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Variable Two Stage Rate-Limit Control forBattery Energy Storage System

CONFERENCE PAPER · NOVEMBER 2015

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Sathish Kumar Kollimalla

Indian Institute of Technology Madras

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Abhisek Ukil

Nanyang Technological University

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Variable Two Stage Rate-Limit Control for Battery

Energy Storage System

Sathish Kumar Kollimalla,  Member, IEEE 

School of Electrical Engineering,

Nanyang Technological University Singapore.skollimalla@ntu.edu.sg

Abhisek Ukil,  Senior Member, IEEE 

School of Electrical Engineering,

Nanyang Technological University Singapore.aukil@ntu.edu.sg

H. B. Gooi,  Senior Member, IEEE 

School of Electrical Engineering,

Nanyang Technological University Singapore.

ehbgooi@ntu.edu.sg

Ujjal Manandhar,  Student Member, IEEE 

School of Electrical Engineering,

Nanyang Technological University Singapore.

ujjal001@ntu.edu.sg

 Abstract—The present work deals with a new energy man-agement control scheme to regulate the battery discharge/chargerates (rate-limit) for a hybrid energy storage system (HESS),

consisting of battery and supercapacitor. In general, batteriesare used to supply slow transient (or steady state) load demand,due to its inherent properties of low power density and highenergy density. The state of charge (SOC) of the battery willdepend on the load demand value, rate limit, the settling timeand path followed by the battery (trajectory) to fulfill the loaddemand. In the proposed control scheme, trajectory of thebattery is controlled such that, the rate limit and the SOC arekept within the limits, while getting optimized. This scheme isadaptable for different power requirements and features variablerate limit control. Furthermore, the scheme proposes two stagerate-limit control. The control scheme is described in detail anddemonstrated using MATLAB simulation results.

 Index Terms—Battery, Energy storage system, Hybrid energy

storage system, Rate-limit control, State of charge, Supercapac-

itor.

I. INTRODUCTION

Renewable energy sources like solar, wind, etc. are gaining a

lot of importance in power generation due to their eco-friendly

nature and abundance. These renewable energy sources are

interfaced to the grid through power electronic converters.

However, the power generation from these sources are inter-

mittent in nature. Therefore, a generation-demand mismatch

always exists, which leads to the power quality issues. These

problems can be solved by introducing the energy storage

system (ESS).

Energy storage system is playing a very important role in

microgrid by solving the problems like energy management,

peak shaving, power quality, load leveling, stability, voltage

regulation and uninterrupted power supply. Batteries and su-

percapacitors (SC) are most commonly used ESS technologies.

Batteries have high energy density but low power density

[1]–[3].   Therefore, under severe load fluctuations, batteries

cannot respond immediately and will be under high stress. It

is reflected as increase in the charging and discharging cycles,

which leads to reduction in battery life span   [4].   However,

batteries can very well be used as achieve large scale and long-

time availability energy storage system. The supercapacitors

are new form of energy storage, storing energy by means

of static charge. Compared to the batteries, the SC possesshigh power density but low energy density. Hence, SCs can

be used to satisfy the quick load fluctuations   [5],   [6]. The

relative properties of the battery and the supercapacitor are

shown in Table I.

TABLE IBATTERY V ERSUS S UPERCAPACITOR  P ERFORMANCE [ 2]

Lead acid battery Supercapacitor

Specific energy density 10-100 (Wh/kg) 1-10 (Wh/kg)

Specific power density   <  1000 (W/kg)   <  10000 (W/kg)

Cycle life 1000   >   500000

Charge/discharge efficiency 70-85 % 85-98 %

Fast charge time 1-5 hr 0.3-30 secDischarge time 0.3-3 hr 0.3-30 sec

Due to the low charge/discharge rates, the battery cannot

usually support rapidly fluctuating load demands, whereas the

supercapacitor can suppport due to its high power density.

However, the supercapacitor cannot usually support the load

demand for longer duration due to its low energy density,

while the battery can do that due to its high energy density.

Therefore, utilization of only one kind of ESS can hardly

meet both the requirements. An ideal energy storage system

should possess both high energy and power density capabili-

ties. Therefore, the concept of hybrid energy storage system

(HESS) is gaining a lot of attention.A variety of control strategies have been proposed in

literature   [7]–[13],   for controlling power sharing between

battery and supercapacitor. Authors in [7] have addressed the

advantages of adding a supercapacitor to a battery for wind

based system. Wei et al. in   [8],   presented a study which

shows that HESS lowers the battery cost and improves the

overall system efficiency. Authors in   [9]   demonstrated the

reduction in battery stresses by using supercapacitor. Authors

in   [10],   [11]   reported analysis of battery lifetime extension

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using supercapacitors for a small-scale wind-energy system.

Authors in   [12]   suggested to use energy storage system to

reduce the rate of change of power demanded from the source

due to highly dynamic loads. Ding et al.   [13],   proposed a

adaptive rate-limit control for batteries, to protect the primary

power source in the system from sudden load transients within

the constraints of the available stored energy.

The basic idea behind these controllers is that the battery

supports the slow transients and the supercapacitor supportsthe fast transients. But the fundamental conventional controller

does not take care about charge/discharge rate (rate-limit)

and state of charge (SOC ) of the battery. In conventional

controller, the charging/discharging of the battery is controlled

by the PI controller, which is nonlinear in nature. In that case,

the charging/discharging rates may cross the maximum value

allowed for the battery, thereby increasing the stress on the

battery. As a result, the battery life span decreases, which is

undesirable. Therefore, in the proposed control scheme the

charging/discharging rates are controlled to reduce the stress

levels on the battery to increase the life span. Further, the

path followed by the battery and rate-limit affects the energy

stored/discharged by it, which will affect the S OC . Therefore,in the proposed control scheme, the path followed by the

battery is controlled by introducing a variable two stage rate-

limit control, along with controlling the rate-limit. Therefore,

in this paper a new energy management control scheme is

proposed to regulate the charging/discharging rate (rate-limit)

and energy stored/discharged by the battery.

The remainder of the paper is organized as follows. In

Section II a general analysis of HESS is presented. The

proposed energy management control scheme is explained

in Section III. Simulation results are reported in Section IV.

Finally, conclusions are summarized in Section V.

I I . GENERAL  A NALYSIS OF HESSFig. 1 shows the conventional controller for HESS. The

control schemes maintain the grid voltage (V  o) at its reference

value (V  ref ). In this scheme, the output of the low-pass

filter is given as reference (I B ref ) to the battery converter,

whereas the the high frequency component which is obtained

by subtracting  I B ref  from total current (I tot ref ) is given as

reference (I SC ref ) to the supercapacitor converter. With this

controller, at any point of time the change in load demand

(∆P L) is supplied by battery and/or supercapacitor, which can

be described by the following equation.

V ref 

V o 

I tot_ref 

  I B_ref 

I SC_ref 

Fig. 1. Schematic of conventional control [5].

∆P L(t) =  P B(t) + P SC (t),   (1)

where   P B   is power supplied by battery and   P SC    is power

supplied by supercapacitor. Typical linear response curves of 

the battery and the supercapacitor for an increase in load

demand (∆P L) are shown in Fig. 2. The area under these

Time (sec)

   P  o  w  e  r   (   W   )

P B 

P SC 

Battery power  Supercapacitor power 

ΔP L

T 

Fig. 2. Battery and supercapacitor responses for increase in load demand.

curves gives the energy supplied by the respective ESS. For

example, the energy discharged by the battery is given by

E B  =

   T 

0

P B(t)dt.   (2)

Depending on the energy levels, the  S OC  of the ESS increases

or decreases or remains within the limits. Therefore, the  S OC 

of the battery is expressed as a function of the energy,

SOC  = f (E B).   (3)

The energy stored/discharged in the battery depends on the

path (trajectory) followed in order to meet the specific load

demand.

P L0 

P L1

P B1

P B2 

E B1

E B2 

E B0 

P L

T 

t M 

Fig. 3. Battery response profiles: a) power, and b) energy.

Fig. 3 shows the two possible power profiles  P B1   and  P B2

followed by battery to meet the load demand of  ∆P L(= P L1−

P L0). As shown in Fig. 3 (a), profile   P B1   supplies the load

demand at linear rate depending on the load demand, as given

by

mlin = ∆P L

T   ,   (4)

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where   T   is the settling time. Profile   P B2   supplies the load

demand at zero discharge rate for a period of   tM . After that,

it discharges at the maximum discharge rate (mmax) allowed

for the battery by the manufacturers. The time period   tM   is

determined by the following relation

tM   = T  −  ∆P L

mmax

.   (5)

From Fig. 3 (a), one can observe that the profile   P B1   is

supplying the load demand with less discharge rate. This

is variable (function of load demand and settling time) in

nature compared to the profile  P B2  which is constant. Energy

delivered by the battery for these power profiles ( E B1, E B2) is

shown in Fig. 3 (b). It shows that, for a specific load demand

and settling time the energy delivered by the profile   P B1   is

higher than profile   P B2. So, for these profiles, there exist a

tradeoff between discharge rate and energy discharged, i.e.

profile with less discharge rate delivers high energy, and vice

versa. Therefore, a new energy management control scheme

is proposed to optimize the rate-limit as well as the energy.

III. NEW  C ONTROL S CHEME FOR  C ONTROLLING E SS

In the proposed control scheme, the fundamental idea of 

battery supplying the low frequency power component and

SC supplying high frequency power component is retained.

However, an additional feature called adaptive rate limit con-

trol is added to the conventional controller, as shown in Fig.

4. The idea of proposed rate limit control scheme is explained

V ref 

V o 

I tot_ref   I B_ref 

I SC_ref 

Fig. 4. Schematic of modified conventional control.

by inserting a new power profile (P B3) with variable two

stage rate-limit (m1, m2), in between the profiles   P B1   and

P B2   as shown in Fig. 5. Here the concept is explained for

increase in load demand, i.e., discharging the battery. The

same explanation is valid for decrease in load demand, i.e.,

charging the battery. The power profile  P B1   follows the path

AC with rate-limit of  mlin, profile  P B2  follows the path AEC

with rate-limit of  mmax and profile P B3  follows the path AFC

with rate-limits of  m1   and  m2. The range of these rate limits

are given as

0  < m1  < mlin   (6)

mlin  < m2  < mmax   (7)

The energy stored by the power profile  P B1   is given as

E B1  =  Area of ∆ACB = 1

2T ∆P L.   (8)

The energy stored by the power profile  P B2   is given as

E B2 =  Area of ∆ECB = 1

2(T  − tM )∆P L.   (9)

t 1

t M 

T 

P L

m1

 m 2

P 1

 m  l i n

  m  m  a  x

P B1

P B2 

P B3 

Fig. 5. Proposed rate-limit control for battery.

Similarly, the energy stored by the power profile  P B3  is given

as

E B   =   Area ofABCFA (10)

=  1

2t1P 1 + (T  − t1)P 1 +

 1

2(T  − t1)(∆P L − P 1).

The proposed control scheme is designed such that, the rate-limit   m2   lies at the mid point of its extreme limits and the

energy delivered is average energy of power profiles  P B1   and

P B2. Therefore, the rate limit  m2  and energy delivered by the

proposed profile  P B3   is given as

m2  =  mlin + mmax

2  ,   (11)

E B  =  E B1 + E B2

2  .   (12)

The equilibrium point F (t1, P 1) satisfying the above two

conditions is given by

t1  =  2(∆P  −

E B−

  1

2 m2T 

2

)∆P  − m2T 

  ,   (13)

P 1  =  m2(∆P  − 2E B)

∆P  − m2T   + ∆P,   (14)

where

m2  = ∆P 

2

2T  − tM 

T (T  − tM ),   (15)

E B  = ∆P 

4  (2T  − tM ).   (16)

From (13) and (14) the rate limit   m1   can be calculated as

given

m1  =  P 1

t1.   (17)

IV. SIMULATION  R ESULTS

To demonstrate the proposed control scheme let us make

the following assumptions:

1) both the charging and discharging rates of the battery

are equal,

2) the maximum allowed charge/discharge rate of the bat-

tery system is 9 kW/sec,

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3) the positive polarity is used for indicating discharging

and negative polarity is used for indicating charging of 

the battery,

4) the difference in load demand and battery power is

supplied by supercapacitor,  P SC (t) = ∆P L(t)− P B(t),

5) power electronic converters are perfectly tuned to track 

the reference powers.

The proposed control scheme is validated for step changes in

load demand and variations in settling time.

 A. Study of Change in Load Demand 

In this study, the load demand is increased and decreased

while keeping the settling time (T ) constant at 1 sec. Fig. 6

shows the simulation results for step increase in load demand.

It demonstrates the different possible power profiles of the

battery satisfying eq. (11), for the increased load demand of 

5 kW. For this particular case, the linear (profile   P B1) and

the maximum (profile   P B2) discharge rates are 5 kW/s and

9 kW/s respectively, and the corresponding discharged energy

values are 2.5 kW-s and 1.39 kW-s respectively. The discharge

rate  m2   is determined using (11), which is equal to 7 kW/s.

The rate-limit  m1   is varied from zero to  mlin, while keepingthe   m2   = 7 kW/s constant to understand the power profiles

and energy discharged, few of them are shown in Fig. 6. Each

power profile discharges the power at different energy levels

for the same load demand. Among them the profile which

satisfies the energy criteria given by (16), is chosen as the

optimized solution. The equilibrium point (t1, P 1) satisfying

the rate limit and energy criteria (m2   = 7 kW/s,   E B   = 1.94

kW-s) is determined as (0.44 s, 1.11 kW).

0 0.2 0.4 0.6 0.8 10

1

2

3

4

P B1

   P  o  w  e  r   (   k   W   )

Time (s)

P B2    P B3  (Proposed) Other  

Fig. 6. Different possible battery power profiles for increase in load demand.

To study the behavior of the proposed control scheme in

discharging mode, the load demand is increased by 1 kW, 3

kW and 5 kW. Similarly, to study the behavior in charging

mode, the load demand is decreased by -1 kW, -3 kW and -5

kW. The simulation results for both charging and discharging

scenarios are shown in Fig. 7. Since the charging and the

discharging rates of the battery are assumed to be equal,

the charging power profile and discharging power profiles

of the battery are symmetrical. The simulation results are

summarized in Table II. Here power is expressed in kW,

charge/discharge rates are expressed in kW/s and energy is

expressed in kW-s. From the results it is observed that the

rate limit (mlin) of profile   P B1   is increasing continuously

with increasing load demand, while the rate limit of profile

P B1   P B2    P B3 

Fig. 7. Response of battery for change in load demand.

P B2   is constant at 9 kW/s. Further, the maximum rate-limit

of the profile   P B3   (proposed scheme) is not exceeding its

maximum charge/discharge rate allowed by the manufacturer.

With this new approach the energy charged/discharged by the

battery is less than that of profile  P B1. It is further observed

that with increase in load demand, time taken by the battery

(T −t1) to charge/discharge the power with rate-limit  m2  also

increases, whereas the time taken (t1) decreases with rate-limit

of  m1. It indicates that as the load demand is increasing, the

operation duration of the battery with higher discharge rate

also increases.

TABLE IISIMULATION RESULTS OF CHANGE IN LOAD DEMAND

∆P t1   P1   mlin   m1   m2   EB1   EB2   EB

5 0.44 1.11 5.00 2.50 7.00 2.50 1.39 1.94

3 0.67 1.00 3.00 1.50 6.00 1.50 0.50 1.00

1 0.89 0.44 1.00 0.50 5.00 0.50 0.06 0.28

-1 0.89 -0.44 -1.00 -0.50 -5.00 -0.50 -0.06 -0.28

-3 0.67 -1.00 -3.00 -1.50 -6.00 -1.50 -0.50 -1.00

-5 0.44 -1.11 -5.00 -2.50 -7.00 -2.50 -1.39 -1.94

 B. Study of Change in Settling Time

In this study, battery response is studied by varying the

settling time (T ) in steps of 2 seconds, while keeping the load

demand constant at 5 kW.

Fig. 8 shows the simulations results for three different

settling times. In these three cases the maximum discharge

rate of profile   P B2   is same but the linear discharge rate of 

profile P B1  is varying. These values are quantified in the Table

III. Here, power is expressed in kW, charge/discharge rates

are expressed in kW/s and energy is expressed in kW-s. It

is observed that as   T   is increasing, the   mlin   is decreasing

continuously, but at the same time the corresponding energy

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0 1 2 3 4 5 60

1

2

3

4

5

Time (s)

   P  o  w  e  r   (   k   W   )

P B1   P B2    P B3  (Proposed)

Fig. 8. Response of battery for change in settling time.

discharge E B1  is increasing significantly. However, the energy

discharged by profile  P B2   is constant. It is observed that with

increase in settling time, the time taken by the battery ( T −t1)

to discharge the power with rate-limit   m2   is decreasing,

whereas the time taken (t1) increases with rate-limit of   m1.

Therefore, if we increase the settling time, then the operation

of battery with higher discharge rate can be reduced for short

duration.

TABLE IIISIMULATION RESULTS OF CHANGE IN SETTLING TIME

T t1   P1   mlin   m1   m2   EB1   EB2   EB

1 0.44 1.11 5.00 2.50 7.00 2.50 1.39 1.94

3 2.44 2.04 1.67 0.83 5.33 7.50 1.39 4.44

5 4.44 2.22 1.00 0.50 5.00 12.50 1.39 6.94

V. CONCLUSION

A new energy management control scheme with an adap-tive two stage variable rate limit control has been proposed

for battery energy storage system. The objective of this

control is to regulate the charge/discharge rates and energy

stored/discharged by battery during changes in load demand.

This scheme allows the battery to operate under slowly varying

conditions, minimizing the life time limiting effects due to

high charge/discharge rates. The proposed control scheme

retains the features of conventional control scheme, that bat-

tery has to support slow transient and supercapacitor has to

support fast transient. The proposed scheme has introduced

two stage variable rate limit control. With this scheme, the

charge/discharge rates are controlled such that battery does

not exceed the maximum allowed rate-limit, and hence stresslevels are under control. The energy or   SOC   of the battery

has been controlled, so that battery can stay within the limits

for more duration. MATLAB simulations substantiate the

feasibility of implementation of proposed control scheme.

VI . ACKNOWLEDGEMENT

This work was supported by the Energy Innovation Pro-

gramme Office (EIPO) through the National Research Foun-

dation and Singapore Economic Development Board.

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