An improvement in operation of a crop cobble shear system for steel rolling mill using direct torque

control induction motor drive

Sorin Deleanu, David Carpenter, Gary Ng Northern Alberta Institute of Technology

(NAIT), Edmonton, Canada sorind@nait.ca,

DCARPENTER@nait.ca GARYNG@nait.ca

Herbert Hess University of Idaho,

Moscow, USA, hhess@uidaho.edu

Mihai Iordache, Neculai Galan “Politehnica” University of

Bucharest, Romania mihai.iordache@upb.ro,

galannicolae@yahoo.com

Abstract- The paper describes how a Direct Torque Control

(DTC) drive technology has been used to improve the operation of a Crop Cobble Shear (CCS) system in a steel rolling mill. The CCS equipment, with emphasis on the motor and drive system, is fully described and the issues with the original system are described. The existing system uses a DTC drive. However, during the cobble cutting mode, depending on the bar length, the original DTC drive experiences over-heating or overcurrent faults that cause production downtimes. A model of the overall system has been developed and introduced into a simulation model such that the Direct Torque Control may be analysed and modified to improve performance. Simulated DTC induction motor drive is compared with the existing platform from a steel plant. Experimental data from measurements on the system in the steel mill are favourably compared with simulation results. This comparison shows the system has been simulated to determine a suitable approach to improving the DTC. Following simulation, the modifications were made to the system and measurements carried out to verify the improvement.

Index Terms-- Crop Cobble Shear (CCS), Direct Torque Control (DTC), Space Vector (SV), Voltage Source Inverter (VSI).

I. NOMENCLATURE

fn- nominal frequency Vn - nominal voltage of the induction motor In - nominal current of the induction motor

s , r , m – stator, respectively rotor flux space vector in per unit vs – stator voltage space vector i s , i s - “ -axis” , respectively “ -axis” component of the stator phase current in the stator reference frame in per unit v s , v s - “ -axis” , respectively “ -axis” component of the stator phase voltage in the stator reference frame in per unit i r , i r - “ -axis” , respectively “ -axis” component of the rotor phase current in the stator reference frame in per unit rs - stator phase resistance in per unit rr - rotor phase resistance in per unit rFe – core loss equivalent resistance in per unit l s- stator phase leakage inductance in per unit l r- rotor phase leakage inductance in per unit lm- magnetizing inductance in per unit

r- rotor angular frequency n - nominal angular frequency)

t, te - electromagnetic (developed) torque in per unit

tL - shaft (load) torque in per unit p – the number of poles of the induction machine fb - base frequency of the induction motor Vb - base voltage of the induction motor Ib - base current of the induction motor

b – base angular electrical speed of the induction motor b – base angular mechanical speed of the induction motor

Sb - base apparent power of the induction motor Tb - base torque power of the induction motor Zb - base impedance of the induction motor Lb - base inductance of the induction motor

s - frequency of the stator in per unit r - relative frequency of the rotor in per unit - angular speed of the induction motor in per unit

II. INTRODUCTION

The DTC concept was introduced in mid 1980s and was adopted more readily by the industry compared to vector control [1]-[8]. Instead of requiring a thorough modelling of the induction machine, the DTC relies on the interaction VSI-IM. In this case the power source is not ideal and is not sinusoidal so the whole method requires the analysis of the supply and IM in commutation. In DTC, the turn on-off of the converter switches is used to decoupling. While recognizing the inverter as a VSI, the DTC control unit is composed of two paralleled closed loops; one for the stator flux and one for the torque [1]-[8]. However, the torque reference can be imposed directly if the DTC operates in torque mode. Alternatively it can be delivered at the output of the speed controller if DTC operates in speed mode. According to [1]-[8], the DTC shows significant differences compared to vector control: • no coordinate transformation is necessary, the IM system of

equations is assembled in the stator reference frame; • the flux and torque are controlled directly; • the instantaneous stator voltages and currents follow the

flux and torque (indirect control); • no separate voltage modulation block is needed (i.e. PWM)

while the vector drives require it; • no current controllers are necessary;

978-1-4799-6557-1/14/$31.00 ©2014 IEEE

• the stator flux linkage space vector position is not accurately: DTC requires only the sector in which the space vector is positioned;

• sensorless control in torque mode; • due to the sensitivity to the variation of the stator

resistance, temperature information/correction may be necessary;

• DTC requires a very accurate model of the IM. Some disadvantages regarding the DTC are: • variable switching frequency; • problems when operating at low frequency as well as

during starting; • torque and current ripples occur when changing sectors.

III. PRINCIPLES OF THE DIRECT TORQUE

CONTROL

The main components of the DTC control system are the torque and flux controllers, both using hysteresis, and the switching program of the inverter. Both estimators are very dependent on the accuracy of the IM model and only the stator resistance variation with temperature has a strong influence on DTC performance. When representing the IM in the stationary reference frame, and the voltage drop along the stator phase winding is neglected, the stator flux results from the integration of the stator applied voltage. The short term variations of the stator flux are proportional to the applied stator voltage [1]. The position of stator flux space vector can be achieved by appropriate commutation of the inverter devices from a previous position [7]:

ttllrl

tlr

skrs

rbmkr

s

sbksks Δ+ΔΨ+Δ−Ψ=Ψ + ν

σω

σω

,,1, 1 (1)

tllrltt

lrj

rs

sbmks

r

rbkrkrkr ΔΨ+ΔΔ−+Ψ=Ψ + σ

ωσ

ωω ,,,1, 1

(2)

211 kkkk tttt Δ+Δ+=+ (3) The electromagnetic torque update can be described as:

σσω

σω t

lr

lr

ttr

rb

s

sbkk

Δ+−=Δ 1 (4)

( )[ ] tjjll

lt krksrks

rs

bmk ΔΨΨ−=Δ ,,,2 νν

σω (5)

rs

m

lll2

1−=σ (6)

All of the equations (1)-(6) are written in per unit. If the voltage space vector is applied in the direction of the shaft’s rotation, the stator flux vector moves away from the rotor linkage flux vector and the machine’s torque will increase. Conversely, if the voltage space vector is null or is applied in the opposite direction to the shaft’s direction of rotation, the torque angle is reduced. The torque is reduced also [1]. In this

way the torque, developed by the IM, is directly controlled by the correct voltage space vector, through a switching algorithm applied to the inverter. An accurate estimation of the stator flux and torque is necessary to establish the operation of the two independent closed loops. The flux and the torque are separately controlled (figure 1), but the latter can be a result of the action of the PI (proportional-integral) type of speed control, when the DTC is applied in speed mode [1]-[8].

Figure 1: Basic DTC for sensorless IM drives with Torque/Speed Control

While the magnitude of the stator flux linkage space vector is required, its instantaneous position is not. The control system needs to know only in which of the six sectors the voltage space vector is located. The DTC control strategy is summarized in Table I. This illustrates the correlation between the torque and flux demand (increasing or decreasing) and the on-off status of the inverter’s switches [2], [7]. In Table 1, the values are interpreted as follows: if the stator flux has to be increased, then s=1; if it has to be decreased, s=0. Similarly for the torque: more torque demand Te=1, less torque demand Te=-1, unchanged torque demand Te=0. V1-V6 denotes the voltage space vectors belonging to the sectors S1-S6. Each sector covers 600 (S1 between -300 and +300 [1]-[3]). For example, in sector S4, if the magnitude of flux has to be increased s=1, will use linear combinations of the space vector voltages V3 and V5, adjacent to V4.

TABLE I SELECTION TABLE FOR DIRECT TORQUE CONTROL (CLASSICAL METHOD [2])

s Ts S1 S2 S3 S4 S5 S6

1 -1 V2 V3 V4 V5 V6 V1

0 V7 V0 V7 V0 V7 V0

1 V6 V1 V2 V3 V4 V5

0 -1 V3 V4 V5 V6 V1 V2

0 V0 V7 V0 V7 V0 V7

1 V5 V6 V1 V2 V3 V4

If the magnitude of the flux has to be decreased, then s=0 and linear combinations of space vector voltages V6

and V2 are required.

The algorithm is detailed in [1], and the voltage space vector is given in Table II (angles in degrees).

( )cbas vaavvv 232 ++= (7)

TABLE II VOLTAGE SPACE VECTOR (CLASSICAL METHOD [2])

V1 (1,4,6)

V2 (1,3,6)

V3 (2,3,6)

V4 (2,3,5)

V5 (2,4,5)

V6 (1,4,5)

0<α 60<α

120<α

180<α

240<α

300<α

For an optimized operation, the switching frequency must

be as low as possible, and the application of the new space vector must involve the commutation of a single switch of the inverter.

The advantages of a relative simplicity and fast response of DTC are unfortunately accompanied by a major problem of the torque and stator flux ripples. Classical methods to overcome these drawbacks rely on either using multilevel inverters or by applying the space vector modulation [9]. Some recent papers [9]-[12] present results following the application of the fuzzy logic control (FLC) techniques. In [9], [11], [12] FLC is used to adjust the bandwidth of the torque hysteresis controller for the purpose of the reduction of the torque and flux ripples. In [10] the overall decoupled flux-torque control was made very effective by using an adaptive neuro-fuzzy inference system. Predictive control schematics are discussed in [13]-[15] in which stability of DTC is improved [13], and torque/flux ripples are minimized by predicting the time delay associated with data processing [14]. The use of branch and bound method of mathematical programming makes the reduction of switching losses and torque/current harmonics possible [15]. In [16]-[24] several DTC techniques are presented that improvement stator flux and torque estimation with direct impact in the dynamic response torque/flux ripple reduction and common mode voltage reduction. In [25], [26], the classical DTC method is applied in conjunction with IM including core loss and the saturation of the magnetic circuit.

IV. DTC APPLIED TO IM WITH CONSTANT PARAMETERS

The induction machine model suitable for the application of the DTC requires the description of the IM in a stationary reference frame in a fifth-order system as the state-space variables (in per unit) are the stator and rotor currents, with respect to rotor angular speed. The equations in per-unit are obtained from the fifth order initial model [1] using the term by term division to base quantities. The base quantities are:

32 LLb VV = ; nb II 2= ; nb fπω 2= ; nnb IVS 3= ;pbb ω2=Ω ; bbb V ωψ = ; bbb IVZ = ; bbbb IpVT ω5.1= ;

bbb IL ψ= ; bΩΩ=ν ; bss ff=ν ; brr ff=ν The equations describing the induction motor, with

constant parameters, used in the MATLAB/Simulink model build-up are presented as follows (per unit):

dtdil

dtdil

irv r

b

ms

b

ssss

αααα ωω

++= (8)

dtdil

dtdil

irv r

b

ms

b

ssss

ββββ ωω

++= (9)

sr slσ rlσ rr

( )mmrrr ililj +σνsv

si

mi

ri

ml

Figure 2: Equivalent Circuit of Induction Motor with constant parameters (Stator Reference Frame)

rrrr

b

rrrsmr

s

b

m ildt

diliril

dtdil

βα

αβα ν

ων

ω++++=0 (10)

dtdil

irildt

dilil r

b

rrrrrr

s

b

msmr

ββα

βα ω

νω

ν ++−+−=0 (11)

( )m

Lrssr

m

mr tiiiildt

dττ

νβαβα −−=

2 (12)

V. DTC APPLIED TO IM WITH CONSIDERATION OF STATOR CORE LOSS

The core loss is represented by a variable resistor connected in parallel to the magnetizing reactance. The value of the variable resistor is a function of the frequency and the magnetizing flux. It is determined from the fundamental value of the core loss power through a least square fitting method [1], [25], [26]. The torque and flux hysteresis controllers will dictate the inverter output voltage with no possibility of prediction for its harmonics. In this case, the theory of multiple reference frames (each frame associated to a determined harmonic) is not applicable.

The equations for the induction motor with the consideration of core loss, used for the MATLAB/Simulink model are the following (per unit):

dtdil

dtdil

irv m

b

ms

b

ssss

αασαα ωω

++= (13)

dtdil

dtdilirv m

b

ms

b

ssss

ββσββ ωω

++= (14)

( )mmrrrm

b

mr

b

rrr ilil

dtdil

dtdil

ir ββσαασ

α νωω

++++=0 (15)

( )mmrrrm

b

mr

b

rrr ilil

dtdil

dtdil

ir αασββσ

β νωω

+−++=0 (16)

( )m

Lrmrm

r

m

m

mr tiiiilll

dtd

ττν

βααβσ

−−=2

(17)

The core loss as a function of frequency can be described

by the following analytical formulas [1], [25], [26]:

Figure 3: Equivalent Circuit of Induction Motor with the consideration of core loss (Stator Reference Frame)

( )>++++≤++++=

HzfqfqfqfqfqHzfkfkfkfkfk

WpFe 60,60,

542

33

24

1

542

33

24

1

(18)

( )>+

≤++=ΩHzffbb

HzffafaaRFe 60,

60,

21

2321 (19)

VI. DTC APPLIED TO IM WITH CONSIDERATION OF STATOR CORE LOSS AND MAGNETIC

CIRCUIT SATURATION

The main difference with respect to the iron loss is represented by the variable magnetizing inductivity [1], [25], [26]. The IM is described in the stator reference frame by the following equations (per unit):

( )m

mFe

s

b

srFesFess l

rdt

dilirirrv αασααα ω

Ψ++++= (20)

( )m

mFe

s

b

srFesFess l

rdt

dilirirrv αασααα ω

Ψ++++= (21)

( ) ( )mrrrm

mFe

r

b

ssFerFes il

lr

dtdil

irirr ββσαασ

αα νω

Ψ++Ψ−+++=0

(22)

( ) ( )mrrrm

mFe

r

b

ssFerFes il

lr

dtdil

irirr ββσαασ

αα νω

Ψ++Ψ−+++=0

(23)

( )m

Lrmrm

m

mr tii

ldt

dττ

νβααβ −Ψ−Ψ=

2 (24)

The core loss equivalent resistance is the same as in (19),

while the saturation can be defined by [26] (per unit):

>++≤≅

=Hzfcicic

Hzfll

mm

nm 60,

60,707.0

32

21 (25)

VII. DTC APPLIED ON CROP COBBLE SHEAR SYSTEM

A Crop Cobble Shear (CCS) system is used in steel rolling mills to chop steel bars into small pieces. This operation is referred to as the cobble cutting mode (continuous cutting) as compared to normal operation, where the CCS performs a single cut to either chop the head or tail of the bar. In the

normal cutting mode, accurate cutting of the bar into a specific length is crucial and so a high performance control system is required. This is a highly dynamic control application and an ideal candidate for torque control. The existing system uses a DTC drive. However, during the cobble cutting mode, depending on the bar length, the original DTC drive experiences over-heating or overcurrent faults that cause production downtimes.

sr slσ rlσ rr

( )mmrrr ililj +σν

sv

si

mi

ri

ml Fei

Figure 4: Equivalent Circuit of Induction Motor with the consideration of core loss and magnetic saturation (Stator Reference Frame)

In addition, if the drive trips the breakers during cobble cutting, it could potentially damage other equipment and even create concern for health and safety of employees. The main contribution factor of over-heating and overcurrent is that, during CCS, the speed reference keeps changing. However, it has been recognized that position control is not necessary during cobble cutting because the accuracy of bar length is not as important as when normal cutting. Therefore, if the drive can be controlled with the constant speed reference in cobble cutting mode, the torque demand will not be as high. Using this approach, the current is lower and less heat generated. This reduces the occurrence of over-heating and overcurrent faults.

A model of the overall system, similar to that displayed in figure 1 has been developed and introduced into a simulation model such that the Direct Torque Control may be analysed and modified to improve performance. Simulated DTC induction motor drive is compared with the existing platform from a steel plant. In this application, the DTC induction motor drive operates in speed mode, in which the output of the speed controller represents the input of the torque controller as torque reference. Stator flux (magnitude and position) and electromagnetic torque estimators are part of the control scheme and are based on the measured voltages and currents at the input of the induction motor.

The system operation is analyzed through simulations performed using MATLAB/Simulink software, in the context of considering the three induction motor dynamic models from sections IV-VI.

In all situations, realistic torque and speed time dependencies are considered determined from the recorded values from operation of the existing Crop Cobble Shear (CCS). The induction motor torque and speed, as functions of time, have been obtained through simulation using all three induction motor dynamic models. The IM has the following data: Pn=480kW, Vn=660V, p=6, In=549A, PF=80%, EFF=95.3%,rs=0.0321pu,xs=0.124pu,xm=2.07pu,rFe=35pu, rr=0.012pu, xr=0.1292pu

In the calculations, we’ve considered the coefficients of equation (19) with the following values:

sr slσ rlσ rr

( )mmrrr ililj +σν

sv

si

mi

ri

ml Fei

a1=5.12; a2=0.33; a3=0.031;b1=73.06; b2=2193.33; c1=0.922; c2=0.0074; c3=-1,018

Figure 5: Simulated DTC for IM with constant parameters. From top to bottom developed torque, reference torque and load torque (per unit)

Figure 6: Simulated DTC for IM with constant parameters. From top to bottom: actual speed and reference speed (per unit)

Figure 7: Simulated DTC for IM with core loss. From top to bottom: load torque and developed torque (per unit)

Figure 8: Simulated DTC for IM with iron loss and saturation. From top to bottom: load torque and developed torque (per unit)

Figure 9: Simulated DTC for IM with core loss. From top to bottom: actual speed and reference speed (per unit)

Figure 10: Simulated DTC for IM with core loss and saturation. From top to bottom: reference speed and actual speed (per unit)

VIII. CONCLUSIONS

Experimental data from measurements on the system in the steel mill are compared favorably with simulation results. This comparison shows the system has been simulated to determine a suitable approach to improving the DTC.

Figure 11: Experimental results. From top to bottom speed reference, actual speed, position and reference torque (per unit)

For the simulations performed with IM modeled considering the core loss respectively core loss and saturation the DTC drive shows initial poor dynamic performance. In both cases the torque controller is not capable to deliver output values to match the load torque demand (fig.7, 8).

Consequently, a longer duration for the application of the output torque was required, while the acceleration process was sluggish (fig. 9, 10) and the IM rotational speed couldn’t follow the reference speed. Following simulation, the modifications were made to the system and measurements (see Figure1, for example) carried out to verify the improvement. Appropriate adjustments have been made to match not only existing recorded speed and torque profiles, but to be able to compensate for the torque and rotor speed steady state errors when core loss and saturation are considered. The modifications affected the PI rotational speed controller as well as the hysteresis torque and flux controllers, and practically compensated for the core loss and saturation effects. These resulted in a stable operation of the DTC cobble shear drive (fig. 5, 11). Final adjustments regarding the reference torque profile eliminated the sudden overload tripping previously encountered.

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