ANALYSIS OF OPTIMAL OPERATING MODES OF THE INDUCTION TRACTION DRIVES FOR ESTABLISHING A CONTROL ALGORITHM OVER A SEMICONDUCTOR TRANSDUCER

Worldwide trend of energy saving is implemented through the improvement of performance efficiency [1]. The rising cost of energy resources and competition between manufacturers requires constant work in order to increase efficiency factor of electrical equipment in different spheres of application [2]. Special attention is paid to electric drives of general designation [3], as well to the traction ones [4], which are designed to drive electric transport [5]. This is understandable as the former are the most common, and thus consume a significant amount of electricity, while the latter form a basis for the creation of environment-friendly “green” transport. As noted in [6], traction drive of electric rolling stock can operate under the following modes: – maximum thrust or braking – regime of maximum torque of the traction motor; – maintaining the preset motion speed ‒ regime of the maximum performance efficiency of the traction motor; – overshooting or mechanical braking is the regime of traction motor without power supply; the rotor is rotating by inertia; energy not consumed – performance efficiency is predetermined by mechanical and ventilation losses only. Under the mode of maximum thrust or braking, the main (basic) is a criterion for providing the maximum torque of the traction motor. Because it allows for the fulfillment of requirements in terms of acceleration of the rolling stock during acceleration and braking, on the one hand. On the other hand, to maintain a preset traffic schedule. Under the mode of keeping the assigned motion speed, the main criterion is the maximum efficiency. ANALYSIS OF OPTIMAL OPERATING MODES OF THE INDUCTION TRACTION DRIVES FOR ESTABLISHING A CONTROL ALGORITHM OVER A SEMICONDUCTOR TRANSDUCER


Introduction
Worldwide trend of energy saving is implemented through the improvement of performance efficiency [1].The rising cost of energy resources and competition between manufacturers requires constant work in order to increase efficiency factor of electrical equipment in different spheres of application [2].Special attention is paid to electric drives of general designation [3], as well to the traction ones [4], which are designed to drive electric transport [5].This is understandable as the former are the most common, and thus consume a significant amount of electricity, while the latter form a basis for the creation of environment-friendly "green" transport.
As noted in [6], traction drive of electric rolling stock can operate under the following modes: -maximum thrust or braking -regime of maximum torque of the traction motor; -maintaining the preset motion speedregime of the maximum performance efficiency of the traction motor; -overshooting or mechanical braking is the regime of traction motor without power supply; the rotor is rotating by inertia; energy not consumed -performance efficiency is predetermined by mechanical and ventilation losses only.
Under the mode of maximum thrust or braking, the main (basic) is a criterion for providing the maximum torque of the traction motor.Because it allows for the fulfillment of requirements in terms of acceleration of the rolling stock during acceleration and braking, on the one hand.On the other hand, to maintain a preset traffic schedule.Under the mode of keeping the assigned motion speed, the main criterion is the maximum efficiency.
Traction drive based on the induction traction motor (ITM) can operate at one and the same point of the traction characteristic.Each point of the traction characteristic corresponds to a certain frequency of rotation and torque on the shaft of the motor.However, the level of losses in the elements of the drive for these points will be different.
That is why the task of determining optimal modes in the traction drive operation can be reduced to defining optimal operation regimes of the link ITM -AVI.In this case, it is necessary to take into account those constraints that are set on the work of mechanical part of the traction drive (constraints on clutch and speed).
At the same time, when powering ITM from AVI, two basic control varieties can be applied.The first is based on using a spatial-vector pulse-width modulation (PWM) of ITM employing the algorithms of vector control [9], or direct control over the moment.
The second mode is the regime of one-time PWM.In it, the motor voltage is set at the highest possible level that allows reduction of the major losses.However, the step shape of voltage creates a spectrum of voltage higher harmonics, causing additional losses in ITM.
An important element in the control system of the traction drive with ITM is to determine transition points of the traction drive from a regime of spatial-vector to the one-time PWM, which can vary depending on the parameters of ITM and which determines the working algorithm of a semiconductor transducer.
Thus, determining optimal operating modes of the induction traction drive in order to enable its maximum performance efficiency is one of the relevant scientific and technical tasks of electric transport.

Literature review and problem statement
The task of improving performance efficiency of the induction traction drive is solved in two ways: by increasing the efficiency of ITM, and through the optimization of its control mode, that is, determining optimal parameters of AVI operation, which makes it possible to reduce losses both in the motor itself and in the semiconductor transducer [10].But the larger effect is achieved only employing a comprehensive study into the entire drive as a whole, therefore, such studies are most common.Thus, in article [11], authors developed a computer model for ITM control, which allows defining power parameters of AVI.Authors of paper [12] focus their attention on improving efficiency of the drive under the mode of acceleration of electric rolling stock.In article [13], authors conducted a comprehensive optimization of various physical parameters of ITM.In order to determine energy indicators of traction motors, authors of paper [14] constructed a virtual model of ITM.Determining operational effectiveness of the traction drive of rolling stock in general is addressed in article [15].
Capabilities for increasing performance efficiency of existing ITM are limited [16], although studies in this di-rection are also conducted [17], moreover, ITM is calculated so that maximum efficiency for one working point is ensured.In the process of ITM operation on electric rolling stock, there are substantial changes in its speed and loading mode, that is, the operating mode, which significantly reduces the overall performance efficiency of the traction electric drive [8].In addition, in order to provide for certain operation modes, it is necessary to switch AVI from a spatial-vector control to the one-time PWM.
Another factor that limits work of the drive is the thermal condition of ITM, that is, the temperature of heating its windings.It affects both the performance efficiency of ITM itself and the reliability of transport operation [18].That is why, in some cases, a transition has to be applied from ventilation to cooling ITM with water [8,19].
Complexity of the task to ensure effectiveness of the traction drive is in the existence of five modes of operation and difference in the performance criteria for each of these modes.In addition, it is necessary to take into account the thermal condition of ITM as a limiting factor.The transition to water cooling of ITM will complicate the design and cost of the drive itself.That is why most researchers try to optimize separate operational modes of the traction drive.Thus, article [20] considers a nominal mode of operation of the traction drive, paper [21] -a mode of braking.From the point of view of the authors of these works, ensuring maximum performance efficiency under nominal operating mode [20] is the most appropriate because the drive spends the largest share of the total operating time under this regime.Optimization of the braking mode [21] will make it possible, through recuperation, to save energy, that is, to reduce the overall cost.However, these studies were carried out by separate techniques with various parameters of the traction drive and by one criterion of effectiveness -performance efficiency.That is why applying these techniques jointly is impossible.
We believe that the most advisable is to determine optimum operating regimes of the entire traction drive as a whole, with unified parameters and criteria of efficiency [7,8].An analysis of this work for each of the modes of semiconductor transducer will make it possible to define the algorithm of its control.The algorithm is understood here as a point of transition in the operation of a semiconductor transducer from a spatial-vector PWM to the one-time.

The aim and objectives of the study
The aim of present work is to analyze optimum operating modes of the traction induction drives of varying capacity in order to identify a point of transition in the operation of a semiconductor transducer from a spatial-vector PWM mode to the one-time regime.
To achieve the set aim, the following tasks have been solved: -optimization of operating modes of the induction traction drive of a tram and a diesel locomotive; -determination of optimum AVI control modes depending on the ITM rotation frequency and the temperature of its windings; -analysis of effect of temperature of the windings of the traction motor on operating modes of the traction drive of a tram and a diesel locomotive.

Technique for the optimization of operating modes of the induction traction drive
The research presented in the given article is a continuation of the studies reported in paper [8].In order to solve the set task, it is necessary to create a technique for determining optimal operating modes of the induction traction drive, which was developed by the authors and described in detail in works [8,22].Employing the specified technique, in paper [8], the optimal modes were defined for ITM operation of the AD931 type, which is used to drive the tram, with the validity of the given technique proven.A further step in the research is to determine the optimal operating modes for the induction traction drive of a diesel locomotive and general (joint) analysis of these regimes, both for the tram and the diesel locomotive.
To determine effectiveness of the traction drive, we shall use a system of equations (1), which consists of separate systems of equations for each operating mode, which was proposed in articles [8,22]: where η 1 is the performance efficiency of link ITM-AVI, U op is the operating mode of the traction drive of a tram, F d is the force of traction or braking, which a tram creates, k F ′ is the limiting force by clutch of the contact wheel-rail, v nc is the speed of the rolling stock, v max is the design motion speed.U op =4 is the overshooting mode without load, which is why it is not considered when determining effectiveness of the drive.
We shall outline basic provisions of the technique that is applied to determine optimal operating modes.To determine the overall performance efficiency of the link ITM-AVI, it is required to solve four problems on the conditional optimization of operating parameters of the traction drive [8].Under the modes: acceleration U op =1, recuperative braking U op =5, maintaining predetermined speed U op =2, 3.
For each of these problems, two control modes are considered: one-time or spatial-vector PWM.The mode of acceleration and recuperative braking are similar.We shall apply a method of vector objective functions, proposed in article [23].We choose a vector function with the following parameters as the objective function for the acceleration mode; for convenience of calculations, we shall denote a maximum of performance efficiency through the function of minimization: We shall select as an objective function for maintaining the mode of predetermined motion speed: For the mode of recuperative braking, vector objective function takes the form: Objective functions make it possible to determine optimal operating modes of the traction drive when using different regimes of PWM.
To assess effectiveness of the traction drive, we selected components of the control vector as parameters: modulation coefficient K m ; the magnitude of rotor sliding s; the mode of operation of the transducer -one-time or spatial-vector PWM.
The study will employ two ITM whose parameters are listed in Table 1.The traction motor of a tram carriage has small electrical magnetic moment, but a rather large frequency of rotation.In contrast, the traction motor of a diesel locomotive has large electrical magnetic moment and the low frequency of rotation.In other words, we explore two boundary cases of the existing range of ITM parameters.In order to solve the optimization problem, we applied the optlab package for MATLAB software, which makes it possible to easily alternate different methods for solving optimization problems [24].To solve this problem, we propose employing at the first stage a method based on genetic algorithms, which is widely used in the optimization of parameters and modes of operation of electric machines [25].
Genetic algorithms possess one shortcoming -they find the optimal solution with low accuracy.To exclude this drawback, we propose a combined method.It consists of a genetic algorithm and the Nelder-Mead method at the final stage of the search.This technique was validated in papers [7,8] in order to search for the optimal modes of traction drives.

Results of optimization of operating modes of the induction traction drive of a diesel locomotive
Based on results of the calculations, we shall construct main characteristics in accordance with the criteria of operational efficiency of the traction drive of a diesel locomotive for different modes of operation.
Fig. 1 shows optimal dependences of performance efficiency and electromagnetic torque of the traction drive of a diesel locomotive under the mode of maintaining preset motion speed.locomotive under the modes of maximal torque: a -performance efficiency during traction, b -electromagnetic torque during traction, c -performance efficiency when braking; d -electromagnetic torque when braking; 1 -while applying one-time PWM and at motor temperature 40 °C, 2 -while applying one-time PWM and at motor temperature 180 °C, 3 -while applying spatial-vector PWM and at motor temperature 40 °C, 4 -while applying spatial-vector PWM and at motor temperature 180 °C For ease of comparison, we shall also present similar characteristics to the traction drive of a tram, obtained in paper [8].
Fig. 3 shows optimal dependences of performance efficiency and electromagnetic torque of traction drive of the tram Tatra T-3 VPA under the mode of maintaining preset motion speed.
Fig. 4 shows optimal dependences of performance efficiency and electromagnetic torque of traction drive of the tram Tatra T-3 VPA under the modes of acceleration and braking.
Having obtained optimal dependences of parameters of the traction drives of a tram carriage and a diesel locomotive, we shall pass over to their comparative analysis.

Analysis of the results of optimization of operating modes of traction induction drives of the tram and the diesel
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Fig. 1 .Fig. 2 .
Fig. 1.Optimal dependences of the AD917 parameters on rotation frequency n of the traction drive of a diesel locomotive under the mode of preset motion speed: a -performance efficiency during traction, b -electromagnetic torque during traction, c -performanceefficiency when braking; d -electromagnetic torque when braking; 1 -while applying one-time PWM and at motor temperature 40 °C, 2 -while applying one-time PWM and at motor temperature 180 °C, 3 -while applying spatial-vector PWM and at motor temperature 40 °C, 4 -while applying spatial-vector PWM and at motor temperature 180 °C

Fig. 3 .Fig. 4 .
Fig.3.Optimal dependences of the AD931 parameters on rotation frequency n of the traction drive of a tram under the mode of preset motion speed: a -performance efficiency during traction, b -electromagnetic torque during traction, c -performance efficiency when braking; d -electromagnetic torque when braking; 1 -while applying one-time PWM and at motor temperature 40 °C, 2 -while applying one-time PWM and at motor temperature 180 °C, 3 -while applying spatial-vector PWM and at motor temperature 40 °C, 4 -while applying spatial-vector PWM and at motor temperature 180 °C

Table 1
Parameters of traction motors of the tram and the diesel locomotive