Application of Two Stage Rate Limit Control for
Different Operating Modes of Battery
Sathish Kumar Kollimalla, Member, IEEE, Abhisek Ukil, Senior Member, IEEE,
H. B. Gooi, Senior Member, IEEE, N. K. Swami Naidu, Member, IEEE, Ujjal Manandhar, Student Member, IEEE,
Kalpesh Chaudhari, Student Member, IEEE
Abstract—The present work deals with the application of two
stage rate limit control for battery energy storage system under
different operating modes. Energy storage systems are playing
very important role in renewable power systems and microgrids.
Depending on the nature of power requirement, utilization of
multiple energy storage units with distinguised characteristics
in terms of power and energy density is quite common in
microgrids. Batteries are one of the most commonly used energy
storage systems in microgrids, to support slow transients or
steady state load demands. The power charge/discharge rates
affects the stress levels in the battery, which in turn affects the
battery life span; and its power pattern affects stored/discharge
energy from the battery, which in turn affects the state of charge
(SOC) of the battery. Therefore, to optimize the charge/discharge
rates a two stage rate limit control scheme is proposed, and its
application for different operating modes is discussed in this
paper. This control scheme is verified in OPAL-RT by creating
real-time control hardware in loop (CHIL) with dSPACE.
Index Terms—Battery, Energy storage system, Hybrid energy
storage system, Rate-limit control, State of charge, Supercapacitor.
I. I NTRODUCTION
In the microgrid (MG), energy storage systems (ESSs) are
used to maintain the power balance between the generation
and load demand, which ensures the regulation of grid voltage
and frequency. Due to the distinguished characteristics, the
most commonly used energy storage technologies are batteries and supercapacitors (SC). Batteries have high energy
density but low power density, whereas supercapacitors have
high power density but low energy density. So batteries can
be used to support the steady state (slow transient) power
demands for longer duration due its high energy density,
whereas supercapacitors can be used to support the pulsed
(fast transient) power demands due to its high power density
[1], [2]. Therefore, two accomplish both the fast transient and
steady state features a hybrid energy storage system (HESS)
has been proposed.
Different possible configurations of the batterysupercapacitor HESS is explained in [3]. In [4]–[13], the
authors have discussed different control algorithms for HESS.
The basic idea of all these strategies is that, batteries have
to support the average power demand, while supercapacitors
have to support the transient power demand. This can be
achieved by decomposing the total power demand into low
frequency power component (steady state component) and
high frequency power component (fast transient component),
by using low pass filter or fast fourier transform technique.
The low frequency component is supplied by the battery and
high frequency component is supplied by the supercapacitor.
But none of the control schemes [4]–[13] considered the
battery charge/discharge rates while supporting the power
demand. As a result, the battery charge/discharge rates may
reaches its safety limits, thereby increasing the stress levels
on the battery, which in turn results decrease in life span
of the battery. To avoid this situation, researchers adopted a
linear rate limiter. The control algorithms having rate-limit
function feature either have a constant rate limit, resulting in
suboptimal solution, or have a complex design for optimal
solution [14]. Further, the power patterns (trajectory) of
the battery during the transient period affects the energy
stored/discharged by it, which affects it state of charge (SOC).
To solve these problems, a two stage rate limit control scheme
is proposed. The two stage rate limit control scheme has
been explained in detail by the authors in [15]. This control
scheme has the advantage that it can protect the battery from
abrupt charge/discharge within the constraints of available
storage capacity.
In this paper the application of two stage rate limit control,
for different modes of battery operation is presented. The
modes of operations includes discharging the battery during
sudden increase and decrease in power demands; charging
the battery during sudden decrease and increase in power
demands; and transition from discharging to charging and viceversa for sudden increase and decrease in power demands.
II. T WO S TAGE R ATE L IMIT C ONTROL
To explain the concept of two stage rate limit control
scheme, let consider a standalone PV system as shown in Fig.
1. The DC loads and the AC system are represented with
equivalent DC load resistance R connected to the DC grid. It
is assumed that:
1) the positive and negative polarity of currents indicate
discharging and charging,
2) the supercapacitor supplies the difference in load
demand (ΔPL (t)) and battery power (PB (t)), i.e.,
PSC (t) = ΔPL (t) − PB (t), and
3) throughout the operation SOC of the supercapacitor is
within the limits .
Let us consider that there is a step increase in load demand
(ΔPL ), and the PV generation is fixed. As the load demand
LSC
IB
ISC
Battery V
B
Super-
m1
VSC capacitor
4
2
LPV
PV
panel VPV
t1
tM
IPV
R V
o
C
5
P2
m2
m lin
PL
ax
3
m
1
P1
m
LB
t2
T
Fig. 4. Proposed rate-limit control for battery.
and
Fig. 1. Equivalent system configuration of DC grid.
is increased the excess load demand is supplied by HESS.
Due to the high power density the supercapacitor supplies the
excess load demand initially and slowly transfers it to battery
as shown in Fig. 2. The block diagram of voltage controller
for HESS is shown in Fig. 3. In the two stage rate limit control
scheme the battery supplies the excess load with two different
discharge rates m1 and m2 as shown in Fig. 4, following the
path AFC.
Power (W)
Battery power
Fig. 2. HESS responses for increase in load demand.
IB
1
VSC
-
Sw1
PI-2
PWM
Sw2
ISC_ref
+
-
+
-
1
VB
+
PI-3
PWM
ISC
m2
=
=
=
P1
,
t1
ΔPL − P1
,
T − t1
Area of ( AFD + FGC + FGBD )
EB1 + EB2 + EB3 ,
(6)
=
fa (m1 , m2 ) = min{EB2 − EB1 }.
The rate-limits m1 and m2 are defined as,
=
EB
At constant t1 and t2 minimization of m2 indicates the
minimization of EB2 and maximization of EB1 from (7) (8). Therefore, the objective function can be defined as
Fig. 3. Schematic of two stage rate limit control.
m1
The energy supplied by the battery is given as
A. Objective Functions:
Time (sec)
Adaptive
rate limiter
(5)
Sw3
T
Vo
mlin = ΔPL /T.
Sw4
PSC
PI-1
(4)
1
1
P2
t1 P1 = m1 t21 = 1 ,
(7)
2
2
2m1
1
1
P2
t2 P2 = m2 t22 = 2 ,
EB2 =
(8)
2
2
2m2
P1 P2
EB3 = t2 P1 = m1 t1 t2 =
.
(9)
m2
The control scheme is designed such that the following three
optimization conditions are satisfied:
1) Energy stored/discharged (EB ) during the transient period is optimized,
2) Maximum possible charge/discharge rate (m2 ) is optimized, and
3) The duration of time (t2 ) for which battery
charges/discharges at its optimized maximum rate
(m2 ) is optimized.
PB
+
-
mlin ≤ m2 ≤ mmax .
where, T is settling time and mmax is maximum discharge
rate of the battery, and
EB1
IB_ref
(3)
where,
Supercapacitor power
PL
Vref
0 ≤ m1 ≤ mlin ,
(10)
(1)
At constant P1 and P2 minimization of m2 indicates the
maximization of EB2 and EB2 , and minimization of EB1 from
(7) - (8). Therefore, the objective functions can be defined as
(2)
fb (m1 , m2 ) = min{EB1 − EB2 }.
(11)
fc (m1 , m2 ) = min{EB1 − EB3 }.
(12)
And at constant P1 and P2 minimization of t2 indicates
minimization of EB3 and maximization of EB1 . Therefore,
the objective function can be defined as
fd (m1 , m2 ) = min{EB3 − EB1 }.
(13)
From the above optimization problems (10) - (13), two
minimization problems are derived as given,
fI (m1 , m2 ) = min{EB1 ∼ EB2 }
(14)
fII (m1 , m2 ) = min{EB1 ∼ EB3 }
(15)
subject to (5) and (4).
B. Solution of Objective Functions:
The ideal solution at which the optimal point occurs for
objective function fI (m1 , m2 ) is obtained by equating (14) to
zero. The optimal power at which (EB1 ∼ EB2 ) = 0 occurs
is derived as,
ΔPL (T − t1 )
.
(16)
P1 =
T
Similarly, the ideal solution at which the optimal point
occurs for objective function fII (m1 , m2 ) is obtained by
equating (15) to zero. The optimal power at which (EB1 ∼
EB3 ) = 0 occurs is derived as,
ΔPL
.
(17)
3
The optimal operating point (topt , Popt ) is obtained by
solving (16) and (17). Therefore, the optimal operating point
‘F’ in Fig. 4 is derived as,
P1 =
2T
,
(18)
3
ΔPL
.
(19)
Popt =
3
Therefore, the optimal two-rates are obtained by solving
(16) and (17) as given,
topt =
m1
=
m2
=
Popt
topt
ΔPL − Popt
.
T − topt
(20)
(21)
C. Different Operating Modes:
Depending on the status of generation demand mismatch
i.e., generation is increased or decreased, load demand is
increased or decreased, and depending on the battery status
i.e., battery is charging or discharging; the battery operates
in six modes. The six modes of operations are tabulated in
Table I. Here, change in load demand positive indicates load
is increased and negative indicates load is decreased. The six
modes of operation are shown in Fig. 5.
In mode-1 initially battery is discharging (PB is positive),
suddenly load demand is increased (ΔPL is positive). Therefore, according to two rate limit control battery follows the
path A1 F1 C1 as shown in Fig. 5 (a) with m1 and m2 rates.
TABLE I
D IFFERENT O PERATING M ODES OF BATTERY
Mode
1
2
3
4
5
6
Battery power (PB )
Positive
Positive
Negative
Negative
Positive to Negative
Negative to Positive
Change in load demand (ΔPL )
Positive
Negative
Negative
Positive
Negative
Positive
In mode-2 initially battery is discharging (PB is positive),
suddenly load demand is decreased (ΔPL is negative). The
decrease in load demand is not high enough to change the
mode from discharging to charging. Therefore, the battery
follows the path A2 F2 C2 as shown in Fig. 5 (b). In this mode
battery is still discharging with reduced power level.
In mode-3 initially battery is charging (PB is negative),
suddenly load demand is decreased (ΔPL is negative). To
balance the power, the battery follows the path A3 F3 C3 as
shown in Fig. 5 (c).
In mode-4 initially battery is charging (PB is negative),
suddenly load demand is increased (ΔPL is positive). The
increase in load demand is not high enough to change the mode
from charging to discharging. Therefore, the battery follows
the path A4 F4 C4 as shown in Fig. 5 (d). In this mode battery
is still charging with reduced power level.
In mode-5 initially battery is discharging (PB is positive),
suddenly load demand is decreased (ΔPL is negative). In this
mode the battery has to transit from discharging mode to
charging mode. Therefore, upto point C5 the battery follows
the path A5 F5 C5 with m1 and m2 rates, and after that it
follows the path C5 G5 E5 with m1 and m2 rates as shown
in Fig. 5 (e).
In mode-6 initially battery is charging (PB is negative),
suddenly load demand is increased (ΔPL is positive). In
this mode the battery has to transit from charging mode to
discharging mode. Therefore, upto point C6 the battery follows
the path A6 F6 C6 with m2 and m1 rates, and after that it
follows the path C6 G6 E6 with m2 and m1 rates as shown
in Fig. 5 (f).
III. E XPERIMENTAL S TUDY
The two rate limit control scheme is validated by using
the real-time control hardware-in-loop (CHIL), comprising of
the OPAL-RT 5600 and the dSPACE 1103, as shown in Fig.
6. The power stage is modeled in OPAL-RT and the control
algorithms are designed and implemented in dSPACE. The
specifications of HESS and controller parameters are given in
Table II. It is assumed that the initial state of charge (SOC)
of the battery is 50%. Fig. 7 shows the OPAL-RT results of
different operating modes of battery. For all the modes the
irradiance is kept at 275 W/m2 and the PV panel is operated
at its maximum power point. The maximum power generated
from the PV panel is 3.63 kW. The controller is designed to
maintain the DC grid voltage at 600 V. The settling time for
two stage rate limit control is considered as 2 sec.
C1
PB +ve
A5
m2
m lin
PL
PB +ve
m
m1
ax
F1
2
m
m
m
lin
m1
F5
ax
0
-PL
B1
mm
A1
Mode-1
C5
D5
0
B5
G5
ax
m1
PB +ve
mm
A2
m
lin
m
2
m
2
m
lin
-PL
m1
F2
mm
PB -ve
ax
E5
B2
0
C2
Mode-5
Mode-2
0
A3
B3
E6
m
lin
m
2
m2
PL
m1
C3
C6
B6
G
m
ax
m lin
PB -ve
m
-PL
PB +ve
ax
F3
mm
m1
0
Mode-3
ax
D6
C4
m
ma
x
B4
m
m
0
F4
PL
m1
m lin
m2
m1
PB -ve
m lin
m2
F6
A6
PB -ve
A4
Mode-4
Mode-6
Fig. 5. Different operating modes of battery.
TABLE II
N OMINAL PARAMETERS OF DC G RID
Subsystem
PV array
@ STC
Battery
Supercapacitor
DC-DC
converters
Controller
parameters
Fig. 6. Experimental setup: (a) OPAL-RT (b) schematic of control hardware
in loop (CHIL).
Fig. 7 (a) shows voltages, powers and SOC results of mode1 operation. In this mode initially the load resistance is kept
at 75 Ω, so the load demand is 4.803 kW. To meet the surplus
power demand from the load, the battery discharges 1.217 kW
power to load, in addition to the PV supply. After 1 sec the
load demand is increased to 6.015 kW by reducing the load
resistance to 60 Ω. The additional load demand is supplied
Specifications
VOC = 375 V, ISC = 66.4 A, PM P P = 19.2 kW.
VM P P = 311 V, IM P P = 61.76 A
Amptek 6-DZM-14 Lead acid - 12 V, 14 Ah
(20 connected in series & 2 connected in parallel).
Maxwell BMOD0058 E016 B02 58 F, 16 V
(20 connected in series & 2 connected in parallel).
LP V = 9.6 mH, LB = 13.8 mH, LSC = 9.6 mH,
C = 277 μF.
Vref = 600 V, switching frequency = 10 kHz
PI-1 Kp = 0.51, Ki = 300.37,
PI-2 Kp = 0.12861, Ki = 428.19,
PI-3 Kp = 0.09063, Ki = 303.93,
PI-4 Kp = 0.085681, Ki = 308.13,
by battery and supercapacitor as shown in Fig. 7 (a), while
maintaining the DC grid voltage at 600 V. The path followed
by the battery is A1 F1 C1 (encircled). The m1 and m2 are
calculated using equations (20) and (21). The results shows
that the battery SOC is decreasing due to discharging. The net
change in energy supplied by the battery by this scheme is
0.662 kW-sec, whereas energy supplied by the battery with
PV parameters
6
500
4
300
2
0
6
500
4
300
1
2
2
Mode-1
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
49.998
A2
F2
2
C2
0
49.994
49.990
49.986
-2
3
49.994
49.990
49.986
1
600
400
C1
F1
A1
3
Power (kW)
Voltage (V)
1
2
Supercapacitor parameters
49.998
% SOC
400
Battery parameters
% SOC
600
Power (kW)
Voltage (V)
Load parameters
1
2
Mode-2
3
4
50.014
500
400
300
1
2
2
0
% SOC
Power (kW)
Voltage (V)
600
A3
-2
C3
F3
3
1
2
Mode-3
50.010
50.006
50.002
3
4
50.018
2
50.014
500
400
300
1
2
% SOC
Power (kW)
Voltage (V)
600
0
C4
F4
A4
-2
1
3
2
Mode-4
50.010
50.006
50.002
3
8
49.999
500
400
4
% SOC
Power (kW)
Voltage (V)
600
A5
0
F5
C5
1
2
E5
1
3
49.995
G5
-4
300
49.997
2
Mode-5
49.993
3
50.009
Power (kW)
Voltage (V)
500
400
300
4
2
-2
1
2
3
C6
F6
0
E6
50.007
50.005
G6
A6
1
% SOC
6
600
50.003
2
Mode-6
3
Fig. 7. OPAL-RT results of different operating modes of battery.
linear rate (i.e., the path followed by battery is AC as shown
in Fig. 4), mlin = ΔP/T , (5) is 1.19 kW-sec. It shows that the
net change is energy is relatively less compared to linear rate
method. Similar results are observed for the remaining modes
as presented in subsequent paragraphs.
Fig. 7 (b) shows voltages, powers and SOC results of mode2 operation. In this mode initially the load resistance is kept
at 60 Ω, so the load demand is 6.015 kW. To meet the load
demand the battery is supplying 2.417 kW power to load. After
1 sec the load demand is decreased to 4.803 kW by increasing
the load resistance to 75 Ω. As the load demand is decreased,
to maintain power balance the battery also reduced its power
to 1.17 kW. The path followed by the battery is A2 F2 C2 . The
results show that the rate at which the SOC is decreasing is
reduced due to reduction in discharge power from 2.417 kW
to 1.17 kW. The net change in energy supplied by the battery
by this scheme is -0.7893 kW-sec, whereas with linear rate is
-1.19 kW-sec.
Fig. 7 (c) shows voltages, powers and SOC results of mode3 operation. In this mode initially the load resistance is kept at
150 Ω, so the load demand is 2.405 kW. To regulate the DC
grid voltage the battery is absorbing 1.167 kW power from PV
generation. After 1 sec the load demand is decreased to 1.203
kW by increasing the load resistance to 300 Ω. To maintain the
power balance the battery further absorbed the power of 2.467
kW. The path followed by the battery is A3 F3 C3 . The results
shows that the battery SOC is increasing due to charging. The
net change in energy absorbed by the battery by this scheme
is 0.8966 kW-sec, whereas with linear rate is 1.204 kW-sec.
Fig. 7 (d) shows voltages, powers and SOC results of mode4 operation. In this mode initially the load resistance is kept
at 300 Ω, so the load demand is 1.203 kW. To meet the load
demand, the surplus generation of 2.467 kW from PV panel
is absorbed by the battery. After 1 sec the load demand is
increased to 2.339 kW by decreasing the load resistance to 150
Ω. To meet the load demand the battery reduced the power to
1.189 kW. The path followed by the battery is A4 F4 C4 . The
results shows that, the rate at which the SOC is decreasing is
due to reduction in charging power from 2.467 kW to 1.189
kW. The net change in energy absorbed by the battery by this
scheme is -0.9064 kW-sec, whereas with linear rate is -1.204
kW-sec.
Fig. 7 (e) shows voltages, powers and SOC results of mode5 operation. In this mode initially the load resistance is kept
at 60 Ω, so the load demand is 6.015 kW. To meet the load
demand the battery is supplying 2.406 kW power to load. After
1 sec the load demand is decreased to 1.203 kW by increasing
the load resistance to 300 Ω. To regulate the DC grid voltage,
the battery changes from discharging mode to charging mode.
The path followed by the battery is A5 F5 C5 G5 E5 . At point
C5 the battery changes it mode as shown in Fig. 7 (e). The
SOC of the battery decreases up to point C5 and after that
SOC increases. The net change in energy by the battery by
this scheme is -0.0139 kW-sec, whereas with linear rate is
-0.0584 kW-sec.
Fig. 7 (f) shows voltages, powers and SOC results of mode6 operation. In this mode initially the load resistance is kept
at 300 Ω, so the load demand is 1.203 kW. To regulate the
DC grid voltage the battery is absorbing 2.474 kW power
from PV panel. After 1 sec the load demand is increased to
6.015 kW by decreasing the load resistance to 60 Ω. To meet
the load demand the battery changes from charging mode
to discharging mode. The path followed by the battery is
A6 F6 C6 G6 E6 . At point C6 the battery changes it mode from
charging to discharging as shown in Fig. 7 (e). The SOC of the
battery increases up to point C5 and after that SOC decreases.
The net change in energy by the battery by this scheme is
-0.0094 kW-sec, whereas with linear rate is 0.0584 kW-sec.
IV. C ONCLUSION
A standalone PV system comprising of battery and supercapacitor is considered to validate the control scheme. The two
stage rate limit control scheme is realized in hardware, by
forming control hardware-in-loop (CHIL) using dSPACE and
OPAL-RT. Six different operating modes of the battery (such
as charging, discharging, changing the mode from charging
to discharging etc...) have been successfully validated using
OPAL-RT. From the experimental results, it is observed that
two stage rate limit control scheme relatively reduces the
charge/discharge rates and stored/discharged energy for all the
six modes. As the charge/discharge rates of battery is relatively
low, it results in reduced stresses levels in the battery. Further,
as the net change in stored/discharged energy is relatively low,
it results in maintaining the SOC within the limits for longer
duration.
V. ACKNOWLEDGEMENT
This work was supported by the Energy Innovation Programme Office (EIPO) through the National Research Foundation and Singapore Economic Development Board.
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