# An Improved AC-Link Voltage Matching Control for the Multiport Modular Multilevel DC Transformer in MVDC Applications

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of AC-Link Voltage Mismatching Phenomenon in M3DCT

_{MV}represents the MVDC-link voltage of the M3DCT; V

_{LV1}to V

_{LVm}represent the LVDC-link voltages of H

_{1}to H

_{m}, respectively; k

_{T1}to k

_{Tm}represent the voltage ratio of the AC transformers connected to H

_{1}to H

_{m}, respectively; v

_{MV}is the MVAC-link voltage; v

_{LV}represents the equivalent voltage of the sum of LVAC-link voltages (v

_{LV1}+ … + v

_{LVm}) on the MVAC side; v

_{LV1}to v

_{LVm}represent the equivalent voltages of LVAC-link voltages in H

_{1}to H

_{m}, respectively, on the MVAC side; ξ

_{DC}and ξ

_{AC}are the DC-link and AC-link voltage mismatch ratios of the M3DCT, respectively.

_{DC}= 0. Conversely, when ξ

_{DC}≠ 0, the state is defined as the DC-link voltage mismatching state. Furthermore, an increment in the magnitude of ξ

_{DC}is indicative of an escalating disparity between the DC voltage and the AC transformer turns ratio. The rationale for the interpretation of ξ

_{AC}is congruent with this line of reasoning. It is important to note that the key distinction between ξ

_{DC}and ξ

_{AC}, as outlined in (1), is due to the variables V

_{MV}and A(v

_{MV}). By actively controlling A(v

_{MV}) within the M3DCT, it is possible to maintain the AC-link voltage in a matching state, regardless of any fluctuations in the DC-link voltage. Conversely, if there is no decoupling between A(v

_{MV}) and V

_{MV}in the M3DCT system, the operational state of the AC-link voltage will be directly linked to the operational state of the DC-link voltage. In other words, ξ

_{AC}= ξ

_{DC}.

_{MV}) of the M3DCT is typically regulated by the upstream power electronic converter connected to the MVDC bus. Thus, even when the transmission power changes, V

_{MV}always remains constant at its rated value (V

_{MVra}). In contrast, the LVDC-link voltages (V

_{LV1}to V

_{LVm}) are subject to change with the power flow because they are usually connected to LVDC systems through DC distribution lines, as illustrated in Figure 1. Since the voltage at LVDC buses in LVDC systems is managed by those systems, the LVDC-link voltages of the M3DCT can be derived as follows:

_{LVnet1}to V

_{LVnetm}represent the LVDC bus voltages of LVDC system1 to LVDC system m, respectively; I

_{LV1}to I

_{LVm}represent the LVDC-link currents of H

_{1}to H

_{m}, respectively; and R

_{linej(j=1…m)}is the equivalent resistance of the DC distribution lines.

_{LV1ra}to V

_{LVmra}are the rated LVDC-link voltages of H

_{1}to H

_{m}, respectively; V

_{LVnetD1}to V

_{LVnetDm}represent the desired LVDC bus voltages of LVDC system1 to LVDC system m, respectively; I

_{LV1ra}to I

_{LVmra}represent the rated LVDC-link currents of H

_{1}to H

_{m}, respectively.

_{LV1}to V

_{LVm}, will experience fluctuations, which can impact the performance of the M3DCT. These fluctuations are particularly pronounced at extremely low power levels, where V

_{LV1}to V

_{LVm}can significantly deviate from their rated voltages. As a result, v

_{LV}, which represents the composite voltage of the sum of LVDC-link voltages (v

_{LV1}+ … + v

_{LVm}) on the MVAC side, will also exhibit significant deviation from its rated value, v

_{LVra}.

_{T1}to k

_{Tm}, within the M3DCT, are typically designed to align with rated conditions:

_{LVj}from V

_{LV}

_{j}

_{ra}indicates that the DC-link voltage of the M3DCT is no longer in the matching state. Since A(v

_{MV}) and V

_{MV}are not decoupled in the conventional control of M3DCT, the mismatch in the DC-link voltage mentioned above will result in a corresponding mismatch in the M3DCT’s AC-link voltage. Consequently, both the AC-link voltage mismatch and the low operating power will decrease the performance of the M3DCT.

_{AC}= 14%), the AC-link current for the M3DCT increases to approximately 0.25 p.u. of the rated current, and the arm current escalates to about 0.16 p.u. of the rated current. That is, the AC-link current stress and the circulating power become exceedingly high when there is a mismatch in the AC-link voltage, which substantially diminishes the performance of the M3DCT. Meanwhile, addressing this issue effectively requires achieving AC-link voltage matching.

## 3. Implementation Scheme for the Proposed Improved AC-Link Voltage Matching Control (IVM)

_{1}+ n

_{2}). Taking arm1 and arm2 as examples, when arm1 has n

_{1}SMs inserted, arm2 has n

_{2}SMs inserted. Conversely, when arm1 has n

_{2}SMs inserted, arm2 has n

_{1}SMs inserted. Meanwhile, both arm1 and arm2 maintain a duty ratio of 50%. This implies that for any arm, if n

_{1}SMs are inserted during the first half of the switching cycle, then n

_{2}SMs will be inserted during the second half of the switching cycle.

_{1}SMs are in the inserted state, the voltage of the arm can be expressed as follows:

_{arm}represents the arm voltage of the discussed arm; V

_{C}represents the capacitor voltage per SM of the discussed arm.

_{2}SMs are in the inserted state, the arm voltage can be expressed as:

_{hs}represents the half-switching period of the M3DCT.

_{MV}in the M3DCT can be obtained based on the arm voltages:

_{MV}and v

_{LV}is DT

_{hs}, the voltage v

_{LV}is:

_{1}and n

_{2}should satisfy the following requirement:

_{1}and n

_{2}should ensure that the capacitor voltage of the MVDC-link SM remains within the required maximum and minimum values. That is:

_{Cmin}and V

_{Cmax}represent the required maximum and minimum values of the capacitor voltage in the M3DCT.

_{LV}) of the M3DCT will decrease as the transmission power decreases. Meanwhile, the MVAC-link voltage (v

_{MV}) and the MVDC-link voltage (V

_{MV}) of the M3DCT remain constant at their rated values. Consequently, Equations (11) and (12) can be reformulated as follows:

_{1}and n

_{2}to achieve ξ

_{AC}= 0 when ξ

_{DC}≠ 0. As a result, the interval during which the voltage is regulated, known as the unit regulated interval, is also a critical factor influencing the efficacy of the control method. The unit voltage-regulated interval for the proposed IVM is analyzed in detail as follows.

_{1}= 0 and n

_{2}= N, the proposed IVM is equivalent to the conventional control; when n

_{1}+ n

_{2}= N, the proposed IVM is equivalent to the CVM. Therefore, the proposed IVM offers more flexible control than both the conventional control and the CVM. In particular, compared to the CVM, the proposed IVM allows for a more flexible adjustment of the unit-regulated interval. As a result, the proposed IVM can overcome the limitations of the CVM.

_{LV1}+ … + v

_{LVm}) is 16 kV. According to the parameters in Table 1, if the CVM is employed in the M3DCT, the unit voltage regulated interval of the MVAC-link voltage would be the twice that of the capacitor voltage (0.5 kV). As a result, the matching control of the M3DCT may not be achievable in certain conditions. Conversely, by applying the proposed IVM method to the M3DCT, these constraints can be circumvented. For example, when (k

_{T1}V

_{LV1}+ …+ k

_{Tm}V

_{LVm}) = 17.5 kV (ξ

_{DC}= 14%), the CVM method would fail to regulate the amplitude of the MVAC-link voltage (v

_{MV}) to match 17.5 kV. With n

_{1}= 2 and n

_{2}= 38, the amplitude of v

_{MV}would be 18 kV, and with n

_{1}= 3 and n

_{2}= 37, it would be 17 kV. However, the proposed IVM method can achieve the desired match with n

_{1}= 2 and n

_{2}= 30. As a result, the voltage per SM capacitor is 0.625 kV, which exceeds the rated value but is still below the maximum allowable capacitor voltage.

_{Crate}/V

_{Cmin}.

## 4. Verification

_{arm1}and v

_{arm2}) are 20 kV and 0 kV, respectively. Consequently, the amplitude of the MVAC voltage (v

_{MV}) of the M3DCT is 20 kV, and the sum of the capacitor voltages per arm is also 20 kV. Meanwhile, the SM capacitor voltage VC is regulated at 0.5 kV, which corresponds to its rated value. Additionally, the maximum values of the arm currents and the AC-link current in this scenario are 0.6 kA and 0.74 kA, respectively. These results demonstrate the effectiveness of the proposed IVM in maintaining system performance at the rated transmission power.

_{T1}V

_{LV1}+ …+ k

_{Tm}V

_{LVm}) are not in a matched state, with a mismatch of 14% (ξ

_{DC}= 14%). During this period, the maximum and minimum values of the arm output voltage (v

_{arm1}and v

_{arm2}) are 18.75 kV and 1.25 kV, respectively. Consequently, the amplitude of the MVAC voltage (v

_{MV}) of the M3DCT is 17.5 kV, and the total capacitor voltages per arm amount to 25 kV. The capacitor voltage in this situation is 0.625 kV, and the maximum values of the arm currents and the AC-link current in this case are 0.11 kA and 0.13 kA, respectively. These results demonstrate the effectiveness of the proposed IVM in low power transmission.

_{DC}) of 14%. As depicted in Figure 7, the maximum and minimum values of the arm output voltage (v

_{arm1}and v

_{arm2}) are 20 kV and 0 kV, respectively. Consequently, the amplitude of the MVAC voltage (v

_{MV}) in the M3DCT is 20 kV, and the sum of the capacitor voltages per arm also amounts to 20 kV. However, the equivalent voltage of the sum of LVAC-link voltages on the MVAC side (v

_{LV}) in the M3DCT is 17.5 kV, indicating that the M3DCT is operating with a mismatch in the AC-link voltage. As a result, the maximum values of the arm currents and the AC-link current in this case are 0.2 kA and 0.26 kA, respectively. Clearly, when compared to the operating results depicted in Figure 6b, the increase in arm currents and the AC-link current has a negative impact on the performance of the M3DCT. These results confirm the correctness of the theoretical analysis.

_{DC}= 14%). It can be observed that, as the sum of the LVC-Link voltage decreases from 20 kV to 17.5 kV, the LVAC-link equivalent voltage of the M3DCT swiftly decreases from 20 kV to 17.5 kV, while the MVAC-link voltage smoothly drops to 17.5 kV under the control of the proposed IVM. During this process, as the sum of the SMs inserted in the upper and lower arms on the MVDC side of the M3DCT simultaneously changes from 40 to 32 at each moment, the capacitor voltage of each SM increases, resulting in a rise in the total capacitor voltage sum of the SMs in each arm.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**AC-link voltage mismatching phenomenon analysis of the investigated M3DCT: (

**a**) AC-link voltage match; (

**b**) AC-link voltage mismatch (ξ

_{AC}= 14%).

**Figure 3.**Implementation principles of the proposed IVM control and the conventional control of M3DCT: (

**a**) the proposed IVM control; (

**b**) the conventional control.

**Figure 6.**Simulation results of the proposed IVM control: (

**a**) rated power and ξ

_{DC}= 0; (

**b**) light load (20%) and ξ

_{DC}= 14%.

**Figure 7.**Simulation results of the conventional control when M3DCT operates at light load (20%) and ξ

_{DC}= 14%.

**Figure 8.**Dynamic simulation results of the M3DCT under the IVM control from rated power to light load (20%,ξ

_{DC}= 14%).

Terms | Parameters |
---|---|

Capacity of M3DCT | 10 MW |

AC-link frequency | 2 kHz |

Modulation methods | nearest level modulation (NLM) |

SM capacitor voltage balancing method | sorting |

V_{MVra} | ±10 kV |

k_{T1}V_{LV1ra} + …k_{Tm}V_{Lvmra} | 20 kV |

Number of LVDC systems (m) | 5 |

V_{LV1ra}…V_{Lvmra} | 0.4 kV |

k_{T1}…k_{Tm} | 10:1 |

I_{Mvra} | 0.5 kA |

N | 40 |

V_{Crate} | 0.5 kV |

V_{C}_{min} | 0.3 kV (60% of the rated value) |

V_{C}_{max} | 0.7 kV (140% of the rated value) |

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**MDPI and ACS Style**

Chen, Y.; Yu, S.; Wang, Y.; Yang, R.; Cheng, X.
An Improved AC-Link Voltage Matching Control for the Multiport Modular Multilevel DC Transformer in MVDC Applications. *Energies* **2024**, *17*, 1346.
https://doi.org/10.3390/en17061346

**AMA Style**

Chen Y, Yu S, Wang Y, Yang R, Cheng X.
An Improved AC-Link Voltage Matching Control for the Multiport Modular Multilevel DC Transformer in MVDC Applications. *Energies*. 2024; 17(6):1346.
https://doi.org/10.3390/en17061346

**Chicago/Turabian Style**

Chen, Yong, Songtao Yu, Yizhen Wang, Ruixiong Yang, and Xu Cheng.
2024. "An Improved AC-Link Voltage Matching Control for the Multiport Modular Multilevel DC Transformer in MVDC Applications" *Energies* 17, no. 6: 1346.
https://doi.org/10.3390/en17061346