A Real-Time ANN for Estimation Digital Twin parameters in Health Indication of Flyback Converter

A Real-Time ANN for Estimation Digital Twin parameters in Health Indication of Flyback Converter | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Real-Time ANN for Estimation Digital Twin parameters in Health Indication of Flyback Converter Ehsan Rahmanian Koushkaki, Amirhosein Rajaei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3861997/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper proposes a real-time artificial neural network (ANN) for estimation digital twin parameters in health indication of flyback converter. Indeed, the ANN is approximated digital twin parameters by using voltage input of the flyback converter and comparison of capacitor voltage and inductance current of simulated model and digital twin. Moreover, the ANN structure is picked out multi-layer perceptron (MLP) with back-propagation training algorithm. Furthermore, the ANN is used in a new real-time technique that is trained during of running of the model. However, the digital twin is calculated output voltage and inductance current by 4th order runge-kutta method. The formula of model is determined with state-space averaged (SSA) model technique. Finally, as the output voltage of simulated model and digital twin are the same, the component parameters are compared with initial values and health of converter is detected. The model is tested in some variety scenarios, such as degradation of capacitor, MOSFET, diode and transformer magnetization inductance, and the outcome of them are presented. Also, the method is tested in changing input voltage of converter and duty cycle. The studied model is simulated in MATLAB/Simulink and the digital twin and the ANN block are done in S-function. Digital Twin Artificial Neural Network flyback Converter Health Indication State Space Averaged model in Power Electronic Converter Runge-kutta method Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1 Introduction Todays, renewable energy sources are popular in power systems, because of significantly advantages. However, power electronic converters are necessary to convert their energy to transfer and consume, so the health of these converters are obligatory. Indeed, some researchers has been done variety project for fault diagnosis which could happen abrupt due to over stress conditions [ 1 ]. In addition, after long-term operation some components of power converter become too fragile to withstand the normal electrical and thermal stresses and a collapse of the entire system may happen [ 2 ]. Alternatively, condition monitoring is important and meaningful for power converters to anticipate of degradation progress and replace the fragile component before breakdown. Monitoring condition is used for capacitor and power electronic component in [ 3 ], [ 4 ]. Most of the condition monitoring methods have need of additional circuits and sensors which could increase complexity and cost of system. Consequently, digital twin has superiority among other methods because of eliminating additional circuit and sensors. In [ 2 ] digital twin and conventional procedure of condition monitoring were compared and previous manners were described. Also, health indication of buck converter is done with digital twin and data analysis was done by particle swarm optimization (PSO) and the result of tests in different condition were clustered. Digital twin also is used to diagnose abrupt fault in distributed photovoltaic (PV) system that followed by the error residual generation PV and evaluation digital twin [ 1 ]. In [ 5 ], an approach is proposed for the online diagnostic analysis of power electronic converters utilizing real-time, probabilistic digital twinning. Under this approach, a digital twin of a power converter is defined as a real time, probabilistic simulation model with stochastic variables, developed using generalized polynomial chaos expansion. Bayesian Regularization along with ANN and random forest based machine learning to model power converters and analyze their performance was presented [ 6 ] and authors were suggested that the data can be used for create digital twins of power converters in practical circuits, optimize performance and predict fault conditions. Artificial Intelligent (AI) has variety usage in different type applications, such as controller [ 7 ], system identification [ 8 ], clustering [ 9 ], estimation. Fuzzy systems, PSO, ANN and genetic algorithm are the most popular because of their significant advantages. However, ANN is so powerful to solve nonlinear equations and based on [ 2 ], it is a potential way for condition monitoring and it needs off-line training to use, so a great deal of data requires for training which the presented technique eliminate this issue. In this paper, a digital twin is presented to indicate health of flyback converter that the component parameters are determined with ANN. Moreover, the equations of digital twin are ascertained from state space averaged (SAA) model of simulated converter. The ANN is multi-layer perceptron (MLP) network with back propagation (BP) training algorithm which the ANN is trained on-line and reduce error, gradually. The case study is tested in different state of circuit and components, such as degradation of capacitor, on-state resistance of MOSFET, forward voltage of diode and transformer magnetization inductance. Also, the method is tested in changing input voltage of converter and duty cycle. 2 Digital twin of flyback converter Digital twin is a digital emulation of a physical system that analytically computes the measurable characteristic outputs in real-time [ 10 ]. In this application, it is a digital replica of physical system that could operate as physical system and the error between them is used to estimate physical component state. This technique doesn’t need physical sensors for modeling of physical system and the actual model is programmed with software. In this paper, a flyback converter is simulated in MATLAB/Simulink and a digital twin is designed to replica the converter with SAA model technique. Also, the state space equations of flyback converter are solved with 4th order Runge-Kutta method. Furthermore, a ANN estimates the digital twin parameters to reduce the error. Figure 1 shows the block diagram of operation of case study. From the figure, input is entered to physical system and digital twin and output of them are compared toogether and the error is sent to ANN for training and estimation of parameters for digital twin. 2.1 Flyback Converter In this paper, a flyback converter is simulated as details of table I. The state of switching is presented in Fig. 2 . As the figure, when the switch is on, the diode is in reverse bias and it turns off. As the switch-off time, the diode in forward bias which the diode forward voltage is 0.2 volt. Moreover, MOSFET is used as the switch that turn-on resistance is 0.001 ohm. Also, magnetization inductance of transformer ( \({\text{L}}_{\text{m}}\) ) is considered in the model and the transformer turns ratio is 1 to simplify of equations. A capacitor is chosen in output to reduce the ripple of output voltage, so the output voltage of converter equals capacitor voltage. 2.2 Digital Twin Digital twin is formula of SSA model of the converter which the state space of equations are solved with 4th order Runge-Kutta method. Indeed, SSA model equations are as below: $$\frac{{\text{d}\text{I}}_{\text{L}}}{{\text{d}}_{\text{t}}}=\left({\text{V}}_{\text{i}\text{n}}-{\text{R}}_{\text{Q}\text{o}\text{n}}{\text{I}}_{\text{L}}\right)\text{D}+\left(\frac{{\text{V}}_{\text{d}}-{\text{V}}_{\text{C}}}{\text{L}}\right)\left(1-\text{D}\right) \left(1\right)$$ $$\frac{{\text{d}\text{V}}_{\text{c}}}{{\text{d}}_{\text{t}}}=-\frac{{\text{V}}_{\text{c}}}{\text{R}}\text{D}-\left(\frac{{\text{V}}_{\text{C}}}{\text{R}\text{C}}+\frac{{\text{I}}_{\text{L}}}{\text{C}}\right)\left(1-\text{D}\right) \left(2\right)$$ Where \({\text{I}}_{\text{L}}\) is the transformer inductor current, \({\text{V}}_{\text{C}}\) is the capacitor voltage that equals with output voltage (load voltage), \({\text{V}}_{\text{i}\text{n}}\) is input voltage of converter; R, C, L, \({\text{R}}_{\text{Q}\text{o}\text{n}}\) and \({\text{V}}_{\text{d}}\) are load resistance, capacitor, inductance of transformer, on-state resistance switch and forward voltage of diode; D is 1 when the switch turns on and 0 as it turns off. Two ways can be applied to solve (1) and (2), and obtain \({\text{I}}_{\text{L}}\) and \({\text{V}}_{\text{C}}\) . One is to calculate the eigenvector and eigenvalue of differential equations and construct the general solution. Then, by using the initial values of \({\text{I}}_{\text{L}}\) and \({\text{V}}_{\text{C}}\) , the specific solution of these differential equations can be obtained [ 11 ]. This method demands heavy computation, especially the calculation of eigenvector and eigenvalue. The other one is to linearize the differential equations with acceptable accuracy, which is used in this paper. Moreover, 4th order Runge-Kutta method is used Table 1 Details of Flyback converter Parameter Value Input Voltage 180 v Switching Frequency 50 kHz Duty Cycle 40% Inductance of Transformer 20 mH Capacitor 3 µF Load Resistance 75 Ω Forward Voltage of diode 0.2 v On-state Resistance of Switch 0.001 Ω Out-put Voltage 150 v in this paper to linearize the differential equations. So, the \({\text{I}}_{\text{L}}\) and \({\text{V}}_{\text{C}}\) are as bellow (3) and (4): $${\text{I}}_{\text{L},\text{n}+1}={\text{I}}_{\text{L},\text{n}}+\frac{\text{h}}{6}\left({\text{K}}_{\text{a}1}+2{\text{K}}_{\text{a}2}+2{\text{K}}_{\text{a}3}+{\text{K}}_{\text{a}4}\right) \left(3\right)$$ $${\text{V}}_{\text{c},\text{n}+1}={\text{V}}_{\text{c},\text{n}}+\frac{\text{h}}{6}\left({\text{K}}_{\text{b}1}+2{\text{K}}_{\text{b}2}+2{\text{K}}_{\text{b}3}+{\text{K}}_{\text{b}4}\right) \left(4\right)$$ Where ka1-ka4 and kb1-kb4 are used to calculate the average change rate between (n)th and (n + 1)th step as shown below: $$\text{f}1({\text{I}}_{\text{L}},{\text{V}}_{\text{c}})=\frac{{\text{d}\text{I}}_{\text{L}}}{{\text{d}}_{\text{t}}} \left(5\right)$$ $$\text{f}2({\text{I}}_{\text{L}},{\text{V}}_{\text{c}})=\frac{{\text{d}\text{V}}_{\text{c}}}{{\text{d}}_{\text{t}}} \left(6\right)$$ $${\text{K}}_{\text{a}1}=\text{f}1({\text{I}}_{\text{L},\text{n}},{\text{V}}_{\text{c},\text{n}}) \left(7\right)$$ $${\text{K}}_{\text{b}1}=\text{f}2({\text{I}}_{\text{L},\text{n}},{\text{V}}_{\text{c},\text{n}}) \left(8\right)$$ $${\text{K}}_{\text{a}2}=\text{f}1({\text{I}}_{\text{L},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{a}1},{\text{V}}_{\text{c},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{b}1}) \left(9\right)$$ $${\text{K}}_{\text{b}2}=\text{f}2({\text{I}}_{\text{L},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{a}1},{\text{V}}_{\text{c},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{b}1}) \left(10\right)$$ $${\text{K}}_{\text{a}3}=\text{f}1({\text{I}}_{\text{L},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{a}2},{\text{V}}_{\text{c},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{b}2}) \left(11\right)$$ $${\text{K}}_{\text{b}3}=\text{f}2({\text{I}}_{\text{L},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{a}2},{\text{V}}_{\text{c},\text{n}}+\frac{\text{h}}{2}{\text{K}}_{\text{b}2}) \left(12\right)$$ $${\text{K}}_{\text{a}4}=\text{f}1({\text{I}}_{\text{L},\text{n}}+\text{h}{\text{K}}_{\text{a}3},{\text{V}}_{\text{c},\text{n}}+\text{h}{\text{K}}_{\text{b}3}) \left(13\right)$$ $${\text{K}}_{\text{b}4}=\text{f}2({\text{I}}_{\text{L},\text{n}}+\text{h}{\text{K}}_{\text{a}3},{\text{V}}_{\text{c},\text{n}}+\text{h}{\text{K}}_{\text{b}3}) \left(14\right)$$ Where h is the calculation step time between nth and (n + 1)th time step. After calculation (7)-(14) and substitute into (3) and (4), output voltage that equals with capacitor voltage be obtained. The equations are done in MATLAB/S-function in the case study and it is worked as digital twin. 2.3 Artificial Neural Network Artificial neural network is a kind of powerful of artificial intelligent which has a lot of application in variety field. Indeed, ANNs have different type with diverse training method. Usually, ANNs train and update weights and biases in off-line method and trained ANN uses for real time applications In this paper, a method is presented to train ANN in on-line method and is used in real time simulation. The ANN is determined digital twin parameters to reduce difference of output of the flyback converter and the digital twin. The structure of ANN is MLP with BP training algorithm as shown in Fig. 3. The flowchart of training method of ANN is plotted in Fig. 4 . From the picture, at the start of simulation, ANN is given some data and is trained in off-line method. Next, as the error equal target value, simulation start and the ANN is gradually trained with more data from simulated model to assess the least error. 3 simulation and results of digital twin for flyback converter Figure 5 . shows a flyback converter with digital twin to indicate health and validate the proposed method. As the figure, parameters of digital twin are estimated with ANN and digital twin is calculated capacitor voltage and inductance current with averaged model equations, which the capacitor voltage equals output voltage of converter and inductance current is input current of converter. Moreover, capacitor voltage and inductance current of simulated model and digital twin are compared together and the errors are used to update of weights and biases of ANN. Furthermore, simulated model is tested in different states and the results are analyzed. First, the case is studied in normal condition and the results are checked out. After that, health indication of flyback converter is tested in various degradation of component. 3.1 Case study in normal condition To identify parameters, the simulated model is runed in normal condition as the table I parameters. Indeed, the initial value of parameters are chosen and the digital twin is calculated capacitor voltage and inductance current. Next, the output of simulated model and digital twin are compared and the error signal is used to training ANN. At the beginning, the weights and biases of ANN are determined with random function, so they are updated with the error signal by back-propagation training method and it is continued until the error is less than threshold. However, input of ANN is the error of capacitor voltage and inductance current and input voltage of flyback converter. In addition, on-state resistance of MOSFET, capacitor capacity, forward voltage of diode and transformer magnetization inductance are obtained with ANN for the digital twin. Moreover, the digital twin is calculated capacitor voltage and inductance current with parameters that are specified by ANN. From the pictures in Fig. 6 , the ANN is accurately estimated component parameters of flyback converter for digital twin. As the figures, values of parameters are not correct at the beginning, so the ANN could correctly find out these parameters with reducing least square error of ANN. According to Fig. 6 (b) and (c), the initial value of capacitor was 20 mF, so it is estimated to 3 µF after 1.5 ms which it is shown the ability of ANN in estimation, also it is obvious for other parameters in Fig. 6 (a), (d) and (e). Figure 7 is presented the error capacitor voltage that is the comparison of flyback converter and digital twin output. From the graph, the error was 160 volt at the beginning and after some fluctuations, the error was less than threshold. Also, it is obviously shown in Fig. 8 which capacitor voltage and inductance current of flyback converter and digital twin are plotted in a graph. The digital twin with the component parameters that the ANN was determined could find out the value of flyback converter outputs in 4 ms which is acceptable. The voltage and current of MOSFET and diode are presented in Fig. 9 . As the picture, when MOSFET is on, diode is off and vice versa. A. Capacitor Degradation After a long-term operation, the capacitance may drop 5–20% because of degradation [ 12 ]. Some variety of condition can affect on changing capacitance, for instance, the temperature of environment or the quality of insulator. In this study, the capacitor is degraded 2.2% of capacitance for every step and the ANN is estimated the capacitance. The results are reported in Table II and the ANN estimation is plotted in Fig. 10 . From the details, the capacitor capacity is declined in 4 steps and it is dropped from 3 µF to 2.736 µF and the ANN is almostly estimated the capacitance for digital twin. However, averaged error of estimation is 0.945% that is suitable to sense capacitor degradation. Table.2. The Capacitance Degradation and ANN Estimation No. of case study Percentage change Capacitor capacity ANN Estimation Case 1 -2.2% 2.934 µF 2.905 µF Case 2 -4.4% 2.868 µF 2.821 µF Case 3 -6.6% 2.802 µF 2.782 µF Case 4 -8.8% 2.736 µF 2.724 µF B. MOSFET Degradation To indicate health of MOSTEF, on-state resistance is effective, because it could determine the switch degradation. As Table III, 4 cases are studied with increasing resistance that the ANN estimation is shown in this table. The table shows that the ANN can not estimate the values exactly, because the input of ANN is comparison of capacitor voltage and inductance current which the changing of on-state resistance of the switch does not affect on them, so the ANN is estimated with more error. However, the details are shown that the ANN could distinguish on-state resistance of MOSFET become greater, regardless of the amount of error. Table.3. The on-state resistance of MOSFET and ANN Estimation No. of case study Ron_MOSFET ANN Estimation Case 1 0.0024 Ω 0.0018 Ω Case 2 0.0043 Ω 0.0033 Ω Case 3 0.0062 Ω 0.0046 Ω Case 4 0.0089 Ω 0.0051 Ω C. Diode health indication Diode health indication is important for flyback converter and estimation forward voltage of diode could aim to specify well-being. The results of this study in changing forward voltage of the diode are presented in table IV. As the table, the estimations are not the same as simulated model because the changing of capacitor voltage and inductance current are a few in changing forward voltage, it is obvious in Fig. 11 . Table.4. The Forward Voltage of Diode and ANN Estimation No. of case study Forward Voltage ANN Estimation Case 1 0.2 V 0.1999 V Case 2 0.5 V 0.411 V Case 3 1 V 0.865 V D. Transformer Inductance Degradation In this study, the transformer magnetization inductance is considered in the model and winding inductances are passed up. Indeed, the digital twin is calculated equations according this model and variation of the inductance is analyzed to indicate inductance degradation. Table V shows the results which the ANN could accurately determine the inductance with the data of digital twin and simulated model. Moreover, changing in inductance has affect on input current which equals with inductance current, so the ANN could sense the variation of it because it is an input of ANN. Table.5. The Transformer Magnetization Inductance and ANN Estimation No. of case study Inductance ANN Estimation Case 1 20 mH 19.97 mH Case 2 15 mH 15.01 mH Case 3 10 mH 9.998 mH Case 4 7 mH 6.898 mH E. Impact of changing in input voltage and duty cycle In flyback converter, input voltage and duty cycle may change in operation and they straightly change the output of the converter. On the other hand, the digital twin is calculated according these inputs and the ANN is estimated parameters from the error of them. So it is significant to validate the method in changing these inputs. Moreover, in this study five circumstances as the table VI are surveyed and the results are plotted in Fig. 12 . From the figure, the digital twin and the ANN can identically estimated parameters. Also, Fig. 13. shows the real component parameters of simulated model with red line and the estimation of ANN with blue dot in five cases as table VI. Table.6. The ANN Estimation in different input voltage and duty cycle No. of case study Input voltage Duty cycle Case 1 180 V 40% Case 2 160 V 40% Case 3 200 V 45% Case 4 180 V 50% Case 5 190 V 35% 4 conclusions In this paper, a real-time method is presented for health indication of flyback converter with digital twin and artificial neural network. The flyback converter is simulated in MATLAB/Simulink with component parameters and a digital twin is proposed to operate as same as the simulated converter. Indeed, the digital twin equations are extracted from SAA model and the equations are solved by 4th order Runge-Kutta technique. Also, an ANN is used to estimate component parameters of the flyback converter for calculation of digital twin equations and health indication of flyback converter is detected. Furthermore, inputs of ANN are input voltage of flyback converter, comparison of capacitor voltage and inductance current of the simulated model and digital twin. Confirming the inputs, the ANN is estimated on-state resistance of MOSFET, capacitance, forward voltage of diode and transformer magnetization inductance. However, the ANN is designed and programmed in new real time method that is trained when simulation is runed and the ANN could reduce the error during the simulation. In conclusion, the method is tested in some variety states (degradation of capacitor, on-state resistance of MOSFET, forward voltage of diode and transformer magnetization inductance and changing input voltage and duty cycle) to verify feasibility of the method and the results are presented. From the results, the capability of the method in health indication of the converter is proved. To compare with previous method, this procedure has more accurate and could identify the system with less time and adaptability of the method is more because of ANN potency. Declarations Author Contribution Ehsan Rahmanian Koushkaki wrote the main manuscript and Amirhosein Rajaei was as supervisor. References Palak Jain, Jason Poon, Jai Prakash Singh, Costas Spanos, Seth R. Sanders, Sanjib Kumar Panda, “A Digital Twin Approach for Fault Diagnosis in Distributed Photovoltaic Systems”, IEEE Transactions on Power Electronics, Volume: 35, Issue: 1, Jan. 2020. Yingzhou Peng, Shuai Zhao, Huai Wang,” A Digital Twin based Estimation Method for Health Indicators of DC-DC Converters” IEEE TRANSACTIONS ON POWER ELECTRONICS, Volume: 36, Issue: 2, Feb. 2021. S. Dusmez and B. Akin, “An accelerated thermal aging platform to monitor fault precursor on-state resistance,” in 2015 IEEE International Electric Machines Drives Conference (IEMDC), May 2015, pp. 1352– 1358. M. A. Vogelsberger, T. Wiesinger, and H. 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Low, “Low sampling rate online parameters monitoring of dc-dc converters for predictive-maintenance using biogeographybased optimization,” IEEE Transactions on Power Electronics, vol. 31, no. 4, pp. 2870–2879, April 2016. H. Soliman, H. Wang, and F. Blaabjerg, “A review of the condition monitoring of capacitors in power electronic converters,” IEEE Transactions on Industry Applications, vol. 52, no. 6, pp. 4976–4989, Nov. 2016. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3861997","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267404285,"identity":"eb8e1619-5b4f-4f49-95c8-e31ecd324ba8","order_by":0,"name":"Ehsan Rahmanian Koushkaki","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYJACZhDBxsDA+ECigoHBgBQtzAYWZ0jRAtIlUdlGhBZ+Bt6Hnwtz7PL42M8ekLg577C8OXvzAYYfFdtwapFsYDeWnrktuZiNJy/BcOa2w4Y7e44lMPacuY1Ti8EBNgZp3m3MiW0MOQbJktsOM264kWPAzNiGW4v9ATbm37zb6hPb+N8YHP4757A9QS0GDGxsQFsOJ7ZJ5Bg2SDYcTiSoReIwG5s177bjQC1vjBkkjqUnbzhzLOEgPr/wt7cx3+bdVp04vz/H/IdEjbXthuPNBx/8qMCtBR4pUNAMJg/gVo8J6khRPApGwSgYBSMEAABkMVQaXR1AUgAAAABJRU5ErkJggg==","orcid":"","institution":"Shiraz University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Ehsan","middleName":"Rahmanian","lastName":"Koushkaki","suffix":""},{"id":267404286,"identity":"fb6db760-b5af-47e8-85a8-fac57e692d8b","order_by":1,"name":"Amirhosein Rajaei","email":"","orcid":"","institution":"Shiraz University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Amirhosein","middleName":"","lastName":"Rajaei","suffix":""}],"badges":[],"createdAt":"2024-01-14 03:46:52","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3861997/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3861997/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49742164,"identity":"71676de7-2b16-4b5c-844f-5d0596d63e52","added_by":"auto","created_at":"2024-01-17 09:37:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":17826,"visible":true,"origin":"","legend":"\u003cp\u003eBlock diagram of case study\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/55f73fed6fc01066eb0efecd.png"},{"id":49742538,"identity":"eb0747ec-fe37-474d-a92c-e2b4bebc4239","added_by":"auto","created_at":"2024-01-17 09:45:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":19016,"visible":true,"origin":"","legend":"\u003cp\u003eCircuit of Flyback converter: (a) the model of case study; (b) switched on mood of converter and the state of the diode; (c) turn-off switch and equivalent model.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/289c9de7744937027eaed5e6.png"},{"id":49741521,"identity":"a3bf16ea-d137-4bf3-8430-84f8f2910dbf","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":38116,"visible":true,"origin":"","legend":"\u003cp\u003eArtificial Neural Network Structure\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/1850d121cba525b055665ef4.png"},{"id":49741520,"identity":"20aaa66d-8c09-4a8d-9e59-0df754c09643","added_by":"auto","created_at":"2024-01-17 09:29:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":17814,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of Artificial Neural Network Training\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/b36b4782c94a659a1c341b75.png"},{"id":49742165,"identity":"2f7a13c3-c587-40bb-adc6-b1919418e03f","added_by":"auto","created_at":"2024-01-17 09:37:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":16890,"visible":true,"origin":"","legend":"\u003cp\u003eBlock Diagram of case study\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/6cf825338d0c9869889db6a9.png"},{"id":49741523,"identity":"92c45cf3-013e-4c8f-8cff-9601a2eaffd9","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":26527,"visible":true,"origin":"","legend":"\u003cp\u003eEstimated parameters with ANN in normal condition: (a) On-state resistance of MOSFET; (b) capacitor capacity; (c) forward voltage of diode; (d) transformer magnetization inductance\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/b7026c0e52644238c011d7f3.png"},{"id":49741528,"identity":"a9d0d3a2-557b-4382-afa1-b3fe4d90826e","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":8695,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of capacitor voltage of flyback converter and digital twin\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/326507059de8065757823b73.png"},{"id":49741526,"identity":"1c20520c-e8ac-45a9-859e-77001ff6e6d2","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":25225,"visible":true,"origin":"","legend":"\u003cp\u003eCapacitor voltage and inductance current of flyback converter and digital twin: (a) capacitor voltage of Simulink (Vc-Sim.) and digital twin (Vc-DT); (b) inductance current of Simulink (IL-Sim.) and digital twin (IL-DT)\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/eb6c1ce80029c400f22e6b54.png"},{"id":49742539,"identity":"c6be53ea-d343-41df-bf73-2ef2fbd3edca","added_by":"auto","created_at":"2024-01-17 09:45:44","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":34427,"visible":true,"origin":"","legend":"\u003cp\u003eState of MOSFET and diode: (a) MOSFET and diode current; (b) MOSFET and diode voltage\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/eca2b27a924962f902b6739d.png"},{"id":49742167,"identity":"8418b4b8-371a-48d8-85bd-88a2bd498948","added_by":"auto","created_at":"2024-01-17 09:37:44","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":11928,"visible":true,"origin":"","legend":"\u003cp\u003eThe capacitance estimation by ANN in capacitor degradation condition\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/263c6777339f9a30d25f2311.png"},{"id":49741530,"identity":"8160c528-f381-4c9f-8cbf-45fcf8d99f7b","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":13589,"visible":true,"origin":"","legend":"\u003cp\u003eThe capacitor voltage in different forward voltage of diode\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/7ce107f17749a3a739d065fa.png"},{"id":49742169,"identity":"89e0ccf8-3b1e-4bd3-a3db-7d2aa88f41cc","added_by":"auto","created_at":"2024-01-17 09:37:44","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":35156,"visible":true,"origin":"","legend":"\u003cp\u003eThe ANN Estimation of component parameters in variety input voltage and duty cycle\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/fabd1f79a5b792b0d2628f3b.png"},{"id":49741532,"identity":"60d34fef-4610-4e9c-9d63-4ea22d80dcd1","added_by":"auto","created_at":"2024-01-17 09:29:44","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":25577,"visible":true,"origin":"","legend":"\u003cp\u003eThe ANN Estimation of component parameters when the input voltage and duty cycle is changed as the table VI: : (a) The on-state resistance estimation of MOSFET; (b) The capacitor estimation; (c) Forward voltage of diode estimation; (d) Magnetization inductance estimation of Transformer\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/798e24137925b8928f7f2dca.png"},{"id":61463995,"identity":"20ddd873-04b0-4798-a672-d39ab1a466f7","added_by":"auto","created_at":"2024-07-31 05:23:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":681096,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3861997/v1/f6974afa-e716-4a2a-babf-cf32c52a07b4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Real-Time ANN for Estimation Digital Twin parameters in Health Indication of Flyback Converter","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eTodays, renewable energy sources are popular in power systems, because of significantly advantages. However, power electronic converters are necessary to convert their energy to transfer and consume, so the health of these converters are obligatory. Indeed, some researchers has been done variety project for fault diagnosis which could happen abrupt due to over stress conditions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In addition, after long-term operation some components of power converter become too fragile to withstand the normal electrical and thermal stresses and a collapse of the entire system may happen [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAlternatively, condition monitoring is important and meaningful for power converters to anticipate of degradation progress and replace the fragile component before breakdown. Monitoring condition is used for capacitor and power electronic component in [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Most of the condition monitoring methods have need of additional circuits and sensors which could increase complexity and cost of system. Consequently, digital twin has superiority among other methods because of eliminating additional circuit and sensors. In [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] digital twin and conventional procedure of condition monitoring were compared and previous manners were described. Also, health indication of buck converter is done with digital twin and data analysis was done by particle swarm optimization (PSO) and the result of tests in different condition were clustered. Digital twin also is used to diagnose abrupt fault in distributed photovoltaic (PV) system that followed by the error residual generation PV and evaluation digital twin [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], an approach is proposed for the online diagnostic analysis of power electronic converters utilizing real-time, probabilistic digital twinning. Under this approach, a digital twin of a power converter is defined as a real time, probabilistic simulation model with stochastic variables, developed using generalized polynomial chaos expansion. Bayesian Regularization along with ANN and random forest based machine learning to model power converters and analyze their performance was presented [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] and authors were suggested that the data can be used for create digital twins of power converters in practical circuits, optimize performance and predict fault conditions.\u003c/p\u003e \u003cp\u003eArtificial Intelligent (AI) has variety usage in different type applications, such as controller [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], system identification [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], clustering [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], estimation. Fuzzy systems, PSO, ANN and genetic algorithm are the most popular because of their significant advantages. However, ANN is so powerful to solve nonlinear equations and based on [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], it is a potential way for condition monitoring and it needs off-line training to use, so a great deal of data requires for training which the presented technique eliminate this issue.\u003c/p\u003e \u003cp\u003eIn this paper, a digital twin is presented to indicate health of flyback converter that the component parameters are determined with ANN. Moreover, the equations of digital twin are ascertained from state space averaged (SAA) model of simulated converter. The ANN is multi-layer perceptron (MLP) network with back propagation (BP) training algorithm which the ANN is trained on-line and reduce error, gradually. The case study is tested in different state of circuit and components, such as degradation of capacitor, on-state resistance of MOSFET, forward voltage of diode and transformer magnetization inductance. Also, the method is tested in changing input voltage of converter and duty cycle.\u003c/p\u003e"},{"header":"2 Digital twin of flyback converter","content":"\u003cp\u003eDigital twin is a digital emulation of a physical system that analytically computes the measurable characteristic outputs in real-time [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In this application, it is a digital replica of physical system that could operate as physical system and the error between them is used to estimate physical component state. This technique doesn\u0026rsquo;t need physical sensors for modeling of physical system and the actual model is programmed with software. In this paper, a flyback converter is simulated in MATLAB/Simulink and a digital twin is designed to replica the converter with SAA model technique. Also, the state space equations of flyback converter are solved with 4th order Runge-Kutta method. Furthermore, a ANN estimates the digital twin parameters to reduce the error. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the block diagram of operation of case study. From the figure, input is entered to physical system and digital twin and output of them are compared toogether and the error is sent to ANN for training and estimation of parameters for digital twin.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Flyback Converter\u003c/h2\u003e \u003cp\u003eIn this paper, a flyback converter is simulated as details of table I. The state of switching is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As the figure, when the switch is on, the diode is in reverse bias and it turns off. As the switch-off time, the diode in forward bias which the diode forward voltage is 0.2 volt. Moreover, MOSFET is used as the switch that turn-on resistance is 0.001 ohm. Also, magnetization inductance of transformer (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{L}}_{\\text{m}}\\)\u003c/span\u003e\u003c/span\u003e) is considered in the model and the transformer turns ratio is 1 to simplify of equations. A capacitor is chosen in output to reduce the ripple of output voltage, so the output voltage of converter equals capacitor voltage.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Digital Twin\u003c/h2\u003e \u003cp\u003eDigital twin is formula of SSA model of the converter which the state space of equations are solved with 4th order Runge-Kutta method. Indeed, SSA model equations are as below:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\frac{{\\text{d}\\text{I}}_{\\text{L}}}{{\\text{d}}_{\\text{t}}}=\\left({\\text{V}}_{\\text{i}\\text{n}}-{\\text{R}}_{\\text{Q}\\text{o}\\text{n}}{\\text{I}}_{\\text{L}}\\right)\\text{D}+\\left(\\frac{{\\text{V}}_{\\text{d}}-{\\text{V}}_{\\text{C}}}{\\text{L}}\\right)\\left(1-\\text{D}\\right) \\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\frac{{\\text{d}\\text{V}}_{\\text{c}}}{{\\text{d}}_{\\text{t}}}=-\\frac{{\\text{V}}_{\\text{c}}}{\\text{R}}\\text{D}-\\left(\\frac{{\\text{V}}_{\\text{C}}}{\\text{R}\\text{C}}+\\frac{{\\text{I}}_{\\text{L}}}{\\text{C}}\\right)\\left(1-\\text{D}\\right) \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{I}}_{\\text{L}}\\)\u003c/span\u003e\u003c/span\u003e is the transformer inductor current, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e is the capacitor voltage that equals with output voltage (load voltage), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e is input voltage of converter; R, C, L, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{R}}_{\\text{Q}\\text{o}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{d}}\\)\u003c/span\u003e\u003c/span\u003e are load resistance, capacitor, inductance of transformer, on-state resistance switch and forward voltage of diode; D is 1 when the switch turns on and 0 as it turns off.\u003c/p\u003e \u003cp\u003eTwo ways can be applied to solve (1) and (2), and obtain \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{I}}_{\\text{L}}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e. One is to calculate the eigenvector and eigenvalue of differential equations and construct the general solution. Then, by using the initial values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{I}}_{\\text{L}}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e, the specific solution of these differential equations can be obtained [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This method demands heavy computation, especially the calculation of eigenvector and eigenvalue. The other one is to linearize the differential equations with acceptable accuracy, which is used in this paper. Moreover, 4th order Runge-Kutta method is used\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDetails of Flyback converter\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInput Voltage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e180 v\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSwitching Frequency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50 kHz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDuty Cycle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInductance of Transformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 mH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCapacitor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLoad Resistance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e75 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eForward Voltage of diode\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2 v\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOn-state Resistance of Switch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.001 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOut-put Voltage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e150 v\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ein this paper to linearize the differential equations. So, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{I}}_{\\text{L}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{V}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e are as bellow (3) and (4):\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${\\text{I}}_{\\text{L},\\text{n}+1}={\\text{I}}_{\\text{L},\\text{n}}+\\frac{\\text{h}}{6}\\left({\\text{K}}_{\\text{a}1}+2{\\text{K}}_{\\text{a}2}+2{\\text{K}}_{\\text{a}3}+{\\text{K}}_{\\text{a}4}\\right) \\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$${\\text{V}}_{\\text{c},\\text{n}+1}={\\text{V}}_{\\text{c},\\text{n}}+\\frac{\\text{h}}{6}\\left({\\text{K}}_{\\text{b}1}+2{\\text{K}}_{\\text{b}2}+2{\\text{K}}_{\\text{b}3}+{\\text{K}}_{\\text{b}4}\\right) \\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ka1-ka4 and kb1-kb4 are used to calculate the average change rate between (n)th and (n\u0026thinsp;+\u0026thinsp;1)th step as shown below:\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\text{f}1({\\text{I}}_{\\text{L}},{\\text{V}}_{\\text{c}})=\\frac{{\\text{d}\\text{I}}_{\\text{L}}}{{\\text{d}}_{\\text{t}}} \\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\text{f}2({\\text{I}}_{\\text{L}},{\\text{V}}_{\\text{c}})=\\frac{{\\text{d}\\text{V}}_{\\text{c}}}{{\\text{d}}_{\\text{t}}} \\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{a}1}=\\text{f}1({\\text{I}}_{\\text{L},\\text{n}},{\\text{V}}_{\\text{c},\\text{n}}) \\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{b}1}=\\text{f}2({\\text{I}}_{\\text{L},\\text{n}},{\\text{V}}_{\\text{c},\\text{n}}) \\left(8\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{a}2}=\\text{f}1({\\text{I}}_{\\text{L},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{a}1},{\\text{V}}_{\\text{c},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{b}1}) \\left(9\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{b}2}=\\text{f}2({\\text{I}}_{\\text{L},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{a}1},{\\text{V}}_{\\text{c},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{b}1}) \\left(10\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equl\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{a}3}=\\text{f}1({\\text{I}}_{\\text{L},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{a}2},{\\text{V}}_{\\text{c},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{b}2}) \\left(11\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equm\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{b}3}=\\text{f}2({\\text{I}}_{\\text{L},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{a}2},{\\text{V}}_{\\text{c},\\text{n}}+\\frac{\\text{h}}{2}{\\text{K}}_{\\text{b}2}) \\left(12\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equn\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equn\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{a}4}=\\text{f}1({\\text{I}}_{\\text{L},\\text{n}}+\\text{h}{\\text{K}}_{\\text{a}3},{\\text{V}}_{\\text{c},\\text{n}}+\\text{h}{\\text{K}}_{\\text{b}3}) \\left(13\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equo\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equo\" name=\"EquationSource\"\u003e\n$${\\text{K}}_{\\text{b}4}=\\text{f}2({\\text{I}}_{\\text{L},\\text{n}}+\\text{h}{\\text{K}}_{\\text{a}3},{\\text{V}}_{\\text{c},\\text{n}}+\\text{h}{\\text{K}}_{\\text{b}3}) \\left(14\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere h is the calculation step time between nth and (n\u0026thinsp;+\u0026thinsp;1)th time step. After calculation (7)-(14) and substitute into (3) and (4), output voltage that equals with capacitor voltage be obtained. The equations are done in MATLAB/S-function in the case study and it is worked as digital twin.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Artificial Neural Network\u003c/h2\u003e \u003cp\u003eArtificial neural network is a kind of powerful of artificial intelligent which has a lot of application in variety field. Indeed, ANNs have different type with diverse training method. Usually, ANNs train and update weights and biases in off-line method and trained ANN uses for real time applications\u003c/p\u003e \u003cp\u003eIn this paper, a method is presented to train ANN in on-line method and is used in real time simulation. The ANN is determined digital twin parameters to reduce difference of output of the flyback converter and the digital twin. The structure of ANN is MLP with BP training algorithm as shown in Fig.\u0026nbsp;3.\u003c/p\u003e \u003cp\u003eThe flowchart of training method of ANN is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e. From the picture, at the start of simulation, ANN is given some data and is trained in off-line method. Next, as the error equal target value, simulation start and the ANN is gradually trained with more data from simulated model to assess the least error.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 simulation and results of digital twin for flyback converter","content":"\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. shows a flyback converter with digital twin to indicate health and validate the proposed method. As the figure, parameters of digital twin are estimated with ANN and digital twin is calculated capacitor voltage and inductance current with averaged model equations, which the capacitor voltage equals output voltage of converter and inductance current is input current of converter. Moreover, capacitor voltage and inductance current of simulated model and digital twin are compared together and the errors are used to update of weights and biases of ANN. Furthermore, simulated model is tested in different states and the results are analyzed. First, the case is studied in normal condition and the results are checked out. After that, health indication of flyback converter is tested in various degradation of component.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Case study in normal condition\u003c/h2\u003e \u003cp\u003eTo identify parameters, the simulated model is runed in normal condition as the table I parameters. Indeed, the initial value of parameters are chosen and the digital twin is calculated capacitor voltage and inductance current. Next, the output of simulated model and digital twin are compared and the error signal is used to training ANN.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAt the beginning, the weights and biases of ANN are determined with random function, so they are updated with the error signal by back-propagation training method and it is continued until the error is less than threshold. However, input of ANN is the error of capacitor voltage and inductance current and input voltage of flyback converter. In addition, on-state resistance of MOSFET, capacitor capacity, forward voltage of diode and transformer magnetization inductance are obtained with ANN for the digital twin. Moreover, the digital twin is calculated capacitor voltage and inductance current with parameters that are specified by ANN.\u003c/p\u003e \u003cp\u003eFrom the pictures in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e, the ANN is accurately estimated component parameters of flyback converter for digital twin. As the figures, values of parameters are not correct at the beginning, so the ANN could correctly find out these parameters with reducing least square error of ANN.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e (b) and (c), the initial value of capacitor was 20 mF, so it is estimated to 3 \u0026micro;F after 1.5 ms which it is shown the ability of ANN in estimation, also it is obvious for other parameters in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a), (d) and (e).\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e is presented the error capacitor voltage that is the comparison of flyback converter and digital twin output. From the graph, the error was 160 volt at the beginning and after some fluctuations, the error was less than threshold. Also, it is obviously shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e which capacitor voltage and inductance current of flyback converter and digital twin are plotted in a graph. The digital twin with the component parameters that the ANN was determined could find out the value of flyback converter outputs in 4 ms which is acceptable.\u003c/p\u003e \u003cp\u003eThe voltage and current of MOSFET and diode are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e. As the picture, when MOSFET is on, diode is off and vice versa.\u003c/p\u003e\u003cp\u003eA. Capacitor Degradation\u003c/p\u003e\u003cp\u003eAfter a long-term operation, the capacitance may drop 5\u0026ndash;20% because of degradation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Some variety of condition can affect on changing capacitance, for instance, the temperature of environment or the quality of insulator. In this study, the capacitor is degraded 2.2% of capacitance for every step and the ANN is estimated the capacitance. The results are reported in Table II and the ANN estimation is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFrom the details, the capacitor capacity is declined in 4 steps and it is dropped from 3 \u0026micro;F to 2.736 \u0026micro;F and the ANN is almostly estimated the capacitance for digital twin. However, averaged error of estimation is 0.945% that is suitable to sense capacitor degradation.\u003c/p\u003e \u003cp\u003eTable.2. The Capacitance Degradation and ANN Estimation\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eNo. of case\u003c/p\u003e \u003cp\u003estudy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePercentage change\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCapacitor capacity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eANN Estimation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e-2.2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.934 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.905 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e-4.4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.868 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.821 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e-6.6%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.802 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.782 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e-8.8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.736 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.724 \u0026micro;F\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eB. MOSFET Degradation\u003c/p\u003e\u003cp\u003eTo indicate health of MOSTEF, on-state resistance is effective, because it could determine the switch degradation. As Table III, 4 cases are studied with increasing resistance that the ANN estimation is shown in this table. The table shows that the ANN can not estimate the values exactly, because the input of ANN is comparison of capacitor voltage and inductance current which the changing of on-state resistance of the switch does not affect on them, so the ANN is estimated with more error.\u003c/p\u003e \u003cp\u003eHowever, the details are shown that the ANN could distinguish on-state resistance of MOSFET become greater, regardless of the amount of error.\u003c/p\u003e \u003cp\u003eTable.3. The on-state resistance of MOSFET and ANN Estimation\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. of case study\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRon_MOSFET\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eANN Estimation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0024 Ω\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0018 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0043 Ω\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0033 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0062 Ω\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0046 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0089 Ω\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0051 Ω\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eC. Diode health indication\u003c/p\u003e\u003cp\u003eDiode health indication is important for flyback converter and estimation forward voltage of diode could aim to specify well-being. The results of this study in changing forward voltage of the diode are presented in table IV. As the table, the estimations are not the same as simulated model because the changing of capacitor voltage and inductance current are a few in changing forward voltage, it is obvious in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTable.4. The Forward Voltage of Diode and ANN Estimation\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. of case study\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eForward Voltage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eANN Estimation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1999 V\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.411 V\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.865 V\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eD. Transformer Inductance Degradation\u003c/p\u003e\u003cp\u003eIn this study, the transformer magnetization inductance is considered in the model and winding inductances are passed up. Indeed, the digital twin is calculated equations according this model and variation of the inductance is analyzed to indicate inductance degradation. Table V shows the results which the ANN could accurately determine the inductance with the data of digital twin and simulated model. Moreover, changing in inductance has affect on input current which equals with inductance current, so the ANN could sense the variation of it because it is an input of ANN.\u003c/p\u003e \u003cp\u003eTable.5. The Transformer Magnetization Inductance and ANN Estimation\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. of case study\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInductance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eANN Estimation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 mH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.97 mH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15 mH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.01 mH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10 mH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.998 mH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7 mH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.898 mH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eE. Impact of changing in input voltage and duty cycle\u003c/p\u003e \u003cp\u003eIn flyback converter, input voltage and duty cycle may change in operation and they straightly change the output of the converter. On the other hand, the digital twin is calculated according these inputs and the ANN is estimated parameters from the error of them. So it is significant to validate the method in changing these inputs. Moreover, in this study five circumstances as the table VI are surveyed and the results are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e. From the figure, the digital twin and the ANN can identically estimated parameters. Also, Fig.\u0026nbsp;13. shows the real component parameters of simulated model with red line and the estimation of ANN with blue dot in five cases as table VI.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable.6. The ANN Estimation in different input voltage and duty cycle\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. of case study\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInput voltage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDuty cycle\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e180 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e160 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e200 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e180 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190 V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4 conclusions","content":"\u003cp\u003eIn this paper, a real-time method is presented for health indication of flyback converter with digital twin and artificial neural network. The flyback converter is simulated in MATLAB/Simulink with component parameters and a digital twin is proposed to operate as same as the simulated converter. Indeed, the digital twin equations are extracted from SAA model and the equations are solved by 4th order Runge-Kutta technique. Also, an ANN is used to estimate component parameters of the flyback converter for calculation of digital twin equations and health indication of flyback converter is detected. Furthermore, inputs of ANN are input voltage of flyback converter, comparison of capacitor voltage and inductance current of the simulated model and digital twin. Confirming the inputs, the ANN is estimated on-state resistance of MOSFET, capacitance, forward voltage of diode and transformer magnetization inductance. However, the ANN is designed and programmed in new real time method that is trained when simulation is runed and the ANN could reduce the error during the simulation.\u003c/p\u003e \u003cp\u003eIn conclusion, the method is tested in some variety states (degradation of capacitor, on-state resistance of MOSFET, forward voltage of diode and transformer magnetization inductance and changing input voltage and duty cycle) to verify feasibility of the method and the results are presented. From the results, the capability of the method in health indication of the converter is proved. To compare with previous method, this procedure has more accurate and could identify the system with less time and adaptability of the method is more because of ANN potency.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eEhsan Rahmanian Koushkaki wrote the main manuscript and Amirhosein Rajaei was as supervisor.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003ePalak Jain, Jason Poon, Jai Prakash Singh, Costas Spanos, Seth R. Sanders, Sanjib Kumar Panda, \u0026ldquo;A Digital Twin Approach for Fault Diagnosis in Distributed Photovoltaic Systems\u0026rdquo;, IEEE Transactions on Power Electronics, Volume: 35, Issue: 1, Jan. 2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYingzhou Peng, Shuai Zhao, Huai Wang,\u0026rdquo; A Digital Twin based Estimation Method for Health Indicators of DC-DC Converters\u0026rdquo; IEEE TRANSACTIONS ON POWER ELECTRONICS, Volume: 36, Issue: 2, Feb. 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. Dusmez and B. Akin, \u0026ldquo;An accelerated thermal aging platform to monitor fault precursor on-state resistance,\u0026rdquo; in 2015 IEEE International Electric Machines Drives Conference (IEMDC), May 2015, pp. 1352\u0026ndash; 1358.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. A. Vogelsberger, T. Wiesinger, and H. Ertl, \u0026ldquo;Life-cycle monitoring and voltage-managing unit for dc-link electrolytic capacitors in pwm\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003econverters,\u0026rdquo; IEEE Transactions on Power Electronics, vol. 26, no. 2, pp. 493\u0026ndash;503, Feb. 2011.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMatthew Milton, Castulo De La O, Herbert L. Ginn and Andrea Benigni ,\u0026rdquo; Controller-Embeddable Probabilistic Real-Time Digital Twins for Power Electronic Converter Diagnostics\u0026rdquo;, IEEE Transactions on Power Electronics Volume: 35, Issue: 9, Sept. 2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHarish S. Krishnamoorthy, Tulasi Narayanan Aayer,\u0026rdquo; Machine Learning based Modeling of Power Electronic Converters\u0026rdquo;, 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eE. Rahmanian, H. Akbari, and G.H. 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Stargel, \u0026ldquo;The digital twin paradigm for future NASA and U.S. air force vehicles,\u0026rdquo; in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Special Session on the Digital Twin, Honolulu, HI, United States, p. 20120008178, April 2012.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. X. Li and K. S. Low, \u0026ldquo;Low sampling rate online parameters monitoring of dc-dc converters for predictive-maintenance using biogeographybased optimization,\u0026rdquo; IEEE Transactions on Power Electronics, vol. 31, no. 4, pp. 2870\u0026ndash;2879, April 2016.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eH. Soliman, H. Wang, and F. Blaabjerg, \u0026ldquo;A review of the condition monitoring of capacitors in power electronic converters,\u0026rdquo; IEEE Transactions on Industry Applications, vol. 52, no. 6, pp. 4976\u0026ndash;4989, Nov. 2016.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Digital Twin, Artificial Neural Network, flyback Converter, Health Indication, State Space Averaged model in Power Electronic Converter, Runge-kutta method","lastPublishedDoi":"10.21203/rs.3.rs-3861997/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3861997/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper proposes a real-time artificial neural network (ANN) for estimation digital twin parameters in health indication of flyback converter. Indeed, the ANN is approximated digital twin parameters by using voltage input of the flyback converter and comparison of capacitor voltage and inductance current of simulated model and digital twin. Moreover, the ANN structure is picked out multi-layer perceptron (MLP) with back-propagation training algorithm. Furthermore, the ANN is used in a new real-time technique that is trained during of running of the model. However, the digital twin is calculated output voltage and inductance current by 4th order runge-kutta method. The formula of model is determined with state-space averaged (SSA) model technique. Finally, as the output voltage of simulated model and digital twin are the same, the component parameters are compared with initial values and health of converter is detected. The model is tested in some variety scenarios, such as degradation of capacitor, MOSFET, diode and transformer magnetization inductance, and the outcome of them are presented. Also, the method is tested in changing input voltage of converter and duty cycle. The studied model is simulated in MATLAB/Simulink and the digital twin and the ANN block are done in S-function.\u003c/p\u003e","manuscriptTitle":"A Real-Time ANN for Estimation Digital Twin parameters in Health Indication of Flyback Converter","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-17 09:29:39","doi":"10.21203/rs.3.rs-3861997/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d633ffa5-48cf-4a9e-8e82-3eefcc914ee0","owner":[],"postedDate":"January 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-31T04:59:31+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-17 09:29:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3861997","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3861997","identity":"rs-3861997","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}