CC BY
16
M. O. KOSTIN, A. V. NIKITENKO (DNURT)
Department of Electrical Engineering and Electromechanics, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazarian, Lazarian Str., 2, office 238, Dnipropetrovsk, 49010, Ukraine, tel. +380563731537, e-mail: nkostin@ukr.net, nikitenko.diit@gmail.com, ORCID: orcid.org/0000-0002-0856-6397, orcid.org/0000-0002-6426-5097
ENERGY OF STARTING UP TO SPEED OF DC TRAIN
Introduction
The proposed autonomous (off-line) mode of recuperative braking in the articles [1, 2] shows that it is more effective to start up the train using the energy which was stored in the last phase of recuperative braking by on-board supercapacitor storage system (OSSS). First of all, the off-line mode allows to save significant volume of energy for the next phase of traction mode. Secondly, it increases the traffic-capacity of overhead line. But these facts lead to the question: which energy is required to starting up the electric rolling stock (ERS) from zero to some operational speed?
The paper describes the method of energy estimation and shows the results of analysis for DC multiple unit train EPL2T.
Methodology and main formulae for energy estimation
As it was established, at the train starting the energy, which is performed by its traction motors, Ast consists of: 1) energy for overcoming the friction Afr in the bearings of wheelpairs; 2) Arr is the energy for overcoming the main forces of the train running resistance; 3) variations of stored the kinetic Ak and the potential Ap energy in the process of train acceleration; 4) AAem is the energy of electrical and mechanical losses of system in the process of energy conversion and transmission. Therefore, the energy balance equation of train starting up is
= V ■ t ■ W = lst ■ W.
At = Ar + Ar + A ± Ap + M*
(1)
Each component of the equation is explained as follows.Firstly, we consider that the train starting carried on a horizontal straight section of track without rises and falls, so potential energy Ap is
absent.The energy sum Afr + Arr is frequently noted like Aw (V). This energy is consumed on overcoming of the total resistance to train motion and is described by next equation: Aw (V) = Afr + Arr = V • t • W = 1st • W
(2)
where V is the speed;
t is the time of starting up;
lst is the distance passed in acceleration period;
W is the total resistance to train motion.
The total resistance W consists of the main running resistance W0 and additional Wfr, which is based on the friction forces in the bearings of wheelpairs, so
W = W0 + Wfr.
(3)
The absolute value of the main running resistance W0 is determined as multiplication of the
specific main running resistance wo on the estimated weight of the train m • g [3, 4]:
Wo = wo ■ m ■ g , N,
(4)
where m is the weight of the train, t; g = 9,8 m/s is the acceleration of gravity. Formulae for determination of the specific main running resistance wo are shown in [4] for most common types of main and urban railway electric transport. Generally, the formula can be written such as:
w0 = a + b • V + c • V2 , H/kN, (5)
where a, b, c are the coefficients; V is the train starting up speed, km/h.
The value of the additional running resistance Wfr at the moment of train starting up can be calculated using the formula:
Wfr = Wfr ■ m ■ ■
(6)
where Wfr is the specific additional running resistance which is calculated in accordance with the Rules of Traction Calculations [3]:
Wfr =
28
mo + 27
(7)
where m0 is the physical weight per one axle of rolling stock, t.
In case when the train has different types of carriages and these carriages have different axial
load «o, the coefficients mo and Wfr should be determined for each type of carriage. That is why the resulting running resistivity is calculated by the following formula:
Wr =
ZW
fr i
(8)
where ni is the quantity of the carriages with similar type;
Wfr i is the specific additional running resistance for i-th carriage is calculated by the formula (7).
Theoretical and experimental researches show that in formula (1) the kinetic energy Ak is fundamental like Afr and Arr. As it is known from [4], the kinetic energy which is transferred to the train weight in the process of train starting up from zero to some operational speed is given by:
Ak =
mr ■V2 m ■ (1 + y) ■V1
, J,
(9)
Ast(v ) = -
nTEM ' npc 'n osss
(10)
As it is known, the energy which stored in the electric field of the capacitor is determined by the expression:
Aosss
C'U,
Cnom
2
(11)
where UCnom is the nominal voltage of fully charged capacitors.
It is not recommended to discharge capacitive storage for structural views completely to [6] and it should have some residual charge, so-called "dead volume". Therefore, the total energy of the storage system has two components and equals:
Aosss - Ac + Ai-
(12)
where Ac is the exchange energy between storage system and traction motors of ERS, Ad is the energy of "dead volume". The exchange energy can be represented as
Ac =
с ' (U2 - и2)
(13)
where mr and m are the reduced and physical (calculated) weights of the train respectively, kg; (1 + y) = 1,08 is the rotational inertia coefficient
[5].
Energy losses AAem in traction electrical
equipment consist of losses in traction electric motor (TEM), mechanical transmission, wires of power circuit, pulse converter, on-board superca-pacitor storage system. The corresponding total power losses determine the efficiency of the relevant units of conversion and transmission system. Therefore, the value AAem in the calculations of Ast takes into consideration the efficiencies of the next elements: TEM nTED, the pulse converter
npc and OSSS nosss .
Abovementioned data determine the energy of train starting up by the expression:
Aw (V) + Ak(V)
2 2
where Uc - Ud is the operational voltage range (charge-discharge);
Uc is the voltage of fully charged storage system; Ud is the voltage of discharged storage system (voltage of "dead volume"). To determine the capacity C by the energy balance of Ast(V) and Ac the formulae (10) and (13) are used:
Aw (V ) + Ak(V )
nTEM ' npc ' nosss
С ' (Uc2 - UI) 2
Finally, equation above allows to get the final formula:
С =
2[ Aw (V ) + Ak(V )]
(Uc - Ud) ' nTEM ' npc ' nosss
(14)
We obtain an expression of the capacity C of OSSS which is necessary to starting up and accelerate the ERS to some speed.
Using the expressions (10) and (14) we calculate energy for EPL2T starting up and appropriate for this storage system capacity.
Calculation and analysis results of the starting up energy of EPL2T
The multiple unit train EPL2T basically consists of 8 carriages: 2C+ 4M + 2T, i.e. 2 carriages with cabs, 4 motor carriages and 2 intermediate (trailer) carriages.
2
Table 1
The starting up energy of train EPL2T
V, km/h V, m/s w0, N/kN W0, N W , N tst, s 4t, m Aw , MJ 4, MJ At, MJ Capacity C , F
Case #1 Case #2
10 2,78 1,4667 8142,7 14471,6 3,71 5 0,074 2,36 3,04 0,517 0,414
20 5,56 1,7468 9697,7 16026,7 7,41 10 0,16 9,44 12 2,04 1,63
30 8,33 2,080 11549,2 17878,1 11,1 23 0,41 21,24 27,06 4,6 3,68
40 11,11 2,467 13697,2 20026,2 14,8 40 0,80 37,77 48,2 8,2 6,56
50 13,89 2,908 16141,6 22470,5 18,52 100 2,25 59,0 76,56 13,02 10,42
60 16,67 3,401 18824 25211,3 22,2 150 3,78 85,0 111,0 18,86 15,10
70 19,45 3,948 21919,8 28248,7 25,9 200 5,65 115,66 151,6 25,79 20,62
80 22,22 4,549 25253,6 31582,5 29,63 300 9,47 151,1 200,7 34,13 27,30
It is necessary to set the starting up speed from zero to 10...80 km/h. The formula calculation (10) starts from evaluation of the energy Aw (V) which is consumed on overcoming the main forces of the train running resistance (2)-(9).
According to the experimental results [7], the main equation of the running resistivity in the range of V = 30...130 km/h is:
wO = 1,24 + 0,02 • V + 0,000267 • V2.
To determine the additional running resistance Wfr by expressions (6) and (7) we obtain the resulting running resistance using expression (8). According to [4], the carriages of the fully loaded train have the next weights: carriages with cabs -63,4 t, motor carriages - 78,6 t, intermediate carriages - 62,7 t. Therefore the weight of two carriages with cabs is 63,4 • 2 = 126,8 t, and values in
formula (7) are m0 = 15,85 t, Wfr = 1,225 N/kN . The weight of four motor carriages is 314,4 t and coefficients are m0 = 19,65 t, Wfr = 1,05 N/kN . Finally, weight of two intermediate carriages is 125,4 t and coefficients are m0 = 15,675 t,
Wfr = 1,24 N/kN .
So the mean square value of the specific additional running resistance Wfr in formula (8) equals 1,14 N/kN.
Then the additional running resistance Wfr, according to (6), is equal to 6328,94 N.
In the process of determining Ast , the formula
(10) uses the efficiency of TEM type 1DT.003.L8U1 which is equal to 0,915 [4]. The efficiency of pulse converter [8-10] and on-board supercapacitor storage system is 0,9 [9]. The results of calculations are given in Table 1. The calculations are made for two cases: the first is for
Uc = 3960 [V], Ud = 1980 [V]; the second is when Uc = 3960 [V], Ud = 990 [V]. In both cases,
V
the starting up time is defined as tst = —, where
a
a = 0,75 m/s2 is the train acceleration [7]. The distance passed by train in starting up period lst is taken from [7] Fig. 5.4 with respect to time tst.
From table 1, the train starting up from zero speed to 10...80 km/h requires the energy from 3,04 to 200,7 MJ. Practical estimation of the amount of energy was performed for EPL2T in the process of operation in the section Dnipropetrovsk-Piatykhatky of Prydniprovsk railway. These results are presented in table 2 and show the speed ranges which can be obtained after stopping.
Table 2
The starting up energy of train EPL2T
Name of the stop/station, where the train starts recuperative braking Stored energy, MJ The possible final speed after starting up, km/h
165 km 50,27 40
160 km 50,67 40
Dniprodzerzhynsk 69,7 45
Voskobinia 71,3 50
139 km 4,05 10
Verhniodniprovsk 38,9 35
128 km 68,62 45
125 km 69,1 45
119 km 59,52 48
114 km 42,2 35
Hranovo 94,2 55
104 km 105,1 60
Vilnohirsk 79,2 52
Zhelezniakovo 150,1 70
88 km 22,1 30
77 km 41,2 35
© Kostin M. O., Nikitenko A. V., 2015 ISSN2307-4221 EneKmpu^imtyH mpaHcnopmy, № 9. - 2015. 83
А* С,
Fig. 1. Graphs of the starting up energy and storage system capacity with respect to the train speed EPL2T
Conclusions
1. Theoretical analysis shows that the additional running resistance should be taken into consideration in the calculations of starting up and acceleration energy of ERS.
2. The values of energy starting up and capacity of on-board supercapacitor storage system increase parabolically with the increasing of the moving speed.
3. The proposed autonomous (off-line) recuperative braking can be fully obtained, but the final speed of the train is different and depends on the track conditions and the quantity of stored energy.
4. The using of stored energy allows to reduce the energy consumption in traction mode on 18...25%.
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In the last 20 ... 25 years the volume of recuperated electric energy is less than 2% of the consumed by traction, while it is possible to return about 10 ... 15%. The main reason is unsatisfactory and inefficient usage of recuperated and transmitted energy to the power supply system. The paper proposes to solve this problem and induce the efficiency and the degree of recuperated energy of DC multiple unit trains by the usage of onboard supercapacitive storage system. The methods of the electric traction theory and the theory of pulse electrical engineering are used for the problem solving. The developed methodology allows to calculate the energy, which is required to starting up the multiple unit train EPL2T to some speed 10 ... 80 km/h after its stopping. Furthermore, the capacity of the on-board storage is calculated in two cases of storing recuperated energy. The novelty of the paper is the new method for estimating energy, which is required to starting up (after the stopping) the train to a certain speed. The analytical expression of the capacity of the on-board storage system was achieved and calculated for the previously estimated energy. For the first time it was found that the energy, which was saved by the on-board supercapacitive storage system, is sufficient to start up the train to some speed and reach the characteristic of full field of the traction motors. The proposed autonomous mode of recuperative braking allows, at first, to increase significantly the efficiency of energy recovery, and secondly, to reduce the weight and size parameters of on-board storage supercapacitors.
Key words: energy; resistance movement; recovery; starting up; speed; train; supercapacitor; on-board storage system; the kinetic energy.
Internal reviewer Kuznetsov V. G. External reviewer Shkrabets F. P.
УДК 629.423 : 621.3.024 : 621.333.4
Н. А. КОСТИН, А. В. НИКИТЕНКО (ДНУЖТ)
Кафедра «Электротехника и электромеханика», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна 2, к. 238 , г. Днепропетровск, 49010, Украина, тел. +380563731537, e-mail: nkostin@ukr.net , nikitenko.diit@gmail.com , ORCID: orcid.org/0000-0002-0856-6397, orcid.org/0000-0002-6426-5097
ЭНЕРГИЯ РАЗГОНА ЭЛЕКТРОПОЕЗДА ПОСТОЯННОГО ТОКА
За последние 20...25 лет объем энергии рекуперации электропоездов не превышает 2% от использованной на тягу, в то же время как возможно возвращать до 10.15%. Одной из причин такого состояния есть неудовлетворительное неэффективное использование электроэнергии, которая рекуперируется и передается в тяговую сеть. В статье предлагается повысить энергетическую эффективность и степень использования электроэнергии рекуперации пригородных электропоездов постоянного тока с помощью бортового емкостного накопителя. Для решения поставленной задачи использованы методы теории электрической тяги и импульсной электротехники, а также методики Правил тяговых расчетов. Изложена методика и численные расчеты электроэнергии, необходимой для разгона электропоезда ЕПЛ2Т после остановки до скоростей 10.80 км/час. Более того, выполнено оценку емкости бортового накопителя для двух случаев накопления энергии рекуперации. Научная новизна статьи заключается в том, что предложен и использован новый метод оценки энергии, необходимой для разгона (после остановки) электропоезда до некоторой скорости. Получено аналитическое выражение емкости бортового накопителя электроэнергии, необходимой для пуска электропоезда после остановки. Установлено, что накопленной в бортовом накопителе энергии достаточно для разгона электропоезда до скорости выхода на характеристику полного возбуждения. Предложенный автономный фазовый режим рекуперативного торможения позволяет, во-первых, значительно повысить эффективность использования энергии рекуперации, во-вторых, снизить массогабаритные показатели бортового емкостного накопителя.
Ключевые слова: энергия, сопротивление движению, рекуперация, разгон, скорость, электропоезд, суперконденсатор, бортовой накопитель, кинетическая энергия.
Внутренний рецензент Кузнецов В. Г. Внешний рецензент Шкрабец Ф. П.
УДК 629.423 : 621.3.024 : 621.333.4
М. О. КОСТИ, А. В. Н1К1ТЕНКО (ДНУЗТ)
Кафедра «Електротехшка та електромехашка», Днтропетровський нацiональнiй унiверситет залiзничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна 2, к. 238 , м. Днтропетровськ, 49010, Укра'на, тел. +380563731537, e-mail: nkostin@ukr.net. nikitenko.diit@qmail.com. ORCID: orcid.org/0000-0002-0856-6397, orcid.orq/0000-0002-6426-5097
В останш 20...25 роюв об'ем енергií рекупераци електропоíздiв не перевищуе 2% вщ затрачено! на тягу, в той час як можливо повертати до 10.15%. Одшею iз причин такого стану е незадовiльне неефективне використання електроенергп, що рекуперуеться i передаеться в тягову мережу. В статт пропонуеться пщ-вищити енергетичну ефектившсть i ступiнь використання електроенергií рекупераци примюьких електро-поíздiв постiйного струму за допомогою бортового емнiсного накопичувача. Для розв'язання поставлено! задачi використано методи теорií електрично! тяги та iмпульсноí електротехнiки, а також методики Правил тягових розрахунюв. Викладено методику i чисельнi розрахунки електроенергií, потрiбноí для розгону електропоíзда ЕПЛ2Т тсля зупинки до швидкостей 10.80 км/год. Бшьш того, виконано оцiнку емност бортового накопичувача для двох випадюв накопичення енергií рекуперацií. Наукова новизна статп полягае в тому, що запропоновано новий метод оцшки енергп, потрiбноí для розгону (тсля зупинки) електропо'|'зда до певноí швидкосп. Одержано аналiтичний вираз емностi бортового накопичувача електроенергп, необ-хiдноí для пуску електропо1зда пiсля зупинки. Встановлено, що заощадженоí в бортовому накопичувачi енергií достатньо для розгону електропо1зда до швидкостi виходу на характеристику повного збудження. Запропонований автономний фазовий режим рекуперативного гальмування дозволяе, по-перше, суттево тдвищити ефективнiсть використання енергп рекупераци, по-друге, знизити масогабаритш показники бортового емшсного накопичувача.
Ключовi слова: енергiя, опiр руху, рекуперашя, розгiн, швидкiсть, електропоíзд, суперконденсатор, бор-товий накопичувач, кiнетична енергiя.
ЕНЕРГ1Я РОЗГОНУ ЕЛЕКТРОПО1ЗДА ПОСТ1ЙНОГО СТРУМУ
Внутршнш рецензент Kuznetsov V. G.
Зовшшнш рецензент Шкрабець Ф. П.
