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Дослiджено режими роботи однофазного
активного випрямляча струму у випадку широт-но^мпульсног модуляцп по прямокутно-стутн-чатому закону i навантаження у виглядi тягового двигуна постшного струму. Розглянуто однофаз-ну мостову схему випрямляча з розрядним дюдом. Розроблено математичну модель випрямляча i визначено основш розрахунковi спiввiдношення для широтнонмпульсног модуляцп при прямокут-но-стутнчатш формi модуляцшного сигналу. На комп'ютернш моделi до^джено електромагнт-н процеси при трьох значеннях частоти модуляцп (900, 1200, 1800 Гц). Встановлено особливостi впливу глибини i частоти модуляцп на коефщент потужностi випрямляча i ступть спотворення синусогдальностi форми кривих напруги та струму в мережi живлення.
Двигун постшного струму на сьогодн зали-шаеться основним типом тягового двигуна маг^тральних електровозiв змтного струму напругою 25 кВ, 50 Гц в Украгн та в рядi тших крагн. Для живлення таких двигутв як правило застосовують випрямлячi на дюдах або тиристорах. Разом з тим вiдомо, що перетворювачi на повтстю керованих напiвпровiдникових при-ладах забезпечують бшьш високу енергетичну ефективтсть.
Проведен до^дження дозволили встановити, при яких значеннях частоти i глибини модуляцп забезпечуеться високий коефщент потужностi (бшьше 0,9) i мiнiмальнi спотворення синусогдаль-ностi форми напруги i струму в мережi живлення. Це дозволяе визначити рац^нальн тдходи до вибо-ру силових схем i алгоритмiв управлЫня активни-ми перетворювачами в тяговому електроприводi електровозiв. Ефективтсть тдвищення коефщ-ента потужностi i зменшення несинусогдальностi напруги та струму полягае, насамперед, в знижен-н витрат електроенергп на тягу погздiв.
За сукуптстю обраних критерпв порiвняння найбшьш прийнятним для реалiзацiг в тяговому електроприводi електровоза е активний ви-прямляч струму з частотою модуляцп 1200 Гц. Забезпечення високих енергетичних характеристик в широкому дiапазонi тягових навантажень може бути досягнуто в багатозоннш схемi такого перетворювача
Ключовi слова: активний випрямляч струму, коефщент потужностi, широтно^мпульсна
модулящя, математична модель -□ □-
1. Introduction
When choosing technical solutions for modern high-voltage converters used in the electric drive, it is necessary to seek for ensuring high power efficiency and electromagnetic compatibility with the mains supply [1, 2]. Economic power
©
UDC 621.314.5:629.423
|DOI: 10.15587/1729-4061.2018.1311501
ANALYSIS OF OPERATING MODES OF SINGLEPHASE CURRENT-SOURCE RECTIFIER WITH RECTANGULAR-STEPPED PULSE-WIDTH MODULATION
O. Krasnov
Leading Researcher* E-mail: uzdlines@gmail.com B. Liubarskyi Doctor of Technical Sciences, Professor Department of electrical transport and diesel
locomotive** E-mail: lboris1911@ukr.net V. Bozhko PhD, Senior Researcher* E-mail: bozhkovv81@gmail.com O. Petrenko PhD, Associate Professor Department of electrical transport O. M. Beketov National University of Urban Economy in Kharkiv Marshala Bazhanova str., 17, Kharkiv, Ukraine, 61002
O . D u b i n i n a Doctor of Pedagogical Sciences, PhD, Associate Professor Department of computer mathematics and data analysis**
E-mail: vovochka88@ukr.net R. N u r i i e v Postgraduate Student Department of electrical transport and diesel locomotive** E-mail: ramkhua@gmail.com *Department of railway infrastructure and traction Branch "Design and survey institute of railway transport" of Public Joint-Stock Company "Ukrainian zaliznytsia" Yevhena Kotliara str., 7, Kharkiv, Ukraine, 61052 **National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002
consumption by electric drives is achieved with optimum control of their operating modes [3]. Active transducers with pulse-width modulation (PWM) have such capabilities [4]. In particular, active current-source rectifiers (ACSR) are used as power sources for autonomous current inverters, as well as for regulating the speed of DC motors [5, 6]. Such
rectifiers can replace diode and thyristor converters used on the 25 kV, 50 Hz AC electric rolling stock for power supply of traction motors and auxiliary machines [7]. Therefore, theoretical studies and practical developments of active current-source rectifiers for railway electric traction systems will be relevant.
2. Literature review and problem statement
As it is fairly noted in [8, 10], the number of works dealing with single-phase active current-source rectifiers is insignificant for today. There are no studies related to the practical application of this class of rectifiers on the electric rolling stock. There are theoretical and pilot studies within the development of a new generation of traction converters for 25 kV, 50 Hz and 15 kV, 16% Hz AC commuter electric trains.
In [9], the control scheme and algorithm for the IGBT four-zone rectifier-inverter converter have been proposed (for the VL80R, 2ES5K electric locomotives). According to the results of pilot studies, the power factor of this converter was 0.95 in the entire load range. However, the converter uses phase control, which does not significantly increase the power factor and reduce the total harmonic current distortion of the electric locomotive.
In [8], the new control strategy for the ACSR based on active suppression of resonant phenomena introduced by the input LC filter and correction of unsinusoidality of the contact line current by direct line voltage measurement has been proposed and investigated. This system provides suppression of low-frequency voltage and current harmonics on the electric locomotive current collector.
In [10], the ACSR with a control system in which PI regulators of the rectified current and phase shift between the current collector voltage and the line current generate a reference signal on the ACSR input current has been considered. The other unit generates a compensation signal for the 3rd, 5th and 7th current harmonics. The sum of these signals is the reference for the PWM unit. The studies have been carried out at a modulation frequency of 2 kHz. The experiments have shown that the proposed control system reduces low-frequency distortion of current and approximates its waveform to sinusoidal, including at a distorted line voltage. The total harmonic current distortion (THDi) was 7.61...158.66 % without compensation and 2.75...16.03 % with compensation.
In [11], the operation of the active current-source rectifier (modulation frequency of 2 kHz) under unfavorable operating conditions of the line (voltage dips, jumps in voltage and load) in the traction mode has been investigated. In this case, the rectifier control strategy, which is based on the phase shift control with the active attenuation of line current harmonics has proved to be effective. The reference signal on the ACSR input current is formed by means of the PI power factor controller.
In [12], electromagnetic processes and the principle of constructing the automatic control system for the traction ACSR with constant PWM frequency have been investigated. In this case, the DC regulation has been carried out by shifting the modulating signal phase to form negative polarity sections in the rectified voltage waveform, as in zone-phase controlled thyristor rectifiers.
In [13], the scheme of "serial input, parallel output" of the active rectifier using PWM and high-frequency transformer has been developed. The control system provides regulation
and stabilization of the rectified voltage, as well as active filtering of the input rectifier current.
In [14], ripple elimination with double line frequency by setting a decoupling capacitor and a diode in the ACSR circuit has been proposed. However, this scheme is designed for low loads. The issue of the operability of such a scheme in traction electric drives will require additional research.
In [15], control characteristics of active current-source rectifiers, based on null and bridge circuits, with sinusoidal PWM have been obtained. However, in this case, the rectifier power factor when the load changes has not been evaluated.
Thus, the ACSR can perform the following functions:
- active filter, capable of operating with both inductive and capacitive cos 9;
- rectified voltage or current regulator (depending on the control system structure).
At the same time, the above works have not taken into account that the implementation of various PWM algorithms - trapezoidal, vector, etc., is possible in the ACSR [16]. In addition, it is of interest to compare power characteristics of the ACSR for different values of modulation depth and PWM frequency.
3. The aim and objectives of the study
The aim of the study is to analyze the operating modes of the single-phase active current-source rectifier as a rectified voltage regulator. The case of pulse-width modulation with the rectangular-stepped modulating signal at the ACSR load in the form of the DC traction motor is considered.
To achieve the aim, the following objectives were accomplished:
- to develop a mathematical model of the ACSR and to determine the main ratios for pulse-width modulation with the rectangular-stepped modulating signal;
- to study electromagnetic processes in the PWM active current-source rectifier at a modulation frequency of 900, 1,200 and 1,800 Hz, to evaluate the nature of the changes in its power factor;
- to evaluate the effect of the PWM frequency and modulation index on total harmonic distortion in the mains supply;
- to select the most suitable active current-source rectifier for further implementation in the traction electric drive.
4. Mathematical model of the active current-source rectifier and selection of criteria of its efficiency
We consider the electromagnetic processes in the single-phase active current-source rectifier on the example of the single-phase discharge diode bridge circuit (Fig. 1) in the rectification mode. The ACSR keys K1-K4 are fully controllable, with unidirectional current conduction. Each key consists of the series-connected IGBT transistor and the diode. Such a converter with minor modification of the power circuit can work in the inverter (regenerative) mode with the transfer of energy to the mains supply.
The AC mains supply in the design scheme (Fig. 1) is represented by equivalent EMF es, inductance Ls and resistance rs. The transformer parameters are: L\, r\, L2, r2 - total inductance and resistance of the primary and secondary windings of the transformer, respectively; M12 - mutual inductance between the primary and secondary windings. Parameters of the ACSR
and rectified current circuit: C - input filter capacity; Ed, Lj, rj - equivalent EMF, inductance and resistance. The scheme also indicates: uc - input filter capacitor voltage; ii, i2, iv, ic, ij -currents in circuit elements.
For the scheme (Fig. 1), the following system of equations can be written:
Fig. 1. Design scheme of the single-phase active current-source rectifier
es =\[2ES ■ sin rat,
(L + L)^ + M„^ + (r+ r)i -e = 0,
ls 1 dt 12 dt y s 1,1 s
di„
di1
L2 — + M12 — + r2i2 + uc = 0, dt dt
dt
-S 'u + L, — + r,i, + E, = 0,
c d 1, d d d '
S =
(s*=i )a(s;=i (s* =1 )a(s; =1
(si =0)a(s2* =0)A(S3* =0)A(S* =0)^0,
where are the switching functions of the ACSR keys. The EMF of the DC traction motor [17]:
Ed =
1-
Ud =tl
JV2u2 sin ede
V2u 2
£[cos ai - cos ßi ], (4)
U = 2.22U,
X(cos al - cos ßi )
(5)
The block diagram of the ACSR control system is shown in Fig. 2, and the PWM pulse-shaping circuits - in Fig. 3. IGBT transistor control pulses are generated at the moments of equality of the stepped modulating signal |xum (|- amplitude modulation index) and the reference sawtooth voltage uref with the clock modulation frequency fm. The waveform of the modulating and reference signals (Fig. 3) is assumed to be unipolar. The pulse-height distribution by the control system is carried out by controlling the sign of the sinusoidal signal u(t), synchronized with voltage u1. As a result, pulse alternating current iv is formed on the AC terminals a, x, and pulse rectified voltage uj - in the DC circuit.
_ ц,—
u(t)
0
AND
AND
* * S2 , S3
** Si , S4
Fig. 2. Block diagram of the ACSR control system
(1)
duc 1 .
~dt = C1' '
i = S 'id, L - i - i = 0.
It follows from (1) that the rectified voltage uj=S*uc and the input current iv depend on the state of the ACSR keys. This state is determined by the unit switching function S *:
(2)
(3)
where ce is the design constant of the engine; ®=f(Id) is the magnetic flux, Wb; n is the engine speed, rpm.
The average value of the rectified voltage, regulated by the pulse-width modulation method, can be calculated from the formula [18]:
Fig. 3. Pulse-shaping circuits with PWM with the rectangular-stepped modulating signal: Uref — reference voltage amplitude; uref — reference voltage; um —modulating
voltage; Tm — pulse-width modulation period; s* — ACSR switching function; xi — relative pulse duration; t0 — relative pause duration; u — voltage; œ — angular line frequency; t — time
The modulating signal is an approximation of a sine wave of the form f(t)=|sin rot| by a step function [16]. In each PWM period, Tm= 1/fm, the sine wave segment is replaced by a straight line segment. Such a signal can be characterized by the following parameters [19]: Um - modulating voltage amplitude; Q{ - phase angle of the ith step A0 - discrete step of changes in the phase angle; i=1...n - step number; n - number of steps.
In general, there can be any number of steps of the modulating voltage. However, for convenience of the mathematical description of the PWM algorithm, we assume that the number of steps is equal to the number of modulation periods. Then for iiot=0...n we have:
where a;, ^ are the angles of transition of transistors to the on and off states; n is the number of pulses per half-cycle T=n; 0=i»t.
The RMS voltage of the secondary winding of the transformer can be obtained from (4):
„ = 4 2 f
де=180° / n,
(6)
(7)
where f is the line frequency, Hz; fm is the modulation frequency, Hz.
r
e
t
>
<
П
Let us write formulas for determining the ith value of the angle 0 and the modulating voltage um(0):
Ud = ^(cos-cosp1) +... + (cosa9 -cosp9)J. (16)
6¿ = i AG;
u (e) = <|(0sin G, Um ( ) {(n/2 <G<n)^|aUm ■ sin (e-AG).
(8) (9)
As can be seen from Fig. 3, the value of the modulating signal on the PWM period is proportional to the relative pulse duration on the same period. Let us denote this value by T1, and the relative pause duration t0. If we assume Um=1, then t and t0 can be determined by the formulas:
(0 <G<n/2)^|a-sin G, [(n /2 <G<rc)^|a-sin (G-AG);
T0 =1
(10)
(11)
Thus, in the PWM under consideration, the ACSR control pulses are formed according to the principle similar to the vector PWM of three-phase active converters [20]. As an example, Table 1 presents the results of the calculation of PWM parameters at /m=900 Hz, |=1.
Table 1
Results of calculation of PWM parameters (/„,=900 Hz, |j=1)
i 1 2 3 4 5 6 7 8 9
e* 20° 40° 60° 80° 100° 120° 140° 160° 180°
0.342 0.643 0.866 0.985 0.985 0.985 0.866 0.643 0.342
T0 0.658 0.357 0.134 0.015 0.015 0.015 0.134 0.357 0.658
At the repetition period T=n, the modulating voltage can be represented as the following sequence of steps:
Um(G)=
(0 < G < G1 J^T. (G1 < G < G2
H 1/
t(G
(12)
(6S-i <e<es (es ).
The reference signal of a unipolar sawtooth waveform:
U„
f (t ) = ^
sin I —— t + — ' 2 2
(13)
where rom=2n/m is the angular modulation frequency, rad/s.
Switching functions of ACSR keys:
[(U2 > 0)A(Um " Uref > 0H 1
(u2 > 0) a (um - uref < 0) ^ 0;
(u2 < 0) a (um - uref > 0) ^ 1, (u2 < 0) a (um - uref < 0) ^ 0.
(14)
(15)
Regulation of the ACSR rectified voltage is carried out by changing the modulation index According to the formula (4) for /m=900 Hz, n=9 the average value of the rectified voltage:
Taking into account the symmetry of the rectified voltage waveform:
Ut A x n
x[2 (cos a1 - cos P1 +.. + cos a3 - cos P3) +
+3(cos a4 - cos P4)]. (17)
Similarly, for /m=1,200 Hz, n=12:
Ud = l~2(cos a1 - cos P1 +... + cos a 6 - cos P6 )]. (18)
n
Equations (1)-(3), (6), (7), (10)-(15) are a mathematical model of the active current-source rectifier. To solve them, the MATLAB model, shown in Fig. 4 is developed. Elements of the power part of the ACSR model are units of the traction transformer TT, input filter C/, active current-source rectifier ACSR and EMF of the traction motor Ed (Fig. 4, a). The control system model consists of shaping units of the modulating voltage U mod, reference voltage U_op, sinusoidal signal Usinhr, synchronized with voltage U1, comparison operators «>», «<» and logical elements AND. The input signals of the control system are the PWM frequency F mod and the modulation index M, and the output signals are IGBT pulse control signals S01, S02.
In the research, the following parameters of the model were adopted: the traction substation with the 40 MV-A transformer, line section of 10 km, the power of the traction transformer of 4.35 MV-A, powered by the ACSR of a single traction engine DTK-820 of electric locomotives 2EL5 Parameters of the mains supply: Es=25,000 V; Ls=0.022922 H rs=1.7597 ohms. Transformer parameters: Li=57.278573 H n=0.314 ohms; U2=1260 V; L2=0.145497 H; r2=0.00351 ohms Mi2=2.882512 H. Parameters of the rectified current circuit Ld=0.00957 H; rd=0.084174 ohms. Electromagnetic processes in the ACSR were investigated for three values of modulation frequency - 900 Hz, 1,200 Hz and 1,800 Hz. The modulation index varied within |=0.2...1.
As the ACSR efficiency criteria, determined in virtual experiments, the following indicators were selected:
- average rectified voltage ( Ud, V);
- power factor, measured at the terminals of the primary winding of the transformer (Kp);
- total harmonic voltage distortion u (Ku, %);
- total harmonic current distortion i\ (Kj, %).
The power factor Kp was calculated by the formula:
ÍT \ I (T \ T
Kp = J Ujijdt /J J u2dt J i12dt
I0 J V U ) V0 )
(19)
The average power factor Kap in the entire range of regulation:
Kp =
S Kp
>1
/ m,
(20)
where j=1...m is the number of the experiment; m is the number of measurements.
b
Fig. 4. Model of the active current-source rectifier in MATLAB: a — power part; b — control system
5. Results of the study of the active current-source rectifier with rectangular-stepped pulse-width modulation
It is known that the capacity of the ACSR input filter is selected on the basis of the permissible magnitude of the capacitor voltage fluctuations [18]. Probably, it is necessary to consider also that the reactive power consumption increases with increasing capacity.
With the help of the developed MATLAB model, the calculation of power factor for different capacity values in the nominal load mode (|=1) was made. The capacitor capacity varied within 200...600 |F. As a result, the dependence of the power factor Kp on the input filter capacity C at a modulation frequency of 900, 1,200 and 1,800 Hz was obtained (Fig. 5). As can be seen from this dependence, the largest power factor is provided at C-270...360 |F. For further calculations, the capacitor capacity was assumed to be C=360 |F at a frequency of 900 Hz and 1,200 Hz, C=300 |F at a frequency of 1,800 Hz.
Fig. 6 shows the wave forms of electromagnetic processes in the ACSR at /m=1,200 Hz; |=1. Since the discharge diode VD0 is used in the ACSR circuit, the rectified voltage waveform has the form of a sequence of positive polarity pulses. Voltage u2 at the terminals of the secondary winding of the transformer has pulsations, the amplitude of which is limited by the capacity of the ACSR input filter capacitor. Current i2 is non-sinusoidal and contains higher harmonics. Current iv has a pulse form. Voltage u at the terminals of the primary winding of the transformer is practically sinusoidal, and current i\ is
non-sinusoidal and has a close-to-zero phase shift relative to the voltage waveform u\. The nature of electromagnetic processes at /m=1,200 Hz; ^=0.6 (Fig. 7), in general, is similar.
0.975
- /1
/ /2
200 300 400 500 C, ^F
Fig. 5. Dependence of the power factor Kp on the ACSR
input filter capacity C: 1 - fm=900 Hz; 2 ■ 3 - fm = 1,800 Hz
fm = 1,200 Hz;
Tables 2-4 present the results of computer simulation of the ACSR. The relative value of rectified voltage Uj/Uj0 (Uj0=1,134 V is the nominal value of the average rectified voltage of the uncontrolled rectifier) does not exceed 0.84, and the ratio Uj/Uj0 decreases with increasing PWM frequency In order to obtain large values of Uj, it is necessary to transfer the ACSR to the over-modulation mode (|>1) or to perform the secondary winding of the transformer for the larger nominal voltage U2.
Kp, r.u
u, V; i, A 2,000 r 1,500 1,000 500 0
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
u, V; i, A 2,000 p— 1,500 i. 1,000
„L.
Ik
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
u, V; i, A 2,000
-2,000
-
«2
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
u, kV 40
20 0
-40
«1
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
1,000 500 0
-500 -1,000
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
i, A 20 0
-4i............;............i......^ i ; I - WYV" 1 f, s
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
7 «1
u, kV 40 r
200;
-20-
-40U-1-i-""-i """"-1-i-1-- t, s
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
i, A 50
0
-50
0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 1.000
Fig. 6. Electromagnetic processes in the ACSR at fm=1,200 Hz; |j=1: a — rectified voltage ud and current id; b — voltage u2 and current i2 of the secondary winding of the transformer; c — ACSR input current iv; d — voltage of the primary winding of the transformer ui; e — current of the primary winding of the transformer i1
According to Tables 2-4, the average power factor was: Kap=0.879 (900 Hz), Kap=0.884 (1,200 Hz), Kap=0.932 (1,800 Hz).
Table 2
Results of the ACSR simulation (fm=900 Hz, C=360 |F)
v, km/h M Ud, V kp KU % Kb % Ud/Ud0
30 0.2 195 0.623 0.43 11.82 0.17
35 0.4 389 0.857 1.03 21.36 0.34
40 0.6 581 0.941 1.60 23.39 0.51
45 0.8 767 0.984 1.68 14.48 0.68
50 1.0 950 0.991 1.74 13.19 0.84
Based on the results of the experiments, the dependences of total voltage (Fig. 8) and current (Fig. 9) harmonic distortion of the primary winding of the transformer on the modulation index are constructed.
Fig. 7. Electromagnetic processes in the ACSR at fm=1,200 Hz; |=0.6: a — rectified voltage ud and current id; b — voltage of the primary winding of the transformer u1; c — current of the primary winding of the transformer i1
Table 3
Results of the ACSR simulation (fm=1,200 Hz, C=360 |F)
v, km/h M Ud, V Kp Ku, % Ki, % Ud/Ud0
30 0.2 192 0.622 0.29 6.50 0.17
35 0.4 383 0.864 0.68 11.97 0.34
40 0.6 573 0.955 1.04 14.05 0.51
45 0.8 759 0.987 1.15 10.37 0.67
50 1.0 941 0.993 1.28 10.75 0.83
Table 4
Results of the ACSR simulation (fm=1,800 Hz, C=360 |jF)
v, km/h M Ud, V Kp Ku, % Ki, % Ud/Ud0
30 0.2 187 0.793 0.22 5.09 0.16
35 0.4 374 0.908 0.49 7.93 0.33
40 0.6 560 0.973 0.74 9.12 0.49
45 0.8 743 0.992 0.84 8.44 0.66
50 1.0 924 0.996 0.93 8.55 0.81
Ku, %
1.00 0.60 +
0.20
X 1
0.20
0.40
0.60
0.80
p, r.u.
Fig. 8. Dependence of the total harmonic voltage distortion KUof the primary winding of the transformer on the modulation index p: 1 - fm=900 Hz; 2 - fm=1,200 Hz; 3 - fm=1,800 Hz
t, s
t, s
a
a
t, s
t, s
b
b
t, s
c
c
d
e
K, %
24 --
20 16 12 8 4
/1
^Z /2
---
3
0.20 0.40 0.60 0.80 n, r.u.
Fig. 9. Dependence of the total harmonic current distortion K/ of the primary winding of the transformer on the modulation index p: 1 - fm=900 Hz; 2 - fm=1,200 Hz; 3 - fm=1,800 Hz
6. Discussion of the results of the study of the active current-source rectifier
As can be seen from Tables 2-4, the power factor of the ACSR for all selected PWM frequencies is 0.62...0.99, and the value of more than 0.9 is provided with the modulation index of |>0.5. It should be noted that as the modulation frequency increases, the power factor increases over the entire load range, while compensation of inactive power components requires the smaller input filter capacity C.
In the paper, only a preliminary selection of the capacitor capacity C was made. The development of a technique for determining the ACSR input filter parameters, taking into account two criteria - the magnitude of the capacitor voltage fluctuations and reactive power consumption - is beyond the scope of the paper and is the subject of further research.
The total harmonic voltage distortion Ku in all considered cases does not exceed 2 %, and at a PWM frequency of 1,800 Hz - no more than 1 %; it increases with increasing modulation index and decreases with increasing PWM frequency
The nature of changes in the total harmonic current distortion KI is different: it reaches the maximum value in the modes where the pulse and pause intervals are approximately equal, i. e., for |=0.5...0.6. As the PWM frequency increases, there is a significant reduction in the total harmonic current distortion: if the maximum value of Ki at a frequency of 900 Hz is 23.39 %, then at a frequency of 1,800 Hz it is 9.12 %. According to this indicator, the ACSR with a modulation frequency of 900 Hz doesn't virtually differ from the traction thyristor converter, for which KI is about 20...30 % with the rectangular current waveform [21]. However, the current waveform distortion in the thyristor converter is
determined mainly by low-frequency harmonics (3rd, 5th, 7th), while in the ACSR the greatest influence on such distortion is exerted by high-frequency harmonics with frequencies close to the PWM frequency (see the current waveform i1 in Fig. 6, e). Given that the considered ACSR operates as a DC regulator, and not as an active filter, the problem of compensation of higher harmonics of the input current requires a separate consideration.
Thus, in the ACSR, the PWM algorithm affects the current waveform to a greater extent. Therefore, when developing automatic control systems for rectifiers of this class, devices should be provided that ensure the input current waveform correction.
The results of the experiments allow concluding that, according to the set of selected comparison criteria, the ACSR with a modulation frequency of 1,200 Hz is considered the most suitable for implementation in the traction electric drive of the electric locomotive. It seems promising to develop a multi-zone converter on the basis of the ACSR and to study its operation in the traction electric drive of the AC electric locomotive with collector traction motors.
7. Conclusions
1. The mathematical model of the active current-source rectifier for the case of single-phase bridge circuit with a discharge diode and load in the form of DC traction motor is developed. The main ratios for pulse-width modulation with the unipolar rectangular-stepped modulating signal are determined. To solve the differential and logical equations describing the operation of the ACSR power part and control system, the MATLAB model is developed.
2. Electromagnetic processes in the rectification mode at three PWM frequencies (900, 1,200, 1,800 Hz) are studied. It is found that when the modulation index is varied within 0.2...1, the power factor of the ACSR is 0.6...0.99 regardless of the modulation frequency.
3. With pulse-width modulation in the active current-source rectifier, the total harmonic voltage distortion Ku in all cases does not exceed 2 %. The choice of a higher PWM frequency leads to an improvement of the AC waveform in the mains supply, but the use of voltage transformer is somewhat degraded.
4. According to the set of selected comparison criteria, the ACSR with a modulation frequency of 1,200 Hz is considered the most suitable for the implementation in the traction electric drive of the AC electric locomotive. The provision of high power characteristics in a wide range of traction loads can be achieved in the multi-zone circuit of such a converter, which should be taken into account in further research.
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