Development and Implementation of Synchronized Phasor Measurements for Dynamic State Power System Monitoring and Fault Identification

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Vijay Babu, Ch.Leelakrishna, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4186838/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 In real time the magnitude and phase angle of the voltage and current signals vary continuously. The measurement of magnitude and phase angles of these signals are very important for the visualization of real-time power systems pictorially and knowing dynamic power flow studies. This work presents the measurement of the voltage and current signal's magnitude and phase angles with time synchronization. The magnitude and phase angle are represented with a single quantity phasor. For the measurement of phasor values two different techniques are used, they are Recursive Discrete Fourier Transform (RDFT), and Non-Recursive Discrete Fourier Transform (NRDFT). With the RDFT the phasor (magnitude and phase angle) values are constant with time variation, with fixed load and constant supply. By varying the load or source the magnitude of the phasor is changed and the phase angle is constant. The values obtained from these results are used for the dynamic power flow calculation of the power system. With the NRDFT the phasor magnitude is constant the phase angle values are varying (rotating) with a speed of (ωt) and with a step of (1/N). The values obtained with this method are used for real-time power system visualization. The values obtained from the RDFT and NRDFT are time-stamped with GPS time. With GPS time stamping, the measurements are time synchronized, and real-time visualization of the power system is obtained. Electrical Engineering Phasor Measurements Fault identification Power Flow DFT TVE Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Nowadays real-time power system monitoring and power flow calculation in a dynamic state is very important [ 1 ]. Because day-to-day power demand increasing rapidly with different types of linear and non-linear loads, to meet this demand lot of generating stations are coming into the picture, and some of the generating stations are installed near the load centers and some are far away distance from the load centers [ 2 ]. Also, to improve the reliability of the power system lot of interconnections are happening and power is transferred over a long distance. Due to this, stress on the transmission lines is increasing, differentiating normal and fault conditions is difficult, and knowing of power flow in the transmission lines in which direction is also complex [ 3 ]. Conventional power system monitoring methods SCADA and Energy Management Systems (EMS) give limited awareness about the power system in a steady state view [ 4 ]. In real time the voltage and current signals are continuous signals, and the instantaneous magnitude and phase angles of these signals change continuously. The power flow in the line depends on the phase angles of the signals[ 5 ]. With a long distance, the local timings are different at different places, and the calculation of power flow studies is difficult. To measure the power flow in the lines, phasors are the best choice. The instantaneous power flow is depending on the instantaneous values of the voltage and current at the same instant [ 6 ]. For this it is required to measure the parameters with time stamping, this timestamp should be the globally same. Once the measured values are stamped with a Global Positioning System (GPS) time, then the measurements are time synchronized [ 7 ]. This time synchronized values are suitable for the dynamic power flow calculations [ 8 – 10 ]. 2. Phasor Calculation Techniques In modern days, with the advancement of power electronics, the usage of power electronic converters is increasing rapidly. However, due to the non-linearity/switching action, harmonics are injected into the current waveforms [ 11 – 12 ]. Due to this, the fundamental current waveforms get disturbed and the total current waveform is distorted. The distorted current waveforms create core saturation problems in the transformers and generators, which leads to the distortion in the voltage waveforms. For the power flow calculation, accurate measurement of magnitude and phase angle is important. For the elimination of harmonics in the current waveforms analog filters can be used, but these filters introduce some time lag in the measurements, measurements are not faster, and due to the aging effect the harmonics are not eliminated properly [ 13 ]. Instead of analog filters digitalized phasor measurement technique is very useful to get the measurement of the fundamental component magnitude and phase angle [ 14 ]. The digitalized phasor measurement techniques are Discrete Fourier Transform (DFT) method, Kalman filter method, Wavelet Transform method, and Taylor Approximation methods are available. Among all these methods DFT methods is a simple and widely used method. By using the DFT method, without any filter, any order component of the signal can be calculated. In the DFT two techniques are available. They are RDFT and NRDFT. By using these techniques, the magnitude and phase angle of the signal can be calculated accurately. Assume the real-time signal is: \(x\left(t\right)={X}_{p}\text{sin}\left(\omega {t}_{n}+\theta \right)\) (i) The signal (i) phasor calculation by using the DFT technique is the Current phasor, \(X=\frac{\sqrt{2}}{M}{\sum }_{n=0}^{M-1}\left({X}_{p}{e}^{-j\frac{2\pi nk}{M}}\right);0\le n\le M-1\) Representation of signal in the time domain discrete manner and frequency domain is shown in Fig. 1 where M = Number of samples in a cycle θ is the initial phase angle of the signal. k is the order of frequency components needed to extract. By using this DFT technique, the fundamental component (k = 1) real magnitude and imaginary magnitude of the signal can be extracted separately without using any real-time physical filters. $${X\left(k\right)}_{real}=\frac{\sqrt{2}}{M}{\sum }_{n=0}^{M-1}\left({V}_{m}\text{cos}\frac{2\pi n}{M}\right) \left(ii\right)$$ $${X\left(k\right)}_{imag}=\frac{\sqrt{2}}{M}{\sum }_{n=0}^{M-1}\left({V}_{m}\text{sin}\frac{2\pi n}{M}\right) \left(iii\right)$$ \(\text{m}\text{a}\text{g}\text{n}\text{i}\text{t}\text{u}\text{d}\text{e}=\sqrt{{\left(\text{R}\text{e} \text{X}\left(\text{k}\right)\right)}^{2}+({\text{I}\text{m}\text{g} \text{X}\left(\text{k}\right))}^{2}}\) (iv) \(\text{P}\text{h}\text{a}\text{s}\text{e}={\text{tan}}^{-1}(\frac{\text{I}\text{m}\text{g} \text{X}\left(\text{k}\right)}{Re X\left(k\right)})\) (v) For the dynamic state monitoring of the power system, according to IEEE Std. C37.118.2.2011 the number of cycles should be at least 10 or at least 240 samples in a second. 3. Phasor calculation of the signal with RDFT In the RDFT initially, total samples of the cycle are considered (i.e. 0 to M-1) for the phasor calculation, and real, imaginary components of the phasor are computed according to the (ii ~ v). For the next instant phasor calculation 0th sample is omitted M th sample is added, but the remaining M-1 sample data is the previous cycle data. The implementation of the 32-point RDFT for the AC signal with harmonic quantity is shown in Fig. 2 . The harmonic signal in the time domain and calculated phasor values with 32-point RDFT are shown in Fig. 3 . The first phasor value is obtained at the 32nd sample and it takes 20 msec time. After the first phasor at every sample one phasor value is obtained with a constant magnitude and phase angle. 4. Phasor calculation of the signal with NRDFT For the same signal, NRDFT is applied and the result is shown Fig. 4 , giving the calculated phasor values. For the post-disturbance analysis purpose, these values are stored in the Excel sheet by using write to measurement file or with table values in the front panel. In this method for each phasor calculation, it takes 20 milliseconds. The calculated phasor magnitude is constant, while the angle is changing. The first phasor value is obtained after one cycle (20 msec) from the starting of the signal, and also for next phasor calculation, takes 20 msec of time. By using Non-Recursive DFT also only the fundamental component phasor value is calculated even in the presence of harmonics, without any external filters. The DFT itself acts as a filter to extract the fundamental component. The phasor measurements obtained from the RDFT and NRDFT are shown in Table 1 . Each measurement value is time stamped with GPS time stamping, for this purpose NEO 6M module is used. From the table, it is noticed that the first phasor measurement of both methods was taken same time. In the RDFT the each phasor calculation the time is 20 msec/M and the obtained phasor magnitude, and angles are constant with time variation. But in the NRDFT the each phasor calculation the time is 20 msec and the obtained phasor magnitude is constant, angles vary with time variation. Table 1 Comparison of RDFT and NRDFT phasor calculation techniques RDFT NRDFT Time Instantaneous Value Magnitude Phase angle Time Instantaneous Value Magnitude Phase angle 1/11/2023 9:58:13:0006 AM 0 - - 1/11/2023 9:26:12:0006 AM 0 - - 1/11/2023 9:58:13:0012 AM 63.456971 - - 1/11/2023 9:26:12:0012 AM 63.4941 - - 1/11/2023 9:58:13:0018 AM 124.475325 - - 1/11/2023 9:26:12:0018 AM 124.5482 - - 1/11/2023 9:58:13:0025 AM 180.710163 - - 1/11/2023 9:26:12:0025 AM 180.8159 - - 1/11/2023 9:58:13:0031 AM 230.000411 - - 1/11/2023 9:26:12:0031 AM 230.135 - - 1/11/2023 9:58:13:0037 AM 270.451871 - - 1/11/2023 9:26:12:0037 AM 270.6101 - - 1/11/2023 9:58:13:0043 AM 300.510018 - - 1/11/2023 9:26:12:0043 AM 300.6858 - - 1/11/2023 9:58:13:0050 AM 319.019734 - - 1/11/2023 9:26:12:0050 AM 319.2064 - - 1/11/2023 9:58:13:0056 AM 325.2697 - - 1/11/2023 9:26:12:0056 AM 325.46 - - 1/11/2023 9:58:13:0062 AM 319.019734 - - 1/11/2023 9:26:12:0062 AM 319.2064 - - 1/11/2023 9:58:13:0068 AM 300.510018 - - 1/11/2023 9:26:12:0068 AM 300.6858 - - 1/11/2023 9:58:13:0075 AM 270.451871 - - 1/11/2023 9:26:12:0075 AM 270.6101 - - 1/11/2023 9:58:13:0081 AM 230.000411 - - 1/11/2023 9:26:12:0081 AM 230.135 - - 1/11/2023 9:58:13:0087 AM 180.710163 - - 1/11/2023 9:26:12:0087 AM 180.8159 - - 1/11/2023 9:58:13:0093 AM 124.475325 - - 1/11/2023 9:26:12:0093 AM 124.5482 - - 1/11/2023 9:58:13:0100 AM 63.456971 - - 1/11/2023 9:26:12:0100 AM 63.4941 - - 1/11/2023 9:58:13:0106 AM 0 - - 1/11/2023 9:26:12:0106 AM 1.14E-13 - - 1/11/2023 9:58:13:0112 AM -63.456971 - - 1/11/2023 9:26:12:0112 AM -63.4941 - - 1/11/2023 9:58:13:0118 AM -124.475325 - - 1/11/2023 9:26:12:0118 AM -124.548 - - 1/11/2023 9:58:13:0125 AM -180.710163 - - 1/11/2023 9:26:12:0125 AM -180.816 - - 1/11/2023 9:58:13:0131 AM -230.000411 - - 1/11/2023 9:26:12:0131 AM -230.135 - - 1/11/2023 9:58:13:0137 AM -270.451871 - - 1/11/2023 9:26:12:0137 AM -270.61 - - 1/11/2023 9:58:13:0143 AM -300.510018 - - 1/11/2023 9:26:12:0143 AM -300.686 - - 1/11/2023 9:58:13:0150 AM -319.019734 - - 1/11/2023 9:26:12:0150 AM -319.206 - - 1/11/2023 9:58:13:0156 AM -325.2697 - - 1/11/2023 9:26:12:0156 AM -325.46 - - 1/11/2023 9:58:13:0162 AM -319.019734 - - 1/11/2023 9:26:12:0162 AM -319.206 - - 1/11/2023 9:58:13:0168 AM -300.510018 - - 1/11/2023 9:26:12:0168 AM -300.686 - - 1/11/2023 9:58:13:0175 AM -270.451871 - - 1/11/2023 9:26:12:0175 AM -270.61 - - 1/11/2023 9:58:13:0181 AM -230.000411 - - 1/11/2023 9:26:12:0181 AM -230.135 - - 1/11/2023 9:58:13:0187 AM -180.710163 - - 1/11/2023 9:26:12:0187 AM -180.816 - - 1/11/2023 9:58:13:0193 AM -124.475325 - - 1/11/2023 9:26:12:0193 AM -124.548 - - 1/11/2023 9:58:13:0200 AM -63.456971 - - 1/11/2023 9:26:12:0200 AM -63.4941 - - 1/11/2023 9:58:13:0206 AM 0 230.0004 -90 1/11/2023 9:26:12:0206 AM 0 230.135 270 1/11/2023 9:58:13:0212 AM 63.456971 230.0004 -90 1/11/2023 9:26:12:0412 AM 63.4941 230.135 281.25 1/11/2023 9:58:13:0218 AM 124.475325 230.0004 -90 1/11/2023 9:26:12:0618 AM 124.5482 230.135 292.5 1/11/2023 9:58:13:0225 AM 180.710163 230.0004 -90 1/11/2023 9:26:12:0825 AM 180.8159 230.135 303.75 The real-time voltage and current signals, and their phasor values are shown in Fig. 5 . Magnified harmonic current signal (50 multiplication factor) is obtained with a non-linear load (Laptop). Even in the presence of harmonics also the fundamental component of the phasor is calculated accurately without any filter. 5. Identification of Faults in Dynamic State With the calculated phasor value, it is possible to identify the fault conditions or disturbance conditions in the power system with Total Vector Error (TVE). $$\%TVE=\sqrt{\frac{\left({X}_{r}^{e}-{X}_{r}^{a}\right)+({X}_{i}^{a}-{X}_{i}^{a})}{({X}_{r}^{a}{)}^{2}+(X{)}^{2}}}*100$$ Here, X r e , X i e are the calculated/estimated phasor real and imaginary values. X r a , X i a are the real/true phasor real and imaginary values. When the fault/ disturbance occurs, then %TVE becomes greater than zero. When a fault occurs, then that fault should be identified before one cycle completion for dynamic state fault identification. Based on the %TVE calculation (> 5%) the fault is identified [ 15 ]. Due to the less computational time of the phasor value calculation, faults can identified with less time. With this, it is possible to identify the faults in the dynamic state. According to the IEEE standard, the allowable %TVE is less than 5% for healthy operations of the power system. If %TVE is greater than 5% for more than half a cycle period, then it is treated as a fault. 7kVA, 400V for 300km proto type transmission line model is used for the fault study and phasor calculations with R = 0.00151Ω/ph /km, XL = 0.0186 mΩ/ph /km, XC = 0.0174MΩ/km Rf = 5.29 Ω and Fault current in Amp. Experimental results are shown in Fig. 6 . For the analysis purpose, the fault is created after one cycle (20 msec). This fault is identified after 1.25 msec from the fault creation. The simulation results are shown in Fig. 6 . The fault is calculated based on the Total Vector Error (%TVE). When the %TVE is greater than 5% then it is observed that a fault occurs in the system. It is very effective than [ 16 ]. 6. Power Flow Calculation A simple two-point model lossless power transmission line model is shown in Fig. 7 . The phase angle difference between the two ends is dependent on the value of inductive reactance and current in the line. The sending and receiving end voltages are represented with V s = V s e jφ and V r = V r e jθ The power in the transmission line is \(P=\frac{\text{V}\text{s}\text{*}\text{V}\text{r} \text{s}\text{i}\text{n}\left({\delta }\right)}{\text{X}}\) Here \({\delta }\) = φ-θ at the same instant. With the phasor calculation, it is possible to calculate the phase angles of the signal, and possible to calculate the power flow in the line accurately. With conventional methods the V s , V r values are obtained once for every 3 to 5 seconds. But with the phasor measurement the values of V s , Vr, and their angles obtained nearly 200 values, so the loss of measurements is reduced. Even if there is a lag in the communication Table 2 Power flow calculation based on voltage magnitude and phase angle. Time Sending End Voltage (Vs) Angle at Sending End Receiving End Voltage (Vr) Angle at Receiving End Power flow (P) 18/05/2023 12:35:51.809 236.9137 10 201.3024 10.1962 2582.51 18/05/2023 12:36:02.038 236.9137 15 201.3024 15.2599 3403.83 18/05/2023 12:36:02.403 236.9137 20 201.3024 20.3215 4185.81 18/05/2023 12:36:02.774 236.9137 25 201.3024 25.3806 4921.18 18/05/2023 12:36:03.139 236.9137 30 201.3024 30.4368 5603.82 18/05/2023 12:36:03.508 236.9137 35 201.3024 35.4895 6229.13 18/05/2023 12:36:03.896 236.9137 40 201.3024 40.5385 6793.91 18/05/2023 12:36:04.263 236.9137 45 201.3024 45.5833 7296.25 18/05/2023 12:36:04.640 236.9137 50 201.3024 50.6235 7735.47 The above table gives better results than the steady-state power flow calculations [ 17 ]. 7. Conclusion In this paper, it is presented that the different phasor calculation methods and their differences. The RDFT is suitable for the dynamic state phasor calculation because it takes 20 msec/M th time for each calculation. The NRDFT is suitable for the real-time visualization of the power system. By using RDFT and NRDFT methods fundamental component of the signal is calculated without any physical filter even in the presence of harmonics. The measured values are stamped with GPS timing. With %TVE faults are identified 1/16th of the cycle time, and if an abnormal condition is sustained for more than half a cycle, then it is identified as a fault in the system. This method is suitable for the dynamic state monitoring and fault identification of the power system. Based on the phasor values the power calculations are accurate. References Y. T. Ju, J. K. Wang, X. Chen, and Y. Lin, “Continuous power flow calculation method for three-phase isolated microgrid considering detailed source and load models,” Power System Technology, vol. 46, no. 2, pp. 718–725, 2022. Sachin Kumar, R.K. 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Sanchez-Gasca, "Steady‐State Power Flow," in Power System Modeling, Computation, and Control , IEEE, 2020, pp.9-46, doi: 10.1002/9781119546924.ch2. Additional Declarations The authors declare no competing interests. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4186838","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":285311392,"identity":"e1a9ac9e-c42d-4a37-8335-2db451d823f2","order_by":0,"name":"Ravi Ponnala","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDUlEQVRIiWNgGAWjYJCCAxCKuYHhw4//cmCRB8RpYWxgnNnDbAwWSSDOMsYGZh425sQGEBufFvP2M4YHGHfY5JmzH2z8wMPDlj4/7PBDoC12croN2LXInMkxOMB4Jq3YsiexWULCgid34+00A6CWZGOzA9i1SDCkJRxgbDucuOFAYoOEAY9E7sbZCSAtBxK34dLC/wyq5fzD5h8JbAbphrPTP+DXIpF8AKLlRmKbxAG2hAR56RwCtkg8PnAg8UwaUMvDNsvGngOGG6RzCg4kGODxC39i84ePO2yADks+fPvPjwPy8rPTN3/4UGEnh0sLGEDiAgoMwCoN8CgHAUZkLfINOFSNglEwCkbBiAUAk1xqonmxGuoAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-3290-3728","institution":"Vasavi College of Engineering(A)","correspondingAuthor":true,"prefix":"","firstName":"Ravi","middleName":"","lastName":"Ponnala","suffix":""},{"id":285313989,"identity":"9af587a6-41bb-4172-add8-7c72b4ea18e7","order_by":1,"name":"Dr.Muktevi Chakravarthy","email":"","orcid":"https://orcid.org/0000-0003-0486-3551","institution":"Vasavi College of Engineering(A)","correspondingAuthor":false,"prefix":"Dr.","firstName":"Muktevi","middleName":"","lastName":"Chakravarthy","suffix":""},{"id":285313990,"identity":"59831d21-6826-453c-a05b-ce7068db0800","order_by":2,"name":"P. 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Narayanamma Institute of Technology and Science","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"","lastName":"Ch.Leelakrishna","suffix":""},{"id":285313992,"identity":"5feb4795-22f2-4b31-85d1-5699b0d85305","order_by":4,"name":"M.Kishore","email":"","orcid":"","institution":"Chaitanya Bharathi Institute of Technology(A)","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"","lastName":"M.Kishore","suffix":""},{"id":285313993,"identity":"a1b0a16b-9f8c-4b44-ab45-aac18a335ef3","order_by":5,"name":"P.Rajasekhara Reddy","email":"","orcid":"","institution":"Vasavi College of Engineering(A)","correspondingAuthor":false,"prefix":"","firstName":"P.Rajasekhara","middleName":"","lastName":"Reddy","suffix":""}],"badges":[],"createdAt":"2024-03-29 08:59:58","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-4186838/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4186838/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53841498,"identity":"4589e9fd-a0ef-4eff-bfc3-cf89cd406876","added_by":"auto","created_at":"2024-04-01 07:30:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":112765,"visible":true,"origin":"","legend":"\u003cp\u003ePhasor representation of the signal\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/ec65a1e914b8d1ed92c25ff4.png"},{"id":53841502,"identity":"88aa0c68-5e1c-4913-8315-6da237d1be9f","added_by":"auto","created_at":"2024-04-01 07:30:31","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":627869,"visible":true,"origin":"","legend":"\u003cp\u003ePhasor calculation of the signal using RDFT in LabVIEW\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/2aff0f2d48aea4b931c1703d.jpeg"},{"id":53842242,"identity":"2b17fc19-2bea-402c-87d5-aca60450b51a","added_by":"auto","created_at":"2024-04-01 07:38:30","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":92697,"visible":true,"origin":"","legend":"\u003cp\u003ePhasor calculation of distorted simulated signal with 32-point RDFT\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/8f7fa064a39c5d15344fc3d8.png"},{"id":53841499,"identity":"67609dd7-6c63-44aa-bf75-ad53353abca3","added_by":"auto","created_at":"2024-04-01 07:30:30","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":97741,"visible":true,"origin":"","legend":"\u003cp\u003ePhasor calculation of distorted simulated signal with 32-point NRDFT\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/ff9d5984eee3eb04f8e01eaa.png"},{"id":53841501,"identity":"d5ace5d0-8e44-4be2-bbdd-7a8b2a46eba8","added_by":"auto","created_at":"2024-04-01 07:30:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":489983,"visible":true,"origin":"","legend":"\u003cp\u003ePhasor calculation of the real signal with harmonic load\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/47252cdbf754569d9e8920e1.png"},{"id":53841503,"identity":"13e6f00b-f840-476e-b870-f468ec9dc6bd","added_by":"auto","created_at":"2024-04-01 07:30:31","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":407405,"visible":true,"origin":"","legend":"\u003cp\u003eFault identification in a dynamic state\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/1c45a267332744db7e6af173.png"},{"id":53841504,"identity":"33778a53-2138-464c-a16e-874e9ec5f5dc","added_by":"auto","created_at":"2024-04-01 07:30:31","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":3764,"visible":true,"origin":"","legend":"\u003cp\u003ePower System Transmission Line\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/331796b01c98d0743969df13.png"},{"id":53842528,"identity":"9e11353b-a3e8-4dc0-a996-b64d9ee1bad1","added_by":"auto","created_at":"2024-04-01 07:46:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1784500,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4186838/v1/d79dc027-0c44-43b8-a1b1-3e32edcf8eed.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eDevelopment and Implementation of Synchronized Phasor Measurements for Dynamic State Power System Monitoring and Fault Identification\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eNowadays real-time power system monitoring and power flow calculation in a dynamic state is very important [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Because day-to-day power demand increasing rapidly with different types of linear and non-linear loads, to meet this demand lot of generating stations are coming into the picture, and some of the generating stations are installed near the load centers and some are far away distance from the load centers [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Also, to improve the reliability of the power system lot of interconnections are happening and power is transferred over a long distance. Due to this, stress on the transmission lines is increasing, differentiating normal and fault conditions is difficult, and knowing of power flow in the transmission lines in which direction is also complex [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Conventional power system monitoring methods SCADA and Energy Management Systems (EMS) give limited awareness about the power system in a steady state view [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. In real time the voltage and current signals are continuous signals, and the instantaneous magnitude and phase angles of these signals change continuously. The power flow in the line depends on the phase angles of the signals[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. With a long distance, the local timings are different at different places, and the calculation of power flow studies is difficult. To measure the power flow in the lines, phasors are the best choice. The instantaneous power flow is depending on the instantaneous values of the voltage and current at the same instant [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. For this it is required to measure the parameters with time stamping, this timestamp should be the globally same. Once the measured values are stamped with a Global Positioning System (GPS) time, then the measurements are time synchronized [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. This time synchronized values are suitable for the dynamic power flow calculations [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Phasor Calculation Techniques","content":"\u003cp\u003eIn modern days, with the advancement of power electronics, the usage of power electronic converters is increasing rapidly. However, due to the non-linearity/switching action, harmonics are injected into the current waveforms [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Due to this, the fundamental current waveforms get disturbed and the total current waveform is distorted. The distorted current waveforms create core saturation problems in the transformers and generators, which leads to the distortion in the voltage waveforms. For the power flow calculation, accurate measurement of magnitude and phase angle is important. For the elimination of harmonics in the current waveforms analog filters can be used, but these filters introduce some time lag in the measurements, measurements are not faster, and due to the aging effect the harmonics are not eliminated properly [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Instead of analog filters digitalized phasor measurement technique is very useful to get the measurement of the fundamental component magnitude and phase angle [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The digitalized phasor measurement techniques are Discrete Fourier Transform (DFT) method, Kalman filter method, Wavelet Transform method, and Taylor Approximation methods are available. Among all these methods DFT methods is a simple and widely used method. By using the DFT method, without any filter, any order component of the signal can be calculated. In the DFT two techniques are available. They are RDFT and NRDFT. By using these techniques, the magnitude and phase angle of the signal can be calculated accurately.\u003c/p\u003e \u003cp\u003eAssume the real-time signal is:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(x\\left(t\\right)={X}_{p}\\text{sin}\\left(\\omega {t}_{n}+\\theta \\right)\\)\u003c/span\u003e \u003c/span\u003e (i)\u003c/p\u003e \u003cp\u003eThe signal (i) phasor calculation by using the DFT technique is the\u003c/p\u003e \u003cp\u003eCurrent phasor, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X=\\frac{\\sqrt{2}}{M}{\\sum }_{n=0}^{M-1}\\left({X}_{p}{e}^{-j\\frac{2\\pi nk}{M}}\\right);0\\le n\\le M-1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eRepresentation of signal in the time domain discrete manner and frequency domain is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003cp\u003ewhere M\u0026thinsp;=\u0026thinsp;Number of samples in a cycle\u003c/p\u003e \u003cp\u003eθ is the initial phase angle of the signal.\u003c/p\u003e \u003cp\u003ek is the order of frequency components needed to extract.\u003c/p\u003e \u003cp\u003eBy using this DFT technique, the fundamental component (k\u0026thinsp;=\u0026thinsp;1) real magnitude and imaginary magnitude of the signal can be extracted separately without using any real-time physical filters.\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equa\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${X\\left(k\\right)}_{real}=\\frac{\\sqrt{2}}{M}{\\sum }_{n=0}^{M-1}\\left({V}_{m}\\text{cos}\\frac{2\\pi n}{M}\\right) \\left(ii\\right)$$\u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Equb\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${X\\left(k\\right)}_{imag}=\\frac{\\sqrt{2}}{M}{\\sum }_{n=0}^{M-1}\\left({V}_{m}\\text{sin}\\frac{2\\pi n}{M}\\right) \\left(iii\\right)$$\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\text{m}\\text{a}\\text{g}\\text{n}\\text{i}\\text{t}\\text{u}\\text{d}\\text{e}=\\sqrt{{\\left(\\text{R}\\text{e} \\text{X}\\left(\\text{k}\\right)\\right)}^{2}+({\\text{I}\\text{m}\\text{g} \\text{X}\\left(\\text{k}\\right))}^{2}}\\)\u003c/span\u003e \u003c/span\u003e (iv)\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\text{P}\\text{h}\\text{a}\\text{s}\\text{e}={\\text{tan}}^{-1}(\\frac{\\text{I}\\text{m}\\text{g} \\text{X}\\left(\\text{k}\\right)}{Re X\\left(k\\right)})\\)\u003c/span\u003e \u003c/span\u003e(v)\u003c/p\u003e \u003cp\u003eFor the dynamic state monitoring of the power system, according to IEEE Std. C37.118.2.2011 the number of cycles should be at least 10 or at least 240 samples in a second.\u003c/p\u003e"},{"header":"3. Phasor calculation of the signal with RDFT","content":"\u003cp\u003eIn the RDFT initially, total samples of the cycle are considered (i.e. 0 to M-1) for the phasor calculation, and real, imaginary components of the phasor are computed according to the (ii\u0026thinsp;~\u0026thinsp;v). For the next instant phasor calculation 0th sample is omitted M\u003csup\u003eth\u003c/sup\u003e sample is added, but the remaining M-1 sample data is the previous cycle data. The implementation of the 32-point RDFT for the AC signal with harmonic quantity is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe harmonic signal in the time domain and calculated phasor values with 32-point RDFT are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The first phasor value is obtained at the 32nd sample and it takes 20 msec time. After the first phasor at every sample one phasor value is obtained with a constant magnitude and phase angle.\u003c/p\u003e"},{"header":"4. Phasor calculation of the signal with NRDFT","content":"\u003cp\u003eFor the same signal, NRDFT is applied and the result is shown Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, giving the calculated phasor values. For the post-disturbance analysis purpose, these values are stored in the Excel sheet by using write to measurement file or with table values in the front panel. In this method for each phasor calculation, it takes 20 milliseconds. The calculated phasor magnitude is constant, while the angle is changing. The first phasor value is obtained after one cycle (20 msec) from the starting of the signal, and also for next phasor calculation, takes 20 msec of time. By using Non-Recursive DFT also only the fundamental component phasor value is calculated even in the presence of harmonics, without any external filters. The DFT itself acts as a filter to extract the fundamental component.\u003c/p\u003e \u003cp\u003eThe phasor measurements obtained from the RDFT and NRDFT are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Each measurement value is time stamped with GPS time stamping, for this purpose NEO 6M module is used. From the table, it is noticed that the first phasor measurement of both methods was taken same time. In the RDFT the each phasor calculation the time is 20 msec/M and the obtained phasor magnitude, and angles are constant with time variation. But in the NRDFT the each phasor calculation the time is 20 msec and the obtained phasor magnitude is constant, angles vary with time variation.\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\u003eComparison of RDFT and NRDFT phasor calculation techniques\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eRDFT\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c8\" namest=\"c5\"\u003e \u003cp\u003eNRDFT\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInstantaneous Value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMagnitude\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" 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align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0031 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0037 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e270.451871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0037 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e270.6101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0043 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e300.510018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0043 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e300.6858\u003c/p\u003e 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colname=\"c2\"\u003e \u003cp\u003e319.019734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0062 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e319.2064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0068 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e300.510018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0068 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e300.6858\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0075 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e270.451871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0075 AM\u003c/p\u003e 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align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0100 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e63.4941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0106 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0106 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.14E-13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0112 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-63.456971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0112 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-63.4941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0118 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-124.475325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0118 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-124.548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0125 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-180.710163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0125 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-180.816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0131 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-230.000411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0131 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0137 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-270.451871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0137 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-270.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0143 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-300.510018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0143 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-300.686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0150 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-319.019734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0150 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-319.206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0156 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-325.2697\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0156 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-325.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0162 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-319.019734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0162 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-319.206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0168 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-300.510018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0168 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-300.686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0175 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-270.451871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0175 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-270.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0181 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-230.000411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0181 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0187 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-180.710163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0187 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-180.816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0193 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-124.475325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0193 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-124.548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0200 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-63.456971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0200 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-63.4941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0206 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e230.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0206 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0212 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e63.456971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e230.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0412 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e63.4941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e281.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0218 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e124.475325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e230.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0618 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e124.5482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e292.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1/11/2023 9:58:13:0225 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e180.710163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e230.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/11/2023 9:26:12:0825 AM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e180.8159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e230.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e303.75\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\u003eThe real-time voltage and current signals, and their phasor values are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Magnified harmonic current signal (50 multiplication factor) is obtained with a non-linear load (Laptop).\u003c/p\u003e \u003cp\u003eEven in the presence of harmonics also the fundamental component of the phasor is calculated accurately without any filter.\u003c/p\u003e"},{"header":"5. Identification of Faults in Dynamic State","content":"\u003cp\u003eWith the calculated phasor value, it is possible to identify the fault conditions or disturbance conditions in the power system with Total Vector Error (TVE).\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\%TVE=\\sqrt{\\frac{\\left({X}_{r}^{e}-{X}_{r}^{a}\\right)+({X}_{i}^{a}-{X}_{i}^{a})}{({X}_{r}^{a}{)}^{2}+(X{)}^{2}}}*100$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, X\u003csub\u003er\u003c/sub\u003e\u003csup\u003ee\u003c/sup\u003e, X\u003csub\u003ei\u003c/sub\u003e\u003csup\u003ee\u003c/sup\u003e are the calculated/estimated phasor real and imaginary values. X\u003csub\u003er\u003c/sub\u003e\u003csup\u003ea\u003c/sup\u003e, X\u003csub\u003ei\u003c/sub\u003e\u003csup\u003ea\u003c/sup\u003e are the real/true phasor real and imaginary values. When the fault/ disturbance occurs, then %TVE becomes greater than zero. When a fault occurs, then that fault should be identified before one cycle completion for dynamic state fault identification. Based on the %TVE calculation (\u0026gt;\u0026thinsp;5%) the fault is identified [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Due to the less computational time of the phasor value calculation, faults can identified with less time. With this, it is possible to identify the faults in the dynamic state. According to the IEEE standard, the allowable %TVE is less than 5% for healthy operations of the power system. If %TVE is greater than 5% for more than half a cycle period, then it is treated as a fault.\u003c/p\u003e \u003cp\u003e7kVA, 400V for 300km proto type transmission line model is used for the fault study and phasor calculations with R\u0026thinsp;=\u0026thinsp;0.00151Ω/ph /km, XL\u0026thinsp;=\u0026thinsp;0.0186 mΩ/ph /km, XC\u0026thinsp;=\u0026thinsp;0.0174MΩ/km Rf\u0026thinsp;=\u0026thinsp;5.29 Ω and Fault current in Amp. Experimental results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFor the analysis purpose, the fault is created after one cycle (20 msec). This fault is identified after 1.25 msec from the fault creation. The simulation results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The fault is calculated based on the Total Vector Error (%TVE). When the %TVE is greater than 5% then it is observed that a fault occurs in the system. It is very effective than [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e"},{"header":"6. Power Flow Calculation","content":"\u003cp\u003eA simple two-point model lossless power transmission line model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The phase angle difference between the two ends is dependent on the value of inductive reactance and current in the line.\u003c/p\u003e \u003cp\u003eThe sending and receiving end voltages are represented with\u003c/p\u003e \u003cp\u003eV\u003csub\u003es\u003c/sub\u003e= V\u003csub\u003es\u003c/sub\u003e e\u003csup\u003ejφ\u003c/sup\u003e and V\u003csub\u003er\u003c/sub\u003e = V\u003csub\u003er\u003c/sub\u003e e\u003csup\u003ejθ\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThe power in the transmission line is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P=\\frac{\\text{V}\\text{s}\\text{*}\\text{V}\\text{r} \\text{s}\\text{i}\\text{n}\\left({\\delta }\\right)}{\\text{X}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eHere\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }\\)\u003c/span\u003e\u003c/span\u003e\u0026thinsp;=\u0026thinsp;φ-θ at the same instant.\u003c/p\u003e \u003cp\u003eWith the phasor calculation, it is possible to calculate the phase angles of the signal, and possible to calculate the power flow in the line accurately. With conventional methods the V\u003csub\u003es\u003c/sub\u003e, V\u003csub\u003er\u003c/sub\u003e values are obtained once for every 3 to 5 seconds. But with the phasor measurement the values of V\u003csub\u003es\u003c/sub\u003e, \u003csub\u003eVr,\u003c/sub\u003e and their angles obtained nearly 200 values, so the loss of measurements is reduced. Even if there is a lag in the communication\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePower flow calculation based on voltage magnitude and phase angle.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSending End Voltage (Vs)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAngle at Sending End\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReceiving End Voltage (Vr)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAngle at Receiving End\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePower flow (P)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:35:51.809\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10.1962\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2582.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:02.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.2599\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3403.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:02.403\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20.3215\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4185.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:02.774\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.3806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4921.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:03.139\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e30.4368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5603.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:03.508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e35.4895\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6229.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:03.896\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40.5385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6793.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:04.263\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e45.5833\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7296.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18/05/2023 12:36:04.640\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e236.9137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e201.3024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.6235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7735.47\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\u003eThe above table gives better results than the steady-state power flow calculations [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e"},{"header":"7. Conclusion","content":"\u003cp\u003eIn this paper, it is presented that the different phasor calculation methods and their differences. The RDFT is suitable for the dynamic state phasor calculation because it takes 20 msec/M\u003csup\u003eth\u003c/sup\u003e time for each calculation. The NRDFT is suitable for the real-time visualization of the power system. By using RDFT and NRDFT methods fundamental component of the signal is calculated without any physical filter even in the presence of harmonics. The measured values are stamped with GPS timing. With %TVE faults are identified 1/16th of the cycle time, and if an abnormal condition is sustained for more than half a cycle, then it is identified as a fault in the system. This method is suitable for the dynamic state monitoring and fault identification of the power system. Based on the phasor values the power calculations are accurate.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eY. T. Ju, J. K. Wang, X. Chen, and Y. Lin, \u0026ldquo;Continuous power flow calculation method for three-phase isolated microgrid considering detailed source and load models,\u0026rdquo; Power System Technology, vol. 46, no. 2, pp. 718\u0026ndash;725, 2022.\u003c/li\u003e\n\u003cli\u003eSachin Kumar, R.K. Saket, Dharmendra Kumar Dheer, Jens Bo Holm-Nielsen, P. Sanjeevikumar, \u0026ldquo;Reliability enhancement of electrical power system including impacts of renewable energy sources: a comprehensive review\u0026rdquo;, Vol. 14, no.10, ISSN-1799-1815 1799-1815 03 April 2020\u003c/li\u003e\n\u003cli\u003eLucian Ioan Dulău, Mihail Abrudean, Dorin Bică, \u0026ldquo;Effects of Distributed Generation on Electric Power Systems\u0026rdquo;, Procedia Technology, Volume 12, 2014, Pages 681-686.\u003c/li\u003e\n\u003cli\u003eM. H. Wakti, L. Multa Putranto, S. P. Hadi, M. Yasirroni and A. F. Derana Marsiano, \u0026quot;PMU Location Determination in a Hybrid PMU-SCADA System,\u0026quot; 2020 12th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia, 2020, pp. 245-250, doi: 10.1109/ICITEE49829.2020.9271728.\u003c/li\u003e\n\u003cli\u003eR. Ponnala, M. Chakravarthy, and S. V. N. L. Lalitha,\u0026ldquo;Development of Laboratory Model PMU for the Phasor Calculation of Fundamental Component for the Power System Fault Identification Dynamic State and Effective Data System for the Post Disturbance Analysis\u0026rdquo; \u003cem\u003eInternational Journal of Electrical and Electronics Research, vol 10, issue 4, pp.1306-1314, Dec-2022.\u003c/em\u003e\u003c/li\u003e\n\u003cli\u003eZHAO, Y., CHAI, J., WANG, S. et al. \u0026quot;Instantaneous power calculation based on the intrinsic frequency of single-phase virtual synchronous generator\u0026quot;, J. Mod. Power Syst. Clean Energy 5, 970\u0026ndash;978 (2017).\u003c/li\u003e\n\u003cli\u003eA. G. Phadke, \u0026quot;Synchronized phasor measurements in power systems,\u0026quot; in IEEE Computer Applications in Power, vol. 6, no. 2, pp. 10-15, April 1993, doi: 10.1109/67.207465.\u003c/li\u003e\n\u003cli\u003eGuangdou Zhang, Jian Li, Dongsheng Cai, Qi Huang, Weihao Hu, \u0026ldquo;Dynamic state estimation of power system with stochastic delay based on neural network,\u0026rdquo; Energy Reports, Volume 7, Supplement 1, 2021, Pages 159-166.\u003c/li\u003e\n\u003cli\u003eAbhinav Kumar Singh, A.P. Sakis Meliopoulos et al. \u0026ldquo;Dynamic State Estimation for Power System Control and Protection\u0026rdquo;, IEEE TRANSACTIONS ON POWER SYSTEMS, VOL5, NO.4, 2020.\u003c/li\u003e\n\u003cli\u003eR. Ponnala, M. Chakravarthy, and S. V. N. L. Lalitha, \u0026quot;Dynamic state power system fault monitoring and protection with phasor measurements and fuzzy based expert system\u003cem\u003e,\u0026rdquo; Bulletin of Electrical Engineering and Informatics\u003c/em\u003e, vol. 11, no. 1, pp. 103\u0026ndash;110, Feb. 2022, doi: 10.11591/eei.v11i1.3585.\u003c/li\u003e\n\u003cli\u003eM. J. H. Rawa, D. W. P. Thomas, and M. Sumner, \u0026quot;Harmonics attenuation of nonlinear loads due to linear loads,\u0026quot; 2012 Asia-Pacific Symposium on Electromagnetic Compatibility, Singapore, 2012, pp. 829-832, doi: 10.1109/APEMC.2012.6237838.\u003c/li\u003e\n\u003cli\u003eR. Ponnala, M. Chakravarthy, and S. V. N. L. Lalitha, \u0026ldquo;Effective monitoring of power system with phasor measurement unit and effective data storage system\u0026rdquo; Bulletin of Electrical Engineering and Informatics, vol. 11, no. 5, pp. 2471\u0026ndash;2478, Oct. 2022 10.11591/eei.v11i5.4085.\u003c/li\u003e\n\u003cli\u003eSenani, R.; Bhaskar, D.R.; Raj, A. 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Sanchez-Gasca, \u0026quot;Steady‐State Power Flow,\u0026quot; in \u003cem\u003ePower System Modeling, Computation, and Control\u003c/em\u003e, IEEE, 2020, pp.9-46, doi: 10.1002/9781119546924.ch2.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"vasavi college of engineering","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":"Phasor Measurements, Fault identification, Power Flow, DFT, TVE","lastPublishedDoi":"10.21203/rs.3.rs-4186838/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4186838/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn real time the magnitude and phase angle of the voltage and current signals vary continuously. The measurement of magnitude and phase angles of these signals are very important for the visualization of real-time power systems pictorially and knowing dynamic power flow studies. This work presents the measurement of the voltage and current signal's magnitude and phase angles with time synchronization. The magnitude and phase angle are represented with a single quantity phasor. For the measurement of phasor values two different techniques are used, they are Recursive Discrete Fourier Transform (RDFT), and Non-Recursive Discrete Fourier Transform (NRDFT). With the RDFT the phasor (magnitude and phase angle) values are constant with time variation, with fixed load and constant supply. By varying the load or source the magnitude of the phasor is changed and the phase angle is constant. The values obtained from these results are used for the dynamic power flow calculation of the power system. With the NRDFT the phasor magnitude is constant the phase angle values are varying (rotating) with a speed of (ωt) and with a step of (1/N). The values obtained with this method are used for real-time power system visualization. The values obtained from the RDFT and NRDFT are time-stamped with GPS time. With GPS time stamping, the measurements are time synchronized, and real-time visualization of the power system is obtained.\u003c/p\u003e","manuscriptTitle":"Development and Implementation of Synchronized Phasor Measurements for Dynamic State Power System Monitoring and Fault Identification","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-01 07:30:22","doi":"10.21203/rs.3.rs-4186838/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":"a07654c8-cb93-4010-a22b-b3d30abe5a86","owner":[],"postedDate":"April 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":30037571,"name":"Electrical Engineering"}],"tags":[],"updatedAt":"2024-04-01T07:30:23+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-01 07:30:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4186838","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4186838","identity":"rs-4186838","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}