# A Circulating Current Suppression Strategy for MMC Based on the 2N+1 PWM Approach

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## Abstract

**:**

## 1. Introduction

## 2. MMC Operation Principle

_{0}. V

_{dc}is the DC-link voltage, v

_{x}(x ∈ {A, B, C}) is the output-phase voltage, i

_{x}is the output current. v

_{x}

_{u}and v

_{x}

_{l}are the voltage of the upper and lower arm, respectively. i

_{x}

_{u}and i

_{x}

_{l}are current of the upper and lower arm, respectively.

_{1}and T

_{2}, with anti-parallel diodes and an energy storage capacitor. The MMC controls the turn-on and turn-off states of each half bridge sub-module power switching device in the upper and lower arms to obtain the required output voltage on the AC side. Each anti-parallel diode ensures that the corresponding IGBT power switching device can be protected from the current when it is turned off, thus ensuring that the MMC can operate normally. When T

_{1}is turned on and T

_{2}is turned off, the energy storage capacitor will be charged or discharged according to the direction of the arm current flowing through it, when the sub-module is in the input state. When T

_{1}is off and T

_{2}is on, the output voltage of the sub-module is 0 V, and the arm current will not flow through the energy storage capacitor, at which time the sub-module is in the removal state. In addition, when both T

_{1}and T

_{2}are switched off, the sub-module will be in the removal state. When the arm current is positive, the capacitor is charged using the anti-parallel diode D

_{1}; when the arm current is negative, the arm current will flow through the anti-parallel diode D

_{2}, and the capacitor will be bypassed. Table 1 shows the output voltage and switch state corresponding to the power switching device and defines the current direction of the arm current from end a to end b as the positive direction, v

_{sm}is expressed as the output voltage of the sub-module unit and v

_{cap}is the capacitance voltage of the sub-module.

_{xki}can be defined as the switching function of the sub-module, as shown in Equation (1).

_{xki}is the switching function of the ith half bridge sub-module of the k-arm in the xth phase (k = u, l), and when S

_{xki}= 1, the corresponding half bridge sub-module is in the input state, and when S

_{xki}= 0, the corresponding half bridge sub-module is in the removal state.

_{xu}and v

_{xl}, of the upper and lower arms in the xth phase unit can be expressed as:

_{sm_xui}and v

_{sm_xni}are the output voltages of the ith half bridge sub-module of the upper and lower arms of the x phase, respectively.

_{cirA}. According to Kirchhoff’s current law (KCL), the upper and lower arm currents can be expressed as:

_{A}is the RMS value of the output-phase voltage, I

_{A}is the RMS value of the output current, ω is the output fundamental angular frequency, and φ is the power factor angle.

## 3. Improved 2N+1 Pulse-Width Modulation Approach

_{c}and the phase difference of π/2. At the same time, since the upper and lower arms in the MMC phase cell operate symmetrically, the phases of the modulated signals of the upper and lower arms need to differ from each other by π. The carrier signals of the upper arm are defined as C

_{p1}~C

_{p4}, and the carrier signals of the lower arm are defined as C

_{n1}~C

_{n}

_{4}. Taking C

_{p1}and C

_{n1}as an example, the phase shifting angle θ between the carrier signals of the upper and lower arm is π/4.

## 4. Circulating Current Suppression Strategy

_{cirA_dc}is the DC component of the circulating current, and I

_{cirA_2}and θ are the RMS value and the phase of the second order harmonic component of the circulating current, respectively.

_{cirA}≤ ${i}_{\mathrm{cirA}\_\mathrm{sum}}^{*}$, the N−1 sub-modules are selected to be put into the phase, so that the circulating current inside the topology rises; conversely, when the voltage level is at the redundant voltage level and i

_{cirA}> ${i}_{\mathrm{cirA}\_\mathrm{sum}}^{*}$, the N+1 sub-modules are selected to be put into the phase, so that the circulating current inside the topology falls and, finally, after the capacitor voltage sequencing algorithm, the trigger pulse is applied to the modular multilevel converter. In particular, the capacitor voltage sorting algorithm [27] in this block diagram, the most widely used method for balancing the capacitive voltage of sub-modules, determines the specific sub-modules to be put into the bridge arm by sorting the capacitive voltage of all sub-modules in the arm and determining the number of sub-modules to be put into the arm at the present time, as well as the direction of the arm current. The purpose of this is that when the arm current is positive, the sub-module with the lower capacitor voltage is engaged for a longer period of time to charge the capacitor, while when the arm current is negative, the sub-module with the higher capacitor voltage is engaged for a longer period of time to discharge the capacitor.

## 5. Experimental Verification

^{®}rapid prototyping system OP5700 was adopted as the controller and the Switzerland Imperix

^{®}PEH2015 power electronic building block was used to compose the MMC (N = 4), as shown in Figure 13. The load condition was set as a simple resistor–inductor (R–L) (resistor–inductor) load. Based on the instantaneous power of the upper and lower arms, it is known that the control performance of the MMC depends on the power factor and, therefore, the simulations and experiments with the proposed 2N+1 pulse-width modulation method and the conventional carrier phase-shifted 2N+1 pulse-width modulation method are carried out under different load power factor conditions. The parameters for the simulations and experiments are shown in Table 3.

_{cirA}, of the proposed method and the conventional method under different load power factor conditions are shown in Figure 14 and Figure 15. For cosφ = 0.954, the simulated ripples of the circulating current are 8.1 A and 41 A for the proposed method and the conventional method, respectively. For cosφ = 0.623, the simulated ripples of the circulating current are 6.2 A and 16.5 A for the proposed method and the conventional method, respectively. It is clear that the proposed method can suppress the circulating current effectively.

_{AB}, the output-phase voltage v

_{A}, and the output current i

_{A}of the proposed method and the conventional method under different load power factor conditions are shown in Figure 16 and Figure 17. As the arm contains eight sub-modules, the number of levels in the output-phase voltage waveform under the 2N+1 modulation is 17 levels for m = 0.9. If the total harmonic distortion rate of the output current is used as the evaluation standard for the MMC output waveform, the total harmonic distortion of the output current I

_{THD}for the proposed method and the conventional method under different load power factor conditions are shown in Figure 18 and Figure 19. The I

_{THD}of the proposed and the conventional methods are approximately the same. This demonstrates the similarity in the output performance between the proposed modulation method and the conventional modulation method.

_{cirA}of the proposed method and the conventional method under different load power factor conditions are shown in Figure 20 and Figure 21. For cosφ = 0.954, the ripples of the circulating current are 3.8 A and 5.8 A for the proposed method and the conventional method, respectively. For cosφ = 0.623, the ripples of the circulating current are 3.4 A and 4.4 A for the proposed method and the conventional method, respectively. It is obvious that the proposed method uses redundant switching states with the 2N+1 modulation to regulate the circulating current of the MMC with its reference value in order to achieve the effect of suppressing the circulating current fluctuations at different load power factors.

_{THD}of the proposed and the conventional methods are approximately the same, as shown in Figure 24 and Figure 25. This proves that the proposed modulation method presents an identical performance to the conventional modulation method. Thus, the proposed method not only reduces the circulating current, but also ensures the quality of the output waveform, the advantages of which are shown in Table 4 and Table 5.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

MMC | Modular multilevel converter |

CPSPWM | Carrier phase-shifted pulse-width modulation |

APODPWM | Alternative phase opposition disposition pulse-width modulation |

HBSM | Half bridge sub-module |

L_{0} | Arm inductance |

V_{dc} | DC-link voltage |

v_{x} | Output-phase voltage (x ∈ {A, B, C}) |

i_{x} | Output current |

v_{xu} | Voltage of upper arm |

v_{xl} | Voltage of lower arm |

i_{xu} | Current of upper arm |

i_{xl} | Current of lower arm |

v_{sm} | Output voltage of the sub-module |

v_{cap} | Capacitance voltage of the sub-module |

N | The total number of sub-modules in the arm |

V_{A} | The RMS value of A-phase output-phase voltage |

I_{A} | The RMS value of A-phase output current |

v_{AB} | The output line voltage of phase A and B |

${\widehat{V}}_{\mathrm{A}}$ | Amplitude of A-phase output-phase voltage |

m | Voltage modulation index |

KVL | Kirchhoff’s voltage law |

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**Figure 4.**The equivalent circuit of phase A. (

**a**) DC-side equivalent circuit, (

**b**) AC-side equivalent circuit.

**Figure 5.**The principle of the conventional carrier phase-shifted 2N+1 pulse-width modulation approach (N = 4).

**Figure 11.**The DC-side equivalent circuit of the MMC. (

**a**) N−1 sub-modules are switched in for phase A, (

**b**) N+1 sub-modules are switched in for phase A.

**Figure 12.**The block diagram of the circulating current suppression strategy based on the improved 2N+1 pulse-width modulation approach.

**Figure 14.**Simulated waveform of the circulating current fluctuation at cosφ = 0.954 (N = 8). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 15.**Simulated waveform of the circulating current fluctuation at cosφ = 0.623 (N = 8). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 16.**Experimental output waveforms of the converter at cosφ = 0.954 (N = 8). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 17.**Experimental output waveforms of the converter at cosφ = 0.623 (N = 8). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 18.**The total harmonic distortion of the output current at cosφ = 0.954 (N = 8). (

**a**) The proposed modulation approach, (

**b**) the conventional modulation approach.

**Figure 19.**The total harmonic distortion of the output current at cosφ = 0.623 (N = 8). (

**a**) The proposed modulation approach, (

**b**) the conventional modulation approach.

**Figure 20.**Experimental waveform of the circulating current fluctuation at cosφ = 0.954 (N = 4). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 21.**Experimental waveform of the circulating current fluctuation at cosφ = 0.623 (N = 4). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 22.**Experimental output waveforms of the converter at cosφ = 0.954 (N = 4). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 23.**Experimental output waveforms of the converter at cosφ = 0.623 (N = 4). (

**a**) The proposed modulation method, (

**b**) the conventional modulation method.

**Figure 24.**The total harmonic distortion of the output current at cosφ = 0.954 (N = 4). (

**a**) The proposed modulation approach, (

**b**) the conventional modulation approach.

**Figure 25.**The total harmonic distortion of the output current at cosφ = 0.623 (N = 4). (

**a**) The proposed modulation approach, (

**b**) the conventional modulation approach.

T_{1} | T_{2} | Arm Current Direction | Output Voltage | Working Status | Description |
---|---|---|---|---|---|

ON | OFF | >0 | v_{cap} | Input state | Capacitive charging |

ON | OFF | <0 | v_{cap} | Input state | Capacitive discharge |

OFF | ON | >0 | 0 | Removal state | Capacitive bypass |

OFF | ON | <0 | 0 | Removal state | Capacitive bypass |

OFF | OFF | >0 | v_{cap} | Blocked state | Capacitive charging |

OFF | OFF | <0 | 0 | Blocked state | Capacitive bypass |

**Table 2.**The relationship between the total number of switched-in sub-modules and the output-phase voltage level.

Phase Voltage Level | Input of Sub-Module Number of Upper Arm | Input of Sub-Module Number of Lower Arm | Input of Sub-Module Number of Phase Leg |
---|---|---|---|

0 | 4 | 0 | 4 |

1 | 4 | 1 | 5 |

3 | 0 | 3 | |

2 | 3 | 1 | 4 |

3 | 3 | 2 | 5 |

2 | 1 | 3 | |

4 | 2 | 2 | 4 |

5 | 2 | 3 | 5 |

0 | 3 | 3 | |

6 | 1 | 3 | 4 |

7 | 1 | 4 | 5 |

0 | 3 | 3 | |

8 | 0 | 4 | 4 |

Parameters | Simulation | Experiment |
---|---|---|

DC-side voltage V_{dc}/V | 800 | 200 |

Number of SMs per arm N | 8 | 4 |

Sub-module capacitance C/mF | 5.04 | 5.04 |

Arm inductance L_{0}/mH | 2 | 1 |

Load resistance R/Ω | 5 | 5 |

Load inductance L/mH | 5/20 | 5/20 |

Rated frequency f/Hz | 50 | 50 |

Carrier frequency f_{c}/kHz | 2 | 2 |

Voltage modulation index m | 0.9 | 0.8 |

Load power factor cosφ | 0.954/0.623 | 0.954/0.623 |

Features | Simulation (N = 8) | Experiment (N = 4) | ||
---|---|---|---|---|

The Proposed Approach | The Conventional Approach | The Proposed Approach | The Conventional Approach | |

Number of carriers per arm | 2 | 8 | 2 | 4 |

Circulating current fluctuation | 8.1 A | 41 A | 3.8 A | 5.8 A |

I_{THD} | 0.92% | 0.90% | 1.68% | 1.64% |

Features | Simulation (N = 8) | Experiment (N = 4) | ||
---|---|---|---|---|

The Proposed Approach | The Conventional Approach | The Proposed Approach | The Conventional Approach | |

Number of carriers per arm | 2 | 8 | 2 | 4 |

Circulating current fluctuation | 6.2 A | 16.5 A | 3.4 A | 4.4 A |

I_{THD} | 0.28% | 0.25% | 1.07% | 1.02% |

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## Share and Cite

**MDPI and ACS Style**

Zhang, G.; Song, J.; Li, C.; Gu, X.
A Circulating Current Suppression Strategy for MMC Based on the 2*N*+1 PWM Approach. *World Electr. Veh. J.* **2023**, *14*, 106.
https://doi.org/10.3390/wevj14040106

**AMA Style**

Zhang G, Song J, Li C, Gu X.
A Circulating Current Suppression Strategy for MMC Based on the 2*N*+1 PWM Approach. *World Electric Vehicle Journal*. 2023; 14(4):106.
https://doi.org/10.3390/wevj14040106

**Chicago/Turabian Style**

Zhang, Guozheng, Jiahui Song, Chen Li, and Xin Gu.
2023. "A Circulating Current Suppression Strategy for MMC Based on the 2*N*+1 PWM Approach" *World Electric Vehicle Journal* 14, no. 4: 106.
https://doi.org/10.3390/wevj14040106