Regulation of PV Panel Voltage using PI-P&O Control Algorithm Master of Technology

Regulation of PV Panel Voltage  using PI-P&O Control Algorithm Master of Technology
Regulation of PV Panel Voltage
using PI-P&O Control Algorithm
A thesis submitted in partial fulfilment of the requirements for the degree of
Master of Technology
in
Electrical Engineering
(Specialization:Control & Automation)
by
Atanu Banerjee
Department of Electrical Engineering
National Institute of Technology, Rourkela
May, 2014
Regulation of PV Panel Voltage
using PI-P&O Control Algorithm
A thesis submitted in partial fulfilment of the requirements for the degree of
Master of Technology
in
Electrical Engineering
(Specialization:Control & Automation)
by
Atanu Banerjee
under the guidance of
Prof. Susovon Samanta
Department of Electrical Engineering
National Institute of Technology, Rourkela
May, 2014
Department of Electrical Engineering
National Institute of Technology, Rourkela
CERTIFICATE
This is to certify that the project entitled, ““Regulation of PV Panel Voltage using PI
PI-P&O
Control Algorithm”” submitted by Atanu Banerjee in “Control & Automation”
Automation specialization is
an authentic work carried out by him under my supervision and guidance for the partial
fulfilment of the requirements for the award of Master of Technology in Electrical
Engineering during the academic session 2013-14 at National Institute of Technology,
Technology
Rourkela. The candidate has fulfilled all the prescribed requirements. The Thesis which is based
on candidate’s own work, has not been submitted
submitted elsewhere for any degree.
degree In my opinion, the
thesis is of standard requirement for the award of a Master of Technology
echnology in Electrical
Engineering.
Date:
Place:
Dr.. Susovon Samanta
Dept. of Electrical Engineering
ACKNOWLEDGEMENT
Firstly, I am grateful to the Department of Electrical Engineering, for giving me the
opportunity to carry out this project, which is an integral fragment of thecurriculum in M. Tech
programme at the National Institute of Technology, Rourkela.
I would like to express my heartfelt gratitude and regards to my project guide, Prof. Susovon
Samanta, for being the corner stone of my project. It was his incessant motivation and guidance
during periods of doubts and uncertainties that has helped me to carry on with this project. I
would also like to thank Prof. A.K Panda, Head of the Department, Electrical Engineering, for
his guidance and support.
I would also like to acknowledge the effort given by my friend and colleague Murlidhar
Killi. I would also like to thank a lot of other friendsfor giving a patient eartomyproblems.I am
also obliged to the staff of ElectricalEngineering for aiding me during the course of our project.
Finally, I would like to take the opportunity to thank my parents and my brother for their
constant support and encouragement during my entire Post Graduate programme.
Atanu Banerjee
212EE3223
Dedicated to my Family
ABSTRACT
The growing demand for the renewable energy resources, especially the solar energy, has drawn
the interest of the researchers. The need for extraction of maximum energy has called for
innovation of newer techniques so that the PV panel can be efficiently operated at its peak power
under partial shading and dynamic atmospheric conditions.
In this thesis, we have discussed the regulation of the output voltage of the PV array. We
have observed the characteristics of the PV Panel under different temperatures and solar
irradiations. Perturb and Observe Maximum power point tracking algorithm has been employed
to operate the panel voltage at its MPP. Firstly, the panel peak voltage is obtained directly by
varying the duty cycle of the converter. The direct duty Ratio control technique causes stress on
the switch of the DC-DC converter besides loss of a significant amount of power. Therefore a PI
controller has been implemented to regulate the panel voltage. A study using both DC-DC buck
and boost converter as an interface between the PV Panel and the load has been presented. The
PI controller prevents oscillation around the MPP apart from improving the steady state response
and the settling time. A detailed analysis of the modeling of the PV array and DC-DC converters
has been produced which helps in designing an efficient PI controller.
.
CONTENTS
List of Figures
List of Tables
Chapter 1 Introduction
1.1 Literature Review
1.2 Thesis Objective
1.3 Thesis Layout
Chapter 2 Analysis and Modeling of a PV based system
2.1 Introduction
2.2 PV Module Modeling
2.3 State Space Modeling Of Boost Converter
2.3.1 With Resistive Load
2.3.2 WithBattery Load
2.4 State Space Modeling Of Buck Converter
2.4.1 With Resistive Load
2.4.2 With Battery Load
Chapter 3 Maximum Power Point Tracking Algorithms
3.1 Introduction
3.2 Fractional Open Circuit Voltage
3.3 Fractional Short Circuit Current
3.4 Incremental Conductance Algorithm
3.5 Perturb and Observe Algorithm
1
2
3
4
5
5
5
8
8
11
14
14
18
20
21
21
22
22
23
Chapter 4 Perturb and Observe Algorithm
25
4.1 Introduction
4.2 Direct Duty Ratio Control .
4.3 PI Control
4.3.1 PI Tuning
25
27
28
29
Chapter 5 Results and Discussions
I Conclusion
II Future Work
III References
30
39
39
40
LIST OF FIGURES
Fig. No.
Figure Description No.
Page No.
Fig. 2.1
Non-linear I-V characteristics of the PV Module
6
Fig. 2.2
Equivalent circuit of a PV cell
6
Fig. 2.3
Linear equivalent circuit at the linearization point
7
Fig. 2.4
On-State circuit diagram of the Boost converter with
resistive load
8
Fig. 2.5
Off-State circuit diagram of the Boost converter with
resistive load
9
Fig. 2.6
On-State circuit diagram of the Boost converter with
battery load
11
Fig. 2.7
Off-State circuit diagram of the Boost converter with
battery load
13
Fig. 4.3
PV Module interfaced with a battery through a input
regulated converter
28
Fig. 5.1
Power versus Voltage of a PV Module
30
Fig. 5.2
Current versus Voltage of a PV Module
30
Fig. 5.3
PV Power of a Buck converter using DDC
31
Fig. 5.4
PV Voltage versus time of a Buck converter using DDC
31
Fig. 5.5
PV Current of a Buck converter using DDC
32
Fig. 5.6
Duty Cycle of a Buck converter using DDC
32
Fig. 5.7
PV Power of a Buck converter using PI
33
Fig. 5.8
PV Voltage of a Buck converter using PI
33
Fig. 5.9
PV Current of a Buck converter using PI
34
Fig. 5.10
Duty Cycle of a Buck converter using PI
34
Fig. 5.11
PV Power of a Boost converter using DDC
35
Fig. 5.12
PV Voltage of a Boost converter using DDC
35
Fig. 5.13
PV Current of a Boost converter using DDC
36
Fig. 5.14
Duty Cycle of a Boost converter using DDC
36
Fig. 5.15
PV Power of a Boost converter using PI
37
Fig. 5.16
PV Voltage of a Boost converter using PI
37
Fig. 5.17
PV Current of a Boost converter using PI
38
Fig. 5.18
Duty Cycle of a Boost converter using PI
38
LIST OF TABLES
Table No.
1.
Table Description
Parameters of the PV Module
Page No.
7
CHAPTER 1
Introduction
With the reserve of fossil fuels diminishing and rise in the global temperature, the
need to look for sustainable energy resources has become indispensable. The sustainable
energy not only reduces the consumption of fossil fuels but also prevents the rising
temperature of the earth besides diminishing the various pollutants emitted by it.
The main forms of renewable energy resources are Solar Energy, Wind Energy
and Hydro Energy. The problem associated with hydro energy is that it is seasonal
dependant where as the main factor that has caused researchers’ inclination for solar
energy a little more than wind energy is that it is plentily available throughout the globe
whereas establishing a wind farm is significantly costlier and depends on geographical
locations. Moreover solar energy can be converted directly into electrical energy with the
implementation of some power electronic devices.
Dynamic atmospheric conditions and partial shading reduces the efficiency of a PV
Panel [11]. So a need for extracting maximum energy from the photovoltaic panel arises
[2],[18]. This problem has been attended by the introduction of various MPPT methods.
MPPT techniques helps in faster tracking and locking of photovoltaic panel MPP which
increases its efficiency.
The growing research in this field has also reduced the cost of solar energy.
Therefore Solar Energy has gained a lot of importance even in the rural areas.
1.1
Literature Review
Many Literatures are proposed on modeling of a Photovoltaic array.
M.G Villava et. al.[3] has modeled and simulated the PV array . The parameters of the
non-linear I-V equation are found by adjusting the curve at open circuit, maximum power
and short circuit points. Kun Ding et.al.[16] proposes a MATLAB-Simulink based PV
module modeling which a controlled current source and an S-Function builder are used.
The modeling in S-Function builder is done by some predigested functions. M.G Villava
et. al.[5] proposes a study which dealt with regulation of the PV voltage. Regulation of
1
the converter input voltage improves the steady state response as well as stability of the
closed loop system instead of regulating the bandwidth limited converter duty cycle,
which makes it easier for the MPPT algorithm to work.
N.Femia et. al.[2] has proposed a method to avoid the negative behavior of the
P&O algorithm during rapidly changing environmental conditions by customizing the
parameters of the P&O algorithm according to the dynamic behavior of a specific type of
converter. Different methods of designing a PI controller was studied from Modern
Control Engineering.
.
1.2 Thesis Objectives
•
•
•
•
To study the solar cell model and observe its characteristics.
State Space Modeling of DC-DC converters with a PV system.
To design and study the performance of a closed loop system with PI controller.
To study and implement Perturb and Observe algorithm in the
MATLAB-Simulink environment.
1.3 Thesis Layout
The first chapter gives a brief introduction about the need for solar energy. Then a
literature review done in this context has also been produced. In the second chapter the
state space modeling of DC-DC converters with a PV system has been done and a PV
module was linearized about its MPP to find the transfer function between the control
variable and the input voltage of the PV Module which is used to design a PI controller.
In the third chapter, a comparative study of different MPP techniques is given. In the
fourth chapter we have done a detailed study of the perturb and observe algorithm which
has been used to simulation. The fifth chapter includes the results and conclusion.
2
CHAPTER 2
Analysis & Modeling of a PV based system
2.1 Introduction
The non-linear characteristics of the I-V curve of a PV panel can be divided into a
current source region and a voltage source region. In this section we have linearized the
PV panel at the MPP and a equivalent model of the PV panel is designed. The
performance of a closed loop system can be improved by using a PI controller. The
Parameters of a PI controller can be obtained by various methods like Frequency domain
Analysis, Ziegler-Nichols criteria, Computational approach etc., for which modeling of a
converter is essential. The aim of modeling a converter for controlling the voltage is to
derive a Small-Signal transfer function that gives a relation between the small signal
voltage
and the control variable
.The negative sign indicates decrements in
duty cycle causes increments in the input voltage [5]. The transfer function is then
derived from the A, B, C and D matrices which is elaborated in the following section.
2.2 PV Module Modeling
The non-linear I-V characteristics of a photovoltaic device is define in
Fig 2.2.The I-V curve of the PV Module is shown in Fig. 2.1. I-V characteristics are
defined as [3]
i
I
I
e
1
3
! "
!
[3]
Current source region
MPP
Iscn=1.9
IPV(A)
Voltage source
region
VPV(V)
Vocn=21
Fig 2.1 PV Modules Non-linear I-V Characteristics
It can be represented by a current source. It has a very high parallel resistance and a low
series resistance. In Fig. 2.2 the equivalent circuit of a photovoltaic cell is shown [3].
Fig 2.2: Equivalent Circuit of a Photovoltaic Cell [3]
4
Where
Table 1: Parameters of the PV Module
‘IPV’ is represented as the photovoltaic current,
‘IO’ represents reverse saturation current,
‘Vt’ represents the thermal voltage,
‘k’ is represented as the Boltzmann
constant(1.381e-23 J/K),
‘q’ represents electron charge(1.602e-19 C),
‘T’ represents junction temperature in K,
‘Rs’ represents equivalent Series Resistance,
‘Rp’ represents equivalent Shunt Resistance,
‘a’ represents ideality constant of the Diode(1-1.3),
IO
Iscn
a
RP
RS
Vocn
9.825*10-8A
1.9A
1.3
210
0.221 Ω
21V
We need to linearize the PV array model at its MPP in order to analyze. The
nominal I-V curve is linearized at the MPP as shown in Fig 2.1.The slope of
the non-linear I-V curve at a certain point(V,I)is given by [5]
g$V, I'
()
*+ ,
e
- +
.+
/
!
[5]
The linear model is given by the tangent to the point at the linearization point (V,I) [5]
iPV =( −gV+I) +gvPV
The equivalent circuit is represented by Fig 2.3 [5] where Req = −1/ g and
Veq = V − I / g
Fig.2.3: Linear equivalent circuit at the linearization point.[5]
5
2.3 State Space Modeling of Boost Converter
2.3.1With Resistive Load
Fig 2.4: On-State Circuit diagram of Boost Converter with Resistive
Load
ON STATE EQUATIONS
IEQ = IC + IL
VEQ − VPV
R EQ
=C
(1)
dVC
+ IL
dt
(2)
(3)
V PV = VC + I C R C
Putting equation (3) in (2) and simplifying, we get
I L R EQ
VEQ
dVC
VC
=−
−
+
dt
C ( R EQ + R C ) C ( R EQ + R C ) C ( R EQ + R C )
(4)
V PV − V L − I L R
(5)
L
= 0
6
Putting equation (3) in (5) and solving
1

 R EQRC 
VEQRC
RC
dIL
=
− VC  −
− IL 

 L L(R + R ) 
 L(R + R ) 
dt L(R EQ + R C )
EQ
C 
EQ
C 


(6)
ICO + IO = 0
(7)
CO
dVCO
(V + I R )
= − CO CO CO
dt
R
(8)
dVCO
VCO
=−
dt
CO (R + R CO )
VPV =
VEQ R C
R EQ + R C
−
I L R EQ R C
R EQ + R C
(9)
+
VC R EQ
R EQ R C

R
−
− L



L ( R EQ + R C ) L
 IL  
R EQ
 ɺ  
 VC  =  − C(R + R )
EQ
C
 ɺ  
 VCO  

 
0

ɺ
(10)
R EQ + R C
R EQ
L(R EQ + R C )
−
1
C(R EQ + R C )
0

RC



 L(R + R ) 
EQ
C



  IL  

1
  VC  + 
0
 VEQ


C(R
+
R
)

EQ
C 

  VCO  

1
0

−


CO (R + R CO ) 


0
(11)
I 
 R EQR C
  L   RC 
R EQ
VPV = −
0  VC  + 
 VEQ
 R EQ + R C R EQ + R C   V   R EQ + R C 
 CO 
7
(12)
Fig 2.5: Off-State Circuit diagram of Boost Converter with resistive
Load
OFF STATE EQUATIONS
IEQ = IC + IL
VEQ − VPV
R EQ
(13)
=C
dVC
+ IL
dt
(14)
(15)
V PV = VC + I C R C
Putting equation (14) in (13) and solving, we get
C D
CE
(F !GH
D
I(!GH !D )
IJ!GH !D K
L
GH
IJ!GH !DK
(17)
IL = ICO + IO
I L = I CO +
VCO + I CO R CO
R
I L R = I CO R + VCO + C
(16)
(18)
dVCO
R CO
dt
(19)
Simplifying equation (18), we get
8
dVCO
VCO
IL R
=
−
dt
CO (R + RCO ) CO (R + RCO )
(20)
VPV − VL − I L R
(21)
L
− VCO − ICO R
CO
= 0
We know,
IC =
VEQ − VC − I L R EQ
ICO =
(22)
R EQ + R C
ILR − VCO
R + R CO
(23)
Replacing equation (21)&(22) in equation (20),we get
VC R EQ
VEQR C
R R 
VCOR
dIL
I  R R
=
− L  EQ C + R L + CO  −
+
(24)
dt L(R EQ + R C ) L  R EQ + R C
R + RCO  L(R + R CO ) L(R EQ + R C )
 −1  R EQ R C

R EQ
R R 
R
RC


+ R L + CO 
−
 




  L  R EQ + R C
R + R CO  L ( R EQ + R C )
L ( R CO + R ) 
L(R EQ + R C ) 


 IL  
  IL 
R EQ


 ɺ  
1
1
 V +
−
−
0
 VC  = 
 C   C(R + R )  VEQ

C
R
+
R
C
R
+
R
(
)
(
)
EQ
C 
EQ
C
EQ
C
 ɺ  
  VCO  
V


 CO  
0
R
1





0
−

CO ( R + R CO )
CO ( R + R CO ) 




ɺ
(25)
I 
 R EQR C
  L   RC 
R EQ
VPV = −
0 VC  + 
 VEQ
R EQ + R C 
 R EQ + R C R EQ + R C  


 VCO 
ɵ
G vd =
Vpv
ɵ
= Y = C [SI − A ] E
−1
d
When RL=RC=RCO=0
G
C
ND
N
O
C
C
X(S'
QSI
ARS/ E
9
(26)
2.3.2 With Battery Load
Fig.2.6: On-State Circuit diagram of Boost Converter with Battery
Load
ON STATE EQUATIONS
ITU
II L IV
VEQ − VPV
R EQ
(27)
(28)
= IC + I L
VEQ − VC − ICRC = ICREQ + ILREQ
IC =
VEQ
R EQ + R C
−
(29)
I R
VC
− L EQ
R EQ + R C R EQ + R C
(30)
VEQ
I L R EQ
dVC
VC
=
−
−
dt
C(R EQ + R C ) C ( R EQ + R C ) C ( R EQ + R C )
(31)
V PV − V L − I L R
(32)
L
= 0
 VEQ

IR
VC
VC + RC 
−
− L EQ  − ILR L − VL = 0
 R +R R +R R +R 
C
EQ
C
EQ
C 
 EQ
10
(33)
IL ( REQRC + RLREQ + R LRC )
VEQRC
VCR EQ
dIL
=
+
−
dt L ( R EQ + RC ) L ( REQ + RC )
L ( R EQ + RC )
VPV =
VEQ R C
R EQ + R C
−
I L R EQ R C
R EQ + R C
+
VC R EQ
(35)
R EQ + R C
 R L R EQ + R EQ R C + R L R C
 ɺ  −
L ( R EQ + R C )
 IL  = 
 ɺ  
R EQ
−
 VC  
C ( R EQ + R C )

(34)


L ( R EQ + R C )   IL 
 V  +
1
 C
−
C ( R EQ + R C ) 
R EQ
RC


 L(R + R ) 0
EQ
C

  VEQ 

  VO 
1
0

 C ( R EQ + R C ) 
(36)
 R R
 V 
REQ   IL   RC
VPV = − EQ C
0  EQ 
 +
 REQ + RC REQ + RC  VC   REQ + RC   VO 
(37)
Fig 2.7: Off-State Circuit diagram of Boost Converter with Battery
Load
11
OFF-STATE EQUATIONS
IEQ = IC + IL
VEQ − VPV
R EQ
(38)
(39)
= IC + I L
VEQ − VC − ICRC = ICREQ + ILREQ
IC =
VEQ
R EQ + R C
−
(40)
I R
VC
− L EQ
R EQ + R C R EQ + R C
(41)
VEQ
I L R EQ
dVC
VC
=
−
−
dt
C(R EQ + R C ) C ( R EQ + R C ) C ( R EQ + R C )
(42)
VC + I C R C − VL − I L R
(43)
L
− VO = 0
IL ( REQRC + RLREQ + RLRC ) VO
VEQRC
VCREQ
dIL
=
+
−
−
dt L(REQ + RC ) L(REQ + RC )
L
L ( REQ + RC )
 R L R EQ + R EQ R C + R L R C
  −
L ( R EQ + R C )
 IL  = 
 ɺ  
R EQ
−
 VC  
C ( R EQ + R C )

ɺ
(44)


L ( R EQ + R C )   IL 
 V  +
1
 C
−
C ( R EQ + R C ) 
R EQ
RC
1

− 
L R + R
L VEQ 
C)
 ( EQ


  VO 
1
0 


 C ( REQ + RC )
(45)
 R R
 V 
REQ   IL   RC
VPV = − EQ C
0  EQ 
 +
 REQ + RC REQ + RC  VC   REQ + RC   VO 
(46)
G
C
C
CQSI
ARS/ E
12
When RL=RC=RCO=0
G
C
D
C
C
X(s)
QSI
ARS/ E
2.4 State Space Modeling of Buck Converter
2.4.1 With Resistive Load
Fig 2.8: On-State Circuit diagram of Buck Converter with Resistive
Load
ON STATE EQUATIONS
VPV − VEQ
R EQ
$47'
+ IC + IL = 0
V PV = R C I C + VC
Putting equation $48' in $47' and simplifying, we get
VEQ
I L R EQ
dVC
VC
=
−
−
dt
C(R EQ + R C ) C(R EQ + R C ) C(R EQ + R C )
I L = I CO +
$48'
$49'
$50'
VO
R
13
IL = C O
dVCO I CO R CO + VCO
+
dt
R
(51)
dVCO
IL R
VCO
=
−
dt
CO (R CO + R) CO ( R CO + R )
(52)
VPV − I L R
(53)
L
− VL − ICO R
CO
− VCO = 0
I C R C + VC − I L R L − R CO C O
dVCO
dI
− VCO = L L
dt
dt
(54)
Putting equation (52) in (54) and Simplifying, we get
 V 

VEQ R C
V 
RC
R CO
dIL
=
+ C 1 −
 − CO 1 −

dt L ( R EQ + R C ) L  L ( R EQ + R C )  L  L ( R + R CO ) 
R EQ R C
 RL
R CO R
−
−
−



L L ( R EQ + R C ) L ( R EQ + R C )
 IL  
R EQ
 ɺ  
−
 VC  = 
C ( R EQ + R C )
 ɺ  

V
 CO 
R

 

C O ( R + R CO )

ɺ
RC
1
−
L L ( R EQ + R C )
−
1
C ( R EQ + R C )
0
RC


L R + R 
C)
 ( EQ



1
+
 VEQ
 C ( R EQ + R C ) 


0




VPV =
VEQ R C
R EQ + R C
+
R CO
1
− 
L ( R + R CO ) L 
  IL 
  VC 
0



V

CO


1

−
CO ( R + R CO ) 
(56)
VC R EQ
R EQ + R C
 R R
VPV =  − EQ C
 R EQ + R C
(55)
−
I L R EQ R C
(57)
R EQ + R C
R EQ
R EQ + R C
I 
  L   RC 
0  VC  + 
 VEQ
R
+
R
 


EQ
C


 VCO 
14
(58)
Fig 2.9: Off-State Circuit diagram of Buck Converter with Resistive
Load
OFF-STATE EQUATIONS
VEQ − VPV
R EQ
IC =
(59)
= IC
VEQ
R EQ + R C
−
VC
( R EQ + R C )
(60)
VEQ
dVC
VC
=
−
dt
C ( R EQ + R C ) C ( R EQ + R C )
(61)
I L = I CO +
VO
R
(62)
I L = I CO +
I CO R CO + VCO
R
(63)
dVCO
IL R
VCO
=
−
dt
CO ( R + R CO ) CO ( R + R CO )
(64)
− IL R
(65)
L
− VL − ICO R
CO
− VCO = 0
15
− I L R L − C O R CO
dVCO
dI
− VCO = L L
dt
dt
(66)
Putting equation (63) in (65), we get
 R


RR CO 
dIL
R
= IL  − L −
 + VCO  −

dt
L
L
R
+
R
L
R
+
R
(
)
(
)
CO
CO




 R
R CO R
L

 − L − L ( R + R )
CO
 IL  

ɺ


0
 VC  = 
 ɺ  
 VCO  
R

 
 CO ( R + R CO )

0
ɺ
−
1
C ( R EQ + R C )
0
(67)

R



L ( R + R CO ) 
0
I




L

1
V
  VC  + 
0
EQ




C ( R EQ + R C )





V
  CO 


1
0

−
CO ( R + R CO ) 
−
(68)
VPV =
VEQ R C
R EQ + R C
+
VC R EQ
I 
  L   RC 
0  VC  + 
 VEQ
 V   R EQ + R C 
 CO 

R EQ
VPV = 0
 R EQ + R C
G
Z
C
C
When R V
G
C
N
O
C
CQSI
RI
ND
C
(69)
R EQ + R C
ARS/ E
RI
QSI
0
ARS/ E
16
(70)
2.3.3 With Battery Load
Fig 2.10: On-State Circuit diagram of Buck Converter with Battery
Load
ON STATE EQUATIONS
IEQ = IC + IL
(70)
V PV = I C R C + VC
(71)
VEQ − VPV
R EQ
IC =
(72)
= IC + I L
VEQ
R EQ + R C
−
I R
VC
− L EQ
R EQ + R C R EQ + R C
(73)
Replacing equation (72) in (73)
VEQ
I L R EQ
dVC
VC
=
−
−
dt
C ( R EQ + R C ) C ( R EQ + R C ) C ( R EQ + R C )
(74)
VPV − VL − I L R
(75)
L
− VO = 0
Replacing equation (72)&(74) in equation (76) and simplifying,
17
 R R + R L R EQ + R L R C 
VC R EQ
VEQ R C
V
dIL
=
− IL  EQ C
− O
+


dt L ( R EQ + R C )
L ( R EQ + R C )

 L ( R EQ + R C ) L
(76)
Putting equation (74) in equation (72) & simplifying,
VPV =
VEQ R C
R EQ + R C
+
VC R EQ
R EQ + R C
−
I L R EQ R C
(77)
R EQ + R C
 R R +R R +R R 

R EQ
EQ C
L EQ
L C


−

 


L ( R EQ + R C )
 L ( R EQ + R C )   IL  +
 IL  =  
 V 
 ɺ  
R EQ
1

 C
V
 C
−
−


C ( R EQ + R C )
C ( R EQ + R C ) 

ɺ
RC
1

− 
L R + R
L VEQ 
C)
 ( EQ


  VO 
1
0



 C ( REQ + RC )
 R R
VPV = − EQ C
 R EQ + RC
(78)
  IL   R C
+

R EQ + RC  VC   R EQ + RC
R EQ
 V 
0  EQ 
  VO 
(79)
Fig 2.11: Off-State Circuit diagram of Buck Converter with Battery
Load
18
OFF STATE EQUATIONS
IC =
VEQ − VPV
IC =
(80)
R EQ
VEQ
R EQ + R C
−
VC
R EQ + R C
(81)
VEQ
dVC
VC
=
−
dt
C ( R EQ + R C ) C ( R EQ + R C )
(82)
− IL R
L
(83)
− VL − VO = 0
V
dI L
I R
=− L L − O
dt
L
L
(84)
V PV = I C R C + VC
(85)
Putting equation (81) in equation (85)
VPV =
VEQ R C
R EQ + R C
 RL
 ɺ  −
 IL  =  L
 ɺ  
VC   0

+
VC R EQ
(86)
R EQ + R C
1


0
− 
I  
L VEQ 
 L +


1
1
V


 C
−
0   VO 


C ( R EQ + R C ) 
 C ( R EQ + R C )

0

 V 
R EQ   IL   RC
VPV = 0
0  EQ 
 +
 R EQ + RC  VC   R EQ + RC   VO 
We can find out small signal transfer function between the output voltage V
control variable dfrom the A, B, C, D Matrices determined.
19
(87)
(88)
and the
CHAPTER 3
Maximum Power Point Tracking Algorithms
3.1 Introduction
When we install a solar panel or a array of solar panels without a MPPT
technique, it often leads to wastage of power, which ultimately requires more number of
panels for the same amount of power requirement. Also whenever a battery is connected
directly to the panel, it results in premature failure of battery or loss capacity owing to
lack of a proper end-of-charge process and higher voltage. So, absence of a MPPT
method results in higher cost. The main aim of a MPPT technique is to automatically find
the operating voltage of the panel that delivers maximum power to the load. When a
single MPPT is connected to large number of panels, it will yield a good result but in case
of partial shading, the combined power output curve will have multiple maximas which
might confuse the algorithm.
3.2 Fractional Open Circuit Voltage
A linear relation with the open circuit voltage is maintained by the maximum
power point voltage under different temperature and irradiance conditions.
Vf
K V
I
Constant KV is always dependable on the type and configuration of the Solar Panel. The
open circuit voltage. For FOCV the open circuit voltage of the panel has to be measured
first in order to determine the MPP voltage. One way of doing it is the system
periodically disconnects the system from the load to measure the open circuit voltage and
calculate the MPP. Clearly this procedure leads to wastage of power. Another method
could be by using one or more monitoring cells but they must also be chosen and placed
very carefully to measure the correct open circuit voltage. Even though the method is
simple and robust, we can only make a crude approximation of the MPP. The value of KV
has been experimentally found out to be between 0.7-0.8
20
3.3Fractional Short Circuit Current
The MPP can also be calculated from the short circuit current of the panel
because IMPP is linearly dependent on the short circuit current under varying
atmospheric conditions.
If
K ( IhI
Measuring ISC is more difficult as compared to VOC, since it not only leads to power
losses and heat dissipation, it requires additional switches and current sensors which
increases the cost of installation. The value of KI is nominally considered between
0.79-0.91.
3.4 Incremental Conductance
It is based on concept that the slope of the power versus voltage curve is zero at
MPP, positive on the left side and negative on the right side of the MPP.
Equation 1
dP
= 0, at the MPP
dV
dP
> 0, left of MPP
dV
dP
< 0, right of MPP
dV
Equation 2
dP d ( IV )
dV
dI
dI
∆I
=
=I
+V
= I +V
≅ I +V
dV
dV
dV
dV
dV
∆V
I + VdI / dV ≅ I + V∆I / ∆V
So the first set of equations can be written as:
Equation 3
∆I
I
= − , at MPP
∆V
V
∆I
I
> − , left of MPP
∆V
V
∆I
I
< − , right of MPP
∆V
V
21
The concept behind this is to make a comparison between the incremental
conductance to the instantaneous conductance. It is operated by this logic until the
MPP is reached by increasing or decreasing voltage.
3.5 Perturb and Observe
Perturb & Observe is generally used algorithms for its simplicity of
implementation. The algorithm introduces a perturbation in the module voltage. The
module voltage is modified by updating the converter duty cycle.
22
CHAPTER 4
Perturb & Observe Algorithm
4.1 Introduction
When an increment is made in the Module voltage, the algorithm checks the
present power reading and the previous one. If the power has increased it keeps
increasing the voltage or it reverses the direction. This process is continued at each
step until the peak power is reached. After reaching there, the algorithm oscillates
about the MPP.
The basic algorithm is based on using a fixed step to increase or decrease the
operating voltage. The deviation while oscillating around the MPP is dependent on
step size chosen. Choosing a small step size reduces the oscillation around the MPP
but increases tracking time adversely, while a bigger step size reduces the tracking
time but increases power loss due to the oscillation. The algorithm for perturb and
observe is shown in Fig. 4.1.
The Perturb and Observe algorithm can be validated either directly by
operating the converter’s duty cycle or by generating a reference voltage or current
signal which is tracked by a PI controller. The output of the PI controller is then
compared with a reference constant value to generate the PWM signal. The different
control loops are elaborated in the following section.
23
Fig 4.1: Algorithm for Perturb & Observe
24
4.2 Direct Duty Ratio Control
In this method the duty cycle of the converter is varied based upon different
MPPT methods which measures the small variations in the solar array input voltage ‘dV’
and input power ‘dP’, in a direction to reach towards the MPP of the solar array.
The duty cycle perturbation at (k+1)th sampling time can be represented by
(
)
(
d ( ( k + 1) Ta ) = d ( kTa ) + d ( kTa ) − d ( ( k − 1) Ta ) .sign P ( ( k + 1) Ta ) − P ( kTa )
)
The oscillations of i(jkl ) around the MPP can be minimized if the sampling interval Ta
is properly chosen. Minimizing ∆d reduces the steady state losses caused due to the
continuous oscillation of the Module operating point about the MPP. The Fig. 4.2 gives a
schematic representation of direct duty cycle control method.
Fig. 4.2: Direct Duty Cycle Control
In this type of control no proper voltage regulation can be achieved. And the power stage
is subjected to increased switching stresses and losses. Therefore a PI compensator is
used for regulating the converter voltage or current. Apart from reducing stresses and
losses owing to the bandwidth constrained regulation of the duty cycle, a compensator
reduces the settling time, avoids oscillation a, which eases the functioning of MPPT
algorithm [5].
25
4.3 PI Control
In this scheme of Fig.4.3 MPP technique generates the reference voltage signal
which is then compared with the input voltage of the converter. The input voltage VPV is
regulated by a PI compensator, the output of which acts on the converter duty cycle.
Fig. 4.3: PV Array regulated by PI controller
The open loop transfer function relating the converter input Voltage Vpv to duty cycle d
is represented by Gvd which can be obtained through the procedure given in [2].,the
feedback gain of the input voltage is Hv and the compensator transfer function is Cvd. The
block diagram representation of the single feedback loop is shown in Fig.4.
4.3.1 PI Tuning
As shown in Fig. 4.3, the MPPT measures the PV voltage and current
and then the Perturb and Observe algorithm decides the reference voltage. The aim
of P&O is to decide the value of VPV* only and it is done at certain intervals time.
The PI control loop tries to reach the input voltage of the converter. It reduces the
error between VPV* and VPV by varying the converter’s duty cycle. The PI loop
control works at a much faster rate and gives a faster response.
26
CHAPTER 5
Results
The PV Module has been interfaced to a load resistance through DC-DC converters. The
simulation results have been obtained for both Boost and Buck converters. The PV
module characteristic has been shown under different irradiations. Secondly, Power and
voltage curves have been obtained under two different irradiations using the direct duty
ratio control technique. Lastly we have shown the input regulated power and voltage
curves of the PV Module with both Buck and Boost converters using PI controller.
PV Current vs PV Voltage
1.4
600 W/m2
400 W/m2
1.2
PV Current(A)
1
Vm=16.23
Im=1.02
0.8
0.6
Vm=15.78
Im=0.6622
0.4
0.2
0
0
5
10
PV Voltage(V)
15
20
Fig. 5.1 Power versus Voltage of a PV Module
PV Power vs PV Voltgae
20
400 W/m2
600 W/m2
PV Power(W)
15
Pm=16.68
Vm=16.23
10
Pm=10.45
Vm=15.78
5
0
0
5
10
PV Voltage(V)
15
20
Fig. 5.2: Current versus Voltage of a PV Module
27
5.1 Buck Converter
5.1.1 Direct Duty Ratio Control
PV Power vs time
PV Power(W)
20
15
g=600w/m2
10
g=400 w/m2
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig.5.3: PV Power of a Buck converter using DDC.
PV Voltage vs time
PV Voltage(V)
20
15
g=600w/m2
g=400w/m2
10
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig.5.4: PV Voltage of a Buck converter using DDC.
28
1.8
2
PV Current vs time
1.4
PV Current(A)
1.2
G=600 W/m2
1
0.8
0.6
0.4
G=400 W/m2
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.5: PV Current of a Buck converter using DDC.
Duty Cycle vs time
0.8
Duty Cycle
0.7
g=600 w/m2
0.6
g=400 w/m2
0.5
0.4
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig. 5.6: Duty cycle of a Buck converter using DDC.
29
1.8
2
5.1.2 Voltage Reference Control using PI Controller
PV Power(W) vs time
20
PV Power(W)
15
g=600w/m2
10
g=400w/m2
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.7: PVPower of a Buck converter using PI.
PV Voltage vs time
PV Voltage(V)
20
15
g=600w/m2
g=400w/m2
10
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig. 5.8: PV Voltage of a Buck converter using PI.
30
1.8
2
PV Current vs time
PV Current(A)
1.5
1
g=600w/m2
0.5
0
0
g=400w/m2
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.9: PV Current of a Buck converter using PI.
Duty Cycle vs time
1
Duty Cycle
0.8
g=600 /m2
0.6
g=400 /m2
0.4
0.2
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig. 5.10: Duty Cycle of a Buck converter using PI.
31
1.8
2
5.2 Boost Converter
5.2.1Direct Duty Ratio Control
PV Power vs time
20
PV Power(W)
15
g=600w/m2
10
g=400w/m2
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.11: PV Power of a Boost converter using DDC.
PV Voltage vs time
20
PV Voltage(V)
15
g=600w/m2
g=400w/m2
10
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
Fig. 5.12: PV Voltage of a Boost converter using DDC.
32
2
PV Current vs time
1.1
PV Current(A)
1
g=600w/m2
0.9
0.8
g=400w/m2
0.7
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig.5.13: PV Current of a Boost converter using DDC.
Duty Cycle vs time
0.5
Duty Cycle
g=600w/m2
0.45
g=400w/m2
0.4
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig. 5.14: Duty cycle of a Boost converter using DDC.
33
1.8
2
5.2.2 Voltage Reference Control using PI controller
PV Power vs time
20
PV Power(W)
15
g=600w/m2
10
g=400w/m2
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.15: PV Power at of a Boost converter using PI.
PV Voltage vs time
20
PV Voltage(V)
15
g=600w/m2
g=400w/m2
10
5
0
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
Fig. 5.16: PV Voltage of a Boost converter using PI.
34
1.8
2
PV Current vs time
1.4
PV Current(A)
1.2
1
g=600w/m2
0.8
0.6
g=400w/m2
0.4
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
2
Fig. 5.17: PV Current of a Boost converter using PI.
Duty Cycle vs time
0.7
Duty Cycle
0.6
0.5
g=600w/m2
0.4
g=400w/m2
0.3
0.2
0
0.2
0.4
0.6
0.8
1
time(s)
1.2
1.4
1.6
1.8
Fig. 5.18: Duty Cycle of a Boost converter using PI.
35
2
I. Conclusion
The results were obtained in the MATLAB-Simulink environment. From the
curves obtained both in the direct duty ratio control and the voltage reference control in
which a PI controller is used to regulate the voltage of the PV array, it is evident that a PI
controller helps in achieving a faster steady state response and avoids oscillations and
overshoot as compared to direct duty ratio control.
A detailed study of the perturb and observe technique was done. We have also made a
comparative analysis of the different MPPT techniques which guides us to choose the
best among the available techniques in a particular environmental condition.
II. Future Work
•
•
Implementation of global MPPT in case of partial shading phenomenon.
Avoiding drift phenomenon in P&O due to change in insolation level.
III. References
[1]W. Xiao, W.G. Dunford, P.R. Palmer, A. Capel ‘Regulation of
photovoltaic voltage’, IEEE Trans. Ind. Electron., Vol 54,No 3,pp.13651374,June 2007.
[2] N. Femia, G. petrone, V. Spagnuolo, M. Vitelli, ‘Optimization of Perturb
and Observe Maximum Power Point Tracking Method’, IEEE Trans. on
Power Electron., Vol. 20, No. 4, July 2005.
[3]M.G Villalva, J.R Gazoli , E.F Ruppert ‘Comprehensive approach to
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