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LPV-H∞ Fault Estimation for Boilers in Sugarcane Processing Plants⁎
2nd IFAC Workshop on Linear Parameter Varying Systems 2nd IFAC Workshop on Linear Parameter Varying Systems Florianopolis, Brazil,on September 3-5, 2018Varying Systems 2nd IFAC Workshop Linear Parameter Available online at www.sciencedirect.com Florianopolis, Brazil, September 3-5, 2018 2nd IFAC Workshop Linear Parameter Florianopolis, Brazil,on September 3-5, 2018Varying Systems Florianopolis, Brazil, September 3-5, 2018
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IFAC PapersOnLine 51-26 (2018) 1–6
LPV -H Fault Estimation for Boilers in ∞ LPV -H Estimation for Boilers in ∞ Fault LPV -H Fault Estimation for Boilers in ∞ Processing Plants LPV Sugarcane -H Fault Estimation for Boilers in ∞ Sugarcane Processing Plants Sugarcane Processing Plants Sugarcane Processing Plants Marcelo Menezes Morato ∗∗ Paulo Renato da Costa Mendes ∗∗
Marcelo Menezes Morato ∗∗ Paulo∗Renato da Costa∗∗Mendes ∗∗ Elias Normey-Rico Carlos Marcelo Julio Menezes Renato da Costa∗∗Mendes ∗ ∗ Paulo∗ EliasMorato Normey-Rico Carlos Bordons Bordons ∗∗Mendes Marcelo Julio Menezes Paulo∗∗Renato da Costa∗∗ Julio EliasMorato Normey-Rico Carlos Bordons ∗ ∗∗ Julio Elias Normey-Rico Carlos Bordons ∗ cc˜ a o ee Sistemas (( DAS), Universidade ∗ Departamento de Automa¸ Departamento de Automa¸ ˜ a o Sistemas DAS), Universidade ∗ ∗ Departamento de Automa¸ c˜ ao e Sistemas ( DAS), Universidade Federal Santa Catarina, Florian´ o Brazil ∗ Federal de de de Santa Catarina, Florian´ opolis-SC, polis-SC, Brazil ∗∗ Departamento Automa¸ cde ˜ ao Sistemas e Sistemas ( DAS), Universidade de Ingenier´ ıa y Autom´ a tica, Universidad Federal de Santa Catarina, Florian´ o polis-SC, Brazil ∗∗ Departamento Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ Federal de Santa Catarina, Florian´ opolis-SC, Brazil ∗∗ de Sevilla, Spain Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ de Sevilla, Spain Departamento de Ingenier´ de Sistemas atica, Universidad deıaSevilla, Spain y Autom´ de Sevilla, Spain Abstract: This short study presents Abstract: This short study presents aa Linear Linear Parameter Parameter Varying Varying (LPV (LPV )) method method for for the the Abstract: of This shortonstudy presents a Linear Parameter Varying (LPV ) method for the estimation faults Boilers of a Grid-Connected Hybrid Power Plant, that processes estimation of faults onstudy Boilers of a Grid-Connected Hybrid Power(LPV Plant, that processes Abstract: This short presents a Linear Parameter Varying ) method for sugarcane. boilers residual biomass from the the cane cane andPower may present present gradual lossthe of estimation These of faults on burn Boilers of a biomass Grid-Connected Hybrid Plant,aa that processes from and may gradual loss of sugarcane. These boilers burn residual estimation of faults on Boilers of a Grid-Connected Hybrid Power Plant, that processes effectiveness, due to internal faults. This renewable energy plant is subject to different processual sugarcane. These boilers burn residual biomass from the cane and may present a gradual loss of renewable energy plant is subject to different processual effectiveness, due to internal faults. Thisbiomass sugarcane. These boilers burn residual from the cane and may present a gradual loss of constraints, having to produce steam, cold water and electric power. The possible faults on effectiveness, due to internal faults. This renewable energy plant is subject to different processual constraints, having to produce steam, cold water and electric power. The possible faults on the the effectiveness, due to internal faults. This renewable energy plant is subject to different processual constraints, having to produce steam, cold water and electric power. The possible faults on the boilers, main source energy, can the system not to its operational constraints, boilers, mainhaving sourcetoof ofproduce energy, steam, can lead lead thewater system not to comply comply its operational constraints, constraints, cold and electric power. The possible faults on the which results in direct economic deprivation. These faults are identified through a proposed boilers, main source of energy, can lead the system not to comply its operational constraints, are identified through constraints, a proposed which results in direct economic deprivation. Thesenot faults boilers, main source of energy, can lead the system to comply its operational Fault Diagnosis approach, based on gain which Detection results inand direct economic deprivation. faultsextended-state are identified observer, through awhose proposed Fault Detection and Diagnosis approach, based These on an an LPV LPV extended-state observer, gain which results inLinear direct economic deprivation. These faults are identified through awhose proposed Fault Detection and Diagnosis approach, based onsolutions an LPV extended-state observer, whose gain is derived from Matrix Inequalities (LMI ) for the H norm minimization. With ∞ for the is derived from Linear Matrix Inequalities (LMI ) solutions H norm minimization. With ∞ Fault Detection and Diagnosis approach, based an LPV extended-state observer, whose gain is derived from Linear Matrix Inequalities (LMI )onsolutions for the H∞ norm minimization. With the aid of high-fidelity simulation results, the method is discussed. ∞ thederived aid of high-fidelity simulation results, (LMI the method is discussed. is Linear Matrix Inequalities ) solutions for the H∞ norm minimization. With the aid of from high-fidelity simulation results, the method is discussed. © 2018, IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. the aid of high-fidelity simulation results, the method is Hosting discussed. Keywords: Keywords: Fault Fault Detection Detection and and Diagnosis; Diagnosis; LPV; LPV; Boilers, Boilers, Microgrids, Microgrids, Renewable Renewable Sources. Sources. Keywords: Fault Detection and Diagnosis; LPV; Boilers, Microgrids, Renewable Sources. Keywords: Fault Detection and Diagnosis; LPV; Boilers, Microgrids, Renewable Sources. 1. INTRODUCTION INTRODUCTION the 1. the diagnosis diagnosis of of boiler boiler faults faults has has been been seen seen in in (Yang (Yang and and 1. INTRODUCTION Liu, 2004) and (Guoxin et al., 2005), with the use of the diagnosis of boiler faults has been seen in (Yang and Liu, 2004) and (Guoxin et al., 2005), with the use of 1. INTRODUCTION the diagnosis of boiler faults hasrespectively. been inClearly, (Yang and Liu, 2004) and (Guoxin et al., 2005),seen with the usethis of data mining and fuzzy methods, The integration of renewable sources to power systems can data mining and (Guoxin fuzzy methods, respectively. Clearly, this The integration of renewable sources to power systems can Liu, 2004) and et al., 2005), with the use of The integration of renewable sources to power systems and can data research path is open for further investigation. mining and fuzzy methods, respectively. Clearly, this be a good alternative to avoid greenhouse emissions research pathand is open for further respectively. investigation.Clearly, this be a integration good alternative to avoid greenhouse emissions and data mining fuzzy methods, The of renewable sources to power systems can be a good alternative greenhouse and research path is open for further investigation. environmental impact, to butavoid problem to be be emissions solved is is how how environmental impact, but aa problem to solved The faults failures on path isof forand further investigation. be integrate a good alternative to avoid greenhouse and research The detection detection ofopen faults and failures on the the boilers boilers of of the the environmental impact, but a problem to loosing be emissions solved is how to these energy sources without efficiency to integrate these energybut sources without loosing efficiency studied hybrid energy can elevate The detection of faultssystems and failures on theinternal boilerssystem of the environmental impact, a problem to be solved is how studied hybrid energy systems can elevate internal system to integrate these energy sources without loosing efficiency and dispatchability of energy plants. This question of The detection of faults and failures on the boilers of the and dispatchability of energy plants. question of studied safety and enable the better management of hybrid systems system to integrate these energy sources withoutThis loosing efficiency stability, safetyenergy and also also enablecan theelevate better internal management of and dispatchability of energy plants. This question of stability, prime importance has been discussed recently by the the studied hybrid energy systems can elevate internal system prime importance has been discussed recently by energy. stability, safety and also enable the better management of and dispatchability of energy plants. This question of prime importance has been discussedRecent recently by have the energy. Control of Energy Systems community. works stability, safety and also enable the better management of Control of Energy Systems community. Recent works have energy. prime importance has been discussed recently by the Control of Energy Systemsofcommunity. Recent considering works have energy. considered the integration integration renewable sources Most considered the renewable sources considering Most Fault Fault Detection Detection and and Diagnosis Diagnosis (FDD) (FDD) methods methods rereControl of Energy Systemsof community. Recent works have considered the integration ofas renewable sources considering the concept of microgrid, presented in (Lasseter and side in linear parity space approaches, as in (Chen and PatMost Fault Detection and Diagnosis (FDD) methods rethe conceptthe ofintegration microgrid, ofasrenewable presentedsources in (Lasseter and side in linear parity space approaches, as in (Chen and Patconsidered considering Most Fault Detection andapproaches, Diagnosis (FDD) methods rethe concept microgrid, presented in (Lasseter and side in linear parity space as in (Chen and PatPaigi, 2004). ofSome Some optimalascontrol control applications for this this ton, 2012). More recently, the Control Systems community Paigi, 2004). optimal applications for ton, in 2012). More recently, the Control as Systems community the concept of microgrid, asal., presented in (Lasseter and side linear parity space approaches, in (Chen and PatPaigi, 2004). Some optimal control applications for this goal are seen in (Mendes et 2016). has given attention to the use of Linear Parameter Varying ton, 2012). More recently, the Control Systems community goal seen in (Mendes et al., 2016).applications for this has given attention to the use of LinearSystems Parameter Varying Paigi,are Some optimal control ton, 2012). More in recently, themodel Control community goal are2004). seen in (Mendes et al., 2016). (LPV )) systems order to monitored plants and has given attention to the use of Linear Parameter Varying (LPV systems in order to model monitored plants and The system under study in this work is a hybrid energy goal are seenunder in (Mendes given attention to the use of Linear Parameter Varying The system study et in al., this2016). work is a hybrid energy has (LPV ) systems inschemes. order toLPV model monitored plants and to develop FDD systems are represented develop FDD schemes. LPV systems are represented The system under study in processing this work isplant, a hybrid energy to plant based on a sugarcane considering (LPV )extension systems inschemes. order to model monitored plants and plant based on a sugarcane processing plant, considering to develop FDD LPV systems are represented as an of Linear Time-Invariant (LTI ) systems, The system under study this power work is a hybrid energy as an extension of Linear Time-Invariant (LTI ) systems, plant based on asolar sugarcane processing plant, considering biomass, biogas, andinwind wind energy as primary primary to develop FDD schemes. LPV systems are represented biomass, biogas, solar and power energy as assuming the classical state-space representation matrices as an extension of Linear Time-Invariant (LTI ) systems, plant based on This asolar sugarcane processing plant, was considering the classical state-space representation biomass, biogas, and wind powersystem energy as primary energy sources. energy generation (firstly) assuming as an extension ofa Linear Time-Invariant (LTI parameter ) matrices systems, energy sources. This energy generation system was (firstly) are dependent on known bounded scheduling the classical state-space representation matrices biomass, biogas, solar andal., wind power energy asdiscussed primary are dependent on a known bounded scheduling parameter energy sources. This energy generation system was (firstly) assuming presented in (Morato et 2018) and further assuming the classical state-space representation matrices presented in (Morato et al., 2018) and further discussed are dependent on a known bounded scheduling parameter ρ. An LPV fault estimation system is to energy sources. This energy (firstly) An LPV -based -based estimation is able ableparameter to adjust adjust presented in et (Morato et al.,generation 2018) andsystem further in (Morato al., 2017b) 2017b) and (Morato et was al.,discussed 2017a), ρ. are dependent on afault known boundedsystem scheduling in (Morato et al., and (Morato et al., 2017a), ρ. An LPV -based fault estimation system is able to adjust itself (autonomously) by scheduling observer (filter) gains presented in (Morato et al., 2018) and further discussed itself (autonomously) by scheduling observer (filter) gains in (Morato etmodern al., 2017b) and (Morato were et al., 2017a), wherein some control techniques applied to ρ. An LPV -based fault estimation system is able to adjust wherein some modern control techniques were applied to depending on the monitored system’s condition. These itself (autonomously) by scheduling observer (filter) gains in (Morato et al., 2017b) and (Morato et al., 2017a), depending on the monitored system’s condition. These wherein some modern control techniques were applied to its control. control. Nonetheless, Nonetheless, aa great great portion portion of of the the energy energy itself (autonomously) by scheduling observer (filter) gains its LPV schemes have been discussed in recent publications: depending on the monitored system’s condition. These wherein some modern control techniques were applied to schemes been discussed in recent publications: its control. in Nonetheless, a great portion of athebiomassenergy LPV production this system system is derived derived from depending onethave the monitored system’s condition. These production in this is from biomassschemes have been discussed in recent publications: in (Grenaille al., 2008), aa framework is presented for its control. Nonetheless, a great portion of a energy LPV in (Grenaille et al., 2008), framework is presented for the the production in this system is derived from athebiomassburning boiler. This kind of boiler is thoroughly reviewed LPV schemes have been based discussed in on recent publications: burning boiler. This kind of boiler is thoroughly reviewed synthesis of FDD filters based on an LMI in (Grenaille et al., 2008), a framework is presented for the production inal., this system is derived from aboiler biomasssynthesis of FDD filters based based on on an LMIforsolusoluburning boiler. This kindPossible of boiler is thoroughly reviewed in (Saidur et 2011). faults on the can in (Grenaille et al., 2008), a framework is presented the in (Saidur et al., 2011). Possible faults on the boiler can tion; in (Abdullah and Zribi, 2013), the authors propose synthesis of FDD filters based based on on an LMI soluburning boiler. This kindPossible of to boiler is thoroughly reviewed in (Abdullah and Zribi, 2013), the authors propose in (Saidur et al., 2011). faults on theconstraints, boiler can tion; lead the plant not to comply its operational synthesis of FDD filters based based on on an LMI solulead the plant not 2011). to comply to its faults operational the design of LPV observer estimate sensor in (Abdullah and Zribi, theto authors in (Saidur et in al., Possible on theconstraints, boiler can tion; the of aa low-order low-order LPV 2013), observer estimatepropose sensor lead the plant noteconomic to comply to its operational constraints, which results deprivation. tion;design in (Abdullah and Zribi, theto which results in economic deprivation. the design of a low-order LPV 2013), observer toauthors estimatepropose sensor faults. lead the plant not to comply to its operational constraints, faults. which results in economic deprivation. the design of a low-order LPV observer to estimate sensor faults. Up to the authors’ knowledge, only few works have prewhich in economic deprivation. Up to results the authors’ knowledge, only few works have pre- faults. Given the presented context, this work will present prelimUp to the authors’ knowledge, onlyforfew works(on have pre- Given the presented context, this work will present prelimsented studies on Fault Fault Detection boilers energy sented studies on Detection boilers (on energy the presented context, this work will present preliminary in of LPV -based FDD Up to the authors’ knowledge, onlyfor few works have pre- Given inary results results in terms terms of using using LPV -based FDD methods methods sented studies on Fault Detection for boilers (on energy generation systems). Some works present some insights Given theand presented context, this work will present prelimgeneration systems). Some works present some insights to detect estimate faults on hybrid energy generation inary results in terms of using LPV -based FDD methods sented studies on Fault Detection for boilers (on energy to detect andinestimate faults onLPV hybrid energy generation generation systems). Some works present some insights on the consequence of faults, as in (Bulloch et al., 2009); inary results terms of using -based FDD methods on the consequence faults,works as in (Bullochsome et al., 2009); to (faulty) biomass boiler. For detect considering and estimateaa faults on hybrid generation systems).of systems, considering (faulty) biomassenergy boiler.generation For this this on the consequence ofSome faults, as in present (Bulloch et al.,insights 2009); systems, to detect and estimate faults on hybrid energy generation The authors thank CNPq and Ministerio de Econom´ ıaal., y Competgoal, an extended observer design methodology is followed, systems, considering a (faulty) biomass boiler. For this on the consequence of faults, as in (Bulloch et 2009); The authors thank CNPq and Ministerio de Econom´ıa y Competgoal, an extended observer design methodology is followed, systems, considering a (faulty) biomass boiler. For this itividad de Espa˜ na for financing the projects The authors thank CNPq and Ministerio de CNPq401126/2014-5, Econom´ıa y Competgoal, an extended observer design methodology is followed, using an LMI for the minimization. ∞ norm itividad de Espa˜ na for financing the projects CNPq401126/2014-5, The authors usingan anextended LMI synthesis synthesis the H H ∞ norm minimization. thank CNPq and Ministerio de CNPq401126/2014-5, Econom´ıa y Competgoal, observerfor design methodology is followed, CNPq303702/2011-7 and DPI2016-78338-R. itividad de Espa˜ n a for financing the projects using an LMI synthesis for the H norm minimization. ∞ CNPq303702/2011-7 and DPI2016-78338-R. ∞ itividad de Espa˜ na forand financing the projects CNPq401126/2014-5, using an LMI synthesis for the H∞ norm minimization. CNPq303702/2011-7 DPI2016-78338-R.
CNPq303702/2011-7 and(International DPI2016-78338-R. 2405-8963 © © 2018 2018, IFAC IFAC Federation of Automatic Control) Copyright 1 Hosting by Elsevier Ltd. All rights reserved. Copyright © under 2018 IFAC 1 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 1 10.1016/j.ifacol.2018.11.177 Copyright © 2018 IFAC 1
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The control-oriented hourly-discrete state-space representation model of the studied plant is given below, by (1). This mathematical model was obtained and validated through simulation based on experimental data; for full details, refer to (Morato et al., 2018):
The rest of this document is organized as follows: an introduction to the Brazilian sugarcane energy generation paradigm is seen in Section 2; in Section 3, the possible faults on the biomass Boilers are discussed and mathematically modelled; in Section 4, the proposed LPV Fault Detection and Diagnosis scheme is detailed; then, in Section 5 simulation results are presented; conclusions are drawn in Section 6.
x(k + 1) = Ax(k) + B1 w(k) + B2 u(k)
(1)
z(k) = C1 x(k) + D11 w(k) + D12 u(k) y(k) = C2 x(k) + D21 w(k) + D22 u(k) Remark 1. This representation describes the plant through its controlled outputs (z), measured outputs (y) and internal states (x). Note that the supervisory controller is responsible and preoccupied with the controlled outputs (z), and that these are not (necessarily) measured. In this system, specifically, the measured outputs are equivalent to the internal states, y(k) = x(k).
2. BRAZILIAN SUGARCANE INDUSTRY In this work, the Brazilian sugarcane industry (largest in the world) is taken into account, given that the sugarcane production process has a great amount of residue and waste that is treated as bio-sources of energy. As visited in (Morato et al., 2018), Brazilian sugar-ethanol plants are bright candidates to be managed as hybrid power plants, considering the use of biomass and biogas for direct-toelectric-energy generation and, also, (external,additional) solar and wind power energy generation.
x(k) = [ XBat (k) XBag (k) XStr (k) XBg (k) XT (k) ]
T
(2)
(3) u(k) = [ SPTAU (k) SPTBU (k) P otN et (k) R(k) . . . Out M B QV (k) QEsc (k) QEsc (k) SPCHP (k) . . . B (k) QTEsc (k) ]T SPCh (k) SPT C (k) P otBat (k) QM V T L (4) z(k) = PP roc (k) QM V (k) QV (k) QCW (k) PSale (k)
Most of the current industrial Brazilian sugar cane processing plants have a similar structure. These plants have internal demands, corresponding to the sugar and ethanol processing requirements: to produce steam in different pressures (used to boost shredders, spray bombs and other equipments), to produce cold water for refrigeration needs (used to cool down generators, oil tanks and other systems) and, finally, to produce electric power to sustain the plant. Apart from these internal demands, these plants also sell the excedent electric energy to a local Distribution Network Operator (DNO).
w(k) = [ W ndin (k) Irrdin (k) . . .
Bagin (k) Strin (k) Bgin (k) ]
(5)
T
The system state vector x is defined as (2), where each entry stands for the normalized percentage of each of the plant’s storage units: battery bank, bagasse stock, straw stock, biogas stock and hot water tank.
Then, for energy management and Control goals, these plants can be treated as microgrids and mathematically modelled following the Energy Hub methodology, as introduced in (Geidl et al., 2007). A generalized microgrid, considering this modelling framework, is comprised of energy conversion units (as turbines and boilers) and energy storage facilities. The inputs to this microgrid, from an energy management control point-of-view are given by uj (set-points to the internal subsystems), and the measured outputs, yj , stand for the plant’s transmission lines (electric network, gas pipes, steam lines, etc). A supervisory controller sets hourly set-points for the plant’s internal subsystems so that each global demand is met and the energy generation is maximized. This control problem has been treated with optimal, predictive schemes in (Morato et al., 2017b) and, also, in (Morato et al., 2017a).
As this is a control-oriented model, the input vector u stands for zero-order-held set-points for the conversion and storage units (subsystems). From an hourly controller’s point-of-view, it is assumed that the sampling period of ∆T = 1 h is large enough so that all these set-points have been accurately tracked by their respective subsystems. The complete control vector is given by (3), where each entry stands, respectively, for: energy boiler’s set-point, lower efficiency turbine’s set-point, higher efficiency turbine’s set-point, set-point of energy flow to (from) the battery bank, CHP ’s set-point, water chiller’s set-point, heat exchanger’s set-point, high-to-middle pressure reduction valve’s set-point, middle-to-low pressure reduction valve’s set-point, hot water escape flow’s set-point, middle pressure steam escape flow’s set-point, low pressure steam escape flow’s set-point, set-point of power available to the external network. In terms of the boilers in this plant: one is mainly responsible for the energy generation, by burning biomass, whereas the other is only used solely for steam production and its set-point is consequence of other variables.
The hybrid energy generation system that is studied in this work, based on a sugarcane power plant, that produces sugar, ethanol and electric power, is composed by the following subsystems: two boilers, with different efficiencies; two steam turbines, with different efficiencies; a combined heat and power system (CHP ); a water chiller; a hot water tank; photovoltaic panels; water heating solar panels; a wind turbine; two pressure reduction valves; one heat exchanger; stocks of bagasse, straw and compressed biogas and a battery bank. The use of intermediate storage units (battery bank and biomass stocks) allows the system to accumulate energy (or biomass, that can be converted into energy) when the renewable generation is high and use it when there is no renewable production.
The system’s controlled outputs z are defined in Eq. (4), being PP roc the electric power produced due to the sugar cane processing demand (kW ); QM V the flow of middle the flow of low pressure steam pressure steam ( Mhg ); QL V Mg ( h ); QCW the flow of chilled water required by the 3 distillery process ( mh ); finally, PSale represents the electric power made available to the external network (kW ). 2
IFAC LPVS 2018 Marcelo Menezes Morato et al. / IFAC PapersOnLine 51-26 (2018) 1–6 Florianopolis, Brazil, September 3-5, 2018
3
Remark 2. (a) As exposes Eq. (6), the loss of effectiveness factor of f (k) = 1 stands for faultless situations; (b) The multiplicative commutative property is valid in Eq. (6), given that both variables f and R, at a given instant k, are scalars; (c) The output energy flow uf , in this work, is not directly measurable. This means that, to compute (or estimate) f (t), one cannot resort to a simple algebra, as only R is known at each instant k.
The disturbances to the system w are defined by Eq. (5), being W ndin the speed of the wind ( km h ) present in the microgrid’s area, used by the wind turbines to generate electric power; Irrdin the amount of solar irradiance W (m 2 ) on the microgrid’s solar panels (photovoltaic and water heating); Bagin , Strin and Bgin represent the income ( Mhg ) of bagasse, straw and biogas to the plant, respectively. 3. THE BOILER’S FAULTY SITUATIONS
The main objective of this work, then, is to continuously and accurately estimate the term Λ = (f − 1). Knowing Λ, the computation of f is direct and, then, one can have a valid notion of whether the energy boiler is, or not, faulty. This serves for surveillance and safety goals, helps with prevention maintenance of the boiler and can even serve as a paradigm for a fault-tolerant control strategy.
Now, this work will analyse with further care the Boiler unit, a conversion unit of the hybrid energy plant that can fail and lead to a problem in terms of complying with the electric power demands. In terms of statical behaviour, the energy boiler γBoiler converts the input biomass mixture to output electric power uf (t) with a gain of Kv ( kWh Mg ). This unit, together with its local controller, can be equivalently represented by Figure 1, where the gain K1v is used such that the local setpoint R(t) is tracked. The possible faults that appear on these boiler units may come from two different situations: a) the accumulation of debris and residues or biomass clogging on ducts, which leads to direct-to-energy gain decrease; b) an emergency stop from the manual operators. In both of these cases, the boiler’s static gain changes.
4. THE FAULT ESTIMATION PROBLEM Considering the problem of the hybrid energy plant subject to possible faults on its energy boiler, the term Λ can be estimated with the use of an FDD scheme that has access, at each instant, to the control inputs u(k) and measured output y(k). An illustration of this fault detection paradigm is given in Figure 2.
Then, to model these faults, a multiplicative loss of effectiveness factor f (t) is considered upon the boiler’s static gain. This means that the local control is not be able to track the references they are given. This multiplicative fault representation has been firstly presented in (Hern´ andez-Alc´ antara et al., 2016), and introduces a solid framework for the modelling of faults. Roughly speaking, this work assumes that the real (faulty) electric power output uf (t) is proportionally dependent to the expected (faultless) output reference R(t), as point out Equation (6). Fig. 2. Fault Detection Paradigm First of all, it has to be remarked that the energy generation set-points u(k) will be determined at each instant by some optimal control scheme, as the one proposed in (Morato et al., 2017b), so that local controllers to the conversion and storage units track these references in some avid settling time smaller than ∆T = 1 h. Then, the studied (faulty) energy system (7) will be described by an extended-state representation, given below:
Fig. 1. Faulty Boiler Problem Representation uf (k) = R(k)f (k)
(6)
Then, whenever a fault occurs on the energy boiler, the mathematical representation that describes the faulty energy systems is given by:
˘ (7) x(k + 1) = Ax(k) + B1 w(k) + B2 u(k) + B2 Λ(k)R(k) ˘ z(k) = C1 x(k) + D11 w(k) + D12 u(k) + D12 Λ(k)R(k)
(8)
Λ(k) = f (k) − 1
(9)
A
xa (k)
a ˘ x(k + 1) x(k) = A B2 R(k) Λ(k + 1) Λ(k) 0 1
(10)
q(k)
Ba
B1 B2 w(k) + u(k) 0 0
˘ y(k) = C2 x(k) + D21 w(k) + D22 u(k) + D22 Λ(k)R(k) where: T ˘ R(k) = [ 01×3 R(k) 01×9 ]
xa (k+1)
Ca
˘ y(k) = C2 D22 R(k) xa (k) Da
T + [ D21 D22 ] [ w(k) u(k) ]
3
(11)
IFAC LPVS 2018 4 Marcelo Menezes Morato et al. / IFAC PapersOnLine 51-26 (2018) 1–6 Florianopolis, Brazil, September 3-5, 2018
level to a given input. So, by minimizing this norm, the observer’s sensitivity to disturbances q is minimized, and, then, the observer’s output (estimation of Λ) will be better achieved and more immune to q. In terms of the estimation error dynamics (13), the term [Aa − LCa ] is to be stable and [Ba − L(ρ)Da ]q small and, as of this, e shall converge to 0. Given this motivation, the H∞ criterion is a suitable choice in order to compute the matrix gain L(ρ). Lemma 1. The H∞ observer synthesis consist in imposing Eq. (14). This is obtained when computing the polytopic LPV observer matrix gain by minimizing the scalar γH∞ and solving the sole following LMI, taking Q(ρ) = P L(ρ), with P being a positive definite matrix affine on ρ. The existence conditions for this observer is the assurance of detectability of the pair [Aa (ρ) , Ca (ρ)] within Ω. More details on this matter are given in (Yamamoto et al., 2015). M1,1 [P Ba − Q(ρ)Da ] −E T E
< 0 , Q > 0 (15) 0 −IγH∞
−IγH∞
Remark 3. (Actuator) faults can be described either as multiplicative or additive terms upon u(k). This work opts for the first option due to conveniencies. Nonetheless, the corresponding additive fault term to a multiplicative one ˘ Notice how this can is given by fa (k) = B2 [f (k) − 1]R(k). ˘ be easily computed if f (k) is estimated, as B2 and R(k) are always known. Remark 4. Thanks to the multiplicative fault representation, the information on the fault Λ(k) is assumed to be constant or slowly varying. This leads to Λ(k + 1) ≈ Λ(k). Reader must understand that the assumption that the fault is constant or slowly varying is sufficient for the purposes of this work. Even if faults do not abide by this rule, they will be, anyhow, sufficiently diagnosed given that the observer-based approach aims to minimize the fault estimation error eΛ , as will be detailed next. It is important to notice that matrices Aa and Ca are affine ˘ on R(k). As this signal is completely known (determined by the supervisory controller) and bounded by the operational constraints of the boiler, it can be considered as a scheduling parameter ρ ∈ Ω, being Ω a compact convex set given by the saturation limits of this set-point. Then, system (10) becomes LPV, defined within the polytope delimited by the boundaries of Ω. Notice that it is only LPV because of the way that faults were represented (multiplicative factors) and under the assumption discussed in Remark 4.
with
M1,1 = ATa (ρ)P + P Aa (ρ)
(16)
− CaT (ρ)QT (ρ)
− Q(ρ)Ca (ρ) The gain matrix L(ρ) is taken, thus, as L(ρ) = P −1 Q(ρ). Proof 1. Straightforward from (Armeni et al., 2009). Guarantees of stability of the error system (13) can be found in (Nguyen et al., 2016); remark that the system (1) is a priori stable, so the instability would only derive from badly proposed matrices L(ρ), which would not be the case as the Bounded Real Lemma is guaranteed. Remark 5. This work considers a discrete-time observer. From this, the solution is computed in continuous-time and, then, discretized with sampling period of ∆T = 1 h.
Then, as the faulty system is represented through an augmented framework with states xa (k) that contain the information on the possible faults, Λ(k), if there exists some asymptotical tracking of xa (k), one has an accurate estimation of f (t). As seen in (Grenaille et al., 2008), a polytopic LPV observer is used for this goals, as follows: x ˆa [k + 1] = Aa (ρ)ˆ xa (k) + L(ρ)[y(k) − Ca (ρ)xˆa (k)](12) ˆ Λ(k) = 0size(x) 1 xˆa (k)
The interest of this polytopic LPV approach is that the presented LMI s are computed offline, at each vertex v of the workspace polytope. Then, the observer gain matrix L(ρ) is given by a linear combination of every Lv , affine on ρ and that guarantees the asymptotic stability of (13).
E
Finally, the estimation error dynamics (eΛ (k) = Λ(k) − ˆ Λ(k)), are given below:
5. RESULTS AND ANALYSIS
e(k + 1) = [Aa − LCa ](ρ)e(k) + [Ba − L(ρ)Da ]q(k)(13) eΛ (k) = Ee(k)
(14)
Now, some simulation results will be presented in order for the accuracy of the proposed FDD scheme to be analysed. The following simulation results were obtained using a high-fidelity hybrid model, refer to (Morato et al., 2018). As already stated, this work considers that a supervisory energy management control loop is working in order to define the set-points u(k), at each sampling period of 1 h, as done by Vergara-Dietrich, Morato, Mendes, Cani, Normey-Rico, and Bordons (2017), guaranteeing that all the plant’s demands are met. These signals are seen in Figure 3. For simplicity, they repeat periodically each 24 h, as does the load demands. The used data for w(k) is taken from real data from the state of Paran´ a, Brazil, refer to (Morato et al., 2017a). Notice that these disturbances w(k) are non-null and influence on the achieved results.
The H∞ norm of a system is understood as the induced energy-to-energy gain, being the worst case attenuation
The solution to the LPV H∞ observer, presented in Lemma 1 is obtained with the aid of the following softwares: MATLAB (Mathworks, 2017), Yalmip (Lofberg,
The dynamics of (13) have to be stable for the correct estimation of faults on the boilers. This stability issue depends on the choice of gain matrix L(ρ) and, so, the following problem is traced, adapted from (Armeni et al., 2009). A solution Lemma is presented in the following. Problem 1. The H∞ LPV observer problem is defined as follows: Find a gain matrix L(ρ), affine on the scheduling parameter ρ and defined within the polytope workspace so that the estimation error dynamics, given by (13), are exponentially stable (considering q(k) is null) and that the following objective function is minimized: JH∞ = ||
eΛ ||∞ ≤ γH∞ under e(k)|k=0 = 0 q
4
IFAC LPVS 2018 Marcelo Menezes Morato et al. / IFAC PapersOnLine 51-26 (2018) 1–6 Florianopolis, Brazil, September 3-5, 2018
5
mized. The minimal γH∞ achieved in such a way that the inequality still remains valid is 4.8724, a very sufficient bound, considering the energy-to-energy gain minimization of q on eΛ . This value is related to the numerical robustness of the LPV -FDD approach towards the (nonnull, always present) disturbances q(k). Although the H∞ norm minimization approach might be conservative, this is not of great importance herein, as the control actions only act every Ts = 1 h, so there is no rush for exceedingly fast responses. Remark 6. This work proposed a fault detection scheme that does not need the addition of new components, such as redundant sensors. In terms of comparisons with alike techniques, (Nguyen et al., 2016) has already discussed that LPV observer-based FDD schemes do present better results than, for instance, the Fast Adaptive Fault Estimation method, proposed by Zhang et al. (2009). As of this, this work is not preoccupied with comparisons, but mostly on the application of an LPV observer-based FDD method to the studied problem. Now that all other signals have been presented, the simulated fault scenario has to be described: i) the energy boiler suffers from continuous accumulation of debris and residues, starting from t = 3 h, this leads to a gain decrease of up to 25 %. ii) then, a sudden stop of the boiler occurs, coming from the manual operator, which leads to a loss of effectiveness of 100 %. For a complete understanding of how the proposed FDD system works, reader is invited to see Figure 4, where a comparison between the faulty output boiler power uf (k) and the expected faultless set-point R(k) is shown; the effect of the faults are noticeable. The detection and estimation of the respective loss of effectiveness fault term f (k) is seen in Figure 5, compared with the actual simulated faults. As it can be seen, the proposed polytopic LPV approach presents some accurate and smooth results in terms of estimating faults on boilers, which is very good. The achieved performance stands for a precise estimation of the possible loss of effectiveness faults on boilers. It must be remarked, nonetheless, that the estimated fault term fˆ(k) can become slightly noisy when estimating emergency stop failures. This is expected, as the H∞ synthesis is not preoccupied with impulse-to-energy minimization, but does not compromise the overall results, as the estimated fault term, when f (k) = 0, stays inside the limited set fˆ(k) ∈ [0 − 0.04 , 0 + 0.04].
Fig. 3. Set-Points u(k) 2004) and SDPT 3 (Toh et al., 1999). The idea behind the algorithm is to find positive definite matrix P and a block amax ρ −ρ ρ−ρmin max matrix Q(ρ) = ρmax + , Q min −ρmin ρmax −ρmin Q
Fig. 4. Faulty and Faultless Signals: R(k) and uf (k)
in such way that the LMI (15) holds and γH∞ is mini5
IFAC LPVS 2018 6 Marcelo Menezes Morato et al. / IFAC PapersOnLine 51-26 (2018) 1–6 Florianopolis, Brazil, September 3-5, 2018
Hern´andez-Alc´antara, D., Tud´on-Mart´ınez, J.C., Am´ezquita-Brooks, L., Vivas-L´opez, C.A., and Morales-Men´endez, R. (2016). Modeling, diagnosis and estimation of actuator faults in vehicle suspensions. Control Engineering Practice, 49, 173–186. Lasseter, R.H. and Paigi, P. (2004). Microgrid: a conceptual solution. In Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, volume 6, 4285–4290. IEEE. Lofberg, J. (2004). Yalmip: A toolbox for modeling and optimization in matlab. In IEEE Int. Symp. on Computer Aided Control Systems Design, 284–289. Mathworks (2017). MATLAB r2017a. Mendes, P.R.C., Isorna, L.V., Bordons, C., and NormeyRico, J.E. (2016). Energy management of an experimental microgrid coupled to a v2g system. Journal of Power Sources, 702–713. Morato, M.M., Cani, A.A., Mendes, P.R.C., Normey-Rico, J.E., and Bordons, C. (2018). Future hybrid local energy generation paradigm for the brazilian sugarcane industry scenario. International Journal of Electrical Power and Energy Systems. Morato, M.M., Mendes, P.R.C., Normey-Rico, J.E., and Bordons, C. (2017a). Advanced control for energy management of grid-connected hybrid power systems in the sugar cane industry. In Proceedings of the 20th IFAC World Congress. IFAC. Morato, M.M., Mendes, P.R.C., Normey-Rico, J.E., and Bordons, C. (2017b). Optimal operation of hybrid power systems including renewable sources in the sugar cane industry. IET Renewable Power Generation, 11, 1237– 1245(8). Nguyen, M.Q., Sename, O., and Dugard, L. (2016). Comparison of observer approaches for actuator fault estimation in semi-active suspension systems. In 3rd Conference on Control and Fault-Tolerant Systems, 227–232. IEEE. Saidur, R., Abdelaziz, E., Demirbas, A., Hossain, M., and Mekhilef, S. (2011). A review on biomass as a fuel for boilers. Renewable and sustainable energy reviews, 15(5), 2262–2289. Toh, K.C., Todd, M.J., and T¨ ut¨ unc¨ u, R.H. (1999). Sdpt3a matlab software package for semidefinite programming, version 1.3. Optimization methods and software, 11(1-4), 545–581. Vergara-Dietrich, J.D., Morato, M.M., Mendes, P.R.C., Cani, A.A., Normey-Rico, J.E., and Bordons, C. (2017). Advanced chance-constrained predictive control for the efficient energy management of renewable power systems. Journal of Process Control. Yamamoto, K., Koenig, D., Sename, O., and Moulaire, P. (2015). Driver torque estimation in electric power steering system using an h∞ /h2 proportional integral observer. In IEEE Conf. on Decision and Control, 843– 848. Yang, P. and Liu, S.S. (2004). Fault diagnosis for boilers in thermal power plant by data mining. In IEEE Control, Automation, Robotics and Vision Conference, volume 3, 2176–2180. Zhang, K., Jiang, B., and Cocquempot, V. (2009). Fast adaptive fault estimation and accommodation for nonlinear time-varying delay systems. Asian Journal of Control, 11(6), 643–652.
Fig. 5. Boiler Fault Detection 6. CONCLUSIONS This paper presented the issue of fault detection and diagnosis for boilers on hybrid generation power systems, considering a polytopic H∞ LPV -based extended observed methodology. As demonstrated by simulation results, the proposed strategy is an efficient one in terms of this work’s intents. Such accurate FDD scheme can be used for faulttolerant control goals of hybrid energy systems in the presence of faults, in order to preserve the system stability and maintain performance objectives (comply to energy demand and others). This work has been pointed as preliminary because authors still plan on investigation the effect of faults on every storage and conversion unit of the hybrid power system analysed herein. Combined H∞ /H2 /H− sensitivity observers shall be tested. Still, the design of fault-tolerant predictive controllers for the global energy management of sugarcane-based power plants is an open topic for further works. REFERENCES Abdullah, A. and Zribi, M. (2013). Sensor-fault-tolerant control for a class of linear parameter varying systems with practical examples. Industrial Electronics, IEEE Transactions on, 60(11), 5239–5251. Armeni, S., Casavola, A., and Mosca, E. (2009). Robust fault detection and isolation for LPV systems under a sensitivity constraint. International Journal of Adaptive Control and Signal Processing, 23(1), 55–72. Bulloch, J., Callagy, A., Scully, S., and Greene, A. (2009). A failure analysis and remnant life assessment of boiler evaporator tubes in two 250mw boilers. Engineering Failure Analysis, 16(3), 775–793. Chen, J. and Patton, R.J. (2012). Robust model-based fault diagnosis for dynamic systems, volume 3. Springer. Geidl, M., Koeppel, G., Favre-Perrod, P., Klockl, B., Andersson, G., and Frohlich, K. (2007). Energy hubs for the future. IEEE Power and Energy Magazine, 5(1), 24. Grenaille, S., Henry, D., and Zolghadri, A. (2008). A method for designing fault diagnosis filters for LPV polytopic systems. Journal of Control Science and Engineering, 2008, 1. Guoxin, X., LiChuan, X., Meihua, B., and Siwei, L. (2005). Fault prediction of boilers with fuzzy mathematics and rbf neural network. In IEEE Int. Conf. on Communications, Circuits and Systems. 6
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IFAC PapersOnLine 51-26 (2018) 1–6
LPV -H Fault Estimation for Boilers in ∞ LPV -H Estimation for Boilers in ∞ Fault LPV -H Fault Estimation for Boilers in ∞ Processing Plants LPV Sugarcane -H Fault Estimation for Boilers in ∞ Sugarcane Processing Plants Sugarcane Processing Plants Sugarcane Processing Plants Marcelo Menezes Morato ∗∗ Paulo Renato da Costa Mendes ∗∗
Marcelo Menezes Morato ∗∗ Paulo∗Renato da Costa∗∗Mendes ∗∗ Elias Normey-Rico Carlos Marcelo Julio Menezes Renato da Costa∗∗Mendes ∗ ∗ Paulo∗ EliasMorato Normey-Rico Carlos Bordons Bordons ∗∗Mendes Marcelo Julio Menezes Paulo∗∗Renato da Costa∗∗ Julio EliasMorato Normey-Rico Carlos Bordons ∗ ∗∗ Julio Elias Normey-Rico Carlos Bordons ∗ cc˜ a o ee Sistemas (( DAS), Universidade ∗ Departamento de Automa¸ Departamento de Automa¸ ˜ a o Sistemas DAS), Universidade ∗ ∗ Departamento de Automa¸ c˜ ao e Sistemas ( DAS), Universidade Federal Santa Catarina, Florian´ o Brazil ∗ Federal de de de Santa Catarina, Florian´ opolis-SC, polis-SC, Brazil ∗∗ Departamento Automa¸ cde ˜ ao Sistemas e Sistemas ( DAS), Universidade de Ingenier´ ıa y Autom´ a tica, Universidad Federal de Santa Catarina, Florian´ o polis-SC, Brazil ∗∗ Departamento Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ Federal de Santa Catarina, Florian´ opolis-SC, Brazil ∗∗ de Sevilla, Spain Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ de Sevilla, Spain Departamento de Ingenier´ de Sistemas atica, Universidad deıaSevilla, Spain y Autom´ de Sevilla, Spain Abstract: This short study presents Abstract: This short study presents aa Linear Linear Parameter Parameter Varying Varying (LPV (LPV )) method method for for the the Abstract: of This shortonstudy presents a Linear Parameter Varying (LPV ) method for the estimation faults Boilers of a Grid-Connected Hybrid Power Plant, that processes estimation of faults onstudy Boilers of a Grid-Connected Hybrid Power(LPV Plant, that processes Abstract: This short presents a Linear Parameter Varying ) method for sugarcane. boilers residual biomass from the the cane cane andPower may present present gradual lossthe of estimation These of faults on burn Boilers of a biomass Grid-Connected Hybrid Plant,aa that processes from and may gradual loss of sugarcane. These boilers burn residual estimation of faults on Boilers of a Grid-Connected Hybrid Power Plant, that processes effectiveness, due to internal faults. This renewable energy plant is subject to different processual sugarcane. These boilers burn residual biomass from the cane and may present a gradual loss of renewable energy plant is subject to different processual effectiveness, due to internal faults. Thisbiomass sugarcane. These boilers burn residual from the cane and may present a gradual loss of constraints, having to produce steam, cold water and electric power. The possible faults on effectiveness, due to internal faults. This renewable energy plant is subject to different processual constraints, having to produce steam, cold water and electric power. The possible faults on the the effectiveness, due to internal faults. This renewable energy plant is subject to different processual constraints, having to produce steam, cold water and electric power. The possible faults on the boilers, main source energy, can the system not to its operational constraints, boilers, mainhaving sourcetoof ofproduce energy, steam, can lead lead thewater system not to comply comply its operational constraints, constraints, cold and electric power. The possible faults on the which results in direct economic deprivation. These faults are identified through a proposed boilers, main source of energy, can lead the system not to comply its operational constraints, are identified through constraints, a proposed which results in direct economic deprivation. Thesenot faults boilers, main source of energy, can lead the system to comply its operational Fault Diagnosis approach, based on gain which Detection results inand direct economic deprivation. faultsextended-state are identified observer, through awhose proposed Fault Detection and Diagnosis approach, based These on an an LPV LPV extended-state observer, gain which results inLinear direct economic deprivation. These faults are identified through awhose proposed Fault Detection and Diagnosis approach, based onsolutions an LPV extended-state observer, whose gain is derived from Matrix Inequalities (LMI ) for the H norm minimization. With ∞ for the is derived from Linear Matrix Inequalities (LMI ) solutions H norm minimization. With ∞ Fault Detection and Diagnosis approach, based an LPV extended-state observer, whose gain is derived from Linear Matrix Inequalities (LMI )onsolutions for the H∞ norm minimization. With the aid of high-fidelity simulation results, the method is discussed. ∞ thederived aid of high-fidelity simulation results, (LMI the method is discussed. is Linear Matrix Inequalities ) solutions for the H∞ norm minimization. With the aid of from high-fidelity simulation results, the method is discussed. © 2018, IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. the aid of high-fidelity simulation results, the method is Hosting discussed. Keywords: Keywords: Fault Fault Detection Detection and and Diagnosis; Diagnosis; LPV; LPV; Boilers, Boilers, Microgrids, Microgrids, Renewable Renewable Sources. Sources. Keywords: Fault Detection and Diagnosis; LPV; Boilers, Microgrids, Renewable Sources. Keywords: Fault Detection and Diagnosis; LPV; Boilers, Microgrids, Renewable Sources. 1. INTRODUCTION INTRODUCTION the 1. the diagnosis diagnosis of of boiler boiler faults faults has has been been seen seen in in (Yang (Yang and and 1. INTRODUCTION Liu, 2004) and (Guoxin et al., 2005), with the use of the diagnosis of boiler faults has been seen in (Yang and Liu, 2004) and (Guoxin et al., 2005), with the use of 1. INTRODUCTION the diagnosis of boiler faults hasrespectively. been inClearly, (Yang and Liu, 2004) and (Guoxin et al., 2005),seen with the usethis of data mining and fuzzy methods, The integration of renewable sources to power systems can data mining and (Guoxin fuzzy methods, respectively. Clearly, this The integration of renewable sources to power systems can Liu, 2004) and et al., 2005), with the use of The integration of renewable sources to power systems and can data research path is open for further investigation. mining and fuzzy methods, respectively. Clearly, this be a good alternative to avoid greenhouse emissions research pathand is open for further respectively. investigation.Clearly, this be a integration good alternative to avoid greenhouse emissions and data mining fuzzy methods, The of renewable sources to power systems can be a good alternative greenhouse and research path is open for further investigation. environmental impact, to butavoid problem to be be emissions solved is is how how environmental impact, but aa problem to solved The faults failures on path isof forand further investigation. be integrate a good alternative to avoid greenhouse and research The detection detection ofopen faults and failures on the the boilers boilers of of the the environmental impact, but a problem to loosing be emissions solved is how to these energy sources without efficiency to integrate these energybut sources without loosing efficiency studied hybrid energy can elevate The detection of faultssystems and failures on theinternal boilerssystem of the environmental impact, a problem to be solved is how studied hybrid energy systems can elevate internal system to integrate these energy sources without loosing efficiency and dispatchability of energy plants. This question of The detection of faults and failures on the boilers of the and dispatchability of energy plants. question of studied safety and enable the better management of hybrid systems system to integrate these energy sources withoutThis loosing efficiency stability, safetyenergy and also also enablecan theelevate better internal management of and dispatchability of energy plants. This question of stability, prime importance has been discussed recently by the the studied hybrid energy systems can elevate internal system prime importance has been discussed recently by energy. stability, safety and also enable the better management of and dispatchability of energy plants. This question of prime importance has been discussedRecent recently by have the energy. Control of Energy Systems community. works stability, safety and also enable the better management of Control of Energy Systems community. Recent works have energy. prime importance has been discussed recently by the Control of Energy Systemsofcommunity. Recent considering works have energy. considered the integration integration renewable sources Most considered the renewable sources considering Most Fault Fault Detection Detection and and Diagnosis Diagnosis (FDD) (FDD) methods methods rereControl of Energy Systemsof community. Recent works have considered the integration ofas renewable sources considering the concept of microgrid, presented in (Lasseter and side in linear parity space approaches, as in (Chen and PatMost Fault Detection and Diagnosis (FDD) methods rethe conceptthe ofintegration microgrid, ofasrenewable presentedsources in (Lasseter and side in linear parity space approaches, as in (Chen and Patconsidered considering Most Fault Detection andapproaches, Diagnosis (FDD) methods rethe concept microgrid, presented in (Lasseter and side in linear parity space as in (Chen and PatPaigi, 2004). ofSome Some optimalascontrol control applications for this this ton, 2012). More recently, the Control Systems community Paigi, 2004). optimal applications for ton, in 2012). More recently, the Control as Systems community the concept of microgrid, asal., presented in (Lasseter and side linear parity space approaches, in (Chen and PatPaigi, 2004). Some optimal control applications for this goal are seen in (Mendes et 2016). has given attention to the use of Linear Parameter Varying ton, 2012). More recently, the Control Systems community goal seen in (Mendes et al., 2016).applications for this has given attention to the use of LinearSystems Parameter Varying Paigi,are Some optimal control ton, 2012). More in recently, themodel Control community goal are2004). seen in (Mendes et al., 2016). (LPV )) systems order to monitored plants and has given attention to the use of Linear Parameter Varying (LPV systems in order to model monitored plants and The system under study in this work is a hybrid energy goal are seenunder in (Mendes given attention to the use of Linear Parameter Varying The system study et in al., this2016). work is a hybrid energy has (LPV ) systems inschemes. order toLPV model monitored plants and to develop FDD systems are represented develop FDD schemes. LPV systems are represented The system under study in processing this work isplant, a hybrid energy to plant based on a sugarcane considering (LPV )extension systems inschemes. order to model monitored plants and plant based on a sugarcane processing plant, considering to develop FDD LPV systems are represented as an of Linear Time-Invariant (LTI ) systems, The system under study this power work is a hybrid energy as an extension of Linear Time-Invariant (LTI ) systems, plant based on asolar sugarcane processing plant, considering biomass, biogas, andinwind wind energy as primary primary to develop FDD schemes. LPV systems are represented biomass, biogas, solar and power energy as assuming the classical state-space representation matrices as an extension of Linear Time-Invariant (LTI ) systems, plant based on This asolar sugarcane processing plant, was considering the classical state-space representation biomass, biogas, and wind powersystem energy as primary energy sources. energy generation (firstly) assuming as an extension ofa Linear Time-Invariant (LTI parameter ) matrices systems, energy sources. This energy generation system was (firstly) are dependent on known bounded scheduling the classical state-space representation matrices biomass, biogas, solar andal., wind power energy asdiscussed primary are dependent on a known bounded scheduling parameter energy sources. This energy generation system was (firstly) assuming presented in (Morato et 2018) and further assuming the classical state-space representation matrices presented in (Morato et al., 2018) and further discussed are dependent on a known bounded scheduling parameter ρ. An LPV fault estimation system is to energy sources. This energy (firstly) An LPV -based -based estimation is able ableparameter to adjust adjust presented in et (Morato et al.,generation 2018) andsystem further in (Morato al., 2017b) 2017b) and (Morato et was al.,discussed 2017a), ρ. are dependent on afault known boundedsystem scheduling in (Morato et al., and (Morato et al., 2017a), ρ. An LPV -based fault estimation system is able to adjust itself (autonomously) by scheduling observer (filter) gains presented in (Morato et al., 2018) and further discussed itself (autonomously) by scheduling observer (filter) gains in (Morato etmodern al., 2017b) and (Morato were et al., 2017a), wherein some control techniques applied to ρ. An LPV -based fault estimation system is able to adjust wherein some modern control techniques were applied to depending on the monitored system’s condition. These itself (autonomously) by scheduling observer (filter) gains in (Morato et al., 2017b) and (Morato et al., 2017a), depending on the monitored system’s condition. These wherein some modern control techniques were applied to its control. control. Nonetheless, Nonetheless, aa great great portion portion of of the the energy energy itself (autonomously) by scheduling observer (filter) gains its LPV schemes have been discussed in recent publications: depending on the monitored system’s condition. These wherein some modern control techniques were applied to schemes been discussed in recent publications: its control. in Nonetheless, a great portion of athebiomassenergy LPV production this system system is derived derived from depending onethave the monitored system’s condition. These production in this is from biomassschemes have been discussed in recent publications: in (Grenaille al., 2008), aa framework is presented for its control. Nonetheless, a great portion of a energy LPV in (Grenaille et al., 2008), framework is presented for the the production in this system is derived from athebiomassburning boiler. This kind of boiler is thoroughly reviewed LPV schemes have been based discussed in on recent publications: burning boiler. This kind of boiler is thoroughly reviewed synthesis of FDD filters based on an LMI in (Grenaille et al., 2008), a framework is presented for the production inal., this system is derived from aboiler biomasssynthesis of FDD filters based based on on an LMIforsolusoluburning boiler. This kindPossible of boiler is thoroughly reviewed in (Saidur et 2011). faults on the can in (Grenaille et al., 2008), a framework is presented the in (Saidur et al., 2011). Possible faults on the boiler can tion; in (Abdullah and Zribi, 2013), the authors propose synthesis of FDD filters based based on on an LMI soluburning boiler. This kindPossible of to boiler is thoroughly reviewed in (Abdullah and Zribi, 2013), the authors propose in (Saidur et al., 2011). faults on theconstraints, boiler can tion; lead the plant not to comply its operational synthesis of FDD filters based based on on an LMI solulead the plant not 2011). to comply to its faults operational the design of LPV observer estimate sensor in (Abdullah and Zribi, theto authors in (Saidur et in al., Possible on theconstraints, boiler can tion; the of aa low-order low-order LPV 2013), observer estimatepropose sensor lead the plant noteconomic to comply to its operational constraints, which results deprivation. tion;design in (Abdullah and Zribi, theto which results in economic deprivation. the design of a low-order LPV 2013), observer toauthors estimatepropose sensor faults. lead the plant not to comply to its operational constraints, faults. which results in economic deprivation. the design of a low-order LPV observer to estimate sensor faults. Up to the authors’ knowledge, only few works have prewhich in economic deprivation. Up to results the authors’ knowledge, only few works have pre- faults. Given the presented context, this work will present prelimUp to the authors’ knowledge, onlyforfew works(on have pre- Given the presented context, this work will present prelimsented studies on Fault Fault Detection boilers energy sented studies on Detection boilers (on energy the presented context, this work will present preliminary in of LPV -based FDD Up to the authors’ knowledge, onlyfor few works have pre- Given inary results results in terms terms of using using LPV -based FDD methods methods sented studies on Fault Detection for boilers (on energy generation systems). Some works present some insights Given theand presented context, this work will present prelimgeneration systems). Some works present some insights to detect estimate faults on hybrid energy generation inary results in terms of using LPV -based FDD methods sented studies on Fault Detection for boilers (on energy to detect andinestimate faults onLPV hybrid energy generation generation systems). Some works present some insights on the consequence of faults, as in (Bulloch et al., 2009); inary results terms of using -based FDD methods on the consequence faults,works as in (Bullochsome et al., 2009); to (faulty) biomass boiler. For detect considering and estimateaa faults on hybrid generation systems).of systems, considering (faulty) biomassenergy boiler.generation For this this on the consequence ofSome faults, as in present (Bulloch et al.,insights 2009); systems, to detect and estimate faults on hybrid energy generation The authors thank CNPq and Ministerio de Econom´ ıaal., y Competgoal, an extended observer design methodology is followed, systems, considering a (faulty) biomass boiler. For this on the consequence of faults, as in (Bulloch et 2009); The authors thank CNPq and Ministerio de Econom´ıa y Competgoal, an extended observer design methodology is followed, systems, considering a (faulty) biomass boiler. For this itividad de Espa˜ na for financing the projects The authors thank CNPq and Ministerio de CNPq401126/2014-5, Econom´ıa y Competgoal, an extended observer design methodology is followed, using an LMI for the minimization. ∞ norm itividad de Espa˜ na for financing the projects CNPq401126/2014-5, The authors usingan anextended LMI synthesis synthesis the H H ∞ norm minimization. thank CNPq and Ministerio de CNPq401126/2014-5, Econom´ıa y Competgoal, observerfor design methodology is followed, CNPq303702/2011-7 and DPI2016-78338-R. itividad de Espa˜ n a for financing the projects using an LMI synthesis for the H norm minimization. ∞ CNPq303702/2011-7 and DPI2016-78338-R. ∞ itividad de Espa˜ na forand financing the projects CNPq401126/2014-5, using an LMI synthesis for the H∞ norm minimization. CNPq303702/2011-7 DPI2016-78338-R.
CNPq303702/2011-7 and(International DPI2016-78338-R. 2405-8963 © © 2018 2018, IFAC IFAC Federation of Automatic Control) Copyright 1 Hosting by Elsevier Ltd. All rights reserved. Copyright © under 2018 IFAC 1 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 1 10.1016/j.ifacol.2018.11.177 Copyright © 2018 IFAC 1
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The control-oriented hourly-discrete state-space representation model of the studied plant is given below, by (1). This mathematical model was obtained and validated through simulation based on experimental data; for full details, refer to (Morato et al., 2018):
The rest of this document is organized as follows: an introduction to the Brazilian sugarcane energy generation paradigm is seen in Section 2; in Section 3, the possible faults on the biomass Boilers are discussed and mathematically modelled; in Section 4, the proposed LPV Fault Detection and Diagnosis scheme is detailed; then, in Section 5 simulation results are presented; conclusions are drawn in Section 6.
x(k + 1) = Ax(k) + B1 w(k) + B2 u(k)
(1)
z(k) = C1 x(k) + D11 w(k) + D12 u(k) y(k) = C2 x(k) + D21 w(k) + D22 u(k) Remark 1. This representation describes the plant through its controlled outputs (z), measured outputs (y) and internal states (x). Note that the supervisory controller is responsible and preoccupied with the controlled outputs (z), and that these are not (necessarily) measured. In this system, specifically, the measured outputs are equivalent to the internal states, y(k) = x(k).
2. BRAZILIAN SUGARCANE INDUSTRY In this work, the Brazilian sugarcane industry (largest in the world) is taken into account, given that the sugarcane production process has a great amount of residue and waste that is treated as bio-sources of energy. As visited in (Morato et al., 2018), Brazilian sugar-ethanol plants are bright candidates to be managed as hybrid power plants, considering the use of biomass and biogas for direct-toelectric-energy generation and, also, (external,additional) solar and wind power energy generation.
x(k) = [ XBat (k) XBag (k) XStr (k) XBg (k) XT (k) ]
T
(2)
(3) u(k) = [ SPTAU (k) SPTBU (k) P otN et (k) R(k) . . . Out M B QV (k) QEsc (k) QEsc (k) SPCHP (k) . . . B (k) QTEsc (k) ]T SPCh (k) SPT C (k) P otBat (k) QM V T L (4) z(k) = PP roc (k) QM V (k) QV (k) QCW (k) PSale (k)
Most of the current industrial Brazilian sugar cane processing plants have a similar structure. These plants have internal demands, corresponding to the sugar and ethanol processing requirements: to produce steam in different pressures (used to boost shredders, spray bombs and other equipments), to produce cold water for refrigeration needs (used to cool down generators, oil tanks and other systems) and, finally, to produce electric power to sustain the plant. Apart from these internal demands, these plants also sell the excedent electric energy to a local Distribution Network Operator (DNO).
w(k) = [ W ndin (k) Irrdin (k) . . .
Bagin (k) Strin (k) Bgin (k) ]
(5)
T
The system state vector x is defined as (2), where each entry stands for the normalized percentage of each of the plant’s storage units: battery bank, bagasse stock, straw stock, biogas stock and hot water tank.
Then, for energy management and Control goals, these plants can be treated as microgrids and mathematically modelled following the Energy Hub methodology, as introduced in (Geidl et al., 2007). A generalized microgrid, considering this modelling framework, is comprised of energy conversion units (as turbines and boilers) and energy storage facilities. The inputs to this microgrid, from an energy management control point-of-view are given by uj (set-points to the internal subsystems), and the measured outputs, yj , stand for the plant’s transmission lines (electric network, gas pipes, steam lines, etc). A supervisory controller sets hourly set-points for the plant’s internal subsystems so that each global demand is met and the energy generation is maximized. This control problem has been treated with optimal, predictive schemes in (Morato et al., 2017b) and, also, in (Morato et al., 2017a).
As this is a control-oriented model, the input vector u stands for zero-order-held set-points for the conversion and storage units (subsystems). From an hourly controller’s point-of-view, it is assumed that the sampling period of ∆T = 1 h is large enough so that all these set-points have been accurately tracked by their respective subsystems. The complete control vector is given by (3), where each entry stands, respectively, for: energy boiler’s set-point, lower efficiency turbine’s set-point, higher efficiency turbine’s set-point, set-point of energy flow to (from) the battery bank, CHP ’s set-point, water chiller’s set-point, heat exchanger’s set-point, high-to-middle pressure reduction valve’s set-point, middle-to-low pressure reduction valve’s set-point, hot water escape flow’s set-point, middle pressure steam escape flow’s set-point, low pressure steam escape flow’s set-point, set-point of power available to the external network. In terms of the boilers in this plant: one is mainly responsible for the energy generation, by burning biomass, whereas the other is only used solely for steam production and its set-point is consequence of other variables.
The hybrid energy generation system that is studied in this work, based on a sugarcane power plant, that produces sugar, ethanol and electric power, is composed by the following subsystems: two boilers, with different efficiencies; two steam turbines, with different efficiencies; a combined heat and power system (CHP ); a water chiller; a hot water tank; photovoltaic panels; water heating solar panels; a wind turbine; two pressure reduction valves; one heat exchanger; stocks of bagasse, straw and compressed biogas and a battery bank. The use of intermediate storage units (battery bank and biomass stocks) allows the system to accumulate energy (or biomass, that can be converted into energy) when the renewable generation is high and use it when there is no renewable production.
The system’s controlled outputs z are defined in Eq. (4), being PP roc the electric power produced due to the sugar cane processing demand (kW ); QM V the flow of middle the flow of low pressure steam pressure steam ( Mhg ); QL V Mg ( h ); QCW the flow of chilled water required by the 3 distillery process ( mh ); finally, PSale represents the electric power made available to the external network (kW ). 2
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Remark 2. (a) As exposes Eq. (6), the loss of effectiveness factor of f (k) = 1 stands for faultless situations; (b) The multiplicative commutative property is valid in Eq. (6), given that both variables f and R, at a given instant k, are scalars; (c) The output energy flow uf , in this work, is not directly measurable. This means that, to compute (or estimate) f (t), one cannot resort to a simple algebra, as only R is known at each instant k.
The disturbances to the system w are defined by Eq. (5), being W ndin the speed of the wind ( km h ) present in the microgrid’s area, used by the wind turbines to generate electric power; Irrdin the amount of solar irradiance W (m 2 ) on the microgrid’s solar panels (photovoltaic and water heating); Bagin , Strin and Bgin represent the income ( Mhg ) of bagasse, straw and biogas to the plant, respectively. 3. THE BOILER’S FAULTY SITUATIONS
The main objective of this work, then, is to continuously and accurately estimate the term Λ = (f − 1). Knowing Λ, the computation of f is direct and, then, one can have a valid notion of whether the energy boiler is, or not, faulty. This serves for surveillance and safety goals, helps with prevention maintenance of the boiler and can even serve as a paradigm for a fault-tolerant control strategy.
Now, this work will analyse with further care the Boiler unit, a conversion unit of the hybrid energy plant that can fail and lead to a problem in terms of complying with the electric power demands. In terms of statical behaviour, the energy boiler γBoiler converts the input biomass mixture to output electric power uf (t) with a gain of Kv ( kWh Mg ). This unit, together with its local controller, can be equivalently represented by Figure 1, where the gain K1v is used such that the local setpoint R(t) is tracked. The possible faults that appear on these boiler units may come from two different situations: a) the accumulation of debris and residues or biomass clogging on ducts, which leads to direct-to-energy gain decrease; b) an emergency stop from the manual operators. In both of these cases, the boiler’s static gain changes.
4. THE FAULT ESTIMATION PROBLEM Considering the problem of the hybrid energy plant subject to possible faults on its energy boiler, the term Λ can be estimated with the use of an FDD scheme that has access, at each instant, to the control inputs u(k) and measured output y(k). An illustration of this fault detection paradigm is given in Figure 2.
Then, to model these faults, a multiplicative loss of effectiveness factor f (t) is considered upon the boiler’s static gain. This means that the local control is not be able to track the references they are given. This multiplicative fault representation has been firstly presented in (Hern´ andez-Alc´ antara et al., 2016), and introduces a solid framework for the modelling of faults. Roughly speaking, this work assumes that the real (faulty) electric power output uf (t) is proportionally dependent to the expected (faultless) output reference R(t), as point out Equation (6). Fig. 2. Fault Detection Paradigm First of all, it has to be remarked that the energy generation set-points u(k) will be determined at each instant by some optimal control scheme, as the one proposed in (Morato et al., 2017b), so that local controllers to the conversion and storage units track these references in some avid settling time smaller than ∆T = 1 h. Then, the studied (faulty) energy system (7) will be described by an extended-state representation, given below:
Fig. 1. Faulty Boiler Problem Representation uf (k) = R(k)f (k)
(6)
Then, whenever a fault occurs on the energy boiler, the mathematical representation that describes the faulty energy systems is given by:
˘ (7) x(k + 1) = Ax(k) + B1 w(k) + B2 u(k) + B2 Λ(k)R(k) ˘ z(k) = C1 x(k) + D11 w(k) + D12 u(k) + D12 Λ(k)R(k)
(8)
Λ(k) = f (k) − 1
(9)
A
xa (k)
a ˘ x(k + 1) x(k) = A B2 R(k) Λ(k + 1) Λ(k) 0 1
(10)
q(k)
Ba
B1 B2 w(k) + u(k) 0 0
˘ y(k) = C2 x(k) + D21 w(k) + D22 u(k) + D22 Λ(k)R(k) where: T ˘ R(k) = [ 01×3 R(k) 01×9 ]
xa (k+1)
Ca
˘ y(k) = C2 D22 R(k) xa (k) Da
T + [ D21 D22 ] [ w(k) u(k) ]
3
(11)
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level to a given input. So, by minimizing this norm, the observer’s sensitivity to disturbances q is minimized, and, then, the observer’s output (estimation of Λ) will be better achieved and more immune to q. In terms of the estimation error dynamics (13), the term [Aa − LCa ] is to be stable and [Ba − L(ρ)Da ]q small and, as of this, e shall converge to 0. Given this motivation, the H∞ criterion is a suitable choice in order to compute the matrix gain L(ρ). Lemma 1. The H∞ observer synthesis consist in imposing Eq. (14). This is obtained when computing the polytopic LPV observer matrix gain by minimizing the scalar γH∞ and solving the sole following LMI, taking Q(ρ) = P L(ρ), with P being a positive definite matrix affine on ρ. The existence conditions for this observer is the assurance of detectability of the pair [Aa (ρ) , Ca (ρ)] within Ω. More details on this matter are given in (Yamamoto et al., 2015). M1,1 [P Ba − Q(ρ)Da ] −E T E
< 0 , Q > 0 (15) 0 −IγH∞
−IγH∞
Remark 3. (Actuator) faults can be described either as multiplicative or additive terms upon u(k). This work opts for the first option due to conveniencies. Nonetheless, the corresponding additive fault term to a multiplicative one ˘ Notice how this can is given by fa (k) = B2 [f (k) − 1]R(k). ˘ be easily computed if f (k) is estimated, as B2 and R(k) are always known. Remark 4. Thanks to the multiplicative fault representation, the information on the fault Λ(k) is assumed to be constant or slowly varying. This leads to Λ(k + 1) ≈ Λ(k). Reader must understand that the assumption that the fault is constant or slowly varying is sufficient for the purposes of this work. Even if faults do not abide by this rule, they will be, anyhow, sufficiently diagnosed given that the observer-based approach aims to minimize the fault estimation error eΛ , as will be detailed next. It is important to notice that matrices Aa and Ca are affine ˘ on R(k). As this signal is completely known (determined by the supervisory controller) and bounded by the operational constraints of the boiler, it can be considered as a scheduling parameter ρ ∈ Ω, being Ω a compact convex set given by the saturation limits of this set-point. Then, system (10) becomes LPV, defined within the polytope delimited by the boundaries of Ω. Notice that it is only LPV because of the way that faults were represented (multiplicative factors) and under the assumption discussed in Remark 4.
with
M1,1 = ATa (ρ)P + P Aa (ρ)
(16)
− CaT (ρ)QT (ρ)
− Q(ρ)Ca (ρ) The gain matrix L(ρ) is taken, thus, as L(ρ) = P −1 Q(ρ). Proof 1. Straightforward from (Armeni et al., 2009). Guarantees of stability of the error system (13) can be found in (Nguyen et al., 2016); remark that the system (1) is a priori stable, so the instability would only derive from badly proposed matrices L(ρ), which would not be the case as the Bounded Real Lemma is guaranteed. Remark 5. This work considers a discrete-time observer. From this, the solution is computed in continuous-time and, then, discretized with sampling period of ∆T = 1 h.
Then, as the faulty system is represented through an augmented framework with states xa (k) that contain the information on the possible faults, Λ(k), if there exists some asymptotical tracking of xa (k), one has an accurate estimation of f (t). As seen in (Grenaille et al., 2008), a polytopic LPV observer is used for this goals, as follows: x ˆa [k + 1] = Aa (ρ)ˆ xa (k) + L(ρ)[y(k) − Ca (ρ)xˆa (k)](12) ˆ Λ(k) = 0size(x) 1 xˆa (k)
The interest of this polytopic LPV approach is that the presented LMI s are computed offline, at each vertex v of the workspace polytope. Then, the observer gain matrix L(ρ) is given by a linear combination of every Lv , affine on ρ and that guarantees the asymptotic stability of (13).
E
Finally, the estimation error dynamics (eΛ (k) = Λ(k) − ˆ Λ(k)), are given below:
5. RESULTS AND ANALYSIS
e(k + 1) = [Aa − LCa ](ρ)e(k) + [Ba − L(ρ)Da ]q(k)(13) eΛ (k) = Ee(k)
(14)
Now, some simulation results will be presented in order for the accuracy of the proposed FDD scheme to be analysed. The following simulation results were obtained using a high-fidelity hybrid model, refer to (Morato et al., 2018). As already stated, this work considers that a supervisory energy management control loop is working in order to define the set-points u(k), at each sampling period of 1 h, as done by Vergara-Dietrich, Morato, Mendes, Cani, Normey-Rico, and Bordons (2017), guaranteeing that all the plant’s demands are met. These signals are seen in Figure 3. For simplicity, they repeat periodically each 24 h, as does the load demands. The used data for w(k) is taken from real data from the state of Paran´ a, Brazil, refer to (Morato et al., 2017a). Notice that these disturbances w(k) are non-null and influence on the achieved results.
The H∞ norm of a system is understood as the induced energy-to-energy gain, being the worst case attenuation
The solution to the LPV H∞ observer, presented in Lemma 1 is obtained with the aid of the following softwares: MATLAB (Mathworks, 2017), Yalmip (Lofberg,
The dynamics of (13) have to be stable for the correct estimation of faults on the boilers. This stability issue depends on the choice of gain matrix L(ρ) and, so, the following problem is traced, adapted from (Armeni et al., 2009). A solution Lemma is presented in the following. Problem 1. The H∞ LPV observer problem is defined as follows: Find a gain matrix L(ρ), affine on the scheduling parameter ρ and defined within the polytope workspace so that the estimation error dynamics, given by (13), are exponentially stable (considering q(k) is null) and that the following objective function is minimized: JH∞ = ||
eΛ ||∞ ≤ γH∞ under e(k)|k=0 = 0 q
4
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mized. The minimal γH∞ achieved in such a way that the inequality still remains valid is 4.8724, a very sufficient bound, considering the energy-to-energy gain minimization of q on eΛ . This value is related to the numerical robustness of the LPV -FDD approach towards the (nonnull, always present) disturbances q(k). Although the H∞ norm minimization approach might be conservative, this is not of great importance herein, as the control actions only act every Ts = 1 h, so there is no rush for exceedingly fast responses. Remark 6. This work proposed a fault detection scheme that does not need the addition of new components, such as redundant sensors. In terms of comparisons with alike techniques, (Nguyen et al., 2016) has already discussed that LPV observer-based FDD schemes do present better results than, for instance, the Fast Adaptive Fault Estimation method, proposed by Zhang et al. (2009). As of this, this work is not preoccupied with comparisons, but mostly on the application of an LPV observer-based FDD method to the studied problem. Now that all other signals have been presented, the simulated fault scenario has to be described: i) the energy boiler suffers from continuous accumulation of debris and residues, starting from t = 3 h, this leads to a gain decrease of up to 25 %. ii) then, a sudden stop of the boiler occurs, coming from the manual operator, which leads to a loss of effectiveness of 100 %. For a complete understanding of how the proposed FDD system works, reader is invited to see Figure 4, where a comparison between the faulty output boiler power uf (k) and the expected faultless set-point R(k) is shown; the effect of the faults are noticeable. The detection and estimation of the respective loss of effectiveness fault term f (k) is seen in Figure 5, compared with the actual simulated faults. As it can be seen, the proposed polytopic LPV approach presents some accurate and smooth results in terms of estimating faults on boilers, which is very good. The achieved performance stands for a precise estimation of the possible loss of effectiveness faults on boilers. It must be remarked, nonetheless, that the estimated fault term fˆ(k) can become slightly noisy when estimating emergency stop failures. This is expected, as the H∞ synthesis is not preoccupied with impulse-to-energy minimization, but does not compromise the overall results, as the estimated fault term, when f (k) = 0, stays inside the limited set fˆ(k) ∈ [0 − 0.04 , 0 + 0.04].
Fig. 3. Set-Points u(k) 2004) and SDPT 3 (Toh et al., 1999). The idea behind the algorithm is to find positive definite matrix P and a block amax ρ −ρ ρ−ρmin max matrix Q(ρ) = ρmax + , Q min −ρmin ρmax −ρmin Q
Fig. 4. Faulty and Faultless Signals: R(k) and uf (k)
in such way that the LMI (15) holds and γH∞ is mini5
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Fig. 5. Boiler Fault Detection 6. CONCLUSIONS This paper presented the issue of fault detection and diagnosis for boilers on hybrid generation power systems, considering a polytopic H∞ LPV -based extended observed methodology. As demonstrated by simulation results, the proposed strategy is an efficient one in terms of this work’s intents. Such accurate FDD scheme can be used for faulttolerant control goals of hybrid energy systems in the presence of faults, in order to preserve the system stability and maintain performance objectives (comply to energy demand and others). This work has been pointed as preliminary because authors still plan on investigation the effect of faults on every storage and conversion unit of the hybrid power system analysed herein. Combined H∞ /H2 /H− sensitivity observers shall be tested. Still, the design of fault-tolerant predictive controllers for the global energy management of sugarcane-based power plants is an open topic for further works. REFERENCES Abdullah, A. and Zribi, M. (2013). Sensor-fault-tolerant control for a class of linear parameter varying systems with practical examples. Industrial Electronics, IEEE Transactions on, 60(11), 5239–5251. Armeni, S., Casavola, A., and Mosca, E. (2009). Robust fault detection and isolation for LPV systems under a sensitivity constraint. International Journal of Adaptive Control and Signal Processing, 23(1), 55–72. Bulloch, J., Callagy, A., Scully, S., and Greene, A. (2009). A failure analysis and remnant life assessment of boiler evaporator tubes in two 250mw boilers. Engineering Failure Analysis, 16(3), 775–793. Chen, J. and Patton, R.J. (2012). Robust model-based fault diagnosis for dynamic systems, volume 3. Springer. Geidl, M., Koeppel, G., Favre-Perrod, P., Klockl, B., Andersson, G., and Frohlich, K. (2007). Energy hubs for the future. IEEE Power and Energy Magazine, 5(1), 24. Grenaille, S., Henry, D., and Zolghadri, A. (2008). A method for designing fault diagnosis filters for LPV polytopic systems. Journal of Control Science and Engineering, 2008, 1. Guoxin, X., LiChuan, X., Meihua, B., and Siwei, L. (2005). Fault prediction of boilers with fuzzy mathematics and rbf neural network. In IEEE Int. Conf. on Communications, Circuits and Systems. 6