This paper is devoted to the development of a hybrid controller for a two-interleaved boost converter dedicated to renewable energy and automotive applications. The control requirements, resumed in fast transient and low input current ripple, are formulated as a problem of fast stabilization of a predefined optimal limit cycle, and solved using hybrid automaton formalism. In addition, a real time estimation of the load is developed using an algebraic approach for online adjustment of the hybrid controller. Mathematical proofs are provided with simulations to illustrate the effectiveness and the robustness of the proposed controller despite different disturbances. Furthermore, a fuel cell system supplying a resistive load through a two-interleaved boost converter is also highlighted.
In this paper, a Wavelet modulated isolated two-stage three-phase bidirectional AC-DC converter is proposed for electric vehicle (EV) charging systems. Half-bridge resonant CLLC converter is proposed due to its high efficiency, wide gain range, galvanic isolation and bidirectional power flow. Wavelet modulation technique is used for three-phase six leg AC-DC converter due to its benefits of high DC component and lower harmonic contents. The proposed two-stage converter is developed and simulated in MATLAB Simulink environment. The contribution of this paper is on the implementation and performance analysis of Wavelet modulation in bidirectional AC-DC converters. The results show that Wavelet modulation is suitable to be implemented for the proposed bidirectional converter. The performance of the proposed converter delivers very low output voltage ripple and total harmonic distortion output current of less than 10% which is within the expected results.
An Efficient Photo Voltaic System for Onboard Ship ApplicationsIJERA Editor
In this paper a high efficient photovoltaic system is proposed for onboard ship applications which convert the
lower voltage obtained from solar modules to higher voltage required by the ship service loads. In a typical
photovoltaic system only step-up /boost converter is used due to which the converter has to operate in extreme
duty ratio, resulting in increase of switching losses and thus decreasing the overall efficiency. But in this paper
the conventional boost converter is used with interleaved inductors and capacitors. The poposed system stores
the energy in inductors and thus reduces the stress in the switches (Without allowing the total voltage to appear
across the switch). The simulation is designed using MATLAB/Simulink with an Input voltage of 40-V to
achieve a output voltage of 300-380 V. The developed simulation results are compared for output powers of
500W and 1kW
Prioritizing Power demand response for Hydrogen PEMFCElectric Vehicles using ...IJECEIAES
PEMFC powered Hybrid vehicle system is one of an interesting issue for the industry due to its high performances. The PEMFC cannot certainly ensure a sustained required energy in some scenarios. To solve this problem related to PEMFC transient response, a Hybrid Electrical Storage System (HES) is a potential candidate for a solution. The proposed Hybrid Storage system is comprised of the battery (BT) and a Super-Capacitor (SC) components. These components are included to control the hydrogen variations and the fast peak powers scenarios respectively. The SC is used to control PEMFC and the BT slow dynamics at the same times. An accurate Multi-Ways Energy Management System (MW-EMS) is proposed which aims to cooperate with the system components through SC/BT state of charge and a flux calculation. The simulation results are discussed and assessed using MATLAB/ Simulink.
Hybrid energy storage system control analogous to power quality enhancement o...IJECEIAES
Increasing nonlinear loads and power electronic converters lead to various power quality issues in microgrids (MGs). The interlinking converters (ILCs) can participate in these systems to harmonic control and power quality enhancement. However, ILC participation deteriorates the dc link voltage, system stability, and storage lifetime due to oscillatory current phenomena. To address these problems, a new control strategy for a hybrid energy storage system (HESS) is proposed to eliminate the adverse effects of the harmonic control operation of ILC. Specifically, battery and super-capacitor (SC) are used as HESSs that provide low and high power frequency load, respectively. The proposed strategy tries to compensate the current oscillation imposed by ILC with fuzzy control of HESS. In this method, a proportional-resonant (PR) controller integrated with harmonic compensator (HC) is employed to control the ILC for power quality enhancement and oscillatory current elimination. The main advantages of the proposed strategy are to reduce DGs power fluctuations, precise DC bus voltage regulation for generation and load disturbances, improved grid power quality under nonlinear load and transition conditions. The performance of the proposed method for isolated and grid-connected modes is verified using simulation studies in the MATLAB software environment.
A REVIEW ON EVALUATION OF PV MODELS BASED ON AN INTEGRATION USING A NEW CONFI...ijiert bestjournal
The effect of linear imbalances and nonlinear loads on the voltage balance of the neutral-point- clamped converters is described in this paper. The Neutral-Point-Clamped inverters are used in the multilevel inverters for high power application s. In this paper a three level NPC inverter that couple accommodate with solar photovoltaic (PV) and battery storage in grid connected system. The three level space vector modulation technique (SVPWM) is proposed. The SVPWM correct the ac voltage under unbalance dc voltage condition .SV-PWM strategy makes it possible to control the neutral point voltage by optimum choice of switch sequence for any position and length of output voltage vector. The control scheme has capability to control the power delivery between the solar PV,battery,and grid,it simulta neously provides maximum power point tracking (MPPT) operation for the solar PV. The res ults of matlab modeling of the system detail the comparative operation of inverter topologies wh ich are the conventional two level inverters and multilevel inverter topology to reduce total ha rmonic distortions in grid voltage and electromagnetic interference. Three-level NPC volta ge source inverter that can integrate both renewable energy and battery storage on the dc side of the inverter has been presented. The effectiveness of the proposed methodology is invest igated by the simulation of several scenarios,including battery charging and discharging with dif ferent levels of solar irradiation.
In this paper, a Wavelet modulated isolated two-stage three-phase bidirectional AC-DC converter is proposed for electric vehicle (EV) charging systems. Half-bridge resonant CLLC converter is proposed due to its high efficiency, wide gain range, galvanic isolation and bidirectional power flow. Wavelet modulation technique is used for three-phase six leg AC-DC converter due to its benefits of high DC component and lower harmonic contents. The proposed two-stage converter is developed and simulated in MATLAB Simulink environment. The contribution of this paper is on the implementation and performance analysis of Wavelet modulation in bidirectional AC-DC converters. The results show that Wavelet modulation is suitable to be implemented for the proposed bidirectional converter. The performance of the proposed converter delivers very low output voltage ripple and total harmonic distortion output current of less than 10% which is within the expected results.
An Efficient Photo Voltaic System for Onboard Ship ApplicationsIJERA Editor
In this paper a high efficient photovoltaic system is proposed for onboard ship applications which convert the
lower voltage obtained from solar modules to higher voltage required by the ship service loads. In a typical
photovoltaic system only step-up /boost converter is used due to which the converter has to operate in extreme
duty ratio, resulting in increase of switching losses and thus decreasing the overall efficiency. But in this paper
the conventional boost converter is used with interleaved inductors and capacitors. The poposed system stores
the energy in inductors and thus reduces the stress in the switches (Without allowing the total voltage to appear
across the switch). The simulation is designed using MATLAB/Simulink with an Input voltage of 40-V to
achieve a output voltage of 300-380 V. The developed simulation results are compared for output powers of
500W and 1kW
Prioritizing Power demand response for Hydrogen PEMFCElectric Vehicles using ...IJECEIAES
PEMFC powered Hybrid vehicle system is one of an interesting issue for the industry due to its high performances. The PEMFC cannot certainly ensure a sustained required energy in some scenarios. To solve this problem related to PEMFC transient response, a Hybrid Electrical Storage System (HES) is a potential candidate for a solution. The proposed Hybrid Storage system is comprised of the battery (BT) and a Super-Capacitor (SC) components. These components are included to control the hydrogen variations and the fast peak powers scenarios respectively. The SC is used to control PEMFC and the BT slow dynamics at the same times. An accurate Multi-Ways Energy Management System (MW-EMS) is proposed which aims to cooperate with the system components through SC/BT state of charge and a flux calculation. The simulation results are discussed and assessed using MATLAB/ Simulink.
Hybrid energy storage system control analogous to power quality enhancement o...IJECEIAES
Increasing nonlinear loads and power electronic converters lead to various power quality issues in microgrids (MGs). The interlinking converters (ILCs) can participate in these systems to harmonic control and power quality enhancement. However, ILC participation deteriorates the dc link voltage, system stability, and storage lifetime due to oscillatory current phenomena. To address these problems, a new control strategy for a hybrid energy storage system (HESS) is proposed to eliminate the adverse effects of the harmonic control operation of ILC. Specifically, battery and super-capacitor (SC) are used as HESSs that provide low and high power frequency load, respectively. The proposed strategy tries to compensate the current oscillation imposed by ILC with fuzzy control of HESS. In this method, a proportional-resonant (PR) controller integrated with harmonic compensator (HC) is employed to control the ILC for power quality enhancement and oscillatory current elimination. The main advantages of the proposed strategy are to reduce DGs power fluctuations, precise DC bus voltage regulation for generation and load disturbances, improved grid power quality under nonlinear load and transition conditions. The performance of the proposed method for isolated and grid-connected modes is verified using simulation studies in the MATLAB software environment.
A REVIEW ON EVALUATION OF PV MODELS BASED ON AN INTEGRATION USING A NEW CONFI...ijiert bestjournal
The effect of linear imbalances and nonlinear loads on the voltage balance of the neutral-point- clamped converters is described in this paper. The Neutral-Point-Clamped inverters are used in the multilevel inverters for high power application s. In this paper a three level NPC inverter that couple accommodate with solar photovoltaic (PV) and battery storage in grid connected system. The three level space vector modulation technique (SVPWM) is proposed. The SVPWM correct the ac voltage under unbalance dc voltage condition .SV-PWM strategy makes it possible to control the neutral point voltage by optimum choice of switch sequence for any position and length of output voltage vector. The control scheme has capability to control the power delivery between the solar PV,battery,and grid,it simulta neously provides maximum power point tracking (MPPT) operation for the solar PV. The res ults of matlab modeling of the system detail the comparative operation of inverter topologies wh ich are the conventional two level inverters and multilevel inverter topology to reduce total ha rmonic distortions in grid voltage and electromagnetic interference. Three-level NPC volta ge source inverter that can integrate both renewable energy and battery storage on the dc side of the inverter has been presented. The effectiveness of the proposed methodology is invest igated by the simulation of several scenarios,including battery charging and discharging with dif ferent levels of solar irradiation.
This paper displays a Fly Back Converter idea to straightforwardly incorporate cascaded flyback converter. The flyback-converter finds a way between DC-source and DC Motor-load. This work covenants with the modeling, simulation, and application of a Fuzzy Logic controlled (FLC) - Cascaded Fly back Converter (CFLB) system. This work recommends FLC to control Parallel cascaded fly-back converter to fabricate essential DC voltage from the input supply voltage. The yield of CFLB is controlled utilizing closed loop configuration. Closed loop PI & Fuzzy logic controlled CFLB systems are simulated and their results are related. The outcomes signify that the FLC based system gave a superior response than the P.I. controlled CFLB system. The FLC controlled CFLB system has benefits like decreased steady state error and enhanced time domain-response.
Multi-level inverters (MLIs), have gained popularity in the last few years as a result of their low total harmonic distortions (THD) as well as their output waveform which is of high quality. The converter which considers more appropriate for applications of photovoltaic (PV)beyond the varying MLIs arrangementsis the Cascaded H-Bridge-(CHB) (MLI), meanwhile each PV panel may be served as an independent DC supply for any CHB unit. Through the use of MATLAB/Simulink, the efficiency of symmetrical single phase MLI in terms of the number of switches, harmonic content in addition to the stresses of voltage through theswitches that exist at photovoltaic cell by means of input source is enhanced; varying parameters like output current, voltage and power, and THD at 5-level 7-level and 9-level Cascaded MLI are observed. In this paper, attention is paid to a multi-level topologies which is flexible and based on cascaded MLI intended for PV grids connected system. An observation of the output voltage becomes closer to the sine wave as the levels increase, while the increase in the levels of Cascaded Multilevel Inverter causes the total harmonic distortion to decrease.
Multiport converters increasingly gain prominance in the recent past to interface renewable energy sources like photovoltaic cells, fuel cells with the load. Energy storage elements like battery and supercapacitors nd major place as an additional and alternate sources in systems with primary renewable energy sources to overcome its intermittency issues. As these energy storage element's charging and discharging cycles are to be controlled, an isolated bidirectional converter topology with transformer is used. The galvanic isolation provided by the high frequency ac link transformers in partly isolated and fully isolated topologies makes these converters most preferrable in high power applications like electric vehicles. A comprehensive review is performed on various three port partly isolated and fully isolated topologies addressed by dierent research groups. The key contributions on soft switching for reducing switching losses and improving overall converter efficiency with help of resonant elements are discussed. In addition, control strategies for power ow control with enhanced soft switching of partly isolated converters are highlighted. A summary of converter topologies is provided comparing power rating, device count, soft switching resonant elements and efficiency which gives an idea for selection of suitable topology for the desired system requirement.
There is need for an energy storage device capable of transferring high power in transient situations
aboard naval vessels. Currently, batteries are used to accomplish this task, but previous research has
shown that when utilized at high power rates, these devices deteriorate over time causing a loss in lifespan.
It has been shown that a hybrid energy storage configuration is capable of meeting such a demand while
reducing the strain placed on individual components. While designing a custom converter capable of
controlling the power to and from a battery would be ideal for this application, it can be costly to develop
when compared to purchasing commercially available products. Commercially available products offer
limited controllability in exchange for their proven performance and lower cost point - often times only
allowing a system level control input without any way to interface with low level controls that are
frequently used in controller design. This paper proposes the use of fuzzy logic control in order to provide
a system level control to the converters responsible for limiting power to and from the battery. A system
will be described mathematically, modeled in MATLAB/Simulink, and a fuzzy logic controller will be
compared with a typical controller.
This paper reviews fuel cell technology status and some of its challenges worldwide. Fuel cells have emerged as an important technology in various non-linear loads in industrial, commercial and residential sectors. A mathematical model of hydrogen fuel cell is described with control parameters. A hydrogen fuel cell design is simulated using MATLAB/SIMULINK and the results are discussed.
A photovoltaic integrated unified power quality conditioner with a 27-level i...TELKOMNIKA JOURNAL
This paper presents a Unified Power Quality Conditioner (UPQC) with a 27-level inverter based on
an asymmetric H-bridge topology. Each phase of the inverter is composed of three H-bridges, supplied by
three DC sources scaled in the power of three. The output of the multilevel inverter is connected directly to
the point of common coupling (PCC) without the need to a transformer or a filter. The calculation of the Shunt
Active Power Filter (SAPF) compensation current is based on the generalized theory of synchronous frame
(d-q theory) while the calculation of a series active filter voltage is based on Instantaneous Reactive Power
(p-q theory). The control of the SAPF is achieved by using a closed-loop vector control followed by a new
multilevel modulation technique. In addition to the capability of harmonic elimination of both current and
voltage drawn from the source, the UPQC can produce real and reactive power to feed the loads during
prolonged voltage outages or source shortage. Batteries pack are used as a dc link, which is charged from
photovoltaic array connected to the battery through a maximum power point tracker and charge controller.
The injection of real and reactive power depends on the state of charge (SOC) of batteries, the frequency of
the system, real and reactive power of the load, and power factor at the point of PCC. The proposed UPQC
strategy is simulated in MATLAB SIMULINK and the results have shown a significant improved in Total
Harmonics Distortion (THD) of both the voltage and currents.
Passivity Based Control for PV Applications by Using a Buck Power Converter
The use of power converters for everyday applications is becoming more and more important. Current technological applications simultaneously demand a high level of precision and performance, so DC-DC converters have a very important role in systems requiring energy level conversion and adaptation. As part of the work of this paper, we are interested in an analysis of modeling and control law synthesis approaches to ensure stability and a certain level of performance in the entire operating domain. The objective of our research work is therefore to propose a control law whose synthesis is based on a formalized (modeling & control) approach with a view to obtaining a control law adapted to the operating point. The principles used are based on the control and observation by the theory of passivity for the synthesis of control law of buck power converter for PV Applications.
Harvesting in electric vehicles: Combining multiple power tracking and fuel-c...IJECEIAES
Exploitation of green energy sources is essential to diminish the deterioration of our environment. The energy harvesting, represents an alternative to achieve greater range in electric and hybrid vehicles. An energy management strategy (EMS) must be optimized to obtain the best benefits in such vehicles, which is not a trivial task. If harvesting or energy recovery devices are added, the EMS becomes a dual-purpose algorithm: minimizing fuel consumption and maximizing energy harvest through maximum power point tracking (MPPT) controllers. Known studies consider separate EMS, one for traction and another for regenerative braking, without considering harvest devices such as solar panels, regenerative suspension, thermal generators, among others. Furthermore, the electronic power converters used, are not designed to handle such unequal power levels. In this article, an electronic platform to include multiple energy harvesting devices in a fuel-cell hybrid electric vehicle, was presented together with a multiple MPPT-EMS. The EMS is easily implementable, and considers quasi-constant cell energy extraction and filtering of current transients to the battery bank ensuring the longevity of the devices. A new mathematical model of the platform, a closed loop stability analysis, and numerical and Hardware-in-the-Loop (HIL) validations were presented. Some experimental validation results were also provided.
Anlysis of a pmsg based offshore wind farm fed to a onshore grid through hybr...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Power electronic interface has reached a new level in the area of hybrid energy integration nowadays. The existence for the concept of hybrid energy integration is truly questionable without a proper power electronic interface. In this paper, a modified dual input DC-DC converter which is capable of incorporating two distinct V-I characteristic sources such as solar-PV, battery, fuel cell, etc., is proposed. The converter has the ability to operate in both unidirectional and bidirectional mode with buck, buck-boost and boost operation. The software simulation of the proposed converter has been conducted in MATLAB/Simulink platform in a detailed manner and an experimental prototype of the propsed converter has been built to validate the simulation results.
Effect of Passive Damping on the Performance of Buck Converter for Magnet Loadpaperpublications3
Abstract: A DC to DC converter is a lossless dc transformer that supply regulated output voltage under varying load and input voltage condition and also the converter parameter values changes with time and physical quantity like temperature etc. This paper presents the design and simulation of an open loop buck converter for magnet load using Simulink and Sim Power System library of MATLAB.
Modelling and Operation of HVDC Based Power Transmission Systemijtsrd
Submodule overcurrent caused by DC pole-to-pole fault in modular multilevel converter HVDC MMC-HVDC system is one of the important research objects about its electrical characteristics. In this paper, the fault mechanism before and after the converter blocked was analyzed respectively and the circuit model for the analysis of submodule overcurrent was explored. The analytic equation for overcurrent calculation was deduced and a detailed analysis was also performed. The changes of submodule overcurrent stress with different circuit parameters were obtained and the key issues were also summed up. The results indicate that the submodule overcurrent is the AC system three-phase short-circuit current superposed the discharging current before the converter blocked, and the submodule overcurrent is the AC system three-phase short-circuit current superposed the valve reactor freewheeling current after the converter blocked. From the computation and simulation results, it is concluded that the analytical method is feasible and its calculation results are comparatively precise. Mohd Liaqat "Modelling and Operation of HVDC Based Power Transmission System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd20319.pdf
Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/20319/modelling-and-operation-of-hvdc-based-power-transmission-system/mohd-liaqat
MATHEMATICAL MODEL OF WIND TURBINE IN GRID-OFF SYSTEM Mellah Hacene
Abstract
This paper deals with the construction of a mathematical model of a wind turbine, which is one of the sources in the Grid-Off
system.
Keywords: mathematical model, wind turbine, Grid-Off system, electric generator, wind conditions.
1 Introduction
As one of the power sources of the Grid-Off system is a wind turbine. It is advantageous to work with a
mathematical model for the need of experimental research. In Fig. 1 is a schematic connection of a wind turbine
to a container, which is a Grid-Off system. [1-4]
DESIGN OF A MULTIFUNCTIONAL FLYBACK DC-DC CONVERTER WITH CURRENT CONTROLIAEME Publication
This paper proposes a set of design techniques to build a DC-DC converter for the interconnection of different sources of renewable energy with storage elements and flexible load profiles. This type of multifunctional DC-DC converter is essential to provide the dispatch of energy generation to storage connected to the DC bus or allow energy exchange with the AC network, with different decision modes as a function of the state of charge of batteries, with the forecast of the consumption of a house with renewable production. This work emphasizes the application of a method to design switched mode flyback converters with current control capabilities on the output side.
Design and Experimental Results of Universal Electric Vehicle Charger Using DSPTELKOMNIKA JOURNAL
Owing to the growing concerns over energy depletion and environmental issues around the
world, more and more attention is given on replacing the fuel -based automobiles with electric vehicles
(EVs) which have the characteristics of zero-emission and low noise. As a result, various countries have
taken specific initiatives to de-carbonize their transport sectors by developing their own EV industry.
Regardless of the environmental and economic benefits, substantial scales of grid-connected EVs impose
incredible difficulties to the power grid. The main issues caused by EV charging to the power grid include
harmonics, voltage drop, system instability, system losses and grid overloading. Therefore, this paper
presents design and development of a novel method, which is by applying voltage-oriented control (VOC)
algorithm in battery charging of electric bus.The power system of this work consists of three-phase PWM
rectifier. The proposed method is based on mathematical analysis. Simulation and experimental works are
performed to investigate behavior and performance of the proposed algorithm. This paperclearly described
implementation of low and medium power laboratory prototype and operation of digital signal processor
(DSP) via MATLAB / Simulink for the proposed method.
This paper displays a Fly Back Converter idea to straightforwardly incorporate cascaded flyback converter. The flyback-converter finds a way between DC-source and DC Motor-load. This work covenants with the modeling, simulation, and application of a Fuzzy Logic controlled (FLC) - Cascaded Fly back Converter (CFLB) system. This work recommends FLC to control Parallel cascaded fly-back converter to fabricate essential DC voltage from the input supply voltage. The yield of CFLB is controlled utilizing closed loop configuration. Closed loop PI & Fuzzy logic controlled CFLB systems are simulated and their results are related. The outcomes signify that the FLC based system gave a superior response than the P.I. controlled CFLB system. The FLC controlled CFLB system has benefits like decreased steady state error and enhanced time domain-response.
Multi-level inverters (MLIs), have gained popularity in the last few years as a result of their low total harmonic distortions (THD) as well as their output waveform which is of high quality. The converter which considers more appropriate for applications of photovoltaic (PV)beyond the varying MLIs arrangementsis the Cascaded H-Bridge-(CHB) (MLI), meanwhile each PV panel may be served as an independent DC supply for any CHB unit. Through the use of MATLAB/Simulink, the efficiency of symmetrical single phase MLI in terms of the number of switches, harmonic content in addition to the stresses of voltage through theswitches that exist at photovoltaic cell by means of input source is enhanced; varying parameters like output current, voltage and power, and THD at 5-level 7-level and 9-level Cascaded MLI are observed. In this paper, attention is paid to a multi-level topologies which is flexible and based on cascaded MLI intended for PV grids connected system. An observation of the output voltage becomes closer to the sine wave as the levels increase, while the increase in the levels of Cascaded Multilevel Inverter causes the total harmonic distortion to decrease.
Multiport converters increasingly gain prominance in the recent past to interface renewable energy sources like photovoltaic cells, fuel cells with the load. Energy storage elements like battery and supercapacitors nd major place as an additional and alternate sources in systems with primary renewable energy sources to overcome its intermittency issues. As these energy storage element's charging and discharging cycles are to be controlled, an isolated bidirectional converter topology with transformer is used. The galvanic isolation provided by the high frequency ac link transformers in partly isolated and fully isolated topologies makes these converters most preferrable in high power applications like electric vehicles. A comprehensive review is performed on various three port partly isolated and fully isolated topologies addressed by dierent research groups. The key contributions on soft switching for reducing switching losses and improving overall converter efficiency with help of resonant elements are discussed. In addition, control strategies for power ow control with enhanced soft switching of partly isolated converters are highlighted. A summary of converter topologies is provided comparing power rating, device count, soft switching resonant elements and efficiency which gives an idea for selection of suitable topology for the desired system requirement.
There is need for an energy storage device capable of transferring high power in transient situations
aboard naval vessels. Currently, batteries are used to accomplish this task, but previous research has
shown that when utilized at high power rates, these devices deteriorate over time causing a loss in lifespan.
It has been shown that a hybrid energy storage configuration is capable of meeting such a demand while
reducing the strain placed on individual components. While designing a custom converter capable of
controlling the power to and from a battery would be ideal for this application, it can be costly to develop
when compared to purchasing commercially available products. Commercially available products offer
limited controllability in exchange for their proven performance and lower cost point - often times only
allowing a system level control input without any way to interface with low level controls that are
frequently used in controller design. This paper proposes the use of fuzzy logic control in order to provide
a system level control to the converters responsible for limiting power to and from the battery. A system
will be described mathematically, modeled in MATLAB/Simulink, and a fuzzy logic controller will be
compared with a typical controller.
This paper reviews fuel cell technology status and some of its challenges worldwide. Fuel cells have emerged as an important technology in various non-linear loads in industrial, commercial and residential sectors. A mathematical model of hydrogen fuel cell is described with control parameters. A hydrogen fuel cell design is simulated using MATLAB/SIMULINK and the results are discussed.
A photovoltaic integrated unified power quality conditioner with a 27-level i...TELKOMNIKA JOURNAL
This paper presents a Unified Power Quality Conditioner (UPQC) with a 27-level inverter based on
an asymmetric H-bridge topology. Each phase of the inverter is composed of three H-bridges, supplied by
three DC sources scaled in the power of three. The output of the multilevel inverter is connected directly to
the point of common coupling (PCC) without the need to a transformer or a filter. The calculation of the Shunt
Active Power Filter (SAPF) compensation current is based on the generalized theory of synchronous frame
(d-q theory) while the calculation of a series active filter voltage is based on Instantaneous Reactive Power
(p-q theory). The control of the SAPF is achieved by using a closed-loop vector control followed by a new
multilevel modulation technique. In addition to the capability of harmonic elimination of both current and
voltage drawn from the source, the UPQC can produce real and reactive power to feed the loads during
prolonged voltage outages or source shortage. Batteries pack are used as a dc link, which is charged from
photovoltaic array connected to the battery through a maximum power point tracker and charge controller.
The injection of real and reactive power depends on the state of charge (SOC) of batteries, the frequency of
the system, real and reactive power of the load, and power factor at the point of PCC. The proposed UPQC
strategy is simulated in MATLAB SIMULINK and the results have shown a significant improved in Total
Harmonics Distortion (THD) of both the voltage and currents.
Passivity Based Control for PV Applications by Using a Buck Power Converter
The use of power converters for everyday applications is becoming more and more important. Current technological applications simultaneously demand a high level of precision and performance, so DC-DC converters have a very important role in systems requiring energy level conversion and adaptation. As part of the work of this paper, we are interested in an analysis of modeling and control law synthesis approaches to ensure stability and a certain level of performance in the entire operating domain. The objective of our research work is therefore to propose a control law whose synthesis is based on a formalized (modeling & control) approach with a view to obtaining a control law adapted to the operating point. The principles used are based on the control and observation by the theory of passivity for the synthesis of control law of buck power converter for PV Applications.
Harvesting in electric vehicles: Combining multiple power tracking and fuel-c...IJECEIAES
Exploitation of green energy sources is essential to diminish the deterioration of our environment. The energy harvesting, represents an alternative to achieve greater range in electric and hybrid vehicles. An energy management strategy (EMS) must be optimized to obtain the best benefits in such vehicles, which is not a trivial task. If harvesting or energy recovery devices are added, the EMS becomes a dual-purpose algorithm: minimizing fuel consumption and maximizing energy harvest through maximum power point tracking (MPPT) controllers. Known studies consider separate EMS, one for traction and another for regenerative braking, without considering harvest devices such as solar panels, regenerative suspension, thermal generators, among others. Furthermore, the electronic power converters used, are not designed to handle such unequal power levels. In this article, an electronic platform to include multiple energy harvesting devices in a fuel-cell hybrid electric vehicle, was presented together with a multiple MPPT-EMS. The EMS is easily implementable, and considers quasi-constant cell energy extraction and filtering of current transients to the battery bank ensuring the longevity of the devices. A new mathematical model of the platform, a closed loop stability analysis, and numerical and Hardware-in-the-Loop (HIL) validations were presented. Some experimental validation results were also provided.
Anlysis of a pmsg based offshore wind farm fed to a onshore grid through hybr...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Power electronic interface has reached a new level in the area of hybrid energy integration nowadays. The existence for the concept of hybrid energy integration is truly questionable without a proper power electronic interface. In this paper, a modified dual input DC-DC converter which is capable of incorporating two distinct V-I characteristic sources such as solar-PV, battery, fuel cell, etc., is proposed. The converter has the ability to operate in both unidirectional and bidirectional mode with buck, buck-boost and boost operation. The software simulation of the proposed converter has been conducted in MATLAB/Simulink platform in a detailed manner and an experimental prototype of the propsed converter has been built to validate the simulation results.
Effect of Passive Damping on the Performance of Buck Converter for Magnet Loadpaperpublications3
Abstract: A DC to DC converter is a lossless dc transformer that supply regulated output voltage under varying load and input voltage condition and also the converter parameter values changes with time and physical quantity like temperature etc. This paper presents the design and simulation of an open loop buck converter for magnet load using Simulink and Sim Power System library of MATLAB.
Modelling and Operation of HVDC Based Power Transmission Systemijtsrd
Submodule overcurrent caused by DC pole-to-pole fault in modular multilevel converter HVDC MMC-HVDC system is one of the important research objects about its electrical characteristics. In this paper, the fault mechanism before and after the converter blocked was analyzed respectively and the circuit model for the analysis of submodule overcurrent was explored. The analytic equation for overcurrent calculation was deduced and a detailed analysis was also performed. The changes of submodule overcurrent stress with different circuit parameters were obtained and the key issues were also summed up. The results indicate that the submodule overcurrent is the AC system three-phase short-circuit current superposed the discharging current before the converter blocked, and the submodule overcurrent is the AC system three-phase short-circuit current superposed the valve reactor freewheeling current after the converter blocked. From the computation and simulation results, it is concluded that the analytical method is feasible and its calculation results are comparatively precise. Mohd Liaqat "Modelling and Operation of HVDC Based Power Transmission System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd20319.pdf
Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/20319/modelling-and-operation-of-hvdc-based-power-transmission-system/mohd-liaqat
MATHEMATICAL MODEL OF WIND TURBINE IN GRID-OFF SYSTEM Mellah Hacene
Abstract
This paper deals with the construction of a mathematical model of a wind turbine, which is one of the sources in the Grid-Off
system.
Keywords: mathematical model, wind turbine, Grid-Off system, electric generator, wind conditions.
1 Introduction
As one of the power sources of the Grid-Off system is a wind turbine. It is advantageous to work with a
mathematical model for the need of experimental research. In Fig. 1 is a schematic connection of a wind turbine
to a container, which is a Grid-Off system. [1-4]
DESIGN OF A MULTIFUNCTIONAL FLYBACK DC-DC CONVERTER WITH CURRENT CONTROLIAEME Publication
This paper proposes a set of design techniques to build a DC-DC converter for the interconnection of different sources of renewable energy with storage elements and flexible load profiles. This type of multifunctional DC-DC converter is essential to provide the dispatch of energy generation to storage connected to the DC bus or allow energy exchange with the AC network, with different decision modes as a function of the state of charge of batteries, with the forecast of the consumption of a house with renewable production. This work emphasizes the application of a method to design switched mode flyback converters with current control capabilities on the output side.
Design and Experimental Results of Universal Electric Vehicle Charger Using DSPTELKOMNIKA JOURNAL
Owing to the growing concerns over energy depletion and environmental issues around the
world, more and more attention is given on replacing the fuel -based automobiles with electric vehicles
(EVs) which have the characteristics of zero-emission and low noise. As a result, various countries have
taken specific initiatives to de-carbonize their transport sectors by developing their own EV industry.
Regardless of the environmental and economic benefits, substantial scales of grid-connected EVs impose
incredible difficulties to the power grid. The main issues caused by EV charging to the power grid include
harmonics, voltage drop, system instability, system losses and grid overloading. Therefore, this paper
presents design and development of a novel method, which is by applying voltage-oriented control (VOC)
algorithm in battery charging of electric bus.The power system of this work consists of three-phase PWM
rectifier. The proposed method is based on mathematical analysis. Simulation and experimental works are
performed to investigate behavior and performance of the proposed algorithm. This paperclearly described
implementation of low and medium power laboratory prototype and operation of digital signal processor
(DSP) via MATLAB / Simulink for the proposed method.
A New Solution to Improve Power Quality of Renewable Energy Sources Smart Gri...iosrjce
This particular article reveals a prototyped interface current control protocol which is ideal for
multilevel converters and it’s utilization with a three-phase cascaded H-bridge inverter. This kind of
administration approach utilizes a discrete-time type of the device to estimate the longer term benefit from the
current for many voltage vectors, as well as decides on the vector which in turn decreases an expense purpose.
A result of the multitude of voltage vectors obtainable in a multilevel inverter, numerous computations are
expected, producing challenging execution with this strategy in a typical control program. A new improved
strategic approach with the demonstration using physical framework as well as Matlab system significantly
decreases the number of computations without influencing the actual system’s effectiveness is suggested.
Experimental outcomes intended for five-level inverters confirm the suggested strategy. Additionally, author
considered the socio-environmental effects occurring due to carbon foot printing as per KYOTO protocol and
demonstrates the implementation of prototype carbon foot printing control sub-protocol for minimization of
carbon foot printing occurring due to microbial fuel cell micro-grid setup. Hence this will help to manage
attitudinal goals to improve electricity resource quality and efficiency.
Supercapacitors and Battery power management for Hybrid Vehicle Applications ...Pradeep Avanigadda
This paper presents supercapacitors and battery association methodology for ECCE Hybrid
vehicle. ECCE is an experimental Hybrid Vehicle developed at L2ES Laboratory in collaboration with
the Research Center in Electrical Engineering and Electronics in Belfort (CREEBEL) and other French
partners. This test bench has currently lead-acid batteries with a rated voltage of 540 V, two motors
each one coupled with one alternator. The alternators are feeding a DC-bus by rectifers. The main
objective of this paper is to study the management of the energy provides by two supercapacitor
packs. Each supercapacitors module is made of 108 cells with a maximum voltage of 270V. This
experimental test bench is carried out for studies and innovating tests for the Hybrid Vehicle
applications. The multi boost and multi full bridge converter topologies are studied to define the best
topology for the embarked power management. The authors propose a good power management
strategy by using the multi boost and the multi full bridge converter topologies. The experimental and
simulation results of the two converter topologies are presented.
The use of a new control method for grid-connected inverters for reducing the output current harmonic distortion in a wide range of grid-connected distributed generation (DG) applications, including wind turbine (WT) and fuel cell (FC) inverters is proposed in this paper. The control method designed to eliminate main harmonics in a microgrid (MG) and between MG and point of common coupling (PCC) and responsible for the correction of the system unbalance. Another advantage of the proposed control method is that it can be easily adopted into the DG control system without the installation of extra hardware. The proposed control method is comprised of the synchronous reference frame method (SRF). Results from the proposed control method are provided to show the feasibility of the proposed approach.
A new bidirectional multilevel inverter topology with a high number of voltage levels with a very reduced number of power components is proposed in this paper. Only TEN power switches and four asymmetric DC voltage sources are used to generate 25 voltage levels in this new topology. The proposed multilevel converter is more suitable for e-mobility and photovoltaic applications where the overall energy source can be composed of a few units/associations of several basic source modules. Several benefits are provided by this new topology: Highly sinusoidal current and voltage waveforms, low Total Harmonic Distortion, very low switching losses, and minimum cost and size of the device. For optimum control of this 25-level voltage inverter, a special Modified Hybrid Modulation technique is performed. The proposed 25-level inverter is compared to various topologies published recently in terms of cost, the number of active power switches, clamped diodes, flying capacitors, DC floating capacitors, and the number of DC voltage sources. This comparison clearly shows that the proposed topology is cost-effective, compact, and very efficient. The effectiveness and the good performance of the proposed multilevel power converter (with and without PWM control) are verified and checked by computational simulations.
Input switched closed-loop single phase SEPIC controlled rectifier with impro...IJECEIAES
DC power supply has become the driving source for some essential modern applications. Thereby, DC power conditioning has become a significant issue for engineers. Typically used rectifiers associated with a bridge structure is nonlinear in nature. Thereby, the current at input side of the rectifier contains harmonics, which also flow through the power line. The presence of harmonics causes several interruptions and reduce power quality. In this regard, a new close loop SEPIC controlled rectifier is proposed in this paper. The conventional scheme is arranged with a rectifier connected to a DC-DC converter, which is an open loop system. Consequently, such system cannot regulate voltage at load varying condition. The proposed SEPIC controlled rectifier can regulate voltage under load varying condition for a wide range. Additionally, the performance in terms of total harmonic distortion (THD) of input current and power factor at AC side are also within satisfactory range for the closed loop configuration. The controlled rectifier has four operating phases associated with switching states and input voltage polarity. The close loop configuration also incorporates a current and a voltage loop at the feedback path. The comparative studies have been performed among the proposed closed loop construction, the open-loop structure as well as the conventional construction. The effectiveness of the proposed controlled rectifier is verified in terms of THD and input power factor considering the results obtained from simulation.
International Journal of Engineering and Science Research. It is a international journal publishing high-quality articles dedicated to all aspects of engineering. IJESR is to publish peer reviewed research and review articles. fastly without delay in the developing field of engineering and science Research.
MLI Power Topologies and Voltage Eminence: An Exploratory Reviewijeei-iaes
Due to their performances and inherent edges, particularly in medium-voltage and dynamic applications, multilevel inverters have received associate degree increasing attention in universe industrial applications. This paper deals with a review of the most structure electrical converter topologies additionally their commonest derived and hybrid structures quoted in previous analysis works. It additionally encompasses associate degree investigation on voltage harmonic elimination and THD estimation. For that reason, the paper summarizes the foremost relevant modulation techniques used to date to boost the output voltage quality. Theoretical formulas elicited within the literature, for calculating the output voltage THD higher and lower bounds area unit reportable and verified by adequate simulations.
Analysis of Fuel Cell Based Multilevel DC-DC Boost Converter for Induction MotorIJMTST Journal
In this paper new topologies and interleaving modulation concepts for multilevel DC-DC boost converter
enabling a significantly less loss and a reduced chip size of the power semiconductors are proposed. The
distributed generation (DG) systems based on the renewable energy sources have rapidly developed in
recent years. These DG systems are powered by micro sources such as fuel cells, photovoltaic (PV) systems,
and batteries. Fuel cells are considered to be one of the most promising sources of distributed energy because
of their high efficiency, low environmental impact and scalability. Non-isolated high step-up DC-DC
converters are required in the industrial applications. Many of these conventional DC–DC converters have the
disadvantages of operating at high duty-cycle, high switch voltage stress and high diode peak current. A
three-level step up converter is implemented to boost the fuel cell stack voltage of 96V to 340V. The proposed
converter consists a system of fuel cell based Multilevel DC-DC converter with PI controller is modeled and
simulated by using Matlab/Simulink.
A Comparison Between Two Average Modelling Techniques of AC-AC Power ConvertersIAES-IJPEDS
In this paper, a comparative evaluation of two modelling tools for switching AC-AC power converters is presented. Both of them are based on average modelling techniques. The first approach is based on the circuit averaging technique and consists in the topological manipulations, applied to a converter states. The second approach makes use of a state-space averaged model of the converter and is based on analytical manipulations using the different state representations of a converter. The two modelling techniques are applied to a same AC-AC called matrix-reactance frequency converter based on buck-boost topology. These techniques are compared on the basis of their rapidity, quantity of calculations and transformations and its limitations.
Similar to Load estimator-based hybrid controller design for two-interleaved boost converter dedicated to renewable energy and automotive applications (20)
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
Urban traffic network model is illustrated by state-charts and object-diagram. However, they have limitations to show the behavioral perspective of the traffic information flow. Consequently, a state space model is used to calculate the half-value waiting time of vehicles. In this study, a combination of the general type-2 fuzzy logic sets and the modified backtracking search algorithm (MBSA) techniques are used in order to control the traffic signal scheduling and phase succession so as to guarantee a smooth flow of traffic with the least wait times and average queue length. The parameters of input and output membership functions are optimized simultaneously by the novel heuristic algorithm MBSA. A comparison is made between the achieved results with those of optimal and conventional type-1 fuzzy logic controllers.
Embedded intelligent adaptive PI controller for an electromechanical systemISA Interchange
In this study, an intelligent adaptive controller approach using the interval type-2 fuzzy neural network (IT2FNN) is presented. The proposed controller consists of a lower level proportional - integral (PI) controller, which is the main controller and an upper level IT2FNN which tuning on-line the parameters of a PI controller. The proposed adaptive PI controller based on IT2FNN (API-IT2FNN) is implemented practically using the Arduino DUE kit for controlling the speed of a nonlinear DC motor-generator system. The parameters of the IT2FNN are tuned on-line using back-propagation algorithm. The Lyapunov theorem is used to derive the stability and convergence of the IT2FNN. The obtained experimental results, which are compared with other controllers, demonstrate that the proposed API-IT2FNN is able to improve the system response over a wide range of system uncertainties.
State of charge estimation of lithium-ion batteries using fractional order sl...ISA Interchange
This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov’s stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estima- tion method is effective, and the designed observers have good performance.
Fractional order PID for tracking control of a parallel robotic manipulator t...ISA Interchange
This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB co-simulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.
Fuzzy logic for plant-wide control of biological wastewater treatment process...ISA Interchange
The application of control strategies is increasingly used in wastewater treatment plants with the aim of improving effluent quality and reducing operating costs. Due to concerns about the progressive growth of greenhouse gas emissions (GHG), these are also currently being evaluated in wastewater treatment plants. The present article proposes a fuzzy controller for plant-wide control of the biological wastewater treatment process. Its design is based on 14 inputs and 6 outputs in order to reduce GHG emissions, nutrient concentration in the effluent and operational costs. The article explains and shows the effect of each one of the inputs and outputs of the fuzzy controller, as well as the relationship between them. Benchmark Simulation Model no 2 Gas is used for testing the proposed control strategy. The results of simulation results show that the fuzzy controller is able to reduce GHG emissions while improving, at the same time, the common criteria of effluent quality and operational costs.
Design and implementation of a control structure for quality products in a cr...ISA Interchange
In recent years, interest for petrochemical processes has been increasing, especially in refinement area. However, the high variability in the dynamic characteristics present in the atmospheric distillation column poses a challenge to obtain quality products. To improve distillates quality in spite of the changes in the input crude oil composition, this paper details a new design of a control strategy in a conventional crude oil distillation plant defined using formal interaction analysis tools. The process dynamic and its control are simulated on Aspen HYSYS dynamic environment under real operating conditions. The simulation results are compared against a typical control strategy commonly used in crude oil atmospheric distillation columns.
Model based PI power system stabilizer design for damping low frequency oscil...ISA Interchange
This paper explores a two-level control strategy by blending a local controller with a centralized controller for the low frequency oscillations in a power system. The proposed control scheme provides stabilization of local modes using a local controller and minimizes the effect of inter-connection of sub-systems performance through a centralized control. For designing the local controllers in the form of proportional-integral power system stabilizer (PI-PSS), a simple and straight forward frequency domain direct synthesis method is considered that works on use of a suitable reference model which is based on the desired requirements. Several examples both on one machine infinite bus and multi-machine systems taken from the literature are illustrated to show the efficacy of the proposed PI-PSS. The effective damping of the systems is found to be increased remarkably which is reflected in the time-responses; even unstable operation has been stabilized with improved damping after applying the proposed controller. The proposed controllers give remarkable improvement in damping the oscillations in all the illustrations considered here and as for example, the value of damping factor has been increased from 0.0217 to 0.666 in Example 1. The simulation results obtained by the proposed control strategy are favorably compared with some controllers prevalent in the literature.
A comparison of a novel robust decentralized control strategy and MPC for ind...ISA Interchange
Abstract: In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, an MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the distillate (XD) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter XD control, while the proposed controller was tighter in β control. The tight XD control allowed the MPC to operate at a higher XD set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favor MPC.
Fault detection of feed water treatment process using PCA-WD with parameter o...ISA Interchange
Feed water treatment process (FWTP) is an essential part of utility boilers; and fault detection is expected for its reliability improvement. Classical principal component analysis (PCA) has been applied to FWTPs in our previous work; however, the noises of T2 and SPE statistics result in false detections and missed detections. In this paper, Wavelet denoise (WD) is combined with PCA to form a new algorithm, (PCA- WD), where WD is intentionally employed to deal with the noises. The parameter selection of PCA-WD is further formulated as an optimization problem; and PSO is employed for optimization solution. A FWTP, sustaining two 1000 MW generation units in a coal-fired power plant, is taken as a study case. Its operation data is collected for following verification study. The results show that the optimized WD is effective to restrain the noises of T2 and SPE statistics, so as to improve the performance of PCA-WD algorithm. And, the parameter optimization enables PCA-WD to get its optimal parameters in an auto- matic way rather than on individual experience. The optimized PCA-WD is further compared with classical PCA and sliding window PCA (SWPCA), in terms of four cases as bias fault, drift fault, broken line fault and normal condition, respectively. The advantages of the optimized PCA-WD, against classical PCA and SWPCA, is finally convinced with the results.
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...ISA Interchange
As higher requirements are proposed for the load regulation and efficiency enhancement, the control performance of boiler-turbine systems has become much more important. In this paper, a novel robust control approach is proposed to improve the coordinated control performance for subcritical boiler-turbine units. To capture the key features of the boiler-turbine system, a nonlinear control-oriented model is established and validated with the history operation data of a 300 MW unit. To achieve system linearization and decoupling, an adaptive feedback linearization strategy is proposed, which could asymptotically eliminate the linearization error caused by the model uncertainties. Based on the linearized boiler-turbine system, a second-order sliding mode controller is designed with the super-twisting algorithm. Moreover, the closed-loop system is proved robustly stable with respect to uncertainties and disturbances. Simulation results are presented to illustrate the effectiveness of the proposed control scheme, which achieves excellent tracking performance, strong robustness and chattering reduction.
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...ISA Interchange
Clock synchronization is an issue of vital importance in applications of wireless sensor networks (WSNs). This paper proposes a proportional integral estimator-based protocol (EBP) to achieve clock synchronization for wireless sensor networks. As each local clock skew gradually drifts, synchronization accuracy will decline over time. Compared with existing consensus-based approaches, the proposed synchronization protocol improves synchronization accuracy under time-varying clock skews. Moreover, by restricting synchronization error of clock skew into a relative small quantity, it could reduce periodic re-synchronization frequencies. At last, a pseudo-synchronous implementation for skew compensation is introduced as synchronous protocol is unrealistic in practice. Numerical simulations are shown to illustrate the performance of the proposed protocol.
An artificial intelligence based improved classification of two-phase flow patte...ISA Interchange
Flow pattern recognition is necessary to select design equations for finding operating details of the process and to perform computational simulations. Visual image processing can be used to automate the interpretation of patterns in two-phase flow. In this paper, an attempt has been made to improve the classification accuracy of the flow pattern of gas/ liquid two- phase flow using fuzzy logic and Support Vector Machine (SVM) with Principal Component Analysis (PCA). The videos of six different types of flow patterns namely, annular flow, bubble flow, churn flow, plug flow, slug flow and stratified flow are re- corded for a period and converted to 2D images for processing. The textural and shape features extracted using image processing are applied as inputs to various classification schemes namely fuzzy logic, SVM and SVM with PCA in order to identify the type of flow pattern. The results obtained are compared and it is observed that SVM with features reduced using PCA gives the better classification accuracy and computationally less intensive than other two existing schemes. This study results cover industrial application needs including oil and gas and any other gas-liquid two-phase flows.
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...ISA Interchange
In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.
Effects of Wireless Packet Loss in Industrial Process Control SystemsISA Interchange
Timely and reliable sensing and actuation control are essential in networked control. This depends on not only the precision/quality of the sensors and actuators used but also on how well the communications links between the field instruments and the controller have been designed. Wireless networking offers simple deployment, reconfigurability, scalability, and reduced operational expenditure, and is easier to upgrade than wired solutions. However, the adoption of wireless networking has been slow in industrial process control due to the stochastic and less than 100% reliable nature of wireless communications and lack of a model to evaluate the effects of such communications imperfections on the overall control performance. In this paper, we study how control performance is affected by wireless link quality, which in turn is adversely affected by severe propagation loss in harsh industrial environments, co-channel interference, and unintended interference from other devices. We select the Tennessee Eastman Challenge Model (TE) for our study. A decentralized process control system, first proposed by N. Ricker, is adopted that employs 41 sensors and 12 actuators to manage the production process in the TE plant. We consider the scenario where wireless links are used to periodically transmit essential sensor measurement data, such as pressure, temperature and chemical composition to the controller as well as control commands to manipulate the actuators according to predetermined setpoints. We consider two models for packet loss in the wireless links, namely, an independent and identically distributed (IID) packet loss model and the two-state Gilbert-Elliot (GE) channel model. While the former is a random loss model, the latter can model bursty losses. With each channel model, the performance of the simulated decentralized controller using wireless links is compared with the one using wired links providing instant and 100% reliable communications. The sensitivity of the controller to the burstiness of packet loss is also characterized in different process stages. The performance results indicate that wireless links with redundant bandwidth reservation can meet the requirements of the TE process model under normal operational conditions. When disturbances are introduced in the TE plant model, wireless packet loss during transitions between process stages need further protection in severely impaired links. Techniques such as re-transmission scheduling, multi-path routing and enhanced physical layer design are discussed and the latest industrial wireless protocols are compared.
Fault Detection in the Distillation Column ProcessISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H1 framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.
A KPI-based process monitoring and fault detection framework for large-scale ...ISA Interchange
Large-scale processes, consisting of multiple interconnected sub-processes, are commonly encountered in industrial systems, whose performance needs to be determined. A common approach to this problem is to use a key performance indicator (KPI)-based approach. However, the different KPI-based approaches are not developed with a coherent and consistent framework. Thus, this paper proposes a framework for KPI-based process monitoring and fault detection (PM-FD) for large-scale industrial processes, which considers the static and dynamic relationships between process and KPI variables. For the static case, a least squares-based approach is developed that provides an explicit link with least-squares regression, which gives better performance than partial least squares. For the dynamic case, using the kernel re- presentation of each sub-process, an instrument variable is used to reduce the dynamic case to the static case. This framework is applied to the TE benchmark process and the hot strip mill rolling process. The results show that the proposed method can detect faults better than previous methods.
An adaptive PID like controller using mix locally recurrent neural network fo...ISA Interchange
Being complex, non-linear and coupled system, the robotic manipulator cannot be effectively controlled using classical proportional integral derivative (PID) controller. To enhance the effectiveness of the conventional PID controller for the nonlinear and uncertain systems, gains of the PID controller should be conservatively tuned and should adapt to the process parameter variations. In this work, a mix locally recurrent neural network (MLRNN) architecture is investigated to mimic a conventional PID controller which consists of at most three hidden nodes which act as proportional, integral and derivative node. The gains of the mix locally recurrent neural network based PID (MLRNNPID) controller scheme are initi- alized with a newly developed cuckoo search algorithm (CSA) based optimization method rather than assuming randomly. A sequential learning based least square algorithm is then investigated for the on- line adaptation of the gains of MLRNNPID controller. The performance of the proposed controller scheme is tested against the plant parameters uncertainties and external disturbances for both links of the two link robotic manipulator with variable payload (TL-RMWVP). The stability of the proposed controller is analyzed using Lyapunov stability criteria. A performance comparison is carried out among MLRNNPID controller, CSA optimized NNPID (OPTNNPID) controller and CSA optimized conventional PID (OPTPID) controller in order to establish the effectiveness of the MLRNNPID controller.
A method to remove chattering alarms using median filtersISA Interchange
Chattering alarms are the most found nuisance alarms that will probably reduce the usability and result in a confidence crisis of alarm systems for industrial plants. This paper addresses the chattering alarm reduction using median filters. Two rules are formulated to design the window size of median filters. If the alarm probability is estimated using process data, one rule is based on the probability of alarms to satisfy some requirements on the false alarm rate, or missed alarm rate. If there are only historical alarm data available, the other rule is based on percentage reduction of chattering alarms using alarm duration distribution. Experimental results for industrial cases testify that the proposed method is effective.
Design of a new PID controller using predictive functional control optimizati...ISA Interchange
An improved proportional integral derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
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Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
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Load estimator-based hybrid controller design for two-interleaved boost converter dedicated to renewable energy and automotive applications
1. Research Article
Load estimator-based hybrid controller design for two-interleaved
boost converter dedicated to renewable energy and
automotive applications
Mohamed Bougrine a,b
, Mohammed Benmiloud a
, Atallah Benalia a
, Emmanuel Delaleau c
,
Mohamed Benbouzid b,d,n
a
University of Laghouat, LACoSERE Lab, Laghouat, Algeria
b
University of Brest, FRE CNRS 3744 IRDL, Brest, France
c
Ecole Nationale d'Ingénieurs de Brest, Mechatronics Department, Plouzané, France
d
Shanghai Maritime University, Shanghai, China
a r t i c l e i n f o
Article history:
Received 8 June 2016
Received in revised form
14 August 2016
Accepted 6 September 2016
Available online 16 September 2016
This paper was recommended for publica-
tion by Dr. Jeff Pieper
Keywords:
Interleaved boost converter
Hybrid dynamical system
Optimal limit cycle
Stabilization
Adaptive control
Fuel cell source
a b s t r a c t
This paper is devoted to the development of a hybrid controller for a two-interleaved boost converter
dedicated to renewable energy and automotive applications. The control requirements, resumed in fast
transient and low input current ripple, are formulated as a problem of fast stabilization of a predefined
optimal limit cycle, and solved using hybrid automaton formalism. In addition, a real time estimation of
the load is developed using an algebraic approach for online adjustment of the hybrid controller.
Mathematical proofs are provided with simulations to illustrate the effectiveness and the robustness of
the proposed controller despite different disturbances. Furthermore, a fuel cell system supplying a
resistive load through a two-interleaved boost converter is also highlighted.
& 2016 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Climate change in the last century, mainly due to the increasing
carbon dioxide (CO2) released through human activities as shown
in Fig. 1, brings to light serious issues like global temperature and
sea level augmentation, ocean warming and acidification, shrink-
ing ice sheets, etc. These facts have pushed the scientific com-
munity for renewable and clean energy solutions to supply various
technological applications via switched converters.
Due to the power source and load constraints, the converter
structures have to meet some practical challenges such as relia-
bility, high power density, high efficiency, and low current/voltage
ripples. Parallel connection of switched converters or specifically
the interleaving approach meets the above requirements with
better power scalability characteristics compared to the classical
ones [2,3]. Fig. 2a depicts the topology of a DC–DC two-interleaved
boost converter, the two-phase boost topology was proposed as an
alternative to the classical single phase boost converter [4], and
the two-phase buck topology as an alternative to the classical buck
converter [5]. These interleaved topologies are widely used in
varieties of applications and systems that incorporate solar panels
or fuel cell sources, as reflected in the literature [6–11]. The
interleaving technique is also investigated for the microprocessors
power supply to achieve better computing performance using the
topology in Fig. 2b, which is known as multiphase/multi-channel
synchronous/interleaved buck converter [12–15]. The interleaved
bidirectional topology, obtained by changing each diode with a
controlled switching device in the interleaved boost converter, is
also explored in systems with rechargeable energy storage ele-
ments like batteries or supercapacitors [16–20].
Research studies have discussed these topologies from different
practical and fundamental points of view. The authors in [21] have
discussed the number of phases that can be used to obtain a tra-
deoff among some indexes such as: the switching losses, the
inductor volume, the input current ripples and the switches cost.
Power management in fuel cell hybrid vehicles involving battery/
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
http://dx.doi.org/10.1016/j.isatra.2016.09.001
0019-0578/& 2016 ISA. Published by Elsevier Ltd. All rights reserved.
n
Corresponding author at: University of Brest, FRE CNRS 3744 IRDL, Brest, France.
E-mail addresses: m.bougrine@lagh-univ.dz (M. Bougrine),
med.benmiloud@lagh-univ.dz (M. Benmiloud), a.benalia@lagh-univ.dz (A. Benalia),
delaleau@enib.fr (E. Delaleau), mohamed.benbouzid@univ-brest.fr (M. Benbouzid).
ISA Transactions 66 (2017) 425–436
2. supercapacitor as an auxiliary regenerative source is thoroughly
explored in [16,22]. A maximum power point tracking (MPPT)
approach in systems with solar module or a fuel cell source
associated to interleaved boost converter is performed in [23,24].
Other works deal with the energetic efficiency improvement by
considering variants of the interleaved topology such as soft
switching and resonant techniques, or coupled inductors [25,26].
Furthermore, the control of interleaved converters has been
dealt using several control strategies. Linear control techniques
based on the average model are effective only around a specific
operation points due to the neglected nonlinearities of the con-
verter model and the power source [27]. In [14,27], a sliding mode
and adaptive sliding mode controllers are designed and defended
to be robust ones. Model predictive control is developed for the
interleaved boost topology in [28]. Regardless of the fact that
several control techniques have been proposed, the transient and
steady-state control problem of the interleaved converter still pose
challenging issues. More precisely, the transient control deals with
a minimal response time and number of commutations require-
ments, which is beneficial for a fast MPPT achievement in a solar
panel based system for example. In addition, in electric vehicles, a
fast tracking of the supercapacitor reference current, may also
require an interleaved bidirectional converter to guarantee the
instantaneous peak power demands or to recover a maximum
energy through regenerative braking [29]. Moreover, information
processing in computers is directly related to the response time of
the microprocessors power supply in fast current variations
tracking [12]. The existing controllers may tackle the problem of a
fast transient with different approaches. Nevertheless, the steady-
state behavior, represented by states ripples, is not directly con-
trolled. Indeed, ripples amplitude and harmonic content of the
current is one of the various phenomena influencing fuel cell
lifespan as well as battery lifetime [11,22]. Besides, a small input
current ripple is advantageous for MPPT to operate around a
maximum power point without too much fluctuation [30].
Motivated by the above facts, we aim to address the control
problem of the transient and steady-state of the two-interleaved
boost converter. For this purpose, an exact instantaneous model of
the converter will be investigated in the next section using the
theory of hybrid dynamical systems. An adaptive transient and
steady-state controllers will be developed in Section 3 to solve the
problem of fast stabilization of a predefined optimal limit cycle.
Simulation results will be discussed in Section 4 and followed by
conclusions and future works that outline the main contributions
of the present paper.
2. Hybrid model of 2IBC and control formulation
We consider the 2IBC presented in Fig. 2a, supplying a resistive
load (R) and operating in continuous conduction mode (CCM).
Phase k consists of a non-ideal inductor ðLk; rkÞ, a diode ðDkÞ, and a
controlled semiconductor device ðswkÞ by a binary input signal
uk Af0; 1g. The instantaneous model of the 2IBC is given by:
diLk
dt
¼
1
Lk
ðvi ÀrkiLk
ÀukvoÞ; k ¼ 1; 2
dvo
dt
¼
1
Co
X2
k ¼ 1
ukiLk
À
vo
R
!
;
8
>>>><
>>>>:
ð1Þ
where iLk
is the inductor current of phase k. The voltages vi and vo
are the input and output voltages respectively. Á : f0; 1g↦f0; 1g is
the Not function.
The input signal ðu1; u2Þ combinations offer four different con-
verter operations without redundancy, known as discrete modes
in hybrid systems vocabulary. From (1), each discrete mode can be
represented by the following affine differential equation:
_x ¼ AqðtÞxþBqðtÞ ¼ f qðtÞðxÞ ð2Þ
with x ¼ ½iL1
iL2
voŠT
AX is the continuous state vector defined in a
physical operating region X DR3
. qðtÞ : Rþ ↦Q is the switching
signal, with Q ¼ fq1; q2; q3; q4g is the set of discrete modes. The
state matrices Aqi
AR3Â3
and Bqi
AR3Â1
are given by:
Aqi
¼
À r1
L1
0 Àu1
L1
0 Àr2
L2
Àu2
L2
u1
Co
u2
Co
À 1
RCo
0
B
B
B
@
1
C
C
C
A
; Bqi
¼
vi
L1
vi
L2
0
0
B
@
1
C
A
For each discrete mode, the corresponding values of the inputs
are given in Table 1.
The control design consists in the adequate state feedback
switching low design q(x) that orchestrates the switching among
the discrete modes to meet the control requirements. In closed
loop, the hybrid automaton H of the 2IBC, operating in CCM, can be
1980 1985 1990 1995 2000 2005 2010 2015
330
350
370
390
410
Years
CO2
(ppm)
Seasonal
Monthly
Fig. 1. Recent global monthly and seasonal mean CO2 in parts per million (ppm)
over marine surface sites (October 2015) [1].
Fig. 2. Topology of interleaved converter.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436426
3. represented by the following 6-tuple:
H ¼ ðQ; X; Sc; T; G; InitÞ ð3Þ
where Sc : ðQ Â XÞ↦R3
is the application that assigns to every discrete
mode a continuous dynamic given by (2). T ¼ fTij; i; jAf1; …; 4gg
represents a set of all possible transitions between discrete modes,
G : T-2X
associates to each transition a continuous set where the
transition is valid (called a guard condition), and InitDX Â Q gives the
initial states.
Based on (3) the switching design corresponds to the free
elements definition of the hybrid automaton ðT; G; InitÞ in order to
solve the stabilization problem discussed in the next subsection. In
the remainder of the paper, we will consider r1 ¼ r2 ¼ r and
L1 ¼ L2 ¼ L.
The control of interleaved boost converters addresses the reg-
ulation of the output voltage vo around the desired voltage Vref by
controlling the input current Iin around an average reference
generated by an outer loop as follows:
Iref ðtÞ ¼ INom
ref þ
Z t
0
K sgnðVref ÀvoðτÞÞ Vref ÀvoðτÞ
α
dτ ð4Þ
where K is a sufficiently large positive real number, αAð0; 1Þ is a
small coefficient to ensure a finite time settling, INom
ref ¼
V2
ref
Rvi
is the
nominal value of Iref in static steady-state out of model uncer-
tainties. To guarantee the balancing of the converter, the input
current must be shared between the two phases. Hence for the
2IBC, the phase currents must be regulated around the average
reference Irefk
¼ 0:5Iref .
On the other hand, it is clear from the hybrid nature of the
converter that the regulation of the phase currents can be
obtained in a cyclic manner. This means that in steady-state, the
converter trajectory converges to a limit cycle. The optimal limit
cycle is characterized by low input ripple which corresponds to the
following condition on the inputs:
1. The input signals have the same duty cycle d.
2. The phase shift between the two phases is equal to π.
The duty cycle d depends on the required output voltage as fol-
lows:
d ¼ 1À
vi ÀrIref
Vref
ð5Þ
Fig. 3 illustrates the hybrid trajectory (x,q) of the 2IBC in the
currents phase plane ðiL1
; iL2
Þ for different duty cycle values and a
fixed desired phase shift ðϕ ¼ πÞ of the input signals. One can
remark that the periodic behavior of the input signals leads to a
cyclic hybrid trajectory, which is one of the important nonlinear
phenomena that may be exhibited by DC–DC power converters
[31]. Note that each phase shift leads to a specific limit cycle where
the optimal one, with respect to input current ripple, is shown in
Fig. 3. Therefore, it is more natural to consider the stabilization
problem of the 2IBC as follows.
Fast optimal limit cycle stabilization: Given the set of discrete
modes Q ¼ fq1; q2; q3; q4g, how should they be selected to guaran-
tee the fast stabilization of the predefined optimal limit cycle
depicted in Fig. 3 with a fast transient property?
This problem is not directly discussed using the continuous
dynamical systems theory. In the next section, we will solve the
above problem efficiently using hybrid systems theory.
3. Hybrid control design: main results
The formulated stabilization problem in the previous section
can be restated based on the closed loop hybrid model (3) as fol-
lows: (1) For a given initial condition x0, how one should select the
convenient discrete modes among the set Q to reach fast the
neighborhood of the optimal limit cycle shown in Fig. 3, and fast
balance of the input current among the two phases. (2) When the
neighborhood of the optimal limit cycle is reached, how to select
the discrete modes to ensure its local stabilization.
In the following, we design an adaptive hybrid controller, illu-
strated in Fig. 4, with two parts: A transient state automaton for
fast transition and a steady-state automaton for local asymptotic
Table 1
The discrete modes of the two interleaved boost converter and their equilibrium
points.
Discrete
modes
Input signals Currents
evolution
Equilibrium point
u1 u2 iL1
iL2 x
qi
eq
q1 0 0 ↘ ↘ vi
2Rþr
vi
2Rþr
2Rvi
2Rþr
!T
q2 1 0 ↗ ↘ vi
r
vi
Rþr
Rvi
Rþr
!T
q3 0 1 ↘ ↗ vi
Rþr
vi
r
Rvi
Rþr
!T
q4 1 1 ↗ ↗ vi
r
vi
r
0
h iT
Iref1
Iref2
1q
1q
2q
3q
Iref1
Iref2
2q
3q
Iref1
Iref2
3q
2q
4q
4q
Fig. 3. Projection of the desired limit cycle in the currents plane.
Fig. 4. The proposed adaptive hybrid control scheme for the interleaved boost
converter.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436 427
4. stability of the desired limit cycle. Besides, an adaptive rule for the
load resistance will be proposed using an algebraic approach.
3.1. Transient automaton controller design
In order to achieve a fast convergence of the inductance cur-
rents to a neighbor of their references Iref1
and Iref2
, one can dis-
tinguish two cases:
x0 AΩ2 with Ω2 ¼ fxAX∣iL2
4iL1
g: The selected discrete mode in
this region should ensure a decreasing value of the current iL2
and an increasing one for the current iL1
to direct the converter
trajectory toward the balancing surface S1ðxÞ ¼ 0, with
S1ðxÞ ¼ iL2
ÀiL1
. From the currents evolution in Table 1, it can be
noticed that mode q2 is the only appropriate choice in this
region.
x0 AΩ3 with Ω3 ¼ fxAX∣iL2
oiL1
g: One should select the discrete
mode that guarantees an increasing value of the current iL2
and
a decreasing one for the current iL1
to reach the balancing sur-
face S1ðxÞ ¼ 0. From Table 1, the mode q3 is the only suitable one
for this purpose.
Once the converter trajectory reaches the surface S1ðxÞ ¼ 0, a
transition should be made to another discrete mode to bring the
converter currents (iL1
; iL2
) toward the reference surface S2ðxÞ ¼ 0,
with S2ðxÞ ¼ iL1
ÀIref1
. Two cases can be distinguished:
xðtsÞAΩ4 with ts is the reaching time of the converter trajectory
to the balancing surface and Ω4 ¼ fxAX∣iL1
ðtsÞoIref1
g: In order
to force the converter currents to reach the surface S2ðxÞ ¼ 0 and
preserving the invariance of the balancing surface, the discrete
mode q4 is the one suitable.
xðtsÞAΩ1 with Ω1 ¼ fxAX∣iL1
ðtsÞ4Iref1
g: In this case, the dis-
crete mode q1 is the appropriate one to reach S2ðxÞ ¼ 0 while
preserving the invariance of the balancing surface as listed in
Table 1.
Fig. 5 shows a graphical representation, in the currents phase
plane, of the transient automaton controller. The converter tra-
jectory evolution can be highlighted as follows: the first initial
condition x01 belongs to the region Ω3 where mode q3 should be
activated. The converter trajectory x(t) evolves through the
dynamics _x ¼ f q3
ðxÞ until hitting the balancing surface S1ðxÞ ¼ 0 at
the instant ts. In this case, the state xðtsÞ belongs to the region Ω4
and hence mode q4 is selected to charge the inductors currents
until reaching the reference surface S2ðxÞ ¼ 0. After that, a steady-
state controller must be activated to ensure the local stability of
the desired cyclic behavior.
Fig. 6 illustrates the hybrid automaton of the developed hybrid
controller with both transient and steady control parts, where
each node represents a discrete mode and the arrows indicate the
possible discrete transitions. The transient automaton controller
corresponds to the above analysis where the elements ðG; T; InitÞ
are defined in the following proposition:
Proposition 1. Under the transient automaton controller shown in
Fig. 6 and defined by the guard conditions (6)–(8), the input current
ðIinÞ of the 2IBC reaches its desired value ðIref Þ in finite time and
within two commutations: q3q4; q3q1; q2q4, or q2q1. The initial dis-
crete mode depends on the initial continuous state as follows:
Init ¼ ðInitðq1Þ Â q1Þ [ ðInitðq2Þ Â q2Þ [ ðInitðq3Þ Â q3Þ
[ðInitðq4Þ Â q4Þ ð6Þ
with
Initðq1Þ ¼ fxAΩ1 ðS1ðxÞ ¼ 0Þg; Initðq2Þ ¼ Ω2
Initðq4Þ ¼ fxAΩ4 ðS1ðxÞ ¼ 0Þg; Initðq3Þ ¼ Ω3
The guard conditions corresponding to the fast balance of the input
current are given by:
Gt
ðT21Þ ¼ fxAX∣ðiL2
riL1
Þ4ðiL1
4Iref1
Þg
Gt
ðT24Þ ¼ fxAX∣ðiL2
riL1
Þ4ðiL1
oIref1
Þg
Gt
ðT31Þ ¼ fxAX∣ðiL2
ZiL1
Þ4ðiL1
4Iref1
Þg
Gt
ðT34Þ ¼ fxAX∣ðiL2
ZiL1
Þ4ðiL1
oIref1
Þg ð7Þ
The guard conditions corresponding to the convergence of the
inductor currents to their references and the transition to the steady-
state controller are defined as follows:
Gts
1 ðT12Þ ¼ fxAX∣ðiL1
rIref1
Þ4ðVref o2viÞg
Gts
2 ðT12Þ ¼ fxAX∣ðiL1
rIref1
Þ4ðVref ¼ 2viÞg
Gts
3 ðT12Þ ¼ fxAX∣ðiL1
rIref1
Þ4ðVref 42viÞg
Gts
1 ðT42Þ ¼ fxAX∣ðiL1
ZIref1
Þ4ðVref o2viÞg
Gts
2 ðT42Þ ¼ fxAX∣ðiL1
ZIref1
Þ4ðVref ¼ 2viÞg
Gts
3 ðT42Þ ¼ fxAX∣ðiL1
ZIref1
Þ4ðVref 42viÞg ð8Þ
Proof. See the Appendix.
3.2. Steady state automaton controller design
The steady-state controller must operate in a cyclic fashion to
guarantee the periodic hybrid motion depicted in Fig. 3, which
corresponds to a three distinct converter operations depending on
the desired output voltage Vref as follows:
Vref o2vi: The limit cycle is characterized by the discrete
sequence q2q1q3q1 where the spent time in mode qi before the
transition to mode qj is denoted tÃ
ij and given by:
tÃ
21 ¼ tÃ
31 ¼ dT; tÃ
12 ¼ tÃ
13 ¼ ð0:5ÀdÞT ð9Þ
with T ¼ tÃ
21 þtÃ
12 þtÃ
31 þtÃ
13 is the period of the limit cycle, which
can be generally fixed depending on the switching frequency
f¼1/T of the controlled semiconductor devices (sw1 and sw2).
Fig. 7a illustrates the hybrid trajectory waveforms of the 2IBC in
this case where the current ripples are listed in Table 2.
Vref ¼ 2vi: This case is a transition one between case 1 and case
3 where the discrete sequence is q2q3. The input current ripple
is equal to zero and the other ripples are provided in Table 2.
balancing
Fig. 5. State space partition of the 2IBC under the proposed transient state
controller.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436428
5. Fig. 6. The proposed hybrid automaton controller of the 2IBC.
Fig. 7. Projection of the desired limit cycle in the currents plane.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436 429
6. The spent time in each mode is given by:
tÃ
23 ¼ tÃ
32 ¼ 0:5T; ð10Þ
The converter trajectory in steady-state is presented in Fig. 7b.
Vref 42vi: The converter trajectory waveforms are illustrated in
Fig. 7c where the limit cycle is defined by the discrete sequence
q2q4q3q4 with the following spent times:
tÃ
24 ¼ tÃ
34 ¼ ð1ÀdÞT; tÃ
42 ¼ tÃ
43 ¼ ðdÀ0:5ÞT ð11Þ
The corresponding current ripples are reported in Table 2.
From the above analysis, we note that the desired limit cycle is
completely defined by the discrete sequence and the spent times,
which depend on the desired switching frequency f, the input
voltage and the desired output voltage.
From the fact that the desired limit cycle has three geometric
shapes, one can conclude that the steady-state controller must
have three parts depending on the desired voltage Vref for a given
switching frequency and input voltage as proposed in Fig. 6. In
each part, we have the desired discrete sequence defined by a
closed unidirectional automaton where the guard conditions,
denoted Gs
ðTijÞ, should be designed to guarantee the local
asymptotic stability of the desired limit cycle. Transitions between
the three parts, denoted ci with iAf1; 2; 3g, occur if the reference
voltage is changed and does not meet the actual part. The condi-
tions c1; c2 and c3 are valid if the reference output voltage verifies
the conditions Vref o2vi; Vref ¼ 2vi and Vref 42vi respectively.
Proposition 2 outlines the steady-state controller of the 2IBC.
Proposition 2. Under the proposed steady-state controller in Fig. 6
with the guard conditions (12)–(14), the desired limit cycle of the
2IBC depicted in Fig. 3 is locally asymptotically stable.
Part 1 ðVref oviÞ:
Gs
ðT21Þ ¼ fxAX∣iL1
ZIref1
þΔi1g
Gs
ðT13Þ ¼ fxAX∣Iin rIref ÀΔig
Gs
ðT31Þ ¼ fxAX∣iL2
ZIref2
þΔi2g
Gs
ðT12Þ ¼ fxAX∣Iin rIref ÀΔig ð12Þ
Part 2 ðVref ¼ viÞ:
Gs
ðT23Þ ¼ fxAX∣iL2
rIref2
ÀΔi2g
Gs
ðT32Þ ¼ fxAX∣iL1
rIref1
ÀΔi1g ð13Þ
Part 3 ðVref 4viÞ:
Gs
ðT24Þ ¼ fxAX∣iL2
rIref2
ÀΔi2g
Gs
ðT43Þ ¼ fxAX∣Iin ZIref þΔig
Gs
ðT34Þ ¼ fxAX∣iL1
rIref1
ÀΔi1g
Gs
ðT42Þ ¼ fxAX∣Iin ZIref þΔig ð14Þ
Proof. See Appendix.
The guard conditions (12)–(14) are obtained from the limit
cycle trajectory computation based on the dynamics of each dis-
crete mode. For example, let us consider the guard conditions
design in part 1 where the discrete sequence is q2q1q3q1.
For the discrete mode q2, the inductor current iL1
increases
(charging case) where an upper constraint ðIref1
þΔi1Þ is chosen.
Besides, the inductor current iL2
decreases (discharging case) but it
is not used due to the necessity of other intermediate ripple cal-
culation, which can be remarked in Fig. 7a. Furthermore, the input
current (Iin) is avoided because its dynamic depends on the con-
verter state. Using the same reasoning and by symmetry, the guard
condition Gs
ðT31Þ is obtained. In mode q1, the input current
decreases, which allows us to add the lower constraint ðIref ÀΔiÞ
for input current ðIinÞ in Gs
ðT12Þ and Gs
ðT13Þ. The same thought is
applied to part 2 and part 3 for the guards design.
The suggested hybrid controller shown in Fig. 6 and defined by
the guard conditions (6)–(8) for the transient part and (12)–(14)
for the steady part requires only one condition to be verified at
each instant to determine the next discrete mode, which is
attractive for practical implementations.
3.3. Adaptive rule based on an algebraic approach
From the guard conditions, the hybrid controller can be clas-
sified as a current control loop with the aim to maintain the
output voltage at a desired level. In fact, the used reference current
depends on the load resistance, which may affect the output vol-
tage regulation. For that purpose, an online estimation of the load
resistance should be developed for online adjustment of the
hybrid control scheme. We opt for algebraic techniques for the
load resistance estimation, which can be reliably achieved in real
time that depends only on the arithmetic precision of the used
processor [32–34].
Let us consider the output capacitor voltage dynamic:
voðtÞ
1
R
¼ ð1Àu1ðtÞÞiL1
ðtÞþð1Àu2ðtÞÞiL2
ðtÞÀCo
dvo
dt
ðtÞ
Using the Laplace transformation for each discrete mode and
taking into account that the control inputs are constant (u1ðtÞ ¼ u1
and u2ðtÞ ¼ u2), one can obtain:
1
R
voðsÞ ¼ ð1Àu1ÞiL1
ðsÞþð1Àu2ÞiL2
ðsÞÀCoðsvoðsÞÀvoð0ÞÞ
with s is the Laplace variable. To get rid of the initial condition
voð0Þ, we differentiate both sides with respect to s as follows:
1
R
dvo
ds
ðsÞ ¼ ð1Àu1Þ
diL1
ds
ðsÞþð1Àu2Þ
diL2
ds
ðsÞÀCoðvoðsÞþs
dvo
ds
ðsÞ
Time differentiations in this expression, i.e. multiplication by s in
the operational form, can be avoided by multiplying both sides by
a give power of sÀ1
. Moreover, as the integral plays the role of a
low-pass filter, one seeks relation in which every time-function
appears inside an integral in the time domain. By multiplication by
sÀ2
, one obtains:
1
s2
dvo
ds
ðsÞ
|fflfflfflfflffl{zfflfflfflfflffl}
nðsÞ
1
R
¼ ð1Àu1Þ
1
s2
diL1
ds
ðsÞþð1Àu2Þ
1
s2
diL2
ds
ðsÞÀCo
1
s2
voðsÞþ
1
s
dvo
ds
ðsÞ
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
dðsÞ
Returning to time domain using the inverse Laplace transforma-
tion, one gets an algebraic estimator of the load resistance:
Table 2
Different state ripples of 2IBC.
Ripples Δi1 Δi1 Δi
Case 1 vi ÀrIref1
2L
dT
vi ÀrIref2
2L
dT
Vref Àvi ÀrIref1
L
ð0:5ÀdÞT
Case 2 vi ÀrIref1
4L
T
vi ÀrIref2
4L
T
0
Case 3 Vref þrIref1
Àvi
2L
ð1ÀdÞT
Vref þrIref2
Àvi
2L
ð1ÀdÞT
vi ÀrIref1
L
ðdÀ0:5ÞT
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436430
7. identification:
~RðtÞ ¼
nðtÞ
dðtÞ
ð15Þ
with:
nðtÞ ¼
Z T
0
ðT ÀσÞðÀσÞvoðtÀσÞdσ ð16aÞ
dðtÞ ¼
Z T
0
ðT ÀσÞ ðÀσÞ ð1Àu1ÞiL1
ðσÞþð1Àu2ÞiL1
ðσÞ
À Á
ÀCovoðσÞ
 ÃÂ
þCoσvoðσÞŠdσ ð16bÞ
This estimator is not asymptotic, it can be evaluated for any
t4T and give a real-time estimation of R. In practice, the integrals
appearing in (16) are calculated by discrete methods (e.g. the
trapezium rule) using a finite number of samples of iL1
, iL1
and vo in
the time-interval ½tÀT; tŠ.
4. Simulation results
For practical purposes, designing the converter parameters,
especially passive components, is of utmost importance. To this
end, it is necessary to reveal the existing links between the
switching frequency, the output voltage, the current and voltage
ripples, and the passive components. This has already been dis-
cussed in the literature. For brevity reasons, only the most
important equations will be mentioned.
In CCM operation, the minimal required values for the passive
components are obtained by considering the worst case in terms
of ripples, which corresponds to the duty cycles d¼0.25 and
d¼0.75. These are given by
Lmin ¼
vo
8ΔIin;CCM;max f
ð17aÞ
Cmin ¼
vo
4RminΔvo;CCM;max f
ð17bÞ
with the output voltage vo, the desired switching frequency f ¼ 1
T,
and the maximum allowed current ripple ΔIin;CCM;max and voltage
ripple Δvo;CCM;max. A typical converter with the parameters in
Table 3 will be studied in closed loop under the hybrid controller
presented in Fig. 6 and defined by the two propositions alongside
the adaptive rule equations (16)–(17). The initial value of the load
estimator R0 is fixed at 15 Ω where the evaluation starts after
ϵ¼0.5 ms and re-initialized each period Te ¼ 2 ms. Performance
and robustness of the adaptive hybrid controller will be checked
through different scenarios and tested with a fuel cell source in the
next subsections.
4.1. Variable reference output voltage
Fig. 8 illustrates the continuous state evolution of the 2IBC in
closed loop for a variable reference output voltage. At startup,
the reference input current Iref that corresponds to Vref ¼ 35 V is
calculated using (4), which is perturbed by the wrong value of
the estimated resistor load ðRe ¼ R0Þ. The hybrid controller forces
the input current to converge rapidly to Iref ¼ 4:08 A, as it can be
remarked from Fig. 8b, which justifies the overshoot in the
output voltage. After ϵ ¼ 0:5 ms, the algebraic estimator pro-
vides the real value of the load resistance, as illustrated in Fig. 9,
to the hybrid controller. The latter overcomes the situation and
stabilizes quickly the converter state around its reference
xref ¼ ½1:53 A 1:53 A 35 VŠT
. The reached limit cycle is depicted in
Fig. 10a, which has the discrete sequence q2q1q3q1. The current
ripples are obtained from Table 2 for a fixed frequency f¼10 Hz.
At t¼0.01 s, the reference voltage Vref is decreased by 5 V. The
hybrid controller allows us to bring the input current in finite time
to the new desired value Iref ¼ 2:25 A and forces the converter
trajectory to converge to the optimal limit cycle using part 1 of the
steady-state controller as it can be observed from the used discrete
modes in Fig. 10b. In the interval [0.02 s, 0.03 s], the reference
voltage is set to 40 V. The hybrid controller uses part 2 of the
steady-state controller to stabilize the optimal limit cycle in this
case as shown in Fig. 10c, which contains only the discrete modes
q2 and q3. It should be noted that the input current ripple is equal
to zero as it can be remarked from the currents evolution in
Table 3
Converter parameters.
Parameter vi L; r Co f R0
Value 20 V 3.3 mH, 1 mΩ 23 μF 10 kHz 15 Ω
Fig. 8. State evolution of the 2IBC for a variable load resistance.
Fig. 9. Load estimation based on the algebraic approach.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436 431
8. Fig. 8b. In the last time interval, the hybrid controller drives the
converter state to its new reference xref ¼ ½2:53 A 2:53 A 45 VŠT
quickly where the reached limit cycle is depicted in Fig. 10d. The
used discrete sequence is q2q4q3q4 because the reference output
voltage Vref verifies the part 3 condition ðVref 42viÞ of the steady-
state controller.
In summary, the adaptive hybrid controller exhibits interesting
properties such as: minimum setting time, zero steady-state error
and a fixed operating frequency in steady-state (f¼10 kHz). Next,
we will proceed with the load resistance variations for adaptive
property test of the hybrid controller.
4.2. Variable load resistance
Fig. 11 shows the obtained results for a desired output voltage
Vref ¼ 35 V and a variable load resistance. The latter is increased by
Fig. 10. Projection of the reached limit cycle in the currents plane ðiL1
; iL2
Þ and the corresponding discrete mode evolution.
Fig. 11. State evolution of the 2IBC for a variable load resistance.
Fig. 12. Evolution of the real and the estimated load resistance value.
Fig. 13. PEM fuel cell characteristics V–I and P–I.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436432
9. 5 Ω from 20 Ω to 30 Ω each 10 ms and decreased by 10 Ω at the
instant 30 ms. Fig. 9 shows the algebraic estimator response under
these disturbances. The algebraic estimator tries to detect and
reject any load variation by the re-initialization of the algebraic
formulae each 2 ms, which is clear from the periodic small over-
shoots in Fig. 12. Once the load resistance is estimated, the hybrid
controller will be updated by a new corrected reference input
current to reject the load perturbation. The obtained results
illustrate the effectiveness and the robustness of the hybrid con-
troller in spite of these fast variations.
4.3. Association of the 2IBC with a fuel cell source
Fuel cell systems are increasingly used in the last decade in
automotive applications, which are classified as clean energy with
zero CO2 emission. In this part, we consider an example of 1.26 kW
proton exchange membrane (PEM) fuel cell with the P–I and V–I
characteristics shown in Fig. 13, which is provided in MATLAB
s
SIMPOWER toolbox.
Fig. 14 illustrates the 2IBC state evolution for the output voltage
reference and a variable load resistance. One can remark that the
fuel cell Vref ¼ 80 V has a minimal ripple in different phases of load
variations. The adaptive hybrid controller is able to drive the
converter state x to its reference quickly and with a good tracking.
The robustness of the controller despite load variations is clearly
observed (Fig. 16). The closed loop maintains the control require-
ments in spite of fuel cell stack voltage variations presented in Fig.
15.
Table 4 shows a qualitative comparison between the proposed
control scheme based on hybrid automata theory and some other
existing control strategies for the conventional boost converter
and the interleaved one. One may read the proposed controller as
an extension for the interleaved case of the controller presented in
[35] for the conventional boost converter. The problem of the
phase shifting between the control signals that does not show up
in the conventional boost has been solved implicitly for the two-
interleaved converter by considering a limit cycle stabilization
problem in CCM. However, the case of DCM is beyond the scope of
this paper and will be dealt with in future work.
5. Conclusions and future works
In this paper, a new adaptive hybrid control scheme is devel-
oped for the asymptotic stabilization of the desired limit cycle of
two phase interleaved boost converter. From practical point of
view, this corresponds to fast transient and low input current
achievements, which is advantageous for many real world appli-
cations such as: fast MPPT with low fluctuations around the
maximum power point, extended lifetime of fuel cell system and
solar panels, high efficiency and enhanced thermal properties of
the converter, etc.
The controller is developed via a hybrid automaton formalism
with two parts: (1) a transient state automaton for fast transient
and (2) a steady-state automaton for local limit cycle stabilization.
An online adaptive rule based on the algebraic approach is also
investigated for robustness purpose. Mathematical proofs and
simulation results confirm the effectiveness and the robustness of
Fig. 14. State evolution of the 2IBC associated with fuel cell source under a variable
load resistance.
Fig. 15. Fuel cell stack voltage.
Table 4
Qualitative comparison.
Previous works Control Model nature Phase shift Studied
modes
Complexity Applicability
Giral et al. [36] Sliding mode-based Instantaneous model Enforced in OL with latch CCM Medium Two-interleaved
Hubber et al. [37] Open loop control Instantaneous model Enforced in OL with delay CCM/DCM Simple Two-interleaved
Thammasiriroj et al. [38] Flatness-based Average model Enforced in OL with PWM CCM Very high N-interleaved
Sreekumar and Agarwal
[35]
Limit cycle
stabilization
Hybrid model – CCM/DCM Simple Conventional DC–DC
boost
Proposed controller Limit cycle
stabilization
Hybrid model Controlled in CL by the limit cycle
stabilization
CCM Medium Two-interleaved
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436 433
10. the suggested controller under varying load and input voltage. A
PEM fuel cell source associated with the 2IBC is also highlighted
where satisfactory results are obtained.
As a future work, a generalization of the proposed hybrid
controller to n-phase interleaved boost converter and other
multilevel topologies will be considered. A complete study of
systems including different renewable and clean energy hybrid
sources will be investigated. An adaptive hybrid controller for
continuous conduction mode (CCM) and discontinuous conduc-
tion mode (DCM) operation of the converter for light loads will
also be discussed.
Appendix A
Proposition 1
Proof. From the transient state automaton configuration and the
developed guard conditions, the input current Iin reaches its
reference Iref in finite time if the following conditions are verified:
Finite time reachability of the balancing surface ðS1ðxÞ ¼ 0Þ for
x0 AΩ2 [ Ω3.
Invariance of the balancing surface.
Finite time reachability of the reference surface ðS2ðxÞ ¼ 0Þ for
xðtsÞAðS1ðxÞ ¼ 0Þ.
Roughly speaking, for any continuous initial condition in X, the
input current has to reach the balancing surface in finite time
(condition 1) and remain there (the invariance condition). Besides,
in the balancing surface, we must choose a discrete mode that
exhibits finite time reachability of the inductor currents to their
references.
By taking into consideration that all the state matrices of the
discrete modes are Hurwitz, the first and the last conditions are
equivalent to the following statements proof:
x
q2
eq AΩ3; x
q3
eq AΩ2; x
q1
eq AΩ4 ðS1ðxÞ ¼ 0Þ;
x
q4
eq AΩ1 ðS1ðxÞ ¼ 0Þ:
Indeed, if for example an initial condition x0 belongs to Ω2 then
the discrete mode q2 will be activated, and from the fact that the
stable equilibrium point is in the complementary region of Ω2, the
converter trajectory must pass through the balancing surface,
which is equivalent to finite time reachability of the balancing
surface ðS1ðxÞ ¼ 0Þ from one side. The same thought is valid in the
other side for x0 AΩ3. Once the converter trajectory hits the bal-
ancing surface a transition to mode q1 or mode q4 will be done.
Fortunately, from the dynamics of these modes, it is clear that the
balancing surface is invariant. It remains to prove that the equili-
brium point of mode q1 is on the balancing surface and belongs to
the opposite region (Ω4) with the same thought for mode q4 to
conclude with the finite time attractivity of the reference surface.
Let us start by the first statement:
x
q2
eq AΩ3⟹ieq
L2
oieq
L1
From Table 1, we have:
ieq
L2
¼
vi
Rþr
oieq
L1
¼
vi
r
which proves the first statement. The second statement x
q3
eq AΩ2
can be verified with same manner.
The third statement can be proved as follows:
x
q1
eq AΩ4 ðS1ðxÞ ¼ 0Þ⟹ieq
L2
¼ ieq
L1
oIref1
From Table 1, one can remark that ieq
L2
¼ ieq
L1
¼ vi
2R þr and it remains to
prove only the following condition:
vi
2Rþr
oIref1
¼
1
2
V2
ref
Rvi
Let us begin by the boost property Vref 4vi and multiplying both
sides by Vref
2Rvi
, one can get:
1
2
V2
ref
Rvi
4
Vref
2R
4
Vref
2Rþr
4
vi
2Rþr
Hence the statement x
q1
eq AΩ4 ðS1ðxÞ ¼ 0Þ is proved. The last
statement can be checked by taking into consideration that the
parasitic resistance r is negligible where a reference input current
cannot be bigger than vi
r . □
0 0.01 0.02 0.03 0.04
40
45
50
Time (s)
LoadResistance()
R
R
e
Ω
Fig. 16. Evolution of the real and the estimated load resistance value.
Fig. 17. Eigenvalues of the Jacobian of the Poincaré map in case 1.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436434
11. Proposition 2
Proof. The local stability of the desired limit cycle can be proved
using the following theorem [39], and the reader may refer to
[40,41,35] for more detail and for various applications to multi-
level and classical power converters.
Theorem 1. Consider a general piecewise linear system with the
form given by (1). Assume that there exists a limit cycle γ with period
T, and defined by the discrete sequence q1q2…qN. Guard condition
between mode qi to mode qj, denoted GðTijÞ, is given by a hyperplane
of dimension nÀ1 as follows:
GðTijÞ ¼ fxAX∣Cijxþdij ¼ 0g ð18Þ
with Cij AR1Ân
and dij AR.
The stability analysis of the limit cycle γ can be checked by looking
at the eigenvalues of the Jacobian of the Poincaré map P as follows:
dP ¼ dPk1…dP34dP23dP12 with dPij ¼ IÀ
f qi
ðxÃ
ijÞCij
Cijf qi
ðxÃ
ijÞ
!
eAitÃ
ij ð19Þ
where xÃ
ij is the switching state between mode qi and mode qj, which
belongs to the guard condition GðTijÞ. The local stability of the limit
cycle γ can be checked as follows:
If the map dP has all its eigenvalues inside the unit circle, then the
limit cycle γ is locally asymptotic stable.
If at least one of the eigenvalues is outside the unit circle, then the
limit cycle γ is unstable.
We will use this theorem to prove the local stability of the
desired limit cycle under the proposed hybrid steady-state con-
troller in the following three cases.
Case 01 ðVref o2viÞ: In this case, the Jacobian of the Poincaré
map that corresponds to the discrete sequence q2q1q3q1 is
dP ¼ dP12dP31dP13dP21. Transitions between the discrete modes of
the discrete sequence occurs in 2-dimensional hyperplanes
respecting (18), which can be defined using (12) as follows:
C12 ¼ ½1 1 0Š; d12 ¼ ÀðIref ÀΔiÞ
C31 ¼ ½0 1 0Š; d31 ¼ ÀðIref2
þΔi2Þ
C13 ¼ ½1 1 0Š; d13 ¼ ÀðIref ÀΔiÞ
C21 ¼ ½1 0 0Š; d21 ¼ ÀðIref1
þΔi1Þ
8
:
The switching points between the discrete modes of the desired
limit cycle are given as follows:
xÃ
12 ¼ ½Iref1
ÀΔi1; Iref2
þΔi1 ÀΔi; Vref þΔvŠT
xÃ
31 ¼ ½Iref1
ÀΔi2 þΔi; Iref2
þΔi2; Vref ÀΔvŠT
xÃ
13 ¼ ½Iref1
þΔi2 þΔi; Iref2
ÀΔi2; Vref þΔvŠT
xÃ
21 ¼ ½Iref1
þΔi1; Iref2
ÀΔi1 þΔi; Vref ÀΔvŠT
8
:
Replacing these results and the corresponding discrete mode
dynamic in (19), one can get the Jacobian of the Poincaré map.
Using the converter parameters in Table 3, the eigenvalues of dP
are evaluated numerically for a variable reference voltage ðVref o
2viÞ and load resistance, which are depicted in Fig. 17. All the
eigenvalues are inside the unit circle, which proves the local sta-
bility of the desired limit cycle under the proposed steady-state
controller in this case.
Case 02 ðVref ¼ 2viÞ: In this case, the discrete sequence q2q3 has
the Jacobian of the Poincaré map dP ¼ dP32dP23. The switching
surfaces in the form (18) and the switching points are given as
Fig. 18. Eigenvalues of the Jacobian of the Poincaré map in case 2.
Fig. 19. Eigenvalues of the Jacobian of the Poincaré map in case 3.
M. Bougrine et al. / ISA Transactions 66 (2017) 425–436 435
12. follows:
C32 ¼ ½1 0 0Š; d12 ¼ ÀðIref1
ÀΔi1Þ
C23 ¼ ½0 1 0Š; d31 ¼ ÀðIref2
ÀΔi2Þ
(
xÃ
32 ¼ ½Iref1
ÀΔi1; Iref2
þΔi2; Vref ŠT
xÃ
23 ¼ ½Iref1
þΔi1; Iref2
ÀΔi2; Vref ŠT
(
Fig. 18 illustrates that all the eigenvalues of the dP are inside
the unit circle for varying load resistance, which proves the local
stability of the desired limit cycle in this case.
Case 03 ðVref 42viÞ: The desired limit cycle has the discrete
sequence q2q4q3q4 where its Jacobian of the Poincaré map is
dP ¼ dP42dP34dP43dP24. From the guard conditions given by (14),
one can get the following switching surfaces parameters:
C42 ¼ ½1 1 0Š; d42 ¼ ÀðIref þΔiÞ
C34 ¼ ½1 0 0Š; d34 ¼ ÀðIref1
ÀΔi1Þ
C43 ¼ ½1 1 0Š; d43 ¼ ÀðIref þΔiÞ
C24 ¼ ½0 1 0Š; d24 ¼ ÀðIref2
ÀΔi2Þ
8
:
The switching points between the discrete modes of the desired
limit cycle are given as follows:
xÃ
42 ¼ ½Iref1
þΔi1; Iref2
ÀΔi1 þΔi; Vref ÀΔvŠT
xÃ
34 ¼ ½Iref1
ÀΔi1; Iref2
þΔi1 ÀΔi; Vref þΔvŠT
xÃ
43 ¼ ½Iref1
ÀΔi2 þΔi; Iref2
þΔi2; Vref ÀΔvŠT
xÃ
24 ¼ ½Iref1
þΔi2 ÀΔi; Iref2
ÀΔi2; Vref þΔvŠT
8
:
Fig. 19 shows that all the eigenvalues of the dP are inside the
unit circle for different values of Vref 42vi and varying load
resistance, which proves the local stability of the desired limit
cycle in this case.
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