Abstract: This paper analyzes the complexity of implementing intelligent operation control of high-voltage circuit breakers using traditional methods. Based on fuzzy theory, the fuzzy relationship between system electrical parameters and system state is studied, leading to the formation of control rules and fuzzy control methods for the circuit breaker's initial opening speed. The hardware structure of the fuzzy controller is presented. Simulation control results show that the fuzzy controller has excellent control performance, and its accuracy and speed fully meet the requirements of intelligent circuit breaker operation. Keywords: Circuit breaker; Fuzzy theory; Intelligent operation; Power system faults Currently, the breaking capacity of arc-extinguishing devices in operational circuit breakers is mainly designed based on breaking short-circuit currents. Regardless of the operating conditions, the circuit breaker's motion characteristics are not adjustable, meaning they all operate based on a single no-load characteristic. However, in actual operation, most breaking operations are performed under normal conditions (such as load or no-load), where arc extinguishing does not require a high opening speed. Full-speed opening not only subjectes the circuit breaker's mechanical components to undue stress, affecting system lifespan and reliability, but may also generate operational overvoltages, threatening the safe operation of other equipment. In view of this, domestic scholars have proposed a new concept of intelligent operation of circuit breakers [1]. The so-called intelligent operation refers to the adaptive control conversion of the moving contact from one position to another. In the circuit breaker breaking process, an important feature of intelligent operation is that it can automatically adjust and control the appropriate breaking speed of the circuit breaker. That is, when the breaking command arrives, the required breaking speed is determined according to the values ​​of parameters such as current, voltage, and power factor that reflect the system state at that time and the relationship between each parameter [2]. Due to the complexity of the power system and the diversity of faults, it is difficult to describe the relationship between the system state and the system parameters using strict logic and mathematical methods. Therefore, it is very difficult to use an accurate mathematical model for control. Based on the power system theory and the characteristics of the breaking speed of the circuit breaker, this paper proposes a fuzzy control model for the operating mechanism of SF6 high voltage circuit breaker by comprehensively using fuzzy reasoning method. With the continuous improvement of this fuzzy system, the reliability and practicality of intelligent operation of circuit breakers will be greatly improved. 1 Mathematical description of fuzzy control model 1.1 Fuzzy relation matrix For circuit breakers with hydraulic breaking operation, an effective method for adjusting the breaking speed is to change the pipeline comprehensive loss coefficient of the hydraulic operating mechanism according to different breaking conditions. Studies have shown that adjusting the opening of the regulating valve installed in the drain line can make the pipeline comprehensive loss coefficient vary over a large range [3]. In the design of this controller, the valve opening is represented by the equivalent orifice diameter. Therefore, by adjusting the orifice diameter of the drain valve according to the relevant electrical parameter values ​​of the system during tripping, the circuit breaker can obtain a suitable tripping speed. As mentioned above, the relationship between the electrical parameters reflecting the state of the power system and the corresponding orifice diameter is difficult to express using precise mathematical methods, but there is indeed a certain connection between them. According to fuzzy control theory, this connection can be described by a fuzzy relation matrix [4], where U = {u1, u2, ..., un} is the set of system electrical parameter values. V = {v1, v2, ..., vm} is the set of equivalent orifice diameters of the drain valve of the hydraulic mechanism. In fuzzy control theory, U and V are two domains with fuzzy relations, and a new domain U×V can be constructed from U and V. The fuzzy set R∈F(U×V) on U×V is called the fuzzy relation between U and V, and is represented by a matrix as [IMG=matrix representation]/uploadpic/THESIS/2008/1/20080107122040659303.jpg[/IMG] where: R is the so-called fuzzy relation matrix; rij＝μR(u,v) is the degree of relation between u and v with respect to R, called the membership function of u and v with respect to R, and its range is [0,1]. The magnitude of rij indicates the probability of vj appearing when ui exists. In particular, rij＝0 indicates that vj is unrelated to the existence of ui; rij＝1 indicates that the existence of ui leads to a high probability of vj appearing. In the intelligent operation of circuit breakers, the magnitude of rij indicates the degree of influence of electrical parameters on the orifice diameter of the drain valve. 1.2 Fuzzy Control Rules The core of fuzzy control is fuzzy decision-making, and the basis of fuzzy decision-making is fuzzy control rules. Fuzzy rules are summarized based on the knowledge and experience of experts, and their form is fuzzy conditional statements represented by linguistic variables. A fuzzy control rule consists of two parts: premises and conclusions. For ease of discussion, only the influence of the magnitude *a* and phase *p* (the phase angle of the current lagging the voltage) of the discharge valve orifice *d* is considered. Therefore, in this fuzzy control system, the premise part of the fuzzy control is the fuzzy set in the universes of discourse A and P of the current *a* and phase *p*, and the conclusion part is the fuzzy set in the universe of discourse D of the discharge valve orifice *d*. The fuzzy sets of the universes of discourse A, P, and D are represented by the following forms: F(A) = NL, NM, NS, ZE, PS, PM, PL; F(P) = NL, NS, ZE, PS, PL; F(D) = NL, NM, NS, ZE, PS, PM, PL, where NL (negative large), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PL (positive large) are the linguistic values ​​of the parameters. In computer-centric control systems, for ease of data processing, the values ​​of the input parameters are usually scaled and discretized. In this control system, the discretized universe of discourse for the current is [0, 14], with 15 levels; the discretized universe of discourse for the phase is [-4, +4], with 9 levels; and the universe of discourse for the control output (equivalent orifice diameter of the drain valve) is [8, 22], in mm, with 15 levels. The fuzzy membership functions of the input and output parameters in the discrete domain are shown in Tables 1, 2, and 3, respectively. Table 1 Membership function of F(A) in the discrete domain μF(A) F(A) A [IMG=Membership function of F(A) in the discrete domain]/uploadpic/THESIS/2008/1/2008010712204755674Z.jpg[/IMG] Table 2 Membership function of F(P) in the discrete domain μF(P) F(P) P [IMG=Membership function of F(P) in the discrete domain]/uploadpic/THESIS/2008/1/2008010712205375818K.jpg[/IMG] Table 3 Membership function of F(D) in the discrete domain μF(D) F(D) d [IMG=Membership function of F(D) in the discrete domain]/uploadpic/THESIS/2008/1/2008010712210228983M.jpg[/IMG] Generally speaking, the larger the interrupted current, the higher the required opening speed; conversely, the smaller the interrupted current, the lower the required opening speed. However, when interrupting a small capacitive current (phase angle p close to -90°), the required opening speed should be greater than that for interrupting the same value of normal load current, in order to improve the dielectric recovery strength of the arc gap and avoid the occurrence of re-breakdown voltage. However, when interrupting a small inductive current (phase angle p close to 90°), a smaller opening speed is required to reduce the overvoltage that may be generated during operation [5, 6]. For a dual-input single-output fuzzy control system with current and phase as inputs and the equivalent orifice diameter d of the drain valve as output, based on expert knowledge and experience, different combinations of current and phase form different control rules. The table consisting of all the rules is called the fuzzy control rule table, as shown in Table 4. Table 4 Fuzzy Control Rule Table PA [IMG=Fuzzy Control Rule Table]/uploadpic/THESIS/2008/1/2008010712211119013L.jpg[/IMG] Each cell in Table 4 represents a rule. The table contains a total of 23 rules, each represented by a corresponding fuzzy condition statement. For example, the first and second cells in the upper left corner of the rule column can be represented by a single rule: "If A = NL or NM, and P = NL, then D = NS"; and the third cell represents "If A = NS, and P = NL, then D = PS". 2. Inference Rules and Calculation For a system with L control rules, there are two basic inference methods: the synthesis method and the parallel method. In the synthetic reasoning method, the corresponding fuzzy relation Rl (l = 1, 2, ..., L) is obtained from each rule, and the total fuzzy relation R = R1∪R2∪...∪RL is calculated from this. During control, based on the fuzzy sets A′ and P′ of the actual input (after discretization and fuzzification), fuzzy reasoning operations are performed using R to obtain the synthesized output fuzzy set D′ = (A′ × P′)R. The parallel reasoning method, on the other hand, obtains the corresponding output D′l = (A′ × P′)Rl based on each rule Rl, and then calculates the synthesized output fuzzy set D′ = D1′∪D2′∪...∪DL′. Using an appropriate defuzzification strategy, the precise value d of the control output can be obtained from the output fuzzy set. Since the calculation of the output D using fuzzy relations is complex and not convenient for online real-time control, the design of this fuzzy controller first obtains the correspondence table between input and output based on the given control rules and algorithm. During online control, the control output can be obtained simply by looking up the table based on the input parameter values. When using minimal fuzzy inference rules, the calculation process of the control table is as follows: (1) Assume the current discrete level is j and the phase is i. According to the membership function values ​​μF(A)(j) and μF(P)(i) of the fuzzy sets of current and phase obtained from Table 1 and Table 2, calculate the excitation intensity α = min{μF(A)(j) and μF(P)(i)} of the corresponding rule; (2) According to Table 3 and Table 4, use the fuzzy inference synthesis method to calculate the output fuzzy set Dl = min{α, μF(D)(k)}, l = 1, 2, ... 16; (3) Calculate D = D1∪D2∪...∪D16; (4) Use the centroid method to perform defuzzification operation to obtain the control output [IMG=control output]/uploadpic/THESIS/2008/1/20080107122149375258.jpg[/IMG] (5) Calculate d for all i and j respectively, and finally obtain the fuzzy control summary table, as shown in Table 5. Table 5 Fuzzy Control Summary Table PA [IMG=Fuzzy Control Summary Table]/uploadpic/THESIS/2008/1/2008010712211524072I.jpg[/IMG] The fuzzy control summary table is obtained through offline calculation and stored in the rule base of fuzzy control. During online control, it is only necessary to use the measured values ​​of input current a and phase p, discretize and quantize them into the corresponding universe of discourse, and then look up the table to obtain the actual control output d. It should be noted that Table 5 is calculated from Tables 1 to 4. If the values ​​of the membership functions of the relevant parameters or the control rule table change, the contents of Table 5 will change accordingly. Furthermore, the current and phase values ​​in Table 5 cover the entire universe of discourse. In actual circuit breaker operation, some breaking conditions in Table 5 will not occur. For example, when P = -4 (no-load long-line phase characteristic), A cannot be 14 (equivalent to the rated short-circuit current value). 3. Control Examples and Discussion In practical applications of fuzzy control, the current and voltage signals at the circuit breaker ports are picked up by current transformers and voltage transformers, respectively. After secondary voltage division, signal conditioning, and detection, the effective value of the current A and the phase difference P between the current and voltage are obtained. After universe of discourse transformation and quantization, these are input to the control unit. The control output can be immediately obtained by looking up a table, and the corresponding aperture d is adjusted through the drive mechanism, thereby obtaining the optimal circuit breaker opening speed. For example, for a circuit breaker with a rated short-circuit breaking current of 40kA, when breaking under normal load, if the measured current value is 3150 A (cosambar value after transformation) and the phase measurement is 28° (cosambar value after transformation), then referring to Table 5, the control output d = 9.9 mm. However, when breaking at the rated short-circuit breaking current, the measured current value is 40kA (cosambar value after transformation) and the phase is 82° (cosambar value after transformation), then the output d is 22.0 mm. For small-current breaking of unloaded long lines and unloaded transformers, if the measured current values ​​are both 31.5 A (cosambar value after transformation), and the phases are -90° and 90° respectively (cosambar values ​​after transformation are -4 and 4), then the output d are 11.9 mm and 11.2 mm respectively. These examples illustrate that the fuzzy controller can provide different outputs according to different breaking states of the system, thus enabling the circuit breaker to have different opening speeds. Reference [3] conducted a simulation analysis on an SF6 circuit breaker with a rated short-circuit breaking current of 40kA, and obtained the corresponding drain hole diameters that the circuit breaker can successfully break under different breaking conditions, as shown in Table 6. The breaking conditions in the table mainly include line charging current breaking (31.5 A) and BTF (terminal short-circuit fault) breaking (including four test modes: 10%Ike, 30%Ike, 60%Ike, and 100%Ike). It can be seen that for different breaking conditions, the fuzzy control output and the simulation analysis results are basically consistent (the difference in the numerical results is due to the different values ​​of the drain hole diameter universe of discourse). The above discussion discussed the influence of the breaking current value and its phase on the breaking speed. In actual control, other fuzzy input parameters can be added according to the specific situation. For example, for a dual-power system, other parameters and analysis methods can be used to add system out-of-step fault parameters to the fuzzy input parameters, and fault location technology can be used to distinguish near-end faults of the system in order to adjust the membership functions of the fuzzy sets of the input and output universes of discourse. The fuzzy control rule table can also be optimized based on the actual control effect to obtain the best control effect. Since the lookup table method is used, the implicit fuzzy inference operation is offline, so the online control speed is very fast. 4 Fuzzy Controller Hardware Structure and Working Principle The simplified structure of the fuzzy control system studied is shown in Figure 1. The grid voltage and the current flowing through the circuit breaker are picked up by PT and CT respectively, and sent to the digital processor through secondary voltage division, A/D converter and other links. In order to realize fast acquisition and digital filtering processing, the processor adopts a 32-bit high-speed digital signal processor TMS320C30. Since this processor has a very high processing speed (it can complete 33×106 floating-point operations per second), conventional numerical calculations and processing can be completed within ms [7], and its processing speed can fully meet the requirements of circuit breaker control. Table 6 Control Output d under Different Interruption Conditions [IMG=Control Output under Different Interruption Conditions]/uploadpic/THESIS/2008/1/2008010712213019782I.jpg[/IMG] [IMG=Block Diagram of Fuzzy Control System Structure]/uploadpic/THESIS/2008/1/20080107122138577787.jpg[/IMG] Figure 1 Block Diagram of Fuzzy Control System Structure After the processor is powered on and reset, it continuously collects current and voltage data. The collected results are stored in a designated RAM area in a first-in-first-out circular queue, thus ensuring that the data in the RAM area always reflects the latest state of the power grid. When the power system is fault-free, parameters such as bus voltage, loop current, and power factor can be measured by processing and calculating the collected values. When the circuit breaker performs a normal tripping operation (non-fault tripping), the tripping signal triggers the processor's INT0 interrupt. The interrupt service routine performs fuzzy inference based on the measured parameters and controls the opening of the drain valve based on the inference result, thereby enabling the circuit breaker to achieve a suitable tripping speed. When a fault occurs in the power system, the current in the power grid suddenly increases while the voltage suddenly decreases. If the changes in current and voltage exceed the set values, the waveform change detection circuit reacts quickly [8] and triggers the processor's INT1 interrupt. The INT1 interrupt service routine completes the acquisition of short-circuit current and voltage, and calculates the fundamental frequency component and attenuated DC component of the short-circuit current through digital filtering, so as to accurately perform fuzzy inference and output accurate control quantities to the regulating valve. Since the TMS320 processor has a very high processing speed, the above calculations and controls are completed before the relay protection device issues the tripping command. Because the INT1 interrupt signal is only generated when a fault occurs, the INT1 interrupt service routine can analyze the cause of the fault based on the parameter values ​​collected before and after the fault, as well as perform fault location and fault type analysis, providing a reliable technical means for reclosing operations. In this system, regardless of whether the power system is faulty, the collected data and calculation results can be transmitted to the microcomputer (host computer) through the serial interface. 5 Conclusion This paper presents a control system for the intelligent tripping operation of circuit breakers based on fuzzy theory. Its features are: ① It can automatically adjust the tripping speed of the circuit breaker according to the breaking conditions. ② It can achieve good coordination between the operating mechanism and the arc-extinguishing chamber, improve the reliability and service life of the hydraulic-mechanical device, and is conducive to the safe operation of other equipment. ③ As a high-performance, low-cost digital signal processor is used as the main control unit, the control system not only has good real-time performance and high reliability, but also low cost. For each ultra-high voltage circuit breaker worth hundreds of thousands or even millions, the control system does not exceed 2% of the total cost. The application of this system will bring about a major breakthrough in the operation technology of circuit breakers, which is of great significance in academic and engineering applications. References: [1] Ma Zhiying, Xu Liming, Li Zhi. 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Beijing: China Water Resources and Electric Power Press, 1995. [7] Wang Yanan. Principles and applications of TMS320 series high-speed single-chip microcomputer. Chengdu: University of Electronic Science and Technology of China Press, 1991. [8] Takamu G, Osamu N, Masaru I, et al. 400 Vclass high-speed current limiting circuit breaker for electric power system, IEEE Trans on Power Delivery, 1994, 9 (3): 1 428～1435.