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It is usual to find single-phase induction motor (SPIM) in several house, office, shopping, farm, and industry applications, which are become each time more sophisticated and requiring the development of efficient alternatives to improve the operational performance of this machine. Although the rotor flux and rotational speed are essential variables in order to optimize the operation of a SPIM, the use of conventional sensors to measure them is not a viable option. Thus, the adoption of sensorless strategies is the more reasonable proposal for these cases. This paper presents a rotor flux and rotational speed observer for sensorless applications involving SPIMs. Computer simulations and the experimental results are used to verify the performance of the proposed observer.

The single-phase induction motor (SPIM) has a very robust design and can be mass produced with relatively low cost. Traditionally used in fractional and subfractional horsepower applications, it is usual to find this motor in several house, office, shopping, farm, and industry appliances such as air conditioning systems, mixers, washers, blowers, dryers, fans, refrigerators, vacuum cleaners, compressors, pumps, and so forth. Due to introduction of low-cost static power converters and the development of more sophisticated appliances, the traditional SPIM applications have required the development of efficient alternatives to improve the performance of this machine.

The SPIM is basically constituted by a squirrel-cage rotor and two stator windings displaced

Many proposals for the better performance of a SPIM are based in the use of an electronically switched series capacitor in the auxiliary winding, which can be controlled to improve the machine performance at different operating conditions [

This paper presents an original proposal of a rotor flux observer for SPIM, from which the rotor speed of this motor can be estimated. This observer can be used in applications involving SPIMs that require the estimation of rotor flux and/or rotor speed, such as optimization strategies, sensorless vector control of the machine based on the philosophy of the direct flux orientation, and so forth. Two half flux observers are designed using the stationary reference frame SPIM model. From these half flux observers, data are obtained to estimate the rotor speed of the SPIM. The performance of the proposed observer is satisfactorily demonstrated from computer simulations and experimental tests considering two situations: a step variation in the stator frequency of the no load SPIM and the application of mechanical load to SPIM shaft.

Traditionally, the dynamic model of a SPIM is described considering a stationary reference frame

where

In order to obtain the convergence of the observed variables to its real value in conventional state observers, a correctional term is usually inserted in the system model to reduce the error between the measurable variables and their respective estimated values. If this principle is applied to observe the rotor fluxes of a SPIM, the resulting observer is nonlinear, since the terms

Considering only the structure of

Considering the close-loop

The design of close-loop

Block diagram of

If the observation of the rotor fluxes is satisfactory, an estimative of the rotor speed

Speed estimation using flux observers and envelope detectors.

The experimental apparatus shown in Figure

SPIM data.

Rated values | |||

Voltage | 110 V | ||

Frequency | 50/60 Hz | ||

Main winding current | 2.3 A | ||

Speed | 2700 RPM | ||

No. of poles | 2 | ||

Power | 0.25 HP (180 W) | ||

Main winding ( | Auxiliary winding ( | ||

5.2 Ω | 29 Ω | ||

9.4 Ω | 35.9 Ω | ||

0.3 H | 0.45 H | ||

0.3068 H | 0.55 H | ||

0.3068 H | 0.55 H | ||

| 0.67 |

Electrical characteristics of the IGBT power converter.

Input voltage (single phase) | 230 VCA |

Motor supply rail | 310 VDC |

Output power peak | 6.5 kW |

Phase current peak (crest) | 30 A |

Phase current cont. | 21 A(RMS) |

Switching frequency | 5 to 20 kHz |

Shunt power peak | 3200 W |

SPIM test bench.

Considering the experimental apparatus presented in the last section, a computer simulation was done using MATLAB/simulink in order to verify the performance of the proposed observer. In the first test, the stator frequency of the no-load SPIM is varied from 10 to 50 Hz and from 50 Hz to 10 Hz. The stator currents of the SPIM are shown in Figure

Stator currents of the no-load SPIM and their estimated values during a step variation from 10 Hz to 50 Hz in the stator frequency (computational simulation): (a) auxiliary winding

Phase portrait

Rotor speed

In the second simulated test, the rated mechanical load is applied to SPIM shaft when the a stator frequency is 50 Hz. In this simulated situation, the application of mechanical load reduces the auxiliary winding current

Stator currents of the SPIM and their estimated values for 50 Hz during a load step (computational simulation): (a) auxiliary winding

Phase portrait

Rotor speed

In order to acquire the electrical and mechanical measurements, the “trigger’’ function of the virtual oscilloscope offered by the dSPACE system is used to register an event occurrence, causing the registrations with negative value for time intervals before the trigger event.

The first experimental test consists of the application of a step variation from 10 to 50 Hz in the stator frequency of the no-load SPIM. Both time response of the auxiliary winding current

Measured and estimated stator currents of the SPIM during the step from 10 Hz to 50 Hz in the frequency stator (experimental results): (a) auxiliary winding

Estimated and measured rotor speed

Estimated rotor fluxes

The second experimental test consists in to apply and remove the rated mechanical load of the SPIM, which is operating with a stator frequency of 50 Hz. The auxiliary winding current

Measured and estimated stator currents of the SPIM when the rated mechanical load is applied (experimental results): (a) auxiliary winding

Measured and estimated currents of the SPIM when the rated mechanical load is removed (experimental results): (a) auxiliary winding

Measured and estimated rotor speed

It is noted that the experimental results practically reproduce the computational simulations, whose differences can be justified by the uncertainties in the parameter estimation of the SPIM, which are greatest for the auxiliary winding and mechanical parameters. The experiments and the simulations demonstrate that the estimations of the stator currents and the rotor speed are satisfactory, indicating that the rotor flux estimation must be correct. Thus, the experimental performance of the proposed observer corroborates the computational simulations, demonstrating that it provides a satisfactory estimation for the rotor flux and the rotor speed of the SPIM with good accuracy within the usual frequency range considered for most SPIM application.

This paper presents the design, simulation, and implementation of a rotor flux and speed observer for the development of sensorless applications involving SPIMs. This observer is based in two half flux observers, which are designed using the stationary reference frame SPIM model. From these half flux observers, data are obtained in order to estimate the rotor speed of the SPIM. The performance of the proposed observer is computationally and experimentally evaluated considering two situations: a step variation in the stator frequency of the no-load SPIM and the application of mechanical load to SPIM shaft. The computational simulations and the experimental results present good agreement, demonstrating that the proposed observer provides satisfactory estimations of the rotor flux and rotor speed of the SPIM, with good accuracy within of the usual frequency range considered for most SPIM applications. In this context, the observer presented in this paper consists in an interesting option to estimate the rotor flux and/or rotational speed for sensorless applications involving the control of variable speed drives and/or development of optimization strategies for SPIMs.

The authors gratefully thank SDESLab (Sustainable Development and Energy Savings Laboratory), University of Palermo, for the support given during the experimental tests, and the financial support of MIUR (Ministero dell’Istruzione dell’Universitá e della Ricerca, Italy), CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnológico, Brazil), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior, Brazil), FAPEMIG (Fundação de Amparo a Pesquisa do Estado de Minas Gerais-Brazil) and Gorceix foundation (Brazil).