# An Advanced Control Technique for Power Quality Improvement of Grid-Tied Multilevel Inverter

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## Abstract

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## 1. Introduction

- A robust and dynamic control scheme for a 15-level (15-L) NPC inverter-fed grid-connected system, which is proposed to improve the system performance;
- The control scheme consists of a proportional-integral resonance (PIR) controller with the feedback of a harmonic compensator (HC) and a lead compensator (LC);
- The harmonic compensator decreases the lower order harmonics of grid voltage and current and the lead compensator provides the addition of phase by increasing the system bandwidth;
- Injected power quality, ability to handle sudden load changes, fault-handling capacity, steady-state response, and stability of the system with the proposed control scheme are investigated to validate the auspicious performance of the controller compared with existing solutions.

## 2. System Description and Modelling

#### 2.1. System Specification and Description

_{d}and i

_{q}are used for calculating the errors. By controlling the errors through current controller, the dq components are generated and transformed to abc components for generating the gate pulses. The design parameters of the system are indexed in Table 1.

#### 2.2. Power Flow Theory

_{inv}represents the inverter voltage, V

_{g}represents the grid voltage and the angle represents phase reference.

#### 2.3. System Modelling

#### 2.4. Grid Synchronization

## 3. Proposed Controller

## 4. Performance Evaluation of the Proposed Controller

#### 4.1. Inverter Performance

#### 4.2. PV Performance

#### 4.3. Grid Performance

#### 4.4. Controller Performance

#### 4.4.1. Stability

#### 4.4.2. Sudden Load-Change Response of Inverter

#### 4.4.3. Fault Analysis in Grid Current

#### 4.5. Comparative Result Analysis

#### 4.5.1. Reference Tracking Capability

#### 4.5.2. Sudden Load-Change Response of Inverter for Different Controllers

#### 4.5.3. THD Analysis

#### 4.5.4. Advantages and Limitations of the Controllers

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

NPC | Neutral point clamped |

THD | Total harmonic distortion |

LC | Lead compensator |

HC | Harmonic compensator |

PLL | Phase-locked loop |

SPWM | Sinusoidal pulse width modulation |

MPPT | Maximum power point tracker |

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**Figure 1.**Block diagram of the grid-tied photovoltaic (PV) system with the proposed proportional-integral resonance controller with a harmonic and lead compensator (PIR + HC + LC controller).

**Figure 3.**Block diagram of the control technique including outer voltage controller and internal current controller.

**Figure 5.**Inverter performance: (

**a**) inverter output voltage, (

**b**) frequency spectrum of the voltage without filter, (

**c**) inverter output current, (

**d**) frequency spectrum of the current without filter, (

**e**) inverter voltage, (

**f**) frequency spectrum of the voltage with filter, (

**g**) inverter current and (

**h**) frequency spectrum of the current with filter.

**Figure 6.**PV array performance: (

**a**) current–voltage (I-V) characteristics for the PV array in different heatstroke conditions using one cell; (

**b**) power–voltage (P-V) characteristics for the PV array in different heatstroke conditions using one cell; (

**c**) DC link voltage supplied by the PV array through the maximum power point tracking (MPPT) controller for the neutral-point-clamped (NPC) converter, and (

**d**) the output power which is fed to the utility grid.

**Figure 7.**Grid performance: (

**a**) grid voltage, (

**b**) grid current, and (

**c**) zero phase shift between grid voltage and current means unity power factor and (

**d**) grid side voltage, power, and inverter phase voltage response under some vibration.

**Figure 9.**Fault analysis in the grid current: (

**a**) fault is applied in phase ‘a’; (

**b**) fault is applied in phase ‘b’; (

**c**) fault is applied in phase ‘c’; (

**d**) fault is applied in phases ‘a’ and ‘b’; (

**e**) fault is applied in phases ‘b’ and ‘c’; (

**f**) fault is applied in phases ‘a’ and ‘c’; and (

**g**) fault is applied in phases ‘a’, ‘b’, and ‘c’.

**Figure 10.**Reference tracking capability of the controllers. (

**a**) Proportional-integral (PI) controller, (

**b**) proportional integral derivative (PID) controller, (

**c**) proportional resonance (PR) controller, (

**d**) proportional-integral resonance (PIR) controller, (

**e**) Resonance + LC controller, and (

**f**) proposed PIR + HC + LC controller.

**Figure 11.**Sudden load-change effect on the grid current for the (

**a**) PI controller, (

**b**) PID controller, (

**c**) PR controller, (

**d**) PIR controller, (

**e**) Resonance + LC controller, and (

**f**) PIR + HC + LC controller.

**Figure 12.**Total harmonic distortion (THD) analysis with the (

**a**) PI controller, (

**b**) PID controller, (

**c**) PR controller, (

**d**) PIR controller, (

**e**) resonance +LC controller, and (

**f**) PIR + HC + LC controller.

Parameters | Symbols | Values |
---|---|---|

PV Array | 1.5 kW | |

Grid voltage | V_{g} | 400 V (L-L) |

DC-link voltage | V_{dc} | 800 V |

Grid frequency | ω_{0} | 50 Hz |

Filter inductance | L_{f} | 4.6 mH |

Filter capacitance | C_{f} | 11 µF |

Carrier frequency | ω_{c} | 10 kHz |

Proportional constant | K_{p} | 25 |

Integral constant | K_{i} | 1000 |

Compensator constant | a | 25 |

Controller | 1st Cycle (%) | 2nd Cycle (%) | 3rd Cycle (%) | 4th Cycle (%) | 5th Cycle (%) |
---|---|---|---|---|---|

PI [14] | 36.96 | 23.77 | 12.32 | 11.29 | 11.62 |

PID [24] | 37.82 | 17.27 | 10.77 | 11.16 | 10.91 |

PR [25] | 35.89 | 12.91 | 10.07 | 10.52 | 10.59 |

PIR | 24.90 | 6.19 | 6.08 | 6.12 | 6.17 |

Resonance + LC [24] | 27.66 | 1.06 | 1.10 | 1.08 | 1.10 |

PIR + HC + LC (Proposed) | 27.11 | 0.54 | 0.55 | 0.55 | 0.52 |

Controller Name | Advantages | Limitations |
---|---|---|

PI controller | Reduces steady-state error; simple operation | Reduces stability; inaccuracy; slow response |

PID controller | Minimizes both transient and steady-state error; simple structure | Slow operational response; cannot work successfully under higher frequency |

PR controller | Zero steady-state error; low computational burden | Controlling harmonics is difficult; rapid change in frequency variation |

PIR controller | Minimizes steady-state error; controls changes in frequency variation | Creates overshoot; unstable for oscillatory response; slow response time |

Resonance + LC controller | Provides phase lead; increases transient response | Implementation complexity; difficulty in reducing harmonics |

Proposed controller | Limits the steady-state error; controls the lower order harmonics; minimizes the magnitude of error signal; easy to tune; increases transient response; successfully works in frequency variation |

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**MDPI and ACS Style**

Jahan, S.; Biswas, S.P.; Hosain, M.K.; Islam, M.R.; Haq, S.; Kouzani, A.Z.; Mahmud, M.A.P.
An Advanced Control Technique for Power Quality Improvement of Grid-Tied Multilevel Inverter. *Sustainability* **2021**, *13*, 505.
https://doi.org/10.3390/su13020505

**AMA Style**

Jahan S, Biswas SP, Hosain MK, Islam MR, Haq S, Kouzani AZ, Mahmud MAP.
An Advanced Control Technique for Power Quality Improvement of Grid-Tied Multilevel Inverter. *Sustainability*. 2021; 13(2):505.
https://doi.org/10.3390/su13020505

**Chicago/Turabian Style**

Jahan, Sumaya, Shuvra Prokash Biswas, Md. Kamal Hosain, Md. Rabiul Islam, Safa Haq, Abbas Z. Kouzani, and M A Parvez Mahmud.
2021. "An Advanced Control Technique for Power Quality Improvement of Grid-Tied Multilevel Inverter" *Sustainability* 13, no. 2: 505.
https://doi.org/10.3390/su13020505