Abstract—As unbalance state of charge (SOC) of storage units

usually leads to the decrease of lifetime, SOC balancing control is

essential. In this paper, a decentralized SOC balancing method is

proposed to balance the SOC of cascaded-type energy storage

systems. Since the method does not rely on any communication, it

possesses higher reliability. As is well known, SOC is a slowly

changing variable compared to other variables such as voltage and

current. Thus, the studied system has obvious two-time scale

characteristic. In addition, the stability analysis of the system

based on the singular perturbation theory is carried out.

Simulation and experiments are performed to verify the validity of

the proposed SOC balancing scheme.

Index Terms—Decentralized control, SOC balancing, Cascaded

converter, Storage units.

I. INTRODUCTION

ICROGRID, as a future smart decentralized power

network, has been developed with high penetration of

renewable generations [1]-[2]. It offers an effective solution to

integrate distributed renewable sources, loads and energy

storage systems [3]-[4]. Meanwhile, the intermittence poses a

challenge to renewable generation application in microgrid,

which worsens the power quality and decreases the stability of

the utility grid.

An energy storage system (ESS) is adopted to restrain the

power fluctuation of these intermittent resources [5]-[6]. Also,

ESSs bring some benefits such as energy shifting and peak

shaving of power system [7]-[10]. Actually, the different initial

SOC values and mismatched output power would cause the

unbalancing SOC problem, which may lead to the over charge

and discharge actions. These factors would decrease the lifetime

of ESSs.

To deal with the unbalanced SOC problem, the SOC levels

of ESSs should be coordinated over long time scales. According

to the interfacing converter topologies, the ESS can be divided

into two categories: the paralleled-type and the cascaded-type

ones. The paralleled-type ESS has been widely studied recently

due to its flexibility as well as plug and play characters, and thus

it is widely used in low voltage microgrid. The control strategies

for SOC balancing in paralleled-type ESS have been

extensively investigated, which are generally divided into three

categories: (a) centralized [11]-[12] (b) distributed and [13]-[15]

(c) decentralized control [16]-[19]. In [11]-[12], the centralized

coordinated secondary control strategies are presented for the

SOC balancing among ESSs. However, the centralized control

would be invalid when the centralized communication fail. To

reduce communication burden and improve network reliability,

the distributed SOC balancing control approaches are studied in

[13]-[15]. In [13], a modified droop control with distributed

communication is studied to balance SOC. The modification on

droop curves can coordinately change the output power of each

storage unit for achieving SOC convergence. In [14-15], a

dynamic consensus algorithm for balancing discharge rates is

proposed based on secondary control. The algorithm proposed

in [15] provides virtual impedance loops, which achieves SOC

balancing by adjusting virtual impedance. However, these

distributed control methods still rely on the communications

which would cause additional cost. Moreover, decentralized

approaches based on droop control [16-19] have been proposed

to deal with the unbalancing SOC problem without any

communication. In [16-18], the output power can be regulated

through adjusting droop coefficients to balance SOC of storage

units autonomously. In [19], with modifying the droop offsets,

the units with lower SOC levels provide smaller share of load

demand, and the units with larger SOC values may supply more

power for load demand. Besides no communication network,

these decentralized control methods also have several

advantages including simplicity, flexibility, and reliability.

Although these aforementioned methods are useful, it is not

enough for the applications of cascaded-type ESS.

Cascaded energy storage system (CESS) are mainly applied

to large-capacity energy storage application. The cascaded

converter topology are emerging in middle and high level

voltage storage system application due to its merits in using

low-voltage semiconductor switches, producing low output-

voltage harmonic distortion and inherent modularity. It can

make the CESS acquire simple voltage-scaling properties

without expensive and bulky transformers. In addition, the

interfacing converters can provide an ability to achieve SOC

balancing among all energy storage units (ESUs) without using

additional balancing circuits [20]. In this occasion, the SOC

balancing control is also indispensable. Some control methods

[21-23] are used to adjust active power of each storage unit in

CESS. The strategy to control the SOC of ESS in [21] enables

power compensation with smaller energy capacity and with less

effect to the compensation result. In [22], a control method for

A Decentralized SOC Balancing Method for

Cascaded-type Energy Storage System

Guangze Shi, Hua Han, Yao Sun, Member, IEEE, Zhangjie Liu, Minghui Zheng and Xiaochao Hou

M

Manuscript received October 9, 2018; revised January 13, 2019，

March 20，2019, May 24, 2019 and September 26, 2019; accepted

January 31 , 2020. This work was supported in part by the National Natural Science Foundation of China under Grant 61573384, 61622311 and 61933011, the Major Project of Changzhutan Self-dependent Innovation Demonstration Area under Grant 2018XK2002, the Project of Innovation-driven Plan in Central South University under Grant 2019CX003, and the Fundamental Research Funds for the Central Universities of Central South University under Grant 2019zzts065. (Corresponding author: Yao Sun.)

G. Shi, H. Han, Y. Sun, Z. Liu and X. Hou are with the School of Automation, Central South University and the Hunan Provincial Key Laboratory of Power Electronics Equipment and Gird, Changsha 410083, China (e-mail: 16414986@qq.com, hua_han@126.com, yaosuncsu@gmail.com, 956142207@qq.com, houxc10@csu.edu.cn).

M. Zheng is with Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, New York, USA (e-mail: mhzheng@buffalo.edu).

SOC balancing of the multiple storage unit is researched with

cascading PWM converters. To manage the SOC values of ESS,

phase-phase SOC-balancing control and inter-phase SOC-

balancing control are analyzed in [23]. The aforementioned

SOC control methods are dependent on a centralized controller

which needs high-bandwidth communication. When the number

of ESUs is very large, the cost of the high-bandwidth

communication would become a heavy load. Moreover, the

possible communication failures may affect the system’s

normal operation. All of the aforementioned drawbacks would

limit the development of the centralized control.

The decentralized control is more attractive because it is not

affected by the communication dependence and limitation of

ESU number, and has higher reliability. Thus, it has been

applied in cascaded converter systems. For example, an

inversed power factor droop control for power sharing is

proposed [24]. However, its application is limited to a certain

load. To overcome the limitation an f-P/Q droop control is

proposed [25]. In addition, some other decentralized control

methods have been presented for cascaded PV [26] and

cascaded STATCOM [27]. Considering the SOC for CESS, the

SOC balancing control methods are almost based on centralized

control. The drawbacks mentioned above lead the

inapplicability in large scale CESS. Therefore, this paper

focuses on studying a decentralized method to achieve SOC

balance.

Up to our knowledge, no other literature has been published

for balancing SOC for CESS in a decentralized manner except

for [28]. In this paper which is the extended version of [28], a

decentralized SOC balancing control algorithm is proposed for

CESS. Under the proposed control strategy, each unit in CESS

is controlled independently only by using its local information,

and the output power of each unit can be regulated according to

its SOC level. Compared with [28], a comprehensive analysis is

introduced to analyze the steady state performance and system

stability based on the singular perturbation theory, due to the

two time scale characteristic of the researched system.

Moreover, the SOC balancing is theoretically proved in steady

state and the detailed parameters selecting ranges are given.

Finally, more simulation results and experiment tests are

presented to validate the feasibility of the proposed control.

Compared with the existing SOC balancing methods, as

shown in Table I, the benefits of the proposed control strategy

are concluded as follows:

1. The SOC balancing among all ESUs is achieved in CESS

autonomously.

2. Without communication dependence, the proposed

decentralized control has the advantages of higher reliability,

stronger fault tolerance and lower construction cost.

3. The proposed control has good extensibility, and its

application is not limited by the number of ESUs.

4. Theoretical proof about SOC balancing is provided based on

the singular perturbation theory.

Under the proposed control strategy, each unit in CESS is

controlled independently only by using its local information,

and the output power of each unit can be regulated according to

its SOC level. The remaining of this paper is organized as

follows. Section II presents the design of SOC balancing control

method. Section III illustrates the stability analysis of the

proposed SOC balancing control based on the singular

perturbation theory and small signal analysis. Section IV and

Section V present simulation and experimental results,

respectively. Section VI concludes the paper.

TABLE I

COMPARISON WITH THE EXISTING METHODS

Features Proposed methods Existing methods for the

cascaded-type ESS[21]-[23]

Decentralized methods for the

paralleled -type ESS[16]-[19]

Synchronization method Automation-synchronization

(Inverse droop control)

Centralized communication

(Centralized control)

Automation-synchronization

(Droop control)

Communication dependence Low High Low

Cost Low High Low

Resilient to communication

failure High Low High

Convergence rate Slow Fast Slow

Extensibility High Low High

Theoretical proof Yes No No

Application Cascaded-type ESS Cascaded-type ESS Paralleled-type ESS

II. PROPOSED SOC BALANCING CONTROL

A. Equivalent Model of Islanded CESS

Fig.1 illustrates an islanded CESS consisting of n ESUs,

interfacing converters and local loads. In this configuration, the

interfacing converters are single phase DC/AC converters, all of

which are connected in series to energize the loads. The by-pass

switch is used to protect the ESU if the SOC of one ESU is not

in its safe range or the ESU has failed.

For simplicity, each DC/AC converter is regarded as a

controlled voltage source (CVS). Thus, the output voltage of the

i-th converter is denoted as Vie jθi and the coupling point

voltage is represented by Vpe jθp The relationship between the

coupling point voltage and the voltages of all controlled voltage

sources is expressed as follows

1

p i

nj j

p i

i

V e V e

(1)

From Fig. 1, the output active power Pi and the reactive

power Qi of the i-th controlled voltage source are derived as

follows

*

/pi loadjj j

i i i p loadP jQ V e V e Z e

(2)

where the |𝑍𝑙𝑜𝑎𝑑| and 𝜃𝑙𝑜𝑎𝑑 are the load impedance

magnitude and angle.

According to (1)-(2), the power transmission characteristics

of the i-th controlled voltage source are obtained as

1

cosn

ii j i load j

jload

VP V

Z

(3)

1

sinn

ii j i load j

jload

VQ V

Z

(4)

Fig. 1 The simplified structure diagram of Islanded CESS

B. Approximate Relationship between SOC and Output Power

A simplified schematic diagram of a controlled voltage source

without output filter is illustrated in Fig. 2, in which the model

of ESU is expressed by a first-order RC model. As show in Fig.

2, vioc and Zi

r are the ideal voltage source and the internal

resistance of the i-th ESU, respectively. The function of Zis and

Cis is to model the chemical diffusion of the electrolyte of the i-

th ESU [29].

VSC

+

iiin

Pi

viin

ESU Model

vioc

Zir

Zis

C s

+ - vis

-

Fig. 2 The simplified structure diagram of controlled voltage source

By Kirchhoff’s circuit laws, we can obtain from Fig. 2

sin s sii i is

i

Vi C V

Z (5)

According to the definition of SOC, the SOC of the i-th ESU

is expressed as follows

0

1i

ini i

i

SoC SoC i dtC

(6)

where SOC0i is the initial SOCi value . Ci and 𝑖𝑖𝑖𝑛 denote the

nominal capacity and terminal current of the i-th ESU,

respectively.

The cell-balancing method [30, 31] is indispensable to

guarantee the safe and reliable operation of the storage units in

application. However, the research subject of this paper is

focused on among modules. Thus, it is assumed that the SOC of

each cell in battery module is balanced. According to [32, 33],

the SOC0i and Ci are calculated as follow

01

0

0 01 1

min

min min 1

i

i i

ij ijj N

i

ij ij ij ijj N j N

SOC C

SOCSOC C SOC C

(7)

0 01 1min min 1

i i

i ij ij ij ijj N j N

C SOC C SOC C

(8)

where SOC0ij and Cij represent the initial SOC value and

capacity of the j-th battery cell in i-th storage unit, respectively.

Ni represents the number of the battery cell in storage units.

Differentiating (5) with respect to time and combining with

(6), the states of the battery model can be derived

1s

s in ii is s

i i

VV i

C Z

(9)

ini

i

i

iSOC

C (10)

As seen in section III, the proposed control only rely on the

SOC information of each storage unit. Therefore, the chemical

dynamics of ESU model is ignored in the following analysis.

Neglecting the power losses in the inverter, the output power

of inverter Pi yields, in in in

i i i iP P v i (11)

where 𝑃𝑖𝑖𝑛 is the output power of the i-th ESU.

Combining (6) and (11), the relationship between SOC and

output power of i-th ESU is obtained, which plays a significant

role in the following analysis.

0 0

max_

ini i

i i i

i i

i dt PdtSOC SOC SOC

C E

(12)

where max_in

i i iE v C .

To realize SOC balancing, it is vital to know accurate SOC

information. However, as the objective of the paper is not the

SOC estimation, the Coulomb Counting approach to estimate

SOC is employed for simplicity. Certainly, to get more accurate

SOC, advanced SOC estimation methods can be used. For more

details, the interested readers may refer to [34].

C. Proposed SOC Balancing Control Method

Q

P

S=P+jQ

III

III IV

Discharging with RL load

Discharging with RC load

Charging with RL load

Charging with RC load

Fig. 3 Four-quadrant working cases in CESS.

According to reference [25], the mechanisms of autonomous

synchronization in islanded cascaded-type system are different

due to the load impedance characteristic. Thus, in this paper,

four quadrant operation for storages, as illustrated in Fig. 3,

should be taken into account. It includes: discharging with

resistive-inductive load (I), charging with resistive-inductive

load (II), charging with resistive-capacitive load (III), and

discharging with resistive-capacitive load (IV).

First of all, the rated power of the power sources should be

ESU#1 LoadsPCCConverter

Converter

Pinjected

ESU#n fL

fC

fLfC

pjpV e

njnV e

Controlled Voltage Source #1

1

1jV e

Controlled Voltage Source #n

By-pass

switch

By-pass

switch

pre-designed to avoid overload with considering the load

demand. This is the precondition for ensuring the safe operation

of the system. Then in order to achieve SOC balancing, the

proposed control scheme is designed as follows,

0

*max_

sgni i i i i i

i i

Q m P n SOC

V E V

(13)

where the sgn() denotes sign function. ωi, and Vi are the angular

frequency reference and voltage amplitude reference of the i-th

controlled voltage source, respectively. ω0 represents the value

of ω with no load. V* is the nominal voltage amplitude value of

the bus voltage. mi is the adjustment coefficient of the proposed

controller which is designed to be inversely proportional to their

control gains, i.e. miEmax_i=K where K is a constant. ni is a SOC

weighted coefficient to modify the droop control adaptively. For

achieving SOC balancing, we choose n1 ==nn =N. The

max_ iE is designed as follow

max_ max_ max_

1

n

i i j

j

E E E

(14)

When the CESS has reached the steady state, the frequency

synchronization and SOC balancing can be achieved. Then we

can obtain

sgn sgni i i j j jm Q P m Q P (15)

Define that φi (φj)is the phase angle difference between the

output voltage Vi (Vj)and the common current I of the i-th (j-th)

CVS. Combine (13), (14) and (15), then

**

max_k max_k

1 1

sgn cossgn cos i ji i

n n

k k

KV I QKV I Q

E E

(16)

From (16), it is obvious that sgn(sin i ) cos i = sgn(sinj )

cos j . Then i = j or i = j can be obtained. As the i =

j is the unfeasible solution, the power angle can keep the

same for all CVS in steady state. Thus the bus voltage amplitude

equals the sum of voltage amplitude of all the CVS i.e. the

nominal voltage amplitude reference of the bus voltage.

*

1

=n

p i

i

V V V

(17)

D. Double Control Loop Design

To obtain a better tracking performance, the double

control loop is applied in this paper, which comprises of

voltage control and current control. As the voltage reference

calculated by proposed method is an AC variable, the

proportional-resonant (PR) is more applicable than PI

control to track the AC variables [33]. The voltage and

current control are respectively designed as follows:

2 2

2

2

rV cVv pV

cV r

k sG s k

s s

(18)

2 2

2

2

rI cIi pI

cI r

k sG s k

s s

(19)

where kpV and krV are the proportional and resonant

parameters of the voltage control, respectively. The kpI and

krI are the proportional and resonant parameters of the current

control, respectively. In addition, the ωr is the resonant

frequency and the ωcV (ωcI) represents the cut-off frequency

of the voltage control (current control).

III. STABILITY OF PROPOSED SOC BALANCING CONTROL

A. Singular perturbation theory

As the studied system is a two-time scale system, it can

be expressed into the following singular perturbation system

[36, 37].

,

,

dxf x y

d

dyg x y

d

(20)

where x, y and ε are the fast variable, the slow variable and the

time scale parameter, respectively.

Rewrite the model in the stretched time scale /t , as

follows

,

,

dxf x y

dt

dyg x y

dt

(21)

where τ and t are referred to as the slow and the fast time scales,

respectively. The models in (20) and (21) represent the

corresponding slow and fast system respectively.

In the slow system, it is usually considered that the fast

variable achieves quasi-steady state while the slow variable is

still varying [37]. Setting ε=0 in (20), the outer system is

expressed as

0 ,

,

s

s

f x y

dyg x y

d

(22)

where xs is the quasi-steady-state value of x.

While in the fast system, the slow variables act several ten

times slower than the fast variables. The variable y can be

considered as a constant parameter. Define �̃� = 𝑥 − 𝑥𝑠 , then

the boundary layer system is expressed as

,

0

dxf x y

dt

dy

dt

(23)

B. System model

From (12)-(13), the dynamic equations (24) of the i-th

controlled voltage source can be written

0 sgn

ii i i i

i i i

dQ m P N SOC

dt

dSOC m P

dt K

(24)

Define i i s , 1K , then

0 sgn

ii i i i s

ii i

dQ m P N SOC

dt

dSOCm P

dt

(25)

where0s st . ωs is a quasi-steady state value of ωi, and

0 depends on the selection of reference phase angle and

is very small.

Rewrite the model (25) in the time scale: t , then

0 sgn

ii i i i s

ii i

dQ m P N SOC

d

dSOCm P

d

(26)

C. Analysis on the outer system

Setting ε=0 in (26), the outer system of the i-th controlled

voltage source is expressed as

0 sgns is i is i

ii is

Q m P N SOC

dSOCm P

dt

(27)

where Pis and Qis are the quasi-steady state value of Pi and Qi,

respectively.

In the quasi-steady state, by combining the outer systems

of both i-th and k-th controlled voltage sources we have

i ki k

dSOC dSOCN SOC N SOC

dt dt (28)

Define z=SOCiSOCk, and (28) can be rewritten as

0dz

zdt

(29)

where 1/ N .

The solution of (29) is derived as

0

t

z t z e

(30)

Clearly, z converges to zero as time goes to infinity. The

convergence rate depends on N. The larger the N, the faster the

convergence rate is. Thus, in the steady state we have

i kSOC SOC (31)

From the analysis above, the SOC balancing of all

controlled voltage sources can be achieved in steady state under

the proposed control.

D. Analysis on the boundary layer system

For simplicity, we assume that max_ max_

1i jE E

n ,

where n is the number of CVS in CESS. Setting ε=0 in (25), we

can regard the ωs and SOCi as invariants. Substitute (3) into (25),

then

*2

21

sgn cosn

i ii i i j load

jload

d mVQ

d n Z

(32)

where 0i s iN SOC .

To prove the stability of the boundary layer system (32),

the small signal analysis is used [36]. It is reasonable to assume the state variable in equilibrium

point are 1 2s s ns , where the is is the quasi-

steady state value of i . By linearizing (32), the small-signal

equations are derived as:

*2

21,

sgn sinn

i iis load is is i j

load j j i

d mVQ

d n Z

(33)

where *2

21

sinn

is is js load

jload

VQ

n Z

.

Rewrite (33) in the matrix form

Δθ A Δθ (34)

where A is the coefficient matrix.

A B L (35)

where 1 2 ndiag b b bB , *2

2sgn i

i is

load

mVb Q

n Z ,

1 12 1

2

21 2 2

1, 2

1

1 2

1

n

j n

j

n

j n

j j

n

n n nj

j n n

l l l

l l l

l l l

L and sinij load is jsl .

According to gerschgorin circle theorem, the eigenvalues of

the system coefficient matrix A fall within the gerschgorin

regions.

1

n

i j

j

G G

A (36)

1,

, 1,2,n

n ni i ij i

j j i

G z z b l R i n

A C (37)

where Ri is the i-th gerschgorin circle radius, 1,

n

i i ij

j j i

R b l

.

To ensure stability, the eigenvalues of the coefficient matrix

A should be on the left half plane. i.e., all gerschgorin circles

should be on the left half plane. From (33)-(37), if all bilij >0,

the system will be stable.

As *2i loadmV Z is positive, the stability condition is

simplified as

sgn sin 0is load is jsQ (38)

From (38), the system is stable, if the following condition

holds.

, {1,2... }max is js load

i j n

(39)

From (3), the quasi-steady state active powers of i-th

and k-th can be expressed as

*2

21

cosn

is is js load

jload

VP

n Z

(40)

*2

21

cosn

ks ks js load

jload

VP

n Z

(41)

Combining (40) and (41), we have

2

*2

1

sin2 2

2 sin2

is ks loadiks

nijs kjs load

j

P P n Z

V

(42)

where iks is ks .

In the quasi-steady state, all controlled voltage sources share

the same frequency. From (13), we can obtain

is ks i k iP P N SOC SOC m (43)

Substituting (43) in (42) results in

2

*2

1

sin2 2

2 sin2

i k loadiks

nijs kjs load

i

j

N SOC SOC n Z

m V

(44)

From (44), ifi kSOC SOC , then 0iks , i.e., all phase

angles are the same. Ifi kSOC SOC , it is suggested to choose

appropriate mi and N to satisfy (39). So the feasible range of m

and n should be discussed. Taking the stability condition and

allowable frequency deviation into condition, the boundary

condition can be derived as follows

, {1,2... }sin max / 2 sin / 2is js load

i j n

(45)

maxi i i im P N SOC (46)

where the ∆ωmax is the maximum allowable frequency deviation

which is often set to be 1 in the microgrid system [39]. The

power Pi has been limited in [-P*max, P*

max], and the P*max is the

nominal rated power, which is set to be 1500W. The safe range

of SOC is set to be [0.1, 0.9].

Fig.4 Feasible range of m and N

To facilitate visualization of the feasible range of m and N,

the results of Fig.4 are based on small signal model around one

quasi-steady state point (t=10s&Zload=4+j8) and the assumption

that all the CVS have the same capacities.

From Fig. 4, the N and m are specified in the N-axis and m-

axis and the boundaries corresponding to stability and

frequency deviation. It is easy to see that a large m and small N

can extend the stable range of the system. But it is worth

mentioning that a very large m may lead to unallowable

frequency deviation and a very small N may decrease the SOC

convergence rate. So selecting a point further away from the

boundary line and a lager N for faster SOC convergence rate can

make the system achieve better performance. Therefore, the

selection of mi and N is a trade-off among the stability,

frequency deviation and the SOC convergence rate.

As in whole, according to the proposed control function (13),

the intercept of P-f curve are modified by the local SOC

information, which is to adjust the output power of ESUs by the

different output voltage angles. The basic principle is described

in Fig. 5. In the discharging mode, higher SOC energy storage

units result in greater power and lower SOC ones result in

smaller power. Likewise, in the charging mode, units with lower

SOC are injected with more power, and ones with larger SOC

are injected with less power. Based on this principle, the SOC

difference will be decreased and the SOC balancing will be

achieved ultimately.

Fig. 5 Principles of the proposed SOC balancing control method: (a)

resistive-inductive load, (b) resistive-capacitive load. Remark: The distinctions of the proposed method in this paper

from the existing decentralized methods [16-19] are

demonstrated in the following: (1) Previous works focus on the

parallel-type ESS, while this paper researched on the cascaded-

type ESS. (2) The control algorithms in [16-19] are based on

droop control. In contrast, our algorithm is derived from inverse

droop control. (3) The SOC balancing is proved based on multi-

time scale analysis. Theoretical proof about SOC balancing has

not been reported in the literatures.

TABLE II SIMULATION PARAMETERS

Case

Control Coefficient Storage unit

Capacities(Ah)

DC

Voltage(V)

Voltage

Reference(V)

Frequency

Reference(Hz)

Load

Characters(Ω)

m1

(10-4)

m2

(10-4)

m3

(10-4)

N

(10-1) Ce1 Ce2 Ce3 v

in V* f* Z

Case A 2 2 2 5 4 4 4 160 300 50 4+j8 and 4-j8 Case B 2 2 2 5 4 4 4 160 300 50 4+j8

Case C 2 2 2 5 4 4 4 160 300 50 4+j8 and 4-j8

Case D 4/3 2 4 5 6 4 2 160 300 50 4+j8 Case E 2 2 2 0(5) 4 4 4 160 300 50 4+j8

m

N0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

1

2

3

4

5

6

7

8 10-4

Frequency deviation boundary (discharge)

Frequency deviation boundary (charge)

Stability boundary

Selected point

Feasible range

fdischarge

Discharging(I)

f

P0Charging(II)

SOC1 < SOC2

P1 < P2 P1 < P2

fcharge

(a)

Discharging(IV)

0

f

SOC1 < SOC2

fdischarge

fcharge

P1 < P2

Charging(III)

P1 < P2 P

(b)

Fig. 6 Detailed control diagram of the proposed method

Fig. 7 Simulation results in case A: (a) performance in first-quadrant mode; (b) performance in second-quadrant mode; (c) performance in third-quadrant mode;

(d) performance in fourth-quadrant mode.

TABLE III DOUBLE CONTROL LOOP PARAMETERS

Type Symbol Value

Voltage Control

kpV 0.05

krV 50

ωcV 2(rad) ω0 314(rad)

Current Control

kpI 0.1

krI 100 ωcI 2(rad)

ω0 314(rad)

IV. SIMULATION RESULTS

To validate the proposed SOC balancing control method, the

simulation model based on three controlled voltage sources are

developed in the MATLAB/Simulink environment. Fig. 6

shows the detailed control diagram of proposed method, which

contains power calculation loop, proposed control block, and

the control block of voltage and current control loops. The

proposed control is to provide a voltage reference based on the

local measured active and reactive power information. Then the

voltage and current controllers use PR control to track the

voltage reference. The system parameters are listed in Table II

and the parameters of double control loop are listed in Table III.

A. Case A: Simulation results of SOC balancing in four-

quadrant operations

In this case, the control gains m1= m2= m3=0.0002, and

N=0.5 are selected for the three energy storage units. Different

initial SOC values of each energy storage units are selected as

follows. SOC01, SOC02 and SOC03 are set to be 90%, 80%, 70%

for the discharging mode and 10%, 20%, 30% for the charging

mode, respectively. The resistive-inductive load Z1=4+j8 Ω, and

resistive-capacitive load Z2=4-j8 Ω are used in this case.

Fig.7 (a), (b), (c) and (d) show the SOC and the output power

of the energy storage units operating in the first, second, third,

and fourth quadrant, respectively. As shown in Fig. 7, the

deviation ΔSOC, ΔP and ΔQ gradually decrease to zero in the

steady state (ΔSOC =SOCmaxSOCmin , and ΔP= PmaxPmin).

From the results in Fig. 7, the proposed SOC balancing

controller perform well and the SOC balancing as well as power

sharing are achieved eventually.

B. Case B: Simulation results in mode switching between

discharging and charging.

The mode switching between the charging and discharging

processes is tested in this section. The parameters of the

simulated system are the same with those in Case A. The mode

switching is enabled at 1000s.

H-bridgeC

ES

S

CV

S#1

CV

S#

2C

VS

#n

Zlo

ad

P

-90 °

+

-m ×

×

N

sgn

×

Q

LPF

LPF

++

ω* V*

PR PR

P

W

M

+

-

+

-

Proposed Control Power Calculation

Voltage Control Current Control

Voltage Reference

Casc

aded F

orm

s

Detail Control Diagram of the i-th CVS

Equation(6)

0

0.2

0.4

0.6

0.8

1

0 200 400 600 1000 1200 14000 800 1600 1800 2000

-1500

-1000

-500

0

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0

0.2

0.4

0.6

0.8

1

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0

500

1000

1500

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0

0.2

0.4

0.6

0.8

1

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0

500

1000

1500

0 200 400 600 1000 1200 14000 800 1600 1800 2000

ESU #1ESU #2

ESU #3

Time(s)

Time(s)

SO

CP

ow

er(W

)

(b.1)

(b.2)

Time(s)

SO

C

-1500

-1000

-500

0 200 400 600 1000 1200 14000

0.2

0.4

0.6

0.8

1

0 800 1600 1800 2000

0

0 200 400 600 1000 1200 14000 800 1600 1800 2000

Po

wer

(W)

SO

C

Time(s)

Time(s)

(c.1)

(c.2)

(d.1)

(d.2)

Po

wer

(W)

Time(s)

SO

C

Time(s)(a.1)

(a.2)

Po

wer

(W)

Time(s)

ΔSOC0%

ΔSOC0% ΔSOC0%

ΔSOC0%

ΔP0W ΔP0WΔP0W ΔP0W

First-quadrant mode(discharging with RL load) Second-quadrant mode(charging with RL load) Third-quadrant mode(charging with RC load) Fourth-quadrant mode(discharging with RC load)

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

Fig. 8 Performance of transferring from discharging to charging process with

proposed method: (a) SOC; (b) Active Power.

Fig. 8 presents the waveforms of energy storage units

operating from the discharging mode to the charging mode

under the resistive-inductive load. In the discharging mode, the

SOC values of the three units are convergent, and the deviation

ΔSOC is reduced from 20% to 1.9%. After switching to the

charging mode, the convergence of SOC is still guaranteed, and

the deviation ΔSOC gradually reduces to zero in the steady state.

Moreover, the deviation ΔP has little fluctuations during the

mode switching process.

Fig. 9 Performance of transferring from charging to discharging mode with

proposed method: (a) SOC; (b) Active Power.

Fig. 9 shows the test results from charging mode to

discharging mode. As shown in Fig. 9, the variation process of

SOC and power are similar to the mode switching from the

discharging to the charging. The SOC balancing and the power

sharing are gradually achieved throughout the whole process

and the fluctuations of mode switching are acceptable. From the

simulation results above, the proposed SOC balancing control

has good performance during mode switching.

C. Case C: Simulation tests under discharging mode with load

characteristics changing.

The dynamic response during the load changing from

inductive-resistive to capacitive-resistive one is shown in Fig.

10. In this case, all of the three energy storage units operate in

the discharging mode. At t=1000s, the load is changed from the

inductive-resistive to the capacitive-resistive one. It shows that

the convergences of SOC and power sharing are not affected by

the changing of the load characteristics.

Fig. 10 Performance of load characteristic changing from inductive-resistive to

capacitive-resistive in discharging mode: (a) SOC; (b) Active Power.

D. Case D: Simulation tests of proposed method with different

capacities of ESU

Po

wer

(W)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

400

800

1200

1600

Mod. #1Mod. #2

Mod. #3

Mod. #1Mod. #2

Mod. #3

SO

C

Time(s)

Time(s)

(a)

(b)

ΔSOC0%

P1=1.11kW

P2=0.738kW

P2=0.364kW

0.4

0.5

0.6

0.7

0.8

0.9

1

-1000

-500

0

500

1000

1500

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0 200 400 600 1000 1200 14000 800 1600 1800 2000

(a)

SO

CP

ow

er(W

)

(b) Time(s)

Time(s)

Mode

changing

Mode

changing

ΔSOC20%

ΔSOC1.9%

ΔSOC0%

ΔP0.101kW

ΔP0kW

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

0

0.1

0.2

0.3

0.4

0.5

0.6

-1500

-1000

-500

0

500

1000

0 200 400 600 1000 1200 14000 800 1600 1800 2000

Time(s)

0 200 400 600 1000 1200 14000 800 1600 1800 2000

Time(s)

Po

wer

(W)

(a)

SO

C

(b)

Mode

changing

Mode

changing

ΔP0kW

ΔP0.101kW

ΔSOC20%

ΔSOC1.9%

ΔSOC0%

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

0

0.2

0.4

0.6

0.8

1

0 200 400 600 1000 1200 14000 800 1600 1800 2000

0

500

1000

1500

0 200 400 600 1000 1200 14000 800 1600 1800 2000

SO

C

Time(s)

Po

wer

(W)

Time(s)

(a)

(b)

Load

changingΔSOC20%

ΔSOC1.8%

Load

changing

ΔSOC0%

ΔP0.101kW ΔP0kW

ESU #1ESU #2

ESU #3

ESU #1ESU #2

ESU #3

Fig. 11 Performance of proposed method with different capacities of ESU: (a)

SOC; (b) Active Power.

In order to show the effectiveness of proposed method with

different capacities of ESU, the capacities of ESU#1, ESU#2,

and ESU#3 are set to 6, 4, and 2Ah, respectively. Meanwhile,

the droop coefficient are changed to be 4/310-4, 210-4, and

410-4, respectively.

Fig. 11 shows the test results of SOC and output active

power when the capacities of ESUs in CESS are different. In

steady state, the SOC balancing has been already achieved and

the output power values of ESUs are measured as 1.11, 0.738,

and 0.364 kW, respectively. It is clearly shown that the power

allocation can be described as an equation: 1 2 3: : 3 : 2 :1P P P

As that the DC voltage are set to the same value, the output

power is in proportion to its capacities, which can be derived as

follows:1 2 3 1 2 3: : : :P P P C C C . From the simulation result, the

SOC balancing and proportional power sharing are proved to be

achieved with different capacities of ESU.

E. Case E: Simulation results of comparison of ESS with and

without SOC balancing control.

The section provides the simulation results of comparison of

ESS with and without SOC balancing control. The initial SOC

values SOC01, SOC02 and SOC03 are set to be 50%, 45%, 40%.

Generally, the safe SOC range of Li-FePO4 battery is between

10% and 90%. From Fig. 12, the ESS without SOC balancing

control works in unsafe range at 868s, while the one with SOC

balancing control still works in safe range. To some extent, the

depth of charge-discharge can be decreased with the proposed

control, i.e. the life of ESS can be increased [40].

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

868

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

Unsafe SOC range

Unsafe SOC range

ESU #1ESU #2ESU #3

Time(s)

SO

C

Time(s)

SO

C

(a)

(b)

ESU #1ESU #2ESU #3

Fig.12 Simulation results of comparison of ESS with and without SOC

balancing control. (a) Without SOC balancing control, (b) with the SOC

balancing control

Fig. 13 Experimental setup of two cascaded storage units

V. EXPERIMENT RESULTS

TABLE IV EXPERIMENT PARAMETERS

Symbol Item Value

V*/ fref Voltage reference 25 V/50 Hz

Ce1=Ce2 Unit capacities 2Ah

vin Output voltages of unit 32V

m1=m2 Control coefficients 3.2e-4

N SOC weighted coefficient 0.15

Zload Inductive-resistive (RL) load

Capacitive-resistive (RC) load 9.39+j4.05 Ω 12.53-j5.99 Ω

In this section, a cascaded-type islanded system with two

storage units is employed to validate the proposed control

method, which is shown in Fig. 13 and the main circuits of the

experiment system is shown in Fig. 14. Each storage unit has 10

battery cells connected in series. The nominal voltage, capacity,

impedance, max charge current and max discharge current of

battery cell are 3.2V, 2Ah, ≤1.3mΩ, 10C and 30C, respectively.

The inverters are controlled by DSP program (TMS320F28335),

to implement the proposed SOC balancing control algorithm.

The variables of active power and SOC are noted with 10s

sampling period. The parameters of experiments are listed in

Table IV. It is noted that the different SOC initial values under

two different type loads are set to verify the validation of the

SOC balancing control under various cases.

PLL

CVS #1

+

-

CVS #2

+

-

Load

Switch

Co

mm

on

load

Local

Controller

Local

Controller

Voltage

Source

Mode

Switch

PR

iref

L

iL

+

—

Controller

I

Vload

θiref

PWM

Fig. 14 Main circuits of the experiment system.

RL Load

LC Filter + Line Impedance

Storage

Module I

Storage

Module II

Inverters

Controller Driver

RC Load

Fig. 15 Experimental waveforms of proposed control starting with RL loads in

discharging mode.

0 200 400 600 800 1000 1200 1400 1600 1800 20000

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400 1600 1800 20000.3

0.4

0.5

0.6

0.7

0.8

0.9

SO

CP

ow

er(

W)

(a)

(b)

Time(s)

Time(s)

Mod. #1

Mod. #2

Mod. #1

Mod. #2

Fig. 16 Experimental results of proposed control method with RL loads in

discharging mode: (a) SOC; (b) Power.

Figs. 15 and 16 show the experimental results of proposed

SOC balancing control under RL loads in discharging mode. In

Fig. 15, the four measured waveforms represent the load voltage

(Vload), the output voltage (V1) of inverter 1, the output voltage

(V2) of inverter 2 and the output current of CESS (I),

respectively. Fig. 16 shows the measured SOC and the output

power curves. In this case, the controller is enabled at t=7s and

the initial SOC values of the two storage units are 0.82 and 0.78.

In the beginning (i.e., t<7s), the corresponding real power

outputs of the ESU #1 and ESU #2 are remaining the same. With

the proposed control strategies, the output power of ESUs has

been changed. The ESU with larger SOC has greater power

output and the one with smaller SOC has lower power output,

which means that the SOC1 decreases faster than SOC2. So the

deviation of SOC and power between ESU#1 and ESU#2

decrease. Until t=1600s, both the SOC balancing and the power

sharing are realized.

Vload

V1 V2

I

Vload 100V/div

V1 50V/div

V2 50V/div

I 6A/div

Fig. 17 Experimental waveforms of proposed control starting with RC loads in

discharging mode.

0 200 400 600 800 1000 1200 1400 1600 1800 20000

10

20

30

40

50

0 200 400 600 800 1000 1200 1400 1600 1800 20000.4

0.5

0.6

0.7

0.8

SO

C

(a)

Po

wer

(W)

(b)Time(s)

Time(s)

Mod. #1

Mod. #2

Mod. #1

Mod. #2

Fig. 18 Experimental results of proposed control method with RC loads in

discharging mode: (a) SOC; (b) Power.

Fig. 17 and 18 show the measured waveforms under RC

loads in discharging mode. The proposed SOC balancing

control is enabled at t=9s, and the initial SOC values are:

SOC01=0.77 and SOC02=0.74. As shown from Fig. 18, under the

proposed control, the output power of ESUs has been adjusted

by following the SOC balancing principle. In the steady state,

the purposes of SOC balancing and the power sharing are

achieved. It is noted that the different SOC initial values under

two different type loads are set to verify the validation of the

SOC balancing control under various cases, which has no effect

on whether we can obtain our conclusion or not.

In charging mode, the DC voltage source is under the

constant current control, which charges ESS and energizes loads.

Figs. 19 and 20 show the measured waveforms under RL loads

in charging mode. The proposed SOC balancing control is

enabled at t=11s, and the initial SOC values are: SOC01=0.23

and SOC02=0.27. As shown from Fig. 20, under the proposed

control, the injected power and the SOC are balancing in the

steady state, which validate the feasibility of the propose control

in charging mode.

Vload

V1 V2

I

Vload 100V/div

V1 50V/div

V2 50V/div

I 6A/div

Vload 100V/div

V1 50V/div

V2 50V/div

I 10A/div

Vload

V1 V2

I

Fig. 19 Experimental waveforms of proposed control starting with RL loads in charging mode.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

-60

-50

-40

-30

-20

-10

0

0.2

0.3

0.4

0.5

0.6

0.7

SO

CP

ow

er(W

)

(a)

(b)

Time(s)

Time(s)

Mod. #2

Mod. #1

Mod. #1

Mod. #2

Fig.20 Experimental results of proposed control method with RL loads in

charging mode: (a) SOC; (b) Power.

VI. CONCLUSIONS

In this paper, we propose a decentralized SOC balancing

scheme for cascaded-type energy storage system. This scheme

achieves SOC balancing of energy storage units through

adjusting P-f curves. Without communication dependence, the

proposed decentralized control obtains higher reliability and

lower construction cost. Meanwhile, the proposed control has

good extensibility, and its application is not limited by the

number of ESUs. Moreover, based on the singular perturbation

theory, the SOC steady state values are proved to be equal. The

stability of the system is proved and a sufficient condition for

the stable operation is provided. Both the simulation and

experiment results have validated the proposed method.

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Guangze Shi received the B.S. degree from the

North China Electric Power University, Beijing,

China, in 2015, and M.S. degree from Central

South University, Changsha, China, in 2018,

where he is currently working toward Ph.D. degree in power electronics and power

transmission. His research interests include

Micro-grid, Energy storage system and power-

electronic enabled power network.

Hua Han was born in Hunan, China, in 1970. She received the M.S. and Ph.D. degrees from the

School of Automation, Central South University,

Changsha, China, in 1998 and 2008, respectively. She was a Visiting Scholar with the University of

Central Florida, Orlando, FL, USA, from 2011 to

2012. She is currently a Professor with the School of Automation, Central South University. Her

research interests include microgrids, renewable

energy power generation systems, and power

electronic equipment.

Zhangjie Liu received the B.S. degree, in 2013, in

Detection Guidance and Control Techniques and

the Ph. D. degree in Control Science and Engineering from the Central South University,

Changsha, China. He is currently an Associate

Professor at School of Automation of Central South University. He is also a Postdoctoral

Research Fellow at the Nanyang Technological

University. He is interested in DC microgrid, power system stability, complex network and

nonlinear circuit.

Yao Sun (M’13) was born in Hunan, China, in 1981. He received the B.S., M.S. and Ph.D. degrees

from the School of Information Science and Engineering, Central South University, Changsha,

China, in 2004, 2007 and 2010, respectively. He is

currently with the School of Automation, Central South University, China, as a Professor.

His research interests include matrix converter,

micro-grid and wind energy conversion system.

Minghui Zheng received the B.E. and M.E.

degrees, in 2008 and 2011 respectively, from

Beihang University, Beijing, China, and the Ph.D. degree in Mechanical Engineering, in 2017, from

University of California, Berkeley, USA. She

joined University at Buffalo, in 2017, where she is currently an assistant professor in Mechanical and

Aerospace Engineering. Her research interests

include advanced learning, estimation, and control

with applications to high-precision systems.

Xiaochao Hou (S’16) received the B.S. and M.S. degrees from the School of Information Science

and Engineering, Central South University,

Changsha, China, in 2014 and 2017, respectively, where he is currently working toward Ph.D. degree

in power electronics and power transmission. Now

he is a joint Ph.D. student supported by the China Scholarship Council with the School of Electrical

and Electronic Engineering of Nanyang

Technological University. His research interests include distributed micro-grid, and power-

electronic enabled power network.