International journal of advanced scientific and technical research
Available online on http://www.rspublication.com/ijst/index.html
Issue 5 volume 1, January-February 2015
ISSN 2249-9954
Design and Development of Optimal Controller for
Photovoltaic System.
K P J Pradeep1, C Chandra Mouli2, K Sai Prasad Reddy3, K Nagabhushan Raju4
1, 2
Research Scholar, Dept of Instrumentation, Sri Krishnadevaraya University, Anantapur, Andhra
Pradesh, India
3
Research Scholar, Dept of Electronics, Sri Krishnadevaraya University, Anantapur, Andhra Pradesh,
India
4
Professor, Dept of Instrumentation, Sri Krishnadevaraya University, Anantapur, Andhra Pradesh, India
Abstract
LQR based MPPT controller has been designed with real time simulations have been carried out
on LabVIEW platform for solar photovoltaic system with boost converter. Performance of the
proposed method has been compared with other methods of maximum power point tracking.
This paper presents an analysis of the Solar PV module and proposed method for tracking
maximum power point.
Keywords: Maximum power point tracking (MPPT), solar photovoltaic system, linear quadratic
regulator (LQR), LabVIEW.
1. Introduction
The world population is increasing day by day and the demand for energy is increasing
accordingly. Oil and coal as the main source of energy nowadays, is expected to end up from the
world during the recent century which explores a serious problem in providing the humanity with
an affordable and reliable source of energy. Renewable energy is derived from natural processes
that are replenished constantly. Renewable energies are inexhaustible and clean. The energy
comes from natural resources such as sun, wind, tides, waves, and geothermal heat. Solar energy
is quite simply the energy produced directly by the sun. Solar energy is radiant light and heat
from the sun harnessed using a range of technologies such as photovoltaic, thermal electricity
and etc. A solar cell (also called a photovoltaic cell) is an electrical device that converts the
energy of light directly into electricity by the photovoltaic effect.
A solar panel is a set of solar photovoltaic modules electrically connected and mounted
on a supporting structure. The majority of modules use wafer based crystalline silicon cells or
thin-film cells based on cadmium telluride or silicon. The structural member of a module can
either be the top layer or the back layer. Electrical connections are made in series to achieve a
desired output voltage and in parallel to provide a desired current capability. Several types of
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International journal of advanced scientific and technical research
Available online on http://www.rspublication.com/ijst/index.html
Issue 5 volume 1, January-February 2015
ISSN 2249-9954
solar cells are available. Mono crystalline Solar Cells, Polycrystalline Solar Cells, Amorphous
Silicon (a-Si) Solar Cells, and Cadmium Telluride (CdTe) Solar Cells. Solar energy is clean,
abundant, renewable and freely available source of the energy [1].
LabVIEW (short for Laboratory Virtual Instrument Engineering Workbench) is a systemdesign platform and development environment for a visual programming language from National
Instruments. The software is perhaps the most important component of the system. The main
routine, or VI, provides a front panel interface that allows the operator to control and monitor the
system. It calls to perform functions that gather analog input, send analog output. The front panel
is what allows the operator to control and monitor the process [2-4].
Optimal control theory is an extension of the calculus of variations, and the
mathematical optimization method for deriving control policies. The solution is provided by
the linear-quadratic regulator (LQR), Linear-Quadratic-Gaussian (LQG). Linear quadratic
regulator (LQR) is one of the methods of optimal control strategy which has been developed and
used in various applications like aviation, satellites. LQR design is based on the selection of
feedback gain such that the cost function J is minimized [5]. In this paper linear quadratic
regulator based controller has been designed using LabVIEW.
2. Design of LQR based MPPT system
The term “linear quadratic” refers to the linear system dynamics and the quadratic cost
function. LQR design is based on the selection of feedback gain such that the cost function J is
minimized.
For a continuous-time linear system, defined on
, described by
With a quadratic cost function defined as
The feedback control law that minimizes the value of the cost is
Where
And
is given by
is found by solving the continuous time Riccati differential equation.
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International journal of advanced scientific and technical research
Available online on http://www.rspublication.com/ijst/index.html
Issue 5 volume 1, January-February 2015
ISSN 2249-9954
With the boundary condition
Where, Q and R are the weight matrices. Q is positive definite or positive semi-definite real
symmetric matrix and R is positive definite symmetric matrix. These matrices are called state
and control penalty matrices respectively.
However, we had to select the Q matrix properly.
𝑄𝑡𝑡 0
Typically Q=
0 0
And R = [1]
From the values of Q and R matrices gain matrix K has been determined. The optimal
regulator for the LTI system with respect to the quadratic cost function is always a linear control
law [6-8].
Figure 1 Block Diagram of General MPPT System
Step response of the closed loop system is obtained from the control design toolkit in
LabVIEW. Above procedure of designing closed loop LQR system and plotting its step response
has been repeated for number of times by varying value of component Q11 of matrix Q from 1 to
10000 while keeping matrix R same. The LQR gain matrix K is given by,
K = [46.7 49.3]
Component values of matrix K have been used to design PI controller with Kp=46.7 and
Ki=49.3. Step response of the closed loop system has been shown in the Figure 5.
3. Modelling and real-time simulation of MPPT algorithms
Various MPPT algorithms have been developed based on real time simulations using
LabVIEW. These algorithms have been carried out for comparing MPPT algorithms [9, 10]. In
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International journal of advanced scientific and technical research
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Issue 5 volume 1, January-February 2015
ISSN 2249-9954
the present work static and dynamic relative error of the PV output power has been analyzed.
The model for implementing LQR based MPPT algorithm is given in the below. The optimal
value of the gain matrix K has been used to design linear quadratic regulator. PV current Ipv is
all the time compared with current at maximum power Imp value of which is determined based
on solar radiation and panel temperature [11, 12].
Figure 2: Block diagram 1 of in the LabVIEW platform.
Figure 3: Block diagram of LQR in the LabVIEW platform.
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Issue 5 volume 1, January-February 2015
ISSN 2249-9954
Figure 4: Front panel of LQR in the LabVIEW platform.
Figure 5: Step response of the closed loop system
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International journal of advanced scientific and technical research
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Issue 5 volume 1, January-February 2015
ISSN 2249-9954
Figure 6: I-V and P-V characteristics
Conclusion: LQR tuned PI based MPPT controller has been proposed using LabVIEW. Real
time simulations of proposed and conventional MPPT algorithms have been carried out for
performance comparison. The experimental results show that the proposed approach can achieve
better efficiency and less settling time under rapidly changing the solar radiations.
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International journal of advanced scientific and technical research
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Issue 5 volume 1, January-February 2015
ISSN 2249-9954
[9]
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