Novel methodology for sizing Lead-Acid Battery

considering the useable capacity under different

discharge durations
Mehrdad Bagheri Sanjareh Mohammad Hassan Nazari, Seyyed Mohammad Sadegh Ghiasi
Electrical Engineering dept. of Seyed Hossein Hosseinian Department of Electrical Engineering,
Sahhid Behesthi University Electrical Engineering dept. of Ahvaz Branch, Islamic Azad University
Tehran, Iran Amirkabir University of Technology Ahvaz, Iran
m.bagheri7124@gmail.com Tehran, Iran smsghiasi@aut.ac.ir
nazary@aut.ac.ir

Abstract— One of important issues regarding the batteries control of a greenhouse MG in islanding mode. In [8], a BESS
are their capacity. Inadequate battery capacity leads to low is used for optimal energy management of smart house with
performance while designing a battery with extra-large capacity the capability of operating in both islanded and grid-connected
imposes unnecessary high cost. In this regard, various modes. The authors of [9] have used BESS to ensure the
researches have addressed the optimal battery capacity for a continuous supply of loads in an MG during temporary
particular task like energy management, frequency regulation islanded operation. The authors of [10] have used a BESS
and etc. Lead-Acid batteries (LABs) are among the most reducing operational cost and load levelling in an islanded
commonly used in grid and industry applications. What has MG. Lead-Acid Batteries (LABs), among various battery
been neglected in previous studies about LAB capacity sizing is
technologies, have been successfully used for grid
that the researchers have assumed the available capacity of the
LAB to be constant. This assumption is not correct because the
applications. They also offer a cost-effective reliable solution
available and effective capacity of the LABs varies under that is applicable for various storage tasks [11].
different discharge durations. In other words, the real and One of important issues regarding the batteries are their
available depends on discharge duration that as the capacity of capacity. Inadequate battery capacity leads to low
the LAB increases, the LAB capacity, which can be discharged, performance while designing a battery with extra-large
increases and vice versa. In order to prove this claim, the capacity imposes unnecessary high cost. Large battery
characteristics of typical LAB including its variable capacities
systems increase the cost while. Therefore, an ESS sizing
under different discharge durations are presented. Then in
approach is needed to size the ESS with minimal size to
order to resolve the shortcoming of the LAB sizing methods in
previous studies, the LAB characteristics are analyzed and a
achieve the desired goals. In [3], the LAB capacity is
novel LAB sizing procedure is presented which considers the determined for frequency control of an islanded MG in
impact of LAB discharge duration on its effective and available Australia. The authors of [12] have determined the LAB
capacity. The proposed procedure is tested by sizing a LAB for capacity for technical loss reduction in distribution networks.
islanded operation of a microgrid. In [13], the optimal number of LAB cell are determined to
ensure reliable and cost-effective operation of a PV-BESS
Keywords— BESS, Lead-acid battery, capacity, discharge MG. The authors of [3], [12], [13] have only considered state
duration; of charge limits and discharge/charge current limits without
taking the effect of discharge duration into consideration. The
I. INTRODUCTION discharge characteristics of a typical LAB in [14] shows that
Microgrids (MGs) can be considered as a group of loads, under different discharge durations, the effective and useable
energy storage systems and distributed generators in the low- LAB capacity is different. As the discharge current increases
voltage distribution network that can operate either in islanded and discharge duration decreases, the useable LAB capacity
mode or grid-connected [1], [2]. The proliferation of inverter- decreases.
based generations like photovoltaic systems has resulted in As previously discussed, the BESS usage is indispensable
frequency stability issues in power system including the MGs. for frequency stability of MG stability. Moreover, during
A promising sloution is to use the fast-responding Battery some periods of islanded operation, the MG power generation
Energy storage systems (BESSs) which can participate in capacity might be deficient to constantly supply MG loads
frequency regulation by quickly injecting/absorbing power which necessitates the utilization of a BESS capacity to
[3]. provide the power generation shortage. Here, a case study is
BESSs are known as one of the most efficient and presented to size the required LAB capacity for MG operation
important of stabilizing grids. They have been used for various during islanded mode. Unlike [3], [12] [13], in addition to
grid applications like peak-shaving, power quality SOC and discharge/current limits, the impact of the duration
improvement, spinning reserve, operational cost reduction, of the LAB discharge duration on its capacity is also taken into
frequency control of islanded MGs and etc. [3]–[5] In [6], the account. The major contribution of this paper is that a novel
potential of a BESS for peak shaving in distribution networks method for precisely determining the LAB capacity is
is investigated. The authors of [7] have used a BESS to control proposed that considers the impact of discharge current and
MG frequency during islanded operation. Also, the authors of duration on its effective capacity.
[1] have used for BESS for energy management and frequency

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

 In next section, the scheme for frequency control and
energy management of an islanded MG is presented. In
section 3, the specifications of a typical LAB is presented and
on its basis, a novel LAB capacity sizing method is proposed.
In section 4, the simulation studies are performed to determine
the LAB capacity for MG operation during islanded mode
using the suggested LAB capacity sizing method.
II. PROPOSED SCHEME FOR ENERGY MANAGEMENT
AND FREQUENCY CONTROL ISLANDED MG
In order to decrease the MG operational cost, it mostly
operates in grid-connected mode to trade power with the main
grid [15]. But, due to the occurrence of a disturbance in the
upstream network, it might not be safe for the MG to continue
its operation in this mode [7]. Therefore, the MG must FIG. 1 PROPOSED SCHEME FOR ENERGY MANAGEMENT AND FREQUENCY
temporarily be disconnected from the main grid till the CONTROL OF AN ISLANDED MG
disturbance is resolved. During islanded operation, the MG The maximum and minimum limits for SOC, which are
loads are supplied by local generations. Due to the absence of max min
utility grid, load variations, the intermittent nature of denoted by SOC LA B and SOC LA B are considered to be 80
renewable sources and etc., the MG may undergo rapid % and 20 %, respectively [18]. As the battery should mainly
frequency variations. The frequency dynamic of the MG in provide the shortage of power generation during the islanded
islanded mode is modelled by Eq. (1) [16], [17]. operation, the SOCref is set to be 75%. By doing this, the
battery has enough charged energy to supply the MG loads
d 0
  PG  PD  (1) and also has 5% free capacity to use for short-term charge
dt 2 H MG cycles. Also, during grid-connected operation, SOCLAB should
Where, the MG frequency and its nominal value are always be kept at 75% to make certain the continuous supply
denoted by ω and ωo, respectively. HMG is overall inertia of of MG loads during the temporary autonomous operation in
the MG. PG and PD are the total demand and generation of the case the MG is unexpectedly islanded.
MG, respectively. During islanded operation, the GH demand
may surpass the total power generation capacity of DGs. Also, III. NOVEL LAB CAPACITY SIZING CONSIDERING ITS
DG with their slow response cannot handle the MG frequency DISCHARGE CHARACTERISITCS
control, which necessitates enough and fast reserve capacity. The LAB is the most commonly used battery technology,
Therefore, the ESS usage is indispensable for energy and due to its promising high-energy density and
management and fast power regulations during the islanded performance/cost ratio, it is fit for energy management [19].
operation. In this paper, an LAB ESS (LABESS) is considered Table 1 expresses the discharge characteristics of a typical
for this task. LAB cell with the voltage rating of 12 V and the capacity
The proposed scheme for energy management and rating of 100 Ah [14]. Previous studies have considered the
frequency control, which uses the coordinated control of an LAB capacity under different discharge currents and durations
LABESS and DGs is shown in Fig. 1. The output of DGs to be constant. However, Table 1 shows that this assumption
blocks represent their power generation. In order to send is not correct, because the LAB capacity and discharge voltage
power setpoint to each of DGs, an input is considered for each are not constant. In fact, as the discharge current increases and
of them except the renewable ones that always operate at are the discharge duration increases, the useable LAB capacity (in
not dispatchable. terms of Ah) and its average discharge voltage decreases.

The proposed frequency control and energy management Table 1 LAB cell characteristics [14]
scheme consists of two stages. The first stage is intercepting Discharge duration (h) 0.133 0.25 1 5 10 20
Battery capacity (A.h) 39.87 50 60 85 93 100
frequency deviation by performing primary frequency control
Battery average voltage
(PFC) using the LABESS. The second stage is to restore (v)
10.96 10.99 11.47 11.67 11.75 11.9
frequency at its nominal value by performing secondary
frequency control (SFC) by dispatchable DGs. The integral During energy management operation, the LAB may go
controllers denoted by k1 and k2 are used for PFC and SFC, through several discharge/charge cycles with different current
respectively. The LABESS participates in SFC and energy rates and durations. The duration of each discharge/charge (
management just in durations that the DGs have reached their LA B
T Dis /Cha ) cycle can be calculated using Eq. (2):
maximum power generation. This minimizes the usage of the
LABESS and hence minimizes its required capacity. For this m 1

/Cha   T (i  1) T (i ) 
LAB
purpose, an controller is used which is indicated with the T Dis (2)
coefficient of K3. If DGs reach their maximum generation i n

capacity, a controller of integral type is used to bring the LAB Where n and m represent the first and the last time step of
power to zero. The coefficient of this controller is indicated by a discharge/charge cycle. During a charge/discharge cycle, the
K4. The LABESS efficiency is represented by Kη. An integral LAB absorbed/injected energy ( E Dis LA B
/Cha ) is equal to the
controller with coefficient of KSOC, is employed to maintain integration of its power over time. Eqs. (3) and (4) use the
the state of charge of LAB (SOCLAB) at reference value ( LA B
ref trapezoidal numerical integration rule to calculate E Dis /Cha by
SOC LAB ).
integrating the charge/discharge energy:
  m 1 P (i )  PLABESS (i  1)  considering the LAB discharge characteristics which is
LAB
E Dis /Cha  K 
LABESS
   ( LABESS ) (3) discussed earlier in previous section. The simulation studies
 i n 2 
are conducted in Simulink/Matlab software. Table 1
T (i  1) T (i )  expresses the discharge characteristics of a typical LAB cell
 LABESS PLABESS  0
(4) with the voltage rating of 12 V and the capacity rating of 100

K LABESS   1 Ah [14]. Previous studies have considered the LAB capacity
 PLABESS  0
under different
 LABESS
T (i ) and PLABESS (i ) are time and LABESS power at A. MG test system under study

the ith time step.  LABESS is the LABESS discharge/charge Fig. 2 shows the MG under study which is the CIGRE low
voltage distribution MG [21], [22]. It is connected to the 20kV
efficiency which is 0.85 [20]. The battery does not go through upstream network through a transformer. The MG consists of
a constant discharge cycle and it experiences several several local DGs such as solid-oxide fuel cell and
charge/discharge cycles. Therefore, the required amount of microturbine. Their power ratings are 31.1 kVA, 10 kVA and
LAB cells should be determined considering each discharge 31.1 kVA, respectively. The models of SOFC and MT which
cycle and its duration. The required amount of LAB cells ( are available in [23] are used. The MG also include a 10 kW
N LAB cell ) for a charge/discharge cycle can be obtained using wind turbine generator (WTG) and two PV arrays with
Eq. (5): generation capacity of 3 kW and 10 kW.
LAB The maximum MG demand surpasses the DGs power
E Dis (j)
N LAB cell ( j )  (5) generation capacity that only two thirds of maximum demand
C LAB V LAB
av
 (SOC LAB
ref
 SOC LAB
min
) can be supplied. In other words, the required power of MG
LAB
E Dis (j) loads cannot be continuously supplied. Therefore, the
 utilization of a BESS is indispensable.
C LAB V LAB  0.55
av
In order to determine LAB stack size for continuous
av
Where, C LAB and V LA B are the effective and useable supply of MG demand during islanded operation, the
capacity (in terms of A.h) the average voltage of the LAB, simulations should be conducted for daily energy
LA B management for all days of at least a year is required. Then,
respectively which can be calculated using T Dis and the day that requires the largest LAB stack size is taken as the
interpolation of data in Table 1. The variable j counts the worst case and the LAB stack size is determined based on the
number of discharge cycles. The term (SOC LAB ref
 SOC LAB min
) energy management of that day. By doing this, it is ensured
represent the charged capacity of an LAB cell that can be used that the LAB stack size is adequate for all possible scenarios.
for discharge. After a discharge cycle, the battery experiences However, the annual data of MG load profile and power
a charge cycle that might not completely charge the LAB cells generation of the WTG and the PVs are not available in
with amount of discharged energy in the previous discharge previous studies like [21], [24]. Therefore, the MG load
cycle. Therefore, an extra part of LAB cells capacities remain profile and power generation of the WTG and the PVs, which
ref are shown in Figs. 3-5, respectively. They are taken as the
empty which makes the SOCLAB to be below SOC LA before
B input data of the worst case of daily energy management.
the next discharge cycle. Using Eq. (6), a residual number of
LAB cells should be calculated and added to the required
amount of LAB cells for the next discharge cycle to
compensate the shortage of energy from SOC of 75%.
LAB
E Dis ( j )  E Cha
LAB
(j)
res
N LAB (j) (6)
cell
C LAB V LAB  0.55
av

Hence, the overall required amount of LAB cells (

NT ( j ) ) for the jth discharge cycle consists of the
LAB cell

required number of LAB cell for that discharge cycle and its
previous discharge cycles as expressed in Eq. (7) :
N TLAB cell ( j )  N LAB
res
cell
( j  1)  N LAB cell ( j ) (7)
T
The maximum value of N LAB cell
for all discharge cycles is
U
taken as the ultimate required LAB cells ( N LAB cell
) for energy
management of islanded MG using Eq. (8):

N ULAB cell  max

1 j TNDC
N T
LAB cell
(j)  (8)
where, the overall number of discharge cycles TNDC is.
IV. SIMULATION STUDIES
The simulation of energy management and frequency
control of an islanded MG is presented in this section. The FIG. 2 MG UNDER STUDY
ultimate required number of LAB cells are determined
 Before 56437th second, the LAB has gone through 26th
discharge cycles. Figs. 6 and 7 shows that after 56437th second
till 83171st second, the LABESS goes through the 27th
discharge cycle which is a major discharge cycle compared to
previous discharge cycles. Its maximum injected energy is
144.78 kWh which is much more than that of previous
discharge cycles. This discharge cycle determines the required
LA B
number of LAB cells. Using the value of T Dis for this
discharge cycle, which is 26734 seconds, and the
interpolation of data in Table 1, the value of C LAB is 88.8 Ah
av
and the value of V LA B is 11.71 V. The value of N LAB cell (27)
can be calculated using Eq. (9):
144.78(kWh )
FIG. 3 MG LOAD PROFILE N LAB cell (27)   254 (9)
88.8(Ah ) 11.71(V )  0.55
U
The value of N can be calculated using Eq. (8):
LAB cell

N ULAB cell  max

1 j TNDC
N T
LAB cell

( j )  N TLAB cell (27)
(10)
 N LAB cell (26)  N LAB cell (27)
res

 0  254  254

If the rated capacity and the rated voltage of the LAB cell were
U
used instead in Eq. (9), N would be 220 which is less
LAB cell

than the required LAB cells in reality. However, the LAB

FIG. 4 WTG POWER GENERATION stack cannot provide the required energy in reality.
U
It should be noted that N LAB cell can be obtained just using
Eqs. (2)-(8). However, we described the sizing procedure to
show how the sizing process in the previous section works.

FIG. 5 PV POWER GENERATION

B. Energy management and Frequency control of islanded

MG
Fig. 6 shows the DGs power generation. The LAB power
is also shown in Fig. 6. The injected power of the LAB minus
its charged energy is shown in Fig. 7. It can be seen that till
24361st second, the total power generation capacity of DGs FIG. 6 POWER GENERATION OF DGS AND LAB
can supply MG loads that there is no need for the LABESS to
participate in energy management. However, the LABESS
handled the short-term frequency regulation in islanded. After
this moment till 56437th second, during some periods the MG
power consumption is more than DGs generation cpacity. The
LABESS goes through several minor discharge cycles to
provide the shortage of power generation by DGs. Between
52654th second and 56437th second, the total discharged
energy of the LAB minus its charged energy is zero. This
means that the LAB is charged with enough energy which has
been totally discharged in previous discharge cycles.
ref
Therefore, SOCLAB has returned to SOC LAB which means that
T
the value of N LAB cell
for the next discharge cycle is zero.
FIG. 7 INJECTED ENERGY OF LAB MINUS ITS CHARGED ENERGY
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