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An Impedance Measurement Method at Controlled Frequency Band for Both Traction Power System and Electric Train
2019 IFAC Workshop on 2019 IFAC Workshop Control of Smart Gridon and Renewable Energy Systems 2019 Workshop on Control of Smart and RenewableAvailable Energy Systems Jeju, IFAC Korea, JuneGrid 10-12, 2019 online at www.sciencedirect.com 2019 IFAC Workshop on Control of Smart and Renewable Energy Systems 2019 Workshop on Jeju, IFAC Korea, JuneGrid 10-12, 2019 Control of Smart Grid and Renewable Energy Systems Jeju, Korea, June 10-12, 2019 Control of Smart and Renewable Energy Systems Jeju, Korea, JuneGrid 10-12, 2019 Jeju, Korea, June 10-12, 2019
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IFAC PapersOnLine 52-4 (2019) 182–187 An Impedance Measurement Method at An Impedance Measurement Method at An Impedance Measurement Method at Controlled Frequency Band for Both Traction An Impedance Measurement Method at Controlled Frequency Band for Both Traction An Impedance Measurement Method at Controlled Frequency Band for Both Traction Power System and Electric Train Controlled Frequency Band for Both Traction Power System and Electric Train Controlled Frequency Band for Both Traction Power System and Electric Train Power System and Electric Train Pengyu Pan* Haitao Hu* Yi Zhou* Zhengyou Power System and Electric Train He* Pengyu Pan* Haitao Hu* Yi Zhou* Zhengyou He*
Pengyu Yi Pengyu Pan* Pan* Haitao Haitao Hu* Hu* Yi Zhou* Zhou* Zhengyou Zhengyou He* He* Yi Zhou* Zhengyou He* Pengyu Pan* Haitao Hu* *School of Electrical Engineering, Southwest Jiaotong University, *School ofChengdu, ElectricalChina. Engineering, Jiaotong University, (e-mail:Southwest [email protected]) *School Electrical Engineering, Jiaotong (e-mail:Southwest [email protected]) *School of ofChengdu, ElectricalChina. Engineering, Southwest Jiaotong University, University, *School ofChengdu, ElectricalChina. Engineering, Southwest Jiaotong University, (e-mail: [email protected]) Chengdu, China. (e-mail: [email protected]) Chengdu, China. (e-mail: [email protected]) Abstract: Electric railway systems occur instability and oscillation frequently for the mismatched Abstract: Electric railway systems occur instability frequently for the (VSC)-based mismatched impedances betweenrailway the traction power system (TPS) and and oscillation the voltage-source-converter Abstract: Electric systems occur instability and oscillation frequently for the mismatched impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based Abstract: Electric railway systems occur instability and oscillation frequently for the mismatched electric train. However, thetraction parameters of both TPS(TPS) and and electric train (hereinafter TPS-train) are not fully Abstract: Electric railway systems occur instability oscillation frequently for the (VSC)-based mismatched impedances between the power system and the voltage-source-converter electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are notpaper fully impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based known so that utilizing the mathematical deduction to quantify the impedances is difficult. This impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are not fully known so that utilizing the mathematical deduction to quantify the impedances is difficult. This paper electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are not fully gives a so method to measure the impedances at controlled frequency band. ATPS-train) chirp-PWM signal is electric train. However, the parameters of both TPS and electric train (hereinafter are notpaper fully known that utilizing the mathematical deduction to quantify the impedances is difficult. This gives a somethod to measure the the impedances atgate controlled frequency band. Amodules signal is known that utilizing the mathematical deduction to quantify the impedances ischirp-PWM difficult. This paper introduced and utilized to drive insulated bipolar transistor (IGBT) of disturbance known somethod that utilizing the mathematical deduction to quantify the impedances ischirp-PWM difficult. This paper gives a to measure the impedances at controlled frequency band. A signal is introduced and can utilized to drive the insulated gate bipolar transistor (IGBT) of disturbance gives method to produce measure impedances controlled frequency band. Amodules chirp-PWM signalThe is circuit,aa which athe broad at spectral excitation at controlled frequency band. gives method to measure thedesired impedances at controlled frequency band. Amodules chirp-PWM signal is introduced and utilized to drive the gate bipolar transistor (IGBT) of disturbance circuit, which can produce a desired broadthespectral excitation at controlled frequency band. after The introduced and utilized to calculated drive the insulated insulated gate bipolar transistor (IGBT) modules of disturbance impedances can be then with corresponding response voltages and currents introduced and can utilized to drive the insulated gate bipolar transistor (IGBT) modules of disturbance circuit, which a desired broad excitation at controlled frequency band. after The impedances cancan beproduce then calculated with thespectral corresponding response voltages and circuit, which produce desired broad spectral at and controlled frequency The connecting the disturbance toaa the tested system. Then, excitation the stability oscillations cancurrents beband. identified circuit, which can produce desired broad spectral excitation at controlled frequency band. The impedances can be then calculated with the corresponding response voltages and currents after connecting the disturbance to the tested system. Then, the stability and oscillations can be identified impedances can be then calculated with the corresponding response voltages and currents after using the measured electric train impedances. The proposed method is easy and tocan implement with impedances candisturbance beTPS thenandcalculated with the corresponding response voltages currents after connecting the to the tested system. Then, the stability and oscillations be identified using the measured TPS andtoelectric trainsystem. impedances. The proposed method easy tocan implement with connecting the disturbance the Then, the stability and be identified its simple hardware structure and tested software control, and also it gives a oscillations highis measurement accuracy. connecting the disturbance toelectric the tested system. Then, the stability and oscillations can be identified using the measured TPS and train impedances. The proposed method is easy to implement with its simple hardware structure and software control, and also it gives a high measurement accuracy. using the measured TPS and electric train impedances. The proposed method is easy to implement with Simulations verify the effectiveness of this impedances. method. using the measured TPS and electric train Thealso proposed method is measurement easy to implement with its simple hardware structure and software control, and it gives a high accuracy. Simulations verify thestructure effectiveness this method. its simple hardware and of software control, and also it gives a high measurement accuracy. its simple hardware structure and software control, and also it gives a high measurement accuracy. Simulations verify the of this method. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. system, All rightselectric reserved. Keywords: Impedance measurement, band, traction power train, Simulations verify the effectiveness effectiveness ofcontrollable this method.frequency Simulations verify the effectiveness this method.frequency band, traction power system, electric train, Keywords: Impedance measurement,ofcontrollable stability analysis. Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, stability analysis. Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, stability stability analysis. analysis. stability analysis. et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION et al. (2014) Roinila et al. (2018a)). Many(PRBS) researches based on the and pseudo-random binary sequences can 1. INTRODUCTION et al. (2014) and Roinila et al. (2018a)). Many researches based on the pseudo-random binary sequences (PRBS) can et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION detect the wide-band impedance with only once injection, Power electronic converters with a negative impedance et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION based on the pseudo-random binary sequences (PRBS) can detect thethe wide-band impedance with only once injection, based on the pseudo-random binary sequences (PRBS) can 1. INTRODUCTION Power electronic converters with a negative impedance such as maximum-length binary sequence (MLBS) in characteristic may converters cause stability issues in the electric based on the pseudo-random binary sequences (PRBS) can detect the wide-band impedance with only once injection, Power electronic with a negative impedance such astheet thewide-band maximum-length binary sequence (MLBS) in detect impedance with only once injection, characteristic may cause stability issues in the electric Roinila al. (2018a), and the discrete-interval binary Power electronic converters with a negative impedance railway systemmay (seeconverters Hu et al. (2018) Liaoinetthe al. (2017)). detectasthethewide-band impedance withsequence only once(MLBS) injection, such maximum-length in Power electronic with aand negative impedance characteristic cause stability issues electric Roinila al. (2018a), andet binary the discrete-interval binary such as et the maximum-length binary sequence (MLBS) in railway system (see Hu et al. (2018) and Liao et al. (2017)). sequence (DIBS) in Roinila al. (2014). The small-power characteristic may cause stability issues in the electric The TPS impedance determines the power system strength such as the maximum-length binary sequence (MLBS) in Roinila et al. (2018a), and the discrete-interval binary characteristic may cause stability issues inetthe electric Roinila railway system (see Hu et al. (2018) and Liao al. (2017)). sequence in Roinila et the al. (2014). The small-power et(DIBS) al. (2018a), and discrete-interval binary The TPS impedance determines the power system strength chirp signal introduced in Saar et al. (2013) and Min et al. railway system (see Hu et al. (2018) and Liao et al. (2017)). that a strong system can endure the negative impedance Roinila et al. (2018a), and the discrete-interval binary sequence (DIBS) in Roinila et al. (2014). The small-power railway system (see Hu et al. (2018) and Liao et al. strength (2017)). sequence The TPS impedance determines power system chirp signal introduced in Saar etbioelectrical al. (2013) and Min et al. intoRoinila et (2014). The small-power that a strong system can(constant endurethe the negative impedance is (DIBS) applied detect theal. impedance at The TPS determines thepower power system strength brought byimpedance electric train load), but a weak (2014) sequence (DIBS) in Roinila et al. (2014). The small-power chirp signal introduced in Saar et al. (2013) and Min et The TPS impedance determines thethe power system strength that a strong system can endure negative impedance (2014) is applied to detect the bioelectrical impedance at chirp signal introduced in Saar et al. (2013) and Min et al. al. brought by electric train (constant power load),research but a weak controlled frequency band, however being futile for the largethat a system strong system can endure theExisting negative impedance power can not tolerate that. has chirp signal introduced in Saar etbioelectrical al. (2013) and Min et al. (2014) is applied to detect the impedance at that a strong system can(constant endure power the negative impedance brought by electric train load), but a weak controlled frequency band, however being futile for the large(2014) is applied to detect the bioelectrical impedance at power system not Existing research has power/capacity brought by electric traintolerate (constant power load), but a weak electric grid.however shown that the can instability can bethat. restrained with improving (2014) is frequency applied toband, detect the bioelectrical impedance at controlled being futile for the largebrought by electric traintolerate (constant power load), but a weak power system can not that. Existing research has power/capacity electric grid. controlled frequency band, however being futile for the largeshown that the instability can be restrained with improving power system converter can not tolerate that. research has controlled the electronic control for aExisting matched impedance frequency band, however being futile for the largeelectric grid. power system can not tolerate that. Existing research has power/capacity shown that the instability can be restrained with improving This paper gives an grid. active method for measuring the electric the electronic converter control for a matched impedance shown that the instability can be(see restrained improving characteristic with power system Wen et with al. (2013)). The power/capacity power/capacity electric This paper atgives an grid. active method the shown that the instability can be for restrained with improving the electronic converter control aa matched impedance impedances controlled frequency bandfor for measuring both TPS and characteristic with power system (see Wen et al. (2013)). The the electronic converter control for matched impedance This paper an method for measuring the impedance characteristic can provide reference to design impedances atgives controlled frequency band both TPS and the electronic converter control for Wen aa matched impedance This paper gives an active active method forfor measuring the characteristic with power system (see et al. (2013)). The electrical train. A chirp-PWM signal is selected to drive impedance characteristic cana provide a reference tosystem. design paper atgives an active method forfor measuring the characteristic withcontrol power for system (see electric Wen et railway al. (2013)). The This impedances controlled frequency band both TPS and the electric train stable electrical train. A chirp-PWM signal is selected to drive at controlled frequency band for both harmonic TPS and characteristic with power system (see Wen et al. (2013)). The impedances impedance characteristic can provide a reference to design disturbance circuit that can excite large-power the electric train control for a stable electric railway system. impedances at controlled frequency band for both TPS and impedance characteristic can provide a reference to design electrical train. A chirp-PWM signal is selected to drive Thus, impedance measurement technique has toasystem. rapid electrical disturbancetrain. circuit that canvoltages excite chirp-PWM signallarge-power is selected tocandrive impedance characteristic can provide a reference design the electric train for electric TheA and currentsharmonic be Thus, impedance measurement has asystem. rapid disturbance. electrical train. A response chirp-PWM signallarge-power is selected to drive the electric train control control for aa stable stabletechnique electric railway railway disturbance circuit that can excite harmonic development. disturbance. The response voltages and currents canmain be disturbance circuit that can excite large-power harmonic the electric train control for a stable electric railway system. Thus, impedance measurement technique has a rapid captured to calculate the tested system impedances. The development. disturbance circuit that canvoltages excite large-power harmonic Thus, impedance measurement technique has a rapid disturbance. The response and currents can be captured to calculate the tested system impedances. The main disturbance. The response voltages and currents can be Thus, impedance measurement technique has a rapid development. in thisresponse paper are:voltages Impedance measurement can be classified into two categories contributions disturbance. The and currentsThe canmain be development. captured to calculate the tested system impedances. contributions in this paper are: captured to calculate the tested system impedances. The main development. Impedance measurement can be classified into two (passive and active methods) via whether thecategories injected captured to calculate the tested system impedances. The main contributions in this paper are: Impedance measurement can be classified into two categories 1) The spectrum injected in thisofpaper are: harmonic disturbance can be (passive and active methods) via whether thecategories injected contributions Impedance measurement can be methods classified into two disturbance is required. Passive utilize mathematical contributions in thisof paper are: 1) The controlled spectrum injected harmonic disturbance can the be Impedance measurement can be classified into two categories (passive and active methods) via whether the injected easily at the desired frequency band by disturbance is required. Passive methods utilize mathematical (passive and active methods) via whether the injected 1) The spectrum of injected harmonic disturbance can be analysis and numerical processing to estimate the impedance easily atmake the the desired frequency band by the The controlled spectrum of injected harmonic disturbance can be (passive and active methods) via whether the injected 1) disturbance is required. Passive methods utilize mathematical operators, and can impedance measurement more analysis andis numerical to estimate impedance 1) The controlled spectrum of injected harmonic disturbance can the be disturbance required. processing Passive methods utilizethe mathematical easily at the desired frequency band by without any disturbance injection (see Cobreces et al. (2009), operators, and can atmake impedance measurement easily controlled the the desired frequency band bymore the disturbance isnumerical required. processing Passive methods utilizethe mathematical analysis and to estimate impedance flexible. without any disturbance injection (see Cobreces et al. (2009), easily controlled at the desired frequency band by the analysis and numerical processing to estimate the impedance operators, and can make the impedance measurement more Yang et any al. and Ciobotaru et (2011)).the However, the flexible. operators, and can make the impedance measurement more analysis and(2010) numerical processing toal.estimate impedance without disturbance injection (see Cobreces et Yang et any al. (2010) and Ciobotaru et al.also (2011)). However, the operators, and can make the impedance measurement more without disturbance injectionand (see Cobreces et al. al.to(2009), (2009), flexible. accuracy can not be guaranteed, the speed obtain 2) The applied hardware structure and software control of flexible. without any disturbance injection (see Cobreces et al. (2009), Yang et al. (2010) and Ciobotaru et al. (2011)). However, the accuracy can not be guaranteed, and also the speed to obtain flexible. Yang et al. (2010) and Ciobotaru et al. (2011)). However, the 2) The applied hardware structure and software control of the impedance is slow due to its complex mathematical disturbance injection strategy is simple that makes the Yang et al. (2010) and Ciobotaru et al. (2011)). However, the accuracy can guaranteed, the to The applied hardware structure and software control of the impedance due to and its also complex mathematical accuracy can not notisbe beslow guaranteed, and also the speed speed to obtain obtain 2) disturbance injection strategy is simple that makes the 2) The applied hardware structure and software control of process. straightforward. accuracy can notisbeslow guaranteed, and also the speed to obtain implementation the impedance due to its complex mathematical 2) The applied hardware structure and software control of disturbance injection strategy is simple that makes the process. the impedance is slow due to its complex mathematical disturbance implementation straightforward. injection strategy is simple that makes the the impedance is slow due to its injection complexthat mathematical process. disturbance injection strategy is simple that makes the implementation straightforward. Active methods rely on disturbance can excite process. 3) The impedance at desired frequency band can be measured implementation straightforward. process. straightforward. Active methods rely on that calculating can excite implementation 3) Theonly impedance at desired frequency band can be measured harmonic response in disturbance the tested injection system for with once harmonic disturbance injection that can Active methods rely on disturbance injection that can excite 3) The impedance at desired frequency band can harmonic response inet al. the(2013), tested Roinila systemet for calculating Active methods rely on disturbance injection that(2014), can excite with only once harmonic disturbance injection that can 3) The impedance at desired frequency band can be be measured measured impedances (see Saar al. Min Active methods rely on disturbance injection that calculating can excite 3) harmonic response in the tested system for The impedance at desired frequency band can be measured only once harmonic disturbance injection that can impedancesresponse (see Saarinet al. al. (2014), Min with harmonic the(2013), tested Roinila systemet for calculating with only once harmonic disturbance injection can harmonic response in al. the tested Roinila system for calculating with only once harmonic disturbance injection that impedances that can impedances (see (see Saar Saar et et al. (2013), (2013), Roinila et et al. al. (2014), (2014), Min Min impedances (see Saar et al. (2013), Roinila et al. (2014), Min
Copyright © 2019, 2019 IFAC 199Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2019 responsibility IFAC 199Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 199 10.1016/j.ifacol.2019.08.176 Copyright © 2019 IFAC 199 Copyright © 2019 IFAC 199
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reduce the measurement time significantly compared with the traditional sine waveform sweep-based technique.
Vt( jw )
The rest of the paper is organized as follows: The impedance based stability analysis is introduced in Section II. Section III presents the harmonic excitation method at controlled frequency band. Section IV gives the impedance measurement of TPS and electric train, and then the stability analysis based on the measured impedances is discussed in detail in Section V.
A B C
110/220 kV
Rβ
ATS
Fα
ATS
Train
Fβ
Traction transformer
1
t
1 Zs ( jw ) / Zt( jw )
(2)
Zs ( j ) / Z t ( j )
(3)
In terms of the single-phase TPS, the equivalent impedance can be regarded as the positive-sequence impedance for the symmetric network. Thus, the positive-sequence impedance of VSC-based electric train is selected there to analyse the stability.
Tβ
Rα
Vs ( jw )
L( j )
Train impedance
27.5 kV
Tα
(1)
Based on the measured impedances, the stability of the TPStrain system can be determined by using the generalized Nyquist stability criterion. The impedance ratio can be defined in (3).
f /Hz
f /Hz
1 Zs ( jw ) / Zt( jw ) s
Vt( jw )
Zt ( j )
TPS impedance
1
s
The autotransformer (AT)-fed TPS is commonly applied in electric railway systems that can be seen in Fig. 1. The traction transformer can transform the three-phase 110/220 kV of utility power system to two single-phase 27.5-kV supply phases (α phase and β phase). The more introductions of this system can be seen in Pan et al. (2018). Zs ( j )
Vs ( jw )
where V ( j ) is the source voltage; Z ( j ) and Z ( j ) represent the measured TPS and electric train impedances in the frequency domain, respectively. (1) can be rearranged as follows:
2. IMPEDANCE BASED STABILITY ANALYSIS
Utility power system
183
The stability can be identified by studying the curves of the measured electric train impedance against the TPS impedance, and the phase difference at their magnitude intersection determines the phase margin (see Song et al. (2017) and Pan et al. (2018)).
SP
Catenary system
Fig. 1. AT-fed TPS and electric train.
PM The impedance-based stability researches of TPS-train system have been greatly accelerated in recent years. The equivalent impedance model of this single-phase system can be seen in Fig. 2 (see Roinila et al. (2018b)). TPS acting as a source can supply electric energy for the VSC-based electric train being deemed as a load. Instability and oscillation issues will occur in TPS-train system due to the mismatch of impedances versus frequency. However, solely utilizing the mathematical deduction to quantify the impedances appears to be difficult owing to unknown detailed parameters of both traction network and electric train. Thus, the measurementbased method to obtain the TPS-train impedances has a rapid development. Source
Zs (jw)
Zt(jw)
(4)
where PM is the phase margin; Zs ( j ) and Zt ( j ) represent the phases of the TPS impedance and the electric train impedance, respectively. 3. HARMONIC EXCITATION CONTROLLED FREQUENCY BAND 3.1 Chirp-PWM Signal Chirp signal is a sine-wave signal having the time-varying frequency, which is given by
ychirp (t )
Load
sin(2 ( f min
( f max
f min )t / T )t )
(5)
where f min and f max are the controlled minimum and
Zs ( j ) Vt ( j ) Vs ( j )
180
maximum frequency, respectively; T is the duration of the chirp waveform.
Zt ( j )
The desired spectrum distribution can be obtained via controlling the frequency f min and f max . The chirp-PWM is a novel PWM scheme, proposed in Uddin et al. (2012), being applied for brushless DC motor drive. In this research, chirpPWM signal can control the disturbance circuit presented in next section for exciting the harmonic disturbance at the interesting spectrum. A converting scheme from chirp signal to chirp-PWM signal is given by
Fig. 2. Equivalent impedance model of Fig. 1. According to the equivalent impedance model in Fig. 2, the voltage V ( j ) at the intersection of TPS and electric train can be expressed in (1). t
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ychirp (t ) ychirp (t )
0 0
3
(6)
1000 - 1500 Hz Magnitude (abs)
1 0
ychirp-PWM (t )
Chirp-PWM value should be converted to “1” when the corresponding chirp is larger than 0 (i.e., ychirp (t ) 0 ), besides, be converted to “0” with the chirp value smaller than 0 (i.e., ychirp (t ) 0 ). The detailed converting scheme is presented in Fig. 3 (Hu et al. (2019)).
2
1
0
0
500
1000 1500 Frequency (Hz)
2000
2500
Chirp-PWM signal
Magnitude
1
Fig. 5. The spectrum excited by the disturbance circuit with a controlled frequency band from 1000 Hz to 1500 Hz.
0
-1
Chirp-PWM signals can control the disturbance circuit for a desired broad spectral excitation. The spectrum distribution is designed by f min and f max . For a case, the f min is set as 1000 Hz, as well as the f max is set as 1500 Hz. The generated chirp-PWM signal is utilized to control the disturbance circuit, and the spectrum distribution excited by the disturbance circuit is shown in Fig. 5. It illustrates that the actual spectrum can spread at the designed frequency band 1000 – 1500 Hz. The large-power harmonic excitation at controlled frequency band can be utilized for measuring the impedance at designed frequency band with only once disturbance, which can greatly reduce the measurement time compared with the traditional sine-sweep method.
Chirp signal Time
Fig. 3. Converting scheme from chirp signal to chirp-PWM signal. 3.2 Disturbance Circuit A disturbance circuit presented in Fig. 4 can be applied to excite a large-power harmonic disturbance for measuring the tested system impedance. The detailed description and operating principle can be found in our previous research (Pan et al. (2018)). In detail, the primary-side of the stepdown transformer is connected between the catenary system and the rail, and the disturbance circuit is connected to the secondary-side. The disturbance circuit produces different frequency components with different driving signals of IGBTs. Moreover, all IGBTs are driven by the same control signal that can greatly simplify the control process. The time between the “ON” and “OFF” states of the IGBTs changes periodically. Meanwhile, the IGBT module 1 will disturb the positive period of the current, and the negative period is perturbed by the IGBT module 2 regularly. Catenary system 1
4.1 Impedance Measurement of TPS The disturbance circuit is connected to the measurement point of the TPS, and the impedance can be calculated with (7) to avoid the effect of the background harmonics (Pan et al. (2018)).
Zs ( j )
Chirp-PWM
0
Switch
Cs Smoothing capacitor
Snubber resistor
Excitation resistor
Us ( j ) Us0 ( j ) Is ( j ) Is0 ( j )
(7)
where Us ( j ) and Is ( j ) are the voltage and current of the measurement point in the frequency domain after imposing disturbance, respectively; Us0 ( j ) and Is0 ( j ) are the voltage and current in the frequency domain before imposing the disturbance, respectively. IGBT module 1
IGBT module 2
Transformer
4. IMPEDANCE MEASUREMENT OF TPS AND TRAIN
A detailed TPS model is built in MATLAB/SIMULINK based on the multiple transmission line (MTL) model presented in Hu et al. (2018) for the validation of proposed measurement method. The schematic of TPS simulation model is shown in Fig. 6.
Re
Rail
Fig. 4. The disturbance circuit to excite the harmonic disturbance.
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Seg me nt 1
Utili ty p ower system
Seg me nt 2
Theoretical value
A Z1n Y1n
110 kV
Disturb ance circuit
Z 2n Y1n
Y2n
Y2n
500 V
Zs
Tβ
Tα
Rβ
Rα
Magnitude (dB)
B C
27.5kV
MTL
MTL
Catenary system
Phase (deg)
Traction tran sformer
Fig. 6. Schematic of traction network simulation model using MTL.
60 40 20 0–1000
1000–2000 2000–3000 3000–4000 4000–5000
100 0 -100 0
Table 1 gives the simulation parameters of TPS model and 6 the simulation time step is set as Ts 110 s . For a given case, the harmonic excitation by disturbance circuit is controlled at 1000 – 1500 Hz and Fig. 7 shows the measured results. It can be seen that the measured impedance at the controlled frequency band 1000 – 1500 Hz is almost consistent with the theoretical value when out of that band is inaccurate since there is no enough harmonic excitation at these frequencies. In order to detect the TPS impedance at a broader band, e.g., 0 – 5000 Hz, we can have a segmental measurement every 1000 Hz (i.e., 0 – 1000 Hz, 1000 – 2000 Hz, 2000 – 3000 Hz, 3000 – 4000 Hz, 4000 – 5000 Hz,) for dispersing the harmonic disturbance energy, and Fig. 8 gives the measured result. The practical measurements can be seen in Hu et al. (2019)
Measured value
80
0
Fβ
Fα
185
1000
2000 3000 Frequency (Hz)
4000
5000
Fig. 8. The measured TPS impedance when specify frequency band at 0 - 10000 Hz with 2000 Hz measurement interval. 4.2 Impedance Measurement of Train Fig. 9 shows the equivalent model of electric train, which works with a dual-loop control method. The inductor current feedback acts as the inner loop and DC voltage feedback is the outer loop. The detailed parameters are given in Table 2. Lt
It
4QC
Cdc Rdc udc
Ut
Table 1. Simulation parameters of TPS Parameter Utility power system voltage Connection of traction transformer Voltage ratio of traction transformer The number of segments Voltage ratio of step-down transformer Excitation resistor Theoretical value
Value 220 kV V/x 220 kV/27.5 kV 10
PLL
i SOGI i dq
0
iq
id
id
L
PLL
uq
kii s k k pi ii s
iq
Current loop
L
dq
k pi
ud
u
SOGI PLL
5Ω
u
ud dq uq
PWM udc
k pv
PLL
27.5 kV/500 V
u
kiv s
* udc
Voltage loop k ppll
kipll s
0
1 s
PLL
Fig. 9. The train model including control.
Measured value
Magnitude (dB)
80
Table 2. Simulation parameters of train
60 40
0
C ontrolled frequ en cy ba nd
-20 200
Phase (deg)
Parameter The input voltage of train The input inductor of train Regulated capacitor DC load DC voltage reference Switching frequency PI parameters of current loop PI parameters of voltage loop
20
10 00–15 00 H z
0
-200
0
500
1000 1500 Frequency (Hz)
2000
2500
Value Ut = 1770 V Lt = 10 mH Cdc = 9 mF Rdc = 100 Ω udc* = 3000 V fs= 1250 Hz Kpi = 2, Kii = 2 Kpv = 0.5, Kiv = 2
The proposed disturbance method is utilized there to excite the harmonic responses for measuring the positive-sequence impedance of VSC-based electric train, which can be calculated by
Fig. 7. The measured TPS impedance when control the frequency band at 1000 - 1500 Hz.
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Zt ( j )
Pengyu Pan et al. / IFAC PapersOnLine 52-4 (2019) 182–187
Ut( j ) / I t( j )
Table 3. Simulation parameters of TPS-train system
(8)
Parameter TPS-side resistors TPS-side inductors TPS-side capacitors
where Ut ( j ) and It ( j ) are the voltage and current of the train input point in the frequency domain, respectively. For a given case, the harmonic excitation by disturbance circuit is controlled at 10 – 600 Hz and Fig. 10 shows the measured results. As it is seen, the measured train impedance curves are smooth and can be almost consistent with the theoretical value at the controlled frequency band 10 – 600 Hz.
100
Magnitude (dB)
100
Measured value
20
0
54 Hz
50
357 Hz
0
Phase difference is 174.2º
Phase difference is 186.6º
0 -100 0
100
200 300 Frequency (Hz)
0
400
500
-100 0
100
200 300 Frequency (Hz)
400
Fig. 12. The measured TPS-train impedances after increasing the network-side inductor from 1mH to 20 mH.
500
Mag (% of Fundamental) Mag (% of Fundamental)
Fig. 10. The measured converter impedance. 5. STABILITY ANALYSIS BASED ON MEASURED IMPEDANCE An equivalent TPS-train system shown in Fig. 11 is built in MATLAB/SIMULINK to verify the effectiveness of impedance measurement and stability analysis. Initially, the TPS-train system can remain stable as it operates with the parameters given in Table 3. At 1.5 s, an increase of the TPSside inductor L1 from 1 mH to 20 mH will weaken the TPS, and Fig. 12 gives the measured TPS-train impedances. The phase difference at the impedance magnitude intersection of 54 Hz is 186.6°. This negative phase margin illustrates that the unexpected harmonics around 54 Hz will occur in this system, which will oscillate the AC and DC voltages with 4 Hz (see Pan et al. (2018)). The actual unexpected harmonics are about around 53.5 Hz (see Fig. 13), which causes the actual oscillation at 3.5 Hz (see Fig. 14). Moreover, there is another weak-phase-margin magnitude intersection at 357 Hz (the phase difference is 174.2°), and the actual unexpected harmonics are around 356 Hz. These small deviations can be accepted. L1 C1
R2
L2
Zs Z t
30
t
1.5 s
t
1.5 s
50 Hz 20 10 0
50 Hz
30
53.5 Hz 20 10
356 Hz
0
0
100
200 300 Frequency (Hz)
400
500
DC Voltage (V)
Fig. 13. AC voltage spectrum when increase L1 from 1 mH to 20 mH. 4000
t
t
1.5 s
1.5 s
3000
Oscillation frequency is 3.5 Hz
2000 4000
AC Voltage (V)
R1 Ug
Train impedance TPS impedance
100 Phase (deg)
Magnitude (dB)
40
Phase (deg)
Theoretical value
Value R1 = 0.006Ω, R2 = 0.008Ω L1 = 1 mH, L2 = 2.5 mH C1 = 10 µF, C2 = 20 µF
Lt Cdc Rdc
C2
2000 0 -2000 -4000 0
PWM
0.5
1
1.5
2 2.5 Time (s)
3
3.5
4
Fig. 14. AC and DC voltage waveforms when increase L1 from 1 mH to 20 mH.
Fig. 11. Train-network simulation system.
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6. CONCLUSION This paper presents a method for measuring the TPS-train impedances that can be used to analyse stability for ensuring a safe and stable electric railway system. A disturbance circuit consisting of series–parallel IGBT modules is driven by the chirp-PWM signal that can excite the large-power harmonic disturbance at the controlled frequency band. Then, the detected voltage and current data can be utilized to calculate the tested system impedances. The measurement time is short for the just once disturbance injection and the controllable measurement frequency band makes this method more flexible. The simulations in MATLAB/SIMULINK verifies the effectiveness of impedance measurement and stability analysis. REFERENCES Cobreces, S., Bueno, E. J., Pizarro, D., Rodriguez, F. J., and Huerta, F. (2009). Grid impedance monitoring system for distributed power generation electronic interfaces. IEEE Trans. Instrum. Meas., 58(9), 3112-3121. Ciobotaru, M., Agelidis, V., Teodorescu, R. (2011). Line impedance estimation using model based identification technique. In Proc. IEEE Power Electron. Appl. Conf., 1-9. Hu, H., Tao, H., Blaabjerg, F., Wang, X., He, Z., and Gao, S. (2018). Train-Network Interactions and Stability Evaluation in High-Speed Railways--Part I: Phenomena and Modeling. IEEE Trans. Power Electron., 33(6), 4627-4642. Hu, H., Pan, P., Song, Y., and He, Z. (2019). A Novel Controlled Frequency Band Impedance Measurement Approach for Single-phase Railway Traction Power System. IEEE Trans. Ind. Electron., DOI: 10.1109/ TIE.2019.2896297. Liao, Y., Liu, Z., Zhang, G., and Xiang, C. (2017). Vehiclegrid system modeling and stability analysis with forbidden region-based criterion. IEEE Trans. Power Electron., 32(5), 3499-3512. Min, M., Land, R., Paavle, T., Parve, T., Annus, P., and Trebbels, D. (2011). Broadband spectroscopy of dynamic impedances with short chirp pulses. Physiol. Meas., 32(7), 945-958. Pan, P., Hu, H., Yang, X., Blaabjerg, F., Wang, X., and He, Z. (2018). Impedance Measurement of Traction Network and Electric Train for Stability Analysis in High-Speed Railways. IEEE Trans. Power Electron., 33(12), 1008610100. Roinila, T., Vilkko, M., and Sun, J. (2014). Online grid impedance measurement using discrete-interval binary sequence injection. IEEE Trans. Ind. Electron., 2(4), 985-993. Roinila, T., Messo, T., and Santi, E. (2018a). MIMOIdentification Techniques for Rapid Impedance-Based Stability Assessment of Three-Phase Systems in DQ Domain. IEEE Trans. Power Electron., 33(5), 40154022. Roinila, T., and Messo, T. (2018b). Online grid-impedance measurement using ternary-sequence injection. IEEE
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187
Trans. Ind. Appl., to be published. DOI: 10.1109/ TIA.2018.2825938. Saar, T., Reidla, M., Martens, O., Land, R., Min, M., and Herranen, H. (2013). Chirp-based piezo-impedance measurement. In Proc. IEEE 8th International Symposium on Intelligent Signal Processing, 83-86. Song, Y., Wang, X., Blaabjerg, F. (2017). Impedance-based high-frequency resonance analysis of DFIG system in weak grids. IEEE Trans. Power Electron., 32(5), 35363548. Uddin, W., Husain, T., Mitra, R., Ofori, E., Sozer, Y., and Husain, I., A chirp PWM scheme for brushless DC motor drives. In Proc. IEEE Energy Convers. Congr. Expo., (ECCE), 3317-3323. Wen, B., Boroyevich, D., Mattavelli, P., Shen, Z., and Burgos, R. (2013). Influence of phase-locked loop on input admittance of three-phase voltage-source converters. In Proc. 28th Annu. Appl. Power Electron. Conf., 897-904. Yang, J., Li, W., Chen, T., Xu, W., and Wu, M. (2010). Online estimation and application of power grid impedance matrices based on synchronized phasor measurements. IET Gener., Transm. Distrib., 4(9), 10521059.
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IFAC PapersOnLine 52-4 (2019) 182–187 An Impedance Measurement Method at An Impedance Measurement Method at An Impedance Measurement Method at Controlled Frequency Band for Both Traction An Impedance Measurement Method at Controlled Frequency Band for Both Traction An Impedance Measurement Method at Controlled Frequency Band for Both Traction Power System and Electric Train Controlled Frequency Band for Both Traction Power System and Electric Train Controlled Frequency Band for Both Traction Power System and Electric Train Power System and Electric Train Pengyu Pan* Haitao Hu* Yi Zhou* Zhengyou Power System and Electric Train He* Pengyu Pan* Haitao Hu* Yi Zhou* Zhengyou He*
Pengyu Yi Pengyu Pan* Pan* Haitao Haitao Hu* Hu* Yi Zhou* Zhou* Zhengyou Zhengyou He* He* Yi Zhou* Zhengyou He* Pengyu Pan* Haitao Hu* *School of Electrical Engineering, Southwest Jiaotong University, *School ofChengdu, ElectricalChina. Engineering, Jiaotong University, (e-mail:Southwest [email protected]) *School Electrical Engineering, Jiaotong (e-mail:Southwest [email protected]) *School of ofChengdu, ElectricalChina. Engineering, Southwest Jiaotong University, University, *School ofChengdu, ElectricalChina. Engineering, Southwest Jiaotong University, (e-mail: [email protected]) Chengdu, China. (e-mail: [email protected]) Chengdu, China. (e-mail: [email protected]) Abstract: Electric railway systems occur instability and oscillation frequently for the mismatched Abstract: Electric railway systems occur instability frequently for the (VSC)-based mismatched impedances betweenrailway the traction power system (TPS) and and oscillation the voltage-source-converter Abstract: Electric systems occur instability and oscillation frequently for the mismatched impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based Abstract: Electric railway systems occur instability and oscillation frequently for the mismatched electric train. However, thetraction parameters of both TPS(TPS) and and electric train (hereinafter TPS-train) are not fully Abstract: Electric railway systems occur instability oscillation frequently for the (VSC)-based mismatched impedances between the power system and the voltage-source-converter electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are notpaper fully impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based known so that utilizing the mathematical deduction to quantify the impedances is difficult. This impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are not fully known so that utilizing the mathematical deduction to quantify the impedances is difficult. This paper electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are not fully gives a so method to measure the impedances at controlled frequency band. ATPS-train) chirp-PWM signal is electric train. However, the parameters of both TPS and electric train (hereinafter are notpaper fully known that utilizing the mathematical deduction to quantify the impedances is difficult. This gives a somethod to measure the the impedances atgate controlled frequency band. Amodules signal is known that utilizing the mathematical deduction to quantify the impedances ischirp-PWM difficult. This paper introduced and utilized to drive insulated bipolar transistor (IGBT) of disturbance known somethod that utilizing the mathematical deduction to quantify the impedances ischirp-PWM difficult. This paper gives a to measure the impedances at controlled frequency band. A signal is introduced and can utilized to drive the insulated gate bipolar transistor (IGBT) of disturbance gives method to produce measure impedances controlled frequency band. Amodules chirp-PWM signalThe is circuit,aa which athe broad at spectral excitation at controlled frequency band. gives method to measure thedesired impedances at controlled frequency band. Amodules chirp-PWM signal is introduced and utilized to drive the gate bipolar transistor (IGBT) of disturbance circuit, which can produce a desired broadthespectral excitation at controlled frequency band. after The introduced and utilized to calculated drive the insulated insulated gate bipolar transistor (IGBT) modules of disturbance impedances can be then with corresponding response voltages and currents introduced and can utilized to drive the insulated gate bipolar transistor (IGBT) modules of disturbance circuit, which a desired broad excitation at controlled frequency band. after The impedances cancan beproduce then calculated with thespectral corresponding response voltages and circuit, which produce desired broad spectral at and controlled frequency The connecting the disturbance toaa the tested system. Then, excitation the stability oscillations cancurrents beband. identified circuit, which can produce desired broad spectral excitation at controlled frequency band. The impedances can be then calculated with the corresponding response voltages and currents after connecting the disturbance to the tested system. Then, the stability and oscillations can be identified impedances can be then calculated with the corresponding response voltages and currents after using the measured electric train impedances. The proposed method is easy and tocan implement with impedances candisturbance beTPS thenandcalculated with the corresponding response voltages currents after connecting the to the tested system. Then, the stability and oscillations be identified using the measured TPS andtoelectric trainsystem. impedances. The proposed method easy tocan implement with connecting the disturbance the Then, the stability and be identified its simple hardware structure and tested software control, and also it gives a oscillations highis measurement accuracy. connecting the disturbance toelectric the tested system. Then, the stability and oscillations can be identified using the measured TPS and train impedances. The proposed method is easy to implement with its simple hardware structure and software control, and also it gives a high measurement accuracy. using the measured TPS and electric train impedances. The proposed method is easy to implement with Simulations verify the effectiveness of this impedances. method. using the measured TPS and electric train Thealso proposed method is measurement easy to implement with its simple hardware structure and software control, and it gives a high accuracy. Simulations verify thestructure effectiveness this method. its simple hardware and of software control, and also it gives a high measurement accuracy. its simple hardware structure and software control, and also it gives a high measurement accuracy. Simulations verify the of this method. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. system, All rightselectric reserved. Keywords: Impedance measurement, band, traction power train, Simulations verify the effectiveness effectiveness ofcontrollable this method.frequency Simulations verify the effectiveness this method.frequency band, traction power system, electric train, Keywords: Impedance measurement,ofcontrollable stability analysis. Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, stability analysis. Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, Keywords: Impedance measurement, controllable frequency band, traction power system, electric train, stability stability analysis. analysis. stability analysis. et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION et al. (2014) Roinila et al. (2018a)). Many(PRBS) researches based on the and pseudo-random binary sequences can 1. INTRODUCTION et al. (2014) and Roinila et al. (2018a)). Many researches based on the pseudo-random binary sequences (PRBS) can et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION detect the wide-band impedance with only once injection, Power electronic converters with a negative impedance et al. (2014) and Roinila et al. (2018a)). Many researches 1. INTRODUCTION based on the pseudo-random binary sequences (PRBS) can detect thethe wide-band impedance with only once injection, based on the pseudo-random binary sequences (PRBS) can 1. INTRODUCTION Power electronic converters with a negative impedance such as maximum-length binary sequence (MLBS) in characteristic may converters cause stability issues in the electric based on the pseudo-random binary sequences (PRBS) can detect the wide-band impedance with only once injection, Power electronic with a negative impedance such astheet thewide-band maximum-length binary sequence (MLBS) in detect impedance with only once injection, characteristic may cause stability issues in the electric Roinila al. (2018a), and the discrete-interval binary Power electronic converters with a negative impedance railway systemmay (seeconverters Hu et al. (2018) Liaoinetthe al. (2017)). detectasthethewide-band impedance withsequence only once(MLBS) injection, such maximum-length in Power electronic with aand negative impedance characteristic cause stability issues electric Roinila al. (2018a), andet binary the discrete-interval binary such as et the maximum-length binary sequence (MLBS) in railway system (see Hu et al. (2018) and Liao et al. (2017)). sequence (DIBS) in Roinila al. (2014). The small-power characteristic may cause stability issues in the electric The TPS impedance determines the power system strength such as the maximum-length binary sequence (MLBS) in Roinila et al. (2018a), and the discrete-interval binary characteristic may cause stability issues inetthe electric Roinila railway system (see Hu et al. (2018) and Liao al. (2017)). sequence in Roinila et the al. (2014). The small-power et(DIBS) al. (2018a), and discrete-interval binary The TPS impedance determines the power system strength chirp signal introduced in Saar et al. (2013) and Min et al. railway system (see Hu et al. (2018) and Liao et al. (2017)). that a strong system can endure the negative impedance Roinila et al. (2018a), and the discrete-interval binary sequence (DIBS) in Roinila et al. (2014). The small-power railway system (see Hu et al. (2018) and Liao et al. strength (2017)). sequence The TPS impedance determines power system chirp signal introduced in Saar etbioelectrical al. (2013) and Min et al. intoRoinila et (2014). The small-power that a strong system can(constant endurethe the negative impedance is (DIBS) applied detect theal. impedance at The TPS determines thepower power system strength brought byimpedance electric train load), but a weak (2014) sequence (DIBS) in Roinila et al. (2014). The small-power chirp signal introduced in Saar et al. (2013) and Min et The TPS impedance determines thethe power system strength that a strong system can endure negative impedance (2014) is applied to detect the bioelectrical impedance at chirp signal introduced in Saar et al. (2013) and Min et al. al. brought by electric train (constant power load),research but a weak controlled frequency band, however being futile for the largethat a system strong system can endure theExisting negative impedance power can not tolerate that. has chirp signal introduced in Saar etbioelectrical al. (2013) and Min et al. (2014) is applied to detect the impedance at that a strong system can(constant endure power the negative impedance brought by electric train load), but a weak controlled frequency band, however being futile for the large(2014) is applied to detect the bioelectrical impedance at power system not Existing research has power/capacity brought by electric traintolerate (constant power load), but a weak electric grid.however shown that the can instability can bethat. restrained with improving (2014) is frequency applied toband, detect the bioelectrical impedance at controlled being futile for the largebrought by electric traintolerate (constant power load), but a weak power system can not that. Existing research has power/capacity electric grid. controlled frequency band, however being futile for the largeshown that the instability can be restrained with improving power system converter can not tolerate that. research has controlled the electronic control for aExisting matched impedance frequency band, however being futile for the largeelectric grid. power system can not tolerate that. Existing research has power/capacity shown that the instability can be restrained with improving This paper gives an grid. active method for measuring the electric the electronic converter control for a matched impedance shown that the instability can be(see restrained improving characteristic with power system Wen et with al. (2013)). The power/capacity power/capacity electric This paper atgives an grid. active method the shown that the instability can be for restrained with improving the electronic converter control aa matched impedance impedances controlled frequency bandfor for measuring both TPS and characteristic with power system (see Wen et al. (2013)). The the electronic converter control for matched impedance This paper an method for measuring the impedance characteristic can provide reference to design impedances atgives controlled frequency band both TPS and the electronic converter control for Wen aa matched impedance This paper gives an active active method forfor measuring the characteristic with power system (see et al. (2013)). The electrical train. A chirp-PWM signal is selected to drive impedance characteristic cana provide a reference tosystem. design paper atgives an active method forfor measuring the characteristic withcontrol power for system (see electric Wen et railway al. (2013)). The This impedances controlled frequency band both TPS and the electric train stable electrical train. A chirp-PWM signal is selected to drive at controlled frequency band for both harmonic TPS and characteristic with power system (see Wen et al. (2013)). The impedances impedance characteristic can provide a reference to design disturbance circuit that can excite large-power the electric train control for a stable electric railway system. impedances at controlled frequency band for both TPS and impedance characteristic can provide a reference to design electrical train. A chirp-PWM signal is selected to drive Thus, impedance measurement technique has toasystem. rapid electrical disturbancetrain. circuit that canvoltages excite chirp-PWM signallarge-power is selected tocandrive impedance characteristic can provide a reference design the electric train for electric TheA and currentsharmonic be Thus, impedance measurement has asystem. rapid disturbance. electrical train. A response chirp-PWM signallarge-power is selected to drive the electric train control control for aa stable stabletechnique electric railway railway disturbance circuit that can excite harmonic development. disturbance. The response voltages and currents canmain be disturbance circuit that can excite large-power harmonic the electric train control for a stable electric railway system. Thus, impedance measurement technique has a rapid captured to calculate the tested system impedances. The development. disturbance circuit that canvoltages excite large-power harmonic Thus, impedance measurement technique has a rapid disturbance. The response and currents can be captured to calculate the tested system impedances. The main disturbance. The response voltages and currents can be Thus, impedance measurement technique has a rapid development. in thisresponse paper are:voltages Impedance measurement can be classified into two categories contributions disturbance. The and currentsThe canmain be development. captured to calculate the tested system impedances. contributions in this paper are: captured to calculate the tested system impedances. The main development. Impedance measurement can be classified into two (passive and active methods) via whether thecategories injected captured to calculate the tested system impedances. The main contributions in this paper are: Impedance measurement can be classified into two categories 1) The spectrum injected in thisofpaper are: harmonic disturbance can be (passive and active methods) via whether thecategories injected contributions Impedance measurement can be methods classified into two disturbance is required. Passive utilize mathematical contributions in thisof paper are: 1) The controlled spectrum injected harmonic disturbance can the be Impedance measurement can be classified into two categories (passive and active methods) via whether the injected easily at the desired frequency band by disturbance is required. Passive methods utilize mathematical (passive and active methods) via whether the injected 1) The spectrum of injected harmonic disturbance can be analysis and numerical processing to estimate the impedance easily atmake the the desired frequency band by the The controlled spectrum of injected harmonic disturbance can be (passive and active methods) via whether the injected 1) disturbance is required. Passive methods utilize mathematical operators, and can impedance measurement more analysis andis numerical to estimate impedance 1) The controlled spectrum of injected harmonic disturbance can the be disturbance required. processing Passive methods utilizethe mathematical easily at the desired frequency band by without any disturbance injection (see Cobreces et al. (2009), operators, and can atmake impedance measurement easily controlled the the desired frequency band bymore the disturbance isnumerical required. processing Passive methods utilizethe mathematical analysis and to estimate impedance flexible. without any disturbance injection (see Cobreces et al. (2009), easily controlled at the desired frequency band by the analysis and numerical processing to estimate the impedance operators, and can make the impedance measurement more Yang et any al. and Ciobotaru et (2011)).the However, the flexible. operators, and can make the impedance measurement more analysis and(2010) numerical processing toal.estimate impedance without disturbance injection (see Cobreces et Yang et any al. (2010) and Ciobotaru et al.also (2011)). However, the operators, and can make the impedance measurement more without disturbance injectionand (see Cobreces et al. al.to(2009), (2009), flexible. accuracy can not be guaranteed, the speed obtain 2) The applied hardware structure and software control of flexible. without any disturbance injection (see Cobreces et al. (2009), Yang et al. (2010) and Ciobotaru et al. (2011)). However, the accuracy can not be guaranteed, and also the speed to obtain flexible. Yang et al. (2010) and Ciobotaru et al. (2011)). However, the 2) The applied hardware structure and software control of the impedance is slow due to its complex mathematical disturbance injection strategy is simple that makes the Yang et al. (2010) and Ciobotaru et al. (2011)). However, the accuracy can guaranteed, the to The applied hardware structure and software control of the impedance due to and its also complex mathematical accuracy can not notisbe beslow guaranteed, and also the speed speed to obtain obtain 2) disturbance injection strategy is simple that makes the 2) The applied hardware structure and software control of process. straightforward. accuracy can notisbeslow guaranteed, and also the speed to obtain implementation the impedance due to its complex mathematical 2) The applied hardware structure and software control of disturbance injection strategy is simple that makes the process. the impedance is slow due to its complex mathematical disturbance implementation straightforward. injection strategy is simple that makes the the impedance is slow due to its injection complexthat mathematical process. disturbance injection strategy is simple that makes the implementation straightforward. Active methods rely on disturbance can excite process. 3) The impedance at desired frequency band can be measured implementation straightforward. process. straightforward. Active methods rely on that calculating can excite implementation 3) Theonly impedance at desired frequency band can be measured harmonic response in disturbance the tested injection system for with once harmonic disturbance injection that can Active methods rely on disturbance injection that can excite 3) The impedance at desired frequency band can harmonic response inet al. the(2013), tested Roinila systemet for calculating Active methods rely on disturbance injection that(2014), can excite with only once harmonic disturbance injection that can 3) The impedance at desired frequency band can be be measured measured impedances (see Saar al. Min Active methods rely on disturbance injection that calculating can excite 3) harmonic response in the tested system for The impedance at desired frequency band can be measured only once harmonic disturbance injection that can impedancesresponse (see Saarinet al. al. (2014), Min with harmonic the(2013), tested Roinila systemet for calculating with only once harmonic disturbance injection can harmonic response in al. the tested Roinila system for calculating with only once harmonic disturbance injection that impedances that can impedances (see (see Saar Saar et et al. (2013), (2013), Roinila et et al. al. (2014), (2014), Min Min impedances (see Saar et al. (2013), Roinila et al. (2014), Min
Copyright © 2019, 2019 IFAC 199Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2019 responsibility IFAC 199Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 199 10.1016/j.ifacol.2019.08.176 Copyright © 2019 IFAC 199 Copyright © 2019 IFAC 199
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reduce the measurement time significantly compared with the traditional sine waveform sweep-based technique.
Vt( jw )
The rest of the paper is organized as follows: The impedance based stability analysis is introduced in Section II. Section III presents the harmonic excitation method at controlled frequency band. Section IV gives the impedance measurement of TPS and electric train, and then the stability analysis based on the measured impedances is discussed in detail in Section V.
A B C
110/220 kV
Rβ
ATS
Fα
ATS
Train
Fβ
Traction transformer
1
t
1 Zs ( jw ) / Zt( jw )
(2)
Zs ( j ) / Z t ( j )
(3)
In terms of the single-phase TPS, the equivalent impedance can be regarded as the positive-sequence impedance for the symmetric network. Thus, the positive-sequence impedance of VSC-based electric train is selected there to analyse the stability.
Tβ
Rα
Vs ( jw )
L( j )
Train impedance
27.5 kV
Tα
(1)
Based on the measured impedances, the stability of the TPStrain system can be determined by using the generalized Nyquist stability criterion. The impedance ratio can be defined in (3).
f /Hz
f /Hz
1 Zs ( jw ) / Zt( jw ) s
Vt( jw )
Zt ( j )
TPS impedance
1
s
The autotransformer (AT)-fed TPS is commonly applied in electric railway systems that can be seen in Fig. 1. The traction transformer can transform the three-phase 110/220 kV of utility power system to two single-phase 27.5-kV supply phases (α phase and β phase). The more introductions of this system can be seen in Pan et al. (2018). Zs ( j )
Vs ( jw )
where V ( j ) is the source voltage; Z ( j ) and Z ( j ) represent the measured TPS and electric train impedances in the frequency domain, respectively. (1) can be rearranged as follows:
2. IMPEDANCE BASED STABILITY ANALYSIS
Utility power system
183
The stability can be identified by studying the curves of the measured electric train impedance against the TPS impedance, and the phase difference at their magnitude intersection determines the phase margin (see Song et al. (2017) and Pan et al. (2018)).
SP
Catenary system
Fig. 1. AT-fed TPS and electric train.
PM The impedance-based stability researches of TPS-train system have been greatly accelerated in recent years. The equivalent impedance model of this single-phase system can be seen in Fig. 2 (see Roinila et al. (2018b)). TPS acting as a source can supply electric energy for the VSC-based electric train being deemed as a load. Instability and oscillation issues will occur in TPS-train system due to the mismatch of impedances versus frequency. However, solely utilizing the mathematical deduction to quantify the impedances appears to be difficult owing to unknown detailed parameters of both traction network and electric train. Thus, the measurementbased method to obtain the TPS-train impedances has a rapid development. Source
Zs (jw)
Zt(jw)
(4)
where PM is the phase margin; Zs ( j ) and Zt ( j ) represent the phases of the TPS impedance and the electric train impedance, respectively. 3. HARMONIC EXCITATION CONTROLLED FREQUENCY BAND 3.1 Chirp-PWM Signal Chirp signal is a sine-wave signal having the time-varying frequency, which is given by
ychirp (t )
Load
sin(2 ( f min
( f max
f min )t / T )t )
(5)
where f min and f max are the controlled minimum and
Zs ( j ) Vt ( j ) Vs ( j )
180
maximum frequency, respectively; T is the duration of the chirp waveform.
Zt ( j )
The desired spectrum distribution can be obtained via controlling the frequency f min and f max . The chirp-PWM is a novel PWM scheme, proposed in Uddin et al. (2012), being applied for brushless DC motor drive. In this research, chirpPWM signal can control the disturbance circuit presented in next section for exciting the harmonic disturbance at the interesting spectrum. A converting scheme from chirp signal to chirp-PWM signal is given by
Fig. 2. Equivalent impedance model of Fig. 1. According to the equivalent impedance model in Fig. 2, the voltage V ( j ) at the intersection of TPS and electric train can be expressed in (1). t
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ychirp (t ) ychirp (t )
0 0
3
(6)
1000 - 1500 Hz Magnitude (abs)
1 0
ychirp-PWM (t )
Chirp-PWM value should be converted to “1” when the corresponding chirp is larger than 0 (i.e., ychirp (t ) 0 ), besides, be converted to “0” with the chirp value smaller than 0 (i.e., ychirp (t ) 0 ). The detailed converting scheme is presented in Fig. 3 (Hu et al. (2019)).
2
1
0
0
500
1000 1500 Frequency (Hz)
2000
2500
Chirp-PWM signal
Magnitude
1
Fig. 5. The spectrum excited by the disturbance circuit with a controlled frequency band from 1000 Hz to 1500 Hz.
0
-1
Chirp-PWM signals can control the disturbance circuit for a desired broad spectral excitation. The spectrum distribution is designed by f min and f max . For a case, the f min is set as 1000 Hz, as well as the f max is set as 1500 Hz. The generated chirp-PWM signal is utilized to control the disturbance circuit, and the spectrum distribution excited by the disturbance circuit is shown in Fig. 5. It illustrates that the actual spectrum can spread at the designed frequency band 1000 – 1500 Hz. The large-power harmonic excitation at controlled frequency band can be utilized for measuring the impedance at designed frequency band with only once disturbance, which can greatly reduce the measurement time compared with the traditional sine-sweep method.
Chirp signal Time
Fig. 3. Converting scheme from chirp signal to chirp-PWM signal. 3.2 Disturbance Circuit A disturbance circuit presented in Fig. 4 can be applied to excite a large-power harmonic disturbance for measuring the tested system impedance. The detailed description and operating principle can be found in our previous research (Pan et al. (2018)). In detail, the primary-side of the stepdown transformer is connected between the catenary system and the rail, and the disturbance circuit is connected to the secondary-side. The disturbance circuit produces different frequency components with different driving signals of IGBTs. Moreover, all IGBTs are driven by the same control signal that can greatly simplify the control process. The time between the “ON” and “OFF” states of the IGBTs changes periodically. Meanwhile, the IGBT module 1 will disturb the positive period of the current, and the negative period is perturbed by the IGBT module 2 regularly. Catenary system 1
4.1 Impedance Measurement of TPS The disturbance circuit is connected to the measurement point of the TPS, and the impedance can be calculated with (7) to avoid the effect of the background harmonics (Pan et al. (2018)).
Zs ( j )
Chirp-PWM
0
Switch
Cs Smoothing capacitor
Snubber resistor
Excitation resistor
Us ( j ) Us0 ( j ) Is ( j ) Is0 ( j )
(7)
where Us ( j ) and Is ( j ) are the voltage and current of the measurement point in the frequency domain after imposing disturbance, respectively; Us0 ( j ) and Is0 ( j ) are the voltage and current in the frequency domain before imposing the disturbance, respectively. IGBT module 1
IGBT module 2
Transformer
4. IMPEDANCE MEASUREMENT OF TPS AND TRAIN
A detailed TPS model is built in MATLAB/SIMULINK based on the multiple transmission line (MTL) model presented in Hu et al. (2018) for the validation of proposed measurement method. The schematic of TPS simulation model is shown in Fig. 6.
Re
Rail
Fig. 4. The disturbance circuit to excite the harmonic disturbance.
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Seg me nt 1
Utili ty p ower system
Seg me nt 2
Theoretical value
A Z1n Y1n
110 kV
Disturb ance circuit
Z 2n Y1n
Y2n
Y2n
500 V
Zs
Tβ
Tα
Rβ
Rα
Magnitude (dB)
B C
27.5kV
MTL
MTL
Catenary system
Phase (deg)
Traction tran sformer
Fig. 6. Schematic of traction network simulation model using MTL.
60 40 20 0–1000
1000–2000 2000–3000 3000–4000 4000–5000
100 0 -100 0
Table 1 gives the simulation parameters of TPS model and 6 the simulation time step is set as Ts 110 s . For a given case, the harmonic excitation by disturbance circuit is controlled at 1000 – 1500 Hz and Fig. 7 shows the measured results. It can be seen that the measured impedance at the controlled frequency band 1000 – 1500 Hz is almost consistent with the theoretical value when out of that band is inaccurate since there is no enough harmonic excitation at these frequencies. In order to detect the TPS impedance at a broader band, e.g., 0 – 5000 Hz, we can have a segmental measurement every 1000 Hz (i.e., 0 – 1000 Hz, 1000 – 2000 Hz, 2000 – 3000 Hz, 3000 – 4000 Hz, 4000 – 5000 Hz,) for dispersing the harmonic disturbance energy, and Fig. 8 gives the measured result. The practical measurements can be seen in Hu et al. (2019)
Measured value
80
0
Fβ
Fα
185
1000
2000 3000 Frequency (Hz)
4000
5000
Fig. 8. The measured TPS impedance when specify frequency band at 0 - 10000 Hz with 2000 Hz measurement interval. 4.2 Impedance Measurement of Train Fig. 9 shows the equivalent model of electric train, which works with a dual-loop control method. The inductor current feedback acts as the inner loop and DC voltage feedback is the outer loop. The detailed parameters are given in Table 2. Lt
It
4QC
Cdc Rdc udc
Ut
Table 1. Simulation parameters of TPS Parameter Utility power system voltage Connection of traction transformer Voltage ratio of traction transformer The number of segments Voltage ratio of step-down transformer Excitation resistor Theoretical value
Value 220 kV V/x 220 kV/27.5 kV 10
PLL
i SOGI i dq
0
iq
id
id
L
PLL
uq
kii s k k pi ii s
iq
Current loop
L
dq
k pi
ud
u
SOGI PLL
5Ω
u
ud dq uq
PWM udc
k pv
PLL
27.5 kV/500 V
u
kiv s
* udc
Voltage loop k ppll
kipll s
0
1 s
PLL
Fig. 9. The train model including control.
Measured value
Magnitude (dB)
80
Table 2. Simulation parameters of train
60 40
0
C ontrolled frequ en cy ba nd
-20 200
Phase (deg)
Parameter The input voltage of train The input inductor of train Regulated capacitor DC load DC voltage reference Switching frequency PI parameters of current loop PI parameters of voltage loop
20
10 00–15 00 H z
0
-200
0
500
1000 1500 Frequency (Hz)
2000
2500
Value Ut = 1770 V Lt = 10 mH Cdc = 9 mF Rdc = 100 Ω udc* = 3000 V fs= 1250 Hz Kpi = 2, Kii = 2 Kpv = 0.5, Kiv = 2
The proposed disturbance method is utilized there to excite the harmonic responses for measuring the positive-sequence impedance of VSC-based electric train, which can be calculated by
Fig. 7. The measured TPS impedance when control the frequency band at 1000 - 1500 Hz.
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Zt ( j )
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Ut( j ) / I t( j )
Table 3. Simulation parameters of TPS-train system
(8)
Parameter TPS-side resistors TPS-side inductors TPS-side capacitors
where Ut ( j ) and It ( j ) are the voltage and current of the train input point in the frequency domain, respectively. For a given case, the harmonic excitation by disturbance circuit is controlled at 10 – 600 Hz and Fig. 10 shows the measured results. As it is seen, the measured train impedance curves are smooth and can be almost consistent with the theoretical value at the controlled frequency band 10 – 600 Hz.
100
Magnitude (dB)
100
Measured value
20
0
54 Hz
50
357 Hz
0
Phase difference is 174.2º
Phase difference is 186.6º
0 -100 0
100
200 300 Frequency (Hz)
0
400
500
-100 0
100
200 300 Frequency (Hz)
400
Fig. 12. The measured TPS-train impedances after increasing the network-side inductor from 1mH to 20 mH.
500
Mag (% of Fundamental) Mag (% of Fundamental)
Fig. 10. The measured converter impedance. 5. STABILITY ANALYSIS BASED ON MEASURED IMPEDANCE An equivalent TPS-train system shown in Fig. 11 is built in MATLAB/SIMULINK to verify the effectiveness of impedance measurement and stability analysis. Initially, the TPS-train system can remain stable as it operates with the parameters given in Table 3. At 1.5 s, an increase of the TPSside inductor L1 from 1 mH to 20 mH will weaken the TPS, and Fig. 12 gives the measured TPS-train impedances. The phase difference at the impedance magnitude intersection of 54 Hz is 186.6°. This negative phase margin illustrates that the unexpected harmonics around 54 Hz will occur in this system, which will oscillate the AC and DC voltages with 4 Hz (see Pan et al. (2018)). The actual unexpected harmonics are about around 53.5 Hz (see Fig. 13), which causes the actual oscillation at 3.5 Hz (see Fig. 14). Moreover, there is another weak-phase-margin magnitude intersection at 357 Hz (the phase difference is 174.2°), and the actual unexpected harmonics are around 356 Hz. These small deviations can be accepted. L1 C1
R2
L2
Zs Z t
30
t
1.5 s
t
1.5 s
50 Hz 20 10 0
50 Hz
30
53.5 Hz 20 10
356 Hz
0
0
100
200 300 Frequency (Hz)
400
500
DC Voltage (V)
Fig. 13. AC voltage spectrum when increase L1 from 1 mH to 20 mH. 4000
t
t
1.5 s
1.5 s
3000
Oscillation frequency is 3.5 Hz
2000 4000
AC Voltage (V)
R1 Ug
Train impedance TPS impedance
100 Phase (deg)
Magnitude (dB)
40
Phase (deg)
Theoretical value
Value R1 = 0.006Ω, R2 = 0.008Ω L1 = 1 mH, L2 = 2.5 mH C1 = 10 µF, C2 = 20 µF
Lt Cdc Rdc
C2
2000 0 -2000 -4000 0
PWM
0.5
1
1.5
2 2.5 Time (s)
3
3.5
4
Fig. 14. AC and DC voltage waveforms when increase L1 from 1 mH to 20 mH.
Fig. 11. Train-network simulation system.
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6. CONCLUSION This paper presents a method for measuring the TPS-train impedances that can be used to analyse stability for ensuring a safe and stable electric railway system. A disturbance circuit consisting of series–parallel IGBT modules is driven by the chirp-PWM signal that can excite the large-power harmonic disturbance at the controlled frequency band. Then, the detected voltage and current data can be utilized to calculate the tested system impedances. The measurement time is short for the just once disturbance injection and the controllable measurement frequency band makes this method more flexible. The simulations in MATLAB/SIMULINK verifies the effectiveness of impedance measurement and stability analysis. REFERENCES Cobreces, S., Bueno, E. J., Pizarro, D., Rodriguez, F. J., and Huerta, F. (2009). Grid impedance monitoring system for distributed power generation electronic interfaces. IEEE Trans. Instrum. Meas., 58(9), 3112-3121. Ciobotaru, M., Agelidis, V., Teodorescu, R. (2011). Line impedance estimation using model based identification technique. In Proc. IEEE Power Electron. Appl. Conf., 1-9. Hu, H., Tao, H., Blaabjerg, F., Wang, X., He, Z., and Gao, S. (2018). Train-Network Interactions and Stability Evaluation in High-Speed Railways--Part I: Phenomena and Modeling. IEEE Trans. Power Electron., 33(6), 4627-4642. Hu, H., Pan, P., Song, Y., and He, Z. (2019). A Novel Controlled Frequency Band Impedance Measurement Approach for Single-phase Railway Traction Power System. IEEE Trans. Ind. Electron., DOI: 10.1109/ TIE.2019.2896297. Liao, Y., Liu, Z., Zhang, G., and Xiang, C. (2017). Vehiclegrid system modeling and stability analysis with forbidden region-based criterion. IEEE Trans. Power Electron., 32(5), 3499-3512. Min, M., Land, R., Paavle, T., Parve, T., Annus, P., and Trebbels, D. (2011). Broadband spectroscopy of dynamic impedances with short chirp pulses. Physiol. Meas., 32(7), 945-958. Pan, P., Hu, H., Yang, X., Blaabjerg, F., Wang, X., and He, Z. (2018). Impedance Measurement of Traction Network and Electric Train for Stability Analysis in High-Speed Railways. IEEE Trans. Power Electron., 33(12), 1008610100. Roinila, T., Vilkko, M., and Sun, J. (2014). Online grid impedance measurement using discrete-interval binary sequence injection. IEEE Trans. Ind. Electron., 2(4), 985-993. Roinila, T., Messo, T., and Santi, E. (2018a). MIMOIdentification Techniques for Rapid Impedance-Based Stability Assessment of Three-Phase Systems in DQ Domain. IEEE Trans. Power Electron., 33(5), 40154022. Roinila, T., and Messo, T. (2018b). Online grid-impedance measurement using ternary-sequence injection. IEEE
204
187
Trans. Ind. Appl., to be published. DOI: 10.1109/ TIA.2018.2825938. Saar, T., Reidla, M., Martens, O., Land, R., Min, M., and Herranen, H. (2013). Chirp-based piezo-impedance measurement. In Proc. IEEE 8th International Symposium on Intelligent Signal Processing, 83-86. Song, Y., Wang, X., Blaabjerg, F. (2017). Impedance-based high-frequency resonance analysis of DFIG system in weak grids. IEEE Trans. Power Electron., 32(5), 35363548. Uddin, W., Husain, T., Mitra, R., Ofori, E., Sozer, Y., and Husain, I., A chirp PWM scheme for brushless DC motor drives. In Proc. IEEE Energy Convers. Congr. Expo., (ECCE), 3317-3323. Wen, B., Boroyevich, D., Mattavelli, P., Shen, Z., and Burgos, R. (2013). Influence of phase-locked loop on input admittance of three-phase voltage-source converters. In Proc. 28th Annu. Appl. Power Electron. Conf., 897-904. Yang, J., Li, W., Chen, T., Xu, W., and Wu, M. (2010). Online estimation and application of power grid impedance matrices based on synchronized phasor measurements. IET Gener., Transm. Distrib., 4(9), 10521059.