Author Contributions
Conceptualization, H.J. and F.D.; formal analysis, H.J.; methodology, H.J.; software, H.J.; validation, H.J.; writing—original draft, H.J.; supervision, F.D.; writing—review and editing, H.J., F.D., H.L., J.T., Y.L. and G.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
(a) The MMC; (b) the SMi.
Figure 1.
(a) The MMC; (b) the SMi.
Figure 2.
Conventional voltage balancing control.
Figure 2.
Conventional voltage balancing control.
Figure 3.
The relationship between the capacitance estimation error, bau_i and Caui in the conventional capacitance monitoring method.
Figure 3.
The relationship between the capacitance estimation error, bau_i and Caui in the conventional capacitance monitoring method.
Figure 4.
The upper arm current iau, switching signal Saui and capacitor voltage ucaui of MMCs under the proposed approach.
Figure 4.
The upper arm current iau, switching signal Saui and capacitor voltage ucaui of MMCs under the proposed approach.
Figure 5.
Proposed VCV-based voltage-balancing control.
Figure 5.
Proposed VCV-based voltage-balancing control.
Figure 6.
Proposed capacitance monitoring strategy.
Figure 6.
Proposed capacitance monitoring strategy.
Figure 7.
Simulated waveforms of the MMC without the offset error bau_i under the proposed strategy: (a) ea, eb, ec; (b) ia, ib, ic; (c) ucau1; (d) iau.
Figure 7.
Simulated waveforms of the MMC without the offset error bau_i under the proposed strategy: (a) ea, eb, ec; (b) ia, ib, ic; (c) ucau1; (d) iau.
Figure 8.
Simulated waveforms of the MMC without the offset error bau_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 8.
Simulated waveforms of the MMC without the offset error bau_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 9.
Simulation results without the offset error bau_i under the proposed strategy: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 9.
Simulation results without the offset error bau_i under the proposed strategy: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 10.
Simulated waveforms of the MMC with the offset error bau_i under the proposed strategy: (a) ea, eb, ec; (b) ia, ib, ic; (c) ucau1; (d) iau.
Figure 10.
Simulated waveforms of the MMC with the offset error bau_i under the proposed strategy: (a) ea, eb, ec; (b) ia, ib, ic; (c) ucau1; (d) iau.
Figure 11.
Simulated results of the MMC with the offset error bau_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 11.
Simulated results of the MMC with the offset error bau_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 12.
Simulation results of the MMC with the offset error bau_i under the proposed strategy: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 12.
Simulation results of the MMC with the offset error bau_i under the proposed strategy: (a) the actual and estimated capacitance of Cau1~Cau4; (b) estimation error.
Figure 13.
The MMC experimental platform.
Figure 13.
The MMC experimental platform.
Figure 14.
Experimental waveforms of the MMC without the offset error bbl_i under the proposed strategy: (a) ia, ib, ic; (b) ibl and ucbl1.
Figure 14.
Experimental waveforms of the MMC without the offset error bbl_i under the proposed strategy: (a) ia, ib, ic; (b) ibl and ucbl1.
Figure 15.
Experimental results of the MMC without the offset error bbl_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 15.
Experimental results of the MMC without the offset error bbl_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 16.
Experimental results of the MMC without the offset error bbl_i under the proposed strategy: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 16.
Experimental results of the MMC without the offset error bbl_i under the proposed strategy: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 17.
Experimental waveforms of the MMC with the offset error bbl_i under the proposed strategy: (a) ia, ib, ic; (b) ibl and ucbl1.
Figure 17.
Experimental waveforms of the MMC with the offset error bbl_i under the proposed strategy: (a) ia, ib, ic; (b) ibl and ucbl1.
Figure 18.
Experimental results of the MMC with the offset error bbl_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 18.
Experimental results of the MMC with the offset error bbl_i under the conventional capacitance monitoring method: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 19.
Experimental results of the MMC with the offset error bbl_i under the proposed strategy: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 19.
Experimental results of the MMC with the offset error bbl_i under the proposed strategy: (a) the actual and estimated capacitance of Cbl1~Cbl4; (b) estimation error.
Figure 20.
Simulation results for the MMC: (a) increased estimation errors under the conventional method and proposed strategy; (b) proportion of the decreased estimation error under the proposed strategy.
Figure 20.
Simulation results for the MMC: (a) increased estimation errors under the conventional method and proposed strategy; (b) proportion of the decreased estimation error under the proposed strategy.
Figure 21.
Experimental results for the MMC: (a) increased estimation errors under the conventional method and proposed strategy; (b) proportion of the decreased estimation error under the proposed strategy.
Figure 21.
Experimental results for the MMC: (a) increased estimation errors under the conventional method and proposed strategy; (b) proportion of the decreased estimation error under the proposed strategy.
Table 1.
Operation modes of SMi.
Table 1.
Operation modes of SMi.
Operation Mode | iau | Saui | ucaui |
---|
Ascending mode | >0 | 1 | Increased |
Ascending mode | >0 | 0 | Unchanged |
Descent mode | ≤0 | 1 | Decreased |
Descent mode | ≤0 | 0 | Unchanged |
Table 2.
Relationship between |bau_i| and accuracy of estimated Caui_es.
Table 2.
Relationship between |bau_i| and accuracy of estimated Caui_es.
|bau_i| | Accuracy of Estimated Caui_es |
---|
↑ | ↓ |
↓ | ↑ |
Table 3.
Simulation parameters.
Table 3.
Simulation parameters.
Simulation Parameter | Value |
---|
Active power | 2 MW |
Reactive power | 0 MVar |
Grid frequency fs | 50 Hz |
Number N of SMs each arm | 8 |
Arm inductance Ls | 2 mH |
SM capacitor voltage Uc | 0.9 kV |
DC-side voltage Udc | 7.2 kV |
Table 4.
Simulation results of the THD of the output current.
Table 4.
Simulation results of the THD of the output current.
Measurement Error | With Proposed Strategy | THD |
---|
Without offset error bau_i | No | 1.79% |
Without offset error bau_i | Yes | 1.79% |
With offset error bau_i | No | 1.77% |
With offset error bau_i | Yes | 1.77% |
Table 5.
Experimental parameters.
Table 5.
Experimental parameters.
Parameter | Value |
---|
Nominal capacitor voltage Uc | 40 V |
DC-side voltage Udc | 160 V |
Number N of SMs each arm | 4 |
Inductance Ls | 3 mH |
Load resistance Ro | 10 Ω |
Table 6.
Simulation results of the THD of the AC side current.
Table 6.
Simulation results of the THD of the AC side current.
Measurement Error | With Proposed Strategy | THD |
---|
Without offset error bbl_i | No | 2.85% |
Without offset error bbl_i | Yes | 2.85% |
With offset error bbl_i | No | 2.82% |
With offset error bbl_i | Yes | 2.84% |