Modeling of energy-efficient direct torque control system for traction induction motor

. A brief analysis of existing control systems for traction electric drives with induction motors has been carried out, as a result of which it has been established that vector control and direct torque control systems are the most promising. The comparative characteristic of these control systems according to different parameters of electric drive quality has shown that in energy-saving algorithms it is appropriate to use the systems of direct torque control. The work aims to simulate the electric drive with a direct torque control system, which provides the reduction of power losses in an asynchronous motor. The value of the stator winding power factor is chosen as a control action. The calculation and functional dependences between the main parameters of the control system and the induction motor are synthesized, the fulfillment of which allows reducing duce power losses. The functional diagram of the electric drive with an energy-efficient control system is given. The hardware of this control system does not differ from the currently used frequency converters. In the power channel of the frequency converter, a three-level autonomous voltage inverter with locking diodes is used. The results of modeling for electric drive with 11 kW motor, analysis of which showed the adequacy of the developed model and performance of the synthesized control system, the efficiency of the electric drive with energy-efficient control system increases to 18% compared with the classical direct torque control system


Introduction
Taking into account modern trends in the development of microprocessor technology, power electronics, and electrical machines, in designing modern traction rolling stock, it is advisable to focus on the use of electric drives with asynchronous motors, which have several advantages over DC motor drives due to the absence of brush-collector node, which leads to increased reliability and efficiency. At the same time, the sense of separate channels for control of flow and torque leads to complications of control algorithms and technical means of their realization. The efficiency of electric drives is determined primarily by the efficiency of motors, the power loss of which depends not only on the resistance torque, which directly affects the values of stator and rotor currents but also on the parameters of the motor substitution scheme, rotor speed, power source parameters, motor power, modes of operation, operating conditions, etc. Nowadays traction electric drive has, as a rule, three variants of asynchronous motor control systems-scalar control system, a vector control system, and a direct torque control system [1,2,3,4].
The obvious advantages of scalar control systems are their simplicity and reliability, as well as the lack of influence of changes in the parameters of the induction motor substitution scheme on the stability of the electric drive in an open system. Disadvantages-the impossibility of torque control in dynamic modes, large torque fluctuations, and low energy efficiency [5].
The introduction of vector control systems and direct torque control in the structure of traction electric drive significantly expands the opportunities to regulate not only the speed of the induction motor but also its torque in steady state and transient processes; allowing you to apply a variety of efficient algorithms for energy-saving control in the presence of a large number of operating restrictions associated with the final power of the power supply source of the drive, the maximum values of current and voltage vectors.
Thus, the issues of synthesis and research of systems of vector control and direct torque control of induction motors are relevant for traction electric drive.

Overview of modern and advanced induction motor control systems
To obtain the required torque in asynchronous machines in all operating modes, including dynamic modes, it is necessary to control not only the amplitude but also the phase of the stator current vector, i.e., to operate with vector values. This is the reason for the introduction of the term "vector" for such a method of control in contrast to the above-considered scalar control, based on the change in frequency and amplitude of the voltage supplying the motor. Separation of stator current into components can be done in different ways. One such way is a division of space current vector into components according to position in space of rotor magnetic flux vector (vector control with orientation by rotor current coefficient) [6,7,8]. One of these components, which is the projection of the current indicator in the direction of the magnetic flux vector, is the magnetizing current, similar to the DC motor excitation current. The other orthogonal component of the stator current vector is the component that forms the motor torque, similar to the DC motor armature current. Thus, to build a vector control system, in addition to the currents in the stator windings, it is necessary to measure the position of the spatial vector of the rotor magnetic flux in the asynchronous motor, as well as the rotor shaft speed. Advantages of vector control with an orientation by rotor flux ratio: relatively simple highly dynamic schema; а well-proven technique used for quite a long time. Disadvantages: relatively low speed of loops due to the use of PI-controllers; changes in parameters of the substitution scheme can cause significant errors in maintaining torque and flux-loss ratio.
The direct torque control (DTC) method was first applied in the middle of the 80s [9,10]. DTC is based on maintaining constant values of electromagnetic torque and stator flux (within the hysteresis loop), which is performed by selecting one of six non-zero or two zero vectors of the two-level inverter. To form a larger number of optimal voltage vectors, threelevel inverters have begun to be used in recent years. Advantages of DTC: high speed of the torque loop; relative simplicity. Disadvantages: strong distortion of phase currents, impossibility to control them; large torque fluctuations; variable switching frequency of power switches.
There are various studies aimed at improving the operation of direct torque control systems [11,12,13]. For example, in [11] it is shown that, based on the measurement of instantaneous values of the stator winding current and voltage, it is possible to obtain the required values of torque and flux for a certain period. The optimum voltage vector calculated in this case is generated using space-vector modulation algorithms. Advantages of such control system variant: high speed of torque loop (equivalent to standard DTC circuit); low torque fluctuations and current distortions (equivalent to classical vector control circuit); constant switching frequency of power switches; more robust system to changes of substitution circuit parameters than classical vector control. Disadvantages: the control algorithm is very complicated about the compared variants; a fast and high-bit microprocessor is required to implement an acceptable switching frequency of the power switches.
Another variant of improving the operation of the direct torque control system can be the variant proposed in [12]. In the steady-state mode of operation, the system of direct torque control commutes the zero and nonzero voltage vectors in series. The nonzero vector is usually chosen to increase the value of torque. After reaching the upper limit of the hysteresis loop, a zero-voltage vector is applied to the stator winding and the torque begins to decrease. By calculating the optimum time for switching between voltage vectors, it is possible to minimize torque fluctuations. Advantages of this approach: high speed of the torque loop; low torque fluctuations in static operating modes. Disadvantages: much larger variations in the coil flux about the DTC algorithm; very high current distortion.
Thus, the brief review of control systems has shown that the most promising variant of the traction induction motor control system is the direct torque control system. In this regard, this paper sets the task of synthesis and research using simulation modeling of an energyefficient control system based on the direct torque control system.

Synthesis of an energy-efficient control system
About the energy efficiency of the electric drive as a whole, it should be taken into account that a large proportion of losses occurs in the copper and iron of the induction motor. In recent years, various extreme control systems have been proposed to minimize losses in the electric drive [14,15,16,17]. The efficiency of asynchronous motor operation depends significantly on the control law and the ratio of the main control variables. When working with a constant rotor current ratio at low speeds, the machine is in a mode close to saturation. Losses in iron in this case are quite high and significantly reduce the energy efficiency of electric drive. To solve this issue, it is necessary to calculate the optimum value of the flux-limit value depending on the current speed and the resistance torque on the machine shaft. By introducing a coordinate system rotating synchronously with the rotor magnetic field and accepting several assumptions, the efficiency of an asynchronous machine can be calculated as follows: Where the following designations are taken: L -mutual inductance of dissipation, Lσrreduced inductance of the rotor winding dissipation, p-number of pole pairs, Telectromagnetic torque of motor, Rc-resistance, equivalent to losses in iron, Rs, Rr-stator active resistance and reduced rotor active resistance respectively, ω-rotor rotation frequency.
Taking the partial derivative of the rotor flux ratio, we obtain the value of the optimal rotor flux ratio: [ L μ 2 R c (R s + R r ) + 2L σr L μ R c R s L μ 2 p 2 ωp 2 + R c R s ] 1 4 √T. (2) Analysis of expression (2) shows that the optimal rotor flux ratio is usually below the nominal value for low resistance torques and greater than the nominal value for low speeds and high resistance torques. The range of variation of the rotor flux ratio is limited to 30...100% of the nominal value to ensure the highly dynamic operation and no saturation of the magnetic system. Maintaining the optimal current ratio allows for an increase in efficiency in a wide range of frequencies. The main difficulty in implementing such an approach to the construction of efficient control systems is the complex functional dependence of the optimal value of the current-to-current reference on the parameters of the substitution scheme and motor torque. During operation in a wide range, both the motor torque (especially when using it for traction purposes) and the parameters of a substitution scheme change, which is associated with the processes of heating and cooling of motor windings and the saturation phenomenon along the main magnetic path. These reasons have caused deterrence of practical application of the majority of energy-efficient control systems and have served as the reason for a large number of researches in this area.
Despite the sufficient number of works in this area, there is still no generally accepted approach to reducing losses in the electric drive, which is associated primarily with the labor intensity of the software part of the proposed solutions, the availability of precision sensors of electrical and mechanical quantities, the complexity of installation of some elements of the automation system, as well as economic feasibility.
For example, in [18] it is proposed to reduce losses by maintaining stator winding voltage as a function of stator active current. To implement the proposed algorithm, two current and stator winding voltage sensors and a fast microprocessor system are required. The main disadvantage of this proposal is that the reduction of power consumption of asynchronous motors can be achieved only in the range of motor loads below the nominal.
In [19], a system is proposed, which is operable in the whole range of resistance torques (at torques higher than the rated value, loss reduction is possible only at reduced stator current frequencies, which fully corresponds to the working conditions of traction electric drive). It has similar requirements to the system [18] for hardware and software implementation but contains an additional stator winding voltage source, which forms a triangular signal, which leads to deterioration of harmonic composition of current and, consequently, torque, which can be critical when implementing traction electric drive control systems with anti-slip protection.
In this article, the authors propose a control system free from the above drawbacks. It is known that it is possible to minimize the total stator winding current and, therefore, power losses in an induction motor, by maintaining a certain ratio between the stator current vector projections in a rectangular coordinate system. If to locate the perpendicular axes in the stator magnetic field in such a way, that one of the projections represents an active component of stator current, and the other one represents a reactive component of stator current, then it is reasonable to solve the issue by maintaining the angle between them or some function of the stator winding power factor, for example. The advantage of these systems is that they do not require the coordinate system to be bound to the rotating rotor, which eliminates the need to measure the rotor current frequency and allows this approach to be used in direct torque control systems. The expression for the power factor of the induction, in this case, the case will be as follows: . (3) The graphical dependence of power factor and power loss on stator current is shown in Fig. 1.   a) b) Fig. 1. Dependence of power loss ∆P (a) and power factor p f (b) on stator current i sαu of 11 kW asynchronous motor (resistance torque Tl1=5Tl2= TT rat , where T rat is nominal torque).
The graphs in Fig. 1 show that the minimum power loss mode and the maximum power factor do not quite correspond to each other in terms of stator current value. It should also be noted that the power factor value corresponding to the power loss minimum is at the steepest section of the dependence p f = f(i sα ) and is 0.707, which provides an angle between the active and reactive components of the stator current of 45° and their equality between each other. The given curves were obtained for nominal speed, with decreasing speed the modes of maximum p f and minimum Δp approach each other.
Thus, the proposed method is workable and a functional diagram of its implementation is shown in Fig. 2. The principle of operation of the direct torque control system is described in detail in [20] and is not given here. Let's not only those dependencies, which are necessary for the realization of this sousing of simulation modeling package. In electric drive and converter technology, mathematical description is carried out in a two-phase coordinate system, so it is necessary to convert voltages from a three-phase coordinate system into a two-phase one: The angle of the stator current-current vector ψ s , through the voltage projections in the αβ axes, is defined as follows: In general, if the phase of the stator current-circuit vector is defined, the calculation of the phase sector number can be performed according to the following inequality.
(n -1) •60° < θ ≤ 2•n•60°, Where n = 1, 2…6. The output vector selection task is the control voltages ΔT and Δψ , taking discrete levels depending on the sign and magnitude of the torque and torque flux-limit error (Tref -T) and (ψ ref -ψ s ) respectively, as well as the flux-limit sector. Projections of the stator flux capacitor ψs on the orthogonal axes: The calculation formula for the stator current coefficient is not difficult: The motor torque is defined by the expression: A proportional-integral-differential regulator is used as a controller.

Simulation results and discussion
The model of electric drive with an energy-efficient direct torque control system (Fig. 2) Fig. 3. The output voltage vectors of the inverter are shown in Fig. 4 (the switching functions for each inverter phase are shown in brackets next to the vector number). Fig. 5 shows the results of the simulation of mechanical and electromechanical characteristics of electric drive with an energy-efficient system of direct torque control of induction motor. Analysis of the results shows the high speed of the system and accuracy of maintaining torque and coincidence when changing the speed reference and jump change of the resistance torque. Fig. 6 shows the results of the simulation of the energy performance of an electric drive with the proposed energy-efficient system of direct control. Modeling was performed for stator current frequency f s =0.5f s,rat , the starting torque of resistance T l =0,3Trat, at the time t=20 s the power factor control circuit, which is external in relation to the control circuit of the fluxloop, is activated. At the moment of time t =30 s there is a step change of the resistance torque up to the value T l = T rat . In Fig. 6, the index 1 indicates the simulation results for the classical system of direct torque control, the index 2-for the synthesized energy-efficient system of direct torque control.  The analysis of the oscillograms shown in Fig. 6 shows the adequacy of the simulation and the operability of the energy-efficient direct torque control system. An increase in efficiency can reach 18%, power losses are reduced more than twice in the classical system of direct torque control. Dependence of power factor on time shows that this effect is achieved by maintaining it at the level of 0.707, which is ensured at the expense of equality of active and reactive components of stator current. The low value of power factor of induction motor, significantly below the rated one, has no effect on the energy efficiency of the electric drive as a whole because the presence of an uncontrolled rectifier (in the general case) at the input of frequency converter determines as a result extremely low (tending to zero in the absence of input filters or reactors) reactive power consumption. Optimization of transients and accuracy of maintaining the power factor in steady-state modes, taking into account the nonlinear nature of the control object, is advisable to carry out by choosing the structure and parameters of the controller in a series of simulation experiments with the selected control object.

Conclusion
Modeling of the synthesized energy-efficient direct torque control system of induction motor showed that the proposed control system provides a decrease in power losses and an increase in efficiency by using an additional power factor control loop, external about the control loop of the flux-loop, and the organization of feedback using standard current and voltage sensors of the stator winding. The hardware and information-measuring support of the electric drive are similar to that of modern frequency converters with direct torque control. The control