Abstract: This paper studies the fuzzy optimization design problem of the output filter of the frequency converter based on the fuzzy set theory. The paper establishes the fuzzy constraint set of the filter inductance value and capacitance value according to the engineering constraint range of fundamental voltage drop, capacitor branch current and total harmonic distortion. The paper proposes a fuzzy optimization objective function with satisfaction as the comprehensive index. It is the weighted sum of cost factors, total harmonic distortion, capacitor harmonic current and inductor fundamental voltage drop. The solution method of the objective function is given. Simulation and example design show that the fuzzy optimization design results can not only meet the requirements of various performance indicators, but more importantly, the safety margin of the transmission system is improved. Keywords: frequency converter; filter; fuzzy optimization; reliability 1 Introduction There are some negative effects in the application of frequency converter-motor system: the harmonic current in the motor is too large, which leads to the increase of motor heat generation and shortens the motor life; in the case of using long cable, the overvoltage at the motor end is caused by the voltage reflection of the cable terminal, which harms the insulation performance of the motor and, in severe cases, leads to motor insulation breakdown and cable bursting [1]. In practical applications, filters are often used at the output of the frequency converter to eliminate or mitigate the above negative effects [2]. The structure of the sinusoidal filter is shown in Figure 1. By properly selecting the filter parameters, the output voltage of the frequency converter can be filtered into an approximate sinusoidal waveform with a total harmonic distortion of less than 5%. Cables that can be several kilometers long can be used without the phenomenon of overvoltage at the motor end caused by voltage reflection [1]. The filter design process includes engineering design and optimization design. In the engineering design, the limitations of the frequency converter motor system on the filter parameters should be considered so that the addition of the filter has the least impact on the system, thereby ensuring the safe operation of the system. Therefore, the filter parameters must meet the limitations of the frequency converter-motor system. The parameters obtained at this time are often not optimal and need to be optimized to comprehensively consider the influence of various factors. In the optimization design process of the frequency converter output filter, the limitations of the frequency converter-motor system on the filter parameters are generally used as the constraints of the optimization model. These constraints include the reasonable range of indicators such as the fundamental voltage drop on the filter, the high-frequency harmonic current in the filter capacitor branch, the fundamental current in the filter capacitor branch, and the cutoff frequency. Based on the above constraints, the constraints of the filter inductor and filter capacitor can be determined. In typical engineering designs, the fundamental voltage drop is approximately 5%, the high-frequency harmonic current is approximately 10% to 20% of the inverter's rated current, and the fundamental current in the capacitor branch is approximately below 10% of the inverter's rated current. However, in conventional optimization processes, these constraints are considered rigid, and the optimized parameters often fall within the boundaries of these constraints. Since these constraints are derived from the perspective of inverter safety, when component parameters are taken at the boundaries of these constraints, the system operates on the boundary between the safe and dangerous operating zones. While some objectives may be optimal, the system's safety performance decreases. When component parameters change, the system may operate in the dangerous operating zone, leading to inverter system protection actions or even damage. In this paper, fuzzy set theory is used to describe the fuzziness of the constraints, and symmetric fuzzy optimization is employed to optimize the established multi-objective function. The symmetric fuzzy optimization process essentially seeks the maximum satisfaction with both the fuzzy constraint set and the fuzzy objective set, thus balancing the optimization of the objectives with the maximum membership degree to the fuzzy constraint set. The optimized parameters satisfy the fuzzy constraint set to the greatest extent possible, so they do not appear on the boundary of the constraint set, thus improving the system's safety performance and increasing the tolerance range of component parameters. 2. Membership Functions of Fuzzy Sets Commonly Used in Fuzzy Optimization In fuzzy optimization, trapezoidal membership functions are commonly used, defined as shown in Figures 2 to 4. When using fuzzy optimization, the boundaries of the constraints are fuzzy, specifically manifested in a transition zone between the allowable and rejection regions.