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Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and PSO
9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and Control 9th IFAC Conference on Manufacturing Modelling, Management and Control Berlin, Germany, August 28-30, 2019 Available 9th IFAC Conference on Manufacturing Modelling, Management and online at www.sciencedirect.com Control Berlin, Germany, August 28-30, 2019 9th IFAC Conference on Manufacturing Modelling, Management and Control Berlin, Germany, August 28-30, 2019 Control Berlin, Germany, August 28-30, 2019 Berlin, Germany, August 28-30, 2019
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IFAC PapersOnLine 52-13 (2019) 2372–2377 Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and Lifetime Improved in Power for BLDC Drives using Fuzzy Logic and Lifetime Improved in Power Electronics Electronics for BLDC Drives using Fuzzy Logic and PSO Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and PSO PSO Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and PSO PSO
Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro A. Soriano**, Molina**, BrianNacional, MacCleery***, DavidMéxico. Romero* * Escuela Superior de Ponce**, IngenieríaLuis Mecánica y Eléctrica, Instituto Politécnico México City, Arturo * Escuela Superior de Ponce**, IngenieríaLuis Mecánica y Eléctrica, Instituto Politécnico Nacional, México City, México. Manuel García*, Pedro A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* e-mail: {magarcial, dromero} @ipnc.mx). * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto Politécnico Nacional, México City, México. e-mail: {magarcial, dromero} @ipnc.mx). * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto PolitécnicoMéxico Nacional, México City, México. ** Escuela de Ingeniería y Ciencias, Tecnológico [email protected]). Monterrey, City, México e-mail: {magarcial, dromero} * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto PolitécnicoMéxico Nacional, México City, México. ** Escuela de Ingeniería y Ciencias, Tecnológico [email protected]). Monterrey, City, México e-mail: {magarcial, dromero} {pedro.ponce, larturo.soriano, armolina} @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico de Monterrey, México City, México e-mail: {magarcial, dromero} @ipnc.mx). {pedro.ponce, larturo.soriano, armolina} @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico de Monterrey, México City, México ***National Instruments, Austinarmolina} Texas, USA {pedro.ponce, larturo.soriano, @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico dearmolina} Monterrey, México City, México ***National Instruments, Austin Texas, USA e-mail: {pedro.ponce, larturo.soriano, @tec.mx). e-mail: {brian.maccleery}@ ni.com). ***National Instruments, Austin Texas, USA e-mail: ***National {pedro.ponce, larturo.soriano, armolina} @tec.mx). e-mail: {brian.maccleery}@ Instruments, Austin ni.com). Texas, USA e-mail: {brian.maccleery}@ ni.com). ***National Instruments, Texas, USA in several applications such as e-mail: {brian.maccleery}@ ni.com). Abstract: The brushless direct current drives (BLDC) are Austin extremely popular Abstract: The brushless direct current drives (BLDC) are extremely popular in several applications such as e-mail: {brian.maccleery}@ ni.com). robotics, and manufacturing, lifetime power electronics special attention in Abstract: transportation, The brushless direct current drives the (BLDC) are of extremely popular indeserves several applications such as robotics, transportation, and manufacturing, the lifetime power electronics deserves special attention in Abstract: The brushless so direct current (BLDC) are of extremely popular several such as industrial applications, this paper drives explores how the lifetime iselectronics affectedinwhen theapplications reference speed is robotics, transportation, and manufacturing, the lifetime of power deserves special attention in Abstract: The brushless direct current drives (BLDC) are extremely popular in several applications such as industrial applications, so this paper explores how the lifetime is affected when the reference speed is robotics, transportation, andthis manufacturing, theishow lifetime of powerpaper electronics deserves in changed when a conventional speed controller deployed. This illustrates how tospecial designattention anspeed optimal industrial applications, so paper explores the lifetime is affected when the reference is robotics, transportation, and manufacturing, the lifetime of power electronics deserves special attention in changed when a conventional speed controller is deployed. This paper illustrates how to design an optimal industrial applications, sologic thisspeed paper explores how the lifetime is affected thetoreference speed is controller based on fuzzy and Particle Swarm Optimization (PSO). The when optimized controller reaches changed when a conventional controller is deployed. This paper illustrates how design an optimal industrial applications, sologic thisspeed paper explores the lifetime is affected thetoreference is controller based on fuzzy and Particle Swarm Optimization (PSO). The when optimized controller reaches changed when a conventional controller ishow deployed. Thisinpaper illustrates how design anspeed optimal the reference speed at thelogic same timeParticle it keeps the temperature the semiconductors of controller the BLDC within controller based on fuzzy and Swarm Optimization (PSO). The optimized reaches changed when a conventional speed controller is deployed. Thisinpaper illustrates how of to controller design an optimal the reference speed at thelogic same timeParticle it keeps the temperature the semiconductors the BLDC within controller based on fuzzy and Swarm Optimization (PSO). The optimized reaches minimum variations to the preserve the in a minimum value ininthe power electronics of stage, the lifetime the reference speed at sameand timeloses it keeps the temperature the semiconductors the so BLDC within controller based on fuzzy logic Particle Optimization (PSO). The optimized controller reaches minimum variations to the preserve the in aSwarm minimum value ininthe power electronics stage, the lifetime the reference speed at same timeloses it keeps the temperature the semiconductors the so BLDC within of the power electronic stage is incremented. A co-simulation of BLDC, which is a of powerful simulation minimum variations to preserve the loses in a minimum value in the power electronics stage, so the lifetime the reference speed at the same timeloses it keeps the temperature inthe thepower semiconductors the so BLDC within of the power electronic stage is incremented. A co-simulation of BLDC, which is a of powerful simulation minimum variations to preserve the in a minimum value in electronics stage, the lifetime tool getting similar result experimental A tests is presented.ofThe validate proposedsimulation optimized of theforpower electronic stage to is incremented. co-simulation the results BLDC,electronics which isthe a stage, powerful minimum variations to preserve the loses in a minimum value in the power so the lifetime tool getting similar result to experimental A tests is presented.ofThe validate proposedsimulation optimized of thefor power stage isincrement incremented. co-simulation the results BLDC, which isthe ainpowerful controller as electronic well as show theto in the lifetime of the power electronic stage the BLDC. tool getting similar result experimental tests is presented. The validate proposed optimized of thefor power stage isincrement incremented. A co-simulation the results BLDC, which isthe ainpowerful simulation controller as electronic well as show theto in the lifetime of the of power electronic stage the BLDC. tool for getting similar result experimental tests is presented. The results validate the proposed optimized controller as well as show the increment in the lifetime of the power electronic stage in the BLDC. Keywords: logic controller, Particle optimization, Lifetime, Electric Drive. tool for getting similar result toincrement experimental tests isswarm presented. The results validate theAll optimized © 2019, IFAC (International Federation ofinAutomatic Control) Hosting by Elsevier Ltd. rights reserved. controller asBLDC, well asFuzzy show the the lifetime of the power electronic stage inproposed the BLDC. Keywords: BLDC, Fuzzy logic controller, Particle swarm optimization, Lifetime, Electric Drive. Keywords:asBLDC, controller,inParticle swarm optimization, Lifetime, Electric controller well asFuzzy show logic the increment the lifetime of the power electronic stage in theDrive. BLDC. Keywords: BLDC, Fuzzy logic controller, Particle swarm optimization, Lifetime, Electric Drive. Keywords: BLDC, Fuzzy logic controller, Particle swarm Electric Drive. the optimization, cooling by theLifetime, circulation of liquid through the heat sink. 1. INTRODUCTION the cooling by the circulation of liquid through the heat sink. However, are circulation no reports that show how a speed controller the coolingthere by the of liquid through the heat sink. 1. INTRODUCTION However, there are circulation no reports that show how a speed controller 1. INTRODUCTION the cooling by the of liquid through the heat sink. can be optimized for keeping the temperature in the Nowadays, electric brushless drives have been used in several However, there are no reports that show how a speed controller 1. INTRODUCTION the cooling by the circulation of liquid through the heat can be optimized for keeping the how temperature in sink. the Nowadays, electric brushless drives have been used in several However, there are no reports that show a speed controller 1. INTRODUCTION semiconductors without temperature ripples. application such as robotics, N (1990), manufacturing be optimized for keeping the temperature in the Nowadays, electric brushlessHemati, drives have been used in several can However, there are no reports that show how a speed controller semiconductors without temperature ripples. application such as robotics, Hemati, N (1990), manufacturing can be optimized fortemperature keeping the temperature in the Nowadays, electric brushless drives have been used several semiconductors process, Shieh (2001) and Hemati, electric Chauin (2008), without ripples. application such as robotics, Nvehicles, (1990), manufacturing be optimized for temperature keeping the in the Nowadays, electric brushless drives have been used several can 2. MODEL OF THE BLDC MOTOR IN temperature STATE-SPACE process, Shieh (2001) and Hemati, electric vehicles, Chauin (2008), semiconductors without ripples. application such as robotics, N (1990), manufacturing amount others. However, electric drives are 2. MODEL OF THE BLDC MOTORripples. IN STATE-SPACE process, Shieh (2001) and when electricthose vehicles, Chau (2008), semiconductors without temperature application such as robotics, Hemati, N (1990), manufacturing 2. MODEL OF THE BLDC MOTOR IN STATE-SPACE amount others. However, when those electric drives are process, Shieh (2001) and when electric Chau (2008), designed,others. the power electronic stagethose isvehicles, not designed always for 2. The BLCD motor dynamic Xia.IN (2012), is expressed in amount However, electric drives are MODEL OF THE BLDCmodel, MOTOR STATE-SPACE process, Shieh (2001) and when electric Chau (2008), designed, the power electronic stagethose isvehicles, not designed always for The BLCD motor dynamic model, Xia.IN (2012), is expressed in amount others. However, electric drives are 2. OF(1)THE BLDC MOTOR STATE-SPACE improving and increasing its lifetime by the speed and position theMODEL equation where themodel, phaseXia. currents ofiswinding, designed, the power electronic stage is not designed always for The BLCD motor dynamic (2012), expressedthe in amount others. However, those electric drives are improving andpower increasing its when lifetime bynot thedesigned speed and position the equation (1) where themodel, phaseXia. currents ofiswinding, the designed, the electronic stage is always for The BLCD motor dynamic (2012), expressedthe in controller and because the complexity of the thespeed controller rises. the angular speed,(1) andwhere the rotor position are considered improving increasing its lifetime by and position equation the phase currents of winding, designed, the power electronic stage isby designed always for angular The equation BLCD motor dynamic model, Xia. iswinding, expressedthe in controller because the complexity ofnot the controller rises. speed, andwhere the rotor position are(2012), considered improving and increasing its lifetime the speed and position the (1) the phase currents of Hence, thisbecause paper shows how the speed controller can be angular speed, controller the complexity of the thespeed controller rises. andwhere the rotor position are considered 𝑅𝑅(1) ψ𝑚𝑚 of winding, the 𝑠𝑠 improving increasing itshow lifetime and position equation the phase currents Hence, thisand paper shows the by speed controller can be the controller because the complexity of the controller rises. angular speed, and the rotor position are considered − 0 0 − 𝑓𝑓 𝑅𝑅𝑠𝑠 ψ𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) optimized keep shows the temperature withoutcontroller drastic changes Hence, thisto paper how the speed can be angular speed, 𝐿𝐿1𝑠𝑠 and the 0rotor position ψ𝐽𝐽𝑚𝑚 𝑓𝑓 𝑟𝑟 ) − 𝑅𝑅 0 controller because the temperature complexity of thecontroller controller rises. are− considered optimized to keep shows the without drastic changes Hence, thisoperation paper how thespeed speed can be 𝑖𝑖𝑎𝑎𝑎𝑎̇ 𝐿𝐿1𝑠𝑠 − 𝑅𝑅 0𝑅𝑅 0 − ψ𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃 ) 𝑖𝑖 during the of atemperature variable BLDC. Sincechanges power optimized to keep the without drastic 𝑠𝑠 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎̇̇ 𝐿𝐿 𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑖𝑖𝑎𝑎𝑎𝑎 Hence, this paper shows how the speed controller can be 1 − 0 0 − during the operation of a variable speed BLDC. Since power 0 − 𝑅𝑅 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎(𝜃𝜃 optimized to keep the temperature without drastic changes 𝑏𝑏𝑏𝑏 𝑅𝑅 ψ ) 𝑟𝑟 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑠𝑠 𝑖𝑖 ̇ 𝑏𝑏𝑏𝑏 𝑟𝑟 𝑠𝑠 𝑚𝑚 electronics stage in ofelectric brushless drives Since is used for 𝑎𝑎𝑎𝑎 during the operation atemperature variable speed BLDC. power 𝐿𝐿1𝑠𝑠 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 ̇̇ −0𝑅𝑅 0 − ψ𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃 −0𝐿𝐿1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏(𝜃𝜃𝑟𝑟𝑟𝑟 ) 𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 optimized to keep the without drastic changes electronics stage in electric brushless drives is used for = 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 𝑖𝑖 ̇ 𝑐𝑐𝑐𝑐 𝐿𝐿 0 − 0 − 𝑓𝑓 during the operation of a variable speed BLDC. Since power 𝑎𝑎𝑎𝑎 𝑖𝑖 𝐿𝐿 𝐽𝐽 𝑏𝑏𝑏𝑏 ) 1 𝑅𝑅 ψ 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑏𝑏𝑏𝑏 1 𝑟𝑟 𝑅𝑅 𝑠𝑠 𝑚𝑚 improving the efficiency and control of electrical processes in𝑖𝑖𝑐𝑐𝑐𝑐̇̇ = electronics stage in electric brushless drives is used for 𝑖𝑖 𝑠𝑠 𝑚𝑚 𝐿𝐿 𝐽𝐽 𝑐𝑐𝑐𝑐 𝑖𝑖 𝜔𝜔 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 𝜔𝜔 −0𝑅𝑅1 − ψ𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏(𝜃𝜃 𝑎𝑎𝑎𝑎 𝑚𝑚 during the the operation ofelectric aand variable speed BLDC. Since power 0 −0𝑅𝑅𝑠𝑠 𝑚𝑚 ̇̇ = 𝑖𝑖𝑏𝑏𝑏𝑏 improving efficiency control of electrical processes in𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟𝑟𝑟)) 𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐 electronics stage in brushless drives is used for 𝑠𝑠 𝜔𝜔 𝐿𝐿 𝐽𝐽 𝜔𝜔 𝐿𝐿 𝑚𝑚 1 𝑅𝑅 ψ vehicle systems, railways, FACTS, HVDC, wind turbines, 0 −0 1𝑠𝑠 𝑚𝑚 ] improving the efficiency and control of electrical processes in𝑖𝑖𝜃𝜃𝑏𝑏𝑏𝑏 ̇̇ ] = 0 − − 𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏(𝜃𝜃 𝑖𝑖 𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟𝑟𝑟) [𝜔𝜔 [ 𝑏𝑏𝑏𝑏 𝑟𝑟 𝑐𝑐𝑐𝑐 𝜔𝜔 𝑐𝑐𝑐𝑐 𝑟𝑟 electronics stage in electric brushless drives is used for 𝑚𝑚 𝐿𝐿 0 0 − − 𝑓𝑓 𝑚𝑚 vehicle systems, railways, FACTS, HVDC, wind turbines, 𝐿𝐿 𝐽𝐽 ) 1 𝑅𝑅 ψ 𝑐𝑐𝑐𝑐(𝜃𝜃 ̇ improving the efficiency andFACTS, control ofHVDC, electrical processes inψ𝑚𝑚 1 ψ𝑚𝑚 𝐿𝐿 𝑠𝑠 𝐵𝐵 𝑟𝑟 [𝜔𝜔 [𝜔𝜔 𝑟𝑟 ] 𝑖𝑖𝜃𝜃𝑐𝑐𝑐𝑐𝑚𝑚 𝑟𝑟̇̇ ] = ψ𝑚𝑚 0 𝑖𝑖𝜃𝜃 𝐽𝐽𝑚𝑚 photovoltaics, and home appliances amount others, the vehicle systems, railways, wind turbines, (1) 𝑐𝑐𝑐𝑐 1 0 − − 𝑓𝑓 𝑚𝑚 [ 𝜃𝜃 𝑓𝑓 𝑓𝑓 𝑓𝑓 − ψ ψ ψ 𝐵𝐵 ) [ ] 𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 𝑟𝑟 ] 𝑅𝑅 ψ𝐽𝐽𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑏𝑏𝑏𝑏(𝜃𝜃𝑟𝑟 ) 𝑐𝑐𝑐𝑐(𝜃𝜃 improving the efficiency andFACTS, control of electrical processes in𝑟𝑟 photovoltaics, and home appliances amount others, the 𝑠𝑠 𝑟𝑟 ) 𝐿𝐿 (1) vehicle railways, turbines, ̇ ] [ψ𝐽𝐽𝑚𝑚 𝐽𝐽𝑚𝑚 𝐽𝐽𝑚𝑚 𝐽𝐽𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟 ) ] [𝜔𝜔 ψ ψ 𝐵𝐵 1 ) 𝑓𝑓 𝑓𝑓 𝑓𝑓 − 𝜃𝜃 0 0 − − 𝑓𝑓 𝑚𝑚 𝑚𝑚 𝑚𝑚 𝑚𝑚 ) ) 𝑎𝑎𝑎𝑎(𝜃𝜃 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 primary systems, goal of and this analysis is to showHVDC, how thewind lifetime in the [𝜔𝜔 𝜃𝜃𝑚𝑚 𝑟𝑟 ] photovoltaics, home appliances amount others, 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟 (1) 𝑟𝑟 ] [ 𝐽𝐽 𝐽𝐽 𝐽𝐽 𝐽𝐽 𝑓𝑓 𝑓𝑓 𝑓𝑓 − 1 𝐿𝐿 𝐽𝐽 vehicle systems, railways, FACTS, turbines, ψ 𝐵𝐵 𝑐𝑐𝑐𝑐(𝜃𝜃 primary goal of and this analysis is to showHVDC, how thewind lifetime in the 1 𝑟𝑟 ) 𝑟𝑟 ) ̇𝑟𝑟 ] [ψ𝐽𝐽𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟) ψ𝐽𝐽𝑚𝑚 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑚𝑚 [ 𝜃𝜃 ] photovoltaics, home appliances amount others, [ 𝜃𝜃 0 ) 0 ] 𝑟𝑟 𝐽𝐽 (1) 1 ) 0 𝐽𝐽 𝑓𝑓𝑐𝑐𝑐𝑐(𝜃𝜃 semiconductors is incremented thehow speed is 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟) ψ 𝑓𝑓L−M − 𝐵𝐵 primary goal of and this analysis is toand show theresponse lifetime in not the 𝑏𝑏𝑏𝑏(𝜃𝜃 ψ ψ 𝑟𝑟 𝑟𝑟 0 0 0 𝑚𝑚 𝑚𝑚 𝑚𝑚 1 𝑣𝑣 photovoltaics, home appliances amount others, the [ ] 𝐽𝐽 𝑓𝑓 𝐽𝐽 𝑓𝑓L−M 01 𝐽𝐽 𝑓𝑓 0 0 𝑎𝑎𝑎𝑎− 𝐽𝐽 semiconductors is incremented and thehow speed response is not (1) primary goal ofThus, this analysis is toand show lifetime in not the ) ) 0 𝑣𝑣 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 𝑟𝑟 𝑟𝑟 compromised. this lifetime study canthe be expanded to semiconductors is incremented the speed response is 0 0 1 𝑎𝑎𝑎𝑎 [ 𝐽𝐽 ] 𝐽𝐽 L−M L−M 𝑏𝑏𝑠𝑠 𝐽𝐽 primary goal ofThus, this analysis is toand show how lifetime in not the 𝑣𝑣𝑎𝑎𝑎𝑎 011 𝐽𝐽 0 0 [𝑣𝑣 compromised. this lifetime study canthe be expanded to 01 semiconductors is incremented the speed response is + ] 𝑣𝑣 L−M 𝑏𝑏𝑠𝑠 several applications tothis increment their lifetime in the power compromised. Thus, lifetime study can be expanded to 01 0 [𝑣𝑣𝑎𝑎𝑎𝑎 0 L−M 𝑐𝑐𝑐𝑐 ] 01 + 0 0 𝑏𝑏𝑠𝑠 semiconductors is incremented andtheir the lifetime speed response is not L−M several applications tothis increment in the power L−M compromised. Thus, lifetime study can be expanded to 𝑐𝑐𝑐𝑐 ] 011 + L−M 𝑇𝑇𝑎𝑎𝑎𝑎 0 L−M 01 01 [𝑣𝑣𝑣𝑣 electronic stage. The switching andlifetime conduction of the several applications to increment their in the power 𝑣𝑣 𝑏𝑏𝑠𝑠 L−M 0 [𝑣𝑣𝑇𝑇𝑐𝑐𝑐𝑐𝑙𝑙𝑙𝑙 ] 0 0 compromised. Thus, this lifetime their study can be in expanded to + 0 01 0 electronic stage. The switching andlifetime conduction of the 0 several applications to increment the power L−M 1 𝑏𝑏𝑠𝑠 L−M [ ] 𝑇𝑇 semiconductors power losses,and which are reflected as electronic stage.cause The switching conduction the 01𝐽𝐽 [ 𝑐𝑐𝑐𝑐𝑙𝑙 ] 0 L−M 01 +[ 0 several applications to power increment their lifetime the of power 𝑣𝑣𝑇𝑇𝑐𝑐𝑐𝑐𝑙𝑙 semiconductors cause losses, which areinreflected as 0 electronic stage. The switching and conduction of the 0 0 01𝐽𝐽𝐽𝐽 ]] 𝑓𝑓 [ temperature oscillations. The temperature oscillations are the semiconductors cause power losses,and which are reflected as where 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃), 𝑓𝑓𝑏𝑏𝑏𝑏 = 𝑓𝑓𝑎𝑎𝑎𝑎 0(𝜃𝜃 −02𝜋𝜋/3) = 𝑓𝑓 (𝜃𝜃 + 2𝜋𝜋/3) L−M 0 and 𝑇𝑇𝑐𝑐𝑐𝑐 electronic stage. The switching conduction of 𝑙𝑙 = 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃 + 2𝜋𝜋/3) temperature oscillations. The temperature oscillations are the [ ] (𝜃𝜃), (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 1 𝐽𝐽 semiconductors cause losses,stress) which reflected as are back-EMF 𝑎𝑎𝑎𝑎 (𝜃𝜃), waveform 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 0 𝑐𝑐𝑐𝑐 cause of the rupture (bypower mechanical of are the union of the temperature oscillations. The temperature oscillations are 02𝜋𝜋/3) 0 phase (𝜃𝜃 of each respectively. ψ𝑚𝑚 is 𝑓𝑓 − and 𝑓𝑓 where 𝑓𝑓 = 𝑓𝑓 = 𝑓𝑓𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 (𝜃𝜃 + 2𝜋𝜋/3) [ ] 𝐽𝐽 semiconductors cause losses,stress) which reflected as are cause of the rupture (bypower mechanical of are the union of the back-EMF waveform of each phase respectively. ψ𝑚𝑚 is temperature oscillations. The are (𝜃𝜃), (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 = flux 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃linkage + 2𝜋𝜋/3) welds of between the wirestemperature with theoscillations semiconductor. 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 cause the rupture (by mechanical stress) of the union of the the maximum value of permanent magnetic is are back-EMF waveform of each phase respectively. ψ𝑚𝑚 of temperature oscillations. The are the the welds of between the wirestemperature with theoscillations semiconductor. (𝜃𝜃), (𝜃𝜃 (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 = 𝑓𝑓 + 2𝜋𝜋/3) maximum value of permanent magnetic flux linkage of cause the rupture (by mechanical stress) of the union of the 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 are back-EMF waveform of each phase respectively. ψ𝑚𝑚 of is Manufacturers of power electronics stages offer a lifetime of the welds between the wires with theof semiconductor. each winding, ψ = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 is the number of winding maximum value of permanent magnetic flux linkage 𝑚𝑚 cause of the rupture (by mechanical stress) the union of the Manufacturers of power electronics stages offer a lifetime of each are back-EMF waveform of each respectively. ψ𝑚𝑚 of is welds between the electronics wires withstages the semiconductor. winding, ψ = of 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 isphase the number oflinkage winding the maximum value permanent magnetic flux 𝑚𝑚 their products according to temperature fluctuations, so it of is each Manufacturers of power offer a lifetime 𝑆𝑆 is the product ofpermanent rotor radius and number the effective length 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 ismagnetic the oflinkage winding winding, ψ 𝑚𝑚 = of welds between the electronics wires withstages the semiconductor. their products according to temperature fluctuations, so it of is turns, the maximum value flux of Manufacturers of power offer a lifetime turns, 𝑆𝑆 is the product of rotor radius and the effective length each winding, ψ𝑚𝑚 = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁value is the number of magnetic winding imperative to according keep the temperature in fluctuations, the semiconductors their products to temperature so it of is of conductors, 𝐵𝐵𝐵𝐵 is maximum of permanent turns, 𝑆𝑆 is the product of rotor radius and the effective length Manufacturers of power stages a lifetime imperative to according keep the electronics temperature in fluctuations, theoffer semiconductors each winding, ψ𝑚𝑚 = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁value is the number of magnetic winding their products to temperature so it is of conductors, 𝐵𝐵𝐵𝐵 is maximum of permanent turns, 𝑆𝑆 distribution is the product of rotor radius and the=effective length without extreme variations. imperative to keep the temperature in the semiconductors density in the air gap, 𝐿𝐿 = 𝐿𝐿 𝐿𝐿 = 𝐿𝐿 is the of conductors, 𝐵𝐵𝐵𝐵 is maximum value of permanent magnetic 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 their products according to temperature fluctuations, so it is without extreme variations. turns, 𝑆𝑆 is the product of rotor radius and the effective length imperative to keep the temperature in the semiconductors density distribution in the air gap, 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the of conductors, 𝐵𝐵𝐵𝐵 is maximum value of permanent magnetic 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏𝑀𝑀 is𝑐𝑐𝑐𝑐the mutual without extreme variations. self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the density distribution in the air gap, 𝐿𝐿 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 permanent 𝑎𝑎𝑎𝑎 of 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 magnetic imperative to keep the temperature the semiconductors Different techniques have been used to in control the elevation of self-inductanc, of conductors, 𝐵𝐵𝐵𝐵 is maximum value without extreme variations. and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 is the mutual density distribution in the air gap, 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 Different techniques have been used to control the elevation of 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏𝑀𝑀 is𝑐𝑐𝑐𝑐the mutual inductance. self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = without extreme variations. 𝑎𝑎𝑎𝑎 air gap, 𝑏𝑏𝑏𝑏 𝐿𝐿 𝑐𝑐𝑐𝑐 𝐿𝐿 the temperature as heat sinks; cooled sinks or Different techniques have been forced used toair control theheat elevation of self-inductanc, density distribution the = is 𝐿𝐿𝑐𝑐𝑐𝑐the = 𝐿𝐿mutual is the inductance. 𝑏𝑏𝑏𝑏𝑀𝑀 and in 𝑀𝑀 𝑀𝑀= the temperature as heat sinks; forced air cooled heat sinks or 𝑎𝑎𝑎𝑎 = 𝑀𝑀𝑏𝑏𝑏𝑏 =𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 = Different techniques have been forced used toair control theheat elevation of inductance. the temperature as heat sinks; cooled sinks or self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 = 𝑀𝑀 is the mutual inductance. Different techniques have been used to control the elevation of the temperature as heat sinks; forced air cooled heat sinks or2422 Copyright © 2019, 2019 IFAC inductance. 2405-8963 © IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. the temperature as heat sinks; forced air cooled heat sinks or2422Hosting Copyright © 2019 IFAC Copyright 2019 responsibility IFAC 2422Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 2422 10.1016/j.ifacol.2019.11.561 Copyright © 2019 IFAC 2422
2019 IFAC MIM Berlin, Germany, August 28-30, 2019
Manuel García et al. / IFAC PapersOnLine 52-13 (2019) 2372–2377
the junction temperature 𝑇𝑇𝑗𝑗 is obtained using the thermal equation (4), according to Infineon, (2012).
Thus, the electromagnetic torque is given by
𝑇𝑇𝑒𝑒 = ψ𝑚𝑚 [𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑎𝑎𝑎𝑎 + 𝑓𝑓𝑏𝑏𝑏𝑏 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑏𝑏𝑏𝑏 + 𝑓𝑓𝑐𝑐𝑐𝑐 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑐𝑐𝑐𝑐 ]
(2)
The complete model of the electromechanical system is described by 𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑙𝑙 = 𝐽𝐽 𝜔𝜔̇ 𝑚𝑚 + 𝐵𝐵𝜔𝜔𝑚𝑚
2373
(3)
where 𝑇𝑇𝑙𝑙 is load torque, 𝐽𝐽 is rotor moment of inertia and 𝐵𝐵 is viscous coefficient 𝜔𝜔̇ 𝑚𝑚 is the angular velocity of rotation and 𝜔𝜔𝑚𝑚 is the angular position.
𝑇𝑇𝑗𝑗 = 𝑊𝑊 ∗ (𝑅𝑅𝑡𝑡ℎ (𝑗𝑗 − 𝑐𝑐) + 𝑅𝑅𝑡𝑡ℎ (𝑐𝑐 − 𝑓𝑓) + 𝑅𝑅𝑡𝑡ℎ (𝑓𝑓 − 𝑎𝑎)) + 𝑇𝑇𝑎𝑎
The commutation and conduction losses as well as the temperature profiles on IGBT junction are given by the averages on a modulation period and modelling electrothermic networks as shown in Fig. 2(b), Wintrich (2011).
W
3. POWER MODULE LOSSES
Most power electronics interface contains multichipsemiconductor, it can comprise of IGBT and Diodes. The power electronics interface losses are given as the sum of losses produces by the IGBT chips and the diode chips. These power losses can be classified as on-state losses and switching losses, Infineon (2012). The on-state IGBT power losses are 2 , where 𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶 is the given by 𝑃𝑃𝐶𝐶𝐶𝐶 = 𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶 ∗ 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑟𝑟𝑐𝑐 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 collector-emitter on-state tension, 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 and 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 are average current value and root mean square current value of IGBT respectively while 𝑟𝑟𝑐𝑐 is the collector-emitter on-state resistance value, 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 , 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 and 𝑟𝑟𝑐𝑐 can be estimated according to Graovac et al. (2009). On-state diode power losses are given by 𝑃𝑃𝐶𝐶𝐶𝐶 = 2 , where 𝑢𝑢𝐷𝐷𝐷𝐷 is the anode-cathode, on𝑢𝑢𝐷𝐷𝐷𝐷 ∗ 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 + 𝑟𝑟𝐷𝐷 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 state, tension, 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 and 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 are average current value and root mean square current value of Diode respectively while 𝑟𝑟𝐷𝐷 is the anode-cathode on-state resistance value. 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 , 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 and 𝑟𝑟𝐷𝐷 could be estimated according to Graovac et al. (2009). The turn-on IGBT energy losses are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡 𝑢𝑢𝐶𝐶𝐶𝐶 (𝑡𝑡) ∗ 𝑖𝑖𝐶𝐶 (𝑡𝑡)𝑑𝑑𝑑𝑑. The turn-off energy losses are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑢𝑢𝐶𝐶𝐶𝐶 (𝑡𝑡) ∗ 𝑖𝑖𝐶𝐶 (𝑡𝑡)𝑑𝑑𝑑𝑑, where: 𝑢𝑢𝐶𝐶𝐶𝐶 and 𝑖𝑖𝐶𝐶 are collector-emitter tension and collector current respectively during IGBT turn on or turn off. Fig.5. shows the switching energy losses. The turn-on diode energy losses are mostly presented when the reverse-recovery energy occur, and these are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝑢𝑢𝐷𝐷 (𝑡𝑡) ∗ 𝑖𝑖𝐹𝐹 (𝑡𝑡))𝑑𝑑𝑑𝑑 , where 𝑢𝑢𝐷𝐷 and 𝑖𝑖𝐹𝐹
(4)
Tj PswQ
Tc
PswD PswQ
Rth(j-c) PcQ
PcQ
PswD
TjQ
Zth_jc_Q
PcD PcD
TjD
Zth_jc_D
Rth(c-f) TcQ
Tf Rth_CH_Q Rth(f-a)
TcD Rth_CH_D Th
Ta
Fig. 2. (a) Thermal resistance equivalent circuit, (b) ElectroThermal model. 4. LIFETIME OF POWER ELECTRONICS INTERFECE The thermal stress is presented as a consequence of the temperature difference ∆𝑇𝑇𝑗𝑗 between silicon and bonding wire, which happens during the changes of temperature. These changes go up and down in a short time cycle, and as a result of this kind of operation, the lifetime of power electronics semiconductors is mainly limited by the aluminium bonding wire joints, Fig. 3 shows an example of these changes of temperature.
are anode-cathode tension and forward current respectively during turn on. Hence, switching losses for IGBT and Diode are given by 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 = (𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 + 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ) ∗ 𝐹𝐹𝑠𝑠𝑠𝑠 and 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 = (𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 + 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ) ∗ (𝐹𝐹𝑠𝑠𝑠𝑠 ) ≈ 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 ∗ (𝐹𝐹𝑠𝑠𝑠𝑠 ) 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 and 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 are given as the product of switching energies and the switching frequency 𝐹𝐹𝑠𝑠𝑠𝑠 . According to Infineon (2012), the switching losses in the diode are normally neglected 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 0. Finally, the total losses of the IGBT module are given by equation (3). 𝑊𝑊 = 𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠
(3)
On the other hand, the semiconductor heat conduction is simulated as an electric circuit with one IGBT module mounted on a heat sink as is shown in Fig. 6(a), where 𝑊𝑊 is a module power loss, 𝑇𝑇𝑗𝑗 is junction temperature IGBT chip, 𝑇𝑇𝑓𝑓 is the heat sink temperature, 𝑇𝑇𝑐𝑐 is module case temperature, 𝑇𝑇𝑎𝑎 is ambient temperature, 𝑅𝑅𝑡𝑡ℎ (𝑗𝑗 − 𝑐𝑐) is thermal resistance between case and heat sink, 𝑅𝑅𝑡𝑡ℎ (𝑐𝑐 − 𝑓𝑓) is contact thermal resistance between case and heat sink, and 𝑅𝑅𝑡𝑡ℎ (𝑓𝑓 − 𝑎𝑎) is thermal resistance between heat sink and ambient air. Thus,
Fig. 3. Pattern diagram flow current of ∆𝑻𝑻𝒋𝒋 power cycle and temperature change. Finally, the estimation of lifetime of semiconductors can be given as the Time Before Failure (TBF) or the Cycles Before Failure (CBF), according to ABB (2014) and Fuji Electric (2015).
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𝐶𝐶𝐶𝐶𝐶𝐶 = 541162959016419 ∗ ∆𝑇𝑇 −5.12121
(5)
where the compute of CBF are given by Eq. 14, where Δ𝑇𝑇 = 2 𝑅𝑅𝑜𝑜𝑜𝑜 , and 𝑍𝑍𝑡𝑡ℎ = 2.3354𝐹𝐹𝑟𝑟−0.165, and, TBF is 𝑃𝑃𝑡𝑡 𝑍𝑍𝑡𝑡ℎ , 𝑃𝑃𝑡𝑡 = 𝐼𝐼𝑟𝑟𝑟𝑟𝑟𝑟 given in years according to the equation (6). 𝑇𝑇𝑇𝑇𝑇𝑇 =
𝐶𝐶𝐶𝐶 ∗ 60 ∗ 24 ∗ 365 [𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦] 𝐹𝐹𝐹𝐹
(6)
where 𝐹𝐹𝑟𝑟 is the frequency of the thermal oscillations, Fuji Electric (2015) and Vincotech (2017). Hence, this estimation considers the thermal losses, which can be computed through equivalent circuit shown in Fig. 6(b) or the power cycling lifetime curve provided by the datasheet of the power electronic semiconductor manufacturer as is shown in Fig. 4, where is presented an example of the IGBT module power cycle capability curve for ∆𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 25℃ and ∆𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 150 ℃ according to ABB (2014) and Fuji Electric (2015).
The controller is designed according to Mamdani inference methodology. The linguistic knowledge base is expressed as a set of linguistic rules such as if-then statements. In this case, the rules have the linguistic expression If 𝑒𝑒(𝑡𝑡) is 𝐴𝐴 𝑎𝑎𝑎𝑎𝑎𝑎 𝑒𝑒̇ (𝑡𝑡) is 𝐵𝐵 then 𝑖𝑖𝑐𝑐 is C, where A, B and C are linguistic values defined in a universe of discourse of three triangular functions (N: negative, Z: zero and P: positive). On the other hand, the inference engine is given by if-then statements. According to Mamdani inference methodology, the inference is given by 𝑛𝑛 𝑛𝑛 𝑛𝑛 𝐶𝐶 ∗ = 𝑈𝑈𝑗𝑗=1 𝐶𝐶í∗ where 𝐶𝐶 ∗ = 𝜇𝜇𝐶𝐶´ (𝑖𝑖𝑐𝑐 ); 𝑦𝑦 𝑈𝑈𝑗𝑗=1 𝐶𝐶í∗ =∪𝑗𝑗=1 [𝛼𝛼𝑗𝑗 ∩ 𝜇𝜇𝐶𝐶𝐶𝐶 (𝑖𝑖𝑐𝑐 )]. Finally, the defuzzification stage gets a crisp value from the rule evaluation stage through the center of gravity method by 𝑧𝑧 ∗ = ∫ 𝜇𝜇𝐴𝐴 (𝑧𝑧) ∙ 𝑧𝑧𝑧𝑧𝑧𝑧⁄∫ 𝜇𝜇𝐴𝐴 (𝑧𝑧) ∙ 𝑧𝑧𝑧𝑧𝑧𝑧 Decrease overshoot
DE
c g Set point
b
d
k
j
h
f
l
i
e
E
a i
Decrease Rise time
E DE
ii
- -
+
iii
iv
+
+ +
-
v
vi vii viii
- - - +
+
ix
+ + + -
x
xi
- - +
Time
Fig. 5. Linguistic phase plane 5. DESIGN OF FUZZY-PSO CONTROLLER 5.1. Particle Swarm Optimization
Fig. 4. Power cycling lifetime curve. 4. DESIGN OF FLC TO SPEED CONTROL OF BLDC MOTOR Fuzzy Logic Controller (FLC) is based on Fuzzy Logic proposed by Zadeh, (1965) and its components are: a Fuzzification interface which transforms crisp input values into fuzzy values, a knowledge base which consists of a database and a linguistic rule base, an inference engine makes decisions employing fuzzy implication and linguistic rules and a defuzzification interface which yields a non-fuzzy control action from an inferred fuzzy control action. A useful methodology to design fuzzy logic controllers is based on a linguistic phase plane, Lee (2005), as shown in Fig. 5. The error 𝑒𝑒𝑐𝑐 (𝑡𝑡) = 𝜔𝜔𝑑𝑑 (𝑡𝑡) − 𝜔𝜔(𝑡𝑡) where 𝜔𝜔𝑑𝑑 (𝑡𝑡) is the desired speed and 𝜔𝜔(𝑡𝑡) is the current speed and change of error 𝑒𝑒̇ (𝑡𝑡) = 𝑒𝑒(𝑡𝑡) − 𝑒𝑒(𝑡𝑡 − 1) are considered as antecedent while 𝑖𝑖𝑐𝑐 is the conclusion (output variable). The range of 𝑖𝑖𝑐𝑐 goes from 0 to 100 percenter of the duty cycle which stablishes the average supply voltage (V1 see Fig. 1) in the VSI. The range of 𝑒𝑒(𝑡𝑡) is [-14, 14] and the 𝑒𝑒̇ (𝑡𝑡) is [-1, 1].
Particle Swarm Optimization (PSO) was developed by [9], this method is based on the behaviour and movement of bird flocks looking for targets, this algorithm was developed to optimization nonlinear optimization and multidimensional functions, Zhang (2015) and Dandy (2018). PSO algorithm works with specific numbers of particles, which are denominated population. The PSO algorithm initializes the population in a random way, where each particle has a position 𝑥𝑥𝑖𝑖 (𝑡𝑡) and velocity 𝑣𝑣𝑖𝑖 (𝑡𝑡) with respect to target, then each particle is evaluated in the main loop, where 𝑥𝑥𝑖𝑖 (𝑡𝑡) and 𝑣𝑣𝑖𝑖 (𝑡𝑡) are updated in each iteration, this new position is compared with the previous best local position 𝑃𝑃𝑖𝑖 (𝑡𝑡), if the new position is better than the previous best local position then the best local position is update with the new position. At the last, the new position also is compared with the best global position 𝑔𝑔(𝑡𝑡), where 𝑔𝑔(𝑡𝑡) is closest with respect to the target and if the new position is better than the best global position then the best glob, al position value is updated. Additionally, the update of velocity is defined by 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1) = 𝜔𝜔𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘) +
𝑟𝑟1𝑗𝑗 𝐶𝐶1 (𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) − 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘)) and the position is defined by 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1) = 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) + 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1), where 𝑖𝑖 = 1,2, … , 𝑁𝑁, and 𝑁𝑁 is the size of population, 𝑗𝑗 = 1,2, … , 𝐷𝐷, and 𝐷𝐷 is the number of dimensions, 𝑘𝑘 = 1,2, … , 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖, and 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 is the maximum iteration number, 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) is the position of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘) is the velocity of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) is the local best position of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑔𝑔𝑗𝑗 (𝑘𝑘) is the global best, 𝜔𝜔 is an inertia factor, 𝐶𝐶1 , 𝐶𝐶2 are the acceleration constant, 𝑟𝑟1 , 𝑟𝑟2 are independent random numbers, uniformly distributed in (0,1). Thus, the primary objective is to find a minimal global value
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from the cost function through be minimized as it is shown in the next pseudocode. Song (2004).
Step 1. Initialization, for each particle of population 𝑁𝑁, do 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘). Step 2. Repeat until the criterion is satisfied, for each particle of population 𝑁𝑁, do, set random numbers to 𝑟𝑟1𝑗𝑗 and 𝑟𝑟2𝑗𝑗 , update 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘). If 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) < 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘), update the best local position 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) If 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) < 𝑔𝑔𝑗𝑗 (𝑘𝑘), update the best global position g(𝑘𝑘) Step 3. Get the best solution 𝑔𝑔(𝑘𝑘).
fuzzy logic process so it is only added to 𝑒𝑒𝑐𝑐 to obtain 𝑓𝑓𝑐𝑐 . So each membership function of the FLC is considered as a decision variable. Figure 6 shows a block diagram of FuzzyPSO control realization. PSO algorithm is implemented to tuning the antecedent and conclusion membership functions parameters of speed feedback loop in order to reach the speed desired and the temperature desired in power electronic stage, the temperature is only used as a change to be added to the objective function, thus it does not have any feedback of the current temperature. The constraints of the optimization are the mechanical capacity value of BLDC motor and the thermal capacity value of IGBTs, which are shown in Table 2.
5.2. Optimization of FLC by PSO
Table 2. Experimental settings
Based on the separability of the objective and constraint functions, defined in Dandy (2018) as "A function 𝑓𝑓(𝑿𝑿) is said to be separable if it can be expressed as the sum of n singlevariable functions,𝑓𝑓1 = (𝑥𝑥1 ), 𝑓𝑓2 = (𝑥𝑥2 ), … … 𝑓𝑓𝑛𝑛 = (𝑥𝑥𝑛𝑛 ) that is 𝑓𝑓(𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑓𝑓𝑖𝑖 (𝑥𝑥𝑖𝑖 ) “ which can be expressed in standard form as: Find 𝑿𝑿 which minimizes 𝑓𝑓(𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑓𝑓𝑖𝑖 (𝑥𝑥𝑖𝑖 ), subject to 𝑔𝑔𝑗𝑗 (𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑔𝑔𝑖𝑖𝑖𝑖 (𝑥𝑥𝑖𝑖 ) ≤ 𝑏𝑏𝑗𝑗 , 𝑗𝑗 = 1,2, … , 𝑚𝑚 where 𝑏𝑏𝑗𝑗 is a constant. Thus, it establishes the objective function.
𝑡𝑡𝑑𝑑
𝜔𝜔𝑑𝑑
𝑒𝑒𝑡𝑡
+-
𝑒𝑒𝑐𝑐
+ +
+-
𝑓𝑓𝑐𝑐
𝑡𝑡
IGBT 10-0B066PA006SB-M992F09 𝑉𝑉𝐶𝐶𝐶𝐶 𝑅𝑅𝐶𝐶𝐶𝐶(𝑂𝑂𝑂𝑂)
Parameter
𝑅𝑅𝐽𝐽−𝑆𝑆 . Thermal Resistance Junction to Sink
Unit
8-6
℃
80 to 175
V Ω A
3,50
K/W
Stator Inductance
0.15
mH
Stator Resistance Velocity constant Torque constant
0.6 0.03 0.03
Ω Vs/rad Nm/A
BLDC motor
Number of pole pairs
PSO Algorithm Objetive function 𝑓𝑓𝑐𝑐
1
Parameter of IGBT in co-simulation MultisimTM IGBT control threshold IGBT on resistance
Tuning Membership Functions
𝜔𝜔
600 0.1
Value
𝐽𝐽𝑐𝑐 𝑇𝑇𝐽𝐽 , Junction Temperature
Temperature Measurement
FLC
2375
INVERTER
BLDC MOTOR
0.5 0.1meg
V Ω
IGBT off resistance
10
Ω
IGBT forward voltage drop
0.7
V
Diode on resistance
1m
Ω
Diode off resistance
10meg
Ω
Number of switches in parallel
1
Triggering Pulse
Hall Effect Sensor
Speed Measurement
Table 3. PSO parameters Parameter Population Size Social rate (𝑐𝑐1 )
Fig. 6. Diagram of Fuzzy-PSO control. The design of the controller considers two objectives, the first one is to reach the desired motor speed, and the second one is to increase the semiconductors lifetime. Hence, the BLDC motor speed control design is based on FLC technique, and PSO algorithm optimize the membership functions of FLC. Furthermore, one of the leading features is the definition of the objective function (𝑓𝑓𝑐𝑐 ), which considers the temperature error 𝑒𝑒𝑡𝑡 and the speed error 𝑒𝑒𝑐𝑐 , is shown in equation (7). 𝑓𝑓𝑐𝑐 = 𝑒𝑒𝑐𝑐 + 𝑒𝑒𝑡𝑡
(7)
𝑒𝑒𝑡𝑡 is defined by the temperature error 𝑒𝑒𝑡𝑡 (𝑡𝑡) = 𝑡𝑡𝑑𝑑 (𝑡𝑡) − 𝑡𝑡(𝑡𝑡), where 𝑡𝑡𝑑𝑑 is the desired temperature and 𝑡𝑡 is the current semiconductors temperature while 𝑒𝑒𝑐𝑐 is defined in paragraph 4. Thus, the objective function defined in the equation (7) is minimized through of PSO algorithm which is accomplished by adjusting the memberships function antecedent and conclusion in each 𝑒𝑒𝑐𝑐 update. On the other hand, 𝑒𝑒𝑡𝑡 has no
Cognitive rate (𝑐𝑐2 ) Inertia factor (𝑊𝑊)
30
Value
0.005 0.002 0.002
6. CO-SIMULATION DESIGN The proposed scheme to validate controllers, PID, Fuzzy and Fuzzy-PSO, is designed in co-simulation through LabviewTM and MultisimTM tools. The BLDC motor, the Hall effect sensors, and the six-steps inverter were designed in MultisimTM software. The parameters utilized of the BLDC motor, National Instruments (2013), and the six IGBT 100B066PA00Sb-M992F09, Vincotech (2017), are shown in Table 2, and the PSO algorithm parameters are selected according to a dynamic system and the sample time of controller through online experimentation as is shown in Table 3. On the other hand, PID, Fuzzy and Fuzzy-PSO controllers are designed in LabviewTM software, National Instruments (2013). The proposed Fuzzy-PSO controller in this work is
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designed with the Fuzzy Logic Toolkit, Ponce et al. (2010), and the PSO optimization was developed in LabviewTM, Fig. 7, shows the block diagram of Fuzzy-PSO implementation.
thus like without and with load (N/m). PID Advanced autotuning VI implemented a PID controller in LabviewTM Toolkit, which includes the features of PID controller such as proportional gain, integral time and derivative time. Besides, this toolkit can be implemented in co-simulation applications. On the other hand, according to the desired parameters of speed and temperature, the PID controller response to reach the reference speed is a short time in comparison with the other two controllers.
Fig. 8. Blockdiagram of the Co-simulation of Fuzzy-PSO controller using LabviewTM and MultisimTM
Fig. 11. Temperature response of PID, FUZZY and FUZZYPSO controllers without load
Fig. 9. Speed response of PID, FUZZY and FUZZY-PSO controllers without Load Fig. 12. Speed response of PID, FUZZY and FUZZY-PSO controllers with Load Acknowledgment This research is a product of the Project 266632 “Laboratorio Binacional para la Gestión Inteligente de la Sustentabilidad Energética y la Formación Tecnológica” [“Bi-National Laboratory on Smart Sustainable Energy Management and Technology Training”], funded by the CONACYT SENER Fund for Energy Sustainability (Agreement: S0019201401). Fig. 10. Speed response of PID, FUZZY and FUZZY-PSO controllers with Load
This research was also supported by National Instruments Austin Texas,
6. DISCUSSION AND RESULT The proposed control law considers two control objectives, the first one is to track the speed reference and the second one is to keep the desired temperature to increase the lifetime of the IGBTs. Furthermore, the optimization trade-off was tasted on PID, Fuzzy and Fuzzy-PSO controllers in the co-simulation program; thus, Fuzzy-PSO controller was evaluated under different desired temperatures, which are 25 °C, 40°C and 80°C, the reference speed was evaluated at 10 m/s and 5 m/s,
REFERENCES ABB Switzerland Ltd, Semiconductors. (2014) Load-cycling capability of Hipak IGBT modules, Application Note 5SYA 2043-04. Chau KT (2015). Electric vehicle machines and drives: design, analysis, and application. IEEE, Wiley, Singapore Chau, K. T., Chan, C. C., & Liu, C. (2008). Overview of permanent-magnet brushless drives for electric and hybrid
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electric vehicles. IEEE Transactions on industrial electronics, 55(6), 2246-2257. Dandy G, Daniell T, Foley B and Warner R. (2018). Planning & Design of Engineering Systems. Boca Raton, FL: CRC Press Taylor & Francis Group. Fuji Electric (2015). FUJI IGBT MODULES APPLICATION MANUAL. Fuji Electric Device Technology Co., Ltd. Gomes C, Thule C, Broman D, et al. (2017). Co-simulation: State of the art. Graovac, D. and Pürschel, M. (2009). Automotive Power: Application Note, V 1.1. Neubiberg, Germany. Published by Infineon TechnologiesAG. Hemati, N., Thorp, J. S., & Leu, M. C. (1990). Robust nonlinear control of brushless DC motors for direct-drive robotic applications. IEEE Transactions on Industrial Electronics, 37(6), 460-468. Infineon (2012) AN 2015-10, Transient Thermal Measurements and thermal equivalent circuit models. National Instruments (2013). Introduction to Digital and Analog Co-simulation Between NI LabVIEW and NI Multisim National Instruments. http://www.ni.com/white-paper/13663/en/. Accessed 14 Oct 2017 Nasseer K. Bachache and Jinyu Wen. (2013). Multi Objective Swarm Optimization Design Fuzzy Controller to Adjust Speed of AC Motor Drive. Advances in Swarm Intelligence. ICSI 2013. Lecture Notes in Computer Science, vol 7928. Springer, Berlin, Heidelberg Ponce P, Molina A, Mata O, Ibarra L and MacCleery B. (2018). Power System Fundamentals. Taylor & Francis Group, LLC. Boca Raton FL. USA. Premkumar K, Manikandan B.V. (2015). Speed control of Brushless DC motor using bat algorithm optimized Adaptive Neuro-Fuzzy Inference System. Appl Soft Comput 32:403–419. doi: 10.1016/j.asoc.2015.04.014 Shieh, N. C., & Tung, P. C. (2001). Robust output tracking control of a linear DC brushless motor for transportation in manufacturing system. IEE Proceedings-Electric Power Applications, 148(2), 119-124. Song M.P, Gu G.C (2004). Research on particle swarm optimization: a review. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826). pp 2236–2241 vol.4 Vincotech (2017). 10-0B066PA006SB-M992F09 Datasheet. Wintrich, A., Nicolai, U., Reimann, T., & Tursky, W. (2011). Application manual power semiconductors. ISLE. Xia, Chang-liang (2012). Permanent magnet brushless DC motor drives and controls. John Wiley & Sons Singapore Pte. Ltd. Sola. Singapore. Zhang Y, Wang S. and Ji G. (2015). A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications. Math. Probl. Eng., vol. 2015, pp. 1–38. Zheng, L. (1992). A practical guide to tune of Proportional and Integral (PI) like fuzzy controller, in Proc. IEEE Int. Conf. Fuzzy Systems, pp 633-640. New Orleans, LA
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IFAC PapersOnLine 52-13 (2019) 2372–2377 Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and Lifetime Improved in Power for BLDC Drives using Fuzzy Logic and Lifetime Improved in Power Electronics Electronics for BLDC Drives using Fuzzy Logic and PSO Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and PSO PSO Lifetime Improved in Power Electronics for BLDC Drives using Fuzzy Logic and PSO PSO
Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro Ponce**, Luis A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* Manuel García*, Pedro A. Soriano**, Molina**, BrianNacional, MacCleery***, DavidMéxico. Romero* * Escuela Superior de Ponce**, IngenieríaLuis Mecánica y Eléctrica, Instituto Politécnico México City, Arturo * Escuela Superior de Ponce**, IngenieríaLuis Mecánica y Eléctrica, Instituto Politécnico Nacional, México City, México. Manuel García*, Pedro A. Soriano**, Arturo Molina**, Brian MacCleery***, David Romero* e-mail: {magarcial, dromero} @ipnc.mx). * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto Politécnico Nacional, México City, México. e-mail: {magarcial, dromero} @ipnc.mx). * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto PolitécnicoMéxico Nacional, México City, México. ** Escuela de Ingeniería y Ciencias, Tecnológico [email protected]). Monterrey, City, México e-mail: {magarcial, dromero} * Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto PolitécnicoMéxico Nacional, México City, México. ** Escuela de Ingeniería y Ciencias, Tecnológico [email protected]). Monterrey, City, México e-mail: {magarcial, dromero} {pedro.ponce, larturo.soriano, armolina} @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico de Monterrey, México City, México e-mail: {magarcial, dromero} @ipnc.mx). {pedro.ponce, larturo.soriano, armolina} @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico de Monterrey, México City, México ***National Instruments, Austinarmolina} Texas, USA {pedro.ponce, larturo.soriano, @tec.mx). ** Escuela dee-mail: Ingeniería y Ciencias, Tecnológico dearmolina} Monterrey, México City, México ***National Instruments, Austin Texas, USA e-mail: {pedro.ponce, larturo.soriano, @tec.mx). e-mail: {brian.maccleery}@ ni.com). ***National Instruments, Austin Texas, USA e-mail: ***National {pedro.ponce, larturo.soriano, armolina} @tec.mx). e-mail: {brian.maccleery}@ Instruments, Austin ni.com). Texas, USA e-mail: {brian.maccleery}@ ni.com). ***National Instruments, Texas, USA in several applications such as e-mail: {brian.maccleery}@ ni.com). Abstract: The brushless direct current drives (BLDC) are Austin extremely popular Abstract: The brushless direct current drives (BLDC) are extremely popular in several applications such as e-mail: {brian.maccleery}@ ni.com). robotics, and manufacturing, lifetime power electronics special attention in Abstract: transportation, The brushless direct current drives the (BLDC) are of extremely popular indeserves several applications such as robotics, transportation, and manufacturing, the lifetime power electronics deserves special attention in Abstract: The brushless so direct current (BLDC) are of extremely popular several such as industrial applications, this paper drives explores how the lifetime iselectronics affectedinwhen theapplications reference speed is robotics, transportation, and manufacturing, the lifetime of power deserves special attention in Abstract: The brushless direct current drives (BLDC) are extremely popular in several applications such as industrial applications, so this paper explores how the lifetime is affected when the reference speed is robotics, transportation, andthis manufacturing, theishow lifetime of powerpaper electronics deserves in changed when a conventional speed controller deployed. This illustrates how tospecial designattention anspeed optimal industrial applications, so paper explores the lifetime is affected when the reference is robotics, transportation, and manufacturing, the lifetime of power electronics deserves special attention in changed when a conventional speed controller is deployed. This paper illustrates how to design an optimal industrial applications, sologic thisspeed paper explores how the lifetime is affected thetoreference speed is controller based on fuzzy and Particle Swarm Optimization (PSO). The when optimized controller reaches changed when a conventional controller is deployed. This paper illustrates how design an optimal industrial applications, sologic thisspeed paper explores the lifetime is affected thetoreference is controller based on fuzzy and Particle Swarm Optimization (PSO). The when optimized controller reaches changed when a conventional controller ishow deployed. Thisinpaper illustrates how design anspeed optimal the reference speed at thelogic same timeParticle it keeps the temperature the semiconductors of controller the BLDC within controller based on fuzzy and Swarm Optimization (PSO). The optimized reaches changed when a conventional speed controller is deployed. Thisinpaper illustrates how of to controller design an optimal the reference speed at thelogic same timeParticle it keeps the temperature the semiconductors the BLDC within controller based on fuzzy and Swarm Optimization (PSO). The optimized reaches minimum variations to the preserve the in a minimum value ininthe power electronics of stage, the lifetime the reference speed at sameand timeloses it keeps the temperature the semiconductors the so BLDC within controller based on fuzzy logic Particle Optimization (PSO). The optimized controller reaches minimum variations to the preserve the in aSwarm minimum value ininthe power electronics stage, the lifetime the reference speed at same timeloses it keeps the temperature the semiconductors the so BLDC within of the power electronic stage is incremented. A co-simulation of BLDC, which is a of powerful simulation minimum variations to preserve the loses in a minimum value in the power electronics stage, so the lifetime the reference speed at the same timeloses it keeps the temperature inthe thepower semiconductors the so BLDC within of the power electronic stage is incremented. A co-simulation of BLDC, which is a of powerful simulation minimum variations to preserve the in a minimum value in electronics stage, the lifetime tool getting similar result experimental A tests is presented.ofThe validate proposedsimulation optimized of theforpower electronic stage to is incremented. co-simulation the results BLDC,electronics which isthe a stage, powerful minimum variations to preserve the loses in a minimum value in the power so the lifetime tool getting similar result to experimental A tests is presented.ofThe validate proposedsimulation optimized of thefor power stage isincrement incremented. co-simulation the results BLDC, which isthe ainpowerful controller as electronic well as show theto in the lifetime of the power electronic stage the BLDC. tool getting similar result experimental tests is presented. The validate proposed optimized of thefor power stage isincrement incremented. A co-simulation the results BLDC, which isthe ainpowerful simulation controller as electronic well as show theto in the lifetime of the of power electronic stage the BLDC. tool for getting similar result experimental tests is presented. The results validate the proposed optimized controller as well as show the increment in the lifetime of the power electronic stage in the BLDC. Keywords: logic controller, Particle optimization, Lifetime, Electric Drive. tool for getting similar result toincrement experimental tests isswarm presented. The results validate theAll optimized © 2019, IFAC (International Federation ofinAutomatic Control) Hosting by Elsevier Ltd. rights reserved. controller asBLDC, well asFuzzy show the the lifetime of the power electronic stage inproposed the BLDC. Keywords: BLDC, Fuzzy logic controller, Particle swarm optimization, Lifetime, Electric Drive. Keywords:asBLDC, controller,inParticle swarm optimization, Lifetime, Electric controller well asFuzzy show logic the increment the lifetime of the power electronic stage in theDrive. BLDC. Keywords: BLDC, Fuzzy logic controller, Particle swarm optimization, Lifetime, Electric Drive. Keywords: BLDC, Fuzzy logic controller, Particle swarm Electric Drive. the optimization, cooling by theLifetime, circulation of liquid through the heat sink. 1. INTRODUCTION the cooling by the circulation of liquid through the heat sink. However, are circulation no reports that show how a speed controller the coolingthere by the of liquid through the heat sink. 1. INTRODUCTION However, there are circulation no reports that show how a speed controller 1. INTRODUCTION the cooling by the of liquid through the heat sink. can be optimized for keeping the temperature in the Nowadays, electric brushless drives have been used in several However, there are no reports that show how a speed controller 1. INTRODUCTION the cooling by the circulation of liquid through the heat can be optimized for keeping the how temperature in sink. the Nowadays, electric brushless drives have been used in several However, there are no reports that show a speed controller 1. INTRODUCTION semiconductors without temperature ripples. application such as robotics, N (1990), manufacturing be optimized for keeping the temperature in the Nowadays, electric brushlessHemati, drives have been used in several can However, there are no reports that show how a speed controller semiconductors without temperature ripples. application such as robotics, Hemati, N (1990), manufacturing can be optimized fortemperature keeping the temperature in the Nowadays, electric brushless drives have been used several semiconductors process, Shieh (2001) and Hemati, electric Chauin (2008), without ripples. application such as robotics, Nvehicles, (1990), manufacturing be optimized for temperature keeping the in the Nowadays, electric brushless drives have been used several can 2. MODEL OF THE BLDC MOTOR IN temperature STATE-SPACE process, Shieh (2001) and Hemati, electric vehicles, Chauin (2008), semiconductors without ripples. application such as robotics, N (1990), manufacturing amount others. However, electric drives are 2. MODEL OF THE BLDC MOTORripples. IN STATE-SPACE process, Shieh (2001) and when electricthose vehicles, Chau (2008), semiconductors without temperature application such as robotics, Hemati, N (1990), manufacturing 2. MODEL OF THE BLDC MOTOR IN STATE-SPACE amount others. However, when those electric drives are process, Shieh (2001) and when electric Chau (2008), designed,others. the power electronic stagethose isvehicles, not designed always for 2. The BLCD motor dynamic Xia.IN (2012), is expressed in amount However, electric drives are MODEL OF THE BLDCmodel, MOTOR STATE-SPACE process, Shieh (2001) and when electric Chau (2008), designed, the power electronic stagethose isvehicles, not designed always for The BLCD motor dynamic model, Xia.IN (2012), is expressed in amount others. However, electric drives are 2. OF(1)THE BLDC MOTOR STATE-SPACE improving and increasing its lifetime by the speed and position theMODEL equation where themodel, phaseXia. currents ofiswinding, designed, the power electronic stage is not designed always for The BLCD motor dynamic (2012), expressedthe in amount others. However, those electric drives are improving andpower increasing its when lifetime bynot thedesigned speed and position the equation (1) where themodel, phaseXia. currents ofiswinding, the designed, the electronic stage is always for The BLCD motor dynamic (2012), expressedthe in controller and because the complexity of the thespeed controller rises. the angular speed,(1) andwhere the rotor position are considered improving increasing its lifetime by and position equation the phase currents of winding, designed, the power electronic stage isby designed always for angular The equation BLCD motor dynamic model, Xia. iswinding, expressedthe in controller because the complexity ofnot the controller rises. speed, andwhere the rotor position are(2012), considered improving and increasing its lifetime the speed and position the (1) the phase currents of Hence, thisbecause paper shows how the speed controller can be angular speed, controller the complexity of the thespeed controller rises. andwhere the rotor position are considered 𝑅𝑅(1) ψ𝑚𝑚 of winding, the 𝑠𝑠 improving increasing itshow lifetime and position equation the phase currents Hence, thisand paper shows the by speed controller can be the controller because the complexity of the controller rises. angular speed, and the rotor position are considered − 0 0 − 𝑓𝑓 𝑅𝑅𝑠𝑠 ψ𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) optimized keep shows the temperature withoutcontroller drastic changes Hence, thisto paper how the speed can be angular speed, 𝐿𝐿1𝑠𝑠 and the 0rotor position ψ𝐽𝐽𝑚𝑚 𝑓𝑓 𝑟𝑟 ) − 𝑅𝑅 0 controller because the temperature complexity of thecontroller controller rises. are− considered optimized to keep shows the without drastic changes Hence, thisoperation paper how thespeed speed can be 𝑖𝑖𝑎𝑎𝑎𝑎̇ 𝐿𝐿1𝑠𝑠 − 𝑅𝑅 0𝑅𝑅 0 − ψ𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃 ) 𝑖𝑖 during the of atemperature variable BLDC. Sincechanges power optimized to keep the without drastic 𝑠𝑠 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎̇̇ 𝐿𝐿 𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑖𝑖𝑎𝑎𝑎𝑎 Hence, this paper shows how the speed controller can be 1 − 0 0 − during the operation of a variable speed BLDC. Since power 0 − 𝑅𝑅 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎(𝜃𝜃 optimized to keep the temperature without drastic changes 𝑏𝑏𝑏𝑏 𝑅𝑅 ψ ) 𝑟𝑟 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑠𝑠 𝑖𝑖 ̇ 𝑏𝑏𝑏𝑏 𝑟𝑟 𝑠𝑠 𝑚𝑚 electronics stage in ofelectric brushless drives Since is used for 𝑎𝑎𝑎𝑎 during the operation atemperature variable speed BLDC. power 𝐿𝐿1𝑠𝑠 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 ̇̇ −0𝑅𝑅 0 − ψ𝐽𝐽𝑚𝑚 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃 −0𝐿𝐿1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏(𝜃𝜃𝑟𝑟𝑟𝑟 ) 𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 optimized to keep the without drastic changes electronics stage in electric brushless drives is used for = 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 𝑖𝑖 ̇ 𝑐𝑐𝑐𝑐 𝐿𝐿 0 − 0 − 𝑓𝑓 during the operation of a variable speed BLDC. Since power 𝑎𝑎𝑎𝑎 𝑖𝑖 𝐿𝐿 𝐽𝐽 𝑏𝑏𝑏𝑏 ) 1 𝑅𝑅 ψ 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑏𝑏𝑏𝑏 1 𝑟𝑟 𝑅𝑅 𝑠𝑠 𝑚𝑚 improving the efficiency and control of electrical processes in𝑖𝑖𝑐𝑐𝑐𝑐̇̇ = electronics stage in electric brushless drives is used for 𝑖𝑖 𝑠𝑠 𝑚𝑚 𝐿𝐿 𝐽𝐽 𝑐𝑐𝑐𝑐 𝑖𝑖 𝜔𝜔 𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎 𝜔𝜔 −0𝑅𝑅1 − ψ𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏(𝜃𝜃 𝑎𝑎𝑎𝑎 𝑚𝑚 during the the operation ofelectric aand variable speed BLDC. Since power 0 −0𝑅𝑅𝑠𝑠 𝑚𝑚 ̇̇ = 𝑖𝑖𝑏𝑏𝑏𝑏 improving efficiency control of electrical processes in𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟𝑟𝑟)) 𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐 electronics stage in brushless drives is used for 𝑠𝑠 𝜔𝜔 𝐿𝐿 𝐽𝐽 𝜔𝜔 𝐿𝐿 𝑚𝑚 1 𝑅𝑅 ψ vehicle systems, railways, FACTS, HVDC, wind turbines, 0 −0 1𝑠𝑠 𝑚𝑚 ] improving the efficiency and control of electrical processes in𝑖𝑖𝜃𝜃𝑏𝑏𝑏𝑏 ̇̇ ] = 0 − − 𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏(𝜃𝜃 𝑖𝑖 𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟𝑟𝑟) [𝜔𝜔 [ 𝑏𝑏𝑏𝑏 𝑟𝑟 𝑐𝑐𝑐𝑐 𝜔𝜔 𝑐𝑐𝑐𝑐 𝑟𝑟 electronics stage in electric brushless drives is used for 𝑚𝑚 𝐿𝐿 0 0 − − 𝑓𝑓 𝑚𝑚 vehicle systems, railways, FACTS, HVDC, wind turbines, 𝐿𝐿 𝐽𝐽 ) 1 𝑅𝑅 ψ 𝑐𝑐𝑐𝑐(𝜃𝜃 ̇ improving the efficiency andFACTS, control ofHVDC, electrical processes inψ𝑚𝑚 1 ψ𝑚𝑚 𝐿𝐿 𝑠𝑠 𝐵𝐵 𝑟𝑟 [𝜔𝜔 [𝜔𝜔 𝑟𝑟 ] 𝑖𝑖𝜃𝜃𝑐𝑐𝑐𝑐𝑚𝑚 𝑟𝑟̇̇ ] = ψ𝑚𝑚 0 𝑖𝑖𝜃𝜃 𝐽𝐽𝑚𝑚 photovoltaics, and home appliances amount others, the vehicle systems, railways, wind turbines, (1) 𝑐𝑐𝑐𝑐 1 0 − − 𝑓𝑓 𝑚𝑚 [ 𝜃𝜃 𝑓𝑓 𝑓𝑓 𝑓𝑓 − ψ ψ ψ 𝐵𝐵 ) [ ] 𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 𝑟𝑟 ] 𝑅𝑅 ψ𝐽𝐽𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑏𝑏𝑏𝑏(𝜃𝜃𝑟𝑟 ) 𝑐𝑐𝑐𝑐(𝜃𝜃 improving the efficiency andFACTS, control of electrical processes in𝑟𝑟 photovoltaics, and home appliances amount others, the 𝑠𝑠 𝑟𝑟 ) 𝐿𝐿 (1) vehicle railways, turbines, ̇ ] [ψ𝐽𝐽𝑚𝑚 𝐽𝐽𝑚𝑚 𝐽𝐽𝑚𝑚 𝐽𝐽𝑐𝑐𝑐𝑐(𝜃𝜃𝑟𝑟 ) ] [𝜔𝜔 ψ ψ 𝐵𝐵 1 ) 𝑓𝑓 𝑓𝑓 𝑓𝑓 − 𝜃𝜃 0 0 − − 𝑓𝑓 𝑚𝑚 𝑚𝑚 𝑚𝑚 𝑚𝑚 ) ) 𝑎𝑎𝑎𝑎(𝜃𝜃 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 primary systems, goal of and this analysis is to showHVDC, how thewind lifetime in the [𝜔𝜔 𝜃𝜃𝑚𝑚 𝑟𝑟 ] photovoltaics, home appliances amount others, 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟 (1) 𝑟𝑟 ] [ 𝐽𝐽 𝐽𝐽 𝐽𝐽 𝐽𝐽 𝑓𝑓 𝑓𝑓 𝑓𝑓 − 1 𝐿𝐿 𝐽𝐽 vehicle systems, railways, FACTS, turbines, ψ 𝐵𝐵 𝑐𝑐𝑐𝑐(𝜃𝜃 primary goal of and this analysis is to showHVDC, how thewind lifetime in the 1 𝑟𝑟 ) 𝑟𝑟 ) ̇𝑟𝑟 ] [ψ𝐽𝐽𝑚𝑚 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟) ψ𝐽𝐽𝑚𝑚 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑚𝑚 [ 𝜃𝜃 ] photovoltaics, home appliances amount others, [ 𝜃𝜃 0 ) 0 ] 𝑟𝑟 𝐽𝐽 (1) 1 ) 0 𝐽𝐽 𝑓𝑓𝑐𝑐𝑐𝑐(𝜃𝜃 semiconductors is incremented thehow speed is 𝑓𝑓𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟) ψ 𝑓𝑓L−M − 𝐵𝐵 primary goal of and this analysis is toand show theresponse lifetime in not the 𝑏𝑏𝑏𝑏(𝜃𝜃 ψ ψ 𝑟𝑟 𝑟𝑟 0 0 0 𝑚𝑚 𝑚𝑚 𝑚𝑚 1 𝑣𝑣 photovoltaics, home appliances amount others, the [ ] 𝐽𝐽 𝑓𝑓 𝐽𝐽 𝑓𝑓L−M 01 𝐽𝐽 𝑓𝑓 0 0 𝑎𝑎𝑎𝑎− 𝐽𝐽 semiconductors is incremented and thehow speed response is not (1) primary goal ofThus, this analysis is toand show lifetime in not the ) ) 0 𝑣𝑣 𝑎𝑎𝑎𝑎(𝜃𝜃𝑟𝑟 ) 𝑏𝑏𝑏𝑏(𝜃𝜃 𝑐𝑐𝑐𝑐(𝜃𝜃 𝑟𝑟 𝑟𝑟 compromised. this lifetime study canthe be expanded to semiconductors is incremented the speed response is 0 0 1 𝑎𝑎𝑎𝑎 [ 𝐽𝐽 ] 𝐽𝐽 L−M L−M 𝑏𝑏𝑠𝑠 𝐽𝐽 primary goal ofThus, this analysis is toand show how lifetime in not the 𝑣𝑣𝑎𝑎𝑎𝑎 011 𝐽𝐽 0 0 [𝑣𝑣 compromised. this lifetime study canthe be expanded to 01 semiconductors is incremented the speed response is + ] 𝑣𝑣 L−M 𝑏𝑏𝑠𝑠 several applications tothis increment their lifetime in the power compromised. Thus, lifetime study can be expanded to 01 0 [𝑣𝑣𝑎𝑎𝑎𝑎 0 L−M 𝑐𝑐𝑐𝑐 ] 01 + 0 0 𝑏𝑏𝑠𝑠 semiconductors is incremented andtheir the lifetime speed response is not L−M several applications tothis increment in the power L−M compromised. Thus, lifetime study can be expanded to 𝑐𝑐𝑐𝑐 ] 011 + L−M 𝑇𝑇𝑎𝑎𝑎𝑎 0 L−M 01 01 [𝑣𝑣𝑣𝑣 electronic stage. The switching andlifetime conduction of the several applications to increment their in the power 𝑣𝑣 𝑏𝑏𝑠𝑠 L−M 0 [𝑣𝑣𝑇𝑇𝑐𝑐𝑐𝑐𝑙𝑙𝑙𝑙 ] 0 0 compromised. Thus, this lifetime their study can be in expanded to + 0 01 0 electronic stage. The switching andlifetime conduction of the 0 several applications to increment the power L−M 1 𝑏𝑏𝑠𝑠 L−M [ ] 𝑇𝑇 semiconductors power losses,and which are reflected as electronic stage.cause The switching conduction the 01𝐽𝐽 [ 𝑐𝑐𝑐𝑐𝑙𝑙 ] 0 L−M 01 +[ 0 several applications to power increment their lifetime the of power 𝑣𝑣𝑇𝑇𝑐𝑐𝑐𝑐𝑙𝑙 semiconductors cause losses, which areinreflected as 0 electronic stage. The switching and conduction of the 0 0 01𝐽𝐽𝐽𝐽 ]] 𝑓𝑓 [ temperature oscillations. The temperature oscillations are the semiconductors cause power losses,and which are reflected as where 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃), 𝑓𝑓𝑏𝑏𝑏𝑏 = 𝑓𝑓𝑎𝑎𝑎𝑎 0(𝜃𝜃 −02𝜋𝜋/3) = 𝑓𝑓 (𝜃𝜃 + 2𝜋𝜋/3) L−M 0 and 𝑇𝑇𝑐𝑐𝑐𝑐 electronic stage. The switching conduction of 𝑙𝑙 = 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃 + 2𝜋𝜋/3) temperature oscillations. The temperature oscillations are the [ ] (𝜃𝜃), (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 1 𝐽𝐽 semiconductors cause losses,stress) which reflected as are back-EMF 𝑎𝑎𝑎𝑎 (𝜃𝜃), waveform 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 0 𝑐𝑐𝑐𝑐 cause of the rupture (bypower mechanical of are the union of the temperature oscillations. The temperature oscillations are 02𝜋𝜋/3) 0 phase (𝜃𝜃 of each respectively. ψ𝑚𝑚 is 𝑓𝑓 − and 𝑓𝑓 where 𝑓𝑓 = 𝑓𝑓 = 𝑓𝑓𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 (𝜃𝜃 + 2𝜋𝜋/3) [ ] 𝐽𝐽 semiconductors cause losses,stress) which reflected as are cause of the rupture (bypower mechanical of are the union of the back-EMF waveform of each phase respectively. ψ𝑚𝑚 is temperature oscillations. The are (𝜃𝜃), (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 = flux 𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃linkage + 2𝜋𝜋/3) welds of between the wirestemperature with theoscillations semiconductor. 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 cause the rupture (by mechanical stress) of the union of the the maximum value of permanent magnetic is are back-EMF waveform of each phase respectively. ψ𝑚𝑚 of temperature oscillations. The are the the welds of between the wirestemperature with theoscillations semiconductor. (𝜃𝜃), (𝜃𝜃 (𝜃𝜃 where 𝑓𝑓 𝑓𝑓 = 𝑓𝑓 − 2𝜋𝜋/3) and 𝑓𝑓 = 𝑓𝑓 + 2𝜋𝜋/3) maximum value of permanent magnetic flux linkage of cause the rupture (by mechanical stress) of the union of the 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎 are back-EMF waveform of each phase respectively. ψ𝑚𝑚 of is Manufacturers of power electronics stages offer a lifetime of the welds between the wires with theof semiconductor. each winding, ψ = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 is the number of winding maximum value of permanent magnetic flux linkage 𝑚𝑚 cause of the rupture (by mechanical stress) the union of the Manufacturers of power electronics stages offer a lifetime of each are back-EMF waveform of each respectively. ψ𝑚𝑚 of is welds between the electronics wires withstages the semiconductor. winding, ψ = of 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 isphase the number oflinkage winding the maximum value permanent magnetic flux 𝑚𝑚 their products according to temperature fluctuations, so it of is each Manufacturers of power offer a lifetime 𝑆𝑆 is the product ofpermanent rotor radius and number the effective length 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁 ismagnetic the oflinkage winding winding, ψ 𝑚𝑚 = of welds between the electronics wires withstages the semiconductor. their products according to temperature fluctuations, so it of is turns, the maximum value flux of Manufacturers of power offer a lifetime turns, 𝑆𝑆 is the product of rotor radius and the effective length each winding, ψ𝑚𝑚 = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁value is the number of magnetic winding imperative to according keep the temperature in fluctuations, the semiconductors their products to temperature so it of is of conductors, 𝐵𝐵𝐵𝐵 is maximum of permanent turns, 𝑆𝑆 is the product of rotor radius and the effective length Manufacturers of power stages a lifetime imperative to according keep the electronics temperature in fluctuations, theoffer semiconductors each winding, ψ𝑚𝑚 = 2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁, 𝑁𝑁value is the number of magnetic winding their products to temperature so it is of conductors, 𝐵𝐵𝐵𝐵 is maximum of permanent turns, 𝑆𝑆 distribution is the product of rotor radius and the=effective length without extreme variations. imperative to keep the temperature in the semiconductors density in the air gap, 𝐿𝐿 = 𝐿𝐿 𝐿𝐿 = 𝐿𝐿 is the of conductors, 𝐵𝐵𝐵𝐵 is maximum value of permanent magnetic 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 their products according to temperature fluctuations, so it is without extreme variations. turns, 𝑆𝑆 is the product of rotor radius and the effective length imperative to keep the temperature in the semiconductors density distribution in the air gap, 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the of conductors, 𝐵𝐵𝐵𝐵 is maximum value of permanent magnetic 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏𝑀𝑀 is𝑐𝑐𝑐𝑐the mutual without extreme variations. self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the density distribution in the air gap, 𝐿𝐿 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 permanent 𝑎𝑎𝑎𝑎 of 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 magnetic imperative to keep the temperature the semiconductors Different techniques have been used to in control the elevation of self-inductanc, of conductors, 𝐵𝐵𝐵𝐵 is maximum value without extreme variations. and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 is the mutual density distribution in the air gap, 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 = 𝐿𝐿 is the 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 Different techniques have been used to control the elevation of 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏𝑀𝑀 is𝑐𝑐𝑐𝑐the mutual inductance. self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 = without extreme variations. 𝑎𝑎𝑎𝑎 air gap, 𝑏𝑏𝑏𝑏 𝐿𝐿 𝑐𝑐𝑐𝑐 𝐿𝐿 the temperature as heat sinks; cooled sinks or Different techniques have been forced used toair control theheat elevation of self-inductanc, density distribution the = is 𝐿𝐿𝑐𝑐𝑐𝑐the = 𝐿𝐿mutual is the inductance. 𝑏𝑏𝑏𝑏𝑀𝑀 and in 𝑀𝑀 𝑀𝑀= the temperature as heat sinks; forced air cooled heat sinks or 𝑎𝑎𝑎𝑎 = 𝑀𝑀𝑏𝑏𝑏𝑏 =𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐 = Different techniques have been forced used toair control theheat elevation of inductance. the temperature as heat sinks; cooled sinks or self-inductanc, and 𝑀𝑀 = 𝑀𝑀 = 𝑀𝑀 𝑎𝑎𝑎𝑎 𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐 = 𝑀𝑀 is the mutual inductance. Different techniques have been used to control the elevation of the temperature as heat sinks; forced air cooled heat sinks or2422 Copyright © 2019, 2019 IFAC inductance. 2405-8963 © IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. the temperature as heat sinks; forced air cooled heat sinks or2422Hosting Copyright © 2019 IFAC Copyright 2019 responsibility IFAC 2422Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 2422 10.1016/j.ifacol.2019.11.561 Copyright © 2019 IFAC 2422
2019 IFAC MIM Berlin, Germany, August 28-30, 2019
Manuel García et al. / IFAC PapersOnLine 52-13 (2019) 2372–2377
the junction temperature 𝑇𝑇𝑗𝑗 is obtained using the thermal equation (4), according to Infineon, (2012).
Thus, the electromagnetic torque is given by
𝑇𝑇𝑒𝑒 = ψ𝑚𝑚 [𝑓𝑓𝑎𝑎𝑎𝑎 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑎𝑎𝑎𝑎 + 𝑓𝑓𝑏𝑏𝑏𝑏 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑏𝑏𝑏𝑏 + 𝑓𝑓𝑐𝑐𝑐𝑐 (𝜃𝜃𝑟𝑟 )𝑖𝑖𝑐𝑐𝑐𝑐 ]
(2)
The complete model of the electromechanical system is described by 𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑙𝑙 = 𝐽𝐽 𝜔𝜔̇ 𝑚𝑚 + 𝐵𝐵𝜔𝜔𝑚𝑚
2373
(3)
where 𝑇𝑇𝑙𝑙 is load torque, 𝐽𝐽 is rotor moment of inertia and 𝐵𝐵 is viscous coefficient 𝜔𝜔̇ 𝑚𝑚 is the angular velocity of rotation and 𝜔𝜔𝑚𝑚 is the angular position.
𝑇𝑇𝑗𝑗 = 𝑊𝑊 ∗ (𝑅𝑅𝑡𝑡ℎ (𝑗𝑗 − 𝑐𝑐) + 𝑅𝑅𝑡𝑡ℎ (𝑐𝑐 − 𝑓𝑓) + 𝑅𝑅𝑡𝑡ℎ (𝑓𝑓 − 𝑎𝑎)) + 𝑇𝑇𝑎𝑎
The commutation and conduction losses as well as the temperature profiles on IGBT junction are given by the averages on a modulation period and modelling electrothermic networks as shown in Fig. 2(b), Wintrich (2011).
W
3. POWER MODULE LOSSES
Most power electronics interface contains multichipsemiconductor, it can comprise of IGBT and Diodes. The power electronics interface losses are given as the sum of losses produces by the IGBT chips and the diode chips. These power losses can be classified as on-state losses and switching losses, Infineon (2012). The on-state IGBT power losses are 2 , where 𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶 is the given by 𝑃𝑃𝐶𝐶𝐶𝐶 = 𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶 ∗ 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑟𝑟𝑐𝑐 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 collector-emitter on-state tension, 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 and 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 are average current value and root mean square current value of IGBT respectively while 𝑟𝑟𝑐𝑐 is the collector-emitter on-state resistance value, 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶 , 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 and 𝑟𝑟𝑐𝑐 can be estimated according to Graovac et al. (2009). On-state diode power losses are given by 𝑃𝑃𝐶𝐶𝐶𝐶 = 2 , where 𝑢𝑢𝐷𝐷𝐷𝐷 is the anode-cathode, on𝑢𝑢𝐷𝐷𝐷𝐷 ∗ 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 + 𝑟𝑟𝐷𝐷 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 state, tension, 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 and 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 are average current value and root mean square current value of Diode respectively while 𝑟𝑟𝐷𝐷 is the anode-cathode on-state resistance value. 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷 , 𝐼𝐼𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 and 𝑟𝑟𝐷𝐷 could be estimated according to Graovac et al. (2009). The turn-on IGBT energy losses are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡 𝑢𝑢𝐶𝐶𝐶𝐶 (𝑡𝑡) ∗ 𝑖𝑖𝐶𝐶 (𝑡𝑡)𝑑𝑑𝑑𝑑. The turn-off energy losses are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑢𝑢𝐶𝐶𝐶𝐶 (𝑡𝑡) ∗ 𝑖𝑖𝐶𝐶 (𝑡𝑡)𝑑𝑑𝑑𝑑, where: 𝑢𝑢𝐶𝐶𝐶𝐶 and 𝑖𝑖𝐶𝐶 are collector-emitter tension and collector current respectively during IGBT turn on or turn off. Fig.5. shows the switching energy losses. The turn-on diode energy losses are mostly presented when the reverse-recovery energy occur, and these are given by 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 = ∫𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝑢𝑢𝐷𝐷 (𝑡𝑡) ∗ 𝑖𝑖𝐹𝐹 (𝑡𝑡))𝑑𝑑𝑑𝑑 , where 𝑢𝑢𝐷𝐷 and 𝑖𝑖𝐹𝐹
(4)
Tj PswQ
Tc
PswD PswQ
Rth(j-c) PcQ
PcQ
PswD
TjQ
Zth_jc_Q
PcD PcD
TjD
Zth_jc_D
Rth(c-f) TcQ
Tf Rth_CH_Q Rth(f-a)
TcD Rth_CH_D Th
Ta
Fig. 2. (a) Thermal resistance equivalent circuit, (b) ElectroThermal model. 4. LIFETIME OF POWER ELECTRONICS INTERFECE The thermal stress is presented as a consequence of the temperature difference ∆𝑇𝑇𝑗𝑗 between silicon and bonding wire, which happens during the changes of temperature. These changes go up and down in a short time cycle, and as a result of this kind of operation, the lifetime of power electronics semiconductors is mainly limited by the aluminium bonding wire joints, Fig. 3 shows an example of these changes of temperature.
are anode-cathode tension and forward current respectively during turn on. Hence, switching losses for IGBT and Diode are given by 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 = (𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 + 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ) ∗ 𝐹𝐹𝑠𝑠𝑠𝑠 and 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 = (𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 + 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ) ∗ (𝐹𝐹𝑠𝑠𝑠𝑠 ) ≈ 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 ∗ (𝐹𝐹𝑠𝑠𝑠𝑠 ) 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 and 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 are given as the product of switching energies and the switching frequency 𝐹𝐹𝑠𝑠𝑠𝑠 . According to Infineon (2012), the switching losses in the diode are normally neglected 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 0. Finally, the total losses of the IGBT module are given by equation (3). 𝑊𝑊 = 𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑃𝑃𝐶𝐶𝐶𝐶 + 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠
(3)
On the other hand, the semiconductor heat conduction is simulated as an electric circuit with one IGBT module mounted on a heat sink as is shown in Fig. 6(a), where 𝑊𝑊 is a module power loss, 𝑇𝑇𝑗𝑗 is junction temperature IGBT chip, 𝑇𝑇𝑓𝑓 is the heat sink temperature, 𝑇𝑇𝑐𝑐 is module case temperature, 𝑇𝑇𝑎𝑎 is ambient temperature, 𝑅𝑅𝑡𝑡ℎ (𝑗𝑗 − 𝑐𝑐) is thermal resistance between case and heat sink, 𝑅𝑅𝑡𝑡ℎ (𝑐𝑐 − 𝑓𝑓) is contact thermal resistance between case and heat sink, and 𝑅𝑅𝑡𝑡ℎ (𝑓𝑓 − 𝑎𝑎) is thermal resistance between heat sink and ambient air. Thus,
Fig. 3. Pattern diagram flow current of ∆𝑻𝑻𝒋𝒋 power cycle and temperature change. Finally, the estimation of lifetime of semiconductors can be given as the Time Before Failure (TBF) or the Cycles Before Failure (CBF), according to ABB (2014) and Fuji Electric (2015).
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𝐶𝐶𝐶𝐶𝐶𝐶 = 541162959016419 ∗ ∆𝑇𝑇 −5.12121
(5)
where the compute of CBF are given by Eq. 14, where Δ𝑇𝑇 = 2 𝑅𝑅𝑜𝑜𝑜𝑜 , and 𝑍𝑍𝑡𝑡ℎ = 2.3354𝐹𝐹𝑟𝑟−0.165, and, TBF is 𝑃𝑃𝑡𝑡 𝑍𝑍𝑡𝑡ℎ , 𝑃𝑃𝑡𝑡 = 𝐼𝐼𝑟𝑟𝑟𝑟𝑟𝑟 given in years according to the equation (6). 𝑇𝑇𝑇𝑇𝑇𝑇 =
𝐶𝐶𝐶𝐶 ∗ 60 ∗ 24 ∗ 365 [𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦] 𝐹𝐹𝐹𝐹
(6)
where 𝐹𝐹𝑟𝑟 is the frequency of the thermal oscillations, Fuji Electric (2015) and Vincotech (2017). Hence, this estimation considers the thermal losses, which can be computed through equivalent circuit shown in Fig. 6(b) or the power cycling lifetime curve provided by the datasheet of the power electronic semiconductor manufacturer as is shown in Fig. 4, where is presented an example of the IGBT module power cycle capability curve for ∆𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 25℃ and ∆𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 150 ℃ according to ABB (2014) and Fuji Electric (2015).
The controller is designed according to Mamdani inference methodology. The linguistic knowledge base is expressed as a set of linguistic rules such as if-then statements. In this case, the rules have the linguistic expression If 𝑒𝑒(𝑡𝑡) is 𝐴𝐴 𝑎𝑎𝑎𝑎𝑎𝑎 𝑒𝑒̇ (𝑡𝑡) is 𝐵𝐵 then 𝑖𝑖𝑐𝑐 is C, where A, B and C are linguistic values defined in a universe of discourse of three triangular functions (N: negative, Z: zero and P: positive). On the other hand, the inference engine is given by if-then statements. According to Mamdani inference methodology, the inference is given by 𝑛𝑛 𝑛𝑛 𝑛𝑛 𝐶𝐶 ∗ = 𝑈𝑈𝑗𝑗=1 𝐶𝐶í∗ where 𝐶𝐶 ∗ = 𝜇𝜇𝐶𝐶´ (𝑖𝑖𝑐𝑐 ); 𝑦𝑦 𝑈𝑈𝑗𝑗=1 𝐶𝐶í∗ =∪𝑗𝑗=1 [𝛼𝛼𝑗𝑗 ∩ 𝜇𝜇𝐶𝐶𝐶𝐶 (𝑖𝑖𝑐𝑐 )]. Finally, the defuzzification stage gets a crisp value from the rule evaluation stage through the center of gravity method by 𝑧𝑧 ∗ = ∫ 𝜇𝜇𝐴𝐴 (𝑧𝑧) ∙ 𝑧𝑧𝑧𝑧𝑧𝑧⁄∫ 𝜇𝜇𝐴𝐴 (𝑧𝑧) ∙ 𝑧𝑧𝑧𝑧𝑧𝑧 Decrease overshoot
DE
c g Set point
b
d
k
j
h
f
l
i
e
E
a i
Decrease Rise time
E DE
ii
- -
+
iii
iv
+
+ +
-
v
vi vii viii
- - - +
+
ix
+ + + -
x
xi
- - +
Time
Fig. 5. Linguistic phase plane 5. DESIGN OF FUZZY-PSO CONTROLLER 5.1. Particle Swarm Optimization
Fig. 4. Power cycling lifetime curve. 4. DESIGN OF FLC TO SPEED CONTROL OF BLDC MOTOR Fuzzy Logic Controller (FLC) is based on Fuzzy Logic proposed by Zadeh, (1965) and its components are: a Fuzzification interface which transforms crisp input values into fuzzy values, a knowledge base which consists of a database and a linguistic rule base, an inference engine makes decisions employing fuzzy implication and linguistic rules and a defuzzification interface which yields a non-fuzzy control action from an inferred fuzzy control action. A useful methodology to design fuzzy logic controllers is based on a linguistic phase plane, Lee (2005), as shown in Fig. 5. The error 𝑒𝑒𝑐𝑐 (𝑡𝑡) = 𝜔𝜔𝑑𝑑 (𝑡𝑡) − 𝜔𝜔(𝑡𝑡) where 𝜔𝜔𝑑𝑑 (𝑡𝑡) is the desired speed and 𝜔𝜔(𝑡𝑡) is the current speed and change of error 𝑒𝑒̇ (𝑡𝑡) = 𝑒𝑒(𝑡𝑡) − 𝑒𝑒(𝑡𝑡 − 1) are considered as antecedent while 𝑖𝑖𝑐𝑐 is the conclusion (output variable). The range of 𝑖𝑖𝑐𝑐 goes from 0 to 100 percenter of the duty cycle which stablishes the average supply voltage (V1 see Fig. 1) in the VSI. The range of 𝑒𝑒(𝑡𝑡) is [-14, 14] and the 𝑒𝑒̇ (𝑡𝑡) is [-1, 1].
Particle Swarm Optimization (PSO) was developed by [9], this method is based on the behaviour and movement of bird flocks looking for targets, this algorithm was developed to optimization nonlinear optimization and multidimensional functions, Zhang (2015) and Dandy (2018). PSO algorithm works with specific numbers of particles, which are denominated population. The PSO algorithm initializes the population in a random way, where each particle has a position 𝑥𝑥𝑖𝑖 (𝑡𝑡) and velocity 𝑣𝑣𝑖𝑖 (𝑡𝑡) with respect to target, then each particle is evaluated in the main loop, where 𝑥𝑥𝑖𝑖 (𝑡𝑡) and 𝑣𝑣𝑖𝑖 (𝑡𝑡) are updated in each iteration, this new position is compared with the previous best local position 𝑃𝑃𝑖𝑖 (𝑡𝑡), if the new position is better than the previous best local position then the best local position is update with the new position. At the last, the new position also is compared with the best global position 𝑔𝑔(𝑡𝑡), where 𝑔𝑔(𝑡𝑡) is closest with respect to the target and if the new position is better than the best global position then the best glob, al position value is updated. Additionally, the update of velocity is defined by 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1) = 𝜔𝜔𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘) +
𝑟𝑟1𝑗𝑗 𝐶𝐶1 (𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) − 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘)) and the position is defined by 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1) = 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) + 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘 + 1), where 𝑖𝑖 = 1,2, … , 𝑁𝑁, and 𝑁𝑁 is the size of population, 𝑗𝑗 = 1,2, … , 𝐷𝐷, and 𝐷𝐷 is the number of dimensions, 𝑘𝑘 = 1,2, … , 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖, and 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 is the maximum iteration number, 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) is the position of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘) is the velocity of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) is the local best position of particle 𝑖𝑖, dimension 𝑗𝑗 at iteration 𝑘𝑘, 𝑔𝑔𝑗𝑗 (𝑘𝑘) is the global best, 𝜔𝜔 is an inertia factor, 𝐶𝐶1 , 𝐶𝐶2 are the acceleration constant, 𝑟𝑟1 , 𝑟𝑟2 are independent random numbers, uniformly distributed in (0,1). Thus, the primary objective is to find a minimal global value
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from the cost function through be minimized as it is shown in the next pseudocode. Song (2004).
Step 1. Initialization, for each particle of population 𝑁𝑁, do 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘). Step 2. Repeat until the criterion is satisfied, for each particle of population 𝑁𝑁, do, set random numbers to 𝑟𝑟1𝑗𝑗 and 𝑟𝑟2𝑗𝑗 , update 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘), 𝑣𝑣𝑖𝑖𝑖𝑖 (𝑘𝑘). If 𝑥𝑥𝑖𝑖𝑖𝑖 (𝑘𝑘) < 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘), update the best local position 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) If 𝑃𝑃𝑖𝑖𝑖𝑖 (𝑘𝑘) < 𝑔𝑔𝑗𝑗 (𝑘𝑘), update the best global position g(𝑘𝑘) Step 3. Get the best solution 𝑔𝑔(𝑘𝑘).
fuzzy logic process so it is only added to 𝑒𝑒𝑐𝑐 to obtain 𝑓𝑓𝑐𝑐 . So each membership function of the FLC is considered as a decision variable. Figure 6 shows a block diagram of FuzzyPSO control realization. PSO algorithm is implemented to tuning the antecedent and conclusion membership functions parameters of speed feedback loop in order to reach the speed desired and the temperature desired in power electronic stage, the temperature is only used as a change to be added to the objective function, thus it does not have any feedback of the current temperature. The constraints of the optimization are the mechanical capacity value of BLDC motor and the thermal capacity value of IGBTs, which are shown in Table 2.
5.2. Optimization of FLC by PSO
Table 2. Experimental settings
Based on the separability of the objective and constraint functions, defined in Dandy (2018) as "A function 𝑓𝑓(𝑿𝑿) is said to be separable if it can be expressed as the sum of n singlevariable functions,𝑓𝑓1 = (𝑥𝑥1 ), 𝑓𝑓2 = (𝑥𝑥2 ), … … 𝑓𝑓𝑛𝑛 = (𝑥𝑥𝑛𝑛 ) that is 𝑓𝑓(𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑓𝑓𝑖𝑖 (𝑥𝑥𝑖𝑖 ) “ which can be expressed in standard form as: Find 𝑿𝑿 which minimizes 𝑓𝑓(𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑓𝑓𝑖𝑖 (𝑥𝑥𝑖𝑖 ), subject to 𝑔𝑔𝑗𝑗 (𝑿𝑿) = ∑𝑛𝑛𝑖𝑖=1 𝑔𝑔𝑖𝑖𝑖𝑖 (𝑥𝑥𝑖𝑖 ) ≤ 𝑏𝑏𝑗𝑗 , 𝑗𝑗 = 1,2, … , 𝑚𝑚 where 𝑏𝑏𝑗𝑗 is a constant. Thus, it establishes the objective function.
𝑡𝑡𝑑𝑑
𝜔𝜔𝑑𝑑
𝑒𝑒𝑡𝑡
+-
𝑒𝑒𝑐𝑐
+ +
+-
𝑓𝑓𝑐𝑐
𝑡𝑡
IGBT 10-0B066PA006SB-M992F09 𝑉𝑉𝐶𝐶𝐶𝐶 𝑅𝑅𝐶𝐶𝐶𝐶(𝑂𝑂𝑂𝑂)
Parameter
𝑅𝑅𝐽𝐽−𝑆𝑆 . Thermal Resistance Junction to Sink
Unit
8-6
℃
80 to 175
V Ω A
3,50
K/W
Stator Inductance
0.15
mH
Stator Resistance Velocity constant Torque constant
0.6 0.03 0.03
Ω Vs/rad Nm/A
BLDC motor
Number of pole pairs
PSO Algorithm Objetive function 𝑓𝑓𝑐𝑐
1
Parameter of IGBT in co-simulation MultisimTM IGBT control threshold IGBT on resistance
Tuning Membership Functions
𝜔𝜔
600 0.1
Value
𝐽𝐽𝑐𝑐 𝑇𝑇𝐽𝐽 , Junction Temperature
Temperature Measurement
FLC
2375
INVERTER
BLDC MOTOR
0.5 0.1meg
V Ω
IGBT off resistance
10
Ω
IGBT forward voltage drop
0.7
V
Diode on resistance
1m
Ω
Diode off resistance
10meg
Ω
Number of switches in parallel
1
Triggering Pulse
Hall Effect Sensor
Speed Measurement
Table 3. PSO parameters Parameter Population Size Social rate (𝑐𝑐1 )
Fig. 6. Diagram of Fuzzy-PSO control. The design of the controller considers two objectives, the first one is to reach the desired motor speed, and the second one is to increase the semiconductors lifetime. Hence, the BLDC motor speed control design is based on FLC technique, and PSO algorithm optimize the membership functions of FLC. Furthermore, one of the leading features is the definition of the objective function (𝑓𝑓𝑐𝑐 ), which considers the temperature error 𝑒𝑒𝑡𝑡 and the speed error 𝑒𝑒𝑐𝑐 , is shown in equation (7). 𝑓𝑓𝑐𝑐 = 𝑒𝑒𝑐𝑐 + 𝑒𝑒𝑡𝑡
(7)
𝑒𝑒𝑡𝑡 is defined by the temperature error 𝑒𝑒𝑡𝑡 (𝑡𝑡) = 𝑡𝑡𝑑𝑑 (𝑡𝑡) − 𝑡𝑡(𝑡𝑡), where 𝑡𝑡𝑑𝑑 is the desired temperature and 𝑡𝑡 is the current semiconductors temperature while 𝑒𝑒𝑐𝑐 is defined in paragraph 4. Thus, the objective function defined in the equation (7) is minimized through of PSO algorithm which is accomplished by adjusting the memberships function antecedent and conclusion in each 𝑒𝑒𝑐𝑐 update. On the other hand, 𝑒𝑒𝑡𝑡 has no
Cognitive rate (𝑐𝑐2 ) Inertia factor (𝑊𝑊)
30
Value
0.005 0.002 0.002
6. CO-SIMULATION DESIGN The proposed scheme to validate controllers, PID, Fuzzy and Fuzzy-PSO, is designed in co-simulation through LabviewTM and MultisimTM tools. The BLDC motor, the Hall effect sensors, and the six-steps inverter were designed in MultisimTM software. The parameters utilized of the BLDC motor, National Instruments (2013), and the six IGBT 100B066PA00Sb-M992F09, Vincotech (2017), are shown in Table 2, and the PSO algorithm parameters are selected according to a dynamic system and the sample time of controller through online experimentation as is shown in Table 3. On the other hand, PID, Fuzzy and Fuzzy-PSO controllers are designed in LabviewTM software, National Instruments (2013). The proposed Fuzzy-PSO controller in this work is
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designed with the Fuzzy Logic Toolkit, Ponce et al. (2010), and the PSO optimization was developed in LabviewTM, Fig. 7, shows the block diagram of Fuzzy-PSO implementation.
thus like without and with load (N/m). PID Advanced autotuning VI implemented a PID controller in LabviewTM Toolkit, which includes the features of PID controller such as proportional gain, integral time and derivative time. Besides, this toolkit can be implemented in co-simulation applications. On the other hand, according to the desired parameters of speed and temperature, the PID controller response to reach the reference speed is a short time in comparison with the other two controllers.
Fig. 8. Blockdiagram of the Co-simulation of Fuzzy-PSO controller using LabviewTM and MultisimTM
Fig. 11. Temperature response of PID, FUZZY and FUZZYPSO controllers without load
Fig. 9. Speed response of PID, FUZZY and FUZZY-PSO controllers without Load Fig. 12. Speed response of PID, FUZZY and FUZZY-PSO controllers with Load Acknowledgment This research is a product of the Project 266632 “Laboratorio Binacional para la Gestión Inteligente de la Sustentabilidad Energética y la Formación Tecnológica” [“Bi-National Laboratory on Smart Sustainable Energy Management and Technology Training”], funded by the CONACYT SENER Fund for Energy Sustainability (Agreement: S0019201401). Fig. 10. Speed response of PID, FUZZY and FUZZY-PSO controllers with Load
This research was also supported by National Instruments Austin Texas,
6. DISCUSSION AND RESULT The proposed control law considers two control objectives, the first one is to track the speed reference and the second one is to keep the desired temperature to increase the lifetime of the IGBTs. Furthermore, the optimization trade-off was tasted on PID, Fuzzy and Fuzzy-PSO controllers in the co-simulation program; thus, Fuzzy-PSO controller was evaluated under different desired temperatures, which are 25 °C, 40°C and 80°C, the reference speed was evaluated at 10 m/s and 5 m/s,
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