# Real-Time Circuit Breaker Availability Assessment in the Transmission Network
## 3 Determining CB State, Variable Definition and the Display of a Fuzzy Regulator  
The general assumption this method uses is that the substation communicates via the SCADA system and that the information from both the SCADA system and the protection devices can be used for exploitation. The Supervisory Control and Data Acquisition (SCADA) system is used for control, communication efficiency to send/receive data, and overall smarter decision making. It monitors the system based on information from event listings, chronology, alarms, changes in circuit breaker states, starts and trips of protection devices, and changes in voltages and currents. The information processing draws on the necessary expertise to analyze it. These properties will be used to determine the relationship between the state determination and the occurrence of a fault on the CB in the transmission network based on fuzzy logic. Modern SCADA systems are very complex. Figure 1 shows a schematic diagram where information is provided to make decisions about the condition and availability of equipment and thus the circuit breaker when operating the power system. For complex faults, due to the large number of different errors that can occur in network events, determining the correct state of the breaker or its network fault status is a great challenge. Determining the diagnostic state of a breaker and its availability at a power system event is a very complex and demanding task. In a power network event, almost all of the breakers' faults can be described by changes in some of the key variables:  
* Change in the CB state in a branch;
* Change in the flow or value of the current on some elements of the network;
* Start or trip of a protection device;
* Switch alarm status. In real-life situations and practical applications, with the use of a fuzzy regulator, these four parameters associated with information represent the necessary and sufficient information for the proper allocation of the breaker state at network events. The use of MFs, the development of conclusion rules, and ultimately the decision making and concluding in conduction of the complex process of determining the diagnostic state of a breaker are based on the operator's knowledge and experience. Figure 2 shows a decision system that uses FL to determine the specified state. Both Figures 1 and 2 show the decision-making process. Figure 2 shows the specific SCADA data in detail, while Figure 1 shows the process from a higher level and with all of the needed information obtained. Figure 1: Schematic diagram of the decision-making process of the breaker diagnostic state. This decision-making process is based on four input variables of fuzzy systems. Each of the input variables is divided into several ranges of values and together they represent the input variables of the fuzzy regulator [31; 32]. For binary relations, a binary fuzzy variable \(R\) with the value \(R(X,Y)=1\) implies that the truth of \(X\) suggests the truth of \(Y\). On the contrary, \(R(X,Y)=0\) implies that there is no inference between \(X\) and \(Y\). The union of two fuzzy sets is stated generally by a function as follows:  
\[\mu:\,[0,1]\times[0,1]\rightarrow[0,1] \tag{28}\]  
The function uses a combination consisting of the element's membership grades in the set as its argument and generates the membership grade of the element in the combination forming the union of \(A\) and \(B\) for each element in the universal set. Thus, we can write:  
\[\mu_{\widetilde{A}\cup\widetilde{B}}(x)=\mu\big{[}\mu_{\widetilde{A}}(x),\mu_ {\widetilde{B}}(x)\big{]}=\max\big{[}\mu_{\widetilde{A}}(x),\mu_{\widetilde{B} }(x)\big{]} \tag{29}\]  
The function specifies the general fuzzy intersection of two fuzzy sets \(A\) and \(B\) as \(i\): [0,1] \(\times\) [0,1] = [0,1]. The argument of this function is a combination consisting of the membership grade of some component in set \(A\) and the membership grade of that same component in set \(B\). The function generates the membership grade of the element in set \(A\cap B\).