SELECTION OF RATIONAL PARAMETERS OF THE NOMINAL MODE ELECTRIC TRAINS WITH ASYNCHRONOUS TRACTION DRIVE

Dep. «Electric Rolling Stock of Railways», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 31, e-mail getman-gk@i.ua, ORCID 0000-0002-3471-6096 Dep. «Electric Rolling Stock of Railways», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 31, e-mail marikutsasergei@gmail.com, ORCID 0000-0002-0429-6633


Introduction
Parameters of the nominal mode are related to the most important performance indicators of the electric rolling stock.Therefore, the problems of determining their optimal values always inevitably arise when forming technical requirements for a new rolling stock.For the railways of Ukraine, these tasks are currently particularly relevant in connection with the need to renovate morally and physically obsolete locomotive fleet in conditions of acute shortage of funds, when it is especially important to avoid the acquisition of inefficient equipment.
Determining the parameters of the nominal mode (traction force, speed of movement and power) of traction means is the main objective of the so-called traction supply problems.Review of the papers on this topic is given in [1,5,6].There one can find the ways of solving such problems with regard to freight and passenger electric locomotives, mainly with a collector traction drive.

Purpose
In the case of electric trains, the tasks of determining the parameters of nominal mode were considered in a smaller volume and only with reference to the collector traction drive [3,4,9].In this article, the features of these traction supply problems for electric trains with an asynchronous traction drive are described.

Methodology
The nominal mode power should be selected in such a way that it would be possible to realize the predetermined travel time along the section (or movement speed).With such a «blurred» statement of the problem, its solution contains many variants, and when determining the rules for selecting the best ones the work [6] proposes to apply the following indicators for a comparative evaluation of the variants: -specific power consumption for train traction; -excess capacity of the required locomotive fleet; -the mean value of the traction multiplicity required for transportations.
Last two indicators make sense for freight and passenger traffic, as the weight (composition) of trains varies widely.
In the case of electric trains only the first of the above-mentioned indicators is used: electricity consumption, since in the general case, when the specific power is distributed along the length of the train, i.e. which accounts for 1 ton of train weight, it does not depend on train composition.For electric trains, where the traction motors are located in the end cars, the maximum train weight should be taken into account.
Based on the above and taking into account that the acceleration value during starting period (acceleration) а s and acceleration at the design speed а r (residual acceleration) refers to the important operational characteristics, the problem of determining the nominal power of the electric train is formulated as follows: for the given traction polygon, it is necessary to find such a value of the nominal mode power and corresponding traction value, so that it would be possible to carry out transportations with a given level of average speed with minimum electricity consumption for traction and the following conditions would be met: -the speed of the train movement in the section does not have to exceed the established limits; -it is possible to realize the given values of acceleration at start (а s ) and the residual one (а r ).
A more detailed consideration of the problem shows that in real conditions, when the starting acceleration and the train weight are given, the task of traction supply of electric trains practically reduces to determining the optimal value of the nominal mode speed.
To be convinced of the validity of the foregoing, let us determine the factors defining the nominal mode power.
The traction force in N, required to realize the given acceleration а, is determined on the basis of the equation of the train motion used for traction calculations [2,12] as where ( ) k F v -tangential traction force (on the rim of the driving wheels) of the motor cars, N; ( ) k W v -total movement resistance, N; m -train weight, t; 1   -inertia coefficient of the rotating masses of the train; a -acceleration, m/s 2 .
Given that the train movement resistance ( ) 9,81 ( ), where ( ) k w v -specific total resistance to train movement, N/kN.
When measuring the movement speed in where kn F -tangential traction force related to one traction motor, N; the index «n» -means the value of the parameter corresponding to the nominal mode.
Expression (5) shows that the power of nominal mode at the given values , , w v dependencies is definitely determined by the value of the optimal mode speed, and thus the problem of choosing the optimal parameters of nominal mode of electric trains reduces to the choice of the movement speed in the nominal power mode from the condition of minimizing the electricity consumption for traction of trains.
To solve the problem, one can use the method proposed in [6].Its implementation is carried out by successively solving the following tasks: -determination of control parameters of the train movement equation; -optimization of train traffic control for minimal electric power consumption; -determination of the nominal mode speed, corresponding to the minimum power consumption when implementing the given travel time.
To solve the last two of the problems posed above, it is possible to apply the approaches used in solving similar problems for passenger electric locomotives [1,5,11].Therefore, we will dwell only on the problem of determining the control parameters of the motion equation.
Traction calculations are based on the integration of the motion equation (6).
where  − is dimensional coefficient, the value of which depends on the accepted units of measurement of physical quantities; u − control parameter; ( ) о w v -basic specific net train resistance; і − the value of the longitudinal path gradient, which is a function of the path ( ) і s .The value ( ) The dependences ' ( ) о w v and ( ) oх w v are de- termined by the corresponding dependences obtained on the basis of the experimental data [7,8,10].
The control parameter depends on the operation mode of the electric train: 0 u  corresponds to the traction mode; 0 u  -to the braking mode; 0 u  to the run-out mode.
Let us consider the traction drive with a smooth control of the traction power.Then, in the power calculation the control parameters that satisfy the following conditions are adopted: -traction mode 0 ( ) where ( ) − limiting traction and braking characteristics respectively, referred to 1 kN of the train weight.
Let us consider the problem of calculating dependencies ( ) k f v for the two most frequently encountered methods of 3-zone (Fig. 1, a) and 2-zone (Fig. 1, b) frequency control of the asynchronous traction drive power for electric trains.
In the case of 3-zone regulation, there is a possibility: -in the zone 1 (0 ) -acceleration with the given starting traction force; − in zone 2 ( ) -the realization of the constant traction power; − in zone 3 ( ) -the traction power control is inversely proportional to the movement speed.
In the 3 rd regulation zone ( ) From the (9) we have the following , We designate , where c v -constructional speed of the train, km/h.Taking into account the specific quantities, we obtain ( ) ( ) 102 (1 ) .
Let us consider the case of two-zone regulation using booster modes, i.e. when the implementation of loading modes providing for the realization of traction forces exceeding the values corresponding to the nominal mode is provided.This mode of operation is used, for example, on the Skoda electric train.In this case, the traction characteristic corresponds to that shown in the Fig. 1, b.Let us introduce the designations ; , where s N -is the maximal traction force, at The limiting traction characteristic for the acceleration section is determined by the expression (8), and ( ) ( ) v -according to the formula (10).

Nominal traction force
.
The value of the nominal mode speed is obtained on the basis of the relation taking into account the expressions (16). .

Findings
The task of choosing the optimal values of the nominal mode speed n v is solved by determining the electric power consumption with the variation of the possible values of the starting speed s v , therefore one should take into account only those its values that ensure the implementation of the given starting s a and residual r a accelerations at the selected control method.
As it can be seen from the Fig. 1a and Fig. 1b, the value of traction force at the design speed, other things being equal, increases with increasing starting speed.Therefore, in order to exclude variants that do not match the conditions of the problem solution, it is necessary to determine the minimal values s v corresponding to the given starting and residual accelerations.
Neglecting the dependence of k w on s v , we obtain ( ) 102( 1) For the case of two zone regulation in the presented expression it should be taken 1, ( ).The value of the starting acceleration at the given train weight determines the tractive effort, and hence the use of the «wheel-rail» contact capabilities to realize the traction creepage.In order to exclude from consideration, the variants, when the traction force cannot be reliably realized according to the adhesion conditions, it is expedient to set the maximum permissible values of the starting acceleration according to the adhesion conditions, i.e. corresponding to the specified design coefficient of adhesion.
Estimated adhesive force The necessary acceleration value is obtained from the well-known law of locomotive traction [2], according to which for the reliable operation of a wheel-rail vehicle, it is necessary to fulfill the condition ( ) ( ).
Based on the expression ( 8) and ( 21) we obtain  1) where ( ) ( ) Notations. 1 The value of weight is presented with the maximum loading of cars by passengers. 2 Total specific movement resistance is determined on condition of movement at the section.

Originality and Practical Value
Originality consists in developing a methodology for determining the optimum values for the parameters of the nominal mode of electric trains with asynchronous traction drive, with two-zone and three-zone frequency regulation of power.
The resulted methodology can serve as a basis at formation of technical requirements for a new rolling stock for railways of Ukraine.

Conclusions
The materials presented in the article provide for the implementation of traction calculations (in terms of plotting the motion curves), in solving problems, selecting parameters for the nominal mode of electric trains with asynchronous traction drive.

Fig. 1 .
Fig. 1.The limiting traction characteristics of the electric trains, HRCS2 series: a -the Hyundai-Rotem Company and b -EJ675 of SKODA Vagonka .

Fig. 2 .
Fig. 2. The family of dependencies of the minimum starting speed on the starting acceleration with the variation of values of residual acceleration and design speed is: a -160 km/h and b -200 km/h

Table 1 Initial data for calculating the dependencies of the minimum permissible starting acceleration using the con- ditions of adhesion on the speed of motion
( ) s a v  .