This document describes the design of a battery charging circuit for a solar photovoltaic (SPV) system. It proposes using an intelligent fuzzy logic based discrete proportional-integral-derivative (FL-DPID) maximum power point tracking (MPPT) algorithm to operate the SPV panel at its maximum power point (MPP) under varying solar irradiance. The output of the FL-DPID MPPT-driven boost converter is used to charge a battery via an optimal proportional-integral-derivative (O-PID) controlled buck converter. The O-PID controller parameters are obtained using genetic algorithm to provide constant voltage and current for effective battery charging. A 200W prototype SPV panel is simulated in MATLAB/Simul

1. Contents lists available at ScienceDirect
Solar Energy
journal homepage: www.elsevier.com/locate/solener
Design of battery charging circuit through intelligent MPPT using SPV
system
Pawan Kumar Pathaka,⁎
, Anil Kumar Yadavb
a
School of Automation, Banasthali Vidyapith, Rajasthan 304022, India
b
Department of Electrical Engineering, National Institute of Technology, Hamirpur, HP 177005, India
A R T I C L E I N F O
Keywords:
Fuzzy logic based DPID (FL-DPID) MPPT
algorithm
Battery charging circuit
Optimal PID (O-PID) controlled buck converter
A B S T R A C T
In a solar photovoltaic (SPV) based hybrid renewable energy system, batteries are used as a power reservoir. SPV
system provides energy under steady operating condition whereas SPV along with batteries serve as the source of
energy under transient operating condition. This paper puts forward the design of a battery charging circuit
through an intelligent fuzzy logic based discrete proportional-integral-derivative (FL-DPID) maximum power
point tracking (MPPT) algorithm. SPV system in conjunction with FL-DPID MPPT technique driven DC-DC boost
converter enhances the output voltage besides tracking maximum power point (MPP) under varying irradiance
in between 400–1000 W/m2
and a constant temperature of 25 °C. The output voltage of the boost converter
drives the optimal PID (O-PID) controlled buck converter to behave as a battery charging circuit under non-
deterministic atmospheric conditions. The objective of this study is to operate the designed SPV system at MPP
under varying environmental condition in order to achieve higher efficacy, minimize overall system cost and
obtain apropos voltage and current for effective charging of battery thereby reducing battery losses and en-
hancing life cycle. A 200 W prototype of an SPV panel has been designed, simulated and investigated in the
MATLAB/Simulink environment.
1. Introduction
Electricity act as a paramount factor in the commercial growth of a
nation. The transition from traditional to the mechanized world has
created a black hole of energy with nearly 1.3 billion sapiens round the
globe not even having regular access to the electricity (World energy
outlook, 2013; Universal access to modern energy for poor). Around 2.7
billion people still rely on long-established bio-energy like wood, crop
residues, animal dung etc. as their prime energy source for cooking and
heating (Ekouevi and Tuntivate, 2012; Weimann et al., 2013). In de-
veloping countries, the marginal population faces adverse effects of
power crunch most significantly on their health and economic growth.
Many such regions have an abundant source of renewable energy such
as solar, wind, and bio-mass. In recent years due to the energy crisis and
environmental concern countries around the world is focusing on green
technology where solar energy has grown as one of the most potent
form of renewable energy. SPV system is used in conjunction with
batteries which act as energy soak pit and are utilized under the tran-
sient condition when the SPV system alone fails to generate the re-
quired power. In remote and rural areas batteries are considered as
most potent and pocket-friendly source for home lightning (Pode, 2015)
whereas it is being widely employed in the battery-powered electric
vehicle (Larminie and Lowry, 2003; Wirasingha and Pihef, 2011) and as
a backup source in the hybrid renewable energy system (Fakham et al.,
2011).
The SPV system is characterized by nonlinear P-V and I-V curves
(Cheng et al., 2015) and it greatly relies on atmospheric conditions
namely solar irradiance and temperature. Change in irradiance and
temperature alter the voltage and current thereby constantly changing
the maximum available power of SPV panel. Hence the conversion ef-
ficacy of the system becomes as low as 7–19% (Haq et al., 2013) and
fabrication cost shoots up. To overcome this setback SPV system is
made to operate at MPP under changing atmospheric conditions
(Agarwal and Patel (2010); Metin et al., 2007; Soto et al., 2006; Graditi
and Adinolfi, 2011; Graditi et al., 2014). To operate SPV panel at MPP
various MPPT techniques have been studied and developed so far such
as perturb and observe (P&O) (Elgendy et al., 2012), incremental
conductance (IC) (Elgendy et al., 2013) and fuzzy logic (FL) based
MPPT (Algazar et al., 2012; EI-Khatib et al., 2017; Chen et al., 2016,
2015; Rezk and Eltamaly, 2015; Al-Majidi et al., 2018). MPPT algo-
rithm utilizes the output of SPV system in terms of voltage and current
to generate PWM gating signal for power switch of the boost converter
https://doi.org/10.1016/j.solener.2018.12.018
Received 15 July 2018; Received in revised form 29 November 2018; Accepted 7 December 2018
⁎
Corresponding author.
E-mail addresses: ppathak999@gmail.com (P.K. Pathak), anilei007@gmail.com (A.K. Yadav).
Solar Energy 178 (2019) 79–89
Available online 12 December 2018
0038-092X/ © 2018 Elsevier Ltd. All rights reserved.
T

2. to modulate its output (Fathabadi, 2016; Singh et al., 2018; Babaei
et al., 2017; Hart, 2011; Adinolfi et al., 2015; Graditi et al., 2010).
Constant voltage and constant currents are the mostly used methods to
charge a battery (Borage et al., 2006; Cho et al., 2013; Chen and Lai,
2012). To render invariable current and voltage to the connected load
PID controlled buck converter is employed as the charging circuit. The
PID controller is widely used in various industrial applications such as
electric vehicles, process control, and power system because of its in-
expensiveness, ease in designing and excellent performance (Yadav and
Gaur, 2016a,b; Ang et al., 2005; Neath et al., 2014). Yilmaz et al.
(2018) proposed FL based SPV system for battery charging circuit under
different atmospheric conditions and analyzed the system response.
Eldahab et al. (2016) develop a novel MPPT technique for SPV based
battery charging controller. The prominent feature of this novel MPPT
technique is remote monitoring and controlling of various system ele-
ments. Mirzaei et al. (2017) designed a control topology for power
management in a standalone hybrid system. Pode (2015) details battery
charging stations which are quite welcomed in lonesome which are yet
not connected to the grid. The implementation of digital control
strategy through DSP has been done by Lopez et al. (2016) for buck
converter charging a battery through solar generated power under
various atmospheric conditions. In Rajani and Pandya et al. (2016)
MPPT based SPV system is utilized for charging battery and ultra-ca-
pacitor individually, and it depicts the enhancement in the charging
rate as compared to non MPPT charging.
The structure of FL-DPID MPPT technique is proposed and im-
plemented for battery charging circuit under varying solar irradiance in
between 400–1000 W/m2
. The proposed MPPT technique has been
designed with a lesser number of rules i.e. nine as compared to existing
literature (Yilmaz et al., 2018). An FL based system with the least
number of rules reduces the computational time and complexity of the
system. The output voltage of FL-DPID MPPT driven boost converter
having least ripple drives the O-PID controlled buck converter to deliver
regulated power to the battery as a load with constant voltage and
constant current irrespective of change in solar irradiance as shown in
Fig. 1. The parameters of the proposed O-PID controller are obtained
utilizing a Genetic Algorithm (GA) with suitable objective function. The
results of O-PID controlled buck converter are compared with Ziegle-
r–Nichols (ZN) tuned PI and PID controllers and named as ZN-PI and
ZN-PID respectively. The expected advantages of O-PID controller over
ZN-PI and ZN-PID controllers are to improve the performances indices
such as rise time (RT), settling time (ST), overshoot (OS), integral of the
absolute error (IAE) and integral of the square of error (ISE) that re-
duces the charging time of the battery thereby enhancing its life. The
key contributions of the paper are summarized as follows: (1) The de-
sign and implementation of intelligent i.e. FL-DPID MPPPT technique
for battery charging circuit under varying solar irradiance i.e.
400–1000 W/m2
and the results are compared with existing P&O and IC
MPPT techniques. (2) A detailed comparative analysis among designed
ZN-PI, ZN-PID and O-PID controllers of buck converter for charging of a
18 V battery. The results are compared with the literature (Yilmaz et al.,
2018). The transient response and ripples in output voltage and current
of the boost converter are considered as the key factors for a compre-
hensive comparison of designed P&O, IC, and FL-DPID MPPT techni-
ques.
The rest of the work is organized as follows. Section 2 deals with
design considerations of one diode model of a crystalline solar cell and
SPV module along with its characteristics under varying atmospheric
condition. In Section 3 the design methodology of P&O, IC, and FL-
DPID MPPT techniques are presented. The design of DC-DC power
converter covers the power conversion system including both DC-DC
boost and buck converter employing control strategies such as ZN-PI,
ZN-PID, and O-PID controllers are discussed in section 4. The obtained
results have been vividly discussed in Section 5 i.e. results and dis-
cussion, and the concluding remarks of this research are presented in
Section 6.
2. Description of SPV system
The output and efficacy of the SPV system completely rely on dif-
ferent array configuration as well as various atmospheric conditions
such as non-uniform solar insolation and varying the environmental
temperature. The P-V and I-V characteristics of an SPV system for a
constant environmental temperature of 25 °C and varying solar insola-
tion have been depicted in Fig. 2(a) and (b), whilst Fig. 3(a) and (b)
represents the P-V and I-V characteristics of an SPV subjected to varying
temperature keeping insolation constant at 1000 W/m2
respectively.
The effect of a change in temperature as seen from Figs. 2 and 3 has
a lesser influence on the characteristic of the SPV system as compared
to the change in solar insolation. Therefore, in this paper, the work is
Optimal
PID
Controller
Battery
Ipv
Vpv
D
Boost Converter
Buck Converter
PWM
Generator 1
FL-DPID MPPT
Vpv
Vdc Vdcb
PWM
Generator 2
D
PV
Array
Ref. Value
Actual
Value
U
u e
+
-
Ipv
Fig. 1. SPV system based battery charging circuit.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
80

3. focused on constant solar temperature i.e. 25 °C and varying solar in-
solation in range of 400–1000 W/m2
for the SPV system based battery
charging circuit.
2.1. Mathematical equation of a solar cell
The simplified electrical circuit of each solar cell can be modeled in
various ways out of which one diode model is considered in the pre-
sented work.
A simplified circuit for the same is represented in the Fig. 4 and the
I–V relation is given below:
= − − −
+
+
{ }
I I I e
V R I
R
1
ph
s
sh
0
q V RsI
AKT
( )
(1)
where Iph denotes photocurrent, Id is the current through diode, I
the sh
denotes shunt current, Rsh denotes shunt resistance, Rs denotes series
connected resistance, I denotes the net output current of SPV, V de-
notes the voltage across SPV, I0 denotes diode reverse saturation cur-
rent, q denotes charge of the electron, A is curve fitting factor andKis
the Boltzmann constant (1.38 × 10−23
J/K).
2.2. Modeling of an SPV module
The last term of (1) can be omitted due to Rsh is assumed to be
infinite and the slope of I-V curve is zero at short circuit condition.
Further replacing Iph by ISC (short-circuit current):
= − −
+
{ }
I I I e 1
SC O
q V RsI
AKT
( )
(2)
In a PV module the appropriate application of (2) +
q V R I
AKT
( )
s
is mod-
ified and substituted by +
q V R I
N AKT
( )
s
s
, where Ns denotes total solar cells
connected back to back in a crystalline type SPV module. Yields (3);
= − −
+
{ }
I I I e 1
SC O
q V RsI
NsAKT
( )
(3)
Under the open-circuit condition of a PV module, =
I 0 and hence
the term q
N AKT
s
in (3) will be written as follows:
=
+
( )
q
N AKT V
ln 1
s
I
I
OC
SC
O
(4)
where VOC denotes module open-circuit voltage. The current can be
obtained from (3) and (4) as:
⎜ ⎟
= ⎧
⎨
⎩
− ⎛
⎝
− ⎞
⎠
⎫
⎬
⎭
⎛
⎝
+ ⎞
⎠
+
I I
I
I
e
1 1
SC
O
SC
I
I
V R I
V
ln 1
( )
SC
O
S
OC
(5)
where =
k I I
/
SC O and after solving (5), obtained (6):
= ⎧
⎨
⎩
− + + ⎫
⎬
⎭
+
I I
k
k
k
1
1
( 1)
1
SC
V RSI
VOC
( )
(6)
(a) (b)
0 5 10 15 20 25 30 34
50
100
150
200
Voltage (V)
Power
(W)
1000 W/m2
800 W/m2
600 W/m2
400 W/m2
0 5 10 15 20 25 30 34
1
2
3
4
5
6
7
8
9
Voltage (V)
Current
(A)
1000 W/m2
800 W/m2
600 W/m2
400 W/m2
Fig. 2. (a) P-V curve and (b) I-V curve on different solar irradiance.
(b)
(a)
0 5 10 15 20 25 30 34
50
100
150
200
Voltage (V)
Power
(W)
25 degC
50 degC
75 degC
0 5 10 15 20 25 30 34
0
2
4
6
8
9
Voltage (V)
Current
(A)
25 degC
50 degC
75 degC
Fig. 3. (a) P-V curve and (b) I-V curve on different temperature.
Rs
Rsh
I
V
Iph
Ish
Id
D
Fig. 4. Equivalent circuit of a solar cell.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
81

4. Usually, kis quite high as ISC is much greater than IO. Few terms in
(6) can be ignored for simplified I–V relation which is represented as
follows:
⎜ ⎟
= ⎛
⎝
− ⎞
⎠
+
−
I I k
1
SC
V R I
V
( )
1
S
OC
(7)
3. Maximum power point tracking (MPPT) techniques
The major setback of a commercial SPV system is less conversion
efficiency. Therefore, to enhance the efficacy of the system MPPT al-
gorithm is employed. The maximum efficiency is expected from an SPV
system when it operates at MPP and as represented in Fig. 5.
3.1. Perturb & observe (P&O)
P&O is based on perturbation in array voltage. From the P-V curve
of an SPV array as shown in Fig. 6 it can be observed that while op-
erating on the left side of MPP increasing/decreasing with increasing/
decreasing the voltage ΔV, whereas it decreases/increases on the right
of MPP. For minimizing the oscillations, the step size of perturbation
can be reduced.
The entire P&O algorithm is depicted as follows:
P&O algorithm:
Step 1: Start
Step 2: Read variables V n
( )andI n
( ).
P&O algorithm:
Step 3: Calculate power: = ∗
P n V n I n
( ) ( ) ( ).
Step 4: Call previous values of P and V from the memory i.e. −
P n
( 1) and −
V n
( 1).
Step 5: Calculate the change in power ‘dP’ and change in voltage‘dV ’ using:
= − −
dV V n V n
( ) ( 1) and = − −
dP P n P n
( ) ( 1).
Step 6: If =
dP 0, Then no change in duty ratio is required and GOTO Step 7.
else If ∗ >
dP dV
( ) 0, Then increase the duty ratio by ΔD and GOTO Step 7.
else decrease the duty ratio by ΔD and GOTO Step 7.
Step 7: Return.
3.2. Incremental conductance (IC)
The P&O technique fails under rapidly changing environmental
conditions; this can be overcome by using the IC technique. The slope of
the P-V curve of an SPV array is the basis of the IC algorithm. The
derivative of the output power of the SPV array is written as follows:
= = + = +
dP
dV
d IV
dV
I V
dI
dV
I V
I
V
( ) Δ
Δ (8)
The entire IC algorithm is depicted as follows:
IC algorithm:
Step 1: Start
Step 2: Read variables V n
( ) andI n
( ).
Step 3: Call previous values of I and V from the memory i.e. −
I n
( 1) and −
V n
( 1).
Step 4: Calculate the change in current‘dI’ and change in voltage‘dV ’ using:
= − −
dV V n V n
( ) ( 1) and = − −
dI I n I n
( ) ( 1).
Step 5: If =
dV 0, Then GOTO Step 6.
else GOTO Step 7.
Step 6: If =
dI 0, Then GOTO Step 8
else If >
dI 0, Then increase duty ratio by ΔD and GOTO Step 8.
else decrease the duty ratio by ΔD and GOTO Step 8.
Step 7: If + < ε
dI
dV
I
V
, Then GOTO Step 8.
else If > −
dI
dV
I
V
, Then increase duty ratio by ΔD and GOTO Step 8.
else decrease the duty ratio by ΔD and GOTO Step 8.
Step 8: Update V n
( ) andI n
( ).
Step 9: Return.
3.3. FL-DPID MPPT technique
The proposed FL-DPID is a powerful MPPT algorithm to operate at
MPP for SPV system. The advantages of FL-DPID MPPT over P&O and
IC MPPTs are a minimum ripples in the output, the capability to handle
nonlinearity, work with inexplicit inputs, and non-requirement of the
exact mathematical model whereas when compared to FL based MPPT
it reduces implementation and computation complexity. The flowchart
and proposed structure of FL-DPID MPPT technique are depicted in
Fig. 7(a) and (b) respectively. The symbols K K K
, ,
e ce p and Ki are the
scaling factors of FL-DPID MPPT controller and are obtained based on
intuition through ZN tuning method (Yadav and Gaur, 2016b).
The error E and change in error CE acts as the input variables of FL-
DPID MPPT and are computed using the output power and voltage of
SPV system as represented by (9) and (10).
= =
− −
− −
E n
P
V
P n P n
V n V n
( )
Δ
Δ
( ) ( 1)
( ) ( 1) (9)
= − −
CE n E n E n
( ) ( ) ( 1) (10)
The output variable of the FL system is UPD and the accumulated
output of FL-DPID MPPT is UPID as shown in Fig. 7(b). The UPID i.e. U is
acts as a reference and provided as an input to PWM genrator−1 that
modifies the duty cycle D as shown in Fig. 1. From Fig. 7(b), the control
law of FL-DPID MPPT i.e. UPID is written as follows:
= +
− −
U K U K
Z
U
· ·
1
1
·
PID p PD i PD
1 (11)
The relation between input variable E and output variable UPD of
product-sum crisp type fuzzy is approximated and described as follows
(Yadav and Gaur, 2016a,b):
PMPP
Power
Maximum Power Point
(MPP)
Current
ISC
IMP
Current
(A)
0
0 Voltage (V) VMPP VOC
Fig. 5. P-V and I-V curve for MPP.
Fig. 6. P-V curve of an SPV array.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
82

5. = + − −
U K E K Z E
· ·(1 )·
PD e ce
1
(12)
From (11) and (12)
= + − +
−
+ −
−
−
−
U K K E K Z E
K
Z
K E K Z E
[ · ·(1 )· ]
1
[ · ·(1 )· ]
PID p e ce
i
e ce
1
1
1
(13)
After solving (13), yields (14)
⏟ ⏟ ⏟
= + + ×
−
+ × −
−
−
U K K K K E K K
Z
E K K Z E
( )· ( )·
1
1
· ( )·(1 )·
PID p e ce i
Proportionalgain
e i
Integralgain
p ce
Derivativegain
1
1
(14)
The final control law (14) represents the generalized equation of
three term PID controller in the discrete domain. Therefore, the pro-
posed structure of FL based MPPT is named as FL-DPID MPPT tech-
nique. The membership functions (MFs) forE and CE, and UPD are
shown in Fig. 8(a), and (b) respectively. The linguistic names of these
MFs are as follows: NB (Negative Big), N (Negative), Z (Zero), P (Po-
sitive) and PB (Positive Big).
Start
Measure V (n)
and I (n)
Calculate
P (n) = V (n)*I (n),
dP and dV
Initialize duty
cycle (D)
Calculate
Error (E) & Change in
error (CE)
Defuzzification
Inference
Fuzzification
Rule base
Update D
Fuzzy set
(a)
Ke
Kce
+
-
Z-1 Z-1
E
+
UPID
Fuzzy Logic
UPD
+
Kp
Ki
+
+
(b)
Fig. 7. (a) Flowchart and (b) Proposed structure of FL-DPID MPPT technique.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
83

6. The E and CE after being calculated and transmuted to the semantic
variables depending on the MFs generates the output of FL-DPID con-
troller in terms of UPID which in turn alter the duty cycle ΔD of the boost
converter. The ΔD is deducted from previous value of D and the new
value acts as the gating signal that controls the boost converter to track
the MPP of the SPV system. The crisp output UPD can be obtained from
the rule base matrix as given in Table 1.
The 9 rules of Table 1 can be expressed as follows: Rule 6: ‘IF E is N
and CE is Z THEN UPD is N’. Similarly, the other rules are described and
used for evaluation of final output of FL-DPID controller (14) and ap-
propriate ΔD is obtained.
4. Design of DC-DC power converters
For maximized power output SPV is made to operate at MPP. To
trace the MPP of SPV the power converter is operated with the corre-
sponding D. With the change in solar insolation the D must vary ac-
cordingly in order to track MPP. Various configuration of the DC-DC
converter studied so far out of which boost converter is widely chosen
and considered in the presented work due to less complexity and higher
reliability as shown in Fig. 1.
4.1. DC-DC boost converter
Metal-oxide-semiconductor field-effect transistor (MOSFET) is em-
ployed as a switching device for the operation of the boost converter.
During time period < <
t DT
0 , MOSFET turns on and diode enters into
reverse biased condition. During this time interval inductor L gets
charged with the voltage =
V V
L in. During time period < <
Dt t T, the
MOSFET goes into off state and the diode is in on state due to forward
biased. In this condition the output voltage = = +
V V V V
out dc in L. In steady
state condition the total energy stored by, L must be equal to the energy
released by L in a period of switching. The values of boost converter
parameters L and C are calculated using formulas as follows: (Hart,
2011)
= =
−
V V
V
D
(1 )
out dc
in
(15)
= −
I D I
(1 )
out in (16)
=
∗
∗
L
V D
f I
Δ
in
s (17)
=
∗
∗
C
I D
f V
Δ
out
s (18)
where C is caapacitor, Iout is the current output of boost converter, I
Δ
denotes ripple in inductor current, V
Δ denotes ripple in output voltage,
fs denotes switching frequency of the power device and Iin is the input
current of boost converter.
4.2. DC-DC buck converter
Buck converter has the property of generating an output voltage
which is lower in magnitude than the input supply. During < <
t DT
0 ,
the MOSFET turns on whereas diode is in off state and charging in-
ductor with a voltage = −
V V V
L dc dcb. MOSFET turns off during
< <
DT t T, diode comes in conduction with voltage developed across
the inductor changing to = −
V V
L dcb. To render invariable current and
voltage for charging a battery ZN-PI, ZN-PID and O-PID controllers are
designed to generate a controlled reference signal u for PWM generator-
2 that gives the updated D to the buck converter as shown in Fig. 1. The
parameters of DC-DC buck converter L and C are calculated using
formulas as given follows: (Hart, 2011)
= ∗
V D V
dcb dc (19)
-0.1 -0.05 0 0.05
N Z P
0
0.5
1
0.1
(a)
0 1
6
6
.
0
-
3
3
.
0
-
1
- 0.33 0.66
NB N Z P PB
0
0.5
1
(b)
Fig. 8. MFs for (a) E and CE, and (b)UPD
Table 1
Rule base matrix.
E
CE
P Z N
P PB (1) P (4) Z (7)
Z P (2) Z (5) N (8)
N Z (3) N (6) NB (9)
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
84

7. =
∗ −
∗
L
V D
f I
(1 )
Δ
dcb
s b (20)
=
∗ −
∗ ∗ ∗
C
V D
L f V
(1 )
8 Δ
dcb
s dcb (21)
where Vdcb is the output voltage generated by the buck converter, Vdc
denotes input dc supply voltage of the buck converter, I
Δ b denotes
ripple in inductor current and V
Δ dcb is the ripple in output voltage.
4.3. Control strategy
In this section, the design methodology of classical ZN-PI and ZN-
PID controllers, and proposed O-PID controller for voltage regulation
using buck converter is presented. The differential equation of a gen-
eralized PID controller is usually represented in ‘parallel form’ or ‘ideal
form’ stated by (22) or (23) respectively.
∫
= + +
u t K e t K e t dt K e t
( ) ( ) ( ) ̇( )
P I D (22)
∫
= ⎡
⎣
⎢
+ + ⎤
⎦
⎥
u t K e t
T
e t dt T e t
( ) ( )
1
( ) ̇( )
P
I
D
(23)
where K K K
, and
P I D denotes proportional, integral and derivative gains
respectively, TI and TD denotes integral and derivative time constants
respectively, and u and e are output and input i.e. error signal of the
controller respectively. The performance parameters of the PID con-
troller are quantified using ZN tuning method (Yadav and Gaur,
2016b); using relations as given below:
For PI control:
= = =
K K T T K K T
0.75 , /1.2, /
P u I u I P I (24)
For PID control:
= = = = =
K K T T T T K K T K K T
0.6 , /2, /8, / and ·
P u I u D u I P I D P D (25)
where Ku and Tu are the ultimate gain and period of the system re-
spectively. Sometimes, the ZN tuned PI and PID controllers give un-
desirable performance in terms of OS, RT, ST, IAE and ISE (Yadav and
Gaur, 2016a; Neath et al., 2014). Therefore, the O-PID controller is
proposed in this paper.
In O-PID controller, the KP, KI, and KD are obtained using GA for
which the objective function j is formulated using IAE and ISE, and
given as follows:
∫ ∫
= +
∞ ∞
j w e t dt w e t dt
· | ( )| · ( )
1
0
2
0
2
(26)
where w1 and w2 are weights to ∫
=
∞
IAE e t dt
| ( )|
0
and
∫
=
∞
ISE e t dt
( )
0
2 respectively, and equal weights for both IAE and ISE
are considered in this paper. The objective is to find out the optimal
values of KP, KI and KD which gives excellent performance in terms of
OS, RT, ST, IAE and ISE. The initial generation of GA is arbitrary;
therefore the PID controller parameters at the preliminary stage could
introduce instability in the system. Hence the lower and upper limit of
the controller parameters is chosen such that the system retains stability
in this limit. The preliminary values of PID controller parameters are
taken from ZN-PID controller that is given in Table 4.
5. Results and discussion
The entire system represented schematically in Fig. 1 has been
formulated and simulated using MATLAB/Simulink software. The nu-
merical values used in the simulation are given in Table 2. The designed
system consists of an SPV array for a peak power of 200 W, a DC-DC
boost converter and a DC-DC buck converter acting as a charge con-
troller for charging a 18 V battery and operating at a fs of 150 kHz. To
operate the SPV system at MPP three distinct MPPT techniques are
employed and a thorough comparative transient analysis of the dy-
namic response of SPV system in terms of the output power of SPV
corresponding to MPP and voltage and current of the boost converter
under rapidly varying solar irradiation has been done.
5.1. Comparative analysis of P&O, IC, and FL-DPID MPPT techniques
under varying solar irradiance
The profile of solar radiation taken into account for the study has
been illustrated in Fig. 9 i.e. varying in between 400–1000 W/m2
(Liu,
et al., 2008). The change in solar irradiance for carrying out the de-
tailed analysis has been considered as trapezoidal in nature divided into
five states as 600 W/m2
at 25 °C, 800 W/m2
at 25 °C, 1000 W/m2
at
25 °C, 800 W/m2
at 25 °C, and 400 W/m2
at 25 °C. According to the
considered solar irradiance profile state 2 and state 4 have been taken
at same irradiance level, thus only state 2 has been considered for the
analysis. The output parameters of boost converter i.e. voltage and
current and maximum obtainable SPV power implementing P&O, IC,
and FL-DPID MPPTs have been depicted in Fig. 10(a)–(c) respectively.
The values of scaling factors K K K
, ,
e ce p and Ki of FL-DPID MPPT
technique are 0.095, 0.007, 0.7 and 0.3 respectively. The output vol-
tage corresponding to MPP of SPV system incorporating FL-DPID MPPT
algorithm along with the voltage after being boosted by the DC-DC
boost converter has been represented in Fig. 11. A vivid comparison of
all the three MPPT techniques in terms of efficiency, dynamic perfor-
mance like ST and the effect of ripples on the performance of boost
converter are summarized in Table 3.
From the obtained results as shown in Fig. 10(a)–(c) and the cal-
culated values as given in Table 3 it can be noted that with the rapid
variation in the solar insolation the designed SPV system is efficiently
able to trace the MPP in all the considered states. It can be spotted from
Fig. 10(c) that under steady state condition P&O technique gives higher
ripple caused due to oscillation around MPP which is substantially re-
duced in IC technique and almost negligible in FL-DPID MPPT algo-
rithm. Higher ripple in the P&O algorithm reduces the average power
output and thereby reduces the efficacy of the SPV system. The max-
imum obtained efficacy under all the considered states of solar insola-
tion is 97.00% for P&O, 98.60% for IC and 99.80% for FL-DPID MPPT
technique.
In terms of dynamic response, FL-DPID MPPT strategy shows better
performance in comparison to P&O and IC techniques. From the
Fig. 10(c) it can be observed that FL-DPID MPPT technique gives least
ST of 20 ms for power whereas in P&O and IC have 110 ms and 340 ms
respectively. Considerable ripple in power leads to high ripple in the
output of the boost converter whose duty cycle ‘D’ in turn is decided by
the implemented MPPT technique. The ripple content in the output
voltage, as well as the current of the boost converter, is highest for P&O
as shown in Fig. 10(a) and (b) with response remaining unsettled for the
entire simulation time and FL-DPID MPPT technique has almost negli-
gible ripple with ST of 23 ms for voltage as well as current. From the
comparative analysis, FL-DPID MPPT algorithm surpasses P&O and IC
algorithms in respect of steady state as well as dynamic response i.e.
Table 2
Numerical values for simulation.
System Symbols Values
SPV VOC/module 10.908 V
ISC/module 8.21 A
Cells in a module 18
Ns 3
NP 1
A 1.36
Boost fs 150 kHz
L 0.1075 mH
C 10.41 µF
Buck fs 150 kHz
L 0.1613 mH
C 1.744 µF
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
85

8. Time (sec.)
Irradiance
(W/m2)
0.0 0.4 0.9 1.4 1.9
600
800
1000
State 1 State 2 State 3 State 4
0.5 1 1.5 2 2.4
State 5
400
800
Fig. 9. Profile of solar irradiance.
(a)
(b)
(c)
0 0.5 1 1.5 2 2.4
0
10
20
30
40
47
Time (sec.)
Voltage
(V)
1.05 1.051 1.052 1.053
24
35
P&O
IC
FL-DPID
0 0.5 1 1.5 2 2.4
0
1
2
3
4
5
6
7
Current
(A)
P&O
IC
FL-DPID
1.05 1.051 1.052 1.053
3.6
4.3
Time (sec.)
0 0.5 1 1.5 2 2.4
0
50
100
150
200
Time (sec.)
Power
(W)
1.05 1.07 1.09 1.1
190
202
1.05 1.07 1.09 1.1
190
202
1.06 1.08 1.1
198
200
P&O
IC
FL-DPID
Fig. 10. (a) Output voltage, (b) Output current of boost converter and (c) Maximum power using P&O, IC and FL-DPID MPPT techniques.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
86

9. efficiently tracking MPP under varying irradiance with least ST and
bearing least ripple in output voltage and current of the boost con-
verter. The output voltage of the boost converter as seen in Fig. 11, is
varying in accordance with solar insolation that is undesirable for
battery charging application. Thus, O-PID controlled buck converter is
proposed in this paper.
5.2. Response of ZN-PI, ZN-PID, and O-PID controlled buck converter
under varying solar irradiance
The parameters of ZN-PI, ZN-PID and O-PID controllers of buck
converter are given in Table 4. The parameters of ZN-PI and ZN-PID
controllers are calculated using (24) and (25) respectively, whereas the
parameters of the O-PID controller is obtained using (26) after 65
generations of GA. The response of output voltage, current, and power
of ZN-PI, ZN-PID, and O-PID controlled buck converter under all four
discussed states are shown in Figs. 12, 13 and 14 respectively. In
Fig. 12, SV is set value i.e. 18 V. A comprehensive steady-state analysis
of ZN-PI, ZN-PID, and O-PID controlled buck converter under four
different states of solar insolation incorporating FL-DPID MPPT algo-
rithm for 200 W SPV system has been summarized in Table 5.
The output voltage and current of buck converter as depicted from
Figs. 12 and 13, and Table 5 are maintained constant irrespective of the
varying solar insolation thereby providing constant voltage and con-
stant current to the load i.e. 18 V battery. The transient analysis of the
obtained responses infers that the ST of voltage, current, and power of
ZN-PI controlled buck converter is 25 ms, 24 ms, and 22 ms respectively
whereas the same for ZN-PID controlled buck converter is 23 ms, 22 ms,
and 19 ms respectively, and for O-PID is 1.6 ms, 1.5 ms, and 1.6 ms
respectively. The transient analysis thereby concludes that O-PID con-
trolled buck converter shows better performance as compared to ZN-PI
and ZN-PID controlled buck converter under dynamic condition. The
performance indices of ZN-PI, ZN-PID and O-PID controllers for the
voltage of buck converter are shown in Table 6. The plot of IAE and ISE
for ZN-PI, ZN-PID, and O-PID tuned buck converter for voltage is shown
in Fig. 15.
From the values of Table 6 and Fig. 15, it is concluded that the ZN-PI
and ZN-PID controllers give almost similar performance whereas O-PID
controller gives significant improvement in terms of RT, ST, IAE, and
ISE i.e. 93.00%, 93.04%, 68.98%, and 90.49% respectively as compared
to ZN-PID controller. Therefore, the proposed O-PID controller is su-
perior among all three designed controllers for charging of a 18 V
battery.
6. Conclusion
In this paper, a 200 W SPV system has been designed and its
0 0.5 1 1.5 2 2.4
0
10
20
30
40
Time (sec.)
Voltage
(V)
Output voltage of SPV
Output voltage of FL-DPID based Boost Converter
Fig. 11. Output voltage of SPV system and boosted output voltage using FL-
DPID MPPT algorithm.
Table 3
Comparative performance analysis using P&O, IC and FL-DPID MPPT techni-
ques.
Parameter States P&O IC FL-DPID
Efficiency State 1 93.05% 93.40% 93.96%
State 2 95.18% 97.45% 96.30%
State 3 97.00% 98.60% 99.80%
State 5 96.70% 98.30% 82.43%
Settling Time Power 0.11 sec 0.34 sec 0.02 sec
Voltage Not settled 0.35 sec 0.023 sec
Current Not settled 0.35 sec 0.023 sec
Ripple in Voltage
(output of
boost
converter)
State 1 High Less Negligible
State 2 High Less Negligible
State 3 High Less Negligible
State 5 High Less Negligible
Average Voltage
(Desired value
31 V)
State 2 i.e.
(800 W/
m2
)
26.00 V 24.05 V 31 V
Range of voltage
variation (V)
– 10.80–41.20 23.30–24.80 constant
31 V
Ripple in Current
(output of
boost
converter)
State 1 High Less Negligible
State 2 High Less Negligible
State 3 High Less Negligible
State 5 High Less Negligible
Average current
(Desired value
3.19A)
State 2 i.e.
(800 W/
m2
)
4.1A 3.785A 3.19A
Range of current
variation (A)
1.7–6.5 3.66–3.91 constant
3.19
Control Strategy Sampling
Method
Sampling
Method
Intelligent
Control
Table 4
Parameters of ZN-PI, ZN-PID and O-PID controllers.
Controller KP KI KD KuandTu
ZN-PI 0.01875 225 – = = × −
K T
0.025& 0.1 10
u u
3
ZN-PID 0.015 300 × −
1.875 10 7
O-PID 0.3157 293.6741 0.40723
0 0.5 1 1.5 2 2.4
0
5
10
15
20
Time (sec.)
Voltage
(V)
SV
ZN-PI
ZN-PID
O-PID
0 0.01 0.02 0.03 0.04
0
10
20
Fig. 12. Output voltage of buck converter.
0 0.5 1 1.5 2 2.4
0
2
4
6
8
Time (sec.)
Current
(A)
ZN-PI
ZN-PID
O-PID
0 0.01 0.02 0.03 0.04
0
5
9
Fig. 13. Output current of buck converter.
0 0.5 1 1.5 2 2.4
0
50
100
150
Time (sec.)
Power
(W)
0 0.01 0.02 0.03 0.04
90
120
150
ZN-PI
ZN-PID
O-PID
Fig. 14. Output power of buck converter.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
87

10. performances under four varying states of solar insolation have been
observed. To operate the SPV system at MPP a novel FL-DPID MPPT
technique with a lesser number of rules has been implemented and
compared with the existing P&O and IC techniques for the battery
charging circuit. In comparison with P&O and IC techniques, the ob-
tained results depict that FL-DPID MPPT technique has higher max-
imum efficiency, effective tracking speed and no deviation from the
MPP under varying atmospheric conditions. Therefore, the FL-DPID
MPPT technique gives an excellent performance as compared to P&O
and IC techniques in terms of the output voltage and current of the
boost converter, which is the main area of concern. In divergence with
the existing literature which employs PI controller for charging a bat-
tery, in this paper a comparative analysis of ZN-PI, ZN-PID and O-PID
controlled buck converter as a battery charging circuit has been done.
The proposed O-PID controller gives excellent performance in terms of
RT, ST, IAE and ISE with the improvement of 93.00%, 93.04%, 68.98%,
and 90.49% respectively as compared to ZN-PID controller. Hence the
O-PID controller is superior among all designed controllers for charging
of a 18 V battery. Thus it can be concluded that FL-DPID MPPT based
SPV system used for charging a battery through O-PID control as charge
controller is highly efficient for fast and effective battery charging
thereby reducing losses and enhancing the battery life cycle. The future
scope of the research work will predominately focus on the perfor-
mance of O-PID controlled charge controller for charging a battery fed
through a partially shaded SPV system. If there is a relevant aid to the
research material, the designed system can be practically realized and
implemented.
References
Adinolfi, G., Graditi, G., Siano, P., Piccolo, A., 2015. Multi-Objective optimal design of
photovoltaic synchronous boost converters assessing efficiency, reliability and cost
savings. IEEE Trans. Ind. Info. 11 (5), 1038–1048.
Agarwal, V., Patel, H., 2010. MATLAB-based modeling to study the effects of partial
shading on PV array characteristics. IEEE Trans. Energy Convers. 23, 302–310.
Al-Majidi, S.D., Abbod, M.F., Al-Raweshidy, H.S., 2018. A novel maximum power point
tracking technique based on fuzzy logic for photovoltaic systems. Int. J. Hydro.
Energy 43, 14158–14171.
Algazar, M.M., AL-monier, H., EL-halim, H.A., Salem, M.E., EI, K., 2012. Maximum power
point tracking using fuzzy logic control. Elec. Pow. Energy Syst. 39, 21–28.
Ang, K.H., Chong, G., Li, Y., 2005. PID control system analysis, design, and technology.
IEEE Transactions on Control Systems Technology. 13 (4), 559–576.
Babaei, E., Abbasnezhad, A., Sabahi, M., Hosseini, S.H., 2017. Analysis and design of a
soft switching boost DC/DC converter. IET J. Pow. Elec. 10, 1353–1362.
Borage, M., Tiwari, S., Kotaiah, S., 2006. Constant-current, constant-voltage half-bridge
resonant power supply for capacitor charging. Inst. Eng. Tech. 153, 343–347.
Chen, Y.-T., Jhang, Y.-C., Liang, R.-H., 2016. A fuzzy-logic based auto-scaling variable
step-size MPPT method for PV systems. Sol. Energy. 126, 53–63.
Chen, P.-C., Chen, P.-Y., Liu, Y.-H., Chen, J.-H., Luo, Y.-F., 2015. A comparative study on
maximum power point tracking techniques for photovoltaic generation systems op-
erating under fast changing environments. Sol. Energy. 119, 261–276.
Chen, B.-Y., Lai, Y.-S., 2012. New digital controlled technique for battery charger with
constant current and voltage control without current feedback. IEEE Trans. Ind. Elec.
59, 1545–1553.
Cheng, P.-C., Peng, B.-C., Liu, Y.-H., Cheng, Y.-S., Huang, J.-W., 2015. Optimization of a
fuzzy logic control based MPPT algorithm using the particle swarm optimization
technique. Energies. 5339–5345.
Cho, S.-Y., Lee, Q., Moon, S.C., Moon, G.-W., Kim, B.-C., Young, K.K., 2013. Constant
current charging in series-series compensated non-radiative wireless power link. IEEE
2792–2795.
EI-Khatib, M.F., Shaaban, S., Mohamed, A.E., 2017. A proposed advanced maximum
power point tracking control for a photovoltaic-solar pump system. Sol Energy. 158,
321–331.
Ekouevi, K., Tuntivate, V., 2012. Household energy access for cooking and heating.
Lesson learned and the way forward, The world bank report, pp. 70276.
Eldahab, Y.A., Saad, N.H., Zekry, A., 2016. Enhancing the design of battery charging
controllers for photovoltaic systems. Renew. Sustain. Energy Rev. 58, 646–655.
Elgendy, M.A., Zahawi, B., Atkinson, D.J., 2012. Assessment of perturb and observe MPPT
algorithm implementation techniques for PV pumping application. IEEE Trans.
Sustainable Energy. 3, 21–33.
Elgendy, M.A., Zahawi, B., Atkinson, D.J., 2013. Assessment of the incremental con-
ductance maximum power point tracking algorithm. IEEE Trans. Sustain. Energy. 4,
108–117.
Fakham, H., Lu, Di, Francois, B., 2011. Power control design of a battery charger in a
hybrid active PV generator for load-following applications. IEEE Trans. on Ind. Ele.
58 (1), 85–94.
Fathabadi, H., 2016. Novel high-efficiency DC/DC boost converter for using in PV sys-
tems. Sol. Energy. 125, 22–31.
Graditi, G., Colonnese, D., Femia, N., 2010. Efficiency and reliability comparison of DC-
DC converters for single phase grid connected photovoltaic inverters. SPEEDAM
140–147.
Graditi, G., Adinolfi, G., 2011. Comparative analysis of synchronous rectification boost
and diode rectification boost converter for DMPPT applications. ISIE 1000–1005.
Graditi, G., Adinolfi, G., Tina, G.M., 2014. Photovoltaic optimizer boost converters:
temperature influence and electro-thermal design. App. Energy 115, 140–150.
Hart, D.W., 2011. Power electronics. McGraw Hill Edu.
Haq, S.S., Wilson, S.S.B., Zameer, M.G., 2013. Design and simulation of MPPT algorithm
of photovoltaic system using intelligent controller. Int J Adv Sci Tech Res. 3,
2249–2254.
Larminie, J., Lowry, J., 2003. Electric vehicle technology explained. Wiley, Newyork.
Liu, F., Duan, S., Liu, F., Liu, B., Kang, Y., 2008. A variable step size INC MPPT method for
PV system. IEEE Trans. Ind. Elec. 81 (7), 2622–2628.
Lopez, J., Seleme Jr, S.I., Donoso, P.F., Cortizo, P.C., Severo, M.A., 2016. Digital control
strategy for a buck converter operating as a battery charger for stand-alone photo-
voltaic systems. Sol. Energy 140, 171–187.
Metin, C., Boztepe, M., Karatepe, E., 2007. Development of a suitable model for char-
acterizing photovoltaic arrays with shaded solar cells. Sol. Energy. 81, 977–992.
Mirzaei, A., Forooghi, M., Ghadimi, A.A., Abolmasoumi, A.H., Riahi, M.R., 2017. Design
and construction of a charge controller for stand-alone PV/battery hybrid system by
using a new control strategy and power management. Sol. Energy 149, 132–144.
Neath, M.J., Swain, A.K., Madawalaand, U.K., Thrimawithana, D.J., 2014. An optimal PID
controller for a bidirectional inductive power transfer system using multiobjective
genetic algorithm. IEEE Trans. Pow. Elec. 29 (3), 1523–1531.
Pode, R., 2015. Battery charging stations for home lighting in mekon region countries.
Renew. Sustain. Energy Rev. 44, 543–560.
Table 5
Steady state analysis of ZN-PI, ZN-PID and O-PID controlled buck converter.
States ZN-PI ZN-PID O-PID
Ibuck(A) Vbuck(V) Ibuck(A) Vbuck(V) Ibuck(A) Vbuck (V)
State 1: (600 W/m2
and 25 °C) 7.57 18.01 7.567 18.02 7.56 18.03
State 2: (800 W/m2
and 25 °C) 7.585 17.93 7.57 18.01 7.56 18.03
State 3: (1000 W/m2
and 25 °C) 7.58 17.97 7.584 17.98 7.563 18.028
State 5: (400 W/m2
and 25 °C) 7.565 18.02 7.57 18.01 7.564 18.02
Table 6
Performance index of ZN-PI, ZN-PID and O-PID controllers.
Controller Performance Parameters
OS (%) RT(ms) ST (ms) IAE ISE
ZN-PI ≈ 0 22 25 0.3763 1weZ
ZN-PID ≈ 0 20 23 0.3585 1.187
O-PID 0.53 1.4 1.6 0.1112 0.1128
Improvement (%) – 93.00% 93.04% 68.98% 90.49%
Fig.15. Plot of IAE and ISE.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
88

11. Rajani, S.V., Pandya, V.J., 2016. Experimental verification of the rate of charge im-
provement using photovoltaic MPPT hardware for the battery and ultracapacitor
storage devices. Sol. Energy 139, 142–148.
Rezk, H., Eltamaly, A.M., 2015. A comprehensive comparision of different MPPT tech-
niques for photovoltaic systems. Sol. Energy. 112, 1–11.
Singh, A.K., Hussain, I., Singh, B., 2018. Double- stage three-phase grid-integrated solar
PV system with fast zero attracting normalized least mean fourth based adaptive
control. IEEE Trns. Indst. Elec. 65, 3921–3931.
De Soto, W., Klein, S.A., Beckman, W.A., 2006. Improvement and validation of a model
for photovoltaic array performance. Solar Energy 80, 78–88.
Universal access to modern energy for poor. http://www.undp.org/content/undp/en/
home/outwork/environmentandenergy/focus_areas/sustainable-energy/universal-
access.html.
Weimann, M., Cantos Gomez, E.M., MiroBaz, L.-C., 2013. Best practices of the alliance for
rural electrification, Third ed. Alliance for rural electrification. http://www.
ruralelec.org.
Wirasingha, S.G., Pihef, A.E., 2011. Plug in hybrid electric factor. IEEE Trans Veh
Technol. 60, 1279–1284.
World energy outlook 2013. International Energy Agency (IEA), Paris, 2013.
Yadav, A.K., Gaur, P., 2016a. Improved self-tuning fuzzy proportional–integral derivative
versus fuzzy-adaptive proportional–integral–derivative for speed control of nonlinear
hybrid electric vehicles. J. Comput. Nonlinear Dynamics 11 (6), 061013–61017.
Yadav, A.K., Gaur, P., 2016b. An optimized and improved STF-PID speed control of
throttle controlled HEV. The Arabian Journal for Science and Engineering. 41 (9),
3749–3760.
Yilmaz, U., Kircay, A., Borekci, S., 2018. PV system fuzzy logic MPPT method and PI
control as a charge controller. Renew. Sustain. Energy Rev. 81, 994–1001.
P.K. Pathak, A.K. Yadav Solar Energy 178 (2019) 79–89
89