Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 129 (2015) 57 – 62
International Conference on Industrial Engineering
Automatic control system of speed of synchronous motor Gasiyarov V.R., Maklakov A.S., Voronin S.S., Maklakova E.A.* South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, Russian Federation
Abstract The article deals a mathematical model of an automatic control system on the basis of field oriented control method of a synchronous motor. The synchronous motor with electromagnet exitation as object control has been considered by a system of differential equations. The proposed the automatic control system consists of two closed current loop, closed torque loop and model of synchronous motor. Experimental results of the automatic control system are presented in this paper. © 2015 The Authors. Published by Elsevier Ltd. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE(http://creativecommons.org/licenses/by-nc-nd/4.0/). 2015). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015) Keywords: closed-loop system, synchronous motor, electric drive, dynamycal mode, mathematical model.
1. Introduction A modern automatic AC electric drives have found application in metallurgy industry, e.g. of rolling mills. These AC electric drives are implemented as a system «frequency converter – synchronous motor». Stator winding of the synchronous motor is usually supplied by the back-to-back convertor, which consist of active front end (AFE) rectifier and voltage source inverter (VSI). Both the AFE and VSI operate on the principle pulse-width modulation (PWM) [1, 2]. Rotor winding is supplied by a nonreversible thyristor converter. Synchronous motors are selected for high power systems at a wide range of adjustable speed. The main advantages of synchronous drives are high energy efficiency [3] and good energy characteristics. A research object is the automatic control system of speed of synchronous motor with parameters: U=3000 V; P=12000 kW; Is=2379 A; Ȧ=6.28 rad/s; J=145000 kgm2; M=1909.9 kNm; f=10 Hz; Rs=0.00954 ohm.
* Corresponding author. Tel.: +7-951-244-75-06 E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015)
doi:10.1016/j.proeng.2015.12.008
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Nomenclature usd, usq, urd isd, isq, ird Rs, Rf Lsd, Lsq, Lrd Mdf Ȍsd, Ȍsq, Ȍrd Ȧ p Tμ xsd, xsq Kif Kc Ȧɫ Zp KȦ Knd, Knq Kf Knf KM M I0f
d-q stator winding voltage and rotor winding voltage d-q stator current and rotor current phase stator active resistance and rotor active resistance d-q stator winding inductances and rotor winding inductance coefficient of mutual inductance between stator winding and rotor winding d-q stator flux and rotor flux rotation speed of d-q system Laplace operator small time constant d-q stator winding reactance resistances stator current feedback coefficient the convertor coefficient break frequency quantity of pole pairs speed feedback coefficient d-q stator flux feedback coefficients rotor current feedback coefficient coefficient current sensor coefficient speed sensor torque no-load rotor current
2. Mathematical description for synchronous motor Operation of all electric motors is determined on the basis of laws of electromagnetic induction. It makes the possible of generalizing properties of electric motors into one model. A typical AC motor is described non-linear differential equations on the basis of a movement equation of electrodynamics system. Solution the system of differential equations is complex because of variable coefficients. In the world literature such equations are simplified by Park´s transformation a-b-c/d-q-0 and Clarke´s transformation a-b-c/Į-ȕ-Ȗ. The transformation a-bc/d-q-0 is a mathematical transformation of the reference frame of system a-b-c in the rotating system d-q-0. The transformation a-b-c/Į-ȕ-Ȗ is a mathematical transformation of the reference frame of system a-b-c in the reference frame of system Į-ȕ-Ȗ. Thus, it allows one to replace the three-phase AC motor by the two-phase unified electrical machine and consider synchronous motor in the frame d-q [4].
u sd Rs isd p \ sd Z \ sq ; ° °u sq Rs isq p \ sq Z \ sd ; °u ° rd R f i f p \ f ; ® °\ sd Lsd isd M df i f ; °\ Lsq isq ; ° sq °¯\ f L f i f M df isd ;
(1)
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3. Model for closed-loop system of synchronous motor 3.1. Model for a closed current loop and a closed flux loop The synchronous motor is considered in the frame d-q, because the closed-loop system has two closed current loops which are located on d-axis and q-axis. Formation of electromagnetic torque in a transient process is required determined response of both the closed current loop and the closed flux loop [5]. However, crucial importance for response is has the closed current loop. Turning of the closed current loop and the closed flux loop is carried out by standard transient process, which accords to the Butterworth filter [6]. Transfer functions of current controllers on d-axis and q-axis are presented as follows: W id p
W iq p
1 ( x sd / R s ) p ; 2 T P p ( K if K c / R s ) 1 ( x sq / R s ) p 2 T P p ( K if K c / R s )
.
(2)
(3)
There is compensation unit of cross-connection on electromotive force rotation in the system. It is applied in order to oscillation of the system reduced when speed increases. Due to compensation unit, isolation the closed current loops in the frame d-q and the closed flux loop is achieved in the system [7]. The block diagram of closed current loops, transient process and bode plot of the frequency response of a system is shown Fig. 1. The closed current loops in the frame d-q which have been tuned using the magnitude optimum method have a step-response overshoot 4.3% [8]. Bode plot of the closed current loops in the frame d-q appears an asymptote with gradient -20 dB and cutoff frequency Ȧc=1/2·Tμ=1/2·0.01=50 rad/s, and phase margin is equal to 15 ࡈ. It confirms stability of the closed current loops.
Fig. 1. a) The block diagram of closed current loops; b) transient process of the closed current loops in the frame d-q; c) bode plot of the frequency response of the closed current loops in the frame d-q
The closed flux loop is built similar of closed current loops. Transfer functions of flux controller are presented as follows:
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W f ( p)
1 (L f / R f ) p 2 TPf p Ʉ f Ʉ ɩf ( L f / R f )
(4)
.
3.2. Model for a closed speed loop Torque is necessary to create on motor shaft for adjustment of synchronous motor speed. The speed controller performs such function. The output voltage of the speed controller acts on nonlinearity units 1, 2, 3 forming necessary magnitude of torque [9]. Signal of the nonlinearity units 1, 2 act on the current controllers and the flux controller. The functions the nonlinearity units 1, 2, 3 have the form [10]: 1
i sq
\ S 1
isd
M
2 sq 2 S
L
2
( 3 Z p \ S ) 2 \ 2
Lsq
\ S 1
M2
1
M2
2 L2sq ( 3 2 Z p \ S )
(5)
;
(6)
2 ( 3 Z p \ S ) 2 \ S 2
1
\f
M ; 3 Z \ p S 2
M2
ª º Lsd Lsq M2 ». u «L f I 0 f (M df / L f ) \ S ( 3 Z p \ S )2 » L2sq «¬ 2 ¼ 2 2
(7)
( 3 Z p \ S ) \ S 2
A closed speed loop is tuned both the magnitude optimum method and the symmetrical optimum depending upon requirements for the droop of the system automatic control [11]. Transfer function of speed controller, which is tuned using the magnitude optimum method is presented as follows: WZ ( p )
J ; 8 TP K M K Z
(8)
Transfer function of speed controller, which is tuned using the symmetrical optimum is presented as follows: WZ ( p )
1 16 TP p 16 TP p
J . 8 TPi K M K Z
(9)
The block diagram of the automatic control system of synchronous motor is shown Fig. 2. The transient process of torque and speed is shown Fig. 3. The closed speed loop, which has been tuned using the symmetrical optimum method, has a step-response overshoot 43% [12].
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Fig. 2. The block diagram of the automatic control system of synchronous motor
Fig. 3. The transient process of torque and speed of synchronous motor
4. Conclusion This article introduced a method of development the mathematical model of the automatic control system the synchronous motor. The automatic control system the synchronous motor has a cascade structure and consists of two closed current loop, closed torque loop and model of synchronous motor. The current control loops are subordinated to the speed control loop. The transfer functions of current controllers on d-axis and q-axis, flux controller and speed controller are given. The speed controller uses PI control [13]. The mathematical model of the automatic control system the synchronous motor is realized in Matlab/Simulink application. The developed model is allowed to theoretical research of dynamic modes of synchronous motors. Future work will involve assessing the oscillation double mass system.
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References [1] A.S. Maklakov, A.A. Radionov, EMC evaluation of three level NPC converter based on space vector PWM, Proceedings of the 2015 IEEE North West Russia Section Young Researchers in Electrical and Electronic Engineering Conference, ElConRusNW 2015. (2015) 236–240. DOI: 10.1109/EIConRusNW.2015.7102269 [2] A.A. Radionov, A.S. Maklakov, E.A. Karyakina, New control method of back to back converter, 2015 International Siberian Conference on Control and Communications, SIBCON 2015 - Proceedings, (2015). DOI: 10.1109/SIBCON.2015.7147135 [3] A.A. Radionov, O.S. Malakhov, S.N. Baskov, A.S. Konkov, M.S. Davydkin, The design features of the converters for synchronous motors vector-pulsed launch control, Proceedings - 2010 IEEE Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering, SIBIRCON-2010. (2010) 608–610. DOI: 10.1109/SIBIRCON.2010.5555140 [4] O.V. Slezhanovskij, L.H. Dackovskij, I.S. Kuznecov, Sistemy podchinennogo regulirovanija jelektroprivodov peremennogo toka s ventil'nymi preobrazovateljami, Energoatomizdat, Moscow, 1983. [5] A.A. Radionov, S.A. Evdokimov, A.S. Karandaev, V.R. Khramshin, Information and measurement system for control of technical state of asynchronous electric motors with group supply from frequency converter, 12th International Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2014 – Proceedings. (2014) 280–285. DOI: 10.1109/APEIE.2014.7040897 [6] P.V. Shilyaev, I.Yu. Andryushin, V.V. Golovin, A.A. Radionov, A.S. Karandaev, V.R. Khramshin, Algorithms of a digital automatic system for tension and loop control in a wide-strip hot-rolling mill, Russian Electrical Engineering. 84(10) (2013) 533–541. DOI: 10.3103/S106837121310009X [7] A.A. Radionov, V.R. Gasiyarov, O.A. Gasiyarova, Automatic gap control of Plan View Pattern Control Mechatronics System, 2015 International Siberian Conference on Control and Communications, SIBCON 2015 – Proceedings. (2015). DOI: 10.1109/SIBCON.2015.7147027 [8] J. Weidauer, R. Messer, Electrical drives, Siemens Aktiengesellschaft, Berlin and Munich, 2010. [9] V.R. Khramshin, A.S. Evdokimov, G.P. Kornilov, A.A. Radionov, A.S. Karandaev, System for speed mode control of the electric drives of the continuous train of the hot-rolling mill, 2015 International Siberian Conference on Control and Communications, SIBCON 2015 – Proceedings. DOI: 10.1109/SIBCON.2015.7147264 [10] V.R. Gasiyarov, E.A. Maklakova, Mathematical Description of Main Electric Drive of Hot Plate Mill 5000, Russian Internet Journal of Electrical Engineering. 2(3) (2015) 62–66. [11] P.C. Krause, O. Wasynczuk, S.D. Sudhoff, Analysis of Electric Machinery and Drive Systems: books in the IEEE press series on power engineering, IEEE, USA, 2002. [12] A.S. Maklakov, A.A. Radionov, Integration prospects of electric drives based on back to back converters in industrial smart grid, 2014 12th International Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2014 - Proceedings, (2014) 770–774. DOI: 10.1109/APEIE.2014.7040790 [13] A.A. Radionov, A.S. Maklakov, V.R. Gasiyarov, Smart Grid for main electric drive of plate mill rolling stand, Proceedings of 2014 International Conference on Mechanical Engineering, Automation and Control Systems, MEACS 2014, (2014). DOI: 10.1109/MEACS.2014.6986842
