Applied sciences

Archives of Electrical Engineering


Archives of Electrical Engineering | 2022 | vol. 71 | No 1

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Aiming at the problems of the negative sequence governance and regenerative braking energy utilization of electrified railways, a layered compensation optimization strategy considering the power flow of energy storage systems was proposed based on the railway power conditioner. The paper introduces the topology of the energy storage type railway power conditioner, and analyzes its negative sequence compensation and regenerative braking energy utilization mechanism. Considering the influence of equipment capacity and power flow of the energy storage system on railway power conditioner compensation effect, the objective function and constraint conditions of the layered compensation optimization of the energy storage type railway power conditioner were constructed, and the sequential quadratic programming method was used to solve the problem. The feasibility of the proposed strategy is verified by a multi-condition simulation test. The results show that the proposed optimization compensation strategy can realize negative sequence compensation and regenerative braking energy utilization, improve the power factor of traction substations when the system equipment capacity is limited, and it also has good real-time performance.
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Authors and Affiliations

Ying Wang
Yanqiang He
Xiaoqiang Chen
Miaomiao Zhao
Jing Xie

  1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou, 730070 China
  2. Xi’an Rail Transit Group Co., LTD Operation Branch Xi’an, 710000 China
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In order to overcome the shortcoming of large switching losses caused by variable switching frequency appears in the conventional finite control set model predictive control (FCS-MPC) algorithm, a model predictive direct power control (MP-DPC) for an energy storage quasi-Z-source inverter (ES-qZSI) is proposed. Firstly, the power prediction model of the ES-qZSI is established based on the instantaneous power theory. Then the average voltage vector in the ���� coordinate system is optimized by the power cost function. Finally, the average voltage vector is used as the modulation signal, and the corresponding switching signal with fixed frequency is generated by the shoot-through segment space vector pulse width modulation (SVPWM) technology. The simulation results show that the ES-qZSI realizes six shoot-through actions per control cycle and achieves the constant frequency control of the system, which verifies the correctness of the proposed control strategy.
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Authors and Affiliations

Min'an Tang
Shangmei Yang
Kaiyue Zhang
Qianqian Wang
Chenggang Liu
Xuewang Dong

  1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, China
  2. College of Electrical Engineering, Lanzhou Institute of Technology, China
  3. College of Electrical and Information Engineering, Lanzhou University of Technology, China
  4. Gansu Province Special Equipment Inspection and Testing Institute, China
  5. Jingtaichuan Electric Power Pumping Irrigation Water Resources Utilization Center of Gansu Province, China
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Transformer efficiency and regulation, are to be maintained at maximum and minimum respectively by optimal loading, control, and compensation. Charging of electric vehicles at random charging stations will result in uncertain loading on the distribution transformer. The efficiency reduces and regulation increases as a consequence of this loading. In this work, a novel optimization strategy is proposed to map electric vehicles to a charging station, that is optimal with respect to the physical distance, traveling time, charging cost, the effect on transformer efficiency and regulation. Consumer and utility factors are considered for mapping electric vehicles to charging stations. An Internet of Things platform is used to fetch the dynamic location of electric vehicles. The dynamic locations are fed to a binary optimization problem to find an optimal routing table that maps electric vehicles to a charging station. A comparative study is carried out, with and without optimization, to validate the proposed methodology.
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Authors and Affiliations

R. Venkataswamy
K. Uma Rao
P. Meena

  1. CHRIST (deemed to be university)
  2. RV College of Engineering©
  3. BMS College of Engineering, India
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The aging of composite insulators in outdoor operation for a long time has a direct impact on the safe and stable operation of the power grid. To solve this problem, fuzzy comprehensive evaluation of composite insulators based on level difference maximum is proposed. To verify the feasibility of this method, insulators in Xinjiang are sampled and the index evaluation system for composite insulators is established based on electrical, mechanical, hydrophobic and other properties, combined with operational years, geographical environment and other factors; Firstly, different membership functions are established according to index types. It is more likely to determine the grade of insulator by comparing measured data with the boundary value. Then, to solve the problem that weights cannot be effectively integrated in the combination weighting, level difference maximization is proposed (during the operation of insulators, the index which has a greater influence on the performance of insulators takes a higher proportion of the weight). Finally, on the basis of fully considering the clarity and ambiguity of grade division, the grade state of insulators is obtained by using the linear weighting method. The results show that compared with the traditional method, the improved method of the membership function and level difference maximum can realize the dynamic adjustment of the index based on the degree of information change. The method can better evaluate the insulator grade. The case study shows that the model can accurately and quickly judge the state of composite insulators, which can be used as a reference for manufacturing and maintenance departments.
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[1] Liang X.D., Gao Y.F., Wang J.F. et al., Rapid development of silicone rubber composite insulators in China, High Voltage Engineering, vol. 42, no. 9, pp. 2888–2896 (2016), DOI: 10.13336/j.1003- 6520.hve.20160907025.

[2] Yuan Z.K., Degradation characteristics and mechanism of materials in composite insulator under high humidity, PhD Thesis, North China Electric Power University, Beijing (2019).

[3] Xoa Y.F., Song X.M., He J.Z. et al., Evaluation method of aging for silicone rubber of compos- ite insulator, Transactions of China Electrotechnical Society, vol. 34, no. S1, pp. 440–448 (2019), DOI: 10.19595/j.cnki.10006753.tces.L80647.

[4] Tang J., Liu Q.S., Liu J.W. et al., Evaluation of composite insulators based on fuzzy comprehen- sive evaluation, Engineering Journal of Wuhan University, vol. 52, no. 5, pp. 451–456 (2019),  DOI: 10.14188/j.1671-8844.2019-05-012.

[5] Huang X., Wang L.Y., Wang Q. et al., Grey fuzzy comprehensive evaluation model of contamina- tion state for insulators based on IFAHP with bayesian modified method, Science Technology and Engineering, vol. 20, no. 13, pp. 5135–5141 (2020), DOI: CNKI:SUN:KXJS.0.2020-13-018.

[6] Liu Y.P., Xu Z.Q., Fu H.C. et al., Insulation Condition Assessment Method of Power Transformer Based on Improved Extension Cloud Theory With Optimal Cloud Entropy, High Voltage Engineering, vol. 46, no. 2, pp. 397–405 (2020), DOI: 10.13336/j.1003-6520.hve.20190215004.

[7] Fan L., Xia F., Su H.Y. et al., Risk assessment of high voltage insulator contamination condition by cloud theory, Power System Protection and Control, vol. 40, no. 15, pp. 57–62 (2012), DOI: CNKI: SUN:JDQW.0.2012-15-014.

[8] Wang S.H., Jing H., Study on method for predicting pollution Flashover insulators in contact network, Journal of the China Railway Society, vol. 40, no. 3, pp. 58–67 (2018), DOI: CNKI:SUN:TDXB.0.2018- 03-011.

[9] Huai M.Q., Research on prediction of contamination state of insulator on catenary based on fuzzy neural network, Master Thesis, Lanzhou Jiaotong University, Gansu (2018).

[10] Yang Z.C., Zhang C.L., Ge L. et al., Comprehensive fuzzy evaluation based on entropy weight method for insulator flashover pollution, Electric Power Automation Equipment, vol. 34, no. 4, pp. 90–94 (2014), DOI: CNKI:SUN:DLZS.0.2014-04-016.

[11] Zhou Y.M., Studies on the degradation depth of silicon composite insulator in service, Master Thesis, Wuhan University, Wuhan (2018).

[12] Chen X.C., Li L.Q., Wu Z.G. et al., Research on shed properties of network operating composite insulators, Guangdong Electric Power, vol. 29, no. 6, pp. 104–108 (2016), DOI: 10.3969/j.issn.1007- 290X.2016.06.019.

[13] Yang L.G., Florian Pauli, Kay Hameyer, Influence of thermal-mechanical stress on the insulation system of a low voltage electrical machine, Archives of Electrical Engineering, vol. 70, no. 1, pp. 233–244 (2021), DOI: 10.24425/aee.2021.136064.

[14] Liu Y., Wang J.G., Han F. et al., Electrical and mechanical properties of composite insulators af- ter different operation periods, High Voltage Engineering, vol. 34, no. 5, pp. 1017–1021 (2008), DOI: 10.13336/j.1003-6520.hve.2008.05.027.

[15] Yao L.N., Wu Y.H., Wang S.H. et al., Electrical and mechanical properties of on-line compos- ite insulators, Insulating Materials, vol. 48, no. 8, pp. 23–27 (2015), DOI: 10.16790/j.cnki.1009-

[16] Jia Z.D., Yang C.X., Wang X.L. et al., Aging characteristics of composite insulators based on hydropho- bicity transfer test, High Voltage Engineering, vol. 41, no. 6, pp. 1907–1914 (2015), DOI: 10.13336/ j.1003-6520.hve.2015.06.019.

[17] Zhang M.M., Research on evaluation Method of Insulator pollution Status Assessment Based on UV Pulse Parameters, Master Thesis, Southwest Jiaotong University, Sichuan (2019).

[18] Mao Y.K., Guan Z.C., Wang L.M. et al., Evaluation of contamination levels of outdoor insulators based on the principal components analysis of leakage current Pulse, Transactions of China Electrotechnical Society, vol. 24, no. 8, pp. 39–45 (2009), DOI: 10.19595/j.cnki.10006753.tces.2009.08.007.

[19] Ning G.T., Fang B., Qin D. et al., Design and application of comprehensive evaluation index system of smart grid based on coordinated planning of major network and power distribution network, Archives of Electrical Engineering, vol. 70, no. 1, pp. 103–113 (2021), DOI: 10.24425/aee.2021.136055.

[20] Zhou L.L., Research of methods and their application of determining the weights of attributes in fuzzy comprehensive evaluation, Master Thesis, Northeastern University, Liaoning (2014).

[21] Li G., Li J.P., Sun X.L. et al., Research on a combined methods of subjective-objective weighting and its rationality, Management Review, vol. 29, no. 12, pp. 17–26+61 (2017), DOI: 10.14120/j.cnki. cn115057/f.2017.12.002.

[22] Chen Y.C., Dai J.Y., Xie D., Comprehensive evaluation of mine ventilation system based on combi- nation weighting cloud model, Systems Engineering, vol. 38, no. 6, pp. 35–42 (2020), DOI: 1001- 4098(2020)06-0035-08.

[23] Wang L.L., Research on cleaner production evaluation index system and grade comprehensive evalua- tion methodologies of wastewater treatment plants in cities and towns, PhD Thesis, Dalian University of Technology, Dalian (2015).

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Authors and Affiliations

Sihua Wang
Long Chen
Lei Zhao
Junjun Wang

  1. Lanzhou Jiaotong University, Lanzhou, 730070, China
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Due to the fixed rotor magnetic field, the main magnetic flux of conventional permanent magnet synchronous motors (PMSMs) cannot be flexibly adjusted. Recently, the axial-radial flux type permanent magnet synchronous machine (ARFTPMSM) based on the hybrid excitation concept is proposed, which provides a new method for the speed and magnetic field regulations for PMSMs. To analyze the mechanism of magnetic field variation inside the ARFTPMSM, in this paper, three – dimensional finite element models for electromagnetic field calculation of the ARFTPMSM are established. On this basis, the influence of the axial device on the motor is discussed, and the mechanism of flux regulation is explained. By the quantitative calculation of air-gap flux density and the noload back-electromotive force (EMF), the flux regulation capability of the ARFTPMSM is verified. In addition, the effect of the excitation magnetomotive force on the magnetic field harmonics is analyzed combined with the winding theory, and the influence of the axial magneto-motive force (MMF) on the torque fluctuation is obtained. The flux regulation performance of the motor and the validity of the numerical calculation analysis are verified by the experiments.
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Authors and Affiliations

Cunxiang Yang
Kun Wang
Ziyang Liu
Bin Xiong
Qiang Zhao

  1. Zhengzhou University of Light Industry, Zhengzhou, Henan, China
  2. Institute of Electrical Engineering of Chinese Academy of Sciences, Beijing, China
  3. Wolong Electric Nanyang Explosion Protection Group Co., LTD.China
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Among the FACTS device, the distributed power flow controller (DPFC) is a superior device. This can be evaluated after eliminating the dc capacitor between shunt and series convertors of the unified power flow controller (UPFC) and placing a number of low rating single phase type distributed series convertors in the line instant of using single large rating three phase series convertors as in the UPFC. The power flow through this dc capacitor as in the UPFC now takes place through the transmission line at a third harmonic frequency in the DPFC. The DPFC uses the D-FACTS that allows the replacement of a large three-phase converter as in the UPFC by several small-size series convertors present in the DPFC. The redundancy of several series convertors increases the system’s reliability of the power system. Also, there is no requirement for high voltage isolation as series convertors of the DPFC are hanging as well as single-phase types. Consequently, the DPFC system has a lower cost than the UPFC system. In this paper, the equivalent ABCD parameters of the latest FACTSdeviceDPFChave been formulated with the help of an equivalent circuit model of the DPFC at the fundamental frequency component. Further, the optimal location in the transmission line and maximum efficiency of the DPFC along with Thyristor Controlled Series Compensator (TCSC), Static Synchronous Shunt Compensator (STATCOM) and UPFC FACTS devices have been investigated using an iteration program developed in MATLAB under steady-state conditions. The results obtained depict that the DPFC when placed slightly off-center at 0.33 fraction distance from the sending end comes up with higher performance. Whereas, when the TCSC, STATCOM and UPFC are placed at 0.16, 0.2815, 0.32 fraction distances from sending end respectively give their best performance.
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[1] Edris A.A., Aapa R., Baker M.H., Bohman L., Clark K., Proposed terms and definitions for flexible ac transmission system (FACTS), IEEE Trans. on Power Delivery, vol. 12, no. 4, pp. 1848–1853 (1997), DOI: 10.1109/61.634216.

[2] Das D., Divan D.M., Harley R.G., Power flow control in networks using controllable network transformers, IEEE Trans. Power Electron., vol. 25, no. 7, pp. 1753–1760 (2010), DOI: 10.1109/ TPEL.2010.2042076.

[3] Ooi B.T., Kazerrani M., Marcean R., Wolanski Z., Galiana F.D., Megillis D., Jms G., Midpoint siting of FACTS devices in transmission lines, IEEE Trans. on power delivery, vo1. 12, no. 4, pp. 1717–1722 (1997), DOI: 10.1109/61.634196.

[4] Hingorani N.G., Gyugyi L., Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems, New York: IEEE Press (2000).

[5] Nabavi-Niak A., Iravani M.R., Steady-State and Dynamic Models of Unified Power Flow Con- troller (UPFC) for Power System Studies, IEEE Trans. Power Systems, vol. 11, no. 4 (1996), DOI: 10.1109/59.544667.

[6] Harjeet Johal, Deepak Divan, Design Considerations for Series-Connected Distributed FACTS Converters, IEEE Transactions on Industry Applications, vol. 43, iss. 6, pp. 1609–1618 (2007), DOI: 10.1109/TIA.2007.908174.

[7] Amir Hamidi, Sajjad Golshannavaz, Daryoush Nazarpour, D-FACTS Cooperation in Renewable Inte- grated Microgrid A Linear Multiobjective Approach, IEEE Transactions on Sustainable Energy, vol. 10, iss. 1, pp. 355–363 (2019), DOI: 10.1109/TSTE.2017.2723163.

[8] Narasimha Rao D., Srinivasa Varma P., Comparison of UPFC and DPFC, Journal of Critical Reviews, vol. 7, iss. 6 (2020), DOI: 10.31838/jcr.07.06.153.

[9]Abhilash Sen, Atanu Banerjee, Haricharan Nannam, A Comparative Analysis between UPFC and DPFC in a Grid Connected Photovoltaic System, IEEE International Conference on Intelligent Techniques in Control, Optimization and Signal Processing (INCOS) (2019), DOI: 10.1109/IN- COS45849.2019.8951352.

[10] Song W., Zhou X., Zhigang Liang, Subhashish Bhattacharya, Huang Alex Q., Modeling and Control Design of Distributed Power Flow Controller based-on Per-phase control, IEEE Energy Conversion Congress and Exposition (2009), DOI: 10.1109/ECCE.2009.5316307.

[11] Chandrakar V.K., Kothari A.G., Optimal Location for Line Compensation by Shunt Connected FACTS Controller, IEEE Power Electronics and Drive Systems Conference, vol. 1, pp. 151–156 (2003), DOI: 10.1109/PEDS.2003.1282736.

[12] Vikash Anand, Sanjeev Kumar Mallik, Power flow analysis and control of distributed FACTS de- vices in power system, Archives of Electrical Engineering, vol. 67, no. 3, pp. 545–561 (2018), DOI: 10.24425/123662.

[13] Zhihui Yuan, de Haan Sjoerd W.H., Ferreira Jan A., Construction and first result of a scaled transmis- sion system with the Distributed Power Flow Controller (DPFC), 13th European Conference on Power Electronics and Applications (2009).

[14] Zhihui Yuan, de Haan Sjoerd W.H., Braham Frreira, Dalibor Cevoric, A FACTS Device: Dis- tributed Power Flow Controller (DPFC), IEEE Trans. Power Electronics, vol. 25, no. 10 (2010), DOI: 10.1109/TPEL.2010.2050494.

[15] Syona Chawla, Sheetal Garg, Bhawna Ahuja, Optimal Location of Series-Shunt FACTS Device for Transmission Line Compensation, IEEE Control, Automation, Communication and Energy Conservation Conference, pp. 1–6 (2009).

[16] Shehata Ahmed A., Refaat Ahmed, Mamdouh K. Ahmed, Korovkin Nikolay V., Optimal placement and sizing of FACTS devices based on Autonomous Groups Particle Swarm Optimization technique, AEE, vol. 70, no. 1, pp. 161–172 (2021), DOI: 10.24425/aee.2021.136059.

[17] Riadh Essaadali, Anwar Jarndal, Ammar B. Kouki, Fadhel M. Ghannouch, Conversion Rules Between X-Parameters and Linearized Two-Port Network Parameters for Large-Signal Operating Conditions, IEEE Transactions on Microwave Theory and Techniques, vol. 66, no. 11, pp. 4745 4756 (2018), DOI: 10.1109/TMTT.2018.2863227.

[18] Divya S., Shyamala U., Power quality improvement in transmission systems using DPFC, IEEE 2nd International Conference on Electronics and Communication Systems (ICECS) (2015), DOI: 10.1109/ ECS.2015.7125035.

[19] Apolinar Reynoso-Hernández J., Pulido-Gaytán M.A., Cuesta R., Loo-Yau J.R., Maya-Sánchez M.C., Transmission Line Impedance Characterization Using an Uncalibrated Vector Network Analyzer, IEEE Microwave and Wireless Components Letters, vol. 30, no. 5, pp. 528–530 (2020), DOI: 10.1109/ LMWC.2020.2984377.

[20] Monika Sharma, Annapurna Bhargava, Pinky Yadav, Oscillation Damping with DPFC Using Opti- mization Techniques, IEEE International Conference on Micro-Electronics and Telecommunication Engineering (ICMETE) (2017), DOI: 10.1109/ICMETE.2016.73.

[21] Mengmeng Xiao, Shaorong Wang, Yong Huang, Chao Zheng, Qiushi Xu, Hongsheng Zhao, Aihong Tang, Dichen Liu, Two-Level Control Method for DPFC Series Units Based on PLC Communication, 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), pp. 20–22 (2018), DOI: 10.1109/EI2.2018.8582109.

[22] Zhai X., Tang A., Zou X., Xu Zheng, Qiushi Xu, Research on DPFC Capacity and Parameter Design Method, IEEE International Conference on Information Technology, Big Data and Artificial Intelligence (ICIBA) (2020), DOI: 10.1109/ICIBA50161.2020.9277315.

[23] Pradhan A.K., Routray A., Banaja Mohanty, Maximum efficiency of flexible AC transmission systems, Electrical Power and Energy Systems, vol. 28, pp. 581–588 (2006), DOI: 10.1016/j.ijepes.2006.03.014.

[24] Seyed Abbas Taher, Muhammad Karim Amooshahi, New approach for optimal UPFC placement using hybrid immune algorithm in electric power systems, International Journal of Electrical Power and Energy Systems, vol. 43, iss. 1, pp. 899–909 (2012), DOI: 10.1016/j.ijepes.2012.05.064.

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Authors and Affiliations

Santosh Kumar Gupta
Jayant Mani Tripathi
Mrinal Ranjan
Ravi Kumar Gupta
Dheeraj Kumar Gupta
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A hybrid multi-infeed HVDC (HMIDC) system is composed of line-commutated converter-based high-voltage direct current (LCC-HVDC) and voltage-source converterbased high-voltage direct current (VSC-HVDC), whose receiving ends have electrical coupling. To solve the problem of low-frequency oscillation (LFO) caused by insufficient damping in the HMIDC system, according to the multi-objective mixed H2/H∞ output feedback control theory with regional pole assignment, an additional robust damping controller is designed in this paper, which not only has good robustness, but also has strong adaptability to the change of system operation mode. In the paper, the related oscillation modes and transfer function of the controlled plant are obtained, which are identified by the total least squares estimation of signal parameters via rotary invariance technology (TLS-ESPRIT). In addition, the control-sensitive point (CSP) for suppressing LFO based on the small disturbance test method is determined, which is suitable for determining the installation position of the controller. The results show that the control sensitivity factor of VSC-HVDC is greater than that of LCC-HVDC so that adding an additional damping controller to VSC-HVDC is better than LCC-HVDC in suppressing the LFO of HMIDC. Finally, a hybrid double infeed DC transmission system with three receiving terminals is built on PSCAD/EMTDC where the time-domain simulations are performed to verify the correctness of the CSP selection and the effectiveness of the controller.
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Authors and Affiliations

Congshan Li
Yan Liu
Yikai Li
Ping He
Yan Fang
Tingyu Sheng

  1. School of Electrical and Information Engineering, Zhengzhou University of Light Industry, China
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The performance of drives with switched reluctance motors (SRMs) depends on magnetic materials used in their construction which influence static parameters such as inductance and electromagnetic torque profiles. The paper deals with simulations of switched reluctance motors in the finite element method and their comparison with measurements. Two kinds of switched reluctance motors were analysed, the modified Emerson Electric motor with a laminated steel core and a prototype, the one with a magnetic core made of iron-based powder composite materials. In the first part of the research, magnetization curves of magnetic materials were measured for static and dynamic conditions with 50 Hz. Next, simulations and measurements of inductance and developed torque were compared and analysed. In the last part of the research, simulations of magnetic flux density in motors were conducted. As the result of the research, it occurred that the simulations and measurements are quite close and two kinds of motors exhibit similar performance.
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[1] Miller T.J.E., Brushless permanent-magnet and reluctance motor drives, Oxford University Press (1989).
[2] Krishnan R., Switched reluctance motor drives: modelling, simulation, analysis, design, and applications, CRC Press (2001).
[3] Ahn J.-W., Switched reluctance motor, in book Torque control Ed. Lamchich M.T., Intech (2011), DOI: 10.5772/10520.
[4] Lawrenson P.J., Stephenson J.M., Blenkinsop P.T., Corda J., Fulton N.N., Variable-speed switched reluctance motors, IEE Proceedings B. (Electric Power Applications), vol. 127, no. 4, pp. 253–265 (1980), DOI: 10.1049/ip-b.1980.0034.
[5] Widmer J.D., Martin R., Kimiabeigi M., Electric vehicle traction motors without rare earth magnets, Sustainable Materials and Technologies, vol. 3, pp. 7–13 (2015), DOI: 10.1016/j.susmat.2015.02.001.
[6] Riba J.-R., López-Torres C., Romeral L., Garcia A., Rare-earth-free propulsion motors for electric vehicles: A technology review, Renewable and Sustainable Energy Reviews, vol. 57, pp. 367–379 (2016), DOI: 10.1016/j.rser.2015.12.121.
[7] Nakamura H., The current and future status of rare earth permanent magnets, Scripta Materialia, vol. 154, pp. 273–276 (2018), DOI: 10.1016/j.scriptamat.2017.11.010.
[8] Coey J.M.D., Magnetism and Magnetic Materials, Cambridge University Press (2010).
[9] Shokrollahi H., Janghorban K., Soft magnetic composite materials (SMCs), Journal of Materials Processing Technology, vol. 189, no. 1–3, pp. 1–12 (2007), DOI: 10.1016/j.jmatprotec.2007.02.034.
[10] Périgo E.A.,Weidenfeller B., Kollár P., Füzer J., Past, present, and future of soft magnetic composites, Applied Physics Reviews, vol. 5, no. 3 (2018), DOI: 10.1063/1.5027045.
[11] Przybylski M., Modelling and analysis of the low-power 3-phase switched reluctance motor, Archives of Electrical Engineering, vol. 68, no. 2, pp. 443–454 (2019), DOI: 10.24425/aee.2019.128279.
[12] Przybylski M., Slusarek B., Di Barba P., Mognaschi M.E.,Wiak S., Temperature and torque measurements of switched reluctance actuator with composite or laminated magnetic cores, Sensors, vol. 20, no. 3065, pp. 1–14 (2020), DOI: 10.3390/s20113065.
[13] Meeker D., Finite element method magnetics – User’s manual, ver. 4.2 (2018).
[14] Miller T.J.E., Optimal design of switched reluctance motors, IEEE Transactions on Industrial Electronics, vol. 49, no. 1, pp. 15–27 (2002), DOI: 10.1109/41.982244.
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Authors and Affiliations

Marek Przybylski

  1. Łukasiewicz Research Network – Tele and Radio Research Institute, Poland
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The use of lithium-ion battery energy storage (BES) has grown rapidly during the past year for both mobile and stationary applications. For mobile applications, BES units are used in the range of 10–120 kWh. Power grid applications of BES are characterized by much higher capacities (range of MWh) and this area particularly has great potential regarding the expected energy system transition in the next years. The optimal operation of BES by an energy storage management system is usually predictive and based strongly on the knowledge about the state of charge (SOC) of the battery. The SOC depends on many factors (e.g. material, electrical and thermal state of the battery), so that an accurate assessment of the battery SOC is complex. The SOC intermediate prediction methods are based on the battery models. The modeling of BES is divided into three types: fundamental (based on material issues), electrical equivalent circuit (based on electrical modeling) and balancing (based on a reservoir model). Each of these models requires parameterization based on measurements of input/output parameters. These models are used for SOC modelbased calculation and in battery system simulation for optimal battery sizing and planning. Empirical SOC assessment methods currently remain the most popular because they allow practical application, but the accuracy of the assessment, which is the key factor for optimal operation, must also be strongly considered. This scientific contribution is divided into two papers. Paper part I will present a holistic overview of the main methods of SOC assessment. Physical measurement methods, battery modeling and the methodology of using the model as a digital twin of a battery are addressed and discussed. Furthermore, adaptive methods and methods of artificial intelligence, which are important for the SOC calculation, are presented. In paper part II, examples of the application areas are presented and their accuracy is discussed.
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[1] Komarnicki P., Kranhold M., Styczynski Z., Sektorenkopplung. Energetisch-nachhaltige Wirtschaft der Zukunft, ISBN: 978-3-658-33559-5, Springer Verlag (2021), DOI: 10.1007/978-3-658-33559-5.

[2] Komarnicki P., Lombardi P., Styczynski Z., Elektrische Energiespeichersysteme - Flexibilitätsoptionen für Smart Gridshardcover, ISBN 978-3-662-62801-0, Springer Verlag (2021), DOI: 10.1007/978-3- 662-62802-7.

[3] Forschungsstelle für Energiewirtschaft e.V. (FfE), Abschlussbericht zum Projekt: Kurzstudie Elektromobilität Modellierung für die Szenarienentwicklung des Netzentwicklungsplan, München (2019).

[4] Dechent P., Epp A., Jöst D., Preger Y., Attia P., Li W., Sauer D.U., ENPOLITE: Comparing lithium-ion cells across energy, power, lifetime, and temperature, ACS Energy Letters, vol. 6, pp. 2351–2335 (2021), DOI: 10.1021/acsenergylett.1c00743.

[5] Sterner M., Stadler I., Handbook of energy storage. Demand, technologies, integration, Springer Verlag (2019), DOI: 10.1007/978-3-662-55504-0.

[6] Rudnicki T., Wojcicki S., Metody wyznaczania stanu naladowania akumulatorow stosowane w pojazdach elektrycznych, Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska (in Polish), vol. 3, ISSN 2083-0157 (2014), DOI: 10.5604/20830157.1121381.

[7] Hannam M.A., Lipu M.S.H., Hussain A., Mohamed A., A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations, Renewable and Sustainable Energy Review, vol. 78 pp. 834–854 (2017), DOI: 10.1016/j.rser.2017.05.001.

[8] Dai H., Jiang B., Hu X.-S., Lin X., Wei X., Pecht M., Advance battery management strategies for sustainable energy future: Multilayer design concept and research trends, Renewable and Sustainable Energy Review, vol. 138, p. 110480 (2021), DOI: 10.1016/j.rser.2020.110480.

[9] Waag W., Fleicher C., Sauer D.U., Critical review of the methods for monitoring of lithium-ion batteries in electric and hybrid vehicles, Journal of Power Sources, vol. 258, pp. 321–339 (2014), DOI: 10.1016/j.jpowsour.2014.02.064.

[10] Zhang Y.-J., Guo C., Liu Y.-G., Ding F., Chen Z., Hao W., A novel strategy for power sources management in connected plug-in hybrid electric vehicles based on mobile edge computation framework, Journal of Power Sources, vol. 477, p. 228650 (2020), DOI: 10.1016/j.jpowsour.2020.228650.

[11] Styczynski P., Lombardi P., Styczynski Z., Electric energy storage systems, Report CIGRE WG C6.15, ISBN: 978-2-85873-147-3, no. 458, CIGRE, Paris (2011), DOI: 10.1007/978-3-662-53275-1.

[12] Rancillo G., Pocha Pinto Lucas A., Kotsakis E., Fulli G., Merlo M., Delfanti M., Masera M., Modelling a large-scale battery energy storage system for power grid application analysis, Energies, vol. 12, no. 17, p. 3312 (2019), DOI: 10.3390/en12173312.

[13] Zeh A., Müller M., Naumann M., Hesse H.C., Jossen A., Witzmann R., Fundamentals of using battery energy storage systems to provide primary control reserves in Germany, Batteries, vol. 2, p. 49 (2016), DOI: 10.3390/batteries2030029.

[14] Komarnicki P., Energy storage systems: power grid and marked use cases, Archives of Electrical Engineering, vol. 65, no. 3, pp. 495–511 (2016), DOI: 10.1515/aee-2016-0036.

[15] Ceran B., A comparative analysis of energy storage technologies, Energy Policy Journal, vol. 21, no. 3, pp. 97–110 (2018), DOI: 10.24425/124498.

[16] Parol M., Rokicki L., Parol S., Towards optimal operation in rural low voltage microgrids, Bul- letin of Polish Academy of Sciences, Technical Sciences, vol. 67, no. 4, pp. 799–812 (2019), DOI: 10.24425/bpasts.2019.130189.

[17] Paliwal N.K., Singh A.K., Singh N.K., Short-term optimal energy management in stand-alone mi- crogrid with battery energy storage, Archives of Electrical Engineering, vol. 67, no. 3, pp. 499–513 (2017), DOI: 10.3390/en13061454.

[18] Kucevica D., Tepe B., Englberger S., Parlikar A., Mühlbauer M., Bohlen O., Jossen A., Hesse H., Standard battery energy storage system profiles: analysis of various applications for stationary energy storage systems using a holistic simulation framework, Journal of Energy Storage, vol. 28, no. 4, p. 101077 (2020), DOI: 10.1016/j.est.2019.101077.

[19] Ghazavidozein M., Gomis-Bellmunt O., Mancarella P., Simultaneous provision of dynamic active and reactive power response from utility-scale battery energy storage system in weak grids, IEEE Transactions on Power System (2021), DOI: 110.1109/TPWRS.2021.3076218.

[20] European Commission, Commission Regulation (EU) 2017/1485 of establishing a guideline on electricity transmission system operation, Official Journal of the European Union, vol. 220, pp. 1–120 (2017).

[21] Li X.-J., Yao L.-Z., Hui D., Optimal control and management of a large-scale battery energy storage system to mitigate fluctuation and intermittence of renewable generations, Journal of Modern Power Systems and Clean Energy, vol. 4, no. 4, pp. 593–603 (2016), DOI: 10.1007/s40565-016-0247-y.

[22] Podder S., Khan M.Z.R., Comparison of lead acid and Li-ion battery in solar home system of Bangladesh, 5th International Conference on Informatics, Electronics and Vision (ICIEV), pp. 434–438 (2016), DOI: 10.1109/ICIEV.2016.7760041.

[23] Hoppmann J., Volland J., Schmidt T.S., Hoffmann V.H., The economic viability of battery storage for residential solar photovoltaic systems – a review and a simulation model, Renewable and Sustainable Energy Reviews, vol. 39, pp. 1101–1118 (2014), DOI: 10.1016/j.rser.2014.07.068.

[24] Zhang R., Xia B., Li B., Cao L., Lai Y., Zheng W., Wang H., Wang W., State of the art of lithium-ion battery SOC estimation for electrical vehicles, Energies, vol. 11, no. 7, p. 1820 (2018), DOI: 10.3390/en11071820.

[25] Hallmann M., Wenge C., Komarnicki P., Evaluation methods for battery storage systems, IEEE 12th International Conference on Electrical Power Quality and Utilization (EPQU) (2020), DOI: 10.1109/EPQU50182.2020.9220321.

[26] Khandorin M.M., Estimation of the residual capacity of a lithium-ion battery in real time, (in Russian), in Khandorin M.M., Bukreev V.G. (eds.), Electrochemical power engineering (in Russian), pp. 65–693 (2014).

[27] May G.J., Standby batteries requirements for telecommunications power, Journal of Power Sources, vol. 158, no. 2, pp. 1117–1123 (2006), DOI: 10.1016/j.jpowsour.2006.02.083.

 [28] Wikipedia, Electrical System of the International Space Station, rical_system_of_the_International_Space_Station, accessed April 2021.

[29] Heussen K., Koch S., Ubig A., Anderson G., Unified system-level modeling of intermittent renewable energy sources and energy storage for power system operation, IEEE System Journal, vol. 6, no. 1, pp. 140–151 (2011), DOI: 10.1109/JSYST.2011.2163020.

[30] Buchholz B., Frey H., Lewaldt N., Stephanblome T., Schwagerl C., Styczynski Z.A., Advanced planning and operation of dispersed generation ensuring power quality, security and efficiency in distribution systems, CIGRE 2004, Invited paper C6-206, CD-ROM, Paris (2004).

[31] Codeca F., Savaresi S.M., Manzoni V., The mix estimation algorithm for battery state-of-charge estimator: analysis of the sensitivity to measurement errors, Proceedings of the 48th IEEE Con- ference on Decision and Control, held jointly with 28th Chinese Control Conference (2009),  DOI: 10.1109/CDC.2009.5399759.

[32] Nejad S., Gladwin D.T., Stone D.A., Enhanced state-of-charge estimation for lithium-ion iron phosphate cells with flat open-circuit voltage curves, IECON2015-Yokohama, Japan (2015),  DOI: 10.1109/IECON.2015.7392591.

[33] Huria T., Ceraolo M., Gazzarri J., Jackey R., Simplified extended Kalman filter observer for SOC estimation of commercial power-oriented LFP lithium battery cells, SAE World Congress, Technical Paper Series (2013), DOI: 10.4271/2013-01-1544.

[34] Baccouche I., Jemmali S., Manai B., Omar N., Amara N., Improved OCV model of a li-ion NMC battery for online SOC estimation using the extended Kalman filter, Energies, vol. 10, no. 6, p. 764 (2017), DOI: 10.3390/en10060764.

[35] Zhang C., Jiang J., Zhang L., Liu S., Wang L., Loh P., A generalized SOC-OCV model for lithium- ion batteries and the SOC estimation for LNMCO battery, Energies, vol. 9, no. 11, p. 900 (2016), DOI: 10.3390/en9110900.

[36] Zheng Y., Ouyang M., Han X., Lu L., Li J., Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles, Journal of Power Sources, vol. 377, pp. 161–188 (2018), DOI: 10.1016/j.jpowsour.2017.11.094.

[37] Chen M., Rincon-Mora G.A., Accurate electrical battery model capable of predicting runtime and I–V performance, IEEE Transactions on Energy Conversion, vol. 21, no. 2, pp. 504–511 (2006), DOI: 10.1109/TEC.2006.874229.

[38] Thanagasundram S., Arunachala R., Makinejad K., Teutsch T., Jossen A., A cell level model for battery simulation, European Electric Vehicle Congress Brussels, Belgium (2012).

[39] Feng J.-H., Yang L., Zhao X.-W., Zhang H.-D., Qiang J., Online identification of lithium-ion bat- tery parameters based on an improved equivalent-circuit model and its implementation on battery state-of-power prediction, Journal of Power Sources, vol. 281, pp. 192–203 (2015), DOI: 10.1016/j.jpowsour.2015.01.154.

[40] Rivera-Barrera J., Muñoz-Galeano N., Sarmiento-Maldonado H., SoC Estimation for lithium-ion Bat- teries: review and future challenges, Electronics, vol. 6, no. 4, p. 102 (2017), DOI: 10.3390/electronics6040102.

[41] He H., Xiong R., Fan J., Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach, Energies, vol. 4, no. 4, pp. 582–598 (2011), DOI: 10.3390/en4040582.

[42] Li Z., Huang J., Kiaw B.Y., Zjhang J., On state of charge determination for lithium-ion batteries, Journal of Power Sources, vol. 348, pp. 281–301 (2017), DOI: 10.1016/j.jpowsour.2017.03.001.

<[43] Attanayaka A., Karunadasa J.P., Hemapala K., Estimation of state of charge for lithium-ion batteries – a review, AIMS Energy, vol. 7, no. 2, pp. 186–210 (2019), DOI: 10.3934/energy.2019.2.186.

[44] Fleicher C., Waag W., Hey H.-M., Sauer D.U., On-line adaptive impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models: Part 2. Parameter and state estimation, Journal of Power Sources, vol. 262, pp. 457–482 (2014), DOI: 10.1016/j.jpowsour.2014.03.046.

[45] Zhang C., Allafi W., Dinh Q., Ascencio P., Marco J., Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique, Energy, vol. 142, pp. 678–688 (2018), DOI: 10.1016/

[46] Keil P., Jossen A., Aufbau und Parametrierung von Batteriemodellen. 19. DESIGN&ELEKTRONIK- Entwicklerforum Batterien & Ladekonzepte, München (2012),, accessed April 2021.

[47] El Mejdoubi A., Oukaour A., Chaoui H., Gualous H., Sabor J., Slamani Y., State-of-charge and state-of- health lithium-ion batteries’ diagnosis according to surface temperature variation, IEEE Transactions on Industrial Electronics, vol. 63, no. 4, pp. 2391–2402 (2016), DOI: 10.1109/TIE.2015.2509916.

[48] Chang W.-Y., The state of charge estimating methods for battery: a review, ISRN Applied Mathematics, pp. 1–7 (2013), DOI: 10.1155/2013/953792.

[49] Kalman R.E., A new approach to linear filtering and prediction problems, Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45 (1960), DOI: 10.1115/1.3662552.

[50] Meng J., Ricco M., Luo G., Swierczynski M., Stroe D.-I., Stroe A.-I., Teodorescu R., An overview and comparison of online implementable SOC estimation methods for lithium-ion battery, IEEE Transactions on Industry Applications, vol. 54, no. 2, pp. 1583–1591 (2018), DOI: 10.1109/TIA.2017.2775179.

[51] Duong V.H., Bastawrous H.A., Lim K.C., See K.W., Zhang P., Dou S.X., SOC estimation for LiFePO4 battery in EVs using recursive least-squares with multiple adaptive forgetting factors, 2014 International Conference on Connected Vehicles and Expo (ICCVE) (2014), DOI: 10.1109/IC-CVE.2014.7297603.

[52] Xia B., Huang R., Lao Z., Zhang R., Lai Y., Zheng W., Wang M., Online parameter identification of lithium-ion batteries using a novel multiple forgetting factor recursive least square algorithm, Energies, vol. 11, no. 11, p. 3180 (2018), DOI: 10.3390/en11113180.

[53] Sun X., Ji J., Ren B., Xie C., Yan D., Adaptive forgetting factor recursive least square algorithm for online identification of equivalent circuit model parameters of a lithium-ion battery, Energies, vol. 12, no. 12, p. 2242 (2019), DOI: 10.3390/en12122242.

[54] Chandra Shekar A., Anwar S., Real-time state-of-charge estimation via particle swarm optimization on a lithium-ion electrochemical cell model, Batteries, vol. 5, no. 1, p. 4 (2019), DOI: 10.3390/batteries5010004.

[55] Qays M.O., Buswig Y., Anyi M., Active cell balancing control method for series-connected lithium-ion battery, International Journal of Innovative Technology and Exploring Engineering (IJITEE) (2019), DOI: 10.35940/ijitee.i8905.078919.

[56] Zhang C.-W., Chen S.-R., Gao H.-B., Xu K.-J., Yang M.-Y., State of charge estimation of power battery using improved back propagation neural network, Batteries, vol. 4, no. 4, p. 69 (2018), DOI: 10.3390/batteries4040069.

[57] Jiménez-Bermejo D., Fraile-Ardanuy J., Castaño-Solis S., Merino J., Álvaro-Hermana R., Using dynamic neural networks for battery state of charge estimation in electric vehicles, Procedia Computer Science, vol. 130, pp. 533–540 (2018), DOI: 10.1016/j.procs.2018.04.077.

[58] Thirugnanam K., Ezhil Reena Joy T.P., Singh M., Kumar P., Mathematical modeling of li-ion battery using genetic algorithm approach for V2G applications, IEEE Transactions on Energy Conversion, vol. 29, no. 2, pp. 332–343 (2014), DOI: 10.1109/TEC.2014.2298460.

[59] Liu F., Ma J., Su W., Unscented particle filter for SOC estimation algorithm based on a dynamic parameter identification, Mathematical Problems in Engineering, no. 6, pp. 1–14 (2019), DOI: 10.1155/2019/7452079.

[60] Rozaqi L., Rijanto E., SOC estimation for li-ion battery using optimum RLS method based on genetic algorithm, 8th International Conference on Information Technology and Electrical Engineering (ICITEE) (2016), DOI: 10.1109/ICITEED.2016.7863224.

[61] Styczynski Z., Rudion K., Naumann A., Einführung in Expertensysteme, Springer Verlag (2018).

[62] Wei K., Wu J., Ma W., Li H., State of charge prediction for UAVs based on support vector machine, 7th International Symposium on Test Automation and Instrumentation (ISTAI) (2018), DOI: 10.1049/joe.2018.9201.

[63] Zhang W., Wang W., Lithium-ion battery SoC estimation based on online support vector regression, 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC) (2018), DOI: 10.1109/YAC.2018.8406438.

[64] Alvarez Anton J.C., Garcia Nieto P.J., Blanco Viejo C., Vilan Vilan J.A., Support vector machines used to estimate the battery state of charge, IEEE Transactions on Power Electronics, vol. 28, no. 12, pp. 5919–5926 (2013), DOI: 10.1109/TPEL.2013.2243918.

[65] Rupp S., Modellierung von Anlagen und Systemen Teil 1, DHBW, CAS 2017, TM20305_1_Modellierung_von_Anlagen_und_Systemen.pdf+&cd=1&hl=en&ct=clnk&gl=de, ac- cessed July 2021,

[66] Wenge C., Pietracho R., Balischewski S., Arendarski B., Lombardi P., Komarnicki P., Kasprzyk L., Multi Usage Applications of Li-Ion Battery Storage in a Large Photovoltaic Plant: A Practical Experience, Energies, vol. 13, no. 18, 4590 (2020), DOI: 10.3390/en13184590.

[67] Dambrowski J., Methoden der Ladezustandsbestimmung – mit Blick auf LiFePO4=Li4Ti5O 12-Systeme.

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Authors and Affiliations

Marcel Hallmann
Christoph Wenge
Przemyslaw Komarnicki
Stephan Balischewski

  1. Magdeburg-Stendal University of Applied Sciences, Germany
  2. Fraunhofer IFF Magdeburg, Germany
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This paper takes a 50 kW interior permanent magnet brushless DC motor as an example, and explores the influence of the degree of stator slot skew on the overall motor magnetic density and air gap magnetic density; then reveals the influences of stator slot skewed structure on a series of key electromagnetic properties like no-load back electromotive force (B-EMF), cogging torque, electromagnetic torque, torque fluctuation, electromagnetic loss, input power, output power and operating efficiency. On this basis, a relatively best range of the skew degrees is obtained. The research work in this paper has direct reference value for the further improvement of design and manufacture, operation and maintenance, control and protection of such motors.
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[1] Zhang Chen, Principle and Application of Brushless DC Motor, China Machinery Industry Press, Beijing (1996).
[2] Tang Renyuan, Modern Permanent Magnet Motor Theory and Design, Mechanical Industry Press, Beijing (2005).
[3] LiWeiqi, LinRongwen, Tao Tao, Optimized design based on the air gap length of the built-in permanent magnet brushless DC motor, Electric Switchgear, vol. 58, no. 05, pp. 58–63 (2020).
[4] Parsa L., Hao L., Interior Permanent Magnet Motors with Reduced Torque Pulsation, IEEE Transactions on Industrial Electronics, vol. 55, no. 2, pp. 602–609 (2008), DOI: 10.1109/TIE.2007.911953.
[5] Ren Dejiang, Huang Qu, Li Jianjun, Wu Ning, Cogging torque optimization analysis of built-in permanent magnet synchronous motor, Explosion-Proof Electric Machine, vol. 54, no. 4, pp. 4–7+43 (2019).
[6] Zhao W., Lipo T.A., Kwon B., Torque Pulsation Minimization in Spoke-type Interior Permanent Magnet Motors with Skewing and Sinusoidal Permanent Magnet Configurations, IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1–4 (2015), DOI: 10.1109/TMAG.2015.2442977.
[7] AimengW., Heming L.,Weifu L., Haisen Z., Influence of skewed and segmented magnet rotor on IPM machine performance and ripple torque for electric traction, IEEE International Electric Machines and Drives Conference, pp. 305–310 (2009), DOI: 10.1109/IEMDC.2009.5075222.
[8] Adrian Młot, Marcin Kowol, Janusz Kołodziej, Andrzej Lechowicz, Piotr Skrobotowicz, Analysis of IPM motor parameters in an 80-kW traction motor, Archives of Electrical Engineering, vol. 69, no. 2 (2020), DOI: 10.24425/aee.2020.133038.
[9] Yang Zhihao, Yang Mengxue, Wang Sinuo, Bao Xiaohua, The influence of stator skew on the performance of permanent magnet synchronous motors, Transactions of the Chinese Society of Electrical Engineering, vol. 14, no. 3, pp. 97–102 (2019).
[10] Wang Dongliang, Chen Wei, Discussion on the electromagnetic design of concentrated winding permanent magnet motor from the perspective of torque fluctuation, Electric Tool, vol. 4, pp. 15–17 (2017), DOI: 10.16629/j.cnki.1674-2796.2017.04.004.
[11] Xiaodong S., Zhou S., Long C., Zebin Y., Skew Angle Optimization Analysis of a Permanent Magnet Synchronous Motor for EVs, IEEE International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD), pp. 1–2 (2018), DOI: 10.1109/ASEMD.2018.8558826.
[12] Wang Changcheng, Guo Hui, Sun Pei, Liu Ningning,Wang Yansong, Qin Yifei, A method for reducing cogging torque of permanent magnet synchronous motors, Light Industry Machinery, vol. 36, no. 6, pp. 62–66 (2018).
[13] He Qiang, Magnetic field analysis and cogging torque study of brushless DC permanent magnet motors, Hefei University of Technology (2016).
[14] Hongwei Fang, Hongxu Chen, Analysis and reduction of the cogging torque of flux-modulated generator for wave energy conversion, Energy Procedia, vol. 158, pp. 327–332 (2019), DOI: 10.1016/j.egypro.2019.01.097.
[15] Fu Lixin et al., GB/T 1029-2005 Three-phase synchronous motor test method, China Standard Press, Beijing (2006).
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Authors and Affiliations

Xue-gui Gan
Zhen-nan Fan
Jing-can Li

  1. The Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu, China
  2. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, China
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The continuous drive towards electrified propulsion systems has been imposing ever more demanding performance and cost targets for the future power electronics, machines and drives (PEMDs). This is particularly evident when exploring various technology road mapping documents both for automotive and aerospace industries, e.g. Advanced Propulsion Centre (APC) UK, Aerospace Technology Institute (ATI) UK, National Aeronautics and Space Administration (NASA) USA and others. In that context, a significant improvement of the specific performance and cost measures, e.g. power density increase by a factor of 10 or more and/or cost per power unit reduction by 50% or better, is forecasted for the next 5 to 15 years. However, the existing PEMD solutions are already at their technological limits to some degree. Consequently, meeting the performance and cost step change would require a considerable development effort. This paper is focused on electrical machines and their thermal management, which has been recognised as one of key enabling factors for delivering high specific output solutions. The challenges associated with heat removal in electrical machines are discussed in detail, alongside with new concepts of thermal management systems. Several examples from the available literature are presented. These include manufacturing techniques, new materials and novel integrated designs in application to electrical machines.
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[1] GOV UK, UK becomes first major economy to pass net zero emission law, available at:, accessed October 2021.
[2] EPA GOV, Global Greenhouse Gas Emissions Data, available at:, accessed October 2021.
[3] APC UK, The Roadmap Report, Towards 2040: A Guide to Automotive Propulsion Technologies, Advanced Propulsion Centre (APC) UK, pp. 1–136 (2018).
[4] ATI UK, Insight – Electrical Power Systems, Aerospace Technology Institute (ATI), pp. 1–16 (2018).
[5] Del Rosario R., A Future with Hybrid Propulsion Systems: A NASA Perspective, Turbine Engine Technology Symposium, Strategic Vision Workshop, Dayton, OH, USA, pp. 1–21 (2014).
[6] El-Refaie A., Osama M., High Specific Power Electrical Machines, CES Transactions on Electrical Machines and Systems, vol. 3, no. 1, pp. 88–9 (2017), DOI: 10.30941/CESTEMS.2019.00012.
[7] Popescu M., Staton D.A., Boglietti A., Cavagnino A., Hawkins D., Goss J., Modern Heat Extraction Systems for Power Traction Machines, IEEE Transactions on Industry Applications, vol. 52, no. 3, pp. 2167–2175 (2016), DOI: 10.1109/TIA.2016.2518132.
[8] Gai Y., Kimiabeigi M., Chong Y.C., Widmer J.D., Deng X., Popescu M., Goss J., Staton D.A., Steven A., Cooling of Automotive Traction Motors: Schemes, Examples, and Computational Methods, IEEE Transactions on Industrial Electronics, vol. 66, no. 3, pp. 1681–1692 (2019), DOI: 10.1109/TIE.2018.2835397.
[9] Yang Y., Bilgin B., Kasprzak M., Nalakath S., Sadek H., Preindl M., Cotton J., Schofield N., Emadi A., Thermal Management of Electric Machines, IET Electrical Systems in Transportation, vol. 7, no. 6, pp. 104–116 (2017), DOI: 10.1049/iet-est.2015.0050.
[10] Bennion K., Electric Motor Thermal Management, National Renewable Energy Laboratory (NREL), U.S. Department of Energy Vehicle Technologies Program Annual Merit Review, pp. 1-28 (2011).
[11] Lambourne A., Opportunities and Challenges of ALM in Electrical Machines, Advanced Propulsion Centre UK (APC UK), Seminar, Bristol, UK (2019).
[12] Wrobel R., Mecrow B., A Comprehensive Review of Additive Manufacturing in Construction of Electrical Machines, IEEE Transactions on Energy Conversion, vol. 34, no. 2, pp. 1054–1064 (2020), DOI: 10.1109/TEC.2020.2964942.
[13] Wu F., El-Refaie A.M., Towards Additively-Manufactured Electrical Machines: Opportunities and Challenges, IEEE Transactions on Industry Applications, vol. 56, no. 2, pp. 1306–1320 (2019), DOI: 10.1109/TIA.2019.2960250.
[14] Wrobel R., Mellor P.H., Popescu M., Staton D.A., Power Loss Analysis in Thermal Design of Permanent-Magnet Machines - Review, IEEE Transactions on Industry Applications, vol. 52, no. 2, pp. 1359–1368 (2016), DOI: 10.1109/TIA.2015.2489599.
[15] Liu H., Ayat S.,Wrobel R., Zhang C., Comparative Study of Thermal Properties of ElectricalWindings Impregnated with Alternative Varnish Materials, IET Journal of Engineering, vol. 2019, no. 17, pp. 3736–3741 (2019), DOI: 10.1049/joe.2018.8198.
[16] Ayat S., Liu H., Kulan M., Wrobel R., Estimation of Equivalent Thermal Conductivity for Electrical Windings with High Conductor Fill Factor, IEEE Energy Conversion Congress and Exposition (ECCE), pp. 6529–6536 (2018).
[17] Wrobel R., Ayat S., Godbehere J., A Systematic Experimental Approach in Deriving Stator-Winding Heat Transfer, IEEE International Electric Machines and Drives Conference (IEMDC), pp. 1–8 (2017).
[18] Chiodetto N., Mecrow B.,Wrobel R., Lisle T., Elector-Mechanical Challenges in the Design of a High- Speed-High-Power-PMSM Rotor for an Aerospace Application, IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, pp. 3944–3951 (2019).
[19] Gerada D., Mebarki A., Brown N.L., Gerada C., Cavagnino A., Boglietti A., High-Speed Electrical Machines: Technologies, Trends, and Developments, in IEEE Transactions on Industrial Electronics, vol. 61, no. 6, pp. 2946–2959 (2014), DOI: 10.1109/TIE.2013.2286777.
[20] Moghaddam R.R., High speed operation of electrical machines, a review on technology, benefits and challenges, IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, pp. 5539–5546 (2014).
[21] Gieras J.F., Advancements in Electrical Machines – Power Systems, Springer (2008). [22] Additive News, Additive Manufacturing moves TUfast, available at:, accessed October 2021.
[23] Wrobel R., Hussein A., A Feasibility Study of Additively Manufactured Heat Guides for Enhanced Heat Transfer in Electrical Machines, IEEE Transactions on Industry Applications, vol. 56, no. 1, pp. 205–215 (2020), DOI: 10.1109/TIA.2019.2949258.
[24] Sixel W., Liu M., Nellis G., Sarlioglu B., Cooling of Windings in Electrical Machines via 3D Printed Heat Exchanger, IEEE Energy Conversion Congress and Exposition (ECCE), pp. 229–235, (2018).
[25] Sixel W., Liu M., Nellis G., Sarlioglu B., Ceramic 3D Printed Direct Winding Heat Exchangers for Improving Electric Machine Thermal Management, IEEE Energy Conversion Congress and Exposition (ECCE), pp. 769–776 (2019).
[26] Lindh P., Petrov I., Pyrhonen J., Scherman E., Niemela M., Immonen P., Direct Liquid Cooling Method Verified with a Permanent-Magnet Traction Motor in a Bus, IEEE Transactions on Industry Applications, vol. 55, no. 4, pp. 4183–4191 (2019), DOI: 10.1109/TIA.2019.2908801.
[27] Lorenz F., Rudolph J.,Werner R., Design of 3D printed High Performance Windings for Switched Reluctance Machines, International Conference on Electrical Machines (ICEM), pp. 2451–2457 (2018).
[28] Pyrhonen J., Montonen J., Lindh P., Vauterin J., Otto M., Replacing Copper with New Carbon Nanomaterials in Electrical Machine Windings, International Review of Electrical Engineering, pp. 12–21 (2015), DOI: 10.15866/IREE.V10I1.5253.
[29] Wohlers C., Juris P., Kabelac S., Ponick B., Design and Direct Liquid Cooling of Tooth-Coil Winding, Electrical Engineering, Springer, vol. 100, no. 4, pp. 2299–2308 (2018), DOI: 10.1007/s00202-018-0704-x.
[30] Ayat S., Daguese B., Khazaka R., Design Considerations ofWindings Formed with Hollow Conductors Cooled with Phase Change Material, IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, pp. 5539–5546 (2019).
[31] Gai Y., Widmer J.D., Steven A., Chong Y.C., Kimiabeigi M., Goss J., Popescu M., Numerical and Experimental Calculations of CHTC in an Oil-Based Shaft Cooling System for a High-Speed High- Power PMSM, IEEE Transactions on Industrial Electronics, vol. 67, no. 6, pp. 4371–4380 (2020), DOI: 10.1109/TIE.2019.2922938.
[32] Davin T., Pelle J., Harmand S., You R., Experimental Study of Oil Cooling System for Electric Motors, Applied Thermal Engineering, Elsevier, vol. 75, no. 2, pp. 1–13 (2015), DOI: 10.1016/j.applthermaleng.2014.10.060.
[33] Brown G.V., Cryogenic Electric Motor Tested, NASA report – propulsion and power (2005).
[34] Arndt T., Basic Considerations and Recent Results in HTS Device Developments for Electric Aircraft, Safran-Group h Scientific Day, Paris, France (2020).
[35] ASuMED – Deliverable System Topology Report, 2017.

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Authors and Affiliations

Rafal Wrobel

  1. Newcastle University, United Kingdom
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[1] Hou C., Zhu M., Chen Y., Cai X., Pre-filter phase-locked loop: principles and effects with inter- harmonic perturbation, IET Renewable Power Generation, vol. 14, no. 16, pp. 3088–3096 (2020), DOI: 10.1049/iet-rpg.2020.0448.

[2] Jove E., Gonzalev C.J.M., Casteleiro R.J.L. et al., An intelligent system for harmonic distortions detection in wind generator power electronic devices, Neurocomputing, vol. 456, pp. 609–621 (2021), DOI: 10.1016/j.neucom.2020.07.155.

[3] Altintasi C., Aydin O., Taplamacioglu M.C. et al., Power system harmonic and interharmonic estima- tion using Vortex Search Algorithm, Electric Power Systems Research, vol. 182, pp. 106187 (2020), DOI: 10.1016/j.epsr.2019.106187.

[4] Sun Y., Lin Y., Wang Y. et al., Theory of symmetric winding distributions and a general method for winding MMF harmonic analysis, IET Electric Power Applications, vol. 14, no. 13 (2021), DOI: 10.1049/iet-epa.2020.0553.

[5] Cao Q., Shen Q.T., An improved �� �� ����harmonic current detecting method and digital LPF filter’s study, Techniques of Automation and Applications, vol. 29, no. 3, pp. 74–76 (2010),

[6] Paplinski J.P., Cariow A., Fast 10-Point DFT Algorithm for Power System Harmonic Analysis, Applied Sciences, vol. 11, no. 15, p. 7007 (2021), DOI: 10.3390/app11157007.

[7] Wu J.Z., Mei F., Chen C., Power system harmonic detection method based on empirical wavelet transform, Power System Protection and Control, vol. 48, no. 6, pp. 136–143 (2020), DOI: 10.19783/j.cnki.pspc.190470.

[8] Li J., Lin H., Teng Z. et al., Digital prolate spheroidal window-based S-transform for time-varying harmonic analysis, Electric Power Systems Research, vol. 187 (2020), DOI: 10.1016/j.epsr.2020.106512.

[9] Zhang Y.L., Chen H.W., Parameter identification of harmonics and inter-harmonics based on ceemd- wpt and Prony algorithm, Power System Protection and Control, vol. 46, no. 12, pp. 115–121 (2018), DOI: 10.7667/PSPC170866.

[10] Yang Y.K., Yang M.Y., Application of prony algorithm in parameter identification of harmon- ics and inter-harmonics, Proceedings of the CSU-EPSA, vol. 24, no. 3, pp. 121–126 (2012),

[11] Zhang Y., Fan W., Zhang Q., Li X., Harmonic separation from grid voltage with EEMD-ICA and SVD, Computer Measurement and Control, vol. 27, no. 3, pp. 39–43 (2019), ch/reader/view_abstract.aspx?file_no=201809061095.

[12] Chen Q., Cai W., Sun L. et al., Harmonic detection method based on VMD, Electrical Measurement and Instrumentation, vol. 55, no. 2, pp. 59–65 (2018),

[13] Thirumala K., Umarikar A.C., Jian T., Estimation of single-phase and three -phase power -quality indices using empirical wavelet transform, IEEE Transactions on Power Delivery, vol. 30, no. 1, pp.445–454 (2015), DOI: 10.1109/TPWRD.2014.2355296.

[14] Desai V.A., Rathore S., Harmonic detection using Kalman filter, In Proceedings of the 2016 Interna- tional Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), Chennai, India, pp. 858–863 (2016), DOI: 10.1109/ICEEOT.2016.7754808.

[15] Tiyarachakun S., Areerak K.L., Areerak K.N., Instantaneous Power Theory with Fourier and Optimal Predictive Controller Design for Shunt Active Power Filter, Model. Simul. Eng., pp. 1–20 (2014), DOI: 10.1155/2014/381760.

[16] Habrouk M., Darwish M.K., Design and implementation of a modified Fourier analysis harmonic current computation technique for power active filters using DSPs, IEEE Proc. Electr. Power Appl., vol. 148, pp. 21–28 (2001), DOI: 10.1049/ip-epa:20010014.

[17] Karimi H., Karimi G.M., Reza I.M., Bakhshai A.R., An adaptive filter for synchronous extraction of har- monics and distortions, IEEE Trans. Power Deliv., vol. 18, pp. 1350–1356 (2003), DOI: 10.1515/ijeeps- 2013-0145.

[18] Musa S., Mohd M.A., Hoon Y., Modified Synchronous Reference Frame Based Shunt Active Power Filter with Fuzzy Logic Control Pulse Width Modulation Inverter, Energies, vol. 10, no. 758 (2017), DOI: 10.3390/en10060758.

[19] Narongrit T., Areerak K.L., Areerak K.N., A New Design Approach of Fuzzy Controller for Shunt Active Power Filter, Electr. Power Compon. Syst., vol. 43, pp. 685–694 (2015), DOI: 10.1080/ 15325008.2014.996680.

[20] Sujitjorn S., Areerak K.L., Kulworawanichpong T., The DQ Axis with Fourier (DQF) Method for Harmonic Identification, IEEE Trans. Power Deliv., vol. 22, pp. 737–739 (2007), DOI: 10.1109/TP- WRD.2006.882465.

[21] Daubechies I., Jianfeng L., Synchrosqueezed wavelet transforms: An empirical mode decomposition- like tool, Applied and Computational Harmonic Analysis, vol. 30, no. 2, pp. 243–261 (2011), DOI: 10.1016/j.acha.2010.08.002.

[22] Li L., Cai H.Y., Jiang Q.T., Ji H.B., Adaptive synchrosqueezing transformwith a time-varying parameter for non-stationary signal separation, Applied and Computational Harmonic Analysis, vol. 49, no. 3, pp. 1884–2020 (2019), DOI: 10.1016/j.acha.2019.06.002.

[23] Gang Y., Zhonghu W., Ping Z., Zhen L., Local maximum synchrosqueezing transform: An energy- concentrated time-frequency analysis tool, Mechanical Systems and Signal Processing, vol. 117, pp. 537–552 (2019), DOI: 10.1016/j.ymssp.2018.08.006.

[24] Lin L., Haiyan C., Qiangtang J., Hongbing J., An empirical signal separation algorithm for multicom- ponent signals based on linear time-frequency analysis, Mechanical Systems and Signal Processing. vol. 121, pp. 791–809 (2019), DOI: 10.1016/j.ymssp.2018.11.037.

[25] Rasoul M.M., Alan F.L., Yunwei L., Adaptive control of an active power filter for harmonic suppres- sion and power factor correction, International Journal of Dynamics and Control, pp. 1–10 (2021), DOI: 10.1007/s40435-021-00825-0.

[26] Avalos O., Cuevas E., Becerra H.G. et al., Kernel Recursive Least Square Approach for Power System Harmonic Estimation, Electric Power Components and Systems, vol. 48, no. 16–17, pp. 1708–1721 (2021), DOI: 10.1080/15325008.2021.1908457.

[27] Mert A., Celik H.H., Emotion recognition using time-frequency ridges of EEG signals based on multivariate synchrosqueezing transform, Biomedizinische Technik. Biomedical Engineering, vol. 66, no. 4, pp. 345–352 (2021), DOI: 10.1515/bmt-2020-0295.

[28] Yang C., Ban L., Research on Harmonic Detection System Based on Wavelet Packet Transform, IOP Conf. Series: Journal of Physics: Conf. Series, vol. 1314, no. 012038 (2019), DOI: 10.1088/1742-6596/1314/1/012038.

[29] Gong M.F. et al., A New Method to Detect Harmonics and Inter-Harmonics Based on Hilbert Marginal Spectrum, Applied Mechanics and Materials, vol. 229–231, pp. 1060–1063 (2012), DOI: 10.4028/

[30] Yu M., Wang B., Wang W.B. et al., An inter-harmonic detection method based on synchrosqueezing wavelet transform, Proceedings of the CSEE, vol. 36, no. 11, pp. 2944–2951 (2016), DOI: 10.13334/j.0258-8013.pcsee.2016.11.010.

[31] Chang G.W. et al., A Hybrid Approach for Time-Varying Harmonic and Interharmonic Detection Using Synchrosqueezing Wavelet Transform, Applied Sciences, vol. 11, no. 2, pp. 752 (2021), DOI: 10.3390/app11020752.

[32] Khoa N.M., Le V.D., Tung D.D., Toan N.A., An advanced IoT system for monitoring and analysing chosen power quality parameters in micro-grid solution, Archives of Electrical Engineering, vol. 70, no. 1, pp. 173–188 (2021), DOI: 10.24425/aee.2021.136060.

[33] Yudaev I.V., Rud E.V., Yundin M.A., Ponomarenko T.Z., Isupova A.M., Analysis of the harmonic composition of current in the zero-working wire at the input of the load node with the prevailing non-linear power consumers, Archives of Electrical Engineering, vol. 70, no. 2, pp. 463–473 (2021), DOI: 10.24425/aee.2021.136996.

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Authors and Affiliations

Lin Sun
Jing Song
Yan Jin

  1. Wuchang University of Technology, China
  2. National University of Defense Technology, China
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A novel magnetically-coupled energy storage inductor boost inverter circuit for renewable energy and the dual-mode control strategy with instantaneous value feedback of output voltage are proposed. In-depth research and analysis on the circuit, control strategy, voltage transmission characteristics, etc., providing the parameter design method of magnetically-coupled energy storage inductors and output filter. The circuit topology is cascaded by the input source ��in, the input filter ��in, a single-phase inverter bridge with a magnetically-coupled energy storage inductor, and a CL filter; The control strategy serves the output voltage as a reference to achieve the switch of step-down and step-up modes smoothly. The simulation results of a 1000 VA 100–200 VDC, 220 V 50 Hz AC inverter show that the proposed inverter can realize single-stage boost power conversion, which can adapt to resistive, capacitive and inductive loads, has high power density and low output waveform distortion. It has good application prospects in small and medium-capacity single-phase inverter occasions with low input voltage.
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[1] Hussain H.M., Narayanan A., Nardelli P.H.J., Yang Y., What Is Energy Internet? Concepts, Technologies, and Future Directions, IEEE Access., vol. 8, pp. 183127–183145 (2020), DOI: 10.1109/access.2020.3029251.

[2] Tao Z., Jiahui J., Daolian C., An efficient and low-cost DMPPT approach for photovoltaic sub-module based on multi-port DC converter, Renewable Energy, vol. 178, pp. 1144–1155 (2021), DOI: 10.1016/j.renene.2021.06.134.

[3] Jiang J., Zhang T., Chen D., Analysis, Design, and Implementation of a Differential Power Processing DMPPT With Multiple Buck–Boost Choppers for Photovoltaic Module, IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10214–10223 (2021), DOI: 10.1109/tpel.2021.3063230.

[4] Xianglin L., Zhiwei X., Xueyu Y., Lixia Z., Wenzhong M., Wei H., Low-complexity multivector-based model predictive torque control for PMSM with voltage preselection, IEEE Transactions on Power Electronics, vol. 36, no. 10, pp. 11726–11738 (2021), DOI: 10.1109/tepl.2021.3073137.

[5] Xianglin L., Zhiwei X., Lixia Z., Wei H., A low-complexity three-vector-based model predictive torque control for SPMSM, IEEE Transactions on Power Electronics, vol. 36, no. 11, pp. 13002–13012 (2021), DOI: 10.1109/TPEL.2016.2532387.

[6] Rahbar K., Chai C.C., Zhang R., Energy cooperation optimization in microgrids with renew- able energy integration, IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 1482–1493 (2018), DOI: 10.1109/tsg.2016.2600863.

[7] Quint R. et al., Transformation of the grid: the impact of distributed energy resources on bulk power systems, IEEE Power and Energy Magazine, vol. 17, no. 6, pp. 35–45 (2019), DOI: 10.1109/mpe. 2019.2933071.

[8] Salem Q., Liu L., Xie J., Dual operation mode of a transformerless h-bridge inverter in low- voltage microgrid, IEEE Transactions on Industry Applications, vol. 55, no. 5, pp. 5289–5299 (2019), DOI: 10.1109/tia.2019.2917807.

[9] Hanchao Z., Daolian C., A single-stage isolated charging/discharging DC-AC converter with sec- ond harmonic current suppression in distributed generation systems, IECON 2017 – 43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, China, pp. 4427–4432 (2017).

[10] Liu S., He Y., Wang G., Wang M., Power Decoupling Control for Boost-Type Single-Phase Inverter with Active Power Buffer, 2019 IEEE Energy Conversion Congress and Exposition, Maryland, USA, pp. 2280–2285 (2019).

[11] Stawiarski Ł., Piróg S., Active power decoupling topology for AC-DC and DC-AC single-phase systems with decoupling capacitor minimization, Archives of Electrical Engineering, vol. 67, no. 1, pp. 193–205 (2018), DOI: 10.24425/aee.2018.119001.

[12] Xu S., Chang L., Shao R., Single-phase voltage source inverter with voltage Boosting and power decoupling capabilities, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 3, pp. 2977–2988 (2020), DOI: 10.1109/jestpe.2019.2936136.

[13] Chen Z., Wu Q., Yuan Y., A novel zero-voltage-switching push–pull high-frequency-link single-phase inverter, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 2, pp. 421–434 (2016), DOI: 10.1109/jestpe.2015.2505171.

[14] Watanabe H., Itoh J., Novel DC to single-phase AC isolated current source inverter with power decou- pling capability for micro-inverter system, 2015 IEEE Energy Conversion Congress and Exposition, Montreal, Canada, pp. 158–165 (2015).

[15] Chakraborty S., Chattopadhyay S., An isolated Buck-Boost type high-frequency link photovoltaic microinverter, 2016 IEEE Applied Power Electronics Conference and Exposition, California, USA, pp. 3389–3396 (2016).

[16] Jiang J., Li Z., Chen D., A quasi single stage isolated Buck-Boost mode multi-input inverter, 2019 10th International Conference on Power Electronics and ECCE Asia, Busan, Korea, pp. 1–6 (2019).

[17] Baoge Z., Deyu H., Tianpeng W., Zhen Z., Donghao W., A novel two-phase interleaved parallel bi-bidrectional DC/DC converter, Archives of Electrical Engineering, vol. 70, no. 1, pp. 219–234 (2021), DOI: 10.24425/aee.2021.136063.

[18] Hong F., Liu J., Ji B., Zhou Y., Wang J., Wang C., Single inductor dual Buck full-bridge inverter, IEEE Transactions on Industrial Electronics, vol. 62, no. 8, pp. 4869–4877 (2015),  DOI: 10.1109/tie.2015.2399280.

[19] Zhang L., Zhang T., Hao Y., Wang B., Two-stage dual-Buck grid-tied inverters with efficiency en-hancement, 2019 IEEE Applied Power Electronics Conference and Exposition, California, USA,  pp. 3251–3256 (2019).

[20] Jagan V., Kotturu J., Das S., Enhanced-Boost quasi-z-source inverters with two-switched impedance networks, IEEE Transactions on Industrial Electronics, vol. 64, no. 9, pp. 6885–6897 (2017), DOI: 10.1109/tie.2017.2688964.

[21] Zhu X., Zhang B., Qiu D., A high Boost active switched quasi-z-source inverter with low input current ripple, IEEE Transactions on Industrial Informatics, vol. 15, no. 9, pp. 5341–5354 (2019), DOI: 10.1109/tii.2019.2899937.

 [22] Leonardo P. Sampaio, Moacyr A.G. de Brito, Luigi G. Junior, Single-phase current-source-Boost inverter for renewable energy sources, 2011 IEEE International Symposium on Industrial Electronics, Gdansk, Poland, pp. 1118–1123 (2011), DOI: 10.1109/ISIE.2011.5984201.

[23] Nattymol Y.J., Shanavas T.N., Power quality analysis of single-phase transformer-less Buck-Boost inverter for compressor load, 2019 IEEE International Conference on Intelligent Techniques in Control, Optimization and Signal Processing (INCOS), Tamilnadu, India (2019), DOI: 10.1109/IN-COS45849.2019.8951345.

[24] Sreekanth T., Lakshmi Narasamma N., Mahesh K. Mishra, Sijo Augustine, A single stage cou- pled inductor based high gain DC-AC Buck-Boost inverter for photovoltaic (PV) applications, 2015 IEEE 42nd Photovoltaic Specialist Conference (PVSC), New Orleans, LA, USA  (2015), DOI: 10.1109/pvsc.2015.7356269.

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Authors and Affiliations

Yiwen Chen
Sixu Luo
Zhiliang Huang
Jiahui Jiang

  1. Fujian Key Laboratory of New Energy Generation and Power Conversion, Fuzhou University, China
  2. Texas Instruments Semiconductor Technologies (Shanghai) Co., Ltd., China
  3. College of Electrical Engineering, Qingdao University, China
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The main objective of this article is to assess the legitimacy of using different tracking systems applied to the photovoltaic panels, for the city of Wroclaw (Poland), using 2 numerical tools: the CM SAF (Climate Monitoring Satellite Application Facility) and PVGIS (Photovoltaic Geographical Information System). In order to identify the solar irradiation, the CM-SAF database (based on the measurements of MFG – Meteosat First Generation – and MSG – Meteosat Second Generation – satellites) was utilised, while the PVGIS (Photovoltaic Geographical Information System) – to calculate the energy yield from PV panels. Particular attention was given to the optimisation of the annual tilt angle and the determination of the energy benefits from the implementation of the various sun tracking systems. Conducted studies showed that up to 30% more electricity yearly can be yielded after the replacement of PV cells with optimally fixed both azimuth and tilt angles by the 2-axis tracking system (179 kWh/m2 instead of 138 kWh/m2). Moreover, by the adequate decreasing of tilt angles in the summer time or obtaining the most favourable local solar exposure conditions, the supply curve of PV units may be significantly flattened, which may be beneficial when energy storage systems have low capacities.
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[1] McKinsey&Company, Assessment of Greenhouse Gas Emissions Abatement Potential in Poland by 2030. Summary of findings, Publications of McKinsey&Company (2009).

[2] Fraunhofer Institute for Solar Energy Systems, PSE AG, Photovoltaics Report, Materials of Fraunhofer ISE (2017).

[3] Ciechanowska M., Energy Policy of Poland by 2050, Nafta-Gaz (in Polish), vol. 11, pp. 839–842 (2014).

[4] Stowarzyszenie Branży Fotowoltaicznej – Polska PV, Development of the Polish PV market in 2010-2020, Główny Urząd Statystyczny (in Polish) (2016).

[5] Ministerstwo Gospodarki RP, Conclusions from forecast analyses for the purposes of Energy Policy of Poland until 2050. Annex 2, Ministerstwo Gospodarki RP (in Polish) (2015).

[6] Strupczewski A., Analysis and evaluation of electricity costs from various energy sources in Poland, National Centre of Nuclear Research (in Polish), Świerk (2015).

[7] Babatunde A.A., Abbasoglu S., Evaluation of field data and simulation results of a photovoltaic system in countries with high solar radiation, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 23, no. 6, pp. 1608–1618 (2015), DOI: 10.3906/elk-1402-313.

[8] Abdul Kareem M.S., Saravanan M., A new method for accurate estimation of PV module parameters and extraction of maximum power point under varying environmental conditions, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 24, no. 4, pp. 2028–2041 (2016), DOI: 10.3906/elk-1312-268.

[9] Khan J., Arsalan M.H., Solar power technologies for sustainable electricity generation – A review, Renewable & Sustainable Energy Reviews, vol. 55, pp. 414–425 (2016), DOI: 10.1016/j.rser.2015.10.135.

[10] Hafiz A.M., Abdelrahman M.E., Temraz H., Economic dispatch in power system networks including renewable energy resources using various optimization techniques, Archives of Electrical Engineering, vol. 70, no. 3, pp. 643–655 (2021), DOI: 10.24425/aee.2021.137579.

[11] Cholewiński M., Tomków Ł., Domestic hydrogen installation in Poland – technical and economic analysis, Archives of Electrical Engineering, vol. 64, no. 2, pp. 189–196 (2015), DOI: 10.1515/aee-2015-0016.

[12] Sharma H., Pal N., Kumar P., Yadav A., A control strategy of hybrid solar-wind energy generation system, Archives of Electrical Engineering, vol. 66, no. 2, pp. 242–251 (2017), DOI: 10.1515/aee- 2017-0018.

[13] Jastrzębska G., Solar cells. Construction, technology and application, Wydawnictwa Komunikacji i Łączności (in Polish) (2013).

[14] Ding R., Feng C., Wang D., Sun R., Wang L., Yuan S., Trade based on alliance chain in energy from distributed photovoltaic grids, Archives of Electrical Engineering, vol. 70, no. 2, pp. 325–336 (2021), DOI: 10.24425/aee.2021.136987.

[15] IHS Markit, Concentrated PV (CPV) Report – 2014, IHS Markit Company (2014).

[16] Huld T., Jäger Waldau A., Ossenbrink H., Szabo S., Dunlop E., Taylor N., Cost Maps for Unsubsidised Photovoltaic Electricity, Report number JRC 91937 Joint Research Centre (2014).

[17] Fraunhofer ISE, Current and Future Cost of Photovoltaics. Long-term Scenarios for Market Develop- ment, System Prices and LCOE of Utility-Scale PV Systems, Study on behalf of Agora Energiewende, 059/01-S-2015/EN (2015).

[18] Bukowski M., Śniegocki A., Megatrends – from acceptance to action, WiseEuropa – Warsaw Institute for Economic and European Studies (in Polish), ISBN 978-83-64813-30-6 (2017).

[19] Badescu V., Modeling Solar Radiation at the Earth’s Surface, Springer (2008), DOI: 10.1007/978-3-540-77455-6.

[20] The German Energy Society, Planning & Installing Photovoltaic Systems. A Guide for Installers, Architects and Engineers, Earthscal (2008), DOI: 10.4324/9781849776998.

[21] Šúri M., Remund J., Cebecauer T., Dumortier D., Wald L., Huld T., Blanc P., First Steps in the Cross- Comparison of Solar Resource Spatial Products in Europe, Proceedings of the EUROSUN 2008, 1����International Conference on Solar Heating, Cooling and Buildings, Lisbon, Portugal, JRC47255 (2008).

[22] Scharmer K., Greif J., The European Solar Radiation Atlas. Vol. 1: Fundamentals and Maps, École des Mines de Paris, ISBN 2-911762-21-5 (2000).

[23] NREL, Best Research-Cell Efficiency Chart, available on-line:, accessed May 2021.

[24] International Renewable Energy Agency (IRENA), Solar Photovoltaics, Renewable Energy Technologies: Cost Analysis Series, Vol. 1: Power Sector, iss. 4/5 (2012).

[25] Saga T., Advances in crystalline silicon solar cell technology for industrial mass production, NPG Asia Materials, vol. 2, pp. 96–102 (2010), DOI: 10.1038/asiamat.2010.82.

[26] Mengi O.O., Altas I.H., Fuzzy logic control for a wind/battery renewable energy production sys- tem, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 2, pp. 187–206 (2012), DOI: 10.3906/elk-1104-20.

[27] Buyukguzel B., Aksoy M., A current-based simple analog MPPT circuit for PV systems, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 24, no. 5, pp. 3621–3637 (2016), DOI: 10.3906/elk-1407-21.

[28] Hafez A.Z., Tilt and azimuth angles in solar energy applications – A review, Renewable & Sustainable Energy Reviews, vol. 77, pp. 147–168 (2017), DOI: 10.1016/j.rser.2017.03.131.

[29] Seddjar A., Kerrouche K.D.E., Wang L., Simulation of the proposed combined Fuzzy Logic Control for Maximum Power Point Tracking and Battery Charge Regulation used in CubeSat, Archives of Electrical Engineering, vol. 69, no. 3, pp. 521–543 (2020), DOI: 10.24425/aee.2020.133916.

[30] Komarnicki P., Energy storage systems: power grid and energy market use cases, Archives of Electrical Engineering, vol. 65, no. 3, pp. 495–511 (2016), DOI: 10.1515/aee-2016-0036.

[31] Michalak P., Atmospheric transparency coefficient at selected stations in the Southern and Eastern Poland, Polska Energetyka Słoneczna (in Polish), vol. 2–4, pp. 23–26 (2011).

[32] Marchel P., Paska J., Modeling of photovoltaic power plants reliability, Rynek Energii (in Polish, abstract in English), vol. 111, no. 2, pp. 81–86 (2014).

[33] Cooper P.I., The absorption of radiation in solar stills, Solar Energy, vol. 12, pp. 333–346 (1969), DOI: 10.1016/0038-092X(69)90047-4.

[34] Shen Ch., He Y.-L., Liu Y.-W., Tao W.-Q., Modelling and simulation of solar radiation data processing with Simulink, Simulation Modelling Practice and Theory, vol. 16, pp. 721–735 (2008), DOI: 10.1016/j.simpat.2008.04.013.

[35] Kamali G.A., Moradi I., Khalili A., Estimating solar radiation on tilted surfaces with various orientations: a study case in Karaj (Iran), Theoretical and Applied Climatology, vol. 84, pp. 235–241 (2006), DOI: 10.1007/s00704-005-0171-y.

[36] Polski Komitet Normalizacyjny, EN 61215-1:2016. Terrestrial photovoltaic (PV) modules. Design qualification and type approval. Test requirements, PKN (2016).

[37] Photovoltaic Geographical Information System (PVGIS), available on-line: jrc/en/pvgis, accessed April 2018.

[38] Amillo A.G., Huld T., Müller R., A New Database of Global and Direct Solar Radiation Using the Eastern Meteosat Satellite, Models and Validation, Remote Sensing, vol. 6, pp. 8165–8189 (2014), DOI: 10.3390/rs6098165.

[39] Shiva Kumar B., Sudhakar K., Performance evaluation of 10 MW grid connected solar photovoltaic power plant in India, Energy Reports, vol. 1, pp. 184–192 (2015), DOI: 10.1016/j.egyr.2015.10.001.

[40] Ministerstwo Klimatu i Środowiska, Energy Policy of Poland by 2040. Annex to the Resolution No. 22/2021 of the Council of Ministers from the 2nd February 2021, Ministerstwo Klimatu i Środowiska RP (in Polish) (2021).

[41] Wood Mackenzie, US solar PV system pricing: H2 2020, Wood Mackenzie (2020).

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Authors and Affiliations

Maciej Cholewiński
Jean-Marc Fąfara

  1. Wrocław University of Science and Technology, Faculty of Mechanical and Power Engineering, Department of Cryogenics and Aviation Engineering, Poland
  2. Wrocław University of Science and Technology, Faculty of Mechanical and Power Engineering, Department of Energy Conversion Engineering, Poland
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This paper proposes two high-order sliding mode algorithms to achieve highperformance control of induction motor drive. In the first approach, the super-twisting algorithm (STA) is used to reduce the chattering effect and to improve control accuracy. The second approach combines the super-twisting algorithm with a quasi-barrier function technique. While the super-twisting algorithm (STA) aims at the chattering reduction, the Barrier super-twisting algorithm (BSTA) aims to eliminate this phenomenon by providing continuous output control signals. The BSTA is designed to prevent the STA gain from being over-estimated by making these gains to decrease and increase according to system’s uncertainties. Stability and finite-time convergence are guaranteed using Lyapunov’s theory. In addition, the two controlled variables, rotor speed, and rotor flux modulus are estimated based on the second-order sliding mode (SOSM) observer. Finally, simulations are carried out to compare the performance and robustness of two control algorithms without adding the equivalent control. Tests are achieved under external load torque, varying reference speed, and parameter variations.
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[1] Senthilnathan N., Comparative analysis of line-start permanent magnet synchronous motor and squirrel cage induction motor under customary power quality indices, Electrical Engineering, vol. 102, no. 3, pp. 1339–1349 (2020), DOI: 10.1007/s00202-020-00955-2.

[2] Morfin O.A., Miranda U., Valenzuela R.R., Valenzuela F.A., Tellez F.O., Acosta J.C., State-feedback linearization using a robust differentiator combined with SOSM super-twisting for controlling the induction motor velocity, 2018 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, México, pp. 1–6 (2018), DOI: 10.1109/ROPEC.2018.8661477.

[3] Acikgoz H., Real-time adaptive speed control of vector-controlled induction motor drive based on online-trained Type-2 Fuzzy Neural Network Controller, International Transactions on Electrical En- ergy Systems (2021), DOI: 10.1002/2050-7038.12678.

[4] Chen C., Wu H., Lin Y., Stator flux oriented multiple sliding-mode speed control design of induction motor drives, Advances in Mechanical Engineering, vol. 13, no. 5, pp. 1–10 (2021), DOI: 10.1177/16878140211021734.

[5] Steinberger M., Horn M., Fridman L., Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice, Springer International Publishing (2020).

[6] Bartolini G., Levant A., Pisano A., Usai E., Adaptive second-order sliding mode control with uncer- tainty compensation, International journal of Control, vol. 89, no. 9 (2016), DOI: 10.1080/00207179.2016.1142616.

[7] Siddique N., Rehman F.U., Hybrid synchronization and parameter estimation of a complex chaotic network of permanent magnet synchronous motors using adaptive integral sliding mode control, Archives of Electrical Engineering, pp. 137056–137056 (2021), DOI: 10.24425/bpasts.2021.137056.

[8] Quintero-Manriquez E., Sánchez E., Felix R., Induction motor torque control via discrete-time sliding mode, World Autom. Congr., WAC, pp. 1–5 (2016), DOI: 10.1109/WAC.2016.7582984.

[9] Martínez-Fuentes C.A., Ventura U.P., Fridman L., Chattering analysis of Lipschitz continuous sliding-mode controllers, ArXiv200400819 Cs Eess (2020).

[10] Utkin V., Poznyak A., Orlov Y.V., Polyakov A., Chattering Problem in Road Map for Sliding Mode Control Design, Springer International Publishing, pp. 73–82 (2020), DOI: 10.1007/978-3-030- 41709-3.

[11] Chaabane H., Djalal Eddine K., Salim C., Sensorless back stepping control using a Luenberger observer for double-star induction motor, Archives of Electrical Engineering, vol. 69, no. 1, (2020), DOI: 10.24425/aee.2020.131761.

[12] Swikir A., Utkin V., Chattering analysis of conventional and super twisting sliding mode control algorithm, in 2016 14th International Workshop on Variable Structure Systems (VSS), pp. 98–102 (2016), DOI: 10.1109/VSS.2016.7506898.

[13] Utkin V., Hoon Lee, Chattering Problem in Sliding Mode Control Systems, in International Workshop on Variable Structure Systems (VSS’06), Alghero, Italy, pp. 346–350 (2006), DOI: 10.1109/VSS. 2006.1644542.

[14] Sun X., Cao J., Lei G., Zhu J., A Composite Sliding Mode Control for SPMSM Drives Based on a New Hybrid Reaching Law With Disturbance Compensation, IEEE Transactions on Transportation Electrification, vol. 7, no. 3, pp. 1427–1436 (2021), DOI: 10.1109/TTE.2021.3052986.

[15] Jin Z., Sun X., Lei G., Zhu J., Sliding Mode Direct Torque Control of SPMSMs Based on a Hybrid Wolf Optimization Algorithm, IEEE Transactions on Industrial Electronics (2021), DOI: 10.1109/ TIE.2021.3080220.

[16] Pérez-Ventura U., Fridman L., Design of super-twisting control gains: A describing function based methodology, Automatica, vol. 99, pp. 175–180 (2019), DOI: 10.1016/j.automatica.2018.10.023.

[17] Lascu C., Argeseanu A., Blaabjerg F., Super twisting Sliding-Mode Direct Torque and Flux Control of Induction Machine Drives, IEEE Transactions on Power Electronics, vol. 35, no. 5, pp. 5057–5065 (2020), DOI: 10.1109/TPEL.2019.2944124.

[18] Krim S., Gdaim S., Mimouni M.F., Robust Direct Torque Control with Super-Twisting Sliding Mode Control for an Induction Motor Drive, Complexity (2019), DOI: 10.1155/2019/7274353.

[19] Zhang L., Laghrouche S., Harmouche M., Cirrincione M., Super twisting control of linear induction motor considering end effects with unknown load torque, in 2017 American Control Conference (ACC), Seattle, USA, pp. 911–916 (2017), DOI: 10.23919/ACC.2017.7963069.

[20] Utkin V.I., Poznyak A.S., Ordaz P., Adaptive super-twist control with minimal chattering effect, in 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, pp. 7009–7014 (2011), DOI: 10.1109/CDC.2011.6160720.

[21] Gonzalez T., Moreno J.A., Fridman L., Variable Gain Super-Twisting Sliding Mode Control, IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2100–2105 (2012), DOI: 10.1109/TAC.2011. 2179878.

[22] Obeid H., Laghrouche S., Fridman L., Chitour Y., Harmouche M., Barrier Function-Based Adaptive Super-Twisting Controller, IEEE Transaction on Automatic Control, vol. 65, no. 11, pp. 4928–4933 (2020), DOI: 10.1109/TAC.2020.2974390.

[23] Obeid H., Fridman L.M., Laghrouche S., Harmouche M., Barrier function-based adaptive sliding mode control, Automatica, vol. 93, pp. 540–544 (2018), DOI: 10.1016/j.automatica.2018.03.078.

[24] Obeid H., Fridman L., Laghrouche S., Harmouche M., Barrier Function-Based Adaptive Twisting Controller, in 2018 15th International Workshop on Variable Structure Systems (VSS), Graz, Austria, pp. 198–202 (2018), DOI: 10.1109/VSS.2018.8460272.

[25] Svečko R., Gleich D., Sarjaš A., The Effective Chattering Suppression Technique with Adaptive Super- Twisted Sliding Mode Controller Based on the Quasi-Barrier Function; An Experimentation Setup, Applied Sciences, vol. 10, no. 2 (2020), DOI: 10.3390/app10020595.

[26] Horch M., Boumédiène A., Baghli L., Sensorless high-order sliding modes vector control for induction motor drive with a new adaptive speed observer using super-twisting strategy, Int. J. Computer Application in Technology, vol. 60, no. 2, pp. 144–153 (2019), DOI: 10.1504/IJCAT.2019.100131.

[27] Morfin O.A., Valenzuela F.A., Betancour R.R., CastañEda C.E, Ruíz-Cruz R., Valderrabano-Gonzalez A., Real-Time SOSM Super-Twisting Combined with Block Control for Regulating Induction Motor Velocity, IEEE Access, vol. 6, pp. 25898–25907 (2018), DOI: 10.1109/ACCESS.2018.2812187.

[28] Listwan J., Application of Super-Twisting Sliding Mode Controllers in Direct Field-Oriented Control System of Six-Phase Induction Motor: Experimental Studies, Power Electronics and Drives, vol. 3, no. 1, pp. 23–34 (2018), DOI: 10.2478/pead-2018-0013.

[29] Lascu C., Blaabjerg F., Super-twisting sliding mode direct torque contol of induction machine drives, in 2014 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 5116–5122 (2014), DOI: 10.1109/ECCE.2014.6954103.

[30] Rao S., Buss M., Utkin V., Simultaneous State and Parameter Estimation in Induction Motors Using First- and Second-Order Sliding Modes, IEEE Transactions on Transportation Electrification, vol. 56, no. 9, pp. 3369–3376 (2009), DOI: 10.1109/TIE.2009.2022071.

[31] Aurora C., Ferrara A., A sliding mode observer for sensorless induction motor speed regulation, International Journal of Systems Science, vol. 38, no. 11, pp. 913–929 (2007), DOI: 10.1080/00207720701620043.

[32] Sun X., Cao J., Lei G., Guo Y., Zhu J., A Robust Deadbeat Predictive Controller With Delay Com- pensation Based on Composite Sliding-Mode Observer for PMSMs, IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10742–10752 (2021), DOI: 10.1109/TPEL.2021.3063226.

[33] Riaz Ahamed S., Chandra Sekhar J.N., Dinakara Prasad Reddy P., Speed Control of Induction Motor by Using Intelligence Techniques, Journal of Engineering Research and Applications, vol. 5, no. 1, pp. 130–135(2015).

[34] Dávila A., Moreno J.A., Fridman L., Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm, in Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, Shanghai, China, pp. 8405–8410 (2009), DOI: 10.1109/CDC.2009.5400466.

[35] Tee K.P., Ge S.S., Tay E.H., Barrier Lyapunov Functions for the control of output-constrained nonlinear systems, Automatica, pp. 918–927 (2009), DOI: 10.1016/j.automatica.2008.11.017.

[36] Obeid H., Fridman L., Laghrouche S., Harmouche M., Golkani M.A., Adaptation of Levant’s differen- tiator based on barrier function, International Journal of Control, vol. 91, no. 9, pp. 2019–2027(2018), DOI: 10.1080/00207179.2017.1406149.

[37] Rolek J., Utrata G., Kaplon A., Robust speed estimation of an induction motor under the conditions of rotor time constant variability due to the rotor deep-bar effect, Archives of Electrical Engineering, vol. 69, no. 2, pp. 319–333 (2020), DOI: 10.24425/aee.2020.133028.

[38] Kiani B., Mozafari B., Soleymani S., Mohammad Nezhad Shourkaei H., Predictive torque control of induction motor drive with reduction of torque and flux ripple, Archives of Electrical Engineering (2021), DOI: 10.24425/bpasts.2021.137727.

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Authors and Affiliations

Salah Eddine Farhi
Djamel Sakri
Noureddine Golèa

  1. Laboratory of Electrical Engineering and Automatic, LGEA, Larbi Ben M’hidi University, Oum El Bouaghi, Algeria
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This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundaryvalue problems. The operators are addressed especially to nonlinear differential equations.
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[1] Richtmayer R.D., Morton K.W., Difference methods for initial-value problems, J.Willey & Sons, New York (1967).
[2] Burden R.L., Faires J.D., Numerical analysis, PWS-Kent Pub. Comp., Boston (1985).
[3] Taflove A., Computational electrodynamics: the finite-difference time-domain method, Artech House, Boston – London (1995).
[4] Strikwerda J.C., Finite Difference Schemes and Partial Differential Equations, Society for Industrial and Applied Mathematics, Second Edition, Philadelphia (2004).
[5] LeVeque R.J., Finite difference methods for ordinary and partial differential equations, Society for Industrial and Applied Mathematics, Second Edition, Philadelphia (2007).
[6] Fortuna Z., Macukow B., Wasowski J., Numerical methods, WNT (in Polish), Warsaw (2009).
[7] Esfandiari R.S., Numerical Methods for Engineers and Scientists Using MATLABr, CRC Press, Taylor & Francis Group (2017).
[8] Zakrzewski K., Łukaniszyn M., Application of 3-D finite difference method for inductance calculation of air-core coils system, COMPEL International Journal of Computations and Mathematics in Electrical Engineering, vol. 13, no. 1, pp. 89–92 (1994).
[9] Demenko A., Sykulski J., On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33, no. 1/2, pp. 47–55 (2014).
[10] Huang J., LiaoW., Li Z., A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface, Engineering Computations, vol. 35, no. 1, pp. 334–362 (2018).
[11] Chapwanya M., Dozva R., Gift Muchatibaya G., A nonstandard finite difference technique for singular Lane-Emden type equations, Engineering Computations, vol. 36, no. 5, pp. 1566–1578 (2019).
[12] Mawlood M., Basri S., AsrarW., Omar A., Mokhtar A., Ahmad M., Solution of Navier-Stokes equations by fourth-order compact schemes and AUSM flux splitting, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 16, no. 1, pp. 107–120 (2006).
[13] Ivanovic M., Svicevic M., Savovic S., Numerical solution of Stefan problem with variable space grid method based on mixed finite element/finite difference approach, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 27, no. 12, pp. 2682–2695 (2017).
[14] Sobczyk T.J., Algorithm for determining two-periodic steady-states in AC machines directly in time domain, Archives of Electrical Engineering, Polish Academy of Science, Electrical Engineering Committee, vol. 65, no. 3, pp. 575–583 (2016), DOI: 10.1515/aee-2016-0041.
[15] Sobczyk T.J., Radzik M., Radwan-Pragłowska N., Discrete differential operators for periodic and two-periodic time functions, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 38, no. 1, pp. 325–347 (2019).
[16] Sobczyk T.J., Radzik M., A new approach to steady state analysis of nonlinear electrical circuits, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 37, no. 3, pp. 716–728 (2017).
[17] Sobczyk T.J., Radzik M., Tulicki J., Direct steady-state solutions for circuit models of nonlinear electromagnetic devices, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 40, no. 3, pp. 660–675 (2021), DOI: 10.1108/COMPEL-10-2020-0324.
[18] Sobczyk T.J., Jaraczewski M., Application of discrete differential operators of periodic functions to solve 1D boundary-value problems, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 39, no. 4, pp. 885–897 (2020).
[19] Sobczyk T.J., 2D discrete operators for periodic functions, Proceedings IEEE Conference Selected Issues of Electrical Engineering and Electronics (WZZE), Zakopane, Poland, pp. 1–5 (2019),
[20] Jaraczewski M., Sobczyk T., Leakage Inductances of Transformers at Arbitrarily Located Windings, Energies, vol. 13, no. 23, 6464 (2020), DOI: 10.3390/en13236464.

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Authors and Affiliations

Tadeusz Jan Sobczyk

  1. Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 24 Warszawska str., 31-155 Kraków, Poland

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[1] Author1 A., Author2 A., Title of paper, Title of periodical, vol. x, no. x, pp. xxx-xxx (YEAR).


[1] Steentjes S., von Pfingsten G., Hombitzer M., Hameyer K., Iron-loss model with consideration of minor loops applied to FE-simulations of electrical machines, IEEE Transactions on Magnetics. vol. 49, no. 7, pp. 3945-3948 (2013).

[2] Idziak P., Computer Investigation of Diagnostic Signals in Dynamic Torque of Damaged Induction Motor, Electrical Review (in Polish), to be published.

[3] Cardwell W., Finite element analysis of transient electromagnetic-thermal phenomena in a squirrel cage motor, submitted for publication in IEEE Transactions on Magnetics.

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[4] Author A., Title of conference paper, Unabbreviated Name of Conf., City of Conf., Country of Conf., pp. xxx-xxx (YEAR).


[4] Popescu M., Staton D.A., Thermal aspects in power traction motors with permanent magnets, Proceedings of XXIII Symposium Electromagnetic Phenomena in Nonlinear Circuits, Pilsen, Czech Republic, pp. 35-36 (2016).

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[5] Author1 A., Author2 A.B., Title of book, Name of the publisher (YEAR).


[5] Zienkiewicz O., Taylor R.L., Finite Element method, McGraw-Hill Book Company (2000).


[6] Author1 A., Author2 A., Title of patent, European Patent, EP xxx xxx (YEAR).


[6] Piech Z., Szelag W., Elevator brake with magneto-rheological fluid, European Patent, EP 2 197 774 B1 (2011).


[7] Author A., Title of thesis, PhD Thesis, Department, University, City of Univ. (YEAR).


[7] Driesen J., Coupled electromagnetic-thermal problems in electrical energy transducers, PhD Thesis, Faculty of Applied Science, K.U. Leuven, Leuven (2000).

For on electronic forms

[8] Author A., Title of article, in Title of Conference, record as it appears on the copyright page], © [applicable copyright holder of the Conference Record] (copyright year), doi: [DOI number].


[8] Kubo M., Yamamoto Y., Kondo T., Rajashekara K., Zhu B., Zero-sequence current suppression for open-end winding induction motor drive with resonant controller,in IEEE Applied Power Electronics Conference and Exposition (APEC), © APEC (2016), doi: 10.1109/APEC.2016.7468259


[9], accessed April 2010.


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