Model Reference Adaptive System with FiniteSet for Encoderless Control of PMSGs in MicroGrid Systems
Abstract
:1. Introduction
2. Modeling and Control of the SMPMSG
3. Classical MRAS Observer for SMPMSGs
4. Proposed MRAS with FiniteSet Observer for SMPMSGs
Algorithm 1 MRASFS Observer for SMPMSGs 

Advantages and Disadvantages of the Proposed MRASFS Observer
 no gains to tune, i.e., the effort and time consumed in the tuning of the fixed gain PI regulator in the conventional MRAS observer are avoided in the proposed MRASFS observer;
 the dynamics of the presented MRASFS observer are better than the traditional dynamics due to the use of FCSMPC principles in the design of the suggested MRASFS observer;
 the suggested algorithm is not complicated and can be used in other types of machines with only small modifications.
 based on Algorithm 1, 64 iterations were essential for estimating the optimal angle of the rotor position of the SMPMSG, in other words, the calculation burden of the suggested MRASFS observer is high. However, the current digital signal processors (DSPs) have a high calculation power, and accordingly, execution of such advanced observers can be easily realized.
5. Description of the Laboratory Setup
6. Experimental Results
6.1. Dynamic Performance
 In Figure 6, step changes in the reference value of the mechanical angular speed ${\omega}_{m,ref}$ from $15\mathrm{rad}/\mathrm{s}$ to $75\mathrm{rad}/\mathrm{s}$ and then back to $45\mathrm{rad}/\mathrm{s}$ were applied to the RSM control system, respectively. The reference electromagnetic torque ${T}_{e}^{\ast}$ is regulated to be fixed at $20\mathrm{N}\mathrm{m}$ by the control algorithm of the SMPMSG.
 In Figure 7, the rotor reference mechanical angular speed ${\omega}_{m,ref}$ is controlled to be constant at $45\mathrm{rad}/\mathrm{s}$ by the RSM. Step changes in the reference electromagnetic torque ${T}_{e}^{\ast}$ from $10\mathrm{N}\mathrm{m}$ to $40\mathrm{N}\mathrm{m}$ and then back to $25\mathrm{N}\mathrm{m}$ were applied to the SMPMSG control scheme, respectively.
6.2. SteadyState Performance
 the rotor reference mechanical angular speed ${\omega}_{m,ref}$ is regulated to $75\mathrm{rad}/\mathrm{s}$ using the RSM, and the reference electromagnetic torque ${T}_{e}^{\ast}$ is regulated to be constant at $30\mathrm{N}\mathrm{m}$ by the control algorithm of the SMPMSG.
6.3. Performance at Variations of the SMPMSG Parameters
 in Figure 9, the reference mechanical angular speed ${\omega}_{m,ref}$ of the rotor is set to $60\mathrm{rad}/\mathrm{s}$ by the RSM control strategy, and the reference electromagnetic torque ${T}_{e}^{\ast}$ is regulated to be constant at $35\mathrm{N}\mathrm{m}$ by the control algorithm of the SMPMSG. The stator resistance ${R}_{s}$ is changed $\mp 50\%$ below/above its nominal value in the realtime model (i.e., within the software model);
 in Figure 10, the reference mechanical angular speed ${\omega}_{m,ref}$ of the rotor is set to $55\mathrm{rad}/\mathrm{s}$ by the RSM control strategy, and the reference electromagnetic torque ${T}_{e}^{\ast}$ is regulated to be constant at $28\mathrm{N}\mathrm{m}$ by the control algorithm of the SMPMSG.The stator inductance ${L}_{s}$ is changed $\mp 50\%$ below/above its nominal value in the realtime model (i.e., within the software model).
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
${u}_{s}^{\alpha}$, ${u}_{s}^{\beta}$, ${u}_{s}^{d}$, ${u}_{s}^{q}$  Stator voltages  SMPMSG  Surfacemounted permanentmagnet synchronous generator 
${i}_{s}^{\alpha}$, ${i}_{s}^{\beta}$, ${i}_{s}^{d}$, ${i}_{s}^{q}$  Stator currents  VSWGS  Variablespeed wind generation system 
${\psi}_{s}^{\alpha}$, ${\psi}_{s}^{\beta}$, ${\psi}_{s}^{d}$, ${\psi}_{s}^{q}$  Stator fluxes  MRASFS  Model reference adaptive system with finiteset 
${R}_{s}$  Stator resistance  DMPC  Directmodel predictive control 
${L}_{s}$  Stator inductance  DGS  Distributed generation system 
${\psi}_{pm}$  PM fluxlinkage  RES  Renewable energy system 
${\omega}_{r}$  Rotor electrical speed  DFIG  Doublyfed induction generator 
${\varphi}_{r}$  Rotor electrical position  BTB  Backtoback 
${T}_{e}$  Electromagnetic torque  WECS  Wind energy conversion system 
${T}_{m}$  Mechanical torque  PI  Proportionalintegral 
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Name  Symbol  Value 

Nominal power  ${p}_{rated}$  $14.5\mathrm{k}\mathrm{W}$ 
Nominal lineline voltage of the SMPMSG stator  ${u}_{s,rated}$  $400\mathrm{V}$ 
Rated voltage of the DClink  ${u}_{dc}$  $560\mathrm{V}$ 
Nominal mechanical angular speed of the rotor  ${\omega}_{m,rated}$  $209\mathrm{rad}/\mathrm{s}$ 
Resistance of the SMPMSG stator  ${R}_{s}$  $0.15\mathsf{\Omega}$ 
Inductance of the SMPMSG stator  ${L}_{s}$  $3.4\mathrm{m}\mathrm{H}$ 
Permanentmagnet flux linkage  ${\psi}_{pm}$  $0.3753\mathrm{Wb}$ 
Number of pole pairs  ${n}_{p}$  3 
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Abdelrahem, M.; Hackl, C.M.; Rodríguez, J.; Kennel, R. Model Reference Adaptive System with FiniteSet for Encoderless Control of PMSGs in MicroGrid Systems. Energies 2020, 13, 4844. https://doi.org/10.3390/en13184844
Abdelrahem M, Hackl CM, Rodríguez J, Kennel R. Model Reference Adaptive System with FiniteSet for Encoderless Control of PMSGs in MicroGrid Systems. Energies. 2020; 13(18):4844. https://doi.org/10.3390/en13184844
Chicago/Turabian StyleAbdelrahem, Mohamed, Christoph M. Hackl, José Rodríguez, and Ralph Kennel. 2020. "Model Reference Adaptive System with FiniteSet for Encoderless Control of PMSGs in MicroGrid Systems" Energies 13, no. 18: 4844. https://doi.org/10.3390/en13184844