indexes of the distribution network equipment more exactly, but is also able to deal with the uncertainty of the evidence efficiently. It provides helpful thoughts for the quantitative risk assessment of distribution network equipment.
This study is funded by the National Natural Science Foundation of China (Grant no. 71071054; 71271084) and “the Fundamental Research Funds for the Central Universities”. The authors appreciate the anonymous reviewers for their valuable comments, which were helpful in improving the paper.