# Performance Improvement of a Grid-Tied Neutral-Point-Clamped 3-φ Transformerless Inverter Using Model Predictive Control

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## Abstract

**:**

## 1. Introduction

- Apply the MPC controller to the proposed system with appropriate consideration of the LC filter and grid impedance.
- Discuss the effect of the MPC on performance factors, such as the earth leakage current, grid current THD, and efficiency.
- Compare the performance of the system using the MPC controller with the system that used the proportional–integral (PI) controller.

## 2. System Description

## 3. System Modelling

- Boost converter losses are neglected.
- Voltage drops and leakage currents of all the switching devices are neglected.
- Snubber circuits are neglected.
- The grid internal impedance is taken into consideration.

#### 3.1. Photovoltaic Panel Model

#### 3.2. Boost Converter Dynamic Model

_{b}is the boost converter input inductance and (V

_{DC}) is the DC link voltage.

#### 3.3. Three-Level Inverter and Filter Model

_{1},….V

_{19}). As stated in Reference [15], there are only seven states with zero common-mode voltage, named (V

_{8}, V

_{10}, V

_{12}, V

_{14,}V

_{16}, V

_{18}, V

_{0}). Hence, to limit the CMV of the NPC three-level inverter, the previous seven switching states were utilized. Consequently, the earth leakage current can be killed.

_{g}) was taken into consideration in the model. The grid was assumed to be an infinite 3-φ bus that had constant frequency and voltage amplitude. All 3-φ voltages and currents are expressed as space vectors using:

_{a}, u

_{b}, and u

_{c}) are the 3-φ quantities, u is the equivalent space vector, and a = e

^{j}

^{(2π/3)}.

_{f}, C

_{f}) is the filter inductance and capacitance. The filter capacitor voltage vector is V

_{c}, the inverter voltage vector is V

_{i}, the grid current vector is I

_{g}, and the filter current vector is I

_{f}.

#### 3.3.1. State Space Form of the 3-φ Transformerless Inverter Model

#### 3.3.2. Discrete-Time Prediction of the 3-φ Transformerless Inverter Model

_{s}is the sampling time. With the help of Equation (10), the state space equation in (8) could be transformed into discrete as:

## 4. System Controllers

_{DC}at a specified value. The third controller is used to regulate the grid current of the NPC transformerless inverter controller.

#### 4.1. MPPT Controller

#### 4.2. DC Link Voltage Controller

#### 4.3. NPC Inverter Controller Implemented Using the MPC Algorithm

**I**

_{g}) to track its sinusoidal reference and achieve unity power factor operation for the power supplied to the grid.

_{g}(k), V

_{s}(k), V

_{c}(k)). Next, the prediction of I

_{g}(k + 1) for each effective switching state was obtained using the system model and measurements. In turn, the prediction assessed the cost function to obtain the control goals. Afterward, the valid switching state—which provides the minimum cost function—was designated for the next sampling period. Figure 7 shows a flow chart for the MPC controller of the NPC transformerless inverter.

#### Cost Function (**F**)

**F**is chosen to minimize the grid current error.

**F**is defined as the square of grid current error, as given by:

_{g}

_{α}, i

_{gβ}) are the real and imaginary components of I

_{g}and (i

^{*}

_{g}

_{α}, i

^{*}

_{gβ}) are the real and imaginary components of the grid current reference.

## 5. Simulation Results

_{DC}for the transformerless inverter was 650 V [1]. To achieve that value of V

_{DC}and output power of 10 Kw, the PV panel structure was 960 series cells × 6 parallel strings. The leakage capacitance (C

_{earth}) between the cells and the grounded frame was modeled with a simple capacitance. It can have values up to 50–150 nF [36], depending on the atmospheric conditions and the structure of the panels. However, the value of (C

_{earth}) in simulation was selected to be 100 nF. The sampling time (T

_{s}) was selected based on the actual time for completing one control algorithm process. The remaining parameters were selected based on the fact they are commonly used, in practice, for 3-φ inverters. Figure 8 is a comparison of the results of the proposed NPC transformerless inverter controlled by the MPC controller (Figure 8a) and the PI current controller with SPW modulation. The 3-φ grid currents, with the two controllers, are sinusoidal and in phase with the grid voltage (unity power factor). The grid current THD with the MPC controller is 1.22% and with the PI controller is 2.23%. The inverter output line voltages have different waveforms as the controller action in each case is different. The PV currents for the two controllers are the same, as the same MPPT controller is used for each case. For earth leakage current, it is very clear that the MPC controller case is much smaller than the PI controller.

_{c}) has been determined for the two controllers using the following equation [37]:

## 6. Conclusions

- (1)
- The MPC controller had the best performance for all factors of comparison.
- (2)
- The 3-φ grid currents, with the two controllers, were sinusoidal and in phase with the grid voltage (i.e., unity power factor).
- (3)
- The grid current THD with the MPC controller was 1.22% and 2.23% for the PI controller.
- (4)
- The leakage current in the MPC case was less than one-third of the value of the PI controller case.
- (5)
- The efficiency of the system that used the MPC was improved compared to the system that used the PI current controller with SPW modulation.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclatures

CMV | Common-mode voltage |

CMC | Common-mode current |

C_{earth} | The leakage capacitance |

DPWM | Discontinuous PWM |

DSP | Digital signal processor |

F | The cost function |

I_{g} | The grid current vector |

I_{f} | The filter current vector |

I_{earth} | The earth leakage current |

I_{SC} | The panel short circuit current |

(i_{gα}, i_{gβ}) | The real and imaginary components of I_{g} |

(i^{*}_{gα}, i^{*}_{gβ}) | The real and imaginary components of the grid current reference |

l_{g} | The source inductance |

L_{b} | The boost converter input inductance |

(L_{f}, C_{f}) | The filter inductance and capacitance. |

MPP | The maximum power point |

MPC | Model predictive control. |

MPPT | Maximum power point tracking |

NPC | Neutral-point-clamped. |

RSPWM | Remote-state PWM |

(R_{p}, R_{s}) | The model parallel and series resistances |

SPWM | Sinusoidal pulse width modulation |

SVPWM | Space vector pulse width modulation |

THD | Total harmonic distortion |

T_{s} | The sampling time |

(u_{a}, u_{b}, and u_{c} ) | The 3-φ quantities |

u | The equivalent space vector |

(V_{pv}, I_{pv}) | The PV terminal voltage and current |

V_{DC} | The DC link voltage |

V_{c} | The filter capacitor voltage vector |

V_{i} | The inverter voltage vector |

ZSI | Z-Source Inverter |

ZVR | Zero-voltage state rectifier |

η_{χ} | Californian efficiency |

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**Figure 1.**The proposed photovoltaic (PV)-powered 3-level transformerless inverter connected to the grid and its controllers.

**Figure 2.**Model of the PV panel, where I

_{SC}is the panel short circuit current and (R

_{p}, R

_{s}) is the model parallel and series resistances.

**Figure 8.**Simulation results of the proposed neutral-point-clamped (NPC) transformerless inverter in terms of grid voltage, grid current, PV current, and earth leakage current with (

**a**) the MPC controller and (

**b**) the proportional–integral (PI) current controller with sinusoidal pulse width modulation (SPWM).

**Figure 9.**Variation of the leakage current with the insolation level for the MPC controller and PI current controller with SPW modulation.

**Figure 10.**Variation of the grid current total harmonic distortion (THD) with the insolation level for the MPC controller and PI current controller with SPW modulation.

**Figure 11.**The spectrum of the grid current for the (

**a**) MPC controller and (

**b**) PI current controller with SPW modulation (@75%insolation).

**Figure 12.**The maximum power point (MPP) power and output power at step insolation variations for the (

**a**) MPC controller and (

**b**) PI current controller with SPWM.

**Figure 13.**Variation of the system efficiency with the insolation level for the MPC controller and PI current controller with SPW modulation.

**Figure 14.**Line diagram of the THD, efficiency, and leakage current for the MPC controller and PI current controller with SPW modulation.

Parameter | Value |
---|---|

PV SC current | 24.53 A |

PV OC voltage | 633 V |

C_{earth} | 100 nF |

V_{DC} | 650 V |

C_{f} | 2 µF |

L_{f} | 3 mH |

Utility voltage | 230 V |

Utility frequency | 50 Hz |

PWM carrier frequency | 10 KHz |

DC link capacitor | 1000 µF |

T_{s} | 35 µs |

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**MDPI and ACS Style**

Albalawi, H.; Zaid, S.A.
Performance Improvement of a Grid-Tied Neutral-Point-Clamped 3-φ Transformerless Inverter Using Model Predictive Control. *Processes* **2019**, *7*, 856.
https://doi.org/10.3390/pr7110856

**AMA Style**

Albalawi H, Zaid SA.
Performance Improvement of a Grid-Tied Neutral-Point-Clamped 3-φ Transformerless Inverter Using Model Predictive Control. *Processes*. 2019; 7(11):856.
https://doi.org/10.3390/pr7110856

**Chicago/Turabian Style**

Albalawi, Hani, and Sherif A. Zaid.
2019. "Performance Improvement of a Grid-Tied Neutral-Point-Clamped 3-φ Transformerless Inverter Using Model Predictive Control" *Processes* 7, no. 11: 856.
https://doi.org/10.3390/pr7110856