*4.2. A Potential Application in a System with a High-Speed PMSM Generator*

The proposed MMCCR converter can be applied in a system with a high-speed PMSM generator. Figure 21 shows a simplified circuit for simulation tests, while the proposed control diagram is presented in Figure 22. The purpose of the simulation tests was as follows:


Precise amplitude control is required during generator start-up and synchronisation with the grid. The SVPWM method based on the three nearest vectors selection has been used. At this stage, simulation studies focused on the verification of the possibility of controlling the active component of the generator current, estimating the THD for selected waveforms, and determining the number of switching of power electronic switches.

**Figure 21.** A potential application scheme with a high-speed PMSM generator: CMC—conventional matrix converter, MMCCR—the proposed converter, THD—calculation of the total harmonic distortion block, LPF—the low–pass filter, and "n"—the star point for the phase voltage measurement.

**Figure 22.** The proposed control scheme: PLL—phase-locked loop, MMCCR—the proposed converter, PI—standard proportional integral controller, *ϕ*i—grid's voltage angle, *ϕ*—the synchronisations angle, *ϕ*g—generator's voltage angle, *i* ∗ *<sup>d</sup>*—an active reference current for generator, *iq*—a reactive reference current for generator, *ω*<sup>g</sup> = *ω*m—for simplicity, mechanical pulsation is equal to electrical pulsation.

Selected results of the comparison CMC and MMCCR converters during SVPWM modulation are shown in Table 8. All presented measurements were carried out for the modulation period equal to 10 μs and the set active current of the generator 200 A. For the MMCCR converter, compared to the CMC topology, the THD factor of the input current and the output voltage is over 2.5 times lower, while maintaining a constant value of the modulation period. In addition, the quality of the generator current is better.

**Table 8.** Selected results of the comparison CMC and MMCCR converters during SVPWMmodulation.


Example waveforms of currents and voltages are shown in Figure 23. The simulation performed for the step change of the reference active generator current, from 0 to 200 A (approximately 75 kW power) in *t* = 0.07 s. As can be seen, the shape of the input current and the voltage generated by the converters have differed. The MMCCR generates a quasi multilevel voltage and the input current shape is near to the sinusoidal waveform. The input current spectrums for both converters are presented in Figure 24.

**Figure 23.** The step change 0–200 A of the reference active generator current in *t* = 0.07 s: (**a**) for CMC converter, (**b**) for MMCCR converter.

**Figure 24.** The input current spectrums for both converters.

The proposed MMCCR topology contains four matrix converters and three-phase shifter circuits. As mentioned in an introduction section, the power is equally divided with among these matrix converters. Example PS currents *i*PS1, *i*PS2, and *i*PS3 are shown in Figure 25.

In steady-state it is possible to change the control strategy. The SVPWM method can be replaced by NVM modulation, which is characterised by a much lower operating frequency of power electronic switches. However, new PI controllers settings should be selected in this case to keep the staircase character of the generated voltage. An obtained example of converter's voltage and other waveforms, during an active NVM modulation, is shown in Figures 26 and 27.

**Figure 25.** Converter's line–to–line output (correspond to Figure 21) voltage and the current sharing among the PS shown in Figure 6—SVPWM modulation.

**Figure 26.** MMCCR converter' output voltage *v*o1 and the generator current *i*g1 for NVM modulation: THD(*i*g1) = 3.5% and THD(*v*o1) = 16%.

**Figure 27.** An input current *i*i1 and its filtered waveform *i*i1LPF for NVM modulation: THD(*i*i1) = 26%.

#### **5. Conclusions**

This article studies nature and presents conceptual research and discusses the different Pulse Width Modulation (PWM) strategies for operating, with a low-switching frequency for the proposed topology. It shows how the unconventional combination of CMC modules and CR could improve the quality of energy conversion. The paper also presents how this solution may be specifically appropriate for the high power systems, that are supplied by the high AC frequency sources, such as the high-speed generators or airport terminals' supply of 400 Hz.

The main features of the proposed approach are as follows:


In the case of MMCCR control with NVM modulation, it is possible to achieve a reasonable compromise between low THD value and relatively low frequency of power switches. However, as shown in Figure 20, in case of NVM modulation, it is difficult to control the output current/voltage with reference amplitude changes. Special switchable algorithms are required. Much better control possibilities, albeit at the cost of increasing THD and about 2 times the switching frequency, can be achieved when implementing the PWR algorithm. A further increase in the precision of the generation and control range of the output current/voltage is possible by means of SVPWM modulation for two rotating spatial vectors. This results in higher switching frequency and control calculation problems for CMC systems, in particular for this 12-pulse MMCCR. In order to reduce the importance of these problems and the related requirements on the capabilities of processor controllers, the authors initially propose to use the barycentric coordinate method [19], which unifies and simplifies calculations.

The research of this method in relation to the MMCCR system, including the hybrid method [25], allowing to minimize the frequency of connections in the converter at fixed points will be presented in the next paper. This study article does not in any way pretend to present the full spectrum of problems associated with MMCCR systems. Its main objective was only to present the possibilities and basic properties of equalising typical CMC modules with chokes coupled with overall power of no more than

about 30% of the rated power of the whole system. The above objective also includes a general discussion of dedicated control algorithms. Considering the generality and the material's size, only the most important theoretical issues verified by simulation are presented. Experimental research on specific cases will be the subject of further publications in the near future.

**Author Contributions:** Conceptualisation: P.S. and N.S., investigation and simulation: P.S. and J.L., validation, formal analysis: A.U., final editing: P.S. and E.R.-C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the LINTE∧2 Laboratory, Gdansk University of Technology. It was also supported by ITMO University Saint Petersburg, Russian Federation.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **Appendix A**

**Table A1.** The **S**MC*<sup>n</sup>* Switch States.



**Table A1.** *Cont.*


**Table A2.** The **S**MC*<sup>p</sup>* Switch States.


**Table A2.** *Cont.*
