Pulse-width modulation in the autonomous voltage inverter in identifying parameters of the three-phase asynchronous motor

. This paper deals with control algorithm of a two-level autonomous voltage inverter with pulse-width modulation in forming test phase voltages for identification of parameters of a three-phase asynchronous motor. Necessary conversion is carried out, the laws of change of phase voltages of an autonomous inverter are obtained. The feasibility of using third order active Butterworth filters for determining first harmonics of phase voltages is shown. By means of computer simulation and experimental research, it is revealed that the required shapes of phase voltages can be implemented in a two-level autonomous voltage inverter with pulse-width modulation, and the presence of Butterworth filters does not introduce significant distortion and allows to obtain necessary phase voltage shapes in the generalized electric machine.


Introduction
For implementation of laws of frequency regulation of speed in the asynchronous motor (AC), it is necessary to be armed with data on current parameter values of phase-substitution and load circuit. This information allows to implement more accurate algorithms of frequency regulation of speed. And this provides energy efficiency and resource saving.
There are various methods of parameters identification [1 -5]. In [6][7][8][9][10][11][12][13] efficiency of using continuous gradient method of minimum search of positive definite function for parametric identification of a three-phase asynchronous motor (AC) and its load is shown. In [7,8,11]  total number of identified parameters is seven. In [7 -10], a computer simulation of the identification processes of the parameters of a threephase asynchronous motor (AC) and its load was carried out. The basis of the asynchronous motor model was the mathematical description of the generalized electrical machine (GEM). When simulating, the phase voltages of the stator winding were set in the form of test signals. The specifics of the operation of the frequency converter and the influence of pulse-width modulation (PWM) were not taken into account. PWM algorithms are given in [14]. In this case, when identifying the parameters of the asynchronous motor, the shape and frequency of the output voltages of the frequency converter (FC) will depend on the laws of change in the test signals The purpose of this article is to analyze the feasibility of technical implementation of the output voltages of the frequency converter with test signals and filtering the high-frequency components of these voltages.

Methods
In most cases, algorithms of frequency regulation of speed are based on mathematical description and parameters of the generalized electric machine [14,15,16]. Thus, for identification of parameters we use the equation system of the generalized electric machine (GEM) on the basis of three-phase asynchronous motor (AC) [7,8,11,17,18]. Transition from parameters and values of a threephase asynchronous motor (AC) to the ones of the generalized electric machine (GEM) and vica versa is discussed in [17,18]. Conversion of phase voltages of a GEM stator in voltages of a stator of the three-phase asynchronous motor (AC) takes the form [17, 18] where 1  is shaft rotation angle of axis d of coordinate system d, q about axis A of stator.
Computer simulation of parameters identification processes of the asynchronous electric drive with motor AIR80A6U2 was carried out in [8]. Voltages ) ( 1 t u d , ) ( 1 t u q and angle velocity ) were changing in accordance with timing diagrams in Figure 1 and were characterized by the parameters presented in Table 1.

Results and Discussion
Results of computer simulation in the form of timing diagrams of angular velocity ) ( 1 t  , rotation angle 1  and voltages ) ( 1 t u q , ) ( 1 t u А are given in Figure 2. shows that phase voltages are amplitude-frequency modulated oscillations. Amplitude changes according to variations of voltage amplitude ) ( 1 t u q , and frequency changes according to angular velocity variations ) In a larger timescale, for the first and the second halves of period 1 Т , the curve ) Figure   3 a, d. During the first half of period 1 Т , voltage ) ( 1 t u А varies with time according to harmonic law with amplitude 75 V and frequency 71.6 Hz, and during the second half of period 1 Т with amplitude 25 V and frequency 23.8 Hz. In a similar way, with angle shift π/3 2 − and π/3 2 , voltages ) will change correspondingly.
To implement phase voltages ) it is necessary to change simultaneously their rootmean-square values and frequency.
In most modern asynchronous electric drives, indirect frequency converters (FC) are used. They comprise uncontrolled rectifier (UR) and two-level autonomous voltage inverter (AVI). To operate transistors of the autonomous voltage inverter, pulse-width modulation (PWM) is applied. Phase voltages of AVI with PWM represent pulse string, amplitude and duration of which change directly with control voltages.
Simulation of AVI with PWM was conducted providing three-phase mains supply of indirect frequency converter (FC) has voltage 390 V, frequency 50 Hz. In this case rectified voltage in DC link [21] takes the form of In simulation, voltage drop in diodes of uncontrolled rectifier and in on-transisters of AVI was taken into consideration. Control voltages of AVI were taken as proportional to voltages ) Results of computer simulation are presented in In pulse-width modulation (PWM), output voltages of frequency converter (FC) represent pulse string. Duration of the pulses changes proportionally to control voltages. Impact of PWM leads to occurrence of highfrequency components in phase voltage spectrum of FC.
Thus, for identification of parameters of three-phase asynchronous motor it is necessary to perform filtration Evidently, that in phase voltage spectrum of FC there are high-frequency components. For high-frequency components cutoff, low-pass filters (LPF) are used. Taking into considerations [24 -28], analysis of circuitry and LPF characteristics was conducted. It was found that for filtration of phase voltages of (FC), it is reasonable to use third order Butterworth filters. Transfer function of such filter is given [28] where f k , f T are transmission factor and filter time  Table 1; 2) circular frequency of reference voltage ref  is determined by PWM frequency which was set equal to 16 kHz; 3) effect of LPF on voltage conversion should be minimal.
In Figure 5 frequency response of third order Butterworth filter with cutoff frequency 5 kHz is shown. The response is determined on account of transfer function proved that f k equals 1. Analysis of amplitude-frequency characteristics (AFC) in Figure 5 shows that with circular frequency 1  lower than circular cutoff frequency с  , it is at the level of 1, while with circular frequency 1  higher than с  , it has the slope of 60 dB/dec. This is decisive advantage when choosing LPF type. Evidently, that amplitude distortion with circular frequencies of the desired signal min 1  and max 1  will be minimal. Analysis of circuit phase responce in Figure 5 shows, that in the field of circular frequency of the desired signal min 1  and max 1  , the filter will not cause significant lag.
Experimental setup scheme is given in Figure 6. The sensor unit in Figure 6 comprises voltage sensing devices and current sensing devices, Hall effect devices, rotation velocity sensors and angular accelerometers. Hall devices are installed in stator bore in orthogonal axes. Filter bank comprises six third order Butterworth filters. Frequency converter (FC) is not shown in Figure  6.
The aim of the experiment is analysis of output voltage curves of third order Butterworth filters and analysis of results of conversion of output voltage of the filters into voltages of coordinate system d, q.
Results of the experiment are presented in Figure 4 c, d, g, h in the form of timing diagrams of phase voltages of frequency converter (FC) and output voltages of LPF for the first and second halves of period 1 Т . In Figure 7b there are timing diagrams of voltages ) Curves of output voltages of LPF in Figure 4 d, h are not ideally smooth harmonic functions. In spectrum of LPF output voltages there is high-frequency ripple. Most significantly they are revealed in the second half of period 1 Т (Figure 4 h). This is explained by relatively small amplitude value of the first harmonic of phase voltage ) ( which is 25V. On account of (5), (9), (10), curves ) are formed, they are given in Figure 7 b. Becaue of the PWM effect, the curves contain high-frequency ripple with amplitude no more than 3 V. For qualitative evaluation of effect of third order Butterworth filters, analysis of frequency response was conducted, it is presented in Figure 5. Results are shown in Table 2.

Conclusion
The conducted analysis allowed to find out that third order Butterworth filters do not significantly influence the desired signal and provide efficient cutoff of highfrequency interference. Experimental research allowed to establish, that the use of indirect frequency converter (FC) with PWM and Butterworth filters makes it possible to a high precision to perform transition in phase voltages of GEM stator winding. When this happens, identification processes stability is reserved, and in identification of the aforementioned parameters of a three-phase asynchronous motor and its load, with initial deflection from true values by 50%, relative error is not higher than 7% [20]