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Wyznaczanie chwilowego przesunięcia kątowego przebiegów prądu i napięcia podczas rozruchu silnika indukcyjnego

Zadrożny J.

Prace Instytutu Elektrotechniki

2001

Z. 208

209-216

Podczas rozruchu, zwłaszcza małych silników indukcyjnych, występują zmiany kąta przesunięcia pomiędzy przebiegami prądu i napięcia zasilania. Omówiono prostą i skuteczną metodę wyznaczania wartości chwilowej tego kąta. Przedstawiono wyniki badań symulacyjnych oraz analizę niepewności otrzymywanych rezultatów.

During the small motor start, esp. induction one, the automodulation phenomenon of current and dynamic torque can be observed. The duration of this phenomenon is no more then few dozen miliseconds, i.e. just a few periods of supply voltage. Therefore, the problem occurs how to measure angle shift between voltage and current transient. In practise, the phase shift measurement in the low frequencies range usually is proceeding by seeking the measurements' signals in specific state i.e. when signals' values became zero [4]. In this case the errors may be of order the few or few dozen angle degrees. The proposed new method to measure phase angle bases on formula (2). In order to test this method the simulation model has been used. This model has been realised using Matlab/Simulink software for the model of 3-phase small induction motor [6]. The basic simulation model has been widened with subsystem to determine the instantaneous phase shift alpha(t) between phase voltage u(a) and phase current i(a) transients - Fig.1. From the analysis of errors' simulation with above derivation methods, to mentioned case applied, stems that with any derivation method the error is not greater than š2°. The smallest error becomes with Richardson method. The error of phase shift determination occurs also in due to the fact, that formula (2) is quite valid when the dependence of this phase shift alpha versus time not exist. But the errors due to this simplification are not greater than š0.5%. From above analysis follows that all uncertainty of the measurement (assuming Gaussian errors' distribution) equals to 2.7° (3). Exemplary results of angle determining for different voltage and current transients during free acceleration of induction motor are depicted in Figs. 4 and 5. The presented algorithm method of determination of the voltage/current signals phase shift, despite its simplicity, gives satisfactory results and is very resistant against measured signals deformation. Applying others known measurement methods does not give valid results at times' values when an angle not equals to the multiplicity of pi/2. It is planned to use the method directly with digital measurement oscilloscope.