# Modified Permanent Magnet Synchronous Generators for Using in Energy Supply System for Autonomous Consumer

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Mathematical Description

_{wi}—is a flux linkage of the stator winding,

_{wi}—are the stator winding currents,

_{w}—is a coil resistance of the stator windings,

_{l}—is the resistance of the autonomous load,

_{n}—is the number of windings connected on the same axis.

_{r}) on the rotor is as follows:

_{w}is the coefficient of the geometric arrangement of stator windings,

_{w}—is the stator windings inductance,

_{r}—is the rotor winding flux linkage, which is calculated for each winding as follows:

_{f}—is the rate speed of the rotor magnet field.

_{w1}, so using the operational format, we obtain the following:

_{w}), which will represent the flux linkage creating an EMF on this winding equal to the following:

_{w}—is the EMF on the stator winding,

_{e}—is an active power,

_{mech}—is the generator shaft speed,

_{M}—is the number of rotor pairs of poles.

#### 3.2. Mathematical Models

#### 3.3. Mathematical Simulation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Liu, J.; Miura, Y.; Ise, T. Comparison of Dynamic Characteristics between Virtual Synchronous Generator and Droop Control in Inverter-Based Distributed Generators. IEEE Trans. Power Electron.
**2015**, 31, 3600–3611. [Google Scholar] [CrossRef] - Yan, X.; Mohamed, S.Y.A. Comparison of virtual synchronous generators dynamic responses. In Proceedings of the 2018 IEEE 12th International Conference on Compatibility, Power Electronics and Power Engineering, CPE-POWERENG, Doha, Qatar, 10–12 April 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Xia, L.; Hai, L. Comparison of dynamic power sharing characteristics between virtual synchronous generator and droop control in inverter-based microgrid. In Proceedings of the 2017 IEEE 3rd International Future Energy Electronics Conference and ECCE Asia, IFEEC—ECCE Asia 2017, Kaohsiung, Taiwan, 3–7 June 2017; pp. 1548–1552. [Google Scholar] [CrossRef]
- Thomas, V.; Kumaravel, S.; Ashok, S. Virtual synchronous generator and its comparison to droop control in microgrids. In Proceedings of the 2018 IEEE International Conference on Power, Instrumentation, Control and Computing, PICC 2018, Thrissur, India, 18–20 January 2018; pp. 1–4. [Google Scholar] [CrossRef]
- Kassem, A.M.; Zaid, S.A. Optimal control of a hybrid renewable wind/ fuel cell energy in micro grid application. In Proceedings of the 2017 19th International Middle-East Power Systems Conference, MEPCON 2017, Cairo, Egypt, 19–21 December 2017; Volume 2018, pp. 84–90. [Google Scholar] [CrossRef]
- Ducar, I.; Marinescu, C. Efficiency analysis of a hydro-pump storage system for frequency support in microgrids. In Proceedings of the 2016 20th IEEE International Conference on Automation, Quality and Testing, Robotics, AQTR 2016, Cluj-Napoca, Romania, 19–21 May 2016. [Google Scholar] [CrossRef]
- Chen, J.-W.; Tran, T.-N.; Liu, Y.-C. Design of DC micro-grid system for integration of PMSM elevator and renewable energy sources. In Proceedings of the PEDG 2019—2019 IEEE 10th International Symposium on Power Electronics for Distributed Generation Systems, Xi’an, China, 3–6 June 2019; pp. 981–985. [Google Scholar] [CrossRef]
- Daftari, M.A.; Nekoui, M.A. Analysing stability of time delayed synchronous generator and designing optimal stabilizer fractional order PID controller using partical swarm optimization technique. In Proceedings of the 2018 2nd IEEE International Conference on Power Electronics, Intelligent Control and Energy Systems, ICPEICES 2018, Delhi, India, 22–24 October 2018; pp. 1062–1066. [Google Scholar] [CrossRef]
- Krishna., V.B.M.; Sandeep, V.; Murthy, S.S. Experimental Study on Three Phase Permanent Magnet Synchronous Generator for Pico Hydro Isolated Systems. In Proceedings of the 2021 International Conference on Sustainable Energy and Future Electric Transportation, SeFet 2021, Hyderabad, India, 21–23 January 2021. [Google Scholar] [CrossRef]
- Colak, I.; Bulbul, H.I.; Sagiroglu, S.; Sahin, M. Modeling a permanent magnet synchronous generator used in wind turbine and the realization of voltage control on the model with artificial neural networks. In Proceedings of the 2012 International Conference on Renewable Energy Research and Applications, ICRERA 2012, Nagasaki, Japan, 11–14 November 2012. [Google Scholar] [CrossRef]
- Effendy, M.; Ashari, M.; Suryoatmojo, H. Performance Comparison of Proportional-Integral and Fuzzy-PI for a Droop Control of DC Microgrid. In Proceedings of the 2020 International Conference on Sustainable Energy Engineering and Application: Sustainable Energy and Transportation: Towards All-Renewable Future, ICSEEA 2020, Tangerang, Indonesia, 18–20 November 2020; pp. 180–184. [Google Scholar] [CrossRef]
- Dar’Enkov, A.B.; Guzev, S.A.; Fedorov, O.V. Autonomous power plant with variable speed based on multi-windings generator. In Proceedings of the 2017 International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2017, St. Petersburg, Russia, 16–19 May 2017. [Google Scholar] [CrossRef]
- Meng, T.; Liu, W.; Jiao, N.; Peng, J.; Zhu, Y. Initial rotor position estimation for wound-rotor synchronous starter/generators based on multi-stage-structure characteristics. In Proceedings of the IEEE Applied Power Electronics Conference and Exposition—APEC, San Antonio, TX, USA, 4–8 March 2018; Volume 2018, pp. 540–545. [Google Scholar] [CrossRef]
- El Hassane, M.; Krami, N. Design and control strategy of micro-wind turbine based PMSM in AC MicroGrid. In Proceedings of the 2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering, STA 2016, Sousse, Tunisia, 19–21 December 2016; pp. 575–581. [Google Scholar] [CrossRef]
- Leng, D.; Polmai, S. Transient respond comparison between modified droop control and virtual synchronous generator in standalone microgrid. In Proceedings of the 5th International Conference on Engineering, Applied Sciences and Technology, ICEAST 2019, Luang Prabang, Laos, 2–5 July 2019. [Google Scholar] [CrossRef]
- Emara, D.; Ezzat, M.; Abdelaziz, A.; Mahmoud, K.; Lehtonen, M.; Darwish, M.M.F. Novel control strategy for enhancing microgrid operation connected to photovoltaic generation and energy storage systems. Electronics
**2021**, 10, 1261. [Google Scholar] [CrossRef] - Ali, E.S.; El-Sehiemy, R.A.; El-Ela, A.A.; Mahmoud, K.; Lehtonen, M.; Darwish, M.M.F. An effective Bi-stage method for renewable energy sources integration into unbalanced distribution systems considering uncertainty. Processes
**2021**, 9, 471. [Google Scholar] [CrossRef] - Blaabjerg, F.; Chen, Z.; Kjaer, S.B. Power electronics as efficient interface in dispersed power generation systems. EEE Trans. Power Electron.
**2004**, 19, 1184–1194. [Google Scholar] [CrossRef] - May, S.; Tatyana, K.; Ilya, I. Single-Phase Alternating Voltage Generator Made on a Brushless Motor. Patent No. 177489, 2018. Available online: https://www.elibrary.ru/item.asp?id=38149624 (accessed on 7 September 2021).
- Kotin, D.; Ivanov, I. New Type Single-Phase Generator for Autonomous Consumer. In Proceedings of the 2020 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), Sochi, Russia, 18–22 May 2020; pp. 1–5. [Google Scholar] [CrossRef]
- May, S.; Tatyana, K.; Ilya, I. Single-Phase Synchronous-Step Alternatorнапряжения. Patent No. 177488, 2018. Available online: https://www.elibrary.ru/item.asp?id=38149623 (accessed on 7 September 2021).
- Halina, T.; Ivanov, I.; Stalnaya, M. Sine-cosine Generator. In Proceedings of the 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), Vladivostok, Russia, 1–4 October 2019; pp. 1–4. [Google Scholar] [CrossRef]
- May, S.; Ilya, I. Sine-Cosine Two-Phase Generator. Patent No. 2667660, 2018. Available online: https://www.elibrary.ru/item.asp?id=37360088 (accessed on 7 September 2021).
- Kotin, D.; Tolstobrova, L.; Ivanov, I. Mathematical modeling of multi-winding synchronous generators with permanent magnets for autonomous consumers. In Proceedings of the 2021 XVIII International Scientific Technical Conference Alternating Current Electric Drives (ACED), Ekaterinburg, Russia, 24–27 May 2021; pp. 1–6. [Google Scholar] [CrossRef]
- May, S.; Sergey, E.; Ilya, I. A Direct Current Source Made on a Synchronous Stepper Motor, with an Increased Voltage. Patent No. 2674466, 2018. Available online: https://www.elibrary.ru/item.asp?id=41023514 (accessed on 7 September 2021).
- May, S.; Sergey, E.; Ilya, I. Direct Current Source, Made on a Synchronous Stepper Motor, with Increased Output Power. Patent No. 2674465, 2018. Available online: https://www.elibrary.ru/item.asp?id=41023510 (accessed on 7 September 2021).
- Vladimir, K.; Alexander, A. On the Physical Nature of Frequency Control Problems of Induction Motor Drives. Energies
**2021**, 14, 4246. [Google Scholar] [CrossRef] - Kodkin, V.L.; Anikin, A.S.; Baldenkov, A.A. Prospects for Increasing the Dynamic Efficiency of Asynchronous Double-Feed Machines and Wind Power Generators Using Structural Methods and Solutions. In Emerging Electric Machines—Advances, Perspectives and Applications; IntechOpen: London, UK, 2021. [Google Scholar] [CrossRef]
- Geraldi, E.L.; Fernandes, T.C.; Piardi, A.B.; Grilo, A.P.; Ramos, R.A. Parameter estimation of a synchronous generator model under unbalanced operating conditions. Electr. Power Syst. Res.
**2020**, 187, 106487. [Google Scholar] [CrossRef] - Spałek, D. Synchronous Generator Model with Nonlinear Magnetic Circuit. Acta Energetica
**2013**, 17, 144–151. [Google Scholar] [CrossRef] - Vins, M.; Nohac, K.; Sirovy, M. Accuracy Evaluation of Synchronous Generator Models in PSAT. In Proceedings of the 2021 IEEE 19th International Power Electronics and Motion Control Conference, PEMC 2021, Gliwice, Poland, 25–29 April 2021; pp. 383–389. [Google Scholar] [CrossRef]
- Vigneshwar, S.T.; Lenin, N.C. Comparison of Radial Flux PMSM and Axial Flux PMSM for Hybrid Electric Tracked Vehicles. In Emerging Solutions for e-Mobility and Smart Grids; Springer: Berlin/Heidelberg, Germany, 2021; pp. 69–78. [Google Scholar] [CrossRef]
- Salari, M.E.; Coleman, J.; Toal, D. Analysis of direct interconnection technique for offshore airborne wind energy systems under normal and fault conditions. Renew. Energy
**2018**, 131, 284–296. [Google Scholar] [CrossRef] - Kłosowski, Z.; Cie´slik, S.C.; Pau, M. The Use of a Real-Time Simulator for Analysis of Power Grid Operation States with a Wind Turbine the Use of a Real-Time Simulator for Analysis of Power Grid Operation States with a Wind Turbine. Energies
**2021**, 14, 2327. [Google Scholar] [CrossRef] - Kłosowski, Z.; Cie´slik, S.C. Real-Time Simulation of Power Conversion in Doubly Fed Induction Machine. Energies
**2020**, 13, 673. [Google Scholar] [CrossRef] [Green Version] - Monakov, Y.V.; Oknin, E.; Polyakov, A.; Soobbotin, P.V. Using the SimInTech Software Package for the Development of Virtual Laboratory Works on the Topic ‘Power Plants and Substations Electrical Equipment Tests and Modes. In Proceedings of the 2018 4th International Conference on Information Technologies in Engineering Education, Inforino 2018, Moscow, Russia, 23–26 October 2018. [Google Scholar] [CrossRef]
- SimInTech. Available online: https://simintech.ru/ (accessed on 20 October 2021).
- Domakhin, E.A.; Spopov, N.; Vilberger, M.E.; Anibroev, V.I.; Singizin, I.I. Comparative analysis and experimental verification of simulation modelling approach in MATLAB-Simulink and SimInTech. J. Phys. Conf. Ser.
**2020**, 1661. [Google Scholar] [CrossRef] - Baum, F.I.; Kozlov, O.S.; Parshikov, I.A.; Petuhov, V.N.; Timofeev, K.A.; Shchekaturov, A.M. SimInTech software for programming control-system devices. At. Energy
**2013**, 113, 443–446. [Google Scholar] [CrossRef] - VEM. Permanent-Magnet Synchronous Motors by VEM. Available online: https://shop.vem-group.com/catalog/website/pdf/kataloge/kataloge/2017/Hauptkatalog_2017_KAP12_en.pdf (accessed on 7 September 2021).

Generator Type | a_{w} | k_{n} | k | k_{M} |
---|---|---|---|---|

Single-phased with simplified construction | a_{w}_{, coaxial} = 1a _{w}_{, non-coaxial} = 1 | 2 | 1 | 1 |

Single-phase generator with increased power | a_{w}_{, coaxial} = 1a _{w}_{, non-coaxial} =1 | 4 | 1 | 2 |

Double-phase generator | a_{w}_{, coaxial} = 1a _{w}_{, non-coaxial} =1 | 2 | 2 | 1 |

Three-phase generator | a_{w}_{, coaxial} = 1a _{w}_{, non-coaxial} =1 | 2 | 3 | 1 |

**Table 2.**Generator parameters [40].

R_{c}, Ohm | µ, mH | L_{s}, mH | ω_{n}, rad/s | Ψ_{R}, Wb | R_{n}, Ohm |
---|---|---|---|---|---|

0.543 | 3.2 | 10.1 | 20 | 1 | 15 |

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**MDPI and ACS Style**

Kotin, D.; Ivanov, I.; Shtukkert, S.
Modified Permanent Magnet Synchronous Generators for Using in Energy Supply System for Autonomous Consumer. *Energies* **2021**, *14*, 7196.
https://doi.org/10.3390/en14217196

**AMA Style**

Kotin D, Ivanov I, Shtukkert S.
Modified Permanent Magnet Synchronous Generators for Using in Energy Supply System for Autonomous Consumer. *Energies*. 2021; 14(21):7196.
https://doi.org/10.3390/en14217196

**Chicago/Turabian Style**

Kotin, Denis, Ilya Ivanov, and Sofya Shtukkert.
2021. "Modified Permanent Magnet Synchronous Generators for Using in Energy Supply System for Autonomous Consumer" *Energies* 14, no. 21: 7196.
https://doi.org/10.3390/en14217196