# Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC

## Abstract

**:**

## 1. Introduction

## 2. WECS System Modeling

#### 2.1. Mechanical Model of a Wind Turbine

_{m}) as a function of the effective wind speed (v) can be described as follows [19,20]:

^{3}); C

_{p}is the coefficient of power conversion; r is the blade tip radius (m); λ is the tip speed ratio (TSR); β is the blade pitch angle in degrees.

_{p}is a function of (λ, β) and can be expressed as follows [20]:

_{m}is the mechanical rotational speed of the PMSG; ω

_{t}is the turbine rotational speed; G

_{r}is the gear ratio (G

_{r}= 1, gearless PMSG); the coefficients c

_{1}to c

_{6}[20] are c

_{1}= 0.5176; c

_{2}= 116; c

_{3}= 0.4; c

_{4}= 5; c

_{5}= 21; c

_{6}= 0.0068.

_{m}is the turbine-driving torque (N·m); J

_{eq}is the total equivalent inertia of the turbine and generator (kg·m

^{2}); B is the damping coefficient representing the turbine and generator rotational losses (N·m·s); T

_{e}is the electromagnetic torque of the generator (N·m).

#### 2.2. PMSG Modeling

_{q}and v

_{d}, expressed in the d–q frame can be written as follows:

_{q}, v

_{d}, i

_{q}, and i

_{d}are the d–q axis components of the stator voltages and currents, respectively; R is the stator resistance; L

_{q}and L

_{d}are the d–q axis inductance; φ

_{f}is the permanent flux linkage; ω

_{e}is the electrical rotating speed of the generator. In addition, the electromagnetic torque can be expressed as follows:

#### 2.3. LCL Filter

#### 2.3.1. Two-Level Converter with LCL Filter

_{1}) and its parasitic resistance (R

_{1}), the grid-side inductance (L

_{2}) and its parasitic resistance (R

_{2}), the filter capacitance (C

_{f}), the capacitor series resistance, and any added damping resistance (R

_{c}). V

_{conv}is the inverter output voltage, v

_{s}is the grid-side voltage, L

_{s}and R

_{s}are the inductance and resistance of the source impedance of the grid bus to the point of common coupling (PCC), respectively, and v

_{pcc}is the vector of the PCC phase voltage.

#### 2.3.2. Filter Parameters Design

- The converter-side inductor was calculated based on the desired current ripple attenuation;
- The filter capacitance (C
_{f}) was designed based on the filter’s resonance frequency; - The capacitor series resistance (R
_{c}) was selected based on the required damping factor.

_{Lmax}) was derived based on the worst case, where the maximum converter current ripple was obtained during the zero-crossing of the phase voltage [26,27], i.e., when the applied converter voltage varied from $\frac{{V}_{DC}}{3}$ to $-\frac{{V}_{DC}}{3}$ (see Figure 7):

_{sw}is the switching frequency and m is the inverter modulation factor.

_{Lmax}= 10%)), the required minimum converter-side inductor can be calculated according to the following equation:

_{f}) was designed with the assumption that the reactive power (Q) was less than α% of the rated power (P

_{rat}), and α was a positive factor [28,29,30]:

_{s}is the stator RMS voltage, and ω

_{g}is the grid angular frequency.

_{b}is the base capacitance calculated based on the nominal values of the voltage (V

_{nom}), power (p

_{nom}), and frequency (ω

_{nom}) and x is the percentage of the reactive power absorbed under rated conditions (e.g., x ≤ 5%):

_{2}was selected according to the grid code requirements related to the harmonic current limits. It can be calculated based on the current ripple attenuation (δ). The current ripple attenuation was defined as the ratio of grid current (i

_{2}) to the converter output current (i

_{1}):

_{res}) should be in the range of 10 times the grid frequency (f

_{g}) and one-half of the switching frequency (f

_{sw}) [31]:

#### 2.4. Modeling of the DC Link

_{DC}) in the DC-link can be estimated as follows:

_{DC}) depends on the DC-link capacitor size and switching frequency. The DC-link capacitor (C

_{DC}) is expressed as follows [33]:

_{nom}is the nominal power of the voltage source converter (VSC), and f is the fundamental frequency of the AC power supply. In this work, the allowed DC-link voltage ripple was ∆V

_{DC}≈ 5% of V

_{DC}.

## 3. Control of the GSC

_{f}and L

_{f}are the resistance and inductance of the equivalent RL filter, respectively.

_{dg}and v

_{qg}are the dq-axis components of the grid voltages; i

_{dg}and i

_{qg}are the dq-axis components of the grid currents; v

_{di}and v

_{qi}are the dq-axis components of the converter voltages.

_{grid}and Q

_{grid}are the active and reactive powers of the grid-side converter, respectively.

_{dg}, as follows:

_{g}) and grid angular frequency (ω

_{g}). As the d-axis grid voltage was aligned to the d-axis, the calculated angle was adjusted until the q-axis grid voltage became zero.

_{gd}was controlled to track the ${i}_{gd}^{ref}$ through the PI regulator. A compensation (decoupling) was used to eliminate the coupling between the d-axis and q-axis current controls. Based on that, the output of the PI regulator was added to a compensation term and, thus, the d-axis reference voltage of the converter v

_{md}was obtained.

_{qg}, see Figure 10. The q-axis current reference (${i}_{qg}^{ref}$) was calculated based on (28). A PI regulator was used to control the q-axis current (i

_{gq}

_{)}. Finally, the q-axis reference voltage of the converter (v

_{mq}) was obtained by adding the output of the PI regulator to the compensation term. Once the reference voltages v

_{mq}and v

_{md}were obtained and transformed into the abc frame, the PWM pulses were generated and fed to the grid converter.

## 4. Direct Torque Control (DTC)

#### 4.1. Conventional 6-Sectors DTC

_{Tem}, which refers to increased (HT = 1), decreased (HT = −1), or constant (HT = 0), depending on the input.

#### 4.2. Torque and Flux Reference Values Definition

_{sα}and φ

_{sβ}are the αβ-axis components of the stator fluxes; v

_{sα}and v

_{sβ}are the αβ-axis components of the stator voltages; i

_{sα}and i

_{sβ}are the αβ-axis components of the stator currents, see Figure 9.

_{ref}) was obtained using a lookup table. The lookup table provides the φ

_{ref}as a function of the speed (ω

_{r}). In this work, the flux was assumed as a constant value, rated value (φ

_{rated}), during the operation in the range of the nominal speed (ω

_{nom}). Conversely, as the speed becomes higher than the base speed, the flux should be reduced:

#### 4.3. Proposed 12-Sectors DTC of the PMSG

_{1}and V

_{4}do not exist in the first sector, and that is right for the other sectors with different voltage vectors. This leads to inaccuracy in the torque and flux within a 60° sector. In this paper, to overcome these drawbacks, a 12-sectors DTC is proposed, where the sector number is increased to 12 sectors of 30° for each sector rather than 60°.

_{Tem}= 2,−2 (T

^{↑↑}, T

^{↓↓}) represents a large increase and decrease in torque; H

_{Tem}= 1, −1 (T

^{↑}, T

^{↓}) represents a small increase and decrease in torque; Hφ = 1, −1 (φ

^{↑}, φ

^{↓}) represents an increase and decrease in flux. The voltage vector plane was divided into 12 sectors, as illustrated in Figure 14.

_{x}) can be determined as follows:

_{Tem}is the torque status signal; ΔT

_{em}is the difference between the reference and actual values of electromagnetic torque ($\Delta {T}_{em}={T}_{em-ref}-{T}_{em})$; HB

_{T}is the hysteresis band of the torque.

## 5. Results and Discussion

_{n}, and the flux hysteresis band value was set at 2%φ. The DC-link was kept at approximately 1200 V. The sampling time of both DTC algorithms was 50 μs.

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Configuration of a gearless PMSG-based WECS connected to a grid through a BTB power converter.

**Figure 5.**(

**a**) A three-phase, two–level VSC with an LCL filter and (

**b**) a single–phase LCL filter equivalent circuit.

**Figure 12.**(

**a**) A two-level hysteresis comparator for stator flux control and (

**b**) a three-level hysteresis comparator for torque control.

**Figure 15.**Electromagnetic torque response with (

**a**) 6−sectors and (

**b**) 12−sectors DTC control strategies.

**Figure 20.**The FFT analysis of the phase-a stator current with (

**a**) 6−sectors and (

**b**) 12−sectors DTC control strategies.

Hφ | H_{Tem} | Sector Number | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

1 | 1 | V_{2} | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} |

0 | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} | |

−1 | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} | V_{5} | |

−1 | 1 | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} | V_{2} |

0 | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | |

−1 | V_{5} | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} |

Hφ | H_{Tem} | Sector Number | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||

1 | 2 | V_{2} | V_{3} | V_{3} | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | V_{6} | V_{1} | V_{1} | V_{2} |

1 | V_{2} | V_{2} | V_{3} | V_{3} | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | V_{6} | V_{1} | V_{1} | |

−1 | V_{1} | V_{1} | V_{2} | V_{2} | V_{3} | V_{3} | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | V_{6} | |

−2 | V_{6} | V_{1} | V_{1} | V_{2} | V_{2} | V_{3} | V_{3} | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | |

−1 | 2 | V_{3} | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | V_{6} | V_{1} | V_{1} | V_{2} | V_{2} | V_{3} |

1 | V_{4} | V_{4} | V_{5} | V_{5} | V_{6} | V_{6} | V_{1} | V_{1} | V_{2} | V_{2} | V_{3} | V_{3} | |

−1 | V_{7} | V_{5} | V_{0} | V_{6} | V_{7} | V_{1} | V_{0} | V_{2} | V_{7} | V_{3} | V_{0} | V_{4} | |

−2 | V_{5} | V_{6} | V_{6} | V_{1} | V_{1} | V_{2} | V_{2} | V_{3} | V_{3} | V_{4} | V_{4} | V_{5} |

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

Rated power, P_{n} | 3.5 kW |

Power frequency, f_{n} | 50 Hz |

Number of pole pairs, P | 4 |

Stator voltage, V_{Grid} | 380 V |

Nominal torque, T_{n} | 23.7 N·m |

Stator resistance, R | 0.997 Ω |

Maximum switching frequency, f_{sw-MAX} | 20 kHz |

6-Sectors DTC | 12-Sectors DTC | |||
---|---|---|---|---|

T_{ref} | T_{ripple} | φ_{ripple} | T_{ripple} | φ_{ripple} |

−0.8∙T_{n} | 8.72% | 4.22% | 2.95% | 2.35% |

−0.4∙T_{n} | 7.33% | 3.10% | 5.23% | 2.10% |

+0.8∙T_{n} | 10.72% | 7.22% | 2.11% | 3.11% |

+0.4∙T_{n} | 9.82% | 8.12% | 3.26% | 2.21% |

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## Share and Cite

**MDPI and ACS Style**

Eial Awwad, A.
Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC. *World Electr. Veh. J.* **2022**, *13*, 123.
https://doi.org/10.3390/wevj13070123

**AMA Style**

Eial Awwad A.
Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC. *World Electric Vehicle Journal*. 2022; 13(7):123.
https://doi.org/10.3390/wevj13070123

**Chicago/Turabian Style**

Eial Awwad, Abdullah.
2022. "Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC" *World Electric Vehicle Journal* 13, no. 7: 123.
https://doi.org/10.3390/wevj13070123