# Improved Model Predictive Current Control of NPC Three-Level Converter Fed PMSM System for Neutral Point Potential Imbalance Suppression

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conventional MPCC

_{dc}is the voltage of the DC source. C

_{1}and C

_{2}are DC-link capacitors. Each phase consists of power devices S

_{x}

_{1}~S

_{x}

_{4}and clamping diodes D

_{x}

_{1}and D

_{x}

_{2}, where x ϵ {A, B, C}.

^{3}= 27 switching states can be output for three phases, corresponding to 19 basic voltage vectors in the space vector diagram, as shown in Figure 2. According to the amplitude, they can be divided into: large vectors (

**V**

_{1},

**V**

_{3},

**V**

_{5},

**V**

_{7},

**V**

_{9},

**V**

_{11}), medium vectors (

**V**

_{2},

**V**

_{4},

**V**

_{6},

**V**

_{8},

**V**

_{10},

**V**

_{12}), small vectors (

**V**

_{13}~

**V**

_{18}) and zero vectors (

**V**

_{19}).

_{o}.

_{o}and neutral point current i

_{o}can be expressed as follows:

_{x}denotes the switching state of each phase, S

_{x}ϵ{1, 0, −1}. Substituting (2) into (1) and discretizing by the forward Euler method, the predictive value of v

_{o}at (k + 1)T

_{s}is obtained as

_{s}is the sample period; k and k + 1 represent the kT

_{s}and (k + 1)T

_{s}sample period, respectively; u

_{d}and u

_{q}are d-axis and q-axis components of the stator voltage, respectively; i

_{d}and i

_{q}are d-axis and q-axis components of the stator current, respectively; L

_{d}and L

_{q}are d-axis and q-axis components of the stator inductance, respectively; R

_{s}is the stator resistance; ψ

_{f}is the stator flux; and ω

_{r}is the rotor electricity angular speed.

**${i}_{d}^{*}$**and

**${i}_{q}^{*}$**are the reference values of i

_{d}and i

_{q}, respectively, and λ

_{i}and λ

_{v}denote the weighted coefficients for the stator current term and the neutral point potential term.

- (1)
- Stator currents and neutral point potentials are sampled at kT
_{s}; - (2)
- From (3) and (4), ${i}_{\mathrm{d}}^{k+1}$, ${i}_{\mathrm{q}}^{k+1}$ and ${v}_{\mathrm{o}}^{k+1}$ at (k + 1)T
_{s}are obtained and can be used as the initial values of the algorithm; - (3)
- The sector in which the optimal vector of the last control period was located is determined, and the alternative vector set can be established as Table 2. The alternative vectors in Table 2 are substituted into (3) and (4) to obtain ${i}_{\mathrm{d}}^{k+1}$(n), ${i}_{\mathrm{q}}^{k+1}$(n) and ${v}_{\mathrm{o}}^{k+1}$(n) at (k + 2)T
_{s}, n = 1, 2,…, m, where m denotes the number of alternative vectors; - (4)
- According to (5), the cost function corresponding to each alternative voltage vector in the FCS is calculated, and the voltage vector corresponding to the minimum value of the cost function is selected to act on the converter.

## 3. Proposed MPCC

#### 3.1. Newton’s Iterative Algorithm

#### 3.2. Dynamic Division of Sectors

_{1}and d

_{2}are defined as follows:

_{c1}and v

_{c2}correspond to the upper and lower voltage of the DC-link capacitor, respectively.

_{1}and R

_{2}in sector S

_{I}as an example, the change of the basic voltage vectors under the imbalanced neutral point potential (d

_{1}= 0.5 and d

_{2}= 1.5) are shown in Figure 4.

**V**

_{2}to ${\mathit{V}}_{2}^{\prime}$. The phase angle of small vectors remains the same while the amplitude changes, from

**V**

_{13}to ${\mathit{V}}_{13}^{\prime}$ (ONN) and ${V}_{13}^{\u2033}$ (POO), respectively, and from

**V**

_{14}to ${\mathit{V}}_{14}^{\prime}$ (ONN) and ${\mathit{V}}_{14}^{\u2033}$ (PPO), respectively. Assuming the reference vector ${\mathit{V}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{k+1}$ is located in the position shown in Figure 4, for conventional MPCC, the distance r

_{4}between

**V**

_{2}and ${\mathit{V}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{k+1}$ is shorter than the distance r

_{3}between

**V**

_{13}and ${\mathit{V}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{k+1}$; thus,

**V**

_{2}is the optimal vector. When the neutral point potential rises,

**V**

_{2}and

**V**

_{13}will become ${\mathit{V}}_{2}^{\prime}$ and ${\mathit{V}}_{13}^{\prime}$/${\mathit{V}}_{13}^{\u2033}$, respectively. The distance r

_{2}between ${\mathit{V}}_{2}^{\prime}$ and ${\mathit{V}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{k+1}$ is greater than the distance r

_{1}between ${\mathit{V}}_{13}^{\u2033}$ and ${\mathit{V}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{k+1}$; thus, ${\mathit{V}}_{13}^{\u2033}$ is actually the optimal vector.

_{1}= 0.5 and d

_{2}= 1.5.

#### 3.3. The Partition Control of Neutral Point Potential Imbalance

- (1)
- The stator current and the neutral point potential are sampled at kT
_{s}; - (2)
- From (3) and (4), ${i}_{\mathrm{d}}^{k+1}$, ${i}_{\mathrm{q}}^{k+1}$ and ${v}_{\mathrm{o}}^{k+1}$ at (k + 1)T
_{s}are obtained and can be used as the initial values of the algorithm; - (3)
- The reference voltage vector is calculated by (6) and the FCS is selected according to the amplitude of the neutral point potential;
- (4)
- The alternative vector with the minimum value of the cost function is selected as the optimal vector and applied to the converter.

## 4. Experimental Results

#### 4.1. Experimental Platform

#### 4.2. Experimental Analysis

#### 4.2.1. Control Performance of the Neutral Point Potential

_{C1}= 140 V, v

_{C2}= 180 V) to verify the neutral point potential balance capability of MPCC1 and MPCC3. Figure 8 shows the variation of the neutral point potential (v

_{o}= v

_{C1}− v

_{C2}). It can be seen that the amplitude of the neutral point potential returns to zero for both MPCC1 and MPCC3. The settling times for MPCC1 and MPCC3 are 0.96 s and 0.61 s, respectively. The settling time of MPCC3 is shorter than that of MPCC1. The control performance of the neutral point potential is improved by the proposed MPCC.

#### 4.2.2. Control Performance under Steady State

_{L}and motor speed n

_{r}operating conditions (case 1: T

_{L}= 5 N·m, n

_{r}= 500 r/min, v

_{c1}= 140 V, v

_{c2}= 180 V; case 2: T

_{L}=10 N·m, n

_{r}= 500 r/min, v

_{c1}= 140 V, v

_{c2}= 180 V), the experimental results of the stator current i

_{A}, electromagnetic torque T

_{e}(The experimental result of torque is estimated by the stator current, flux linkage and rotator position), amplitude of stator flux |

**ψ**| and neutral point potential v

_{s}_{o}are shown in Figure 9 and Figure 10. It can be seen that when the amplitude of the neutral point potential is large, the current and torque fluctuation of MPCC3 is lower than that of MPCC1 and MPCC2. As for MPCC3, the change of the amplitude and the phase angle of basic vectors are fully considered and the actual optimal vector is selected.

_{T}and flux fluctuation rate D

_{ψ}are used as torque performance and flux performance indicators and are defined as follows:

_{e}_max and T

_{e}_min represent the maximum and minimum values of electromagnetic torque and |

**ψ**|_max and |

_{s}**ψ**|_min represent the maximum and minimum values of stator flux.

_{s}_{THD}is used as the current performance evaluation index and is defined as follows.

_{1}denotes the rms value of the fundamental component of the output current and I

_{n}denotes the rms value of the nth harmonic component. Figure 11 shows the D

_{T}, D

_{ψ}and I

_{THD}for case 1 and case 2.

_{T}, D

_{ψ}and I

_{THD}of MPCC3 are all lower than those of MPCC1 and MPCC2, which verifies that the steady state performance of the improved MPCC is superior to that of conventional MPCC.

#### 4.2.3. Control Performance under Dynamic State

_{L}= 0 N·m→5 N·m, n

_{r}= 500 r/min), the experimental results of the stator current i

_{A}, electromagnetic torque T

_{e}, amplitude of stator flux |

**ψ**| and neutral point potential v

_{s}_{o}are shown in Figure 12.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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State | S_{x}_{1} | S_{x}_{2} | S_{x}_{3} | S_{x}_{4} | Output Voltage |
---|---|---|---|---|---|

P | 1 | 1 | 0 | 0 | V_{dc}/2 |

O | 0 | 1 | 1 | 0 | 0 |

N | 0 | 0 | 1 | 1 | −V_{dc}/2 |

Vectors Used in the Last Control Period | Alternative Voltage Vectors | ||||||
---|---|---|---|---|---|---|---|

V_{1} | V_{1} | V_{2} | V_{12} | V_{13} | V_{19} | ||

V_{2} | V_{1} | V_{2} | V_{3} | V_{13} | V_{14} | V_{19} | |

V_{3} | V_{2} | V_{3} | V_{4} | V_{14} | V_{19} | ||

V_{4} | V_{3} | V_{4} | V_{5} | V_{14} | V_{15} | V_{19} | |

V_{5} | V_{4} | V_{5} | V_{6} | V_{15} | V_{19} | ||

V_{6} | V_{5} | V_{6} | V_{7} | V_{15} | V_{16} | V_{19} | |

V_{7} | V_{6} | V_{7} | V_{8} | V_{16} | V_{19} | ||

V_{8} | V_{7} | V_{8} | V_{9} | V_{16} | V_{17} | V_{19} | |

V_{9} | V_{8} | V_{9} | V_{10} | V_{17} | V_{19} | ||

V_{10} | V_{9} | V_{10} | V_{11} | V_{17} | V_{18} | V_{19} | |

V_{11} | V_{10} | V_{11} | V_{12} | V_{18} | V_{19} | ||

V_{12} | V_{1} | V_{11} | V_{12} | V_{13} | V_{18} | V_{19} | |

V_{13} | V_{1} | V_{2} | V_{12} | V_{13} | V_{19} | ||

V_{14} | V_{2} | V_{3} | V_{4} | V_{14} | V_{19} | ||

V_{15} | V_{4} | V_{5} | V_{6} | V_{15} | V_{19} | ||

V_{16} | V_{6} | V_{7} | V_{8} | V_{16} | V_{19} | ||

V_{17} | V_{8} | V_{9} | V_{10} | V_{17} | V_{19} | ||

V_{18} | V_{10} | V_{11} | V_{12} | V_{18} | V_{19} | ||

V_{19} | V_{13} | V_{14} | V_{15} | V_{16} | V_{17} | V_{18} | V_{19} |

Sectors | Alternative Voltage Vectors | |||
---|---|---|---|---|

R_{1} | V_{1} | V_{2} | V_{13} | V_{19} |

R_{2} | V_{2} | V_{3} | V_{14} | V_{19} |

R_{3} | V_{3} | V_{4} | V_{14} | V_{19} |

R_{4} | V_{4} | V_{5} | V_{15} | V_{19} |

R_{5} | V_{5} | V_{6} | V_{15} | V_{19} |

R_{6} | V_{6} | V_{7} | V_{16} | V_{19} |

R_{7} | V_{7} | V_{8} | V_{16} | V_{19} |

R_{8} | V_{8} | V_{9} | V_{17} | V_{19} |

R_{9} | V_{9} | V_{10} | V_{17} | V_{19} |

R_{10} | V_{10} | V_{11} | V_{18} | V_{19} |

R_{11} | V_{11} | V_{12} | V_{18} | V_{19} |

R_{12} | V_{12} | V_{1} | V_{13} | V_{19} |

Sectors | Alternative Voltage Vectors | ||
---|---|---|---|

R_{1} | ${\mathit{V}}_{13}^{\prime}$ | ${\mathit{V}}_{13}^{\u2033}$ | ${\mathit{V}}_{2}^{\prime}$ |

R_{2} | ${\mathit{V}}_{14}^{\prime}$ | ${\mathit{V}}_{14}^{\u2033}$ | ${\mathit{V}}_{2}^{\prime}$ |

R_{3} | ${\mathit{V}}_{14}^{\prime}$ | ${\mathit{V}}_{14}^{\u2033}$ | ${\mathit{V}}_{4}^{\prime}$ |

R_{4} | ${\mathit{V}}_{15}^{\prime}$ | ${\mathit{V}}_{15}^{\u2033}$ | ${\mathit{V}}_{4}^{\prime}$ |

R_{5} | ${\mathit{V}}_{15}^{\prime}$ | ${\mathit{V}}_{15}^{\u2033}$ | ${\mathit{V}}_{6}^{\prime}$ |

R_{6} | ${\mathit{V}}_{16}^{\prime}$ | ${\mathit{V}}_{16}^{\u2033}$ | ${\mathit{V}}_{6}^{\prime}$ |

R_{7} | ${\mathit{V}}_{16}^{\prime}$ | ${\mathit{V}}_{16}^{\u2033}$ | ${\mathit{V}}_{8}^{\prime}$ |

R_{8} | ${\mathit{V}}_{17}^{\prime}$ | ${\mathit{V}}_{17}^{\u2033}$ | ${\mathit{V}}_{8}^{\prime}$ |

R_{9} | ${\mathit{V}}_{17}^{\prime}$ | ${\mathit{V}}_{17}^{\u2033}$ | ${\mathit{V}}_{10}^{\prime}$ |

R_{10} | ${\mathit{V}}_{18}^{\prime}$ | ${\mathit{V}}_{18}^{\u2033}$ | ${\mathit{V}}_{10}^{\prime}$ |

R_{11} | ${\mathit{V}}_{18}^{\prime}$ | ${\mathit{V}}_{18}^{\u2033}$ | ${\mathit{V}}_{12}^{\prime}$ |

R_{12} | ${\mathit{V}}_{13}^{\prime}$ | ${\mathit{V}}_{13}^{\u2033}$ | ${\mathit{V}}_{12}^{\prime}$ |

Parameters | Symbol | Value | Unit |
---|---|---|---|

Poles | p | 4 | - |

Permanent magnet flux | ψ_{f} | 0.45 | Wb |

Stator resistance | R_{s} | 0.635 | Ω |

d-axis inductance | L_{d} | 4.25 | mH |

q-axis inductance | L_{q} | 4.25 | mH |

Rated speed | n_{r} | 1500 | r/min |

Rated torque | T_{N} | 10 | N·m |

Rated voltage | V_{N} | 220 | V |

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## Share and Cite

**MDPI and ACS Style**

Zhang, G.; Liu, Q.; Wang, J.; Li, C.; Gu, X.
Improved Model Predictive Current Control of NPC Three-Level Converter Fed PMSM System for Neutral Point Potential Imbalance Suppression. *World Electr. Veh. J.* **2022**, *13*, 113.
https://doi.org/10.3390/wevj13070113

**AMA Style**

Zhang G, Liu Q, Wang J, Li C, Gu X.
Improved Model Predictive Current Control of NPC Three-Level Converter Fed PMSM System for Neutral Point Potential Imbalance Suppression. *World Electric Vehicle Journal*. 2022; 13(7):113.
https://doi.org/10.3390/wevj13070113

**Chicago/Turabian Style**

Zhang, Guozheng, Qiyuan Liu, Jian Wang, Chen Li, and Xin Gu.
2022. "Improved Model Predictive Current Control of NPC Three-Level Converter Fed PMSM System for Neutral Point Potential Imbalance Suppression" *World Electric Vehicle Journal* 13, no. 7: 113.
https://doi.org/10.3390/wevj13070113