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1 ISSN (Print) / ISSN (Online) The Transactions of the Korean Institute of Electrical Engineers Vol. 64, No. 8, pp. 1180~1185, 전압적분법을이용한 SRM 의자동화된인덕턴스측정 Automated Inductance Measurement of a Switched Reluctance Motor Using Voltage Integration Method 노정민 * 김재혁 (Jeongmin Noh Jaehyuck Kim) Abstract This paper describes the accurate inductance measurement of a switched reluctance motor (SRM). Conventionally, the inductance of the SRM is measured using the equivalent circuit of a stator phase or time constant of exponential current transient. This paper presents an effective method to measure the SRM inductance accurately and rapidly using automated voltage integration. The proposed method is validated experimentally by comparison with the existing equivalent circuit method (ECM) and the FEA(finite element analysis) simulation. Key Words : Inductance measurement, Switched reluctance motor, Voltage integration method 1. 서론 SRM은가격이저렴하고고신뢰성, 고내구성, 단순한구조등의장점과함께과직류직권전동기와유사한속도-토크특성을가지고있어산업기기, 항공기, 선반뿐만아니라자동차전동부품등의다양한분야에점차적용이확대되고있다 [1]. 단점인고유의토크리플과소음은지속적인연구개발을통하여개선되고있으며, 릴럭턴스토크를극대화하기위해회전자와고정자모두돌극형의구조를가지며권선은고정자에만집중권으로감겨있어전자계구조상여자전원이각상권선에독립적이고순차적으로인가되어구동되므로낮은스위칭주파수로운전이가능하여고속운전이가능한장점이있는반면회전자위치에따른적절한스위칭동작을위해서는회전자위치각에대한정보를검출하기위한위치검출장치가필수적이라는취약점을가지고있다 [2]. 이러한 SRM의최적제어를위해서는필수적으로정확한인덕턴스의값을측정하는것이중요하다. SRM의인덕턴스는회전자의위치와여자전류의함수로써드라이브의성능을결정하는중요한파라미터이다 [3]. 기존의인덕턴스측정방법에는등가회로를이용하여측정하는방법, 시정수를이용하여측정하는방법, 쇄교자속을직접측정하는방법 [4], 전류를쵸핑하여측정하는방법 [5], AC중첩방법 (AC Superposition)[6] 등이있다. 등가회로방법은정밀한 AC 전압공급기가필요하며 SRM 고주파스위칭에대한주파수응답특성을제대로반영하지못하는단점이있으며시정수방법은적절한시정수조절을위해외부저항이 필요하다. 쇄교자속을직접측정하는방법은자기센서를이용하여모터가조립될때모터의내부에설치해야하는불편과높은비용으로인한단점이있고전류를쵸핑하여측정하는방법은쵸핑구간에서의제한된스위칭주파수와일정하지않은증가시간과감소시간에서의계산으로인한오차가발생한다. AC중첩방법 (ACS) 은 DC전류에작은진폭의 AC 전류를중첩시킨후 AC 전류는고정밀전류계로 AC 전압은멀티미터로측정되는값을계산하여인덕턴스를얻는다. 본논문에서는등가회로를이용한측정법 (ECM : Equivalent Circuit Method) 과본논문에서제시할전압적분법 (VIM : Voltage Integration Method) 을비교분석하였다. 2. 등가회로를이용한 SRM의인덕턴스측정법와전류를고려한 SRM의한상의등가회로를이용하여인덕턴스를측정하는방법 [7] 은그림 1에도시된바와같다. Corresponding Author : Dept. of Electrical Engineering Wonkwang University, Korea jaehkim@wku.ac.kr * Dept. of Electrical Engineering, Wonkwang University, Korea Received : March 2, 2015; Accepted : July 27, 2015 그림 1 와전류가포함된 SRM 한상의등가회로 Fig. 1 Per-Phase equivalent circuit of an SRM including the eddy current 1180 Copyright c The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( licenses/by-nc/3.0/)which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Trans. KIEE. Vol. 64, No. 8, AUG, 2015 그림 1 은정지된상태에서 SRM 의등가회로이며, 는상전압, 는상전류, 은권선의유도성전압, 은자화전류, 는와전류, 은고정자권선의저항, 는와전류가흐르는저항, 고정자권선의인덕턴스이다. 그림 1의등가회로에서의전력관계는다음과같다. (1) (2), (3) 여기서 는전체유효전력, 은동손, 는와전류손, 는상전류의실효치이다. 과 의관계는다음과같다., 여기서 은 의실효치이며, 식 (4) 로부터 는아래와같다.,,, 및 은오실로스코프를통하여직접측정을할수있고, 식 (3) 으로부터 를얻을수있으며옴의법칙에의하여아래와같이와전류와자화전류를다음과같이계산할수있다. (6) (7) 최종적으로고정자권선의인덕턴스는식 (8) 과같이구할수있다. (4) (5) 이표현되며 (10) 여기서, 는쇄교자속, 는상전류, 는회전자위치각이다. 임의의시간 에서쇄교자속을산출하기위해식 (10) 의양변을적분하면 (11) 이며이때 는초기쇄교자속이다. 만약초기쇄교자속이 0이고회전자의위치를알면쇄교자속은전류만의함수로표현할수있다. (12) 또한인덕턴스는식 (12) 의쇄교자속을전류로나누어얻을수있다. (13) 식 (12) 우변의적분은그림 2와같이상전압과상전류파형의정적분을통하여다음과같이계산될수있다. (14) 여기서 ( ) 는측정하고자하는상전류지령치, (8) (9) 여기서 은 의실효치이다. 3. 전압적분법을이용한 SRM 의인덕턴스측정법 SRM의전압방정식을적분하여쇄교자속을얻는방법 [3, 8] 은등가회로를이용한방법에비하여좀더빠르고정밀하게인덕턴스를측정할수있으며, 그림 2에도시된본논문에서제안하는자동화된전압적분법은다음과같다. SRM의한상의쇄교자속의시간에따른변화율은다음과같 그림 2 전압적분법에의한 SRM의상전압및상전류파형 Fig. 2 Phase voltage and current waveforms of an SRM by the voltage integration method 전압적분법을이용한 SRM 의자동화된인덕턴스측정 1181

3 전기학회논문지 64 권 8 호 2015 년 8 월 ( ) 이며, 최대지령전류를 로설정한다. 그림 2와같이상권선에전압을인가하면전류가상승하면서최대지령치전류 에도달할때까지각전류지령치에도달할때마다그구간 ( ) 에서의상전류와상전압파형의면적은각각 과 이다. 그림 3은전압적분법에의해 SRM의인덕턴스측정을위한실제상전압및상전류파형이며상권선에전압을인가하여전류지령치에도달했을때스위치를오프하여지령치에도달했을때까지의전압파형면적과전류파형의면적을연산처리하여각지령전류에서의인덕턴스를얻을수있다. 측정하고자하는 SRM의회전자를그림 5와같은구속시험장치에고정시킨후회전자의위치를 1 단위로변화시켜인덕턴스를측정하였다. Phase Voltage (100V/div) Final Current Command Phase Current (1A/div) Time (1ms/div) 그림 3 전압적분법에의한 SRM의상전압및상전류실험파형 Fig. 3 Measured phase voltage and current waveforms of an SRM by the voltage integration method 그림 5 모터회전자구속시험장치 Fig. 5 Locked rotor test equipment 4. 실험결과제안한 VIM을검증하기위해 2개의시제품 SRM의인덕턴스를 ECM과 VIM을이용하여각각측정하였다. 측정한결과를유한요소해석 (Finite element analysis, FEA) 시뮬레이션을통하여얻어낸인덕턴스데이터와비교하였다 kW 3상 SRM의인덕턴스측정 그림 4는전압적분법을이용하여인덕턴스를측정하기위한장치에대한개념도이다. 그림 5에나타낸모터구속장치를사용하여 SRM의회전자를고정시키고, 비대칭브리지컨버터를사용하여한상의권선에펄스전압을인가하여, 이때의흐르는상전류와상전압을측정한다. 미리설정해놓은전류지령치에도달할때실제상전류와상전압을측정하고적분연산을수행하여인덕턴스를자동으로계산하여메모리에저장시킨다. 따라서, 주어진회전자위치에대하여최대전류범위의내의다양한전류변화에따른쇄교자속및인덕턴스를얻을수있게된다. 이와같은자동화된연속적인측정프로세스를마이크로컨트롤러에프로그래밍하여 SRM의인덕턴스를보다정확하고빠르게측정할수있게된다. 그림 6과표 1은인덕턴스측정에사용한첫번째시제품모터인 15kW 3상 SRM의형상과제원이다. 그림 6 인덕턴스측정을위한 15kW SRM 모델 Fig. 6 15kW SRM for Inductance measurement 그림 4 다양한상전류에대한인덕턴스값을얻기위해 SRM의상전압및상전류측정 Fig. 4 Measurement of phase current and voltage to obtain inductance data with respect to difference current 15kW 3상 SRM의여자주기는 90 이며 5 씩회전자위치를변화시켜인덕턴스를측정하였다. 그림 7은 FEA 시뮬레이션을통하여얻어낸 10A, 15A, 20A, 25A의상전류변화에따른인덕턴스그래프이다. 그림 7의인덕턴스그래프에서각각의상전류는포화상태에도달하지못해상전류변화에따른인덕턴스값에큰차이가나지않는다. 그림 7과그림 8은 ECM과 VIM을이용하여각각측정한인덕턴스그래프이며, 회전자가고정자와정렬 (aligned) 된위치인 0 에서부터비정렬 (unaligned) 된위치인 45 를지나그다음정렬 (aligned) 된위치인 90 까지인덕턴스의 1182

4 Trans. KIEE. Vol. 64, No. 8, AUG, 2015 표 1 15kW SRM 제원 Table 1 15kW SRM Specification Parameter Value Unit Input voltage 300 V Rated power 1,500 W Rated speed 12,000 r/min Number of phases 3 - Number of stator poles 6 - Number of rotor poles 4 - Stator outer diameter 180 mm Stack length 60 mm Phase winding resistance Ω 치에서 ECM과 VIM 모두 FEA와근소한차이를보였으며 ECM 의경우정렬 (aligned) 된위치에서 FEA와 VIM 비교결과보다오차가큼을알수있다. 25A일때인덕턴스프로파일비교결과비정렬 (unaligned) 된위치에서 ECM과 VIM 모두 FEA와근소한차이를보였으며 ECM의경우정렬 (aligned) 된위치에서는 10A에서의 FEA와 VIM 비교결과보다오차가더욱큼을알수있다. 그림 9 VIM을이용하여측정한 15kW SRM의인덕턴스프로파일 Fig. 9 Measured Inductance profiles of 15kW SRM using VIM 그림 7 FEA 시뮬레이션을이용하여얻은15kW SRM의인덕턴스프로파일 Fig. 7 Inductance profiles of 15kW SRM obtained from FEA simulation 그림 10 10A에서세가지방법에의한 15kW SRM의인덕턴스프로파일비교 Fig. 10 Comparison of inductance profiles of 15kW SRM at 10A by three different methods 그림 8 ECM을이용하여측정한 15kW SRM의인덕턴스프로파일 Fig. 8 Measured Inductance profiles of 15kW SRM using ECM 프로파일을보여준다. 그림 7의 ECM 측정결과를 FEA와비교해볼때정렬 (aligned) 된위치일수록오차가심해지는반면그림 8 의 VIM은 FEA와유사한프로파일경향을보인다. 측정결과를좀더자세히비교하기위해상전류 10A와 25A에서 FEA, ECM, VIM 측정결과를비교한그래프는그림 10과그림 11과같다. 10A 일때인덕턴스프로파일비교결과비정렬 (unaligned) 된위 그림 11 25A에서세가지방법에의한 15kW SRM의인덕턴스프로파일비교 Fig. 11 Comparison of inductance profiles of 15kW SRM at 25A by three different methods 전압적분법을이용한 SRM 의자동화된인덕턴스측정 1183

5 전기학회논문지 64 권 8 호 2015 년 8 월 W 2 상 SRM 의인덕턴스측정 그림 12와표 2는인덕턴스측정에사용한두번째시제품모터인 15kW 2상 SRM의형상과제원이다. 스프로파일비교결과정렬 (aligned) 된위치에서다음정렬 (aligned) 된위치까지 FEA와근소한차이를보였으나 ECM의경우 FEA와 VIM 비교결과보다오차가큼을알수있다. 그림 12 인덕턴스측정을위한 50W SRM 모델 Fig W SRM for Inductance measurement 표 2 50W SRM 제원 Table 2 50W SRM Specification Parameter Value Unit Input voltage 170 V Rated power 50 W Rated speed 1,600 r/min Number of phases 2 - Number of stator poles 8 - Number of rotor poles 10 - Stator outer diameter 82.5 mm Stack length 16 mm Phase winding resistance Ω 50W 2상 SRM의여자주기는 36 이며 2 씩회전자위치를변 화시켜인덕턴스를측정하였다. 그림 13은 FEA 시뮬레이션을통 하여얻어낸 1A, 1.5A, 2A, 2.5A의상전류변화에따른인덕턴스 그래프이다. 그림 14와그림 15는 ECM과 VIM을이용하여각각 측정한인덕턴스그래프이며, 회전자가고정자와정렬 (aligned) 된 위치인 0 에서부터비정렬 (unaligned) 된위치인 16 를지나그 다음정렬 (aligned) 된위치인 36 까지인덕턴스의프로파일을보 여준다. 그림 14의 ECM 측정결과를 FEA와비교해볼때정렬 (aligned) 된위치에서다음정렬 (aligned) 된위치까지오차가발 생한반면그림 15의 VIM은 FEA와유사한프로파일경향을보 인다. 측정결과를좀더자세히비교하기위해상전류 1A와 1.5A 에서 FEA, ECM, VIM 측정결과를비교한그래프는그림 16과 그림 17과같다. 1A 일때인덕턴스프로파일비교결과정렬 (aligned) 된위치에서 ECM과 VIM 모두 FEA와근소한차이를 보였으며 ECM의경우비정렬 (unaligned) 된위치에서 FEA와 VIM 비교결과보다오차가큼을알수있다. 1.5A일때인덕턴 그림 13 FEA 시뮬레이션을이용하여얻은 50W SRM의인덕턴스프로파일 Fig. 13 Inductance profiles of 50W SRM obtained from FEA simulation 그림 14 ECM을이용하여측정한 50W SRM의인덕턴스프로파일 Fig. 14 Measured Inductance profiles of 50W SRM using ECM 그림 15 VIM을이용하여측정한 50W SRM의인덕턴스프로파일 Fig. 15 Measured Inductance profiles of 50W SRM using VIM 1184

6 Trans. KIEE. Vol. 64, No. 8, AUG, 2015 그림 16 1A에서세가지방법에의한 50W SRM의인덕턴스프로파일비교 Fig. 16 Comparison of inductance profiles of 50W SRM at 1A by three different methods 그림 A에서세가지방법에의한 50W SRM의인덕턴스프로파일비교 Fig. 17 Comparison of inductance profiles of 50W SRM at 1.5A by three different methods [2] M. Ehsani, I. husain, and A.B. Kulkarni, Elimination of Discrete Position Sensor and Current Sensor in Switched Reluctance Motor Drives, IEEE Trans on IA, Vol. 28, pp , Feb [3] R. Krishnan and P. Materu, Measurement and Instrumentation of a Switched Reluctance Motor, IEEE IAS Annual Meeting, vol. 1, pp , October [4] J. C. Prescot and A. El-Khavashi, A method for measuring self inductances applicable to large electrical machines, Proc. Inst. Electr. Eng.,vol. 106, pt. A, pp , Apr [5] R. Krishnan, Switched Reluctance Motor Drives -Modeling, Simulation, Analysis, Design and Applications. Boca Raton, FL :CRC, [6] R. Gobbi, N.C. Sahoo, and R. Vejian, Experimental Investigations on Computer-Based Method for Determination of Static Electromagnetic Characteristics of Switched Reluctance Motors, IEEE Trans. Instrum. Meas., vol.57, no. 10, pp , Oct [7] K. Ha, S.-G. Oh, B. MacCleery, and R. Krishnan, An automated reconfigurable FPGA-based magnetic characterization of switched reluctance machines, in Proc. IEEE ISIE, pp , June [8] Benjamin Rudolph, Nonlinear Deadbeat Current Control of a Switched reluctance Motor, MS thesis, Virginia Tech, Nov 결론 본논문에서는 SRM의인덕턴스를측정하기위하여등가회로를이용한측정법과전압적분법을이용한측정법을제시하였다. 15kW SRM과 50W SRM 두시제품을이용하여제시한두가지방법을비교한결과고정자와회전자간의정렬 (aligned) 구간에서비정렬 (unaligned) 구간그리고전류가높아질수록마이크로컨트롤러를사용하여자동화된전압적분법을이용한측정법이등가회로를이용한측정법보다정확한결과를보였다. 등가회로를이용한측정법이전압적분법보다오차가발생한이유는등가회로를이용한측정법은전류및전압을계측기를통하여측정자가수동으로측정하고계산하는과정에서측정오차가발생하였고이부분이오차발생의가장큰요인중하나이다. 두측정방법모두측정시험동안높은전류에서의온도상승에따른상권선의저항변화는고려되지않았고추가로개선하기위해차폐회로및오차를좀더개선할수있는방안을모색할필요가있다. References [1] Bimal K. Bose, Power Electronics and Motor Drives Recent Progress and Perspective, IEEE Trans. Ind. Electron., Vol. 56, No. 2, pp , Feb 저자소개 노정민 (Jeongmin Noh) 1985년 4월 30일생. 2012년원광대전기전자및정보공학부졸업. 2013년 ~2014년 Hexpower system, 기술지원팀 2014년 ~ 현재동대학원전기공학과석사과정 Tel : rismajung7@gmail.com 김재혁 (Jaehyuck Kim) 1973년 4월 25일생. 1992년한양대전기공학과졸업. 1998년 ~ 2000년 UL Korea, Engineer, 2004년 Univ. of Wisconsin at Madison 졸업 ( 석사 ), 2010년 Virginia Tech 졸업 ( 박사 ), 2010년 Ramu Inc. Senior Engineer, 현재원광대학교전기공학과교수 Tel : jaehkim@wku.ac.krㅛ 전압적분법을이용한 SRM 의자동화된인덕턴스측정 1185

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