Application of Model Reference Adaptive PI Control to FTCC of a Wind Farm

10th 10th IFAC IFAC Symposium Symposium on on Fault Fault Detection, Detection, 10th IFAC Symposium on Fault Detection, 10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes 10th IFAC Symposium on Fault Detection, Available Supervision and Safety for Technical Processes Supervision and Safety for Technical Processesonline at www.sciencedirect.com Supervision and Safety for Technical Processes 10th IFAC Symposium on Fault Detection, Warsaw, Poland, August 29-31, 2018 10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes Warsaw, Poland, August 29-31, 2018 Warsaw, Poland, August 29-31, 2018 Warsaw, August 29-31, 2018 Supervision and Technical Supervision and Safety Safety for Technical Processes Warsaw, Poland, Poland, Augustfor 29-31, 2018 Processes Warsaw, Warsaw, Poland, Poland, August August 29-31, 29-31, 2018 2018

ScienceDirect

IFAC PapersOnLine 51-24 (2018) 280–285

Application Application of of Model Model Reference Reference Adaptive Adaptive PI PI Control Control to to FTCC FTCC of of a a Wind Wind Farm Farm Application of Model Reference Adaptive PI Control to FTCC of a Wind Farm Application of Model Hamed Reference Adaptive PI Control to FTCC of a Wind Farm Badihi, Saeedreza Saeedreza Jadidi, Jadidi, Youmin Youmin Zhang* Zhang* Hamed Badihi,

Hamed Badihi, Saeedreza Jadidi, Youmin Zhang* Hamed Hamed Badihi, Badihi, Saeedreza Saeedreza Jadidi, Jadidi, Youmin Youmin Zhang* Zhang* Hamed Badihi, Saeedreza Jadidi, Youmin Zhang* Hamed Badihi, Saeedreza Jadidi, Youmin Zhang* Dept. of Mechanical, Industrial and Aerospace Engineering, Concordia University, Dept. of of Mechanical, Mechanical, Industrial Industrial and and Aerospace Aerospace Engineering, Engineering, Concordia Concordia University, University, Montreal, Montreal, Quebec Quebec H3G H3G 1M8, 1M8, Canada Canada Dept. Montreal, Quebec H3G 1M8, Canada Dept. Dept. of of Mechanical, Mechanical, Industrial Industrial and and Aerospace Aerospace Engineering, Engineering, Concordia Concordia University, University, Montreal, Montreal, Quebec Quebec H3G H3G 1M8, 1M8, Canada Canada Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Dept. of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec H3G 1M8, Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Dept. of Mechanical, Industrial Aerospace Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada Canada Emails: and {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Emails: {Hamed.Badihi;Saeedreza.Jadidi;Youmin.Zhang}@concordia.ca Abstract: High reliability and availability are crucial for cost-effective operation of any wind farm. In this Abstract: Abstract: High High reliability reliability and and availability availability are are crucial crucial for for cost-effective cost-effective operation operation of of any any wind wind farm. farm. In In this this Abstract: High reliability and availability are for operation of wind farm. Abstract: High reliability and availability are crucial crucial for cost-effective cost-effective operationneed of any any wind farm. In In this this regard, effective schemes for fault detection, diagnosis and accommodation to be developed to regard, effective schemes for fault detection, diagnosis and accommodation need to be developed to regard, effective schemes for fault detection, diagnosis and accommodation need to be developed to Abstract: High reliability and availability are crucial for cost-effective operation of any wind farm. In this regard, effective effective schemes for fault detection, detection, diagnosis and consequently accommodation need to wind be developed to Abstract: High reliability and availability are crucial for cost-effective operation offarms any farm.ofInwind this regard, schemes for fault diagnosis and accommodation need to be developed to improve the reliability and availability of wind turbines and wind (groups improve the reliability and availability of wind turbines and consequently wind farms (groups of wind improve the reliability and availability of wind turbines and consequently wind farms (groups of wind regard, effective schemes for fault detection, diagnosis and accommodation need to be developed to improve the reliability and availability ofemploys winddiagnosis turbines and consequently wind farms (groups of wind wind regard, effective schemes for fault detection, and consequently accommodation need to be developed to improve the reliability and availability of wind turbines and wind farms (groups of turbines). To address issue, this an adaptive proportional-integral (PI) approach turbines). To address this issue, this paper employs an adaptive proportional-integral (PI) control approach turbines). To reliability address this this issue, this paper paperof employs an adaptive proportional-integral (PI) control control approach improve the and availability wind turbines and consequently wind (groups of turbines). To address this issue, this paper employs an adaptive adaptive proportional-integral (PI) control approach improve the reliability and availability ofemploys wind turbines and and consequently windoffarms farms (groups of wind wind turbines). To address this issue, this paper an proportional-integral (PI) control approach in a cooperative framework that is oriented to the design development a novel fault-tolerant in framework that is oriented to design and development of aa novel fault-tolerant in aaa cooperative cooperative framework that ispaper oriented to the the design and development of novel fault-tolerant turbines). To address this this employs an adaptive proportional-integral control approach in framework that oriented to design and development of novel fault-tolerant turbines). Tocontrol address this issue, issue, thisis employs an adaptive (PI) control approach in a cooperative cooperative framework that ispaper oriented to the the designto and development of aa(PI) novel fault-tolerant cooperative (FTCC) scheme in aaa wind farm. Applied aaaproportional-integral wind farm, this scheme handles decreased cooperative control (FTCC) scheme in wind farm. Applied to wind farm, this scheme handles decreased cooperative control (FTCC) scheme in wind farm. Applied to wind farm, this scheme handles decreased in a cooperative framework that is oriented to the design and development of a novel fault-tolerant cooperative control (FTCC) scheme in a wind farm. Applied to a wind farm, this scheme handles decreased in a cooperative framework that is oriented to the design and development of a novel fault-tolerant cooperative control (FTCC) scheme in a wind farm. Applied to a wind farm, this scheme handles decreased Different power generation faults that may be caused by icing or debris build-up on the blades over time. Different power that may caused icing or on over time. Different power generation generation faults thatscheme may be bein caused byfarm. icingApplied or debris debris build-up on the the blades over time.decreased cooperative controlfaults (FTCC) windby to aabuild-up wind farm, farm, thisblades scheme handles decreased Different power generation that may be caused by icing or build-up on blades over time. cooperative control (FTCC) aa wind to wind this scheme handles Different power generation faults thatscheme may bein caused byfarm. icingApplied or debris debris build-up on the the blades over time. simulations on aaa faults high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory simulations on high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory simulations on high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory Different power generation faults that may be caused by icing or debris build-up on the blades over time. simulations on a high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory Different power generation faults that may be caused by icing or debris build-up on the blades over time. simulations on a high-fidelity offshore wind farm of benchmark show the effectiveness and and satisfactory performance of the proposed scheme in the presence of wind turbulences, measurement noises and realistic performance of the proposed scheme in the presence wind turbulences, measurement noises realistic performance of the proposed scheme in the presence of wind turbulences, measurement noises and realistic simulations on a high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory performance of the proposed scheme in the presence of wind turbulences, measurement noises and simulations on a high-fidelity offshore wind farm benchmark show the effectiveness and satisfactory performance of the proposed scheme in the presence of wind turbulences, measurement noises and realistic realistic fault scenarios. fault scenarios. fault scenarios. performance of the proposed scheme in the presence of wind turbulences, measurement noises and fault scenarios. scenarios. performance of the proposed scheme in the presence of wind turbulences, measurement noises and realistic realistic fault Keywords: Fault-Tolerant Cooperative Control (FTCC), Adaptive Proportional-Integral (PI) Control, Wind Keywords: Fault-Tolerant Cooperative Control (FTCC), Adaptive Proportional-Integral (PI) Control, Wind fault scenarios. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Fault-Tolerant Cooperative Control (FTCC), Adaptive Proportional-Integral (PI) Control, fault scenarios. Keywords:Wind Fault-Tolerant Cooperative Control Control (FTCC), (FTCC), Adaptive Adaptive Proportional-Integral Proportional-Integral (PI) (PI) Control, Control, Wind Wind Keywords: Fault-Tolerant Cooperative Wind Turbines, Farms Turbines, Wind Farms Turbines, Farms Keywords: Fault-Tolerant Turbines, Wind Farms Cooperative Keywords:Wind Fault-Tolerant Cooperative Control Control (FTCC), (FTCC), Adaptive Adaptive Proportional-Integral Proportional-Integral (PI) (PI) Control, Control, Wind Wind Turbines, Wind Farms Turbines, Turbines, Wind Wind Farms Farms performed All performed based based on on aaa model-based model-based FDD FDD method. All of of the the performed based on model-based FDD method. All All of the 1. INTRODUCTION performed on FDD method. of 1. INTRODUCTION 1. INTRODUCTION performed based based works on aa model-based model-based FDD method. All of the the aforementioned works are unable to handle multiple, aforementioned are unable to handle multiple, 1. INTRODUCTION aforementioned works are unable to handle multiple, 1. INTRODUCTION performed based on a model-based FDD method. All of aforementioned works are unable to handle multiple, As source of large-scale performed based onina amodel-based FDD All of the the energy supply, wind turbines are As aaa source of large-scale aforementioned works are farm. unable to method. handle multiple, simultaneous faults wind farm. Moreover, they depend on 1. INTRODUCTION As source of large-scale energy supply, wind turbines are simultaneous faults in a wind Moreover, they depend on 1. INTRODUCTION As of large-scale energy supply, wind are simultaneous faults faults in aa wind wind farm. Moreover, they depend depend on works are unable to handle multiple, As aa source source of in large-scale energywind supply, windAnturbines turbines are aforementioned simultaneous in farm. Moreover, they on aforementioned works are unable to handle multiple, often installed clusters called farms. individual simultaneous faults in a wind farm. Moreover, they depend on the wind speed or its estimation which is normally related to often installed in clusters called wind farms. An individual the wind speed or its estimation which is normally related to As a source of large-scale energy supply, wind turbines are often installed in clusters called wind farms. An individual the wind speed or its estimation which is normally related to As a source of large-scale energy supply, wind turbines are simultaneous faults in a wind farm. Moreover, they depend on often installed in clusters called wind farms. An individual the wind speed or its estimation which is normally related to the simultaneous faults in a wind farm. Moreover, they depend on offshore wind farm can produce enough power to supply the the wind speed or its estimation which is normally related to wind direction and the farm layout. More recently, the offshore wind farm can produce enough power to supply the the wind direction and the farm layout. More recently, the often installed in clusters called wind farms. An individual offshore wind farm can produce enough power to supply the the wind direction and the farm layout. More recently, the often installed in clusters called wind farms. An individual wind speed or its estimation which is normally related to offshore wind farm can produce enough power to supply the the wind direction and the farm layout. More recently, the wind speed or its estimation which is normally related to annual electricity demand of thousands of households. In view the wind direction and the farm layout. More recently, the authors in Badihi et al. (2017a; 2017b) present different annual electricity demand of thousands thousands of power households. In view view authors indirection Badihi and et al. al.the(2017a; (2017a; 2017b)More present different offshore wind farm can produce enough to supply the annual electricity demand of of households. In authors in Badihi et 2017b) present different offshore wind farm canusages produce enough power tocomplexity, supply the authors the wind farm layout. recently, the annual electricity demand of thousands of households. In view in Badihi et al. (2017a; 2017b) present different of the more and wider worldwide, higher the wind direction and the farm layout. More recently, the of the more and wider usages worldwide, higher complexity, authors in Badihi et al. (2017a; 2017b) present different schemes of FTC in a cooperative framework referred to as of the more and wider usages worldwide, higher complexity, schemes of Badihi FTC in inetaa cooperative cooperative framework referred to as as annual electricity demand of thousands of In view of and usages worldwide, higher schemes FTC framework referred to annual electricity demand of thousands of households. households. In wind view schemes authors in al. (2017a; 2017b) present different of the the more more and wider wider usages worldwide, higher complexity, complexity, of Badihi FTC inetaa cooperative cooperative framework referred to conditions authors inof al.control (2017a; 2017b)The present different limited accessibility and harsh climate in conditions schemes of FTC in framework referred to as as fault-tolerant cooperative (FTCC). FTCC schemes limited accessibility and harsh climate conditions in wind fault-tolerant cooperative control (FTCC). The FTCC schemes of the more and wider usages worldwide, higher complexity, limited accessibility and harsh climate conditions in wind fault-tolerant cooperative control (FTCC). The FTCC schemes of the more and wider usages worldwide, higher complexity, schemes of FTC FTC in aa cooperative cooperative framework referred to as as limitedgeneration accessibility and harshoffshore), climate conditions in wind fault-tolerant cooperative control (FTCC). The FTCC schemes schemes of in framework referred to power (particularly rates and effects of fault-tolerant cooperative control (FTCC). The FTCC schemes do not depend on speed and direction of wind and they can power generation (particularly offshore), rates and effects of do not depend dependcooperative on speed speed and and direction of The windFTCC and they they can limited accessibility and harsh climate conditions in power (particularly rates effects of do not on direction of wind and can limitedgeneration accessibility andwind harshoffshore), climate become conditions in wind wind fault-tolerant control (FTCC). schemes power generation (particularly offshore), rates and andlarger effects of do not depend on speed and direction of wind and they can fault-tolerant cooperative control (FTCC). The FTCC schemes faults and failures in turbines and do not dependmultiple on speedsimultaneous and directionfaults of wind and than they one can accommodate multiple simultaneous faults in more than one faults and failures in wind offshore), turbines become larger and accommodate in more power (particularly rates and effects of faults and in turbines become larger and accommodate multiple simultaneous faults in more more than one power generation generation (particularly offshore), rates and effects of accommodate do not depend on speed and direction of and they can faults and failures failures in wind wind turbines become larger and multiple simultaneous faults in than one do notturbine depend on speed andarbitrary direction of wind wind and theyaims can significantly. This issue highlights the need for applying accommodate multiple simultaneous faults inThis more than one wind in a farm with layouts. This paper significantly. This issue highlights the need for applying wind turbine in a farm with arbitrary layouts. paper aims faults and failures in wind turbines become larger and significantly. This issue highlights the need for applying wind turbine in a farm with arbitrary layouts. This paper aims faults and failures in wind turbines become larger and accommodate multiple simultaneous faults in more than one significantly. This issue highlights the need forand applying wind turbine in a farm with arbitrary layouts. This paper aims accommodate multiple simultaneous faults in more than one advanced fault detection and diagnosis (FDD) faultwind turbine in a farm with arbitrary layouts. This paper aims to extend the works in Badihi et al. (2017a; 2017b) by advanced fault detection and diagnosis (FDD) and faultto extend the works in Badihi et al. (2017a; 2017b) by significantly. issue highlights the need applying advanced faultThis detection and to diagnosis (FDD)for and fault- to to extend thein works in Badihi Badihi et layouts. al. (2017a; (2017a; 2017b) by significantly. This issue highlights theturbines need for applying wind turbine aa farm with arbitrary This paper aims advanced fault detection and diagnosis (FDD) and faultextend the works in et al. 2017b) by wind turbine in farm with arbitrary layouts. This papermodel aims tolerant control (FTC) strategies wind for improved to extend the works in Badihi et al. (2017a; 2017b) by introducing a novel FTCC scheme based on an efficient tolerant control (FTC) strategies to wind turbines for improved introducing a novel FTCC scheme based on an efficient model advanced fault detection and diagnosis (FDD) and faulttolerant control (FTC) strategies to wind turbines for improved introducing a novel FTCC scheme based on an efficient model advanced fault detection and diagnosis (FDD) and faultto extend the works in Badihi et al. (2017a; 2017b) by tolerant control (FTC) strategies to wind turbines for improved introducing a novel FTCC scheme based on an efficient model to extendadaptive the works in scheme Badihi based et al.(PI) (2017a; 2017b) by reliability and Depending on the and nature a novel FTCC on ancontrol efficient model reference proportional-integral approach reliability and availability. availability. Depending on the type type and nature introducing reference adaptive adaptive proportional-integral (PI) control approach tolerant control (FTC) to wind turbines for improved reliability and Depending the type nature reference proportional-integral (PI) control approach tolerant control (FTC) strategies strategies to windon turbines forand improved aa novel FTCC scheme on efficient model reliability and availability. availability. Depending on the type and nature introducing reference adaptive proportional-integral (PI) approach of faults, such strategies can be developed at both individual introducing novel FTCC scheme based based on an ancontrol efficient model of faults, such strategies can be developed at both individual reference adaptive proportional-integral (PI) control approach that is used in the cooperative framework. The proposed of faults, such strategies can be developed at both individual that is is used in the the cooperative framework. framework. The approach proposed reliability and availability. Depending on and nature of such strategies can be developed at both individual that in cooperative The proposed reliability andand availability. Depending on the the type and nature reference adaptive proportional-integral (PI) control of faults, faults, such strategies can be developed at type both individual that is used used in the the cooperative framework. The proposed reference adaptive proportional-integral (PI) control approach wind turbine entire wind farm levels. Most of the recent that is used in cooperative framework. The proposed scheme acts against decreased power generation fault caused wind turbine and entire wind farm levels. Most of the recent scheme acts against decreased power generation fault caused of faults, such strategies can be developed at both individual wind turbine and entire wind farm levels. Most of the recent scheme acts against decreased power generation fault caused of faults, such strategies can be developed at both individual that is used in the cooperative framework. The proposed wind turbine and entire wind farm levels. Most of the recent scheme acts against decreased power generation fault caused that is used in the cooperative framework. The proposed works have rather focused on the application of FDD and FTC scheme acts against decreased power generation fault caused by icing or debris build-up on the blades over time. It is is works have rather focused on the application of FDD and FTC by icingacts or against debris build-up build-up onpower the blades blades overfault time.caused It wind turbine and wind farm levels. Most of the works have focused on the application of FDD and FTC by icing or debris the over time. It wind turbine and entire entire wind farm levels. Most ofSloth the recent scheme decreased generation works have rather rather focused on the application ofsee FDD andrecent FTC by icingacts or debris build-up onpower the thus blades overnot time. It is is scheme against decreasedon generation fault caused at individual wind turbine level (for example et al., by icing or debris build-up on the blades over time. It is independent of FDD information, and it does deal with at individual wind turbine level (for example see Sloth et al., independent of FDD information, and thus it does not deal with works have on the application of FDD and at wind turbine level example Sloth et al., independent FDD information, and thus it does deal with works have rather rather focused on the(for application ofsee FDD and2014; FTC icing or of debris build-up on the blades over It at individual individual windfocused turbine level (for example see Sloth etFTC al., by independent of FDD build-up information, thus it related does nottime. deal with et al., 2012; by icing or debris on and the blades overnot time. It is is 2011; Tabatabaeipour Simani and Castaldi, et al., 2012; independent of FDD information, and thus it does not deal with FDD uncertainties and time time delays to fault fault 2011; Tabatabaeipour et al., 2012; Simani and Castaldi, 2014; FDD uncertainties and time delays related to fault at individual wind turbine level (for example see Sloth et al., 2011; Tabatabaeipour et al., 2012; Simani and Castaldi, 2014; FDD uncertainties and delays related to at individual wind turbine level (for example see Sloth et al., independent of FDD information, and thus it does not deal with 2011; Tabatabaeipour etBadihi al., 2012; Simani and Castaldi, 2014; FDD uncertainties and time delays related to fault independent of FDD information, and thus it does not deal with Badihi et al., 2014; et al., 2015b). Recent new FDD uncertainties and time delays related to fault detection/isolation process. process. In In addition addition to to the the abovementioned abovementioned Badihi et et al., 2015b). Recent new detection/isolation process. In addition to abovementioned 2011; et al., and 2014; Badihi et al., al.,on2014; 2014; Badihi et Simani al.,reviewed 2015b). Recent new detection/isolation 2011; Tabatabaeipour Tabatabaeipour etBadihi al., 2012; 2012; Simani and Castaldi, Castaldi, 2014; FDD uncertainties and time delays related to fault Badihi et al., 2014; Badihi et al., 2015b). Recent new detection/isolation process. In addition to the the abovementioned developments this direction were in Badihi et al. FDD uncertainties andscheme time delays related fault developments on this direction were reviewed in Badihi et al. detection/isolation process. In addition to the abovementioned benefits, the fact that this employs a type of PI PItocontrol control developments on this direction were reviewed in Badihi et al. benefits, the fact that this scheme employs a type of PI control Badihi et al., 2014; Badihi et al., 2015b). Recent new developments on this direction were reviewed in Badihi et al. benefits, the fact that this scheme employs a type of Badihi et al., 2014; Badihi et al., 2015b). Recent new detection/isolation process. In addition to the abovementioned developments on this direction were reviewed in Badihi et al. benefits, the fact that this scheme employs a type of PI control (2013). At a wind farm level, the available literature detection/isolation process. In addition to the abovementioned is (2013). At a wind farm level, the available literature benefits, the fact that this scheme employs a type of PI control approach makes it more industry-friendly, as opposed to other (2013). At aa on wind farm level, the available literature is approach makes itthat more industry-friendly, as opposed to other developments this direction were reviewed in et (2013). At wind farm level, the available literature is makes more industry-friendly, opposed other developments this direction were reviewed in Badihi Badihi et al. al. benefits, the fact this scheme aa type of control (2013). Atscarce a on wind level, theof is approach approach makes itthat more industry-friendly, as opposed to other relatively and the works limited benefits, the fact it this scheme employs employs as type of PI PIto control relatively scarce andfarm the majority majority of available works are areliterature limited to to approach makes it industry-friendly, as opposed to other cited approaches inmore the literature. relatively scarce and the majority of works are limited to cited approaches in the literature. (2013). At a wind farm level, the available literature is relatively scarce and the majority of works are limited to cited approaches in the literature. (2013). At a wind farm level, the available literature is makes industry-friendly, as opposed opposed to to other other relatively scarce and and the fault majority of works are limited to approach cited approaches inmore the literature. literature. condition monitoring detection only. For instance, approach makes it itin more industry-friendly, as condition monitoring and fault detection only. For instance, cited approaches the condition monitoring and fault detection only. For instance, relatively scarce and the majority of limited to condition monitoring and detection only. For instance, relatively scarce andmethods the fault majority of toworks works are limited to cited Different simulations on a high-fidelity offshore wind farm approaches in the literature. condition monitoring and fault detection only.are Formodels instance, Different simulations on a high-fidelity offshore wind farm cited approaches in the literature. various data mining are used improve for Different simulations on aa high-fidelity offshore wind various data mining methods are used to improve for Different simulations on turbines) high-fidelity offshore wind farm farm condition monitoring and fault only. For instance, various data mining methods are used models for condition monitoring and farms fault detection only. Formodels instance, Different on a high-fidelity offshore wind farm benchmarksimulations (with 10 wind show the effectiveness and various data mining methods aredetection used to to improve improve models for benchmark benchmark (with 10 wind turbines) show the effectiveness and fault prediction in wind (Kusiak and Verma, 2011; (with 10 wind turbines) show the effectiveness and Different simulations on aa high-fidelity offshore wind farm fault prediction in wind farms (Kusiak and Verma, 2011; benchmark (with 10 wind turbines) show the effectiveness and various data mining methods are used to improve models for Different simulations on high-fidelity offshore wind farm fault prediction in wind farms (Kusiak and Verma, 2011; various data mining methods are used to improve models for benchmark (with 10 wind turbines) show the effectiveness and satisfactory performance of the proposed scheme in the fault prediction in 2012). wind farms (Kusiak andlearning Verma,models 2011; benchmark satisfactory (with performance of proposed scheme the Kusiak and Verma, Different machine satisfactory performance of the the show proposed scheme in in and the 10 wind turbines) the effectiveness Kusiak and Verma, 2012). Different machine learning models satisfactory performance of the proposed scheme in the fault prediction in wind farms (Kusiak and Verma, 2011; benchmark (with 10 wind turbines) show the effectiveness and Kusiak and Verma, 2012). Different machine learning models fault prediction in wind farms (Kusiak and Verma, 2011; satisfactory performance of the proposed scheme in the presence of wind turbulences, measurement noises and Kusiak anddeveloped Verma, 2012). Different machine learning models presence of performance wind turbulences, turbulences, measurement noisesin and have been to estimate the relationship between the presence of wind noises and satisfactory of proposed the have developed to estimate the relationship between the presence of wind turbulences, turbulences, measurement noisesin and and Kusiak and Verma, 2012). Different machine learning models satisfactory of the the measurement proposed scheme scheme the have been been developed to estimate the relationship between the realistic Kusiak andpower Verma, 2012). Different machine learning models presence of performance wind measurement noises realistic fault fault scenarios. have been developed to estimate the relationship between the fault scenarios. generated of a wind farm and wind speed (Marvuglia realistic scenarios. presence of wind turbulences, measurement noises and generated power of a wind farm and wind speed (Marvuglia realistic fault scenarios. have been developed to estimate the relationship between the presence of wind turbulences, measurement noises and generated power of aa to wind farmthe andmodels wind speed speed (Marvuglia have been power developed estimate the relationship between the realistic fault scenarios. generated of wind farm and wind (Marvuglia and Messineo, 2012). However, in and The remainder remainder of this this paper paper is is organized organized as as follows: follows: the the used used realistic fault and Messineo, 2012). However, the models in Marvuglia Marvuglia and The The of is as the generated power of wind farm and wind (Marvuglia realistic fault scenarios. scenarios. and Messineo, 2012). models in Marvuglia and of generated power ofareaa However, wind farmthe andisolating wind speed speed (Marvuglia and Messineo, 2012). However, the models in Marvuglia and Messineo (2012) incapable of and identifying The remainder remainder of this this paper paper isisorganized organized as follows: follows: the used used Messineo (2012) are However, incapable the of isolating isolating and identifying The remainder of this paper organized as follows: the used wind farm benchmark benchmark modelis briefly described described in Section Section 2. Messineo (2012) are incapable of and identifying wind farm benchmark model is briefly described in Section 2. and Messineo, 2012). models in Marvuglia and Messineo (2012) are incapable of isolating and identifying wind farm model is briefly in 2. and Messineo, 2012). However, the models in Marvuglia and The of this is as the Messineo (2012)farm. are incapable of isolating and on identifying wind farm benchmark benchmark model isorganized briefly described in Section Section 2. faults in wind A data-driven set based TakagiThe remainder remainder ofpower this paper paper is organized as follows: follows: the used used wind farm model is briefly described in Section 2. The considered loss fault is discussed in 3. faults in wind farm. A data-driven set based on TakagiThe considered powermodel loss fault fault is discussed discussed inin Section Section 3. Messineo (2012)farm. are incapable incapable of isolating isolating and on identifying faults in wind A set TakagiThe power loss is in 3. Messineo (2012) are of and identifying wind farm benchmark is described Section 2. faults in models wind farm. A data-driven data-driven setet based based on TakagiThe considered power lossscheme fault isagainst discussed inin Section Section 3. Sugeno’s is proposed by Simani al. (2014) for fault windconsidered farm benchmark model is briefly briefly described Section 2. The considered power loss fault is discussed in 3. Section 4 presents presents a FTCC the fault fault discussed Sugeno’s models is proposed by Simani et al. (2014) for fault Section 4 presents a FTCC scheme against the fault discussed faults in wind farm. A data-driven set based on TakagiSugeno’s models is proposed by Simani et al. (2014) for fault Section 4 a FTCC scheme against the discussed faults in wind farm. A data-driven set based on TakagiThe considered power loss fault is discussed in Section 3. Sugeno’s and models is proposed by in Simani etetal. (2014) for fault Section Section 4 presents a FTCC scheme against the fault discussed detection isolation. Authors Blesa al. (2015) present The considered power loss fault is discussed in Section 3. 4 presents a FTCC schemethe against the fault discussed in Section Section 3. Section Section presents the simulation results with detection and isolation. Authors in Blesa al. (2015) present in Section 3. presents simulation results with Sugeno’s models is proposed by Simani fault and isolation. Authors in Blesa et al. (2015) present 3. 5555 presents the simulation results with Sugeno’s models is approach proposed by Simani etet al. (2014) for fault in Section 44 presents aa FTCC FTCC scheme against the discussed detection and isolation. Authors in Blesaet etal. al.(2014) (2015)for present in Section 3. Section Section presents the simulation results witha aadetection fault diagnosis by interval parameter-varying Section presents scheme against the fault fault discussed in Section 3. Section 5 presents the simulation results with some comments and discussions. Finally, Section 6 provides fault diagnosis approach by interval parameter-varying some comments and discussions. Finally, Section 6 provides a detection and isolation. Authors in Blesa et al. (2015) present aadetection fault diagnosis approach by comments and discussions. Section provides and isolation. Authors ininterval Blesa etparameter-varying al.and (2015) present some in 3. 55 presents the with fault equations diagnosis approach bysome interval parameter-varying some comments anddiscussion. discussions. Finally, Section 666results provides parity considering noises modelling in Section Section 3. Section Section presents Finally, the simulation simulation results withaaa some comments and discussions. Finally, Section provides brief summary and parity equations considering some noises and modelling brief summary and discussion. aparity fault diagnosis approach by interval parameter-varying parity equations considering some noises and scheme modelling brief a fault equations diagnosis approach bysome interval parameter-varying some comments and discussions. noises and modelling an active FTC is brief summary summary and discussion. errors. In Badihi considering et al. (2015a), some commentsand anddiscussion. discussions. Finally, Finally, Section Section 66 provides provides aa an active FTC scheme is brief summary and discussion. errors. In et an is parity some noises and modelling errors. equations In Badihi Badihi considering et al. al. (2015a), (2015a), an active active FTC scheme is brief parity equations considering some noises FTC and scheme modelling summary and discussion. errors. In Badihi et al. (2015a), an active FTC scheme is brief summary and discussion. 2405-8963 2018, IFAC (International Automatic Control) errors. Badihi et (2015a), an scheme is errors. In In© et al. al. (2015a), Federation an active active ofFTC FTC scheme is 280Hosting by Elsevier Ltd. All rights reserved. Copyright © Badihi 2018 IFAC Peer review© under of International Federation of Automatic Control. Copyright 2018 responsibility IFAC 280 Copyright © 280 Copyright © 2018 2018 IFAC IFAC 280 Copyright © 2018 IFAC 280 10.1016/j.ifacol.2018.09.589 Copyright 280 Copyright © © 2018 2018 IFAC IFAC 280

IFAC SAFEPROCESS 2018 Warsaw, Poland, August 29-31, 2018

Hamed Badihi et al. / IFAC PapersOnLine 51-24 (2018) 280–285

present in this block acts upon the power demand 𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑,𝑞𝑞𝑞𝑞 in (1) through a wind turbine level control system. This control system basically is composed of a blade-pitch controller and a generator torque controller to compute appropriate reference blade-pitch angle 𝛽𝛽𝛽𝛽𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 and reference generator torque 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 , respectively. Note that the generator torque controller is set to be active during not only below rated wind speeds but also above rated wind speeds.

2. OVERVIEW OF THE BENCHMARK MODEL This paper considers an advanced simulation benchmark model obtained from SimWindFarm toolbox (Soltani et al., 2009). The toolbox generates a realistic wind farm simulation benchmark model that allows researchers to study farm level control and diagnosis algorithms under different operating conditions. The considered layout for a wind farm with ten 5MW wind turbines, and the block diagram of the benchmark model under consideration are illustrated in Fig. 1. T8 Wind

3. POWER LOSS FAULTS D2

T5

Wind Field: Aerodynamic interactions between wind turbines in the wind farm is simulated by the wind field model.

T1

T9

D3

Icing or debris build-up on the blades due to dirt, ice, etc., constitute the most probable fault which results in a lower power generation because of changes in the aerodynamics of the wind turbine. The fault can be simply modeled by scaling the generated power in a wind turbine. For example, a realistic scaling factor of 0.97 (3% power loss) is used here. Therefore, the benchmark model is modified with a generic fault scenario representing occurrence of 3% power loss in a designated number of wind turbines in the wind farm shown in Fig. 1 (a). Total simulation time is 1000 seconds in which T1 is faulty during [225,400], T2 is faulty during [800,1000], T3 is faulty during [450,1000], T4 is faulty during [125,300], T7 is faulty during [350,1000], T8 is faulty during [100,1000], and T10 is faulty during [700,1000] seconds. From this fault scenario, it is obvious that during some periods of the simulation time, the considered power loss fault has occurred simultaneously in more than one turbine in the farm.

T7

T6

D2

D3 T2

T1

D1

D1 D1=600 m

T4

T3 D1

D2=500 m

D3=300 m

(a) Wind Turbines (q=1,2,…,N)

Aerodynamic Properties

Wind Field

𝑷𝑷𝑷𝑷𝒅𝒅𝒅𝒅 = �𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑,𝑞𝑞𝑞𝑞 �

Measurements 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴

𝑃𝑃𝑃𝑃𝐴𝐴𝐴𝐴

Wind Farm Controller

𝑃𝑃𝑃𝑃𝐷𝐷𝐷𝐷

Network Operator

4. FTCC DESIGN

(b) Fig. 1. Wind farm benchmark model: (a) layout, and (b) functionality block diagram

This section presents a novel FTCC scheme based on an efficient model reference adaptive PI control approach that is used in a cooperative framework. As it is shown in Fig. 2, this cooperative framework is similar to the framework already used in Badihi et al. (2017a; 2017b) that is mainly based on checking the consistency of the generated powers from all wind turbines in real-time. Such a framework covers the entire wind farm with any layouts and any wind directions. More precisely, the FTCC scheme enables fault-tolerant regulation of the generator torque in each individual turbine in the wind farm in the presence of both model uncertainties and faults. Interestingly, this scheme offers the possibility of online reconfiguration of the control action without any explicit knowledge about the potential faults.

As it is shown in Fig. 1(b), the wind farm benchmark model includes four major components as recalled below: Network Operator: the network operator works in different modes such as absolute, delta, and frequency regulation modes to determine the total active power demand 𝑃𝑃𝑃𝑃𝐷𝐷𝐷𝐷 required for reliable connection of the wind farm to the grid.

Wind Farm Controller: The wind farm controller is an interface between the network operator and wind turbines. It provides an estimate of total available power 𝑃𝑃𝑃𝑃𝐴𝐴𝐴𝐴 in the wind farm to the network operator, and distributes the operator’s total demanded power 𝑃𝑃𝑃𝑃𝐷𝐷𝐷𝐷 among wind turbines in the farm based on a proportional distribution algorithm shown in (1) at the time-step 𝑘𝑘𝑘𝑘. 𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑,𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘) = 𝑃𝑃𝑃𝑃𝐷𝐷𝐷𝐷 (𝑘𝑘𝑘𝑘)

𝑃𝑃𝑃𝑃𝑎𝑎𝑎𝑎,𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘) 𝑃𝑃𝑃𝑃𝐴𝐴𝐴𝐴 (𝑘𝑘𝑘𝑘)

,

𝑞𝑞𝑞𝑞 = 1, 2, … , 𝑁𝑁𝑁𝑁

281

As already mentioned in Section 2, each turbine in the wind farm is equipped with a torque controller that provides a nominal torque reference signal denoted by 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 in turbine 𝑞𝑞𝑞𝑞. Using the linear transformation shown in (2), the FTCC scheme acts on the nominal torque reference signal to apply the reconfiguration of the control action under fault conditions for accommodation of faults, and to maintain the torque reference signal as close to its nominal values as possible under fault-free conditions.

(1)

Here, 𝑃𝑃𝑃𝑃𝑎𝑎𝑎𝑎,𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘) and 𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑,𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘) are the estimated available power and the power demand from turbine 𝑞𝑞𝑞𝑞, respectively.

Wind Turbines: This block simulates the dynamics of 𝑁𝑁𝑁𝑁 turbines installed in the wind farm using simple models of an offshore 5-MW turbine that has been already proposed by the U.S. National Renewable Energy Laboratory (NREL) (see Jonkman et al., 2009). In addition to total active power, the wind turbines block provides a set of measurements 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 to be used in the wind farm controller. Each individual wind turbine

𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (𝑘𝑘𝑘𝑘) = 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘)�2𝛾𝛾𝛾𝛾𝛿𝛿𝛿𝛿𝑞𝑞𝑞𝑞 (𝑘𝑘𝑘𝑘) + 1 − 𝛾𝛾𝛾𝛾� , 𝑞𝑞𝑞𝑞 = 1, 2, … , 𝑁𝑁𝑁𝑁

281

(2)

Here, 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 is the compensated reference generator torque, 𝛾𝛾𝛾𝛾 is a positive scaling factor between [0, 1] , and 𝛿𝛿𝛿𝛿𝑞𝑞𝑞𝑞 is a

IFAC SAFEPROCESS 2018 282 Warsaw, Poland, August 29-31, 2018

Hamed Badihi et al. / IFAC PapersOnLine 51-24 (2018) 280–285

normalized tuneable parameter between [0.5, 1] that is determined on-line using the FTCC scheme with more details shown in Fig. 2(b). Note that 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 should be ideally equal with 𝜏𝜏𝜏𝜏𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 under fault-free conditions (i.e., 𝛿𝛿𝛿𝛿𝑞𝑞𝑞𝑞 = 0.5). Aerodynamic Properties

Wind Turbines (q=1,2,…,N)

4.1 Module Blocks (M)

Wind Field

From 𝑅𝑅𝑅𝑅 modules used in the FTCC scheme shown in Fig. 2(b), consider an example module 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗 that corresponds to checking the consistency of the generated powers from turbine Ti and turbine Tj in a farm (𝑖𝑖𝑖𝑖 ≠ 𝑗𝑗𝑗𝑗). A diagram illustrating the overall structure of the module designed using the model reference adaptive PI control approach is shown in Fig. 3.

𝜹𝜹𝜹𝜹

Measurements 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴

FTCC 𝑷𝑷𝑷𝑷𝒅𝒅𝒅𝒅 = �𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑,𝑞𝑞𝑞𝑞 �

modules M and a set of Post-Processing (Post-Proc.) Blocks that each corresponds to an individual wind turbine and is used to perform post-processing on the results obtained from the modules related to that specific wind turbine. The following subsections provide more details about functionality of M and Post-Proc. blocks.

𝑃𝑃𝑃𝑃𝐴𝐴𝐴𝐴

Wind Farm Controller

Network Operator

𝑃𝑃𝑃𝑃𝐷𝐷𝐷𝐷

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑖𝑖𝑖𝑖 +

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑗𝑗𝑗𝑗 − 𝑃𝑃𝑃𝑃𝑔𝑔𝑔𝑔𝑖𝑖𝑖𝑖 +

(a)

M1,2

M1,3

M1,N-1

𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴

𝑷𝑷𝑷𝑷𝒓𝒓𝒓𝒓 𝑷𝑷𝑷𝑷𝒈𝒈𝒈𝒈

M1,N

M2,3

2,N

M

MN-1,N

𝛿𝛿𝛿𝛿11,2

𝛿𝛿𝛿𝛿21,2

1,2

∆𝑃𝑃𝑃𝑃

1,2

∆𝑃𝑃𝑃𝑃

∆𝑃𝑃𝑃𝑃1,3 , 𝛿𝛿𝛿𝛿11,3

𝛿𝛿𝛿𝛿11,3

∆𝑃𝑃𝑃𝑃1,3

∆𝑃𝑃𝑃𝑃𝑍𝑍𝑍𝑍−2,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍−2,𝑍𝑍𝑍𝑍

1,𝑁𝑁𝑁𝑁−1 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁−1

∆𝑃𝑃𝑃𝑃𝑍𝑍𝑍𝑍−1,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍−1,𝑍𝑍𝑍𝑍

1,𝑁𝑁𝑁𝑁−1

∆𝑃𝑃𝑃𝑃

∆𝑃𝑃𝑃𝑃𝑍𝑍𝑍𝑍,𝑍𝑍𝑍𝑍+1 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍,𝑍𝑍𝑍𝑍+1

𝛿𝛿𝛿𝛿11,𝑁𝑁𝑁𝑁 𝛿𝛿𝛿𝛿22,3

Post-Proc. (Turbine TZ)

𝛿𝛿𝛿𝛿32,3

∆𝑃𝑃𝑃𝑃2,3 𝛿𝛿𝛿𝛿22,𝑁𝑁𝑁𝑁

∆𝑃𝑃𝑃𝑃𝑁𝑁𝑁𝑁−1,𝑁𝑁𝑁𝑁

FTCC

𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍

Post-Proc. (Turbine TN)

𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁

∆𝑃𝑃𝑃𝑃𝑍𝑍𝑍𝑍,𝑍𝑍𝑍𝑍+2 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍,𝑍𝑍𝑍𝑍+2

∆𝑃𝑃𝑃𝑃𝑁𝑁𝑁𝑁−2,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁−2,𝑁𝑁𝑁𝑁

𝜹𝜹𝜹𝜹 = �𝛿𝛿𝛿𝛿𝑞𝑞𝑞𝑞 �

𝑷𝑷𝑷𝑷𝒓𝒓𝒓𝒓 = �𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟,𝑞𝑞𝑞𝑞 � ,

𝑷𝑷𝑷𝑷𝒈𝒈𝒈𝒈 = �𝑃𝑃𝑃𝑃𝑔𝑔𝑔𝑔,𝑞𝑞𝑞𝑞 �

𝑃𝑃𝑃𝑃𝑔𝑔𝑔𝑔 𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

− ∑

Adaptive PI Control (Ti)

+

Adaptive PI Control (Tj)

𝑟𝑟𝑟𝑟𝑒𝑒𝑒𝑒𝑟𝑟𝑟𝑟 = 0 𝑢𝑢𝑢𝑢 = 𝛿𝛿𝛿𝛿𝑗𝑗𝑗𝑗

𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

𝛿𝛿𝛿𝛿𝑖𝑖𝑖𝑖

𝑦𝑦𝑦𝑦 = ∆𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

Threshold Filter

𝑢𝑢𝑢𝑢

𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

𝛿𝛿𝛿𝛿𝑗𝑗𝑗𝑗

Online Model Identification

𝑦𝑦𝑦𝑦

𝑞𝑞𝑞𝑞 = 1,2, … , 𝑁𝑁𝑁𝑁

𝑟𝑟𝑟𝑟𝑒𝑒𝑒𝑒𝑟𝑟𝑟𝑟

(b) Fig. 2. FTCC scheme: (a) external view in the control loop with the other components of the wind farm benchmark, and (b) internal view including 𝑅𝑅𝑅𝑅 modules M each for conducting model reference adaptive PI control between any two specific turbines in a wind farm. Here, turbine T𝑍𝑍𝑍𝑍 with (𝑍𝑍𝑍𝑍 ∈ ℕ and 1 < 𝑍𝑍𝑍𝑍 < 𝑁𝑁𝑁𝑁) represents any turbine except T1 and T𝑁𝑁𝑁𝑁

𝜣𝜣𝜣𝜣

+

−

∑

Error 𝑒𝑒𝑒𝑒

𝑷𝑷𝑷𝑷 𝑰𝑰𝑰𝑰

∑

Adaptive PI Control

Fig. 4. Adaptive PI control with three inputs and one output To further explain the adaptive PI control algorithm in Fig. 4, consider the general continuous-time PI controller given by 𝑢𝑢𝑢𝑢(𝑡𝑡𝑡𝑡) = 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃 �𝑒𝑒𝑒𝑒(𝑡𝑡𝑡𝑡) +

As it is shown in Fig. 2(b), the FTCC scheme computes a set of tuneable parameters 𝛅𝛅𝛅𝛅 using a set of reference powers 𝑷𝑷𝑷𝑷𝒓𝒓𝒓𝒓 (computed as the product of reference generator torque and generator speed in each turbine) and a set of generated powers 𝑷𝑷𝑷𝑷𝒈𝒈𝒈𝒈 as inputs. For a wind farm with 𝑁𝑁𝑁𝑁 turbines (labelled as T1 , T2 , … , T𝑁𝑁𝑁𝑁 ), the FTCC scheme in Fig. 2(b) consists of 𝑅𝑅𝑅𝑅 = 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2

Reference Dynamic Model

𝑢𝑢𝑢𝑢 = 𝛿𝛿𝛿𝛿𝑖𝑖𝑖𝑖

𝑟𝑟𝑟𝑟𝑒𝑒𝑒𝑒𝑟𝑟𝑟𝑟 = 0

The module shown in Fig. 3 employs a Reference Dynamic Model of the system that estimates the nominal (fault-free) performance of the system. This model is obtained using a data-driven modelling approach based on fuzzy modeling and identification technique (see Babuska (1998)). The Threshold Filter block conducts a simple threshold testing on the difference between nominal performance and real performance of the system and filter out any normal deviations due to modelling errors and measurement uncertainties. The module also includes two Adaptive PI Control blocks that each has the general structure shown in Fig. 4.

∆𝑃𝑃𝑃𝑃𝑁𝑁𝑁𝑁−1,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁−1,𝑁𝑁𝑁𝑁

Post-Proc. (Turbine TN)

∑

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟

Fig. 3. Module 𝑀𝑀𝑀𝑀

∆𝑃𝑃𝑃𝑃𝑍𝑍𝑍𝑍,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍,𝑁𝑁𝑁𝑁

∆𝑃𝑃𝑃𝑃𝑁𝑁𝑁𝑁−3,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁−3,𝑁𝑁𝑁𝑁

∆𝑃𝑃𝑃𝑃2,𝑁𝑁𝑁𝑁

𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁−1,𝑁𝑁𝑁𝑁

𝜹𝜹𝜹𝜹

Post-Proc. (Turbine TZ)

∆𝑃𝑃𝑃𝑃1,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁1,𝑁𝑁𝑁𝑁

𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁2,𝑁𝑁𝑁𝑁

𝑁𝑁𝑁𝑁−1,𝑁𝑁𝑁𝑁 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁−1

𝛿𝛿𝛿𝛿1

∆𝑃𝑃𝑃𝑃1,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍1,𝑍𝑍𝑍𝑍

𝛿𝛿𝛿𝛿11,𝑁𝑁𝑁𝑁−1

𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁1,𝑁𝑁𝑁𝑁

Post-Proc. (Turbine T1)

∆𝑃𝑃𝑃𝑃1,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿11,𝑁𝑁𝑁𝑁

𝛿𝛿𝛿𝛿31,3

∆𝑃𝑃𝑃𝑃1,𝑁𝑁𝑁𝑁

, 𝛿𝛿𝛿𝛿11,2

∆𝑃𝑃𝑃𝑃1,4 , 𝛿𝛿𝛿𝛿11,4

Post-Proc. (Turbine T1)

𝑃𝑃𝑃𝑃𝑔𝑔𝑔𝑔𝑗𝑗𝑗𝑗 −

∑

𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

1 𝑡𝑡𝑡𝑡 � 𝑒𝑒𝑒𝑒(𝜏𝜏𝜏𝜏) 𝑑𝑑𝑑𝑑𝜏𝜏𝜏𝜏� 𝑇𝑇𝑇𝑇𝐼𝐼𝐼𝐼 0

(3)

where 𝑢𝑢𝑢𝑢 is the controller output, 𝑒𝑒𝑒𝑒 is the tracking error between the reference input and the output of the process, and the controller parameters 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃 and 𝑇𝑇𝑇𝑇𝐼𝐼𝐼𝐼 are the proportional gain and integral time constant, respectively. The PI controller in (3) can be expressed in a digital form using trapezoidal method of discretization as follows:

282

IFAC SAFEPROCESS 2018 Warsaw, Poland, August 29-31, 2018

𝑢𝑢𝑢𝑢(𝑘𝑘𝑘𝑘) = 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃 �𝑒𝑒𝑒𝑒(𝑘𝑘𝑘𝑘) +

Hamed Badihi et al. / IFAC PapersOnLine 51-24 (2018) 280–285

𝑘𝑘𝑘𝑘−1 𝑇𝑇𝑇𝑇𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒(0) + 𝑒𝑒𝑒𝑒(𝑘𝑘𝑘𝑘) � +� 𝑒𝑒𝑒𝑒(𝑖𝑖𝑖𝑖) �� 𝑇𝑇𝑇𝑇𝐼𝐼𝐼𝐼 2 𝑖𝑖𝑖𝑖=1

where the vector 𝚽𝚽𝚽𝚽(𝑘𝑘𝑘𝑘) contains the past process inputs 𝑢𝑢𝑢𝑢 and outputs 𝑦𝑦𝑦𝑦. The process parameters are updated at each instant of time by the recursive expression below

(4)

where 𝑇𝑇𝑇𝑇𝑠𝑠𝑠𝑠 is the sampling period and 𝑘𝑘𝑘𝑘 is the discrete-time instant (step).

𝜣𝜣𝜣𝜣(𝒌𝒌𝒌𝒌) = 𝜣𝜣𝜣𝜣(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) +

𝑢𝑢𝑢𝑢(𝑘𝑘𝑘𝑘)

where the matrix 𝑪𝑪𝑪𝑪 is given by 𝑪𝑪𝑪𝑪(𝑘𝑘𝑘𝑘) = �

(5)

In (5), the controller parameters are determined based on Ziegler and Nichols criterion by relations in (6) where the variables 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃𝑢𝑢𝑢𝑢 and 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢 are the closed-loop ultimate proportional gain and the ultimate period of oscillations, respectively (Ziegler and Nichols, 1942). 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃 = 0.6 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃𝑢𝑢𝑢𝑢

,

𝑇𝑇𝑇𝑇𝐼𝐼𝐼𝐼 = 0.5 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢

𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢 =

2𝜋𝜋𝜋𝜋𝑇𝑇𝑇𝑇𝑠𝑠𝑠𝑠 cos −1 𝛼𝛼𝛼𝛼

,

𝛼𝛼𝛼𝛼 =

𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) =

𝐵𝐵𝐵𝐵(𝑧𝑧𝑧𝑧 −1 ) 𝑏𝑏𝑏𝑏1 𝑧𝑧𝑧𝑧 −1 + 𝑏𝑏𝑏𝑏2 𝑧𝑧𝑧𝑧 −2 + 𝑏𝑏𝑏𝑏3 𝑧𝑧𝑧𝑧 −3 = 𝐴𝐴𝐴𝐴(𝑧𝑧𝑧𝑧 −1 ) 1 + 𝑎𝑎𝑎𝑎1 𝑧𝑧𝑧𝑧 −1 + 𝑎𝑎𝑎𝑎2 𝑧𝑧𝑧𝑧 −2 + 𝑎𝑎𝑎𝑎3 𝑧𝑧𝑧𝑧 −3

𝜆𝜆𝜆𝜆(𝑘𝑘𝑘𝑘)

�𝑦𝑦𝑦𝑦(𝑘𝑘𝑘𝑘) −

𝑇𝑇𝑇𝑇 𝚯𝚯𝚯𝚯𝑇𝑇𝑇𝑇(𝑘𝑘𝑘𝑘−1) 𝚽𝚽𝚽𝚽(𝑘𝑘𝑘𝑘) � �𝑦𝑦𝑦𝑦(𝑘𝑘𝑘𝑘)

𝜆𝜆𝜆𝜆(𝑘𝑘𝑘𝑘)

− 𝑇𝑇𝑇𝑇

(15) 𝚯𝚯𝚯𝚯𝑇𝑇𝑇𝑇(𝑘𝑘𝑘𝑘−1) 𝚽𝚽𝚽𝚽(𝑘𝑘𝑘𝑘) �

�𝑦𝑦𝑦𝑦(𝑘𝑘𝑘𝑘) − 𝑦𝑦𝑦𝑦�(𝑘𝑘𝑘𝑘) � �𝑦𝑦𝑦𝑦(𝑘𝑘𝑘𝑘) − 𝑦𝑦𝑦𝑦�(𝑘𝑘𝑘𝑘) � = 𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) �𝜆𝜆𝜆𝜆(𝑘𝑘𝑘𝑘−1) + � 1 + 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1)

(16) (17)

Algorithm. Post-processing function for the wind turbine TZ : 𝑍𝑍𝑍𝑍 ∈ ℕ , 1 < 𝑍𝑍𝑍𝑍 < 𝑁𝑁𝑁𝑁, ℕ: natural numbers set. 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗

Inputs: �∆𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 , ∆𝑃𝑃𝑃𝑃 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 � 𝑖𝑖𝑖𝑖, 𝑗𝑗𝑗𝑗 ∈ ℕ, 𝑖𝑖𝑖𝑖 < 𝑍𝑍𝑍𝑍 < 𝑗𝑗𝑗𝑗 ≤ 𝑁𝑁𝑁𝑁� ∆𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 , ∆𝑃𝑃𝑃𝑃 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗 : error signals in each module 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗

𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 : control signals coming from each module

Output: 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 1. for each 𝑖𝑖𝑖𝑖, 𝑗𝑗𝑗𝑗 ∈ ℕ, 𝑖𝑖𝑖𝑖 < 𝑍𝑍𝑍𝑍 < 𝑗𝑗𝑗𝑗 ≤ 𝑁𝑁𝑁𝑁 do 1.1. if ∆𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 < 0 or ∆𝑃𝑃𝑃𝑃 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗 > 0 then

As it is shown in (11), the estimated output of the process 𝑦𝑦𝑦𝑦�(𝑘𝑘𝑘𝑘) at each instant of time can be expressed in the following vector form 𝑻𝑻𝑻𝑻

𝜈𝜈𝜈𝜈(𝑘𝑘𝑘𝑘) = 𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) �𝜈𝜈𝜈𝜈(𝑘𝑘𝑘𝑘−1) + 1�

As it is shown in Fig. 2(b), the results obtained from the modules need to be post-processed through N blocks called Post-Proc. that each corresponds to a wind turbine in the farm. Fig. 2(b) shows the appropriate inputs to each Post-Proc. block. For example, the Post-Proc. block for wind turbine TZ works based on the following function:

(10)

𝜱𝜱𝜱𝜱(𝒌𝒌𝒌𝒌) = �−𝒚𝒚𝒚𝒚(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) , ⋯ , −𝒚𝒚𝒚𝒚(𝒌𝒌𝒌𝒌−𝟑𝟑𝟑𝟑) , 𝒖𝒖𝒖𝒖(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) , ⋯ , 𝒖𝒖𝒖𝒖(𝒌𝒌𝒌𝒌−𝟑𝟑𝟑𝟑) �

(14)

4.2 Post-Processing (Post-Proc.) Blocks

(8)

in which the structure of the model is defined through the polynomials 𝐴𝐴𝐴𝐴(𝑧𝑧𝑧𝑧 −1 ) and 𝐵𝐵𝐵𝐵(𝑧𝑧𝑧𝑧 −1 ), whereas 𝑧𝑧𝑧𝑧 is the so-called discrete-time complex variable. Here, the least squares method (LSM) with adaptive directional forgetting technique is used to identify online the following time-varying parameters of the process described by the above transfer function (Kulhavý, 1987; Ljung, 1999).

�(𝒌𝒌𝒌𝒌) = 𝜣𝜣𝜣𝜣𝑻𝑻𝑻𝑻(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) ∙ 𝜱𝜱𝜱𝜱(𝒌𝒌𝒌𝒌) 𝒚𝒚𝒚𝒚

1

The above-mentioned recursive identification technique, with the well-defined start-up conditions 𝚯𝚯𝚯𝚯(𝟎𝟎𝟎𝟎) , 𝑪𝑪𝑪𝑪(𝟎𝟎𝟎𝟎) , 𝜑𝜑𝜑𝜑(0) , 𝜆𝜆𝜆𝜆(0) , 𝜌𝜌𝜌𝜌, and 𝜈𝜈𝜈𝜈(0) , computes the time-varying parameters in (10) for the discrete-time linear model in (9) which is an approximation of the nonlinear process under control. Accordingly, these parameters will be used by the adaptive PI controller through substituting them in (7) and (8).

(9)

𝑇𝑇𝑇𝑇 𝜣𝜣𝜣𝜣(𝑘𝑘𝑘𝑘) = �𝑎𝑎𝑎𝑎�1 , 𝑎𝑎𝑎𝑎�2 , 𝑎𝑎𝑎𝑎�3 , 𝑏𝑏𝑏𝑏�1 , 𝑏𝑏𝑏𝑏�2 , 𝑏𝑏𝑏𝑏�3 �

𝜀𝜀𝜀𝜀(𝑘𝑘𝑘𝑘) = 0 (13)

𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1) �𝜈𝜈𝜈𝜈(𝑘𝑘𝑘𝑘−1) + 1�𝜂𝜂𝜂𝜂(𝑘𝑘𝑘𝑘−1) 1 + (1 + 𝜌𝜌𝜌𝜌) �𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙�1 + 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1) � + � − 1� � 1 + 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1) + 𝜂𝜂𝜂𝜂(𝑘𝑘𝑘𝑘−1) 1 + 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1)

𝜂𝜂𝜂𝜂(𝑘𝑘𝑘𝑘) =

The transfer function of the time-varying controlled process has the following third-order form: 𝐺𝐺𝐺𝐺(𝑧𝑧𝑧𝑧) =

1 − 𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) = 𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) − 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘−1)

𝜀𝜀𝜀𝜀(𝑘𝑘𝑘𝑘) > 0

with the following auxiliary variables

(7)

𝑎𝑎𝑎𝑎�3 − 𝑎𝑎𝑎𝑎�1 + 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃𝑢𝑢𝑢𝑢 �𝑏𝑏𝑏𝑏�3 − 𝑏𝑏𝑏𝑏�1 � 2

𝑪𝑪𝑪𝑪(𝑘𝑘𝑘𝑘−1)

−1 𝜀𝜀𝜀𝜀(𝑘𝑘𝑘𝑘) + 𝜉𝜉𝜉𝜉(𝑘𝑘𝑘𝑘)

(12)

The adaptive forgetting coefficient 𝜑𝜑𝜑𝜑(𝑘𝑘𝑘𝑘) is then updated by

(6)

1 − 𝑎𝑎𝑎𝑎�1 + 𝑎𝑎𝑎𝑎�2 − 𝑎𝑎𝑎𝑎�3 𝑏𝑏𝑏𝑏�1 − 𝑏𝑏𝑏𝑏�2 + 𝑏𝑏𝑏𝑏�3

𝑪𝑪𝑪𝑪(𝑘𝑘𝑘𝑘−1) ∙ 𝜱𝜱𝜱𝜱(𝑘𝑘𝑘𝑘) ∙ 𝜱𝜱𝜱𝜱𝑇𝑇𝑇𝑇(𝑘𝑘𝑘𝑘) ∙ 𝑪𝑪𝑪𝑪(𝑘𝑘𝑘𝑘−1)

𝑪𝑪𝑪𝑪(𝑘𝑘𝑘𝑘−1) −

𝜀𝜀𝜀𝜀(𝑘𝑘𝑘𝑘)

In the standard PI control algorithm, the controller parameters remain fixed during control after they have been optimally tuned or chosen using the Ziegler-Nichols tuning formula (Ziegler and Nichols, 1942; Hang et al., 1991). However, in the adaptive PI control algorithm, the controller parameters are adapted online based on a parameter estimation approach. This requires certain knowledge of the process using an online model identification technique. In particular, considering a third-order process model described by its estimated timevarying parameters �𝑎𝑎𝑎𝑎�1 , 𝑎𝑎𝑎𝑎�2 , 𝑎𝑎𝑎𝑎�3 , 𝑏𝑏𝑏𝑏�1 , 𝑏𝑏𝑏𝑏�2 , 𝑏𝑏𝑏𝑏�3 � , the ultimate variables 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃𝑢𝑢𝑢𝑢 and 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢 required by the Ziegler-Nichols method are computed at each time-instant from the following relations with further details given in Bobál et al. (2005): 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃𝑢𝑢𝑢𝑢 =

𝑪𝑪𝑪𝑪(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) ∙ 𝜱𝜱𝜱𝜱(𝒌𝒌𝒌𝒌) ∙ �𝒚𝒚𝒚𝒚(𝒌𝒌𝒌𝒌) − 𝜣𝜣𝜣𝜣𝑻𝑻𝑻𝑻(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) 𝜱𝜱𝜱𝜱(𝒌𝒌𝒌𝒌) � 𝟏𝟏𝟏𝟏 + 𝝃𝝃𝝃𝝃(𝒌𝒌𝒌𝒌)

𝝃𝝃𝝃𝝃(𝒌𝒌𝒌𝒌) = 𝜱𝜱𝜱𝜱𝑻𝑻𝑻𝑻(𝒌𝒌𝒌𝒌) ∙ 𝑪𝑪𝑪𝑪(𝒌𝒌𝒌𝒌−𝟏𝟏𝟏𝟏) ∙ 𝜱𝜱𝜱𝜱(𝒌𝒌𝒌𝒌)

Based on the incremental algorithm given in Bobál et al. (2005), the recurrent relation obtained from (4) can be written in the following form. 𝑇𝑇𝑇𝑇𝑠𝑠𝑠𝑠 = 𝐾𝐾𝐾𝐾𝑃𝑃𝑃𝑃 �𝑒𝑒𝑒𝑒(𝑘𝑘𝑘𝑘) − 𝑒𝑒𝑒𝑒(𝑘𝑘𝑘𝑘−1) + �𝑒𝑒𝑒𝑒 + 𝑒𝑒𝑒𝑒(𝑘𝑘𝑘𝑘−1) �� + 𝑢𝑢𝑢𝑢(𝑘𝑘𝑘𝑘−1) 2𝑇𝑇𝑇𝑇𝐼𝐼𝐼𝐼 (𝑘𝑘𝑘𝑘)

283

𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗

2.

(11)

3. 4. 283

1.2. 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 = 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 = 0.5 1.3. end if end for 𝑍𝑍𝑍𝑍,𝑗𝑗𝑗𝑗

𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 = 𝑚𝑚𝑚𝑚𝑎𝑎𝑎𝑎𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖𝑚𝑚𝑚𝑚𝑢𝑢𝑢𝑢𝑚𝑚𝑚𝑚�𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍𝑖𝑖𝑖𝑖,𝑍𝑍𝑍𝑍 , 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍 � 𝑖𝑖𝑖𝑖, 𝑗𝑗𝑗𝑗 ∈ ℕ, 𝑖𝑖𝑖𝑖 < 𝑍𝑍𝑍𝑍 < 𝑗𝑗𝑗𝑗 ≤ 𝑁𝑁𝑁𝑁� return 𝛿𝛿𝛿𝛿𝑍𝑍𝑍𝑍

IFAC SAFEPROCESS 2018 284 Warsaw, Poland, August 29-31, 2018

Hamed Badihi et al. / IFAC PapersOnLine 51-24 (2018) 280–285

Generator Power [MW] (Turbine 7)

Note: For the first wind turbine denoted by T1 , the inputs 1,𝑗𝑗𝑗𝑗 are �∆𝑃𝑃𝑃𝑃1,𝑗𝑗𝑗𝑗 , 𝛿𝛿𝛿𝛿1 � 𝑗𝑗𝑗𝑗 ∈ ℕ, 𝑗𝑗𝑗𝑗 ≤ 𝑁𝑁𝑁𝑁�, and for the last wind turbine denoted by TN the inputs are �∆𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖,𝑁𝑁𝑁𝑁 , 𝛿𝛿𝛿𝛿𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖,𝑁𝑁𝑁𝑁 � 𝑖𝑖𝑖𝑖 ∈ ℕ, 𝑖𝑖𝑖𝑖 < 𝑁𝑁𝑁𝑁�. For both T1 and TN the remaining procedure is the same as mentioned above.

4.6 4.4 4.2 4 3.8 3.6 350

Generator Power [MW] (Turbine 8)

5. SIMULATION RESULTS

To evaluate the performance of the proposed FTCC scheme against the considered faults in Section 3, simulations are performed in MATLAB/Simulink using the nonlinear benchmark model described in Section 2. Fig. 5 shows the generator power responses under fault-free and faulty operations with or without using the FTCC scheme. For the sake of brevity and clarity, Fig. 5 only shows the power responses around the beginning of fault activity periods in the wind turbines designated by the faults scenario described in Section 3. As seen in Fig. 5, the proposed FTCC scheme is able to accommodate effectively the faults in the wind turbines under faulty operation, while it shows very slight impact on the nominal performance of the system under fault-free operation.

Generator Power [MW] (Turbine 1)

Generator Power [MW] (Turbine 10)

3.4

Generator Power [MW] (Turbine 2)

Generator Power [MW] (Turbine 3)

350

400

4.4 4.2 4 3.8 3.6

950

1000

4.5

250

4.6 4.4 4.2 4 750

800 Time [s]

850

900

Extending the proposed FTCC approach to accommodation of other frequent faults in wind farms such as misalignment of blades due to incorrect installation and change in the drivetrain damping due to wear and tear remain as our future works.

4

Generator Power [MW] (Turbine 4)

200

Different simulations on an offshore wind farm benchmark with 10 wind turbines show the effectiveness and satisfactory performance of the proposed scheme in the presence of wind turbulences, measurement noises, and realistic fault scenarios.

3.4

3.5

150

This paper addressed the design and development of a novel fault-tolerant cooperative control (FTCC) scheme based on an efficient model reference adaptive proportional-integral (PI) control approach that is used in a cooperative framework. The proposed scheme acts against decreased power generation fault caused by icing or debris build-up on the blades over time. It provides online reconfiguration of the control action without any explicit knowledge about the potential faults. It is independent of fault diagnosis information, and thus does not deal with uncertainties and time delays related to fault diagnosis process.

3.6

900 Time [s]

2.5

6. CONCLUSIONS

3.8

850

3

Fig. 5. Power response under fault-free and faulty operations

4

800

550

3.5

700

4.2

300 Time [s]

500

Time [s]

4.4

250

450 Time [s]

4

100

Fault-Free Operation Faulty Operation with FTCC Faulty Operation without FTCC

200

400

500

450

650

600

550 Time [s]

ACKNOWLEDGMENTS This work was supported in part by Concordia University through a team project and the Natural Sciences and Engineering Research Council of Canada (NSERC).

4

3.5

REFERENCES 3 100

150

200 Time [s]

250

Babuska, R. (1998) Fuzzy Modeling for Control. Kluwer Academic Publishers, Springer. Badihi, H., Zhang, Y. M. & Hong, H. (2013) A Review on Application of Monitoring, Diagnosis, and FaultTolerant Control to Wind Turbines. Proc. of International Conference on Control and FaultTolerant Systems (SysTol'13). Nice, France.

300

284

IFAC SAFEPROCESS 2018 Warsaw, Poland, August 29-31, 2018

Hamed Badihi et al. / IFAC PapersOnLine 51-24 (2018) 280–285

Badihi, H., Zhang, Y. M. & Hong, H. (2014) Fuzzy GainScheduled Active Fault-Tolerant Control of a Wind Turbine. Journal of the Franklin Institute, 351 (7), 3677–3706. Badihi, H., Zhang, Y. M. & Hong, H. (2015a) Active Fault Tolerant Control in a Wind Farm with Decreased Power Generation Due to Blade Erosion/Debris Build-Up. IFAC-PapersOnLine, 48 (21), 1369-1374. Badihi, H., Zhang, Y. M. & Hong, H. (2015b) Wind Turbine Fault Diagnosis and Fault-Tolerant Torque Load Control against Actuator Faults. IEEE Transactions on Control Systems Technology, 23 (4), 1351-1372. Badihi, H., Zhang, Y. M. & Hong, H. (2017a) Fault-Tolerant Cooperative Control in an Offshore Wind Farm Using Model-Free and Model-Based Fault Detection and Diagnosis Approaches. Applied Energy, 201, 284-307. Badihi, H., Zhang, Y. M., Pillay, P. & Rakheja, S. (2017b) Application of FMRAC to Fault-Tolerant Cooperative Control of a Wind Farm with Decreased Power Generation due to Blade Erosion/Debris Build-Up. International Journal of Adaptive Control and Signal Processing, 1-18. Blesa, J., Jiménez, P., Rotondo, D., Nejjari, F. & Vicenç Puig (2015) An Interval NLPV Parity Equations Approach for Fault Detection and Isolation of a Wind Farm. IEEE Transactions on Industrial Electronics, 62 (6), 3794-3805. Bobál, V., Böhm, J., Fessl, J. & Machácek, J. (2005) Digital Self-Tuning Controllers: Algorithms, Implementation and Applications. Springer. Hang, C. C., Astrom, K. J. & Ho, W. K. (1991) Refinements of the Ziegler-Nichols Tuning Formula. IEE Proceedings D - Control Theory and Applications, 138 (2), 111-118. Jonkman, J., Butterfield, S., Musial, W. & Scott, G. (2009) Definition of a 5 MW Reference Wind Turbine for Offshore System Development. IN NREL/TP-50038060, Colorado, USA, National Renewable Energy Laboratory. Kulhavý, R. (1987) Restricted Exponential Forgetting in Realtime Identification. Automatica, 23 (9), 589–600. Kusiak, A. & Verma, A. (2011) A Data-Driven Approach for Monitoring Blade Pitch Faults in Wind Turbines. IEEE Transactions on Sustainable Energy, 2 (1), 8796. Kusiak, A. & Verma, A. (2012) A Data-Mining Approach to Monitoring Wind Turbines. IEEE Transactions on Sustainable Energy, 3 (1), 150-157. Ljung, L. (1999) System Identification: Theory for the User. Prentice-Hall, Englewood Cliffs, N.J. Marvuglia, A. & Messineo, A. (2012) Monitoring of Wind Farms' Power Curves using Machine Learning Techniques. Applied Energy, 98, 574-583. Simani, S. & Castaldi, P. (2014) Active Actuator FaultTolerant Control of a Wind Turbine Benchmark Model. International Journal of Robust and Nonlinear Control, 24, 1283-1303. Simani, S., Farsoni, S. & Castaldi, P. (2014) Residual Generator Fuzzy Identification for Wind Farm Fault

285

Diagnosis. Proc. of the 19th IFAC World Congress. Cape Town, South Africa. Sloth, C., Esbensen, T. & Stoustrup, J. (2011) Robust and Fault-Tolerant Linear Parameter-Varying Control of Wind Turbines. Mechatronics, 21 (4), 645-659. Soltani, M., Knudsen, T. & Bak, T. (2009) Modeling and Simulation of Offshore Wind Farms for Farm Level Control. European Offshore Wind Conference and Exhibition (EOW). Stockholm, Sweden. Tabatabaeipour, S. M., Odgaard, P. F., Bak, T. & Stoustrup, J. (2012) Fault Detection of Wind Turbines with Uncertain Parameters: A Set-Membership Approach. Energies, 5 (7), 2424-2448. Ziegler, J. G. & Nichols, N. B. (1942) Optimum Settings for Automatic Controllers. ASME Transactions, 64, 759768.

285