Control of an Outer Rotor Doubly Salient Permanent Magnet Generator for Fixed Pitch kW Range Wind Turbine Using Overspeed Flux Weakening Operations
Abstract
:1. Introduction
- − Energy conversion optimization with variable speed operations;
- − Direct coupling of turbine and generator by eliminating the gearbox.
2. Wind Turbine and OR−DSPMG Modelling
2.1. Wind Turbine Modelling
2.2. OR−DSPMG Modelling
3. WECS Control
3.1. OR–DSPMSG–Side Converter Control
3.1.1. Maximum Torque Per Ampere Strategy
3.1.2. Flux Weakening Control
3.1.3. Fuzzy Logic Controller (FLC)
3.2. Grid–Side Inverter Control
4. Simulation Results and Discussion
4.1. Wind Turbine
4.2. OR−DSPMG
4.3. DC Bus and Grid
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Variables | Parameters | |
---|---|---|
Wind turbine | vt: wind speed (m/s) | ρ: air density (1.225 kg/m3) |
Cp: power coefficient | R: wind turbine radius (4.2633 m) | |
λ: tip speed ratio | Cpmax: maximum power coefficient (0.4369) | |
Tm: mechanical torque (Nm) | λopt: optimal tip speed ratio (2.41) | |
Pt: aerodynamic power (kW) | vn: rated wind speed (8.70 m/s) | |
Pt-max: maximum extracted power (kW) | Pn: rated wind turbine power (10 kW) | |
Ω: mechanical speed (rpm) | vcut-in: cut-in speed (2.5 m/s) | |
ΩMPPT: optimal mechanical speed (rad/s) | Number of blade: 3 | |
OR–DSPMSG | P(θe): Park transformation matrix | Rs: stator resistance (88.37 mΩ) |
vd, vq: direct and quadrature voltages (V) | L0: continuous self-inductance (25.5 mH) | |
id, iq: direct and quadrature currents (A) | L1: first harmonic self-inductance (2.5 mH) | |
φd, φq: direct and quadrature flux (A) | M0: continuous mutual inductance (−12.4 mH) | |
emd: direct magneto-mortice forces (V) | M1: first harmonic mutual inductance (2.5 mH) | |
emd: quadrature magneto–mortice forces (V) | φ1: first harmonic PM flux (0.4805 Wb) | |
we: electrical velocity (rad/s) | Nr: number of teeth in the rotor (64) | |
θe: electrical position (rad) | Jt: rotor inertia (Nm s−1) | |
Ld, Lq: direct and quadrature inductance (H) | fv: viscous friction coefficient | |
Mdq: mutual inductance (H) | Br: PMs magnetization (1.29 T) | |
Tem: electromagnetic torque (Nm) | µr: relative permeability (1.049) | |
Tem-mean: average torque value | Em: magnet thickness (27.05 mm) | |
Tem-max: maximum torque | Ns: stator teeth (48) | |
Tem-min: minimum torque | Nr: rotor teeth (64) | |
Cr: torque ripples | Nps: stator pole (12) | |
Pem: electromagnetic power (kW) | hs: stator teeth depth (7.70 mm) | |
Pa: active power (kW) | hr: rotor teeth depth (7.70 mm) | |
Q: reactive power | Es: stator yoke thickness (40.90 mm) | |
Pcu, Joule loss (kW) | Er: rotor yoke thickness (29.65 mm) | |
Pir: iron losses (kW) | Rr-out: outer rotor radius (300 mm) | |
Pa-mean: mean active power (kW) | Ra: slot radius (218.5 mm) | |
Qmean: mean reactive power (kVAR) | L: axial length (200 mm) | |
cosψ: power factor | g: air gap thickness (0.5 mm) | |
Ia(θe): current amplitude (A) | M: active masse (184.4 kg) | |
Tout: average output torque (3504 Nm) | ||
n: rated speed (50 rpm) | ||
DC bus and electrical grid | Vdc: DC bus voltage (V) | Vdc-ref: DC bus voltage reference (1200 V) |
Idc: converter–side current (A) | C: DC capacitance (8 × 10−4 F) | |
Iinv: inverter side current (A) | Rf: filter resistance (0.001 Ω) | |
Pdc: DC bus active power (kW) | Lf: filter inductance (Lf) | |
igd, vgd: grid direct current and voltage (A, V) | Vg-rms: voltage RMS value (690 V) | |
igq, vgq: grid quadrature current and voltage (A, V) | kp: proportional regulator gain (10) | |
θg: electrical grid angle (rad) | τd: time constant (1 × 10−3 s) | |
Pg,: grid active power (kW) | ||
Qg: grid reactive power (kVAR) |
Definition | Numerical Value | |
---|---|---|
MTPA and flux weakening | Load angle (θ0) | π/72 |
Voltage limit (Vlim) | 526 V | |
Maximum current (Imax) | 45 A | |
Speed limit Ω1 | 4.9218 rad/s | |
Speed limit Ω2 | 5.4375 rad/s | |
Constant: | 0.006 | |
Constant: | 0.1784 | |
Fuzzy logic controller | Coefficient: ke | 0.1 |
Coefficient: kde | 10 | |
Coefficient: kdu | 100 |
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Output Signal (dU) | Error (E) | |||||||
---|---|---|---|---|---|---|---|---|
NB | NM | NS | Z | PS | PM | PB | ||
Change of error (dE) | NB | NVB | NVB | NVB | NB | NM | NS | Z |
NM | NVB | NVB | NB | NM | NS | Z | PS | |
NS | NVB | NB | NM | NS | Z | PS | PM | |
Z | NB | NM | NS | Z | PS | PM | PB | |
PS | NM | NS | Z | PS | PM | PB | PVB | |
PM | NS | Z | PS | PM | PB | PVB | PVB | |
PB | Z | PS | PM | PB | PVB | PVB | PVB |
Time (s) | Ω (rad/s) | id (A) | iq (A) | Φd (Wb) | Φq (Wb) |
---|---|---|---|---|---|
1 | 2.453 | −0.95 | 13.52 | 0.512 | 0.553 |
5 | 4.92 | −14.3 | 54.5 | 0.05 | 2.06 |
Speed (rad/s) | 0.5 × Ω1 | Ω1 | 1.5 × Ω1 | 2.5 × Ω1 |
---|---|---|---|---|
Current amplitude (A) | 11.1 | 46 | 33.25 | 26.2 |
Mean torque value (N.m) | −510 | −2025 | −1298 | −978 |
Torque ripples (%) | 8.37% | 37.5% | 29.35% | 23.95% |
Mean active power value (kW) | − 1.265 | −10.230 | −9.705 | −9.680 |
Joule losses (kW) | 0.016 | 0.281 | 0.146 | 0.091 |
Mean Reactive power (kVAR) | 0.989 | 34.73 | 23.61 | 17.55 |
Power factor | 0.79 | 0.28 | 0.38 | 0.48 |
Base Frequency | Harmonic Order | Voltage (V) | Current (A) |
---|---|---|---|
25 Hz | Fundamental (25 Hz) | 96.48 (100%) | 11.09 (100%) |
2nd harmonic (50 Hz) | 13.17 (13.65%) | 0.024 (0.22%) | |
4th harmonic (100 Hz) | 0.45 (0.47%) | 0.006 (0.06%) | |
50 Hz | Fundamental (50 Hz) | 525.4 (100%) | 45.98 (100%) |
2nd harmonic (100 Hz) | 109.33 (20.81%) | 0.15 (0.33%) | |
4th harmonic (200 Hz) | 6.83 (1.3%) | 0.06 (0.14%) | |
75 Hz | Fundamental (75 Hz) | 516.4 (100%) | 33.22 (100%) |
2nd harmonic (150 Hz) | 124.92 (24.19%) | 0.14 (0.44%) | |
4th harmonic (300 Hz) | 4.28 (0.83%) | 0.03 (0.10%) | |
100 Hz | Fundamental (100 Hz) | 506.9 (100%) | 26.16 (100%) |
2nd harmonic (200 Hz) | 137.57 (27.14%) | 0.15 (0.60%) | |
4th harmonic (400 Hz) | 12.92 (2.55%) | 0.04 (0.16%) |
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Remli, A.; Guerroudj, C.; Charpentier, J.-F.; Kendjouh, T.; Bracikowski, N.; L. Karnavas, Y. Control of an Outer Rotor Doubly Salient Permanent Magnet Generator for Fixed Pitch kW Range Wind Turbine Using Overspeed Flux Weakening Operations. Actuators 2023, 12, 168. https://doi.org/10.3390/act12040168
Remli A, Guerroudj C, Charpentier J-F, Kendjouh T, Bracikowski N, L. Karnavas Y. Control of an Outer Rotor Doubly Salient Permanent Magnet Generator for Fixed Pitch kW Range Wind Turbine Using Overspeed Flux Weakening Operations. Actuators. 2023; 12(4):168. https://doi.org/10.3390/act12040168
Chicago/Turabian StyleRemli, Aziz, Cherif Guerroudj, Jean-Frédéric Charpentier, Tarek Kendjouh, Nicolas Bracikowski, and Yannis L. Karnavas. 2023. "Control of an Outer Rotor Doubly Salient Permanent Magnet Generator for Fixed Pitch kW Range Wind Turbine Using Overspeed Flux Weakening Operations" Actuators 12, no. 4: 168. https://doi.org/10.3390/act12040168
APA StyleRemli, A., Guerroudj, C., Charpentier, J. -F., Kendjouh, T., Bracikowski, N., & L. Karnavas, Y. (2023). Control of an Outer Rotor Doubly Salient Permanent Magnet Generator for Fixed Pitch kW Range Wind Turbine Using Overspeed Flux Weakening Operations. Actuators, 12(4), 168. https://doi.org/10.3390/act12040168