권선 및 샤프트 간 결합 특성을 고려한 3상 유도 전동기의 수동 매크로모델 = Passive Macromodel of a Three-Phase Induction Motor Considering Winding-to-Shaft Coupling Characteristics

다국어 초록 (Multilingual Abstract)

In electric vehicle drive systems, high-speed switching of the inverter can induce common-mode （CM） current, shaft voltage, bearing voltage, and bearing current through parasitic coupling paths inside the motor. These phenomena are closely related to electromagnetic compatibility （EMC） issues in electrified propulsion systems. To analyze such high-frequency phenomena, a broadband model that considers not only the three-phase winding terminals of the motor but also the shaft- and bearing-related paths is required. However, conventional high-frequency motor models are often constructed based on specific impedance characteristics or specific responses, which limits their ability to directly represent broadband port-to-port coupling characteristics between the winding terminals and the shaft terminals.
In this thesis, a five-port S-parameter-based macromodeling method is proposed to represent the high-frequency coupling characteristics between the winding terminals and the shaft terminals of a motor based on measurement data and to utilize the model for time-domain analysis. For this purpose, a five-port network was defined, including the three-phase winding terminals U, V, and W, and the drive-end （DE） and non-drive-end （NDE） shaft terminals of an induction motor. Considering the measurement environment in which the complete five-port S-parameters cannot be directly measured using a two-port network analyzer, partial two-port S-parameter measurements were performed for multiple port combinations. The unmeasured ports were terminated with auxiliary loads, and an S-parameter matrix renormalization technique was applied to account for the frequency-dependent impedance characteristics of the auxiliary loads.
Through the renormalization process, a five-port S-parameter matrix including the coupling characteristics among the three-phase windings and shaft terminals was obtained. The extracted five-port S-parameters were converted into a macromodel using rational approximation based on the AAA algorithm for application to time-domain circuit simulation. The measured frequency responses were represented as a sum of poles and residues, and a SPICE netlist macromodel was generated through passivity verification and enforcement. Frequency-domain comparison results showed that the macromodel generally reproduced the five-port S-parameter responses obtained through renormalization.
To verify the validity of the model in the time domain, input conditions were selected based on the comparison of the BVR frequency responses, and the measured common-mode input voltage waveforms were applied to the macromodel to calculate the bearing voltage response. Comparison between the measured and simulated waveforms showed that although some differences existed in the magnitude of the bearing voltage, the main waveform shape and temporal variation trend were generally similar. These results confirm that the proposed five-port S-parameter-based macromodel can be utilized to reproduce the time-domain bearing voltage response according to the input voltage.

국문 초록 (Abstract)

전기차 구동 시스템에서 인버터의 고속 스위칭은 전동기 내부의 기생 결합 경로를 통해 공통모드（Common Mode, CM） 전류, 샤프트 전압, 베어링 전압 및 베어링 전류를 유발할 수 있으며, 이는 전동화 시스템의 전자기 적합성（Electromagnetic Compatibility, EMC） 문제와 밀접하게 관련된다. 이러한 고주파 현상을 해석하기 위해서는 전동기의 3상 권선 단자뿐만 아니라 샤프트 및 베어링 관련 경로를 함께 고려한 광대역 모델이 필요하다. 그러나 기존의 전동기 고주파 모델은 특정 임피던스 또는 특정 응답을 중심으로 구성되는 경우가 많아, 권선 단자와 샤프트 단자 사이의 광대역 포트 간 결합 특성을 직접적으로 표현하는 데 한계가 있다.
본 논문에서는 전동기의 권선 단자와 샤프트 단자 사이의 고주파 결합 특성을 측정 기반으로 표현하고, 시간 영역 해석에 활용하기 위한 5포트 S-파라미터 기반 매크로모델링 방법을 제안한다. 이를 위해 유도 전동기의 3상 권선 단자인 U, V, W와 구동측（Drive End, DE） 및 비구동측（Non-Drive End, NDE） 샤프트 단자를 포함하는 5포트 네트워크를 정의하였다. 전체 5포트 S-파라미터를 직접 측정할 수 없는 2포트 네트워크 분석기 환경을 고려하여, 여러 포트 조합에 대한 부분 2포트 S-파라미터 측정을 수행하였다. 측정하지 않는 포트는 보조 부하로 종단하였으며, 보조 부하의 실제 임피던스가 주파수에 따라 변화하는 특성을 반영하기 위해 S-파라미터 행렬 재정규화 기법을 적용하였다.
재정규화 과정을 통해 3상 권선 및 샤프트 간 결합 특성을 포함하는 5포트 S-파라미터 행렬을 도출하였다. 도출된 5포트 S-파라미터는 시간 영역 회로 시뮬레이션에 적용하기 위해 AAA 알고리즘 기반 유리함수 근사를 이용하여 매크로모델로 변환하였다. 측정된 주파수 응답은 극점과 유수의 합으로 표현하였으며, 수동성 검토 및 보정 과정을 거쳐 SPICE 넷리스트 형태의 매크로모델을 생성하였다. 주파수 영역 비교 결과, 매크로모델은 재정규화로 도출된 5포트 S-파라미터 응답을 전반적으로 재현하였다.
시간 영역에서의 모델 유효성을 확인하기 위해 BVR 주파수 응답 비교 결과를 바탕으로 입력 조건을 선정하고, 실제 측정된 공통모드 입력 전압 파형을 매크로모델에 인가하여 베어링 전압 응답을 계산하였다. 측정 파형과 시뮬레이션 파형을 비교한 결과, 베어링 전압의 크기에는 일부 차이가 존재하였으나, 주요 파형 형태와 시간적 변화 경향은 전반적으로 유사하게 나타났다. 이를 통해 제안한 5포트 S-파라미터 기반 매크로모델이 입력 전압에 따른 시간 영역 베어링 전압 응답을 재현하는 데 활용될 수 있음을 확인하였다.

목차 (Table of Contents)

• 제1장 서 론 ··········································································································1
• 제1절 연구의 배경 및 목적 ·········································································1
• 제2절 연구의 범위 및 방법 ·········································································4
• 제2장 재정규화를 이용한 S-파라미터 측정 ···············································7
• 제1절 S-파라미터 행렬 재정규화를 활용한 다단자망 네트워크 파라미터 측정 ··········································································································8
• 1. S-파라미터 행렬 재정규화 기법 ······················································8
• 2. S-파라미터 행렬 재정규화 기법 적용 과정 ······························· 10
• 제2절 2.2kW 유도 전동기 S-파라미터 측정 및 재정규화 ··············13
• 1. 측정 셋업 ·······························································································13
• 2. 1차 재정규화 과정 ··············································································20
• 3. 2차 재정규화 과정 ··············································································36
• 제3장 유리함수 근사 매크로모델링 ····························································45
• 제1절 유리함수 근사의 절차 및 수식 표현 ··········································46
• 1. 유리함수 근사 수식 표현 ··································································46
• 2. 유리함수 근사 과정 ············································································47
• 제2절 유리함수 근사 매크로모델 추출 및 주파수 영역 검증 ········ 50
• 1. 매크로모델 추출 과정 ········································································50
• 2. 주파수 영역에서의 매크로모델 검증 ·············································52
• 제3절 시간 영역 베어링 전압 파형 검증 ··············································56
• 제4장 결 론 ········································································································69
• 참 고 문 헌 ··································································································71
• ABSTRACT ······································································································77