In this paper, a new systematic approach for stability analysis and controller design of nonlinear solar photovoltaic (PV) power system is proposed. Based on a nonquadratic Lyapunov function (NQLF), a model-based dynamic nonparallel-distributed compensation (non-PDC) controller and descriptor representation, the problem of the output tracking is formulated in terms of linear matrix inequalities (LMIs). Furthermore, some slack LMI variables are introduced in the problem formulation which lead to more relaxed conditions. Finally, to illustrate the merits of the proposed approach, it is applied to a PV power system in which the reference voltage is calculated from the maximum power point tracking (MPPT) method.

References

References
1.
Jacobson
,
M. Z.
, and
Delucchi
,
M. A.
,
2011
, “
Providing All Global Energy With Wind, Water, and Solar Power, Part I: Technologies, Energy Resources, Quantities and Areas of Infrastructure, and Materials
,”
Energy Policy
,
39
(
3
), pp.
1154
1169
.
2.
Fthenakis
,
V.
,
Mason
,
J. E.
, and
Zweibel
,
K.
,
2009
, “
The Technical, Geographical, and Economic Feasibility for Solar Energy to Supply the Energy Needs of the US
,”
Energy Policy
,
37
(
2
), pp.
387
399
.
3.
Zeinalzadeh
,
A.
,
Ghorbani
,
R.
, and
Yee
,
J.
,
2016
, “
Stochastic Model of Voltage Variations in the Presence of Photovoltaic Systems
,”
American Control Conference
(
ACC
), July 6–8, pp.
5032
5037
.
4.
Sharma
,
A.
,
2011
, “
A Comprehensive Study of Solar Power in India and World
,”
Renewable Sustainable Energy Rev.
,
15
(
4
), pp.
1767
1776
.
5.
Finley, M.,
2011
, “
BP Statistical Review of World Energy (2007)
,” BP, London, accessed Mar. 2015, www.bp.com
6.
E. P. I. Association
,
2012
, “
Solar Photovoltaics Competing in the Energy Sector, on the Road to Competitiveness
,”
European Photovoltaic Industry Association
, Brussels, Belgium.
7.
E. P. I. Association
,
2012
, “
Solar Generation 6 Solar Photovoltaic Electricity Empowering the World
,”
European Photovoltaic Industry Association
, Brussels, Belgium.
8.
Subudhi
,
B.
, and
Pradhan
,
R.
,
2013
, “
A Comparative Study on Maximum Power Point Tracking Techniques for Photovoltaic Power Systems
,”
IEEE Trans. Sustainable Energy
,
4
(
1
), pp.
89
98
.
9.
Rahim
,
N. A.
,
Che Soh
,
A.
,
Radzi
,
M. A. M.
, and
Zainuri
,
M. A. A. M.
,
2014
, “
Development of Adaptive Perturb and Observe-Fuzzy Control Maximum Power Point Tracking for Photovoltaic Boost dc–dc Converter
,”
IET Renewable Power Gener.
,
8
(
2
), pp.
183
194
.
10.
Hussein
,
K. H.
,
Muta
,
I.
,
Hoshino
,
T.
, and
Osakada
,
M.
,
1995
, “
Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Condition
,”
Inst. Electron. Eng. Proc. Gener. Transm. Distrib.
,
142
(
1
), pp.
59
64
.
11.
Lalouni
,
S.
,
Rekioua
,
D.
,
Rekioua
,
T.
, and
Matagne
,
E.
,
2009
, “
Fuzzy Logic Control of Stand-Alone Photovoltaic System With Battery Storage
,”
J. Power Sources
,
193
(
2
), pp.
899
907
.
12.
El Khateb
,
A.
,
Rahim
,
N. A.
,
Selvaraj
,
J.
, and
Uddin
,
M. N.
,
2014
, “
Fuzzy-Logic-Controller-Based SEPIC Converter for Maximum Power Point Tracking
,”
IEEE Trans. Ind. Appl.
,
50
(
4
), pp.
2349
2358
.
13.
Veerachary
,
M.
,
Senjyu
,
T.
, and
Uezato
,
K.
,
2003
, “
Neural-Network-Based Maximum-Power-Point Tracking of Coupled-Inductor Interleaved Boost-Converter-Supplied PV System Using Fuzzy Controller
,”
IEEE Trans. Ind. Electron.
,
50
(
4
), pp.
749
758
.
14.
Koutroulis
,
E.
,
Kalaitzakis
,
K.
, and
Voulgaris
,
N. C.
,
2001
, “
Development of a Microcontroller-Based, Photovoltaic Maximum Power Point Tracking Control System
,”
IEEE Trans. Power Electron.
,
16
(
1
), pp.
46
54
.
15.
Valenciaga
,
F.
,
Puleston
,
P. F.
, and
Battaiotto
,
P. E.
,
2001
, “
Power Control of a Photovoltaic Array in a Hybrid Electric Generation System Using Sliding Mode Techniques
,”
Inst. Electron. Eng. Proc. Control Theory Appl.
,
148
(
6
), pp.
448
455
.
16.
Patcharaprakiti
,
N.
,
Premrudeepreechacharnb
,
S.
, and
Sriuthaisiriwong
,
Y.
,
2005
, “
Maximum Power Point Tracking Using Adaptive Fuzzy Logic Control for Grid-Connected Photovoltaic System
,”
Renewable Energy
,
30
(
11
), pp.
1771
1788
.
17.
Solodovnik
,
E. V.
,
Liu
,
S.
, and
Dougal
,
R. A.
,
2004
, “
Power Controller Design for Maximum Power Tracking in Solar Installations
,”
IEEE Trans. Power Electron.
,
19
(
5
), pp.
1295
1304
.
18.
Sha Sadeghi
,
M.
,
Vafamand
,
N.
, and
Babaei
,
M. S.
,
2014
, “
Non-Quadratic Exponential Stabilisation of Non-Linear Hyperbolic Partial Differential Equation Systems
,”
IET Sci. Meas. Technol.
,
8
(
6
), pp.
537
545
.
19.
Sadeghi
,
M. S.
,
Vafamand
,
N.
, and
Khooban
,
M. H.
,
2016
, “
LMI-Based Stability Analysis and Robust Controller Design for a Class of Nonlinear Chaotic Power Systems
,”
J. Frankl. Inst.
,
353
(
13
), pp.
2835
2858
.
20.
Khooban
,
M. H.
,
Vafamand
,
N.
, and
Niknam
,
T.
,
2016
, “
T–S Fuzzy Model Predictive Speed Control of Electrical Vehicles
,”
ISA Trans.
,
64
(1), pp.
231
240
.
21.
Asemani
,
M. H.
, and
Vatankhah
,
R.
,
2016
, “
Tracking Control of Chaotic Spinning Disks Via Nonlinear Dynamic Output Feedback With Input Constraints
,”
Complexity
,
21
(
S1
), pp.
148
159
.
22.
Rakhshan
,
M.
,
Vafamand
,
N.
,
Sha Sadeghi
,
M.
,
Dabbaghjamanesh
,
M.
, and
Meeini
,
A.
, “
Design of Networked Polynomial Control Systems With Random Delays: Sum of Squares Approach
,”
Int. J. Autom. Control
,
10
(
1
), pp.
73
86
.
23.
Safarinejadian
,
B.
,
Gharibzadeh
,
M.
, and
Rakhshan
,
M.
,
2014
, “
An Optimized Model of Electricity Price Forecasting in the Electricity Market Based on Fuzzy Timeseries
,”
Syst. Sci. Control Eng.
,
2
(
1
), pp.
677
683
.
24.
Guerra
,
T. M.
,
Bernal
,
M.
,
Guelton
,
K.
, and
Labiod
,
S.
,
2012
, “
Non-Quadratic Local Stabilization for Continuous-Time Takagi–Sugeno Models
,”
Fuzzy Sets Syst.
,
201
(1), pp.
40
54
.
25.
Dahmane
,
M.
,
Bosche
,
J.
, and
El-Hajjaji
,
A.
,
2013
, “
Robust Control Approach for Photovoltaic Conversion System
,”
2013 International Conference on Renewable and Sustainable Energy Conference
(
IRSEC
), Mar. 7–9, pp.
123
129
.
26.
Aitouche
,
A.
, and
Kamal
,
E.
,
2013
, “
Robust Fuzzy Control of PV Systems With Parametric Uncertainties
,”
IET
Conference on Control and Automation 2013: Uniting Problems and Solutions
, p.
22
.
27.
Ouachani
,
I.
,
Rabhi
,
A.
,
Tidhaf
,
B.
,
Zouggar
,
S.
, and
Elhajjaji
,
A.
,
2013
, “
Optimization and Control for a Photovoltaic Pumping System
,”
2013 International Conference on Renewable Energy Research and Applications
(
ICRERA
), Oct. 20–23, pp.
734
739
.
28.
Chiu
,
C.-S.
,
2010
, “
T-S Fuzzy Maximum Power Point Tracking Control of Solar Power Generation Systems
,”
IEEE Trans. Energy Convers.
,
25
(
4
), pp.
1123
1132
.
29.
Chiu
,
C.-S.
, and
Ouyang
,
Y.-L.
,
2011
, “
Robust Maximum Power Tracking Control of Uncertain Photovoltaic Systems: A Unified T-S Fuzzy Model-Based Approach
,”
IEEE Trans. Control Syst. Technol.
,
19
(
6
), pp.
1516
1526
.
30.
Jafarzadeh
,
S.
, and
Fadali
,
M. S.
, “
On the Stability and Control of Continuous-Time TSK Fuzzy Systems
,”
IEEE Trans. Cybern.
,
43
(
3
), pp.
1073
1087
.
31.
Sha Sadeghi
,
M.
, and
Vafamand
,
N.
,
2014
, “
More Relaxed Stability Conditions for Fuzzy TS Control Systems by Optimal Determination of Membership Function Information
,”
J. Control Eng. Appl. Inform.
,
16
(
2
), pp.
67
77
.
32.
Jafarzadeh
,
S.
,
Fadali
,
M. S.
, and
Sonbol
,
A. H.
,
2011
, “
Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design
,”
IEEE Trans. Fuzzy Syst.
,
19
(
6
), pp.
1001
1013
.
33.
Wang
,
W.-J.
, and
Sun
,
C.-H.
, “
Relaxed Stability and Stabilization Conditions for a T–S Fuzzy Discrete System
,”
Fuzzy Sets Syst.
,
156
(
2
), pp.
208
225
.
34.
Cao
,
Y.-Y.
,
Sun
,
Y.-X.
, and
Cheng
,
C.
,
1998
, “
Delay-Dependent Robust Stabilization of Uncertain Systems With Multiple State Delays
,”
IEEE Trans. Autom. Control
,
43
(
11
), pp.
1608
1612
.
35.
Scherer
,
C.
, and
Weiland
,
S.
,
2004
, “
Linear Matrix Inequalities in Control
,”
Dutch Institute for Systems and Control
, Delft, The Netherlands.
36.
Mendes
,
E. M. A. M.
,
Palhares
,
R. M.
, and
Mozelli
,
L. A.
,
2010
,“
Equivalent Techniques, Extra Comparisons and Less Conservative Control Design for Takagi–Sugeno (TS) Fuzzy Systems
,”
IET Control Theory Appl.
,
4
(
12
), pp.
2813
2822
.
37.
Mahmud
,
M. A.
,
Pota
,
H. R.
, and
Hossain
,
M. J.
,
2014
, “
Nonlinear Current Control Scheme for a Single-Phase Grid-Connected Photovoltaic System
,”
IEEE Trans. Sustain. Energy
,
5
(
1
), pp.
218
227
.
You do not currently have access to this content.