Modified AC/DC Unified Power Flow and Energy-saving

0018-9545 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2021.3104309, IEEETransactions on Vehicular Technology

Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the

IEEE by sending a request to [email protected].

Abstract— Energy feedback systems (EFSs) have been widely

applied in urban rail transit, and a power flow algorithm and

energy-saving evaluation of urban rail power supply systems with

EFSs are studied in this paper. First, trains, the reflux system, and

traction substations with EFSs are modeled, and the multimode

transitions are analyzed, including the maximum power state of

the EFS. Then, a modified AC/DC unified power flow algorithm

for the DC power supply system, which simplified the DC reflux

system is proposed, and a field case study based on a multiple train

scenario is presented to validate the algorithm. Furthermore,

system-level energy-saving evaluation indexes are applied

according to system power flow analysis. When the headway time

decreases, the proposed indexes decrease in general mainly as

there is more regenerative braking energy absorbed by adjacent

trains. The higher the load rates of the step-down substations are,

the more daily feedback energy is utilized. When the start voltage

of the EFS ranges from 1650 V to 1770 V, the maximum energy-

saving rate reaches 11.9%, which occurs when the start voltage is

1670 V. When the no-load voltage is relatively high, the start

voltage should not be higher than 1750 V to keep the system

running in high efficiency. These results can provide advice for the

design and operation of traction power supply systems with EFSs.

Index Terms—Unified AC/DC power flow, energy

feedback system (EFS), energy-saving evaluation

I. INTRODUCTION

N recent years, urban rail transit has been constructed in large

and medium-sized cities worldwide. In DC traction power

supply systems, if the regenerative energy is not fully recovered

by adjacent trains, the energy will be dissipated into onboard

resistors or in mechanical braking, contributing to energy waste

and thermal loss. Several technologies have been adopted to

utilize regenerative braking energy. Energy storage devices can

be introduced to reinject electricity through DC buses, such as

supercapacitors, new batteries, and flywheels [1]-[3]. Energy

feedback systems (EFSs) have also been widely applied.

In urban rail, two 12-pulse rectifier units operate in parallel

to form a 24-pulse DC output by ±7.5° phase shifting at the

primary side. The AC side of the EFS can be connected to the

primary side of the power rectifier transformer through a

dedicated medium voltage transformer, as shown in Fig. 1. (a).

The AC side of the EFS can also be connected to the secondary

side of the auxiliary transformer through a dedicated

transformer, as shown in Fig. 1. (b) [4]. In [5], an EFS model

was designed and verified in simulation and field tests. In [6],

the operating characteristics of EFSs were studied and

optimized for system design and optimization.

With the wide application of EFSs, the power supply

calculation algorithm needs to be further studied. An AC/DC

hybrid iteration algorithm considering the regenerative braking

conditions and the connection between the converters was

discussed in [7]. However, rectifier and inverter devices are

uniformly modeled without considering power reversal during

inversion. In [8], train movement and electrical networks were

modeled by a new method. In [9], the Newton-Raphson power

flow algorithm was applied to AC/DC power systems. In [10],

a detailed model of the R-L-fed inverting substation was

presented and applied in the mentioned system. A hybrid

AC/DC calculation algorithm of a traction power supply system

for urban rail was studied in [10-12], but an EFS model was not

considered. In [13] and [14], different types of traction

substations, including inverting substations, were modeled, but

an EFS model was not mentioned. In [15], an EFS was modeled

as a thyristor, but power inversion was not considered. In [16]-

[20], a reasonable steady-state model for a voltage source

converter (VSC) was created, and an alternative algorithm of

the AC/DC hybrid system power flow was proposed. However,

the alternative algorithm was applied to high-voltage direct

current (HVDC) transmission. It is noteworthy that the moving

load model in urban rail is quite different from the load model

of an HVDC system. In [21]-[23], hybrid and unified AC/DC

calculation algorithms of the traction power supply system were

studied.

Energy-saving evaluations also need to be studied. In [23],

system-level energy-saving evaluation indexes were proposed.

Modified AC/DC Unified Power Flow and

Energy-saving Evaluation for Urban Rail Power

Supply System with Energy Feedback Systems

Wei Liu, Member, IEEE, Jian Zhang, Hui Wang, Tuojian Wu, Ying Lou, and Xiaowen Ye

I

Bus I Bus II AC

Middle

Voltage

DC

AC

low

voltage

AC

middle

voltage

DC

Bus I Bus II

AC

low

voltage

(a) (b)

Fig. 1. Structure of EFS: (a) Middle voltage EFS; (b) Low voltage EFS.

Authorized licensed use limited to: SOUTHWEST JIAOTONG UNIVERSITY. Downloaded on October 12,2021 at 14:57:09 UTC from IEEE Xplore. Restrictions apply.



> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

2

A case was simulated, and the energy savings rate was 8.71%.

In [24], an energy audit was implemented in a DC system, and

the regenerative braking of trains could achieve 27% energy

savings. In [25], the energy flow in a DC system was analyzed;

the energy consumption of traction substations and the

efficiency of usable regenerative braking energy were

compared between systems with and without EFSs.

In this paper, a unified AC/DC power flow algorithm for

urban rail considering the multimode transition of traction

substations with EFSs considering Bang-bang control is

proposed. The multiple operation modes of traction substations

include the rectifier mode, the turn-off mode, and the inverter

mode. The control strategy of stabilizing traction network

voltage and compensating reactive power is presented. In this

paper, system-level energy-saving evaluation indexes that

consider the energy returned to the main substations are

proposed, including the daily feedback energy, energy feedback

rate, and system-level energy-saving rate. A subway is tested in

the field to verify the algorithm. The load processes of traction

substation and energy are compared. In addition, different

headway times, load rates of step-down substations, and start

voltages of the EFS are discussed.

II. MODEL OF THE TRACTION POWER SUPPLY SYSTEM

The traction power supply system includes traction

substations, step-down substations, traction networks, and

trains. Step-down substations are modeled as PQ loads. Trains

are modeled as movable loads according to the operating

timetable [26]. For DC traction substations installed with an

EFS, there are three working modes: rectifier mode, turn-off

mode, and inverter mode.

A. Trains

In the power supply system of urban rail, trains can be

equivalently modeled as constant current sources or constant

power sources.

For the constant current source model, the current can be

obtained from the field test data or simulation results. The

mathematical model is

( , )=I f T p (1)

where I is the current of the train, T is the time and p is the

position of the train.

Fig. 2. shows the equivalent model of the constant current

source of the train, which is applied in this paper.

B. The Reflux System

In urban rail transit, the reflux system includes the rail, the

stray current collection network, and the earth [33]. In this paper,

the stray current collection network is neglected. For the

realization of fast calculation, the distributed parameters of the

reflux system should be converted to lumped parameters. The

distributed parameter model is shown in Fig. 3. The equivalent

lumped parameter model is shown in Fig. 4. In which, x, x1 and

x2 are positions; i(x), i(x1) and i(x2) are the current; u(x), u(x1)

and u(x2) are rail potential. R is the longitudinal resistance of

rail per unit

I=f (T,p)

Traction

network

Rail

Fig. 2. The equivalent constant current model of the train.

Earth

Rail...

...

R dx

Rg/dx

i(x)

u(x)

x x+dx

Fig. 3. The distributed parameter model of the reflux system.

yg

zr

yg

i(x1) i(x2)

u(x1) u(x2)

x1 x2 Fig. 4. The lumped parameter model of the reflux system.

length; Rg is the insulation resistance of rail to ground per unit

length. The longitudinal resistance of rail is zr; the insulation

resistance of rail to the ground is yg. The infinitesimal is dx. In

the distributed model, i(x) and u(x) are:

( ) ( )

( )( )

/x

du x i x Rdx

u xdi x

R dx

= −

= −

(2)

The general solutions are

1 2

1 2

( ) 2

( )

2

x

x

C Ce

i x

u x C Ce

−

+

= −

H (3)

In which, =g

R

R ; C1 and C2 are determined by the boundary

conditions in the section; H and its inverse matrix, H-1 are:

1 1

1 1

g gRR RR

= −

H (4)

1 11 12-1

2 21 22

h h

h h

= =

hH

h (5)

For the two ports, x1 and x2, their relationship is:

2 1

2 1

( )2 1

( )2 1

( ) ( )

( ) ( )

x x

x x

i x e i x

u x u xe

−

− −

=

1

2

hH

h (6)

From (7), i(x2) is

2 1 1 2 1( )=c ( )+c ( )i x i x u x (7)

In which, c1 and c2 are:

( ) ( )

( ) ( )

2 1 2 1

11 21

2 1 2 1

22

' '1

' '2 12

c =

c =

x x x x

x x x x

h e h e

h e h e

− − −

− − −

+

+

(8)





3

Ps,Qs

1:kt

Id

Utposr Utnegr

Ut

Us θs,φs

Fig. 5. Interface model of the rectifier.

When the system is expressed as the lumped model as Fig.

4., according to the KCL and KVL, i(x2) can be expressed as:

2 g 1 1( ) (1 ) ( ) (2 ) ( )r g g ri x y z i x y y z u x= + − + (9)

For the x1- x2 section, zr, and yg can be obtained as:

2

1

2

2g

1

1

1

r

cz

c

cy

c

−=

= − +

(10)

C. Traction Substations in Rectifier Mode

The interface model of the rectifier unit is shown in Fig. 5.

[27]. At the AC side of the rectifier unit, Us is the node voltage,

θs is the phase angle, φs is the power factor angle, and Ps and Qs

are the active power and reactive power, respectively. At the

DC side of the rectifier unit, Ut is the voltage between the

positive and negative nodes, Id is the rectifier current, kt is the

transformation ratio of the rectifier transformer, and Utposr and

Utnegr represent the positive and negative bus voltages,

respectively. ηT is the efficiency of the rectifier unit, taking 0.98;

XC is the converter reactance of a single bridge; nt is the number

of converter bridges, taking 24; and k is a constant of 0.995.

To simplify the model, the influence of the phase shift

process is neglected. The AC/DC power supply calculation

model of the rectifier unit is shown in (11).

t ds

T

s t d s

t tposr tnegr

t s C d

t

=

=

=

3 2 3 =

3 2 = cosγ t s s

U IP

η

Q U I tanφ

U U -U

k U X Iπ πn

k k U φπ

−

(11)

When the traction substations are in rectifier mode, ΔPsr and

ΔQsr are power deviations at the AC side of the traction

substation; ΔItposr and ΔItnegr are the current deviations of the

positive and negative nodes at the DC side, as shown in (12).

( )

( )

sr s s s s s t d

=1

sr s s s s s t d s

=1

tposr d tpos

=1

tnegr d tneg

=1

cos sin

sin cos tan

M

i i i i i

i

M

i i i i i

i

N

j j

j

N

j j

j

P U U G B U I

Q U U G B U I

I I U G

I I U G

= − + −

= − − −

= −

= − −

(12)

where at the AC side, M is the number of AC nodes; Ui is the

node voltage; Gsi is the conductance between node s and node

i; Bsi is the susceptance between node s and node i; θsi is the

voltage phase angle between node s and node i. At the DC side,

N is the number of DC nodes; Uj is the node voltage; Gtposj is the

conductance between positive node t and node j; Gtnegj is the

conductance between negative node t and node j.

The modified equations with Id and φs as variables are:

1 t t s C d

t

2 t γ t s s

3 2 3

3 2cos

d U k U X In

d U k k U

= − +

= −

(13)

D. Traction Substations in Turn-off Mode

When the traction network voltage is between the no-load

voltage of the rectifier unit and the start voltage of the EFS, the

traction substations work in turn-off mode. The AC side power

deviations, ΔPso and ΔQso, are shown in (14).

( )

( )

so s i si si si si

i=1

so s i si si si si

i=1

cos sin

sin cos

M

M

P U U G B

Q U U G B

= +

= −

(14)

E. Traction Substations in Inverter Mode

When the traction network voltage exceeds the start voltage

of the EFS, the traction substations work in inverter mode. The

DC output characteristics are shown in Fig. 6. The voltage and

the injection current of the converter at the DC side are Ut and

Ir, respectively. The start voltage of the EFS is Uset, and the

corresponding maximum current is Imax. The rated power is PN.

The EFS consists of the voltage source converter bridge, the

converter reactor, and the DC capacitor [28]. A basic

schematic is shown in Fig. 7. The voltage and injected power

at the AC side of the EFS are Us∠θs，Ps+jQs. The equivalent

impedance of the converter is Rs+jXs. The voltage and

injection power at the converter bridge side are Uc∠θc, Pc+jQc.

Set δs=θs-θc, 2 2

s s s1= +Y R X and αs=arctan (Xs/Rs). The AC/DC

power supply calculation model of the EFS is shown in (15).

( )

( )

( )

2s ss s t s s s s s s

2s ss s t s s s s s

2

2s s s st r s t s s s t s s

cos cos2

sin sin2

cos cos2 2

mP U U Y U Y

mQ U U U Y

m mU I U U Y U Y

= − + +

= − + +

= − −

(15)

where μs is the utilization rate of DC voltage, μs[0,1]; ms is the

modulation degree, ms[0,1].

When the traction substations work in inverter mode, ΔPsi

and ΔQsi are the AC side node power deviations of the traction

substations, and ΔItposj and ΔItnegj are the current deviations of

the positive and negative nodes on the DC side. They are shown

in (16).





4

Ir

Ut

PN

Uset

Imax0

a b

c

Fig. 6. DC output characteristic of EFS.

Ps,Qs

Us θs

Pc,Qc Ir

UtRs Xs

Utposr Utnegr

Uc θc

Fig. 7. Basic schematic of EFS.

Rectifier

Mode

Ut Ud0

βUset Ut

Ir 0

Ut<Ud0

Turn-

off

Mode

Inverter

Mode 1

Inverter

Mode 2

P PN

Ut<βUset

Fig. 8. Multimode transition process.

( )

( )

( )

( )

s s s s s s

=1

2s

s t s s s s s s

s s s s s s

=1

2s

s t s s s s s s

tpos r tpos

=1

tneg r tneg

=

cos sin

cos cos2

sin cos

sin sin2

M

i i i i i i

i

M

i i i i i i

i

N

j j j

j

j j j

j

P U U G B

mU U Y U Y

Q U U G B

mU U Y U Y

I I U G

I I U G

= − +

+ + −

= − −

+ + −

= −

= − −

1

N

(16)

There are four control strategies for the EFS: 1) constant

control of Us and Ut; 2) constant control of Qs and Ut; 3)

constant control of Us and Ps; 4) constant control of Ps and Qs.

The second control strategy is applied to achieve the function

of reactive power compensation and stabling traction network

voltage in this paper. The set reactive power is Qset. During the

operation of the EFS, the AC side voltage fluctuates due to the

change in load, and the no-load voltage of the rectifier unit also

fluctuates correspondingly. Considering the dynamic

adjustment of the start voltage, the voltage fluctuation

coefficient is set as β, which is the ratio of the voltage at the AC

side of the traction substation to the rated voltage at the AC side.

The modified equations with Ir, δs, and ms are shown in (17)

considering the power limitation.

When P<PN, the ∆d4 corresponds to ab part in Fig. 6. and the

inverter mode 1 in Fig. 8; when P≥PN, the ∆d4 corresponds to

bc part in Fig. 6. and the inverter mode 2 in Fig. 8.

( ) ( ) ( )

( ) ( )

22

3 t r s s t s s s s t s s

t set

4

t r

25 s s t s s s s s s set

2 cos 2 cos

2 sin sin

N

N N

d U I m U U Y m U Y

U U P Pd

P U I P P

d m U U Y U Y Q

= − − +

− =

−

= − + + −

(17)

F. Multimode Transitions of Traction Substations

For each iteration of power flow, it is necessary to determine

the working mode of traction substations according to Ut, Id and

Ir. The multimode transition rules of the traction substations are

shown in Fig. 8. Ud0 is the no-load voltage of the rectifier unit.

The bang-bang control is adopted when judging the states.

Let S(k) be the state of the traction substation of the kth iteration,

and S(k+1) be the state of the traction substation of the k+1th

iteration. The traction substation state switching control

strategy is (18), in which the W1 is the voltage width, and W2 is

the current width. In the following part, W1 is 10V, and W2 is

5A. ( )

0

( )

0 U

( )

0

( )

0 U

( )

I( 1)

( )

Rectifier & Rectifier when

Turn-off &

Rectifier &

Turn-off when Turn-off &

Inverter 1 &

Turn-of

Inverter 1 when

k

t d

k

t d

k

t d

k

d t set

k

rk

k

S U U

S U U W

S U U

S U W U U

S I WS

S

+

−

−

−=

=

=

=

=

=

=

( )

I N

( )

U

( )

N

( )

U

f &

Inverter 1 & &

Inverter 2 &

Inverter 1& Inverter 2 when

Inverter 2 &

t set

k

r

k

t set

k

k

t set

U U

S I W P P

S U U W

S P P

S U U W

− −

−

=

=

=

=

(18)

III. MODIFIED AC/DC UNIFIED POWER FLOW ALGORITHM IN

URBAN RAIL POWER SUPPLY SYSTEM

A. The simplification of the DC reflux system

The voltage of the traction substations is the difference

between the traction network and the rail. When calculating

power flow, the traditional algorithms calculate the voltage of

the traction network voltage and the rail separately, which is not

necessary. If the traction network and the rail node can be

merged as one node, the number of the DC nodes will decrease,

which is helpful to speed up the calculation, while the voltage

of traction substations and trains can still be obtained. The

simplification of the DC side equivalent circuit is shown in Fig.

9.

Before simplification, there are traction network nodes and

rail nodes. In the traction substation, the positive nodes

correspond to traction nodes, and the negative nodes correspond

to rail nodes. The voltage and injection current of the traction

network node is Up and Ip; the voltage and injection current of





5

the rail node is Un and In. zt and zr are the traction network

resistance

...

traction

network

rail

earth

yg

zr

zt

+traction

substation

—

train

Ip

In +

—

train

Ip

Up

Un

Up - Un

traction network node

rail node

merged node

traction

substation

earth

Before simplification After simplification Fig. 9. The simplification of the DC side equivalent circuit.

and the longitude resistance of rail. The relationship of current

and voltage is:

=

p 11 12 p

n 21 22 n

I Y Y U

I Y Y U (19)

In which Y11, Y12, Y21, and Y22 are the parts of the admittance

matrix. Up, Ip, Un, and In are the vectors of all Up, Ip, Un, and In.

It can be found that Ip=-In. To speed the calculation, the

traction network nodes and rail nodes are merged. For the newly

merged node, its voltage is the difference between the traction

network node and rail node, while the current is that of the

traction network node. The relationship of current and voltage

is:

( )= − np eq pI Y U U (20)

In which Yeq= (Y11+ Y12·a) (1-a)-1, a=- (Y 12+Y 22) -1(Y11+Y21).

B. Unified AC/DC Power Flow Algorithm

When adopting the unified AC/DC power flow algorithm in

an urban rail power supply calculation, the per-unit value

system is the same as in [10]. The unified AC/DC power flow

algorithm is shown in Fig. 10.

In the algorithm, before the calculation starts, the parameters

are input, including the traction calculating results, the system

structure information, the parameters of each component, like

the capacity of transformers, the operation timetable of trains,

iteration error ε, and the maximum iteration number nmax.

Through the traction calculating results and the system

structure information, the locations and current demand of

trains can be attained, and the DC side conductance matrix can

also be obtained.

After the initialization of iteration time k, voltage, and

working mode of traction substations, the admittance matrix of

the AC and DC side is merged, and the mismatch vector F is

calculated. All the mismatch equations and corrections

equations are collected into vector-matrix F and D as shown in

(21).

=[ ]

=[ ]

=

T

pv ac ac trac dc

T

pv ac ac trac dc

F ΔP ,ΔP ,ΔQ ,ΔF ,ΔI

D Δθ ,Δθ ,ΔU ,ΔD ,ΔU

F J D

(21)

where ∆Ppv and ∆θpv are the active power mismatch vectors and

phase correction vectors of the PV nodes; ∆Pac, ∆Qac, ∆θac and

∆Uac are the active power mismatch vectors, reactive power

mismatch vectors, voltage phase correction vectors, and

magnitude corrections of the PQ nodes except for the AC nodes

of the traction substations. ∆Ftrac and ∆Dtrac are the mismatches

Start

Set simulation

time t as 0

DC side

conductance matrix

is obtained.

Set the iteration time k=0 and the

convergence accuracy ε. Set AC

side voltage as 1 0°and DC

voltage as 1. Set initial working

mode of each traction substation as

rectifier mode.

Deviation vector F is created

A

A

max(F) < ε or

k nmax

Establish the jacobian

matrix J. Solve the

modified vector D for

the kth iteration.

Update each node value

according to D

Do the working modes of the

traction substations change?

Update node

type

Y

t=t+1

t >

headway

time?

Y

End

Y

B

N

AC/DC nodes admittance matrix

Y is obtained.

N

N

B

Fig. 10. Unified AC/DC power flow algorithm.

vectors and correction vectors of the traction substations. ∆Idc

and ∆Edc are the current mismatch vectors and voltage

magnitude correction vectors of the DC nodes, which do not

contain the DC nodes of the traction substations or the rail

nodes. J is the Jacobian matrix. ∆Ftrac and ∆Dtrac are shown in

(22). When the mode changes, the matrix dimensions of F, J,

and D will also change.

3 4 5

if rectifier mode, [ ]

= if turn-off mode,[ ]

if inverter mode, [ ]

if rectifier mode, [ (

=

T

sr sr 1 2 tposr

T

trac so so

T

si si tposi

sr sr d s tp

trac

ΔP ,ΔQ ,Δd ,Δd ,ΔI

ΔF ΔP ,ΔQ

ΔP ,ΔQ ,Δd ,Δd ,Δd ,ΔI

Δθ ,ΔU ,ΔI ,Δφ , ΔU

ΔD

)]

if turn-off mode, [ ]

if inverter mode, [ ( )]

−

−

T

osr tnegr

T

so so

T

si si r s s tposi tnegi

ΔU

Δθ ,ΔU

Δθ ,ΔU ,ΔI ,Δδ ,Δm , ΔU ΔU

(22)

where for the AC nodes of the traction substations in rectifier

mode, turn-off mode, and inverter mode, ∆Psr, ∆Pso, and ∆Psi

are the active power mismatch vectors; ∆Qsr, ∆Qso, and ∆Qsi

are the reactive power mismatch vectors; ∆θsr, ∆θso, and ∆θsi

are the voltage angle correction vectors; and ∆Usr, ∆Uso and

∆Usi are the voltage magnitude correction vectors. When the

traction substations are in rectifier mode, ∆d1 and ∆ d2 are the

mismatch vectors, and ∆Id and ∆φs are the correction vector of

the DC current and the power factor angle of the AC side,

respectively; ∆Itposr is the correction vectors of the positive DC

current; and (∆Utposr - ∆Utnegr) is the correction vectors of the

difference between the positive DC voltage and the negative

DC voltage. When the traction substations are in inverter mode,

∆d3, ∆ d4, and ∆ d5 are the mismatch vectors, and ∆Ir, ∆δs, and

∆ms are the correction vectors of the DC current, δs, and the

modulation degree of the traction substations, respectively.

∆Itposi is the correction vector of the positive DC current;

(∆Utposi - ∆Utnegi) is the correction vector of the difference

between the positive DC voltage and the negative DC voltage.





6

TABLE I VARIABLES AND SYMBOLS OF ENERGY

Variable Case 1 Case 2

Traction energy of all rectifier units WT1 WT2

Active energy consumed by all main substations

WM WM'

Feedback energy at the DC side WF

Feedback energy at AC side WF' Energy fed from the EFS to the main

substations

WR

Energy consumed by the on-board resistors

Wres Wres'

Regenerative braking energy

consumed by the adjacent trains

Wres-trac Wres-trac'

Energy consumed by all step-down

substations

WS

Traction energy of all trains Wtrac

Regenerative braking energy of all

trains

Wreg

If the maximum value in F is less than ε, the iteration of time

t ends, and the calculation of the next second starts; else the

calculation keeps going. J is established and D is obtained. The

working state of traction substations is updated. The iteration

continues until the maximum number of simulations is reached

or it converges. And the calculation ends when t meets the

headway time, cause after that the calculation is repetitive. The

output parameters include node voltages, currents.

IV. ENERGY-SAVING EVALUATION INDEXES

To evaluate the energy-saving effect of reversible substations

in different cases, the average daily energy consumption and

annual energy consumption need to be taken into account [29],

[30].

The regenerative braking energy is fed back to the medium-

voltage network through the EFSs. Usually, it is consumed by

the step-down substations, but part of it is returned to the main

substations. This portion of the energy cannot be used by urban

rail power supply systems. Therefore, it should be deducted

when evaluating the energy-saving effect.

To compare the energy-saving effect, Case 1 represents the

power supply system without EFSs or where EFSs are not in

operation, and Case 2 represents the power supply system with

EFSs in operation. The load processes of the step-down stations,

trains, and their operation timetable in the two cases are strictly

the same.

The energy flow diagram is shown in Fig. 11. It is assumed

that power losses on the cables and transformers are ignored.

The variables and symbols of energy are shown in TABLE I.

The energy flow relation is shown in (23). The system

feedback energy WFr and feedback rate of regenerative braking

energy λ are defined in (24). It is worthy to mention that WFr is

the energy truly utilized by the system, because the energy fed

back to main stations, meanly WR, can not be utilized in the

system.

M S

M R F F S

trac T reg T reg

T1

T2

T1 -trac T2 -t

reg

rac

-trac -trres reg F ar ces reg

W W W

W W W W W

W W W W W

W W W W W W

= +

− = − +

= + +

= + += +

=

(23)

Main

Substations

Step-down

substations

WM

WT1

Wreg Wres On-board

resistance

Wreg-trac

Traction

trains

Braking

trains

Rectifier

units

WS

Wtrac

ηT WT1

Traction

power

supply

System

(a)

Main

Substations

Step-down

substations

WM' WR

WT2

WF'WS

Wtrac Wreg Wres'

On-board

resistance

Wreg-trac'

EFSsRectifier

units

Traction

trains

Braking

trains

ηT WT2WF

Traction

power

supply

system

(b)

Fig. 11. Energy flow diagram: (a) Case 1; (b) Case 2.

P1 P2

P3

Rectifier

unitStep-down

load

Main

transformer

P4

Fig. 12. Schematic diagram of circulation calculation.

Fr F R

F

T2

100%

W W W

W

W

= −

=

(24)

The essential of energy-saving of EFSs in traction power

supply systems is reducing the energy consumption of onboard

resistors, while the negative effect of EFS that it feeds back

energy to main stations should also be noticed. Compared with

Case 1, the energy-saving rate of the traction power supply

system, ξ, can be described in (25).

res R

T

re

1

T T1 T2 F

T1

s

R

= 100%

( )+ = 100%

W W W

W

W W W

W

W

− −

− −

(25)





7

It is undeniable that the WF' used by step-down loads is

appropriate, and WR is disadvantageous. As to WF' used by

rectifier units, it is called circulating power. The circulating

power can be calculated as in Fig. 12.

In Fig. 12, only the structure of one bus is shown, and the left

side is connected to the main substation. Set that the direction

of power in Fig. 12 is the positive direction. P4 is greater than

0. If P1 ≥ 0, P2 > 0, P3 > 0, and P2 > P4, the circulating power

is (P2 - P4). If P1 < 0, P2 > 0, P3 > 0, the circulating power is P3.

V. CASE STUDIES

Two subway projects are studied. The first subway case is

Guangzhou Metro Line 21. Its length is 25.69 km. For the line

in operation, there are 2 main substations, 9 stations, including

8 traction substations and 1 step-down substation, and 2 interval

substations. The installation capacity of the main transformers

is 2×40 MVA. The rated power of the rectifier units is 2×2500

kW, and the no-load voltage is 1680 V. S1, S9, and S10 are

equipped with EFSs. The trains are 6B marshaling, with the top

speed of 120 km/h. The resistance of the overhead contact

system is 0.0136 Ω/km, and the rail resistance is 0.02 Ω/km.

The structure is shown in Fig. 13, and the locations of each

traction substation are shown in Table Ⅱ.

The second subway case is Chongqing Rail Transit Line 9,

which has 2 main substations and 29 stations, including 23

traction substations and 6 step-down substations. Its length is

40.45 km. The installation capacities of the main transformers

are 2×50 MVA and 2×25 MVA. The rated power of the rectifier

units is 2×3000 kW, and the no-load voltage is 1593 V. EFSs

are installed at every other traction substation. The trains are

6As marshaling, with a top speed of 100 km/h. The resistance

parameters are the same as Guangzhou Metro Line 21. The

structure is shown in Fig. 14, and the locations of each traction

substation are shown in Table Ⅲ.

A. Convergence performance

To verify the validity of the unified AC/DC power supply

calculation algorithm, the convergence accuracy is set as ε=10-

3(pu), and the initial modes of all traction substations are

rectifier modes.

Chongqing Rail Transit Line 9 has more stations than

Guangzhou Metro Line 2. Set that the headway time is 300 s.

All time steps in the simulation period can converge. Taking

289 s as an example, the convergence tolerance is 7.53*10-5(pu),

and after 3 iterations, the algorithm with bang-bang control

converges, as shown in Fig. 15, while the algorithm without

bang-bang control converges after 12 iterations.

All tests were run using a personal computer with an Intel(R)

Core (TM) i9-9900K CPU @ 3.60 GHz and 12 GB of RAM.

The convergence time and iteration numbers are shown in Table

IV. It can be seen that the calculating time is shorter when the

headway time is longer, and that is because the trains are less.

The mean time before and after simplification is shown, which

illustrates that the simplification of the DC reflux system is

S1S2 S3

S4 S5 S6

S7

S8 S9 S10

Traction substation

Step-down substation

Interval substation

Fig. 13. Structure of Guangzhou Metro Line 21.

TABLE Ⅱ

LOCATION DISTRIBUTION OF TRACTION SUBSTATIONS OF GUANGZHOU

METRO LINE 21

Traction

substation Location/km

Traction


S1 0.243 S6 13.9 S2 2.456 S7 15.995

S3 4.568 S8 20.235

S4 7.804 S9 23.322 S5 10.67 S10 25.650

Traction substation

Step-down substation

Fig. 14. Structure of Chongqing Rail Transit Line 9.

TABLE Ⅲ LOCATION DISTRIBUTION OF TRACTION SUBSTATIONS OF CHONGQING RAIL

TRANSIT LINE 9

Traction


Traction


1 0.02 12 21.52

2 1.56 13 23.04 3 3.66 14 26.53

4 5.99 15 28.21

5 7.11 16 30.23

6 10.59 17 31.42

7 12.31 18 33.53

8 15.16 19 35.98

9 16.24 20 38.61

10 17.43 21 40.02

11 20.16

more efficient when there are more nodes in the system. The

results for all time steps converge. The results show that the

convergence performance of the algorithm is acceptable, and

the simulation time can be saved up to 14.3% through the

simplification of the DC matrix.





8

1 2 3 4 5 6 7 8 9 10 11 12

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

Without Bang-bang control

With Bang-bang control

Number of times

Conver

ge

tole

rance

Fig. 15. Convergence with iteration at 289 s.

TABLE IV

THE CONVERGE TIME UNDER DIFFERENT HEADWAY TIMES

Headway

time/s

Mean time per before

simplification per time step(s)

Mean time after

simplification per time step(s)

Average

iteration number

120 3.1 2.8 5.2

180 2.1 1.8 5.3

240 1.7 1.5 5.1

300 1.3 1.1 4.8

400 1.1 1.0 4.6

450 1.0 0.9 4.5

600 0.7 0.7 3.2

900 0.4 0.4 2.9

33 kV

Inverter feedback device~

DC1500 V+

-

~

Current measurement

Voltage measurement

Up traction networkDown traction network

Fig. 16. Measurement positions.

B. Verification

To verify the simulation results, a field test is implemented

at S1, S9, and S10 on Guangzhou Metro Line 21. The current

and voltage sensors are installed at the DC feeder of the EFS

and the DC feeder of the rectifier unit. The measurement

positions are shown in Fig. 16.

During the test, the start voltage of the EFS is set to 1720 V,

1750 V, and 1770 V separately for one day. The no-load voltage

of rectifiers is set to 1680V according to the field test data.

Taking S9 as an example, the simulation and the field test

results with different EFS start voltages are shown in Fig. 17.

The Pearson correlation coefficient is used to evaluate the

correlation between two variables, as shown in (26).

,

cov( , )X Y

X Y

X Y

= (26)

where cov (X, Y) is the covariance between variables X and Y.

σX and σY are the standard deviation of X and Y.

The closer the Pearson correlation coefficient gets to 1, the

higher the positive correlation of the two curves is [31]. When

the start voltage is 1720 V, 1750 V, and 1770 V, the Pearson

correlation coefficients are 0.85, 0.76, and 0.92, respectively,

TABLE V

COMPARISON BETWEEN THE SIMULATIONS AND MEASUREMENTS OF

TRACTION SUBSTATION S9

Start voltage/V 1720 1750 1770

Traction energy per

hour / kWh

Field test 461.6 577.7 683.3

Simulation 439.4 604.4 678.7

Feedback energy per

hour / kWh Field test 117.2 78.3 27.1

Simulation 110.8 71.9 28.8

Fig. 18. The δ under different start voltage of EFS.

showing that the simulation results are close to field test results.

The trains operation, timetable, no-load voltage of different

rectifiers, start of the onboard resistor will influence the load

process in the simulation.

0.0

0.2

0.4

0.6

δ

The start voltage of EFSs is 1720V.



The EFSs are turned off.

0.0

0.2

0.4

0.6

Section

(a) The δ in field test

δ

(b) The δ in simulation

S9-S10S6-S9S5-S6S4-S5S3-S4S2-S3S1-S2

S1-S2 S2-S3 S3-S4 S4-S5 S5-S6 S6-S9 S9-S10Section

(a)

(b)

(c)

Fig. 17. Comparison of the field tests and simulations of the traction substation with different EFS start voltages: (a) 1720 V; (b) 1750 V; (c) 1770 V.

-1500

-1000

-500

0

500

1000

1500

2000

Cu

rren

t /A

Time / minute: second

08:0007:0006:0005:0004:0003:0000:00 01:00 02:00

Simulation Test in field

-1000

-500

0

500

1000

1500

2000

Time / minute: second

Cu

rren

t /A

08:0007:0006:0005:0004:0003:0000:00 01:00 02:00

Test in fieldSimulation

-500

0

500

1000

1500

2000

Cu

rren

t /A

Time / minute: second08:0007:0006:0005:0004:0003:0000:00 01:00 02:00

Test in fieldSimulation





9

Table V shows the energy of the simulation and field test of

S9. When the start voltage of the EFS is higher, the greater the

hourly traction energy consumption is. In the field test, the

traction energy changes from 461.6 kWh/h to 683.3 kWh/h

when the start voltage changes from 1720V to 1770V; the field

feedback energy changes from 117.2 kWh/h to 23.1 kWh/h.

The simulation results differ from the measured data by no

more than 8.2%. Through the above results, the accuracy of the

algorithm can be verified.

According to (25), the energy consumed on on-board

resistance and WR play important roles in energy saving. Due to

the limitation of site conditions, WR is not recorded. The ratio

of energy consumption of on-board resistance to regenerative

braking energy is set as δ. The δ in the field test is as Fig. 18.

(a), and δ in simulation is shown in Fig. 18. (b).

It can be seen that when the start voltage of EFS is 1720V,

1750V, 1770V, and EFSs are turned off, the δ of the field test

in section S9-S10 is 0%, 1.57%, 32.17%, and 41.73%,

respectively, while δ of the simulation is 1.57%, 7.06%, 28.33%,

and 39.76%. When the start voltage of EFS is higher than

1750V, the energy consumption on the on-board braking

resistor increases significantly. It can be seen that in subway

cases that the high no-load voltage of rectifiers is relatively high,

to keep the system run in the maximum efficiency, the start

voltage of the EFSs should be lower than 1750V.

What is more, the circulating power is also measured

according to Fig. 16, and the result turns out to be 0. Therefore,

in the following part, the circulating power will not be discussed.

C. System-level Energy-saving Evaluating

The system-level energy-saving effect can be affected by

several factors, including the headway time, the load rate of the

step-down substations, and the EFS start voltage. The load rate

is the ratio of the actual load to the installed capacity.

To explore the energy-saving effect in various cases,

Chongqing Rail Transit Line 9 is studied. The operation

timetable of Chongqing Rail Transit Line 9 is shown in Table

VI. The following is the impact analysis of the mentioned

factors.

1) Impact of the headway time

Assume that the load rate is 20%, and the EFS start voltage

is 1720 V. The daily energy is shown in Table VII. The energy-

saving evaluation indexes are shown in Fig. 19. WT1 is 222376.5

kWh.

It can be observed in Table VII and Fig. 19 that WT2 is

generally larger than WT1, because Wreg-trac′ is less than Wreg-trac

and the sum of WF and Wres′ is larger than Wres according to Fig.

11. and (23). When the headway time decreases, more trains

operate at a time, so the total regenerative braking energy

increases. Meanwhile, more energy is absorbed by adjacent

trains. That is the reason why WFr and ξ are not always

positively correlated with the headway time. When the headway

time decreases, WT2 increases significantly, while WF decreases

TABLE Ⅵ

OPERATION TIMETABLE OF CHONGQING RAIL TRANSIT LINE 9

Headway time/s Operation time

120 7:30-8:30

180 8:30-9:00 240 7:00-7:30

300 18:00-19:00

400 9:00-18:00,19:00-21:00 450 6:00-7:00

600 21:00-22:00

900 5:00-6:00,22:00-23:00

TABLE VII AVERAGE ENERGY PER HOUR WITH DIFFERENT HEADWAY TIMES

Headway

time/s WT1/kWh WT2/kWh WF/kWh WR/kWh

120 31503.8 31522.5 714.8 71.0

180 24550.0 24735.1 633.2 50.1

240 19400.6 19629.4 863.2 23.4 300 15442.0 15618.8 857.5 22.1

400 12509.5 12119.1 826.7 12.5

450 11226.4 11359.5 938.6 31.9

600 8385.0 8538.3 829.6 12.1

900 6461.6 6196.5 1041.0 7.1

Fig. 19. Indexes of energy-saving evaluation with different headway times.

TABLE VⅢ

DAILY ENERGY WITH DIFFERENT LOAD RATES AND START VOLTAGES

Start

voltage / V

Load

rate: 0.1

Load

rate: 0.15

Load rate:

0.2

WF / kWh 1690 24668.1 24534.5 24301.0 1730 15086.5 14806.0 14716.4

1770 4216.2 4102.7 3992.3

WR / kWh 1690 2868.7 1505.3 487.8 1730 1975.6 818.5 261.7

1770 365.1 102.2 1.9

WT2 / kWh 1690 218571.9 218621.5 218413.5

1730 212727.7 213091.7 212457.6 1770 208914.4 208821.9 208792.0

overall. Therefore, λ decreases. When the headway is 900

seconds, WFr is the highest.

2) Impact of the load rate and start voltage

The influence of the load rate and start voltage is studied.

Table VIII shows the daily energy with different load rates and

start voltages; Fig. 20 and Fig. 21 show WFr and ξ with different

load rates and start voltages.

900 600 450 400 300 240 180 120

250

750

1250

0

500

1000W

Fr(

kW

h)

Headway time / second

WFr

0.00

0.05

0.10

0.15

0.20

、





10

Fig. 20. WFr with different load rates and start voltages.

Fig. 21. ξ with different load rates and start voltages.

Fig. 22. Indexes of energy-saving evaluation with different start voltages.

The load rate of the step-down substations is usually below

22% [32], so the maximum load rate is set as 0.20. When the

load rate of the step-down substations increases and the start

voltage remains constant, WF' can be utilized more in the middle

voltage system of urban railways, so WR decreases obviously.

WR is reduced by 83%, 87%, and 99% when the load rate

changes from 10% to 20% and the start voltage is 1690 V, 1730

V, and 1770 V, respectively. WFr and ξ increase according to

(24) and (25). However, when the start voltage is higher, the

increase of load rate has less influence on WFr and ξ, because

WF decreases. When the start voltage is 1690 V, WFr and ξ are

increased by 9.2% and 8.5% when the load rate changes from

10% to 20%, respectively; when the start voltage is 1770 V, WFr

and ξ are increased by 3.6% and 1.4%, respectively.

3) Impact of the start voltage

To study the influence of the start voltage in detail, the load

rate is set as 20%. The indexes of the energy-saving evaluation

with different start voltages are shown in Fig. 22.

When the start voltage increases, WFr decreases, and so does

λ. When the start voltage changes from 1650 V to 1770 V, WFr

changes from 32275 kWh to 3851 kWh, and λ changes from

15.8% to 2.0%.

When the start voltage of the EFS changes from 1650 V to

1770 V, ξ increases first and then decreases. As the start voltage

increases, the difference between the energy consumed on the

onboard resister in Case 1 and Case 2 decreases, and WR

decreases. According to (12), when the start voltage changes

from 1650 V to 1670 V, WR decreases more than the energy

consumed on the onboard resister in Case 1 and Case 2

decreases, and when the start voltage changes from 1670 V to

1770 V, WR decreases less. The maximum ξ is 11.9% when the

start voltage is 1670 V. The start voltage of the EFS should be

chosen based on the actual no-load voltage of the rectifier units.

VI. CONCLUSION

A modified AC/DC unified power flow algorithm for urban

rail traction power supply system with the EFS is proposed. The

EFS is modeled as the VSC model with traction network

voltage stabilization and the reactive power compensation

control strategy. The multimode transition of traction

substations is analyzed. The modified AC/DC unified power

flow algorithm is proposed to calculate the urban rail power

flow with EFSs. It is verified that the algorithm has the

characteristics of fast convergence speed and high convergence

accuracy, and the simplification of the DC reflux system

accelerates the calculation. The following conclusions can be

obtained from this work:

1) The Pearson correlation coefficients between the

simulation load process and field test load process in

Guangzhou Metro Line 2 of the traction substations are 0.85,

0.76, and 0.92 when the start voltage of the EFS is 1720 V, 1750

V, and 1770 V, respectively. The accuracy of the algorithm is

verified.

2) The energy flow relations in the system with and without

EFSs are analyzed and system-level energy-saving evaluating

indexes are proposed, including daily feedback energy,

feedback rate of regenerative braking energy, and energy-

saving rate of traction power supply system.

3) The decrease of the headway time will lead to the increase

of the regenerative braking energy of trains, meanwhile the

regenerative braking energy absorbed by adjacent trains

increases more. As a result, energy-saving evaluating indexes

generally decrease. The increase of load rates of step-down

substations is beneficial to the increase of energy-saving

evaluating indexes.

4) The DC reflux system is modelled. By simplifying the

reflux system, the simulation speed can be accelerated, and the

simulation time can be saved up to 14.3%.

5) When the start voltage of EFSs decreases, the daily

feedback energy and feedback rate of regenerative braking

energy increases, while the energy-saving rate does not change

linearly. When the start voltage changes from 1770 V to 1650

V, the maximum energy-saving rate is 11.9% when the start

voltage is 1670V. When the no-load voltage is relatively high,

the start voltage should not be higher than 1750V to keep the

system running in high efficiency. The results can guide the

operation of EFSs.

1690 1730 17700

10000

20000W

Fr /

kW

h

Start voltage / V

0.10

0.15

0.20

1690 1730 1770

0.075

0.090

0.105

0.120

ξ

Start voltage / V

0.10

0.15

0.20

1650 1670 1690 1710 1730 1750 1770

5000

15000

25000

35000

0

10000

20000

30000

WF

r (k

Wh

)

Start voltage / V

WFr

0.00

0.05

0.10

0.15

、





11

REFERENCES

[1] A. Allegre, A. Bouscayrol, P. Delarue, P. Barrade, E. Chattot and S. El-

Fassi, “Energy storage system with supercapacitor for an innovative

subway,” IEEE Transactions on Industrial Electronics, vol. 57, no. 12,

pp. 4001-4012, Dec. 2010.

[2] D. Linzen, S. Buller, E. Karden and R. W. De Doncker, “Analysis and

evaluation of charge-balancing circuits on performance, reliability, and

lifetime of supercapacitor systems,” IEEE Transactions on Industrial Applications, vol. 41, no.5, pp. 1135-1141, Sept.2005.

[3] S. Nomura and H. Tsutsui, “Structural limitations of energy storage

systems based on the virial theorem,” IEEE Transactions on Applied Superconductivity, vol. 27, no. 4, pp.1-6, June 2017.

[4] P. C. Han, X. Q. He, Y. Wang, H. J. Ren, X. Peng and Z. L. Shu,

“Harmonic analysis of single-phase neutral-point-camped cascaded

inverter in advanced traction power supply system based on the big

triangular carrier equivalence method,” Energies, vol. 11, no. 2, pp. 431-

446, Feb. 2018.

[5] S. Lin, D. Huang, A. M. Wang, Y. J. Huang, L. P. Zhao, R. Luo, G.-T.

Lu, “Research on the regeneration braking energy feedback system of

urban rail transit,” IEEE Transactions on Vehicular Technology, vol. 68,

no. 8, pp. 7329 - 7339, Aug. 2019.

[6] G. Zhang, Z. B. Tian, P. Tricoli, S. Hillmansen, Y. Wang, and Z.G. Liu,

“Inverter operating characteristics optimization for DC traction power

supply systems,” IEEE Transactions on Vehicular Technology, vol. 68,

no. 4, pp. 3400 - 3410, Apr. 2019.

[7] N. Y. Zhang, J.K. Liu, Q. Zhou, H. M. Hu and Z. Chen, “Double-

decoupled power flow for AC/DC hybrid power system considering reactive power control characteristics,” Transactions of China

Electrotechnical Society, vol. 31, no. S2, pp. 102-109, Dec. 2016.

[8] M. Z. Chymera, A. C. Renfrew, M. Barnes and J. Holden, "Modeling electrified transit systems," IEEE Transactions on Vehicular Technology,

vol. 59, no. 6, pp. 2748-2756, July 2010.

[9] D. J. Tylavsky and F. C. Trutt, “The Newton- Raphson load flow applied to AC/DC systems with communication impedance,” IEEE Transactions

on vehicular technology, vol. 59, no. 6, pp. 940-948, Nov. 1983.

[10] Y.S. Tzeng, N. Chen and R. N. Wu, “A detailed R-L fed bridge converter model for power flow studies in industrial AC/DC power systems,” IEEE

Transactions on Industrial Electronics, vol. 42, no.5, pp. 531-538, Oct.

1995. [11] H. T. Hu, Z. Y. He and J. F. Wang, “AC/DC power flow method for

metro system considering harmonic power,” Proceedings of the CSEE,

vol. 32, no. 11, pp. 112-119, Nov. 2012. [12] Y.S. Tzeng, N. Chen and R. N. Wu, “Unified AC/DC power flow for

system simulation in DC electrified transit railways,” IEE Proceedings -

Electric Power Applications, vol. 142, no. 6, pp. 345-354, Nov. 1995. [13] A. Pablo, M. Bassam and E.S. Islam, “DC railway simulation including

controllable power electronic and energy storage devices,” IEEE

Transactions on Power Systems, vol.33, no. 5, pp. 5319-5329, Sept. 2018. [14] A. Pablo, D. Guzman and C. Manuel, “Unified AC/DC power flow for

traction systems: A new concept,” IEEE Transactions on Vehicular

Technology, vol. 61, no. 6, pp. 2421-2430, July 2012. [15] Y. S. Tzeng, R. N. Wu and N. M. Chen, “Electric network solutions of

DC transit systems with inverting substations,” IEEE Transactions on

Vehicular Technology, vol. 47, no. 4, pp. 1405-1412, Nov. 1998. [16] C. Zheng, X. X. Zhou, R.M. Li and C.H. Sheng, “Study on the steady

characteristic and algorithm of power flow for VSC-HVDC,”

Proceedings of the CSEE, vol. 25, no. 6, pp. 4-8, Mar. 2005. [17] Z. N. Wei, W. W. Hu, G.Q. Sun, Q. Li and J. K. Liu, “Transient stability

constrained optimal power flow considering of VSC-HVDC integration,”

Proceedings of the CSEE, vol. 33, no. 28, pp. 50-58+59, Oct. 2013. [18] Z. N. Wei, C. Ji, Y. P. Zheng, G. Q. Sun and Y. H. Sun, “Optimal power

flow of AC/DC systems with VSC-HVDC based on a novel unified

hybrid algorithm,” Proceedings of the CSEE, vol. 34, no. 4, pp. 635-643, Feb. 2014.

[19] B. Liu and Z. C. Du, “Unified Newton’s solution to three-phase har-

monic power flow of VSC-HVDC based AC/DC power systems,”

Proceedings of the CSEE, vol. 38, no. 8, pp.2284-2295, Apr. 2018.

[20] R. L. José, M. M. Paulo and P. H. W. Edson, “Hybrid HVDC (H2VDC)

system using current and voltage source converters,” Energies, vol. 11,

no. 6, pp. 1323-1338, Apr. 2018.

[21] W. Liu, L. L. Xu, J. Liao, C. Liu and R. L. Liu, “Calculation of AC-DC Hybrid Power Flow in Urban Rail Traction Power Supply System with

Regenerated Energy Feedback Device,” Journal of China Railway

Society, vol. 41, no. 11, pp. 1-7, Nov. 2019. [22] W. Liu, Y. X. Zhang, J. Zhang, K. P. Li and Q. Z. Li, Calculation of

Urban Rail AC/DC Power Supply with Traction Substation in Multi-

Operation modes,” Journal of Southwest Jiaotong University, [Online]. Available:

http://kns.cnki.net/kcms/detail/51.1277.U.20191210.1725.013.html.

[23] W. Liu, Y. Lou, J. Zhang, X. W. Ye and R. B. Zhou, “Unified AC/DC Power Supply Calculation Taking into Account Urban Rail Inverter

Feedback Devices,” Transactions of China Electrotechnical Society,

vol.34, no. 20, pp. 4381-4391, Oct. 2019. [24] Z. B. Tian, S. Hillmansen, C. Roberts, P. Weston, N. Zhao, L. Chen and

M.W. Chen, “Energy evaluation of the power network of a DC railway

system with regenerating trains,” IET Electrical System in Transportation, vol. 6, no. 2, pp. 41-49, June 2016.

[25] Z. B. Tian, G. Zhang, N. Zhao, S. Hillmansen, P. Tricoli, and C. Roberts,

“Energy evaluation for DC railway systems with inverting substations,” 2018 IEEE International Conference on Electrical Systems for Aircraft,

Railway, Ship Propulsion and Road Vehicles & International

Transportation Electrification Conference (ESARS-ITEC), pp. 1-6, 2018

[26] A.J. Rabih and D. Izudin, “Solution of DC railway traction power flow

systems including limited network receptivity,” IEEE Transactions on

Power Systems, vol. 33, no. 1, pp. 962-969, Jan. 2018. [27] H. Vahedi and K. A. Haddad, “A novel multilevel multioutput

bidirectional active buck PFC rectifier,” IEEE Transactions on Industrial Electronics, vol. 63, no. 9, pp.5442-5450, Sept.2016.

[28] V. Hani, A.L. Philippe and A.H. Kamal, “Balancing three-level neutral

point clamped inverter DC bus using closed-loop space vector modulation: Real-time implementation and investigation,” IEEE

Transactions on Power Electronics, vol. 9, no. 10, pp. 2076–2084, Aug.

2016. [29] X. B. Sun, H. Lu and H.R. Dong, “Energy-efficient train control by

multi-train dynamic cooperation,” IEEE Transactions on Intelligent

Transportation Systems, vol. 18, no.11, pp. 3114-3121, Nov. 2017. [30] A. Saeed, D. Ali and A. Mohsen, “Improving energy-efficient train

operation in urban railways: employing the variation of regenerative

energy recovery rate,” IEEE Transactions on Intelligent Transportation Systems, vol. 11, no. 6, pp. 349-357, June 2017.

[31] L. Sheugh and S. H. Alizadeh, “A note on Pearson correlation coefficient

as a metric of similarity in recommender system,” 2015 AI & Robotics (IRANOPEN), pp.1-6, Sept. 2015.

[32] X. W. Ye, W. Liu, R.L. Liu, J. Dong and K. P. Li, “Measurement and

evaluation of the load process at metro step-down substation,” Urban mass Transit, vol. 21, no. 9, pp.108-112+117, Sept. 2018.

[33] G. F. Du, J. Wang, X. X. Jiang, D. Zhang, L. Y. Yang and Y. H. Hu,

“Evaluation of rail potential and stray current with dynamic traction networks in multitrain subway systems,” IEEE Transactions on

Transportation Electrification, vol. 6, no. 2, pp. 784-796, June 2020.

Wei Liu (M’) received the B.S., M.S., and Ph.

D degrees in Electrical Engineering from

Southwest Jiaotong University, Chengdu,

China, in 2003, 2006, and 2009, respectively.

He is currently an associate professor in the

School of Electrical Engineering at


China. His research interests include

theoretical and simulation research of traction

power supply system of urban rail, regenerative braking energy

utilization, the theory, and control research of stray current and

rail potential.





12

Jian Zhang received the B.S. degree in

Electrical Engineering from Southwest

Jiaotong University, Chengdu, China, in 2017.

He is currently working toward a Ph.D.

degree in Southwest Jiaotong University,

Chengdu, China.

His research interest includes regenerative

braking energy utilizing in the power supply

system of urban rail transit.

Hui Wang received B.S. and M.S. degrees

in Electrical Engineering from Southwest

Jiaotong University, Chengdu, China, in

2014 and 2017, respectively. He is currently

working toward a Ph.D. degree in


China.

His research interests include theoretical

and simulation research of traction power

supply system, power quality analysis, and control.

Tuojian Wu received the B.S. degree in

Electrical Engineering from Southwest

Jiaotong University, Chengdu, China, in 2018.

He is currently working toward an M.S.

degree in Southwest Jiaotong University,

Chengdu, China.

His research interest includes the simulation

of traction power supply system regenerative

braking energy and optimal configuration of the energy storage

system.

Ying Lou. received the B.S. and M.S.

degrees in Electrical Engineering from


China, in 2016 and 2019.

Her research interest includes regenerative

braking energy utilizing in the power supply

system of urban rail transit.

Xiaowen Ye received the B.S. and M.S.

degrees in Electrical Engineering from


China, in 2015 and 2018.

Her research interest includes the utilizing of

regenerative braking energy in urban rail.


Documents

Modified AC/DC Unified Power Flow and Energy-saving