A least squares induction motor parameters identification based on three level system Bianchunyuan1,a,Liuhaijing1,b, Caoruixia1,c, Songchonghui1,d 1,2,3,4 School of Information Science & EngineeringˈNortheastern University Shenyang ,China a [email protected], b [email protected],[email protected] d songchonghui@ ise.neu.edu.cn method, model reference adaptive method, Kalman filter, genetic algorithm and neural networks [ 3] . In recent years, wavelet theory applied in the motor parameter identification has been applied [ 2 ] . Abstract—In recent years, with parameter self-tuning of the drive is concerned by national experts and scholars, which has become the focus of research. Because the induction motor has a strong coupling, nonlinear, operating parameters and other II. significant characteristics change, many scholars do a lot of PARAMETERS research on the induction motor parameters identification, the parameters identification theory, many of the results of modern A. Three-level system architecture In Figure 1, A, B, C three terminals are connected with induction motor. U-phase bridge inverter is a wall with anti-parallel diode ( D1 ~ D4 ) of the four source switch ( S1 ~ S4 ) component. In a real system, switching devices are IGBT. The midpoint of the two DC capacitor is given in inverter DC side. DZ 1 and DZ 2 are the clamping diodes. Common three-phase bridge arm 12 and the continued flow of power electronic switching diodes control theory are applied directly to vector control systems to develop into a high-precision vector converter. This article describes an experiment based on single-phase improved methods, the least square off-line identification, only one experiment can measure the motor parameters. According to the simulation results , we obtain a satisfactory result. Keywords-least square; induction motor; identification I. LEAST SQUARE IDENTIFICATION OF MOTOR parameter INTRODUCTION At present, the inverter plays a more and more important role in energy saving and speed control so that it has been experienced rapid development and wide application. The application of higher voltage and better performance inverter gets more and more attention. Therefore, three-level inverter based on space vector control is a hot topic in the future development. This study is based on the three-level system to research the motor parameter identification. Accuracy of motor parameters is an important factor in determining the inverter performance. The inverter with parameter identification technology research can be divided into offline and online identification[1 2 ] two research directions. Offline parameter identification is mainly used to complete the self-setting, identification of the parameters of which is higher initial value of precision, or the direct use value under not very high work environment. Online identification key is used to track changes in the motor parameters, calibration of electrical parameters to meet the operating environment of relatively high precision. The main methods used in domestic vector inverter are the least squares 978-1-4577-0321-8/11/$26.00 ©2011 IEEE Fig. 1 T Diagram of three-level NPC inverter and six clamping diodes, all the same as the pressure tubes. The two capacitors of the DC parameters are the same, the voltage is half of the DC voltage[6]. Capacitance for two capacitors is limited, the midpoint of the capacitor charge and discharge current will produce the mid-point voltage drift[4 5 7]. 29 Authorized licensed use limited to: Consortium - Algeria (CERIST). Downloaded on July 09,2020 at 09:54:07 UTC from IEEE Xplore. Restrictions apply. ls Rr + lr Rs RR R 1 , n0 = r s , m1 = , m0 = r , we can σ ls lr σ ls lr σ ls σ ls lr see n1 , n0 , m1 , m0 the four parameters are closely related to the motor parameters ,so we must first identify the four parameters. In order for this least squares transfer function model parameters identification, which must be turned into a linear form of variables, we should get their differential from the stator voltage and current signals, here we use second-order filter to replace differential. We can select the filter in the form: B. Linear model of induction motor parameters n1 = The core of this method is to detect the rotor stationary motor parameters, here we use two-phase stationary reference frame of the motor mathematical model, expressing as formula (1) - (2). Voltage equation: Lm p 0 0 ªusα º ª Rs + Ls p º ªisα º «u » « » «i » R L p L p 0 + 0 s s m « sβ » = « » « sβ » (1) «uγα » « Lm p Rr + Lr p ω Lm ω Lr » «iγα » « » « »« » Lm p Rr + Lr p ¼ «¬ iγβ »¼ −ω Lr «¬ uγβ »¼ ¬ −ω Lm s 2 iα s 1 1 = , making z = , H ( s ) ( s + ω0 )( s + ω1 ) ( s + ω0 )( s + ω1 ) According to the definition of z , we can get Flux equation: ªψ sα º ª Ls «ψ » « « sβ » = « 0 «ψ γα » « Lm « » « ¬«ψ γβ ¼» ¬ 0 0 Ls 0 Lm Lm 0 Lr 0 0 º ªisα º « » Lm »» «isβ » 0 » «iγα » »« » Lm ¼ ¬« iγβ ¼» (10) (2) Here is a integral part, commonly used in practice to s2 be replaced by low-pass filter, to avoid saturation points, so 1 we used instead. We can get H (s) For the squirrel cage induction motor with rotor measured voltage is 0. From the mathematical model of induction motor voltage and flux equations, derived a linear induction motor model in (2) into (1), we can obtain state equation of the stator currents is and rotor flux ψ r : < ψ γα = < ψ γβ = lm τr lm τr isα − isβ − < i sα = −γ isα + 1 τr K τr < i sβ = −γ isβ + 1 τr ψ γα − ωψ γβ (3) ψ γβ + ωψ γα (4) (5) ψ γβ − K ωψ γα + α s usβ (6) K (ω1 + ω0 ) s + ω1ω0 z H ( s) (ω + ω0 − n1 ) s + (ω1ω0 − n0 ) m s + m0 iα s + 1 uα s = 1 H (s) H (s) iα s = z + iα s = θ T X l Rs lm2 Rr 1 + , K = m , αs = . If only the σ ls σ ls lr σ ls σ ls lr2 α -axis exciting, this time the motor does not turn, in this case uβ = 0, iβ =ψ β =0, we get formula (7) and formulas (8) < < lm τr isα − i sα = −γ isα + 1 ψ γα (7) ψ γα + α s usα (8) τr K τr We can get the domain transfer function S, such as formula (9) isα m s + m0 = 2 1 isβ s + n1s + n0 (12) ª m0 − m1ω1 º ª 1 º « » « s + ω usα » − ω1 ω 0 1 « » « » » ª x1 º « 1 ª a1 º « m1ω1 − m0 » usα » » « « » «a » « − ω ω 0 1 « » » « x2 » = « s + ω0 θ = « 2» = « 2»ˈX = » « x3 » « 1 « a3 » −n0 + n1ω1 − ω1 » usα » « » « « » « ω0 − ω1 » ¬ a4 ¼ « ¬ x4 ¼ « s + ω1 » « » « » 2 1 « n0 − n1ω1 + ω1 » usα » « « » ¬« s + ω0 ¼» ω0 − ω1 ¬ ¼ Where θ is the parameter vector which can be identified, X is measurable signal, these signals can all be measured through the first order filter, the model has been simplified. In the calculation , We assumed the stator and rotor leakage inductance are equal. These parameters and the actual relationship of the motor parameters: Where γ = ψ γα = (11) Using some fractions, we obtained following the linear model: ψ γα + K ωψ γβ + α s usα τr 1 (9) Where 30 Authorized licensed use limited to: Consortium - Algeria (CERIST). Downloaded on July 09,2020 at 09:54:07 UTC from IEEE Xplore. Restrictions apply. n1 = ω1 + ω0 − a3 − a4 n0 = ω1ω0 − ω0 a3 − ω1a4 m1 = a1 + a2 2) The determination of filter parameters: We transformed the form above to avoid the differential, but the introduction of the integrator, which uses second-order low-pass filter to replace the second integral, in the transformation of the various models, we get the first-order low-pass filter with model the equivalent of first-order points. a) First-order low-pass filter equivalent to the (13) m0 = ω0 a1 + ω1a2 The relationship between the above we can get: n Rs = 0 m0 n Rr = 1 − Rs m1 lr = ls = (14) We can draw the low-pass filter cutoff frequency of the input signal frequency is not the same time, low-pass filter of the following approximate relationship: (15) Rr m1 m0 (16) ls m1 (17) lm = ls2 − principle of the integrator When ωe ωc , G ( s ) ≈ b) First-order low-pass filter parameter selection Obtained by the above analysis, the larger of ωc , the smaller of τ = 1 ωc ωe = 5 or 6 to meet ωc . We choose requirement. 3) Sampling time selection: In order to make algorithm on the actual realization of digital controller, system must be discretized. We often select under experience formula of the sampling frequency; as follows the empirical formula of sampling frequency: a) Selected in accordance with transition time T p The following we analysis the role of the state vector SVPWM switching time. We conducted the analysis from the above, Vβ = 0. Vα > 0, the interaction vector for the OOO, POO, PON, PNN, NNN; Vα <0, the interaction vector for the NNN, NNO, NNP, NOP, OOP, OOO. D. The resolution of the key technology in linear induction Ts = (1/15 ~ 1/ 5)T p motor model the the the are (21) b) Selected in accordance with main time constant of the system Tls In the concrete realization of the process, many specific needs of key technologies need to solve, as following we will introduce. Ts = (0.05 ~ 0.1)Tls 1) Stimulus selection: In the parameter identification process, the selection of stimulus parameters play a decisive role in whether the convergence. The continuous transfer function of Identification of the object is: 1 + a1 s + ! an s n 1 ; s to a pure integrator. Three level work vector analysis In this paper, an improved on the basis of a single-phase experiments were carried out off-line least squares identification. Three-level inverter switching state the main use of PNN and NNN, as in the P-type in the SVPWM vector and N-type vector can not be switched directly to the transition through the zero vector. G (s) = , when, ωe ωc , G ( s ) ≈ ωc ωe we can get, when 1 , Low-pass filter can be equivalent ωc C. b0 + b1s + ! + bm s m 1 (22) c) Selected in accordance with minimum time constant of the system Tmin Ts = (1 ~ 2)Tmin (23) Combination of the above calculation, and considering the actual situation, the final choice of the sampling time is 0.0005s. (18) III. PARAMETERS IDENTIFICATION OF INDUCTION MOTOR SIMULATION BASED ON LEAST SQUARES ALGORITHM We can see transfer function contain (m + n + 1) parameters, Therefore, in order to identification (m + n + 1) parameters, the persistent excitation signal shall include different frequency components at least: j ≥ (m + n + 1) / 2 . By simplifying the transfer function, we can get the requirement of different frequency number j ≥ (2 + 1 + 1) / 2 = 2 . Therefore, the selected excitation signal is a linear combination of three different frequency signals. Discussed above analysis, under the Matlab / Smiulink environment build a simulation model of least squares. We used in the experiment AC motor nameplate: YB2-100L1-4, Pe =2.2KW, U 1e =380V/660V( Δ / Y ) 31 Authorized licensed use limited to: Consortium - Algeria (CERIST). Downloaded on July 09,2020 at 09:54:07 UTC from IEEE Xplore. Restrictions apply. I1e =5.05/2.92A( Δ / Y ), ne =1410rpm, cos ϕ =0.82, Continuous duty GB series of parameters required λm =2.1. Calculated by the motor electrical parameters calculation module, we get the simulation. Here we can see a1, a2, a3, a4 has a good convergence in Figure 3. Fig.3 Waveform for the parameters of the induction machine with system From the figure, we can conclude the effect of convergence is satisfactory. This result was confirmed by using the proposed method in practice for the feasibility of induction motor parameter identification. ACKNOWLEDGEMENT The auther would like to thank the reviewers constructive comment. Thank the National Science Foundation(60974141) and the Natural Science Foundation of Liaoning Province (20092007) to support this project. REFERENCES [1] [2] Fig.2 Waveform for the intermediate variables The following simulation experiment we added a three-level inverter and svpwm module. We conducted simulation results shown in Figure 3. 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Three-level PWM rectifier and the midpoint of the double-loop control of voltage balance control technique[J]ˈCSEEˈ 2006,26(20)˖64-68 32 Authorized licensed use limited to: Consortium - Algeria (CERIST). Downloaded on July 09,2020 at 09:54:07 UTC from IEEE Xplore. Restrictions apply.
