Power Quality Analysis of Traction Supply Systems with High Speed Train Cai-fei SHENG Yu-jie LIU Fei LIN Xiao-jie YOU Trillion Q Zheng School of Electrical Engineering Beijing Jiaotong University Beijing, China
[email protected] Abstract—The characteristic of harmonic currents of high speed train is significantly different from DC-drived locomotives. The rectifier of CRH5 Electric Multiple Units (EMUs) in China is researched in this paper.The principle of four-quadrant converter and its predictive current control strategy are studied. The formula of fundamental and harmonic currents of the parallel two-level four-quadrant converter is given under different power and grid voltage based on double Fourier Transform Method. Therefore the distribution characteristics of harmonic currents are analyzed. The simulation software based on Matlab / Simulink is developed for harmonic analysis of CRH5 EMUs. With different traction power, braking power and traction grid voltage, the harmonic currents of EMUs injecting to the traction grid are studied and compared. This work is supported by State Grid Corporation of China (SGKJ[2007]102)
In this paper, the principle of four-quadrant converter(4QC) and its control strategy of CRH5 EMUs are studied. The formula of fundamental and harmonic currents of the parallel two-level four-quadrant converter is given based on double Fourier Transform Method.The software which is used to calculate and analysis the harmonic current is developed by the simulink module of Matlab. II.
Index Terms—power quality; high speed train; harmonic currents; double Fourier Transform ;simulation
I.
measured results showed that 3th, 5th and 7th low harmonic content of grid current were significantly reduced, but harmonic spectrum was widen, which means that usually there can be measured harmonic currents in the range of 1kHz ~ 10kHz. There are many accidents occurred since new types of EMUs and AC locomotives are put into use, which increase the harmonic currents, even cause the resonant over-voltage and pose a threat to the system's running security.
INTRODUCTION
In recent years, China's railway construction has entered a stage of rapid development. The railway electrification rate will reach 50% in 2020 and to carry more than 80% of the transportation capacity. In the planning and design of highspeed railway traction substations, power quality problems must be considered. Therefore the establishment of main circuit models for various high speed trains and the analysis of the harmonic characteristics of the traction load should be started. There are already many theoretical and simulation studies about "Shaoshan" series DC-drived locomotives in China which adopt thyristor rectifiers. And several large-scale field measurements works also have been organized to verify the simulation results [1-2]. After April 2007, with the introduction high speed train technology, CRH series EMUs and the HX series AC locomotives have been put into use, and will gradually replace the existing DC-drived locomotives. These EMUs and AC locomotives commonly adopt "AC-DC-AC"- type traction drive transmission system, whose AC-DC converter is the fourquadrant PWM rectifier -Its main circuit topology and electrical characteristics has a significantly difference from the previous "Shaoshan" series electric locomotive [5-9]. The
978-1-4244-2800-7/09/$25.00 ©2009 IEEE
MATHEMATICAL MODEL OF CRH5 EMUS
CRH5 EMUs are produced by the Changchun Railway Vehicles Factory. They are running from Harbin to Beijing and the maximum operating speed is up to 250km / h. CRH5 EMUs adopt 8 grouping, and may even be linked to run the two groups. EMUs have two relatively independent main traction systems, one of which is composed of three EMUs units and a trailer, the other of which is composed of two units EMUs and two trailers. A. Th e Principle of 4QC for CRH5 EMUs The four-quadrant converter of EMUs is single-phase fullbridge circuit, which enables two-direction flow of electrical energy, and to ensure that the power factor of the net side to approximate 1. Each unit of the EMUs adopts parallel twolevel by the two groups of four-quadrant converters through the transformer winding, through which can further reduce the harmonic currents of the grid side. Figure 1 shows the main circuit of CRH5 rectifier. Here, Ls and Rs are transformer secondary leakage and resistance, Cd is the support capacitor of the DC side, RL is equivalent to the load resistance, L2 and C2 constitute the second filter loop, uN is the secondary transformers voltage, us is the converter input voltage, udc is the DC voltage, i1 and i2 are the input currents of converter 1 and 2.The resonant frequency of L2 and C2 is two times of the fundamental frequency, which results the reduce of the 2th harmonic of DC voltage.
ICIEA 2009 2252
T1 RS
i1
D1
LS
a
us
T2
uN 25kV
T3
D2
T4
control system at present, including the DC voltage outer control ring and AC current inner control ring. The DC voltage outer control loop adopts the traditional PI regulator, whose output is the amplitude command of the AC current called im* .
D3 U0
b D4
L2
t
Udc i2
T5
LS
RS
* * im* = k p (u dc − u dc ) + k i ∫ (u dc − u dc )dt
Cd
conv er t er 1
D5
T6
D6
T7
T8
D7
RL
0
Here, u*dc is the DC command voltage, kp and ki are parameters of the PI regulator.
C2
The secondary transformers voltage uN can be written as follows:
D8
c onve r t er 2
Figure 1.
LS
RS
Here, us1 is the fundamental component of AC voltage, i11 is the current fundamental component of i1 , ω is the frequency of the grid voltage. The following formula is relative to the fundamental phase.
G G G G U N = U s1 + Rs I 11 + jωLs I 11 (1) Four-quadrant converter can achieve unity power factor in G G traction and braking conditions. As a result, U N 1 and I11 is in the same phase in traction condition. From formula (1) we can see JJK G the phase diagram in Figure 3 (a) - U S1 lags behind U N 1 . In regenerative braking condition, as to achieve the purpose of a stable DC voltage and unity power factor ,the phase between G G U N 1 and I11 should be 180 degrees, which is shown in Figure 3 G JJK (b) - U N 1 lags behind U S1 . We can see that as long as properly JJK control the amplitude and phase of U S1 , it will be able to control G the amplitude and phase of I11 . JG U JG U
JG UN
G I 11
β
R
JG U S1
(a) In traction condition Figure 3.
JG U S1
L
G I
frequency, i1* is the command current of converter 1. In order
JG U
(4
) The inner current control loop is in need to guarantee that the actual current track like the command value as shown in formula (4). To that end, this paper adopts the forecast current control method as follows [3]. The equations of the inductor current for the four-quadrant converter can be inferred from Figure 2: Ls
d i1 = uN − Rs i1 − us dt
(5
) Taking into account that RS is relatively small in the actual system, it can be negligible. The discrete form of formula (5) can be shown as follows. Ls
i1 (tk +1 ) − i1 (tk ) = uN (tk ) − us (tk ) TC
(6
)
JG UR
β
Here, U Nm is the peak of the grid voltage, U N is the RMS of the grid voltage, ωm is the modulation waveform angular
i1* = im* cos ω m t
Figure 2. Four-Quadrant Converter Equivalent Circuit
L
(3)
to achieve high power factor, the frequency of i1* should be the same as the frequency of the grid voltage. The expression of i1* is shown as follows.
uS
uN
JG U
u N = U Nm cos ω m t = 2U N cos ω m t
Principle Diagram of CRH5 Converter
Figure 2 shows the four-quadrant converter equivalent circuit. By switching devices appropriately through turn-on and turn-off control, the frequency of the converter input voltage us can be the same with that of the grid voltage.
i1
(2)
Here, TC is the control period. When the inductor current can track current orders in the next period, that is to say, there is i1 (tk +1 ) = i1* (tk +1 ) at the end of cycle control and the switching frequency of the four-quadrant converter is high enough, the control law can be inferred from formula (6) as follows.
N
11
us* (tk ) = uN (tk ) − Ls
(b) In braking condition
Phasor Diagram of Four-Quadrant Converter
i1* (tk +1 ) − i1 (tk ) TC
(7)
B. Contro Principle of Four-quadrant Converter In order to achieve high performance control, the fourquadrant converter of EMUs usually adopts a dual closed-loop
2253
After the voltage order is received, switches signals of driving the device are inferred according to the PWM algorithm. The control block of four-quadrant converter of EMUs is shown in Figure 4. Here, PLL is the phase-locked
loop, which is for access to phase of the grid voltage. Ideally, input voltages of the two interlaced PWM converters are the same order. But PWM converters will be arranged with phase shifts of 00 , 1800 in order to further reduce the harmonic content of the input current. u dc u *dc uN
PLL
θ
i *1
∞
∞
∑ ∑
us = MU dc cos(ωmt + β ) +
i1
i *m
PI
(10) Here, β is the phase of modulation wave. The expression of converter input voltage calculated by double Fourier Transform is shown as follows: fb (t ) = − M cos(ωmt + β )
m = 2,4... n = ±1, ±3...
u *s Ls/Tc
Jn (
PWM
cos
Figure 4. The Control Block of Four-Quadrant Converter
C. Harmonic Analysis of the Grid Current The grid harmonic distribution of Four-quadrant converter is primarily determined by the PWM modulation methods. For full-bridge circuit, the frequency spectrum of the harmonics is centered at two times of the carrier waveform angular frequency using bipolar frequency modulation. After the use of parallel two-level, its harmonics frequency spectrum of the input current will be similar to a single converter which doubles the switching frequency. The harmonic contents of the grid current for parallel two-level PWM converter have also been analyzed theoretically with double Fourier Transform. Figure 5 shows the modulation principle diagram of parallel two-level PWM rectifier which adopts RP-wave modulation method. Here, the amplitude of triangle carrier waveform is 1, α is the carrier waveform phase, ωc is the carrier waveform angular frequency. The mathematical formula of the carrier wave is shown as follows:
mM π m n ) cos π sin π cos(mωc t + nωmt + nβ + mα ) 2 2 2
(11) Here, the first part is the fundamental component of us and the rest is the harmonic components. J n ( x) is the n-order Bessel function [7]. Taking into account that the fundamental component of the input converter current and grid voltage u N have the same phase, the formula is shown as follows after Rs is neglected: (12)
MU dc cos β = 2U N
Then the RMS of the fundamental input converter current is shown as follows: I11 =
MU dc
ωS Ls 2
( MU dc )2 − 2U N 2
sin β =
2ωm LS
(13)
Because of the non-harmonic grid voltage, the n-order current harmonics component of the input converter current must meet the following voltage constraints: LS
di1n = −usn dt
(14)
Therefore, the input current of converter 1 is shown as follows:
2ωc 2α 2pπ (2p + 1)π ⎧ ) ⎪1 + 4 p − ( π t + π ) t ∈ [ ω , ω ⎪ c c f c (t ) = ⎨ + + 1)π 2 ω 2 α (2 1) π 2( p p ⎪ −3 − 4 p + ( c t + ) t ∈[ , ) ⎪⎩ π π ωc ωc
p=0，1，2，…
4U dc × mπ
i1 = ±
(8)
Jn (
( MU dc ) 2 − 2U N 2
ωm Ls
cos(ωmt ) −
∞
∞
∑ ∑
m = 2, 4... n = ±1, ±3...
4U dc × mπ LS (mωc + nωm )
mM π m n ) cos π sin π sin(mωc t + nωmt + nβ + mα1 ) 2 2 2
(15) Where "+" means the traction condition , and "-" means the braking condition. The input current of converter 2 can be calculated by the same method. i2 = ± Jn (
( MU dc ) 2 − 2U N 2
ωm Ls
cos(ωm t ) −
∞
∞
∑ ∑
m = 2, 4... n = ±1, ±3...
4U dc × mπ LS (mωc + nω m )
mM π m n ) cos π sin π sin( mωc t + nω mt + nβ + mα 2 ) 2 2 2
(16)
Figure 5.
Modulation Principle Diagram of PWM rectifier
As M is the amplitude modulation ratio, that is, and the modulation wave amplitude divide the carrier wave amplitude, the modulation waveform can be shown as follows. f a (t ) = M cos(ωm t + β )
Here, α1 and α 2 are respectively the carrier phase of converter 1 and converter 2. As the four-quadrant converter is running at the form of parallel two-level, α1 and α 2 have a difference of 180 degrees. If variable ratio of transformer is 1:1:1, the current of the original transformer is the sum currents of the two secondary transformers, so the total input current is shown as follows: i = i1 + i2 = ± Jn (
(9)
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2 ( MU dc ) 2 − 2U N 2
ωm Ls
cos(ωmt ) −
∞
∞
∑ ∑
m = 4,8... n = ±1, ±3...
mM π m n ) cos π sin π sin( mωct + nωm t + nβ + mα1 ) 2 2 2
8U dc × mπ Ls ( mωc + nωm )
(17)
500
It can be deduced by the active and reactive power of fourquadrant converter fundamental formula as follows: U N MU dc ⎧ sin β = I11U N sin β ⎪P = ωm Ls 2 ⎨ ⎪ ⎩ MU dc cos β = 2U N
? ?
? ?
c ur r en t
vo lta ge /k V
? ?
v ol t ag e
100 0 -100
? ? /A ? ? /kV
vo ? ltag ? e
200
cu rrent/A
? ? /kV v olt age /kV
? ? /A
300
100
0
-100
-200 -200
-300 -400 1.94
1.95
1.96
1.97 t/s
1.98
1.99
2
-300 1.94
1.95
1.96
1.97
1.98
1.99
2
t/s
(b) In braking condition Figure 6. Grid Voltage and Current Waveform in Traction and Braking Conditions of CRH5
(a) In traction condition
Figure 7 (a) and (b) shows the input currents frequency spectrum of converter 1 and 2, Figure 7 (c) shows the grid current frequency spectrum. For the input currents of converter 1 and 2, it is mainly centered at 2 times of the carrier frequency, which is 500Hz.But because of cancelling of the odd harmonics for 500Hz, it is mainly centered at 4 times of the carrier frequency, that is 1000Hz. What is more, the THD drops from 64.5 percent to 14.6 percent. We can see that the interlaced PWM converters can reduce the harmonic current content.
(18
) Further deduced: ⎧ 2 U N 4 + ( Pωm Ls )2 ⎪M = U NU dc ⎪ ⎨ Pωm Ls ⎪β = arcsin ⎪ 4 U N + ( Pωm Ls ) 2 ⎩
cur r ent ( % of f undam en at l )
(19) Put the formula (19) into the formula (17), the harmonic grid current can be calculated when the grid voltage and the power are known. .
f r e qu en c y/ H Z
The software to calculate and analysis the characteristic of harmonic current is developed by the simulink module of Matlab. First of all, the operating conditions are determined by the data provided by traction calculation software. Then set up the simulation parameters and run the simulation program. The results can be used for harmonic flow calculation of electric railway traction power supply system and transmission system. Simulation parameters of CRH5 EMUs are as follows: Rs = 0.039 Ω , Ls=2mH, Cd=9.01mF, C2=2.5mF, L2=1mH, u*dc=3600V, the carrier frequency of the four-quadrant converter is 250Hz. When the grid voltage is 25kV, simulate the model under the traction condition with 5500kW power and the braking condition with 5500kW power. The waveform of the grid voltage and current are shown as Figure 6 (a) and (b) . It can be seen that it can achieve unity power factor both in traction and braking conditions. Meanwhile the grid voltage and current have the same phase under the traction condition, but the opposite under the braking condition.
(a) The Input Current Frequency Spectrum of Converter 1
curr ent ( % of f undament al)
SIMULATING RESULTS
f r e qu en c y/ H Z
(b) The Input Current Frequency Spectrum of Converter 2
curr ent ( % of f undam ent al)
III.
c urre nt
200
cu r ent / A
This shows that when the four-quadrant converter is running at the form of parallel two-level, the harmonic characteristics is similar with the double-time switch frequency. As a result, interlaced PWM converters can reduce the harmonic grid current with the same switching losses in the same frequency. From the above formula, we can know that the harmonic grid current can be calculated when M and β are known.
300
400
f r eq u en cy/ H Z
(c) The Grid Current Frequency Spectrum Figure 7. Current Harmonic Analysis of CRH5 EMUs
When the traction power is 5500kW, simulate the model in conditions when the grid voltages are set to 20kV, 22.5kV, 25kV, 27.5kV and 29kV. Table I shows THDs of net current under different net voltage. Figure 8 shows grid current harmonic amplitudes under different grid voltages. As the grid voltage is increased, the fundamental current will be reduced under the same power. But due to a sharp increase of the current THD, the grid current is increased as the grid voltage is increased. Figure 8 shows that the amplitude of 13th, 15th and
2255
25th and 27th harmonic currents are increased more obvious as the grid voltage is increased, while the amplitude of 17th, 23th and 33th and 47th harmonic current remain unchanged. TABLE I.
THDS OF GRID CURRENT UNDER DIFFERENT GRID VOLTAGES
voltage (kV) THD (%)
20 9.82
22.5 11.62
25 14.54
27.5 17.01
29 17.96
Compared with the original “Shaoshan” series locomotives, EMUs use PWM rectifier, thus the power factor is close to 1 and the low harmonic content is obviously decreased, but the high-order harmonic content is slightly increased. In this paper, the preparation of the electric locomotives and EMUs simulation software, data interface can be called for other software to further analyze the spread law of the harmonic grid current in traction and the probability distribution of harmonic currents and so on. REFERENCES [1]
30
[2]
20 15
[3]
nu mb er
10
47 45 43 41 39 37 35 33 27 25 ? ? ? ? 23 21 19 17 15 13 on ic
? ?har?mon ? ?litud?e/A /A ic amp
25
ha rm
5 0 20
22. 5
25
27.5
29
[4]
v o lta g e /k V
? ? /v
Figure 8.
Harmonic Current Amplitude of Grid Current under Different Grid Voltages
[5]
When the grid voltage is 25kV, simulate the model in the condition when the traction power are set to 1375kW, 2750kW, 4125kW, 5500kW and the braking power are set to 1375kW, 2750kW. Table II shows THDs of grid current under different loads. Figure 8 shows the harmonic grid current amplitude under different loads. As the power is increased, the THDs of grid current will be reduced under the same grid voltage, while the harmonic grid current amplitude remains unchanged. In the same power, the THD of grid current in the braking condition is slightly smaller than in the traction condition. The main difference is caused by the AC equivalent resistance. TABLE II.
THDS OF GRID CURRENT UNDER DIFFERENT LOADS
1375 57.5
power(kW)
THD(%)
2750 29.2
4125 19.4
5500 14.5
-2750 28.8
-1375 54.2
25 20 15 10
4547 43 41 39 37 35 33 27 25 2123 19 17 15 13 ? ? ? ? h arm on ic nu m be r
? ?ha mr o?nic amp ? lit ud ? e/A? /A
30
5 0 1375
275 0
41 25
5500
-2750
-1375
p o w e r /k W
? ? /kW
Figure 9. Harmonic Current Amplitude of Grid Current under Different Loads
I.
CONCLUSION
This article studies the mathematical model and simulation of four-quadrant converter of CRH5 EMUs, specially studies the current distribution under the steady condition.
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[6]
[7] [8]
[9]
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