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: [email protected], [email protected], [email protected], [email protected], [email protected]).
M. Zheng is with Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, New York, USA (e-mail: [email protected]).
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.