IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERINGIEEJ Trans 2019; 14: 1532–1542Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.22973

Paper

A Novel Locomotive Auxiliary Converter Control Strategy with HarmonicSuppression for Avoiding Resonance Voltage Accidents in an

Electrified Railway

Meijun Mu, Non-member

Zhongping Yang, Non-member

Fei Lin, Non-member

Shihui Liu, Non-member

In recent years, the AC-DC-AC electric locomotives have been wildly applied in electrified railways, deteriorating the currentquality of network. Therefore, filters in electrified railways are essential. However, considering the volume and weight of filters, itis inappropriate to install them on locomotives. And resonance accident caused by high-frequency harmonics is hard to suppressbecause of the low switching speed of high-power Si-based devices. In this article, a novel locomotive auxiliary convertercontrol strategy with harmonic suppression function is proposed to filter harmonic currents injected into the traction supplynetwork. By controlling the auxiliary converter, the strategy could complete the function of rectification and filtering, convertingpower for auxiliary equipment, filtering the harmonic current, and suppressing resonance accidents with the high-frequencycharacteristics of SiC devices. For compensating high-frequency harmonics, the parameters of main circuit and control scheme areanalyzed to ensure a stable system. The feasibility of the scheme is verified by simulation and RT-LAB hardware-in-loopexperiment. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Keywords: electrified railway; electric locomotive; resonance suppression; power quality

Received 1 June 2018; Revised 29 March 2019

1. Introduction

With the development of electrified railways, AC-DC-AC elec-tric locomotives have been widely used, so multiple frequencyharmonic current would be injected into public supply networksduring the operation of electric locomotives, deteriorating thepower quality and causing overvoltage protection [1]. In addition,resonance accidents might happen, which means the voltage oftraction network would rise significantly, leading to breakdown ofequipment along the network. In Zurich, Switzerland, locomotiveswere automatically shut down by protective equipment becauseof high harmonic current. In 2017, the HXD2 electric locomotivecaused a resonance accident at Datong substation in China, leadingto the tripping operation of the locomotive. The accident frequencyis 1750 Hz [2]. The frequency of harmonic current focuses on150 Hz, 250 Hz, 350 Hz etc., as well as the high-order frequencyaround integral multiple of the switching frequency.

As for measures to suppress the harmonics, first of all, we canreconstruct traction substation, such as installing passive or activefilters. The passive filter methods like installing a inductance andcapacity filter or a high pass filter at traction substation can filterspecific harmonics, but are unable to compensate the harmoniccurrent dynamically when frequency changes [3,4]. Based onpower electronic technology, we can also install active powerfilter equipment along with a step-down transformer to realizethe dynamic compensation of harmonic current [5,6], such asthe method of using two ‘back to back’ single-phase full bridgeconverters and a power quality compensation system composed of

a Correspondence to: Zhongping Yang. E-mail: zhpyang@bjtu.edu.cn

College of Electrical Engineering, Beijing Jiaotong University, ShangyuanNo. 3, Haidian District Beijing, China

a three-phase voltage source converter and a thyristor switchingcapacitor. For the methods mentioned above, high-power switchingdevices and step-down transformers are required, leading to thecomplexity of the system and large capacity of the active part,which are difficult to be applied in project [7,8].

For compensation methods on electric locomotives, similarto mentioned above, passive filters like a inductance, capacityand inductance filter is inappropriate when parameters change[9]. Active filters increase the weight of locomotives, whichis not conducive for lightweight rail transit [10]. The methodof eliminating the resonant frequency point by modifying theswitching frequency of traction converters could avoid resonanceat some certain frequency, unable to eliminate all the resonancefrequency as well as the 150 Hz, 250 Hz etc. harmonic currents.

In this article, a novel locomotive auxiliary converter controlstrategy is proposed, which means we can control the auxiliaryconverter to improve the power quality of the network withoutinstalling extra devices. At the same time, the auxiliary convertercould convert power for auxiliary equipment such as lightsand air conditioners on electric locomotives. In this strategy, adirect current (DC) voltage controller and a fundamental currentcontroller are applied to complete the rectification function, theharmonic current controller is applied to track and compensatethe harmonic current of the grid side until the harmonic currentis filtered, thereby improving the power quality of the electrifiedrailway and suppressing resonance voltage. The scheme use SiCdevices to produce compensation current whose frequency is highand around the integer times of switching frequency of tractionconverters. Meanwhile, the application of SiC devices couldreduce the loss and weight of converters.

The scheme use SiC devices for the auxiliary converter toproduce compensation current whose frequency is a few integertimes higher than the switching frequency of traction converters.

© 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A NOVEL LOCOMOTIVE AUXILIARY CONVERTER CONTROL STRATEGY

Meanwhile, the application of SiC devices also reduces the lossand weight of the auxiliary converters.

However, if full SiC devices are applied in traction converters,the switching frequency could be increased significantly and henceboth resonance frequencies could be avoided and power quality inthe electric traction network could be improved. This advancedmethod has been applied in N700s in Japan [11]. Because thehigh-power full SiC technology has not been easily available,the strategy proposed in this article is mainly aimed at reform-ing the existing locomotives with Si-based traction inverters tosolve the resonance problems. The auxiliary converters on theselocomotives operate at lower power and hence SiC technologycould be easily adopted for them.

The tracking control method of harmonic current loop in thisscheme plays an important part in compensating harmonics. Pro-portional integral (PI) control is hard to track AC reference currentwith no error [12]. The control method based on the synchronousreference frame has to invent a q-axis component, which is com-plicated in a single-phase bridge circuit [13,14]. The proportionalresonance (PR) controller could track the sinusoidal signal with noerror by producing an infinite gain at the resonance frequency, butparameter tuning and digitization are complex to obtain a stableand optimized system [15–17]. For the purpose of compensatingmultiple-frequency harmonic currents generated during the opera-tion of electric locomotives, multiple PR controllers are applied totrack the harmonic current commands without error in this article.

To apply the proposed control scheme to practice, we need todigitalize it and tuning the parameters of the controller. Tustinwith prewarping method would keep frequency from shifting atthe resonance frequency point, and the phase delay of the systemat this point is tiny after discretization, ensuring a larger gain atthe resonance point [18]. In references [19–22], parameters ofmultiple parallel resonant controller are designed, respectively, tosatisfy the stability of the system, but the parameter design wasnot mentioned at high frequency.

For high-frequency harmonic controllers, the digital delay linkcauses phase lags in current loop during discretization. With theincrease of the harmonic frequency, the phase frequency charac-teristics will probably pass through 180◦, leading to instability ofthe current loop. Also, when the resonant frequency approaches tothe Nyquist frequency, the system tends to be unstable.

In view of the above problems in digital implementation, thisarticle adopts the Tustin with prewarping method to discretize thecontrol scheme, and design the critical parameters of the controllerin the discrete domain, so as to maintain the stability of the systemand get a superior control effect. The stability issue is analyzed,and feedback control is introduced to solve the problem of phaselag caused by digital delay.

This article is organized as follows. Section 2 introduces thecauses and effects of the harmonic generation of electrified rail-ways. Section 3 explains the control principle of a multifunctionconverter, and the analysis of the main circuit. Section 4 presentsthe control scheme of the converter and its digital implementation,including its parameter and stability analysis. Section 5 verifiesthe control scheme by simulation and hardware-in-the-loop exper-iment. Section 6 is conclusion.

2. Causes and Effects of Harmonics in ElectrifiedRailways

Figure 1 shows the main circuit of the AC-DC-AC electriclocomotive. T represents traction connect network and R is therail. The single-phase alternating current provided by tractionsubstation flows to the traction drive system and auxiliary powerunit through the main transformer, drives the locomotive, andprovides power for the locomotive auxiliary equipment. At the

M

Auxiliaryequipment

APU

T

Rphi shi

Traction

Transformer

4QC InverterDC Motor

Fig. 1. Main circuit of electric locomotive connected into thetraction network

same time, the electric locomotive, as a nonlinear load, injectssome specific harmonics into the traction network. The mainharmonic source is the single-phase four quadrant converter (4QC)of the traction side.

2.1. Causes of harmonics The DC-side output voltageof the single-phase 4QC contains the second harmonic component,which introduces the 3rd harmonic component to the referencecurrent through the DC voltage control loop, thus generating the3rd harmonic on the AC side. The 3rd harmonic generates 4thharmonic component on the DC side, leading to the 5th AC sideharmonic. In this way, the low harmonic of 3rd, 5th, 7th, and 9thharmonic current will flow into the traction network during theoperation of locomotive.

Due to the application of pulse width modulation (PWM) mod-ulation technology, the expression of harmonic current injectedinto the traction network of the traction side single-phase 4QC isshown as follows [23]:

iNn(t) =∞∑

m=2,4 ...

∞∑n=±1,±3 ...

4Ud2mπL2(mωc+nω1)

Jn(

mπM2

)cos mπ

2

sin nπ2 sin(mωc t + nω1t + mα + nβ)

(1)

In this formula, U d2 is the DC voltage, L2 is the inductanceat the AC side, ωc is the switching angle frequency, ω1 is thefundamental angle frequency, M is the modulation, α is the carrierinitial angle, and β the initial phase angle of the modulated wave.J n is the Bessel function.

The harmonic component frequencies of the input currentconcentrate on the high frequency round the even times of theswitching frequency. The larger the value of m in the formula, thesmaller the harmonic amplitude. The harmonic content is affectedby the modulation, the magnitude of the DC voltage, the effectivevalue of the grid voltage, the net voltage frequency, and the PWMmodulation carrier frequency. The amplitude of harmonic is alsorelated to the inductance value of the AC side.

2.2. Effects of harmonics As the main harmonic sourceof electrified railways, electric locomotives generate a great dealof power harmonics during operation, and the harmonics flow intothe power grid through the traction power supply system, leadingto distortion of the voltage waveform. Figure 2 shows the effectsof harmonics.

1. Harmonics not only affect the life of electrical equipmentin the power grid, but also shorten the life of the equipmentof the electrified railway. They would cause obviousinterference to the adjacent communication system, causemisoperation of protective relays, and bring about greatererrors in electrical measurement instruments and energymetering.

2. During the operation of the locomotive, the harmoniccurrent generated by the traction converter would be

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M. MU ET AL.

Public power grid

M

AuxiliaryEquipment

APU

iph

ish

+2

1

T

R

Model of tractionnetwork

38.5kVOvervoltage

Ih×Rh

Affecting power qua lityResonance accidents

Fundamental

……

Harmonics

+

Fig. 2. Effects of harmonics

SS SP

TISS

Z

2l

1l

1TZ

1TZ

1TY

2TZ

2TZ

2TY

Fig. 3. Traction network T type equivalent circuit

injected into the traction network, which forms a resonancecircuit with the impedance of the traction network, causingthe train terminal voltage to rise obviously.

To analyze the characteristics of the traction network, we usuallybuild a T-type equivalent circuit model [24].

The train is equivalent to a current source I T . Z ss, Z Tn , andY Tn are equivalent parameters of the traction substation and line(Fig. 3).

Let Z 1 and Z 2 be the impedance from the locomotive positionto the traction substation and the direction of the partition,respectively.

Z1 = ZcZss cosh(γ L1) + Zc sinh(γ L1)

Zss sinh(γ L1) + Zc cosh(γ L1)

Z2 = Zccosh(γ L2)

sinh(γ L2)(2)

γ and Z c are the propagation constant and characteristicimpedance, respectively:

γ =√

Z0Y0 (3)

Zc =√

Z0

Y0(4)

Z 0 ,Y 0 are unit length impedance and admittance parameters.The impedance of the location of the train is shown in formula(5).

Zq = Z1Z2

Z1 + Z2

=Z0Y0

cosh(√

Z0Y0l2)(Zss cosh(√

Z0Y0l1) + Zc sinh(√

Z0Y0l1))

Zss sinh(√

Z0Y0l) + Z0Y0

cosh(√

Z0Y0l)

(5)

When the resonance happens,

Zss sinh(√

Z0Y0l) + Z0

Y0cosh(

√Z0Y0l) = 0 (6)

M

AuxiliaryEquipment

Mutipul function APU

T

R

1 AC DC 3-phace AC

……

Compensation

2

……

Harmonics

iph=0

1 Rectification Filter2

ish

+

Harmonics

Fig. 4. Introduction of auxiliary converter function

Therefore, Z q approaches to ∞. The resonance frequency is:

fh = 1

2π√

Lss C(7)

If the frequency of the harmonic current injected by the tractionconverter is equal to this resonance frequency, locomotive terminalvoltage amplitude approaches to ∞ .

u(jωh) = Zq · iT (jωh) (8)

The harmonic current injected into the traction network willcause the voltage rise at a specific frequency, resulting in the res-onance accident. Therefore, we consider to suppress the resonanceby filtering the harmonic current.

3. Control Principle of Multifunction Converter

To filter the harmonic current injected into the traction networkby electric locomotive, a novel converter control strategy isproposed in this article, as shown in Fig. 4.

Considering the low power of the auxiliary converter, we applySiC power devices to the auxiliary converter, and achieve thefunction of rectification and filtering by changing the controlalgorithm of the auxiliary converter simultaneously.

Figure 4 shows the two functions of the auxiliary converter.

1. For the single-phase rectification function, the single-phasealternating current from the traction power supply networkis converted to direct current through 4QC, and thenconverted to three-phase alternating current for the auxiliaryequipment on the locomotive by the inverter.

2. The filtering function is realized by detecting the primaryside current of the transformer and controlling the auxiliaryconverter to produce the compensation current that isinverse to the harmonic current, so that the harmonic currentin the traction network is filtered, improving power qualityof the power grid, and avoiding the occurrence of resonanceaccident.

3.1. Analysis of the control principle The equivalentmodel of the locomotive main circuit is shown in Fig. 5. n1 , n2 ,and n3 are ratios of the transformer, corresponding to the primarywinding, traction winding, and auxiliary winding, respectively.vp , i p , v s, i s , and vc , i c are the voltages and currents of theoriginal side, the traction side, the auxiliary side of the transformer,respectively, in Fig. 5, the value is converted to the auxiliary side.x ,r is the equivalent impedance, and uab is the pulse voltage.

In Fig. 6, V c , I c is the voltage and current in the AC side ofthe auxiliary converter, Uab is the pulse voltage. jωL3 I c is thevoltage of the inductor. C is the capacitor of the DC side. R is theequivalent impedance. Ud is the DC voltage. It shows the voltageand current vector diagrams on the AC side and the equivalent

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A NOVEL LOCOMOTIVE AUXILIARY CONVERTER CONTROL STRATEGY

……1r 1x

21r 21x

24r 24x

31r 31x

32r 32x

3

1p

nv

n

31

2s

nv

n

34

2s

nv

n

1cv

2cv

1

3p

ni

n

21

3s

ni

n

24

3s

ni

n

1ci

2ci

uab1

uab4

uab5

uab6

Traction windings = 4

Auxiliary windings = 2

Fig. 5. Electric locomotive equivalent circuit

C

R

+

–

UdUab

Vc

Ic

jωL3Ic

Fig. 6. Equivalent circuit diagram of rectification function

circuit diagram on the DC side when the converter operates atrectification mode. At this time, the pulse rectifier guarantees thesinusoidal output of the AC side by pulse width modulation, andthe stable voltage output in the DC side.

The formula (9) indicates the current relationship of the trans-former winding in Fig. 5, and the formula (10) is obtained aftersimplification. Therefore, the harmonic current expression is (11).By controlling the auxiliary current transformer to generate thecompensation current i ch , the primary side harmonic current i ph

can be reduced to zero, so as to improve the power quality andsuppress the resonance.

n1

n3ip = n2

n3

4∑n=1

isn +2∑

n=1

icn (9)

n1ip = n2is + n3ic (10)

n1iph = n2ish + n3ich (11)

3.2. Inductance analysis of the main circuit Toachieve the rectification and filtering function simultaneously, weneed to design the inductance of the auxiliary converter. Forrectifier function, the converter should achieve unit power factorrectification. Therefore, to ensure a low harmonic componentvalue, the inductance value should not be too small. For the filterfunction of the converter, it is required to produce a compensationcurrent that is reverse to the primary harmonic current. Especiallyfor the middle and high frequency harmonics, it is requiredthat the compensation current can track the harmonic currentinstruction without error. At this time, the inductance value cannotbe too large. Therefore, the two functions need to be taken intoconsideration in analyzing the inductance value, which is related tothe change rate of harmonic current, switching frequency, currentamplitude, and so on.

3.2.1. Inductance design of the rectification functionFigure 7 is the equivalent circuit diagram of the auxiliary con-verter, uc is the voltage of the auxiliary winding, L3 is the equiva-lent inductance, C is the supporting capacitor, R is the equivalentload, and U d is the auxiliary DC voltage. For the function ofrectification, the value of inductance is shown in formula (12)[23].

L3 <

√U 2

d − U 2m

Imω1(12)

uc C R

+

–

IdL3ic

Multiple function APU

Ud

Fig. 7. Auxiliary converter circuit

ic

ic*

Fig. 8. Tracking principle of reference current

where U m is the peak value of AC voltage, I m is the peak valueof AC current, ic = I m cosωt .

At the same time, in accordance with the AC side current rippleof no more than 10% [25],

L3 ≥ | Um sin ωt − sU d |4fs Im × 10%

(13)

f s is the switching frequency, s is the switching function (1/0).

3.2.2. Inductance design for tracking performance TheAC side inductance current of the auxiliary winding is zigzaggedalong the reference current, as shown in Fig. 8.

i c* is the reference current, i c is the tracking current.For this topology, the inductance current is shown as follows:

di L3

dt= 1

L3(uc − sU d ) (14)

In this formula, i L3 is the inductance current, uc is the voltageof auxiliary winding, s is the switching function.

From formula (14), we can find that with the increase of L3 ,the slope of the inductance current gets smaller, and the trackingperformance of compensation current is poorer.

The harmonic current produced by the four quadrant converteris shown in formula (1).

To ensure that the inductor current can track the referenceharmonic current, the change rate of inductance current shouldbe greater than the change rate of the harmonic current.

di L3

dt> i

′chmax (15)

i′chmax = iNn

′(t) · n2

n3= 4Udc2

mπL2Jn

(mπM

2

)cos

mπ

2sin

nπ

2· n2

n3

(16)

The range of the inductor value:

L3 <|uc − sU d |

|i ′chmax|

(17)

According to formula (17), the range of inductance is relatedto the switching frequency of the traction side, it is also relatedto the highest harmonic frequency that needs to be suppressed. Tosatisfy the tracking performance of current, the larger the i chmax

′,the smaller the upper limit of the inductance.

Considering the current tracking performance of the filterfunction, rectifying function and the converter unit power factor,

1535 IEEJ Trans 14: 1532–1542 (2019)

M. MU ET AL.

and ripple characteristic of the AC side, the inductance value rangeis shown in formula (18).⎧⎪⎨

⎪⎩|Um sin ωt−sU d |

4fs Im ×10% ≤ L3 ≤ |uc−sU d ||i ′chmax|

L3 ≤√

U 2d −U 2

m

Im ω1

(18)

From formula (18), we can find that the inductance value isinfluenced by switching frequency, with the increase of switchingfrequency f s , the limit of inductance gets lower, and the trackingperformance of the reference current becomes better. The inductorvalue is also affected by the harmonic frequency and amplitude,as well as the current of the auxiliary side.

4. Digital Implementation of Multi-FunctionConverter Control Scheme

4.1. Introduction of the converter control schemeIn the proposed method, the active filter function is not alwaysenabled. In this scheme, the compensation current is generatedonly when the possibility of resonance accident is identified.

For the identification method, the method mentioned in ref-erences 26, 27 is used. We define the resonance characteristicvalue H:

H = Upcch

Uabh(19)

Here, uabh is the pulse voltage of the traction converter, upcch

is the voltage at pantograph. If the value of H is larger than a setvalue, the active filter function is active to avoid resonance untilthe value of H is detected to be lower than the set value. The setvalue is designed according to the voltage by the sensors, whichis related to parameters of lines and locomotives.

Figure 9 shows the control block diagram of the main circuitand multifunction converter. Fundamental current control andDC voltage control are mainly applied to achieve unity powerfactor rectification function. The error of reference value ud *and measured value ud of DC voltage is transferred to thePI controller, where the reference value of amplitude of ACside current I c31 * is obtained, then the reference fundamentalcurrent i c31 * is produced by multiplying the phase. The error ofreference current and measured current would flow through theproportional controller to realize fast tracking of the fundamentalcurrent.

Harmonic current controller is applied to complete the filterfunction of the converter. The harmonic current of the primaryside i ph is obtained by detecting and discrete Fourier analyzing ofthe primary side current. The reference current is i ph * = 0 , andproportional resonance controller is applied to track the referencecurrent with no error. Therefore, the compensation current isgenerated.

There are two auxiliary converters. To have a better performanceon active filter function, only one auxiliary converter is used togenerate the compensation current.

Block diagram of Discrete Fourier Analysis is shown as follows:In this article, sliding window Fourier transform is used.

i (k) =Nmax∑n=1

{An cos

(nk

2π

N

)+ Bn sin

(nk

2π

N

)}(20)

An = 2

N

xnew −N +1∑x=xnew

i(x) cos

(nx

2π

N

)

= 2

N

⎧⎪⎪⎨⎪⎪⎩

xnew −N∑x=xnew −1

i (x) cos(nx 2π

N

) − i(xnew − N)

cos[n (xnew − N ) 2π

N

]+i (xnew ) cos

(nx new

2πN

)

⎫⎪⎪⎬⎪⎪⎭ (21)

M

n3/n1

DFT

∑

PLL

SPWMPI

DC voltage control

PFundamental

current controller

M-PR

Harmonic current controller

Auxiliaryequipment

iph*=0

iph

ic31

ic31*

uch

uc1

uabh

Upcch

i3h

i31

u3

ω3

ω3L3I

3COSω3t

ud*ud

i2h

Fig. 9. Electric locomotive main circuit and control scheme blockdiagram

K

GPWM

+

cu+

-GPR3+

-+

3 3

1

L s R+-

+

+

+

3ci

*31ciGPRn

…… +

iph

ish

iph*=0ich

Fig. 10. Auxiliary converter current loop control block diagram

An

Bn

Cos(nwt)

Sin(nwt) +

+

-

+

DFT

pi phichin1/n3

Fig. 11. Fourier analysis block diagram

Bn = 2

N

xnew −N +1∑x=xnew

i(x) sin

(nx

2π

N

)

== 2

N

⎧⎪⎪⎨⎪⎪⎩

xnew −N∑x=xnew −1

i (x) sin(nx 2π

N

) − i(xnew − N)

sin[n (xnew − N ) 2π

N

]+i (xnew ) sin

(nxnew

2πN

)

⎫⎪⎪⎬⎪⎪⎭ (22)

In the formula (22) above, N is the window length, xnew is thenew data point, when n = 1, the fundamental current is extracted,the harmonic current is obtained by primary side current minusfundamental current.

Current loop control block diagram is shown in Fig. 10, i c31

is the AC side current of the auxiliary converter. The error flowsthrough the controller K to track the fundamental current, GPWM

is a PWM link, which is usually replaced by a first order inertialink (Fig. 11).

i ph * is the reference harmonic current of the primary side,whose value is zero. The input of the multiple-proportionalresonance (M-PR) controller is the error of the reference value andthe feedback value. M-PR is applied to produce the compensationcurrent until the harmonic current is filtered. In formula (23), K p isthe proportional coefficient, K rh is the resonance coefficient, andhω0 is the resonance angle frequency.

GPR(s) = Kp +∑

h=2,5,7,11 ...

Krh s

s2 + (hωo)2(23)

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A NOVEL LOCOMOTIVE AUXILIARY CONVERTER CONTROL STRATEGY

101

–225–225–135

–90–45

04590

102 103

Frequency (rad/s)

Bode diagramPh

ass

(deg

)

–100

–50

0

50

100

Mag

nitu

de (

dB)

104 105

K=0K>0

Fig. 12. The influence of feedback K on the phase margin

In practical applications, it is necessary to consider the roundingerror and truncation error existing in the digital control system,where the quasi-resonant controller is used instead of the ideal PRcontroller.

GPR(s) = Kp +∑

h=3,31,33,35

2Krhωchs

s2 + 2ωchs + hω20

(24)

When the input of the fundamental is 0, the transfer functionabout the input and output of the harmonic is obtained, and afeedback K is introduced at this time. Open loop transfer functionof harmonic current control is shown in (25).

H0(s) = GPR(s)Gi (s) (25)

where Gi (s):

Gi (s) = GPWM (s) · 1

(Ls S + R)/

[1 + GPWM (s) · 1

(Ls s + R)· K

](26)

The closed loop transfer function of the harmonic controller:

Hc(s) = H0(s)

1 + H0(s)(27)

To achieve fast tracking control of reference currents, andcomplete rectification and filtering function without affecting thestability of the system, we need to design K rh and other parametersfor the resonant controller. The commonly used design method is toutilize the amplitude-frequency and phase-frequency characteristiccurves in the continuous domain. We can design parameters atresonant frequencies to achieve higher gain at these frequenciesand to satisfy the phase-angle margin. This method is simple tounderstand, but the results cannot be directly applied to the digitalsystem because of the obvious error. Therefore, in this article, thestability and parameter design of the system are analyzed by usingthe root locus in the discrete domain.

4.2. Discretization and stability analysis of controllerFigure 9 shows the control block diagram of the main circuit and

multifunction converter.To obtain a good tracking performance at the resonant fre-

quency, the discretized resonant controller should keep the res-onant frequency from shifting and have a large gain at this point.In this article, Tustin with prewarping method is adopted. Thephase lag at the resonance point is smaller and the system is sta-ble. And the frequency does not shift with the sampling frequencyafter discretization. The discrete factor is:

s = ω

tan(T/2)· z − 1

z + 1(28)

The traditional Bode diagram of the resonant controller transferfunction is shown as the dotted line in Fig. 12, here K = 0.

1

0.5

Root locus

K increase

0

Imag

inar

y ax

is

–0.5

–1

–1 –0.5 0

Real axis

0.5 1

Fig. 13. Effect of K value on system stability

From the parameters provided by Toshiba China Co., Ltd.,the switching frequency of traction 4QC is 450 Hz, and unipolarmodulation is applied, so the equivalent switching frequency is900 Hz, the harmonics are near the integer time of the switchingfrequency, for example two times of 900 Hz (1800 Hz). Afterinvestigation of a large number of accidents happened in China, theaccident frequency focused on 1550, 1650, and 1750 Hz, which arearound 1800 Hz, so we choose these three frequencies to analyze.

When considering the digital control delay T PWM of the currentloop, a pole p = −1/(1.5T PWM ) on the real axis is added to theopen loop transfer function of the current loop. The pole is farfrom the origin and can be ignored when the harmonic frequencyis low. However, as the harmonic frequency increases, the digitaldelay will reduce the phase margin of the current loop. The higherthe frequency of the harmonic, the greater the phase lag causedby the digital delay link. Because the PR controller in the currentloop has a phase jump near the resonant frequency, if it is notproperly compensated, the phase angle margin of the system willcontinuously decrease, leading to instability of the system. With theincrease of the harmonic frequency that needs to be suppressed, thephase frequency characteristics will probably pass through 180◦,making the current loop unstable. Therefore, for a conventionalresonant controller, when the number of suppressed harmonics ishigh, the delay of the current loop must be compensated. Thesystem would be more complex.

In this article, a feedback controller is introduced into theharmonic current controller. When K > 0, the phase margin of thesystem is obviously improved, and the system can remain stableat a higher resonance frequency. When the value of the parameterK changes, the root locus of the closed loop system is shown inFig. 13, at this time, the root trajectory is within the unit circle,which means the system can remain stable. When K increases, theroot locus approaches to the border, the system is more sensitive tothe disturbance. Therefore, K should be limited to the appropriaterange, here the value of K is chosen as 5.

4.2.1. Effects of sampling frequency and the numberof paralleled controllers When the sampling frequency ishigh, the system could be transformed from continuous domainto discrete domain with a better performance. However, when thesampling frequency is low, the Nyquist frequency of the controlsystem approaches to the resonant frequency, leading to instabilityof the system. Figure 14 shows the root locus of the systemwhen the sampling frequencies are 5, 10, and 20 kHz, respectively.

1537 IEEJ Trans 14: 1532–1542 (2019)

M. MU ET AL.

1

0.5

Root locus

0

Imag

inar

y ax

is

–0.5

–1

–1 –0.5 0Real axis

0.5 1

Fig. 14. Closed loop root locus when sampling frequency changes

1

0.5

Root locus

0

Imag

inar

y ax

is

–0.5

–1

–1 –0.5 0Real axis

Increase ofPR controller(fs=5kHz)

0.5 1

Number=4, fs=20 kHz

Number=4, fs=5 kHz

Fig. 15. Closed-loop root locus when the number of parallelresonant controllers changes

As can be seen from the diagram, with the reducing samplingfrequency, the stable range of the system gets smaller.

When the sampling frequency is constant, the system tendsto be unstable with the increase of the resonant controllers. Asshown in Fig. 15, at a sampling frequency of 5 kHz, the root locusmoves to out of the unit circle with the number of resonancecontrollers increasing. For the control strategy in this article,multiple resonance controllers are required. Under the conditionthat the sampling frequency is 20 kHz, part of the system rootlocus is within the unit circle. To ensure that the system is in astable state, a higher sampling frequency should be adopted whenmultiple resonant controllers are connected in parallel.

4.2.2. Parametric design and its effect on stability Inthis article, the resonance coefficient of the resonant controllerand the cut-off frequency near the resonant point are analyzedand designed by the root locus method. For the multiplied PRcontroller, each resonant term has a high gain only near itsresonance frequency. Therefore, when the parameters are analyzed,the resonant coefficient can be set separately to find the criticalvalue of the resonant coefficient K r at the corresponding frequency

1

0.5

–0.5

–1

0

Root locus

Kr3 = 5200

Kr3 increase

Real axis–1 –0.5 0 0.5 1

Imag

inar

y ax

is

Fig. 16. Root locus when Kr3 changes

Root locus

1

0.5

0

–0.5

–1

–1 –0.5 0

Real axis

0.5 1

Imag

inar

y ax

isKr31 = 400

Kr31 increase

Fig. 17. Root locus when Kr31 changes

to simplify the process. Meanwhile, the cut-off frequency ωch isreasonably designed.

Figure 16 shows the root locus of the system when the resonantfrequency is 150 Hz. As K r increases, the root locus moves to outof the unit circle, that is, the system tends to be unstable. Thedistance between the closed-loop zero and pole increases, so thedynamic response of the system accelerates. After designing, thecritical value of K r3 at this frequency is 5200.

In the same way, Fig. 17 is the root locus of the system whenthe resonant frequency is 1550 Hz, and the critical value of K r31 is400. We can obtain the critical values of K r33 < 375, K r35 < 350.

ωch is the cut-off frequency around resonance frequency, anddecides the sensitiveness to the frequency offset. According tostandard of ‘GB/T15945-2008’ in China, offset frequency of apower system is no more than 0.2 Hz, for h-order harmoniccurrent, offset frequency < (0.2 × h)Hz.

According to the definition of bandwidth, we get the formula:∣∣∣∣ 2Krhωch (jω)

(jω)2 + 2ωch(jω) + ω2o

∣∣∣∣ = Krh√2

(29)

At this time, the bandwidth is ωch /π , so:

ωch/π ≥ 2 × 0.2 × hHz (30)

1538 IEEJ Trans 14: 1532–1542 (2019)

A NOVEL LOCOMOTIVE AUXILIARY CONVERTER CONTROL STRATEGY

Fig. 18. Tracking performance at different switching frequencies

Table I. Main circuit parameter

Winding Primary Traction Auxiliary

Rated power 7051 kVA 6400 kVA 2 × 217 kVARated voltage 25 kV 4 × 1950 V 2 × 304 VRated current 282 A 4 × 820 A 2 × 714 ADC voltage — 3500 V 600 VSwitching frequency — 450 Hz 20 kHz

5. Simulation and Experimental Results

This article mainly focuses on the electric locomotive, andthe control strategy is verified by Matlab/Simulink. First of all,the influence of the inductance value on tracking performance isverified. Then, the feasibility of the novel control strategy of theauxiliary converter is verified by observing the power quality ofthe traction network.

The hardware in loop experiment is carried out by RT-LAB. Thecontrol scheme is digitalized with digital signal processor (DSP)to verify the feasibility of the control scheme for improving thepower quality and restraining resonance.

5.1. Simulation verification of inductance value InSection 2.2, the inductance value is analyzed in detail. From theformula (18), the switching frequency determines the inductancevalue, which affects the tracking performance.

Figure 18 compares the tracking performance at differentswitching frequencies for the same reference current. Converterparameters are shown in Table I. The y-axis is the AC current inthe auxiliary converter, the x -axis shows time.

At a frequency of 5 kHz, L = 100 μH; When the frequency is20 kHz, L = 50 μH. The harmonic current frequency is around1550 Hz. From the simulation results, we can conclude that forthe same reference harmonic current, the higher the switchingfrequency is, the better the tracking performance of the currentis, that is, the compensation current can compensate the harmoniccurrent generated by the traction converter better. The applicationof SiC devices can increase the switching frequency and generatehigh-frequency compensation current while reducing the volumeand losses of the converter. Therefore, this article considers theuse of SiC devices in auxiliary converters.

5.2. Simulation verification of converter functionand resonance suppression To verify the function ofimproving power quality in the traction network, the current is

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

TH

D%

2000 2500 3000

Fig. 19. Spectrum of primary side before compensation

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

TH

D%

2000 2500 3000

Fig. 20. Spectrum of primary side after compensation

900

800

700

600

Vol

tage

(V

)

500

400

300

200

100

00 1 2 3 4 5

Time (s)6 7 8 9 10

Fig. 21. DC output voltage of auxiliary converter

detected and analyzed by Fourier transform. Before the filterfunction is applied, the current spectrum of the primary side isshown in Fig. 19. Harmonic current frequencies are around 3times of the fundamental frequency and 4 times of the switchingfrequency. As explained in Section 4.2, the odd harmonic valuesnear 1800 Hz are high.

After the filter function is enabled, the current spectrum isshown in Fig. 20. The harmonic contents near the third harmonicand integer multiples of the switching frequency are significantlyreduced, which means the harmonics generated by the tractionconverter could be filtered by the scheme, improving the powerquality of the traction network.

Figure 21 shows the DC output voltage of the auxiliary con-verter. Before the filter function operates, the converter transfersthe voltage of AC 304 V to DC 600 V for the inverter to sup-ply power for auxiliary equipment. When the filtering function isstarted at the time of 1 s, the output voltage is disturbed and thenresumes to a stable state of 600 V after the time of 2 s, whichmeans the rectifier function of the converter can still be realized.

The T-type equivalent circuit of a certain line is established byadopting the method in Section 2.2. The impedance characteristicof the network is shown in Fig. 22. It can be seen from the diagramthat the impedance of the transmission line is higher near 1550 Hz.When the certain harmonic current is injected into the line, thevoltage would rise, leading to resonance accident.

1539 IEEJ Trans 14: 1532–1542 (2019)

M. MU ET AL.

00

1000

2000

3000

4000

500 1000 1500Frequency (Hz)

Impe

danc

e (Ω

)

2000 2500 3000

Fig. 22. Impedance characteristic of the network

Vo

ltage

(V)

2.1 2.2 2.3 2.4 2.5

Time (s)

21.91.81.71.61.5–8

–6

–4

–2

0

2

4

6

8

Fig. 23. Voltage of traction network

Figure 23 shows the voltage waveform of the traction network.Before the time of 2 s, the current injected by the traction converterinto the traction network contains a large number of harmonics at1550 Hz, causing resonance accident and a resonant peak voltageof over 55 kV. After the time of 2 s, the filtering function isoperated, and the resonant voltage is suppressed. The peak valueof the traction network voltage is 27.5

√2 kV, which is a normal

state.The control scheme of the vehicle converter could complete two

functions of rectification and filtering, converting power for theauxiliary equipment, improving the power quality of the tractionnetwork, and suppressing the resonance voltage. Aiming at high-frequency harmonic, the SiC devices are applied to auxiliaryconverters, thereby improving switching frequency, reducing lossand weight, and meeting the trend of lightweight in rail transit.

5.3. Analysis of the experimental results To verifythe feasibility of the control algorithm, the RT-LAB semi physicalplatform is used to carry out the experiment and digitize the controlscheme.

5.3.1. Introduction of the RT-LAB platform Figure 24shows the block diagram of the hardware in the loop experimentalplatform, which is composed of the computer, the OP5600simulator, and the DSP + field-programmable gate array (FPGA)controller.

In the experiment, due to the low calculation precision of theplatform, the maximum switching frequency is 5 kHz, which ismuch lower than the frequency of 20 kHz applied in simulation.Therefore, the harmonic to be suppressed should be lower.The rectifier function and harmonic suppression function of theconverter are verified when the harmonic frequencies are 150and 850 Hz. Another characteristic frequency of the resonanceaccidents is 850 Hz.

5.3.2. Experimental results of harmonic suppressionWhen the harmonic current is 3.6 A, 150 Hz is injected into thetraction network, the measured fundamental current value in theprimary side is 371 A. Before filtering, the spectrum of the primaryside current is shown in Fig. 25, total harmonic distortion (THD)%at 150 Hz is 1.05%.

PC:OPAL-RT;CCS6.0

RT-LAB OP5600

DSP controller

Fig. 24. RT-LAB platform

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

THD% (150 Hz) = 1.05%

TH

D%

2000 2500 3000

Fig. 25. Spectrum of the primary side before compensation(150 Hz)

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

THD% (150 Hz) = 0.279%TH

D%

2000 2500 3000

Fig. 26. Spectrum of the primary side after compensation(150 Hz)

After filtering, the THD% at 150 Hz is decreased to 0.279%.For the 850 Hz harmonic current, THD% is decreased from

0.927 to 0.292%.From the experimental results, we can come to the conclusion

that for the harmonic current at 150 and 850 Hz, the converter canimprove the power quality of the traction network.

6. Conclusion

To improve the quality of electric power injected into the tractionnetwork and to suppress the resonance voltage, the novel controlscheme for auxiliary converter is proposed.

For this scheme, the main circuit inductance of the auxiliaryconverter is analyzed, the value is influenced by switchingfrequency of auxiliary converter and harmonic frequency of thetraction converter. To compensate the high frequency current, theswitching frequency of the auxiliary side is chosen as 20 kHz,At the same time, by applying SiC devices, a good suppressionperformance can be achieved, reducing losses, volume, and weight

1540 IEEJ Trans 14: 1532–1542 (2019)

A NOVEL LOCOMOTIVE AUXILIARY CONVERTER CONTROL STRATEGY

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

THD% (850 Hz) = 0.927%

TH

D%

2000 2500 3000

Fig. 27. Spectrum of the primary side before compensation(850 Hz)

00

0.5

1.0

1.5

500 1000 1500Frequency (Hz)

THD% (850 Hz) = 0.292%

TH

D%

2000 2500 3000

Fig. 28. Spectrum of the primary side after compensation(850 Hz)

of the converter, which is conducive to the lightweight andenvironmentally friendly development of rail transit.

For the purpose of putting this method into practice, the digitalimplementation of the control scheme is produced. Tustin withprewarping method and root locus is applied to analyze the criticalvalue of parameters and to analyze the stability of the system.For the multiple resonance controller, the sampling frequency is20 kHz. At the same time, the feedback control is introduced toincrease the phase margin so as to obtain a stability system. Bysimulations and experiments, the feasibility of the control schemeof the multifunction converter is verified, the power quality of theelectrified railway is improved, and the resonance accident couldbe suppressed.

Acknowledgments

This work was supported by the Fundamental Research Funds forthe Central Universities under Grant 2018YJS158 of China. In addition,Toshiba China Co., Ltd also provided support in testing.

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M. MU ET AL.

Meijun Mu (Non-member) received her B.S. degree in electricalengineering from Beijing Jiaotong Univer-sity, Beijing, China in 2016. She is currentlypursuing her Master’s degree in electricalengineering at Beijing Jiaotong University.Her research interests are power electronicsand electrical drives.

Zhongping Yang (Non-member) received his B.Eng. degree fromTokyo University of Mercantile Marine,Tokyo, Japan in 1997, and received hisM.Eng. degree and Ph.D. degree from theUniversity of Tokyo, Tokyo, Japan in 1999and 2002, respectively, all in electrical engi-neering. He is currently a Professor withthe School of Electrical Engineering, Bei-jing Jiaotong University, Beijing, China. His

research interests include high-speed rail integration technology,traction & regenerative braking technology, and wireless powertransfer of urban rail vehicles. Prof. Yang received the ZhanTianyou Award for Science and Technology in 2010, the ExcellentPopular Science and Technology Book Award in 2011, and the Sci-ence and Technology Progress Award (second prize) of Ministryof Education in China in 2016.

Fei Lin (Non-member) received his B.S. degree from Xi’an Jiao-tong University, Xi’an, China, M.S. degreefrom Shandong University, Jinan, China,and Ph.D. degree from Tsinghua Univer-sity, Beijing, China, in 1997, 2000, 2004,respectively, all in electrical engineering. Heis currently a Professor with the Schoolof Electrical Engineering, Beijing JiaotongUniversity, Beijing, China. His research

interests include traction converter and motor drives, energymanagement for railway systems, and digital control of power-electronic-based devices.

Shihui Liu (Non-member) received her B.S. degree in electricalengineering from Beijing Jiaotong Univer-sity, Beijing, China in 2014. She is cur-rently working toward her Ph.D degree atthe School of Electrical Engineering, BeijingJiaotong University. Her current researchinterests are in the areas of electric trac-tion systems for rail vehicles, vehicle-powersupply network coupling system, and power

quality.

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