# Online Estimation of Short-Circuit Fault Level in Active Distribution Network
## 2 Short-Circuit Fault Level Estimation for Active Distribution Networks
### The Fuzzy Logic Identifier to Distinguish Useful Disturbance
#### 2.3.2 Linguistic and Universal Terms of Input-Output Variables  
It is of great importance to represent the problem in fuzzy terms when fuzzy logic is used for problem-solving scenarios. As stated above, only the load-side disturbance which satisfies \(Dir>\varepsilon\), is with useful information. Therefore, \(\Delta\hat{U}\) and \(\Delta\hat{I}\) are considered to be the input signals for the identifier. They are both positive values. Consequently, four linguistic terms, namely Zero, Small, Medium, and Large, are picked out to describe the input variables in the fuzzy system [31]:  
(O, PS, PM, and PL)  
O--Zero;  
PS--Positive Small;  
PM--Positive Medium;  
PL--Positive Large.  
Different from the fuzzy logic controller, whose output signal is used as the tuning parameters of the control strategy, the fuzzy logic identifier in this paper is dedicated to classify the input states. The output variable herein is namely the confidence level (CL) of a certain disturbance. It represents the reliability or the confidence of the voltage and current changes caused by such a disturbance. As the proposed method is based on the least-square solution, the confidence of the disturbance affects the estimation results. If the disturbance is more desirable, i.e., definitely occurring downstream and incurring more effective changes in voltage and current, then the corresponding results derived from it should be more reliable. To make the segmentation of CL more accurate, seven terms of nonnegative value are required:  
(O, PVS, PS, PLM, PM, PML, and PL)  
O--Zero;  
PVS--Positive Very Small;  
PS--Positive Small;  
PLM--Positive Light Medium;PM--Positive Medium;  
PML--Positive Medium Large;  
PL--Positive Large.  
The input variables of a fuzzy logic identifier usually change within a range, which cannot be confirmed in advance. However, the fuzzy logic rules require the input signals to be dispersed in the first place. Consequently, the actual variation range shall be projected to a proper closed interval to facilitate the calculation. According to the feasible operation states and experiments, the input signals involved in the fault level estimation have the following numerical features. \(\Delta\hat{U}\) normally lies in the range of \([0,\ 0.2]\), as the operating voltage of the power is system seldom below 0.8 pu, except in the fault. For \(\Delta\hat{I}\), it can vary in a wide range of \([0,\ 2]\), supposing the load has a large overload capacity. Therefore, two input signals, \(\Delta\hat{U}\) and \(\Delta\hat{I}\), are first projected to the interval of \([0,\ 0.2]\) and \([0,\ 2]\), respectively. If the values of the input signals go beyond the corresponding lower and upper limit, they will be assigned to the values in the boundary. For example, if the relative change of voltage is greater than 0.3, the nominal input of \(\Delta\hat{U}\) will still be fixed as 0.2.  
To make the input-output signals more uniform and simplify their transformation to linguistic terms, the universe mapping is introduced to further project the input signals to a series of dispersed numbers. It is required that the number of elements in the basic universe is more than twice the number of fuzzy linguistic terms. Therefore, the fuzzy sets can fully cover the input-output domain without losing important information. Herein, the universes \(\Delta\hat{U}\) and \(\Delta\hat{I}\) are uniformly mapping as \((0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7)\), while the universe of the output variable CL is set as \((0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10,\ 11,\ 12,\ 13)\).