# High-Reliability Rotor Position Detection Method for Sensorless Control of Synchronous Condenser

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dual Rotor Initial Position Detection Method

#### 2.1. Start up Analysis of SFC

#### 2.2. Voltage Detection Method

_{0}, b

_{1}, b

_{2}, a

_{0}, a

_{1}, and a

_{2}are the filter coefficients. The filter G(z) described in Equation (2) is a second-order low-pass filter, which is used to filter out the high-frequency signal in the line voltage signal, and K in Equation (1) is the amplification factor, which is used to properly amplify the filtered line voltage signal.

_{abp}, u

_{bcp}, and u

_{cap}were filtered using the above filters, the u

_{AB}, u

_{BC}, and u

_{CA}signals were generated, and the instantaneous values u

_{ABm}, u

_{BCm}, and u

_{CAm}were obtained.

_{a}, u

_{b}, and u

_{c}are the terminal voltages of the synchronous condenser, θ Is the rotor position angle, m

_{af}, m

_{bf}, and m

_{cf}are the maximum mutual inductance between the stator and rotor, and ω and ω

_{f}are the equivalent turns of the stator and rotor windings, respectively, and λ

_{ad}is the permeability of the d axis breath magnetic flux path.

#### 2.3. Magnetic Flux Detection Method

_{α}and u

_{β}denote the induced voltage components of the α-β axis generator terminal, and λ

_{max}is set according to the step value of excitation voltage.

_{c}denotes the cut-off frequency of the first-order low-pass filter.

_{1}and θ

_{2}, and VT

_{n1}, VT

_{m1}, VT

_{n2}, and VT

_{m2}(n = 1,3,5; m = 2,4,6) are the same, it is judged that the rotor position calculation is successful, the system is unlocked, and the converter is started for the first time, as illustrated in Figure 5a. The variables VT

_{n1}and VT

_{m1}denote the thyristor numbers that θ

_{1}needs to turn on, and VT

_{n2}and VT

_{m2}are the thyristor numbers that θ

_{2}needs to turn on. Otherwise, it is determined that the calculation of the rotor position fails and the startup is terminated, as shown in Figure 5b,c. Moreover, S1–S6 indicate the possible directions of the magnetic field axes formed by the stator currents in space. XYZ represents the port for the connection port of the stator three-phase winding, and ABC represents the input current port of the stator three-phase winding.

## 3. Method for Detecting Rotor Position during Operation

#### 3.1. Synchronous Phase Compensation

_{s}denotes the sampling period of the controller and $n=[0,\frac{INT({t}_{\mu})}{{T}_{s}}+1]$ represents the number of sampling points in the selected interpolation interval. The variable ω

_{m}denotes the frequency of the voltage signal.

- (1)
- Waveform distortion is significantly reduced and symmetrical.
- (2)
- The zero-crossing time is the same as that of the original signal without a phase offset.

#### 3.2. Software Phase-Locked Loop Based on Rotating Coordinate System

_{a}, U

_{b}, and U

_{c}represent the input voltage, and the three-phase voltage in the abc coordinate system is transformed into αβ. The two-phase voltage in the coordinate system is transformed into U

_{d}and U

_{q}two-phase voltages in the rotating coordinate system, where ω

_{0}and θ

_{0}represent the angular frequency and phase angle, respectively, of the rotating coordinate system.

## 4. RTDS Verification

_{ac}is 276.98°. The detection result at the zero-crossing point (theoretical value of 90°) of the descending edge of the bridge U

_{ac}is 97.26°, with a deviation of approximately 7°. This large deviation is not conducive to reliable operation and accurate control of the inverter bridge of the static inverter. Figure 13 presents the rotor position detection results obtained using synchronous phase compensation. As the synchronous compensation algorithm performs sinusoidal interpolation at the selected interval, it can effectively eliminate the effect of synchronous voltage distortion on synchronous phase detection. As shown by the dotted line in Figure 13, The detection result at the zero-crossing position on the descending edge of the bridge U

_{ac}is 90.35°, whereas the detection result at the zero-crossing position on the rising edge of the bridge U

_{ac}is 270.79°.

## 5. Conclusions

- Two position detection methods are used to check each other, which can effectively avoid reverse rotation when the unit starts and improve the safety of large synchronous motors.
- Synchronous phase compensation can effectively reduce the influence of a distorted waveform on detection accuracy and improve phase detection accuracy to within 1%, thus providing technical support for the high-performance control of SFCS.
- The algorithm does not need additional hardware circuits, has few parameters, and can be easily applied in engineering.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Ramachandra Sekhar, K.; Vinoth Kumar, N.; Harada, Y. Impact of renewable energy control center on voltage stability and transmission network efficiency in wind farm integrated grid. In Proceedings of the 2014 IEEE International Conference on Power Electronics, Drives and Energy Systems, Mumbai, India, 16–19 December 2014; pp. 1–6. [Google Scholar]
- Teleke, S.; Abdulahovic, T.; Thiringer, T.; Svensson, J. Dynamic Performance Comparison of Synchronous Condenser and SVC. IEEE Trans. Power Deliv.
**2008**, 23, 1606–1612. [Google Scholar] [CrossRef] - Wang, Y.; Wang, L.; Jiang, Q. Impact of Synchronous Condenser on Sub/Super-Synchronous Oscillations in Wind Farms. IEEE Trans. Power Deliv.
**2021**, 36, 2075–2084. [Google Scholar] [CrossRef] - Wang, P.; Mou, Q.; Liu, X.; Gu, W.; Chen, X. Start-Up Control of a Synchronous Condenser Integrated HVDC System With Power Electronics Based Static Frequency Converter. IEEE Access
**2019**, 7, 146914–146921. [Google Scholar] [CrossRef] - Tan, J.; Xue, R.; Tan, H.; Zhang, T.; Zhao, Y.; Zhao, B.; Wu, S.; Zhai, Y.; Dang, H. Design and Experimental Investigations on the Helium Circulating Cooling System Operating at Around 20 K for a 300-kvar Class HTS Dynamic Synchronous Condenser. IEEE Trans. Appl. Supercond.
**2022**, 32, 5400405. [Google Scholar] [CrossRef] - Hadavi, S.; Rathnayake, D.B.; Jayasinghe, G.; Mehrizi-Sani, A.; Bahrani, B. A Robust Exciter Controller Design for Synchronous Condensers in Weak Grids. IEEE Trans. Power Syst.
**2022**, 37, 1857–1867. [Google Scholar] [CrossRef] - Hadavi, S.; Mansour, M.Z.; Bahrani, B. Optimal Allocation and Sizing of Synchronous Condensers in Weak Grids With Increased Penetration of Wind and Solar Farms. IEEE J. Emerg. Sel. Top. Circuits Syst.
**2021**, 11, 199–209. [Google Scholar] [CrossRef] - Hadavi, S.; Saunderson, J.; Mehrizi-Sani, A.; Bahrani, B. A Planning Method for Synchronous Condensers in Weak Grids Using Semi-Definite Optimization. IEEE Trans. Power Syst.
**2023**, 38, 1632–1641. [Google Scholar] [CrossRef] - Magsaysay, G.; Schuette, T.; Fostiak, R.J. Use of a static frequency converter for rapid load response in pumped-storage plants. IEEE Trans. Energy Convers.
**1995**, 10, 694–699. [Google Scholar] [CrossRef] - Ryu, H.; Kim, B.; Lee, J.; Lim, I. A Study of Synchronous Motor Drive using Static Frequency Converter. In Proceedings of the 2006 12th International Power Electronics and Motion Control Conference, Portoroz, Slovenia, 30 August–1 September 2006; pp. 1496–1499. [Google Scholar]
- Liu, T.-H.; Lin, C.-Y.; Yang, J.-S.; Chang, W.-Y. Modeling and harmonics elimination for a static frequency converter driving a 300 MVA synchronous machine. In Proceedings of the IEEE International Symposium on Industrial Electronics, Warsaw, Poland, 17–20 June 1996; Volume 2, pp. 602–607. [Google Scholar]
- Meghana, R.; Singh, R.R. Sensorless Start-Up Control for BLDC Motor using Initial Position Detection Technique. In Proceedings of the 2020 IEEE International Conference on Power Electronics, Smart Grid and Renewable Energy (PESGRE2020), Cochin, India, 2–4 January 2020; pp. 1–6. [Google Scholar]
- Song, X.; Han, B.; Zheng, S.; Chen, S. A Novel Sensorless Rotor Position Detection Method for High-Speed Surface PM Motors in a Wide Speed Range. IEEE Trans. Power Electron.
**2018**, 33, 7083–7093. [Google Scholar] [CrossRef] - Yeh, H.-C.; Yang, S.-M. Phase Inductance and Rotor Position Estimation for Sensorless Permanent Magnet Synchronous Machine Drives at Standstill. IEEE Access
**2021**, 9, 32897–32907. [Google Scholar] [CrossRef] - Wang, Z.; Yao, B.; Guo, L.; Jin, X.; Li, X.; Wang, H. Initial Rotor Position Detection for Permanent Magnet Synchronous Motor Based on High-Frequency Voltage Injection without Filter. World Electr. Veh. J.
**2020**, 11, 71. [Google Scholar] [CrossRef] - Iturra, R.G.; Thiemann, P. Sensorless Rotor Position detection of Synchronous Machine using Direct Flux Control—Comparative evaluation of rotor position estimation methods. 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]
- Martin, F.; Leibfried, T. An universal high voltage source based on a static frequency converter. In Proceedings of the Conference Record of the 2006 IEEE International Symposium on Electrical Insulation, Toronto, ON, Canada, 11–14 June 2006; pp. 420–423. [Google Scholar]

**Figure 5.**Schematic diagram of judging rules for dual initial position detection. (

**a**) Successful startup case (

**b**) Failed startup case 1 (

**c**) Failed startup case 2.

**Figure 14.**Waveform diagram of the whole process. (

**a**) the three-phase stator terminal voltage, (

**b**) the phase of the input voltage.

Parameter | Value |
---|---|

Transformer turn ratio | 10 kV/0.9 kV/0.9 kV |

Direct current reactor | 2.4 mH |

Voltage of power grid | 500 kV |

Rated power of Synchronous Condensers | 300 MVar |

Rated voltage of Synchronous Condensers | 20 kV |

Rated current of Synchronous Condensers | 8660 A |

Rated speed of Synchronous Condensers | 3000 r/min |

Parameter | Value |
---|---|

G_{1}(z) | (0.000375 + 0.000750∙z^{−1} + 0.000375∙z^{−2})/(1 − 1.9445∙z^{−1} − 0.9460∙z^{−2}) |

G_{2}(z) | 200∙z − 194 |

K_{P} | 5.0 |

K_{I} | 20.0 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shi, X.; Liu, T.; Mu, W.; Zhao, J.
High-Reliability Rotor Position Detection Method for Sensorless Control of Synchronous Condenser. *World Electr. Veh. J.* **2023**, *14*, 299.
https://doi.org/10.3390/wevj14100299

**AMA Style**

Shi X, Liu T, Mu W, Zhao J.
High-Reliability Rotor Position Detection Method for Sensorless Control of Synchronous Condenser. *World Electric Vehicle Journal*. 2023; 14(10):299.
https://doi.org/10.3390/wevj14100299

**Chicago/Turabian Style**

Shi, Xiangjian, Teng Liu, Wei Mu, and Jianfeng Zhao.
2023. "High-Reliability Rotor Position Detection Method for Sensorless Control of Synchronous Condenser" *World Electric Vehicle Journal* 14, no. 10: 299.
https://doi.org/10.3390/wevj14100299