# Characteristics and Current Harmonic Control of N* Three-Phase PMSG for HVDC Transmission Based on MMC

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The System Topology and Working Principles

#### 2.1. System Topology

#### 2.2. Analysis of Electromagnetic Characteristics of N* Three-Phase PMSG

## 3. Mathematical Model of N* Three-Phase PMSG

_{ai}, u

_{bi}, u

_{ci}and u

_{di}, u

_{qi}represent the stator voltage and d-q axis voltage of the ith three-phase PMSG unit, respectively. The state equation of the N* three-phase PMSG in a d-q coordinate system can be expressed as:

**x**

_{i}and

**u**

_{i}are the state variables and system output of the ith three-phase PMSG unit, respectively, which can be defined as follows:

_{di}, i

_{qi}, L

_{di}, L

_{qi}, R

_{i}, ψ

_{ri}are stator current, inductance, resistance, and PM flux of the ith three-phase PMSG unit in the d-q coordinate system. The N* three-phase phase PMSG is composed of n sets of three-phase PMSG units with identical output characteristics. It can be seen that the PM flux, stator resistance, inductance, output voltage and torque of each unit are equal.

_{e}can be formulated by:

_{e}is the electromagnetic torque of the N* three-phase PMSG and p is the pole-pair of the three-phase PMSG unit.

## 4. Harmonic Current Control Strategy of Side Converter of N* Three-Phase PMSG

#### 4.1. Design of Proportional Integral-Nonideal Resonance Controller

_{i}is the integral coefficient and ω

_{c}is the cut-off frequency) is substituted into Equation (12), G

_{ac}can be formulated by:

_{c}reasonably, which could reduce the sensitivity of the controller to the change of signal frequency and improve the stability of the control system. Combining NRC with the traditional PI controller, an adaptive proportional integral-nonideal resonance controller (PI-NRC) is formed to realize the steady-state error-free control of the AC and DC signals. The transfer function of PI-NRC can be expressed by:

_{p}and K

_{i}are the ratio and integral coefficients of PI, h is the number of harmonics, and K

_{hwi}is the resonance gain coefficient of ith harmonic. Concerning the PI-NRC controller, the proportion coefficient has been determined in the design of the PI controller, so the harmonic signal can only be controlled by adjusting the parameters K

_{i}and ω

_{c}of the resonance controller. Assuming the angular frequency of the controlled object ω = 314 rad/s, ω

_{c}= 10 and keeping K

_{i}unchanged, the transfer function Bode diagram corresponding to Equation (14) is shown in Figure 10a. Through the adjusting of K

_{i}, the amplitude-frequency curve can be shifted up or down, which not only affects the controller gain, but also affects the controller bandwidth. Therefore, in an ideal situation, the adjustment without static difference of the AC harmonic signal can be realized by a reasonable K

_{i}, eliminating the harmonic.

#### 4.2. Harmonic Suppression Strategy of N* Three-Phase PMSG Machine-Side Converter

_{dref}and U

_{qref}are obtained by adjusting the error though PI-NRC. Six identical SVPWM modulation switching signals are inputted to the converters of six generator units, respectively. Finally, the control of the whole N* three-phase PMSG is completed.

#### 4.3. Simulation and Analysis

_{d}= 0 control strategy and is set to a given speed mode.

_{q}under full-load is twice as much as that under half-load. The d-q axis current response could well follow the given current, and the static error in steady-state is small. There also are apparent fluctuations in the d-q axis current.

_{q}under full load is twice that of the half-load. The current response in the d-q axis follows the given current well and the static error in steady-state is small. Concurrently, the current fluctuation in the q-d axis is well suppressed.

## 5. Experimental Results and Analysis

## 6. Conclusions

- (1)
- The N* three-phase PMSG proposed in this paper is composed of several three-phase generator units with the same electromagnetic characteristics. Each generator unit has advantages of good electrical isolation, simple structure and strong fault tolerance.
- (2)
- The current harmonics can be suppressed by the machine-side converter control strategy of an N* three-phase PMSG proposed in this paper, which could eliminate the harmonics with higher amplitude in the stator current and improve the generating efficiency of the generator.
- (3)
- The generator proposed in this paper is suitable for the field of offshore large-capacity wind power generation, which could provide some references for engineering practice.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- De Prada, M.; Corchero, C.; Gomis-Bellmunt, O.; Sumper, A. AC-DC offshore wind power plant topology optimal design. IEEE Trans. Power Syst.
**2015**, 30, 1868–1876. [Google Scholar] - Jeremy, L. Integrating the first HVDC-based offshore wind power into PJM system—A real project case study. IEEE Trans. Ind. Electron.
**2015**, 52, 1970–1978. [Google Scholar] - Shoudao, H.; Wu, G.; Rong, F.; Zhang, C.; Huang, S.; Wu, Q. Novel Predictive Stator Flux Control Techniques for PMSM Drives. IEEE Trans. Power Electron.
**2019**, 34, 8916–8929. [Google Scholar] - Zhang, C.; Wu, G.; Rong, F.; Feng, J.; Jia, L.; He, J.; Huang, S. Robust Fault-Tolerant Predictive Current Control for Permanent Magnet Synchronous Motors Considering Demagnetization Fault. IEEE Trans. Ind. Electron.
**2018**, 65, 5324–5334. [Google Scholar] [CrossRef] - Zhou, D.; Blaabjerg, F.; Franke, T.; Tønnes, M.; Lau, M. Comparison of wind power converter reliability with low speed and medium speed permanent magnet synchronous generators. IEEE Trans. Power Syst.
**2015**, 62, 6575–6584. [Google Scholar] - Potgieter, J.H.; Kamper, M.J. Modeling and stability analysis of a direct drive direct grid slip synchronous permanent magnet wind generator. IEEE Trans. Ind. Appl.
**2014**, 50, 1738–1747. [Google Scholar] [CrossRef] - Zhang, X.; Chen, J.; Ma, Y.; Wang, Y.; Xu, D. Bandwidth Expansion Method for Circulating Current Control in Parallel Three-phase PWM Converter Connection System. IEEE Trans. Ind. Electron.
**2014**, 29, 6847–6856. [Google Scholar] - Hou, C.C. A Multicarrier PWM for Parallel Three-Phase Active Front-End Converters. IEEE Trans. Power Electron.
**2013**, 28, 2753–2759. [Google Scholar] [CrossRef] - Zhang, X.; Fu, Z.; Xiao, Y.; Wang, G.; Xu, D. Control of Parallel Three-Phase PWM Converters Under Generalized Unbalanced Operating Conditions. IEEE Trans. Power Electron.
**2017**, 32, 3206–3214. [Google Scholar] [CrossRef] - Monni, A.; Marongiu, I.; Serpi, A.; Damiano, A. Design of a fractional slot multi-phase PMSG for a direct drive wind turbine. In Proceedings of the 2014 International Conference on Electrical Machines, Berlin, Germany, 2–5 September 2014; pp. 2087–2093. [Google Scholar]
- Levi, E. Advances in converter control and innovative exploitation of additional degrees of freedom for multiphase machines. IEEE Trans. Ind. Electron.
**2015**, 63, 433–448. [Google Scholar] [CrossRef] - Elserougi, A.A.; Daoud, M.I.; Abdel-Khalik, A.S.; Massoud, A.M.; Ahmed, S. Series connected multi-half-bridge modules converter for integrating multi-megawatt wind multi phase permanent magnet synchronous generator with dc grid. IET Electr. Power Appl.
**2017**, 11, 981–990. [Google Scholar] [CrossRef] - Zhou, S.; Rong, F.; Yin, Z.; Huang, S.; Zhou, Y. HVDC Transmission Technology of Wind Power System with Multi-Phase PMSG. Energies
**2018**, 11, 3294. [Google Scholar] [CrossRef][Green Version] - Gjerde, S.S.; Olsen, P.K.; Ljøkelsøy, K.; Undeland, T.M. Control and fault handling in a modular series-connected converter for a transformerless 100 kV low-weight offshore wind turbine. IEEE Trans. Ind. Appl.
**2014**, 50, 1094–1105. [Google Scholar] [CrossRef] - Carmeli, M.S.; Castelli-Dezza, F.; Marchegiani, G.; Mauri, M.; Rosati, D. Design and analysis of a medium voltage DC windfarm with a transformer-less wind turbine generator. In Proceedings of the 2010 International Conference on Electrical Machines (ICEM), Rome, Italy, 6–8 September 2010; pp. 1–6. [Google Scholar]
- Prasai, A.; Yim, J.S.; Divan, D.; Bendre, A.; Sul, S.K. A new architecture for offshore wind farms. IEEE Trans. Power Electron.
**2008**, 23, 1198–1204. [Google Scholar] [CrossRef] - Zabaleta, M.; Levi, E.; Jones, M. A Novel Synthetic Loading Method for Multiple Three-Phase Winding Electric Machines. IEEE Trans. Energy Convers.
**2019**, 34, 70–78. [Google Scholar] [CrossRef] - Jung, E.; Yoo, H.; Sul, S.K.; Choi, H.S.; Choi, Y.Y. A Nine-Phase Permanent-Magnet Motor Drive System for an Ultrahigh-Speed Elevator. IEEE Trans. Ind. Appl.
**2012**, 48, 987–994. [Google Scholar] [CrossRef] - Andriollo, M.; Bettanini, G.; Martinelli, G.; Morini, A.; Tortella, A. Analysis of Double-Star Permanent-Magnet Synchronous Generators by a General Decoupled d–q Model. IEEE Trans. Ind. Appl.
**2009**, 45, 1416–1424. [Google Scholar] [CrossRef] - Liu, J.; Yang, G.J.; Li, Y.; Gao, H.W.; Su, J.Y. Eliminating the third harmonic effect for six phase permanent magnet synchronous generators in one phase open mode. IEEE Trans. Power Electron.
**2014**, 14, 92–104. [Google Scholar] [CrossRef][Green Version] - Mekri, F.; Elghali, S.B.; Benbouzid, M.E.H. Fault tolerant control performance comparison of three and five phase PMSG for marine current turbine applications. IEEE Trans. Sustain. Energy
**2013**, 4, 425–433. [Google Scholar] [CrossRef] - Han, X.; Jiang, D.; Zou, T.; Qu, R.; Yang, K. Two-segment three-phase PMSM drive with carrier phase-shift PWM for torque ripple and vibration reduction. IEEE Trans. Power Electron.
**2019**, 34, 588–599. [Google Scholar] [CrossRef] - Luise, F.; Pieri, S.; Mezzarobba, M.; Tessarolo, A. Regenerative testing of a concentrated-winding permanent-magnet synchronous machine for offshore wind generation—Part I: Test concept and analysis. IEEE Trans. Ind. Appl.
**2012**, 48, 1779–1790. [Google Scholar] [CrossRef] - Luise, F.; Pieri, S.; Mezzarobba, M.; Tessarolo, A. Regenerative testing of a concentrated-winding permanent-magnet synchronous machine for offshore wind generation—Part II: Test implementation and results. IEEE Trans. Ind. Appl
**2012**, 48, 1791–1796. [Google Scholar] [CrossRef] - Yuan, X.; Allmeling, J.; Merk, W.; Stemmler, H. Stationary frame generalized integrators for current control of active power filters with zero steady state error for current harmonics of concern under unbalanced and distorted operation conditions. IEEE Trans. Ind. Appl.
**2002**, 38, 2134–2150. [Google Scholar] - Zmood, D.N.; Holmes, D.G.; Bode, G. Frequency domain analysis of three phase linear current regulators. IEEE Trans. Ind. Appl.
**2001**, 37, 601–610. [Google Scholar] [CrossRef]

**Figure 1.**The topology of the proposed wind power generation system with N* three-phase PSMG based on HVDC.

Parameters | Values | Parameters | Values |
---|---|---|---|

Rated power | 20 kW | Rotor flux | 0.058 Wb |

Rated voltage | 380 V | Stator resistance | 0.07 Ω |

Rated speed | 500 r/min | d-q inductance | 0.51 mH |

DC bus voltage | 250 V | Pole pairs | 2 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rao, Z.; Zhang, Z.; Huang, S.; Long, Z.; Wu, G. Characteristics and Current Harmonic Control of N* Three-Phase PMSG for HVDC Transmission Based on MMC. *Energies* **2020**, *13*, 178.
https://doi.org/10.3390/en13010178

**AMA Style**

Rao Z, Zhang Z, Huang S, Long Z, Wu G. Characteristics and Current Harmonic Control of N* Three-Phase PMSG for HVDC Transmission Based on MMC. *Energies*. 2020; 13(1):178.
https://doi.org/10.3390/en13010178

**Chicago/Turabian Style**

Rao, Zhimeng, Zhigang Zhang, Shoudao Huang, Zhuo Long, and Gongping Wu. 2020. "Characteristics and Current Harmonic Control of N* Three-Phase PMSG for HVDC Transmission Based on MMC" *Energies* 13, no. 1: 178.
https://doi.org/10.3390/en13010178