Adaptive Control Scheme for PV Based Induction Machine

38 International Journal for Modern Trends in Science and Technology
Volume: 2 | Issue: 07 | July 2016 | ISSN: 2455-3778IJMTST
Adaptive Control Scheme for PV Based
Induction Machine
M. Siva Kumar1
| D. Ramesh2
1PG Scholar, Department of Electrical & Electronics Engineering, Malla Reddy Engineering College,
Maisammaguda, Medchal (M), Rangareddy (Dt), Telangana, India.
2AssistantProfessor, Department of Electrical & Electronics Engineering, Malla Reddy Engineering
College, Maisammaguda, Medchal (M), Rangareddy (Dt), Telangana, India.
An adaptive control scheme for maximum power point tracking of a single-phase grid-connected
photovoltaic system is presented. The difficulty on design a controller that may operate a photovoltaic system
on its maximum power point (MPP) is that, this MPP depends on temperature and solar irradiance, ambient
conditions that are time-varying and difficult to measure. A solution using an on-line sliding mode estimator
is presented. It estimates three different parameters that depend on solar irradiance and temperature,
eliminating the necessity of having any sensor for these environmental variables. It is capable of estimate
time-varying parameters. A complete analysis was done taking into account the non-linearity’s showed by
the closed-loop system. An adaptive law was found to substitute a perturbation bound and also to eliminate
possible chattering due to the discontinuous controller term. Computer simulations are presented to show the
good performance of the controller. The controller detects the deviation of the actual trajectory from the
reference trajectory and corresponding changes the switching strategy to restore the tracking. Prominent
characteristics such as invariance, robustness, order reduction, and control chattering are discussed in
detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered
The proposed concept can be implemented to adaptive control scheme for induction machine using
Matlab/Simulink software.
KEYWORDS: Grid-connected photovoltaic (PV) system, matching conditions, nonlinear controller, partial
feedback linearzing scheme, structured uncertainty.
Copyright © 2016 International Journal for Modern Trends in Science and Technology
All rights reserved.
I. INTRODUCTION
The utilization of grid-connected photovoltaic
(PV) systems is increasingly being pursued as a
supplement and an alternative to the conventional
fossil fuel generation in order to meet increasing
energy demands and to limit the pollution of the
environment caused by fuel emissions. The major
concerns of integrating PV into the grid are
stochastic behaviors of solar irradiations and
interfacing of inverters with the grid. Because of
the high initial investment, variations in solar
irradiation, and reduced life-time of PV systems, as
compared with the traditional energy sources, it is
essential to extract maximum power from PV
systems [1].
Maximum power point tracking (MPPT)
techniques are widely used to extract maximum
power from the PV system that is delivered to the
grid through the inverter [2]–[4]. Recent
improvements on MPPT can be seen in [5] and [6].
Interconnections among PV modules within a
shaded PV field can affect the extraction of
maximum power [7]. A study of all possible shading
scenarios and interconnection schemes for a given
PV field, to maximize the output power of PV array,
is proposed in [7]. Inverters interfacing PV modules
with the grid perform two major tasks—one is to
ensure that PV modules are operated at maximum
power point (MPP), and the other is to inject a
sinusoidal current into the grid. In order to perform
these tasks effectively, efficient stabilization or
control schemes are essential. In a grid-connected
ABSTRACT

Adaptive Control Scheme for PV Based Induction Machine
PV system, control objectives are met by a strategy
using a pulse width modulation (PWM) scheme
based on two cascaded control loops [8].
The two cascaded control loops consist of an
outer voltage control loop to settle the PV array at
the MPP, and an inner current control loop to
establish the duty ratio for the generation of a
sinusoidal output current, which is in phase with
the grid voltage [8]. The current loop is also
responsible for power quality issues and current
protection for which harmonic compensations and
dynamics are the important properties of the
current controller.
Linear controllers such as proportional-integral
(PI), hysteresis, and model predictive controllers
are presented in [9]–[14], which provide
satisfactory operation over a fixed set of operating
points as the system is linearized at an equilibrium
point. Since the PV source exhibits a strongly
nonlinear electrical behavior due to the variation of
solar irradiance and nonlinear switching functions
of inverters. As linear controllers for nonlinear PV
systems affects all the variables in the system and
the electrical characteristics of the PV source are
time varying, the system is not linearizable around
a unique operating point or trajectory to achieve a
good performance over a wide variation in
atmospheric conditions. The restrictions of
operating points can be solved by implementing
nonlinear controllers for nonlinear PV systems.
A sliding-mode current controller for a
grid-connected PV system is proposed in [15],
along with a new MPPT technique to provide robust
tracking performances. In [15], the controller is
designed based on a time-varying sliding surface.
However, the selection of a time-varying surface is
a difficult task, and the system stays confined to
the sliding surface. Feedback linearization has
been increasingly used for nonlinear controller
design. It transforms the nonlinear system into a
fully or partly linear equivalent by canceling
nonlinearities. A feedback linearizing technique
was first proposed in [16] for PV applications where
a superfluous complex model of the inverter is
considered to design the controller. To overcome
the complexity, a simple and consistent inverter
model is used in [17], and a feedback linearization
technique is employed to operate the PV system at
MPP. In [16] and [17], a feedback linearizing
controller is designed by considering the dc-link
voltage and quadrature-axis grid current as output
functions. Power-balance relationships are
considered to express the dynamics of the voltage
across the dc-link capacitor. However, this
relationship cannot capture nonlinear switching
functions between inverter input and output; to
accurately represent a grid-connected PV system
but it is essential to consider these switching
actions. The current relationship between the
input and output of the inverter can be written in
terms of switching functions rather than the power
balance equation. Therefore, the voltage dynamics
of the dc-link capacitor include nonlinearities due
to the switching actions of the inverter.
The inclusion of these nonlinearities in the model
will improve the accuracy; however, the
grid-connected PV system will be partially, rather
than exactly, linearized, as presented in [18].
Although the approaches presented in [16]–[18]
ensure MPP operation of the PV system, they do not
account for inherent uncertainties in the system.
In the design of both linear and nonlinear
controllers for grid-connected PV systems, most of
the difficulties stem from the analytical complexity
of the dynamic model of a PV system,
which, on one hand, exhibits a nonlinear
parametric dependence on the PV array
current–voltage characteristics varying with the
irradiation and temperature levels and, on the
other, a sinusoidal time dependence due to the grid
connection of PV systems. These difficulties may
lead to some barriers in developing a meaningful
and realistic mathematical model. The mismatch
between the mathematical model and true system
may lead to serious stability problems for the
system. Therefore, the designs of robust control
strategies that consider the model uncertainties
are of great importance to design nonlinear
controllers. Variable structure control with sliding
mode, or sliding-mode control is one of the effective
nonlinear robust control approaches since it
provides system dynamics with an invariance
property to uncertainties once the system
dynamics are controlled in the sliding mode.
A sliding-mode controller for grid connected PV
system is presented in [19] and [20] to achieve
robust MPPT under uncertainties within the
system model. With this control approach, the
insensitivity of the controlled system to
uncertainties exists in the sliding mode but not
during the reaching phase, i.e., the system
dynamic in the reaching phase is still influenced by
uncertainties. A mini-max LQG technique is
proposed in [21] to design a robust controller for
the integration of PV generation into the grid where
the higher order terms during the linearization is
considered as the uncertainty. A feed forward
mechanism is proposed in [22] to control the

current and dc-link voltage and the robustness of
this mechanism is analyzed through modal
analysis. A robust fuzzy controlled PV inverter is
presented in [23] for the stabilization of a grid
connected PV system where the robustness is
adopted by using the Taguchi-tuning algorithm.
However, the main difficulties of the robustness
algorithm, as presented in [21] [23], are the
consideration of linearized PV system models that
are unable to maintain the stability of the PV
system over a wide changes in atmospheric
conditions. Although there are some advances in
the robust control of grid-connected PV systems,
research into the robustness
Fig. 1. Three-phase grid-connected PV system.
analysis and the controller design of nonlinear
uncertain PV systems remains an important and
challenging area. Since the feedback linearization
technique is widely used in the design of nonlinear
controllers for power systems, this paper proposed
the extension of the partial feedback linearizing
scheme, as presented in [18], by considering
uncertainties within the PV system model. In this
paper, matching conditions are used to model the
uncertainties in PV systems for given upper
bounds on the modeling error, which include
parametric and state-dependent uncertainties.
These uncertainties are bounded in such a way
that the proposed controller can guarantee the
stability and enhance the performance for all
possible perturbations within the given upper
bounds of the modeling errors of nonlinear PV
systems. The effectiveness of the proposed
controller is tested and compared with that of a
partial feedback linearizing controller without
uncertainties, following changes in atmospheric
conditions.
II. PHOTOVOLTAIC SYSTEM MODEL
The schematic diagram of a three-phase
grid-connected PV system, which is the main focus
of this paper, is shown in Fig. 1. The considered PV
system consists of a PV array, a dc-link capacitor
C, a three-phase inverter, a filter inductor L, and
grid voltages ea, eb, ec. In this paper, the main aim
is to control the voltage vdc (which is also the
output voltage of PV array vpv) across the capacitor
C and to make the input current in phase with grid
voltage for unity power factor by means of
appropriate control signals through the switches of
the inverter.
A. Photovoltaic Cell and Array Model: A PV cell
is a simple p-n junction diode that converts the
irradiation into electricity. Fig. 2 shows an
equivalent circuit diagram of a PV cell that consists
of a light generated current source IL, a parallel
diode, a shunt resistance Rsh, and a series
resistance Rs. In Fig. 2, ION is the diode current
that can be written as
(1)
where α = qAkTC , k = 1.3807 × 10−23 JK−1 is the
Boltzmann’s constant, q = 1.6022 × 10−19 C is the
charge of electron, TC is the cell’s absolute working
temperature in Kelvin, A is the p-n junction ideality
factor whose value is between 1 and 5, Is is the
saturation current, and vpv is the output voltage of
the PV array which is also the voltage across C, i.e.,
vdc. Now,
Fig. 2. Equivalent circuit diagram of the PV cell.
Fig. 3. Equivalent circuit diagram of the PV array.

by applying Kirchhoff’s current law (KCL) in Fig. 2,
the output current (ipv) generated by a PV cell can
be written as
(2)
The light generated current IL depends on the solar
irradiation that can be related by the following
equation:
(3)
where Isc is the short-circuit current, s is the solar
irradiation, ki is the cell’s short-circuit current
coefficient, and Tref is the reference temperature of
the cell. The cell’s saturation current Is varies with
the temperature according to the following
equation [17]:
(4)
Where Eg is the band gap energy of the
semiconductor used in the reference temperature
and solar irradiation.
Since the output voltage of a PV cell is very low, a
number of PV cells are connected together in series
in order to obtain higher voltages. Then, they are
encapsulated with glass, plastic, and other
transparent materials to protect them from harsh
environments and are called a PV module. To
obtain the required voltage and power, a number of
modules are connected in parallel to form a PV
array. Fig. 3 shows an electrical equivalent circuit
diagram of a PV array, where Ns is the number of
cells in series, and Np is the number of modules in
parallel. In this case, the array ipv can be written
as
(5)
B. Three-Phase Grid-Connected Photovoltaic
System ModelIn the state-space form, Fig. 1 can
be represented through the following equations
[17], [18]:
(6)
where Ka, Kb, and Kc are the input switching
signals. Now, by applying KCL at the node where
the dc link is connected, we obtain
(7)
However, the input current of the inverter idc can
be written as [19]
(8)
which yields
(9)
The complete model of a three-phase
grid-connected PV system can be presented by (6)
and (9), which are nonlinear and time variant and
can be converted into a time invariant model by
applying dq transformation using the angular
frequency (ω) of the grid, rotating the reference
frame synchronized with grid where the d
component of the grid voltage Ed is zero [17]. By
using dq transformation, (6) and (9) can be written
as
(10)
where Idq = Tabc dq iabc, edq = Tabc dq eabc, Kdq =
Tabc dq Kabc. Equation (10) represents the
complete mathematical model of a three-phase
grid-connected PV system and this model is a
nonlinear model due to the nonlinear behavior of
the switching signals and the output current (ipv)
of the PV array. The transformation matrix T dqabc

can be written as
(11)
At this point of mathematical modeling, the key
issue the selection of the current component that
can be obtained from the power delivered into the
grid. Since Ed = 0, the real power delivered to the
grid can be written as
(12)
From (12), it can be seen that the maximum power
delivery into the grid can be maintained by
controlling the q component of the grid current,
i.e., Iq . Based on this mathematical model, the
overview of the partial feedback linearizing
stabilization scheme is shown in the following
section.
III. OVERVIEW OF PARTIAL FEEDBACK LINEARIZING
STABILIZATION SCHEME
As the three-phase grid-connected PV system as
represented by (10) has two control inputs (Kd and
Kq) and two control outputs (Iq and vpv), the
mathematical model can be represented by the
following form of a nonlinear multi-input
multi-output (MIMO) system
(13)
The partial feedback linearizing scheme transforms
the nonlinear grid-connected PV system into a
partially linearized PV system, and any linear
controller design technique can be employed to
obtain the linear control law for the partially
linearized system. However, before obtaining a
control law through partial feedback linearizing
scheme, it is essential to ensure the partial
feedback linearizability and internal dynamics
stability of the PV system. The details of partial
feedback linearizability and internal dynamics
stability of the considered PV system are presented
in [18] from where it can be seen that the PV
system is partially linearized and that the internal
dynamic of the PV systems is stable. The partially
linearized PV system can be written
(14)
where z͂ represents the transformed states, and v
represents the linear control inputs that are
obtained through the PI design approach [18]. The
nonlinear control law can be written as
(15)
Equation (15) is the final control law that is
obtained through a partial feedback linearizing
scheme, and the controller ensures the stability of
the PV system for the considered nominal model
and exact parameters of the system need to be
known. However, in practice, it is very difficult to
determine the exact parameters of the system.
Thus, the considered partial feedback linearizing
scheme is unable to maintain the stability of the PV
system with changes in system conditions and the
consideration of uncertainties within the PV
system is necessary, which is shown in the
following section.
IV. UNCERTAINTY MODELING
In a practical PV system, atmospheric conditions
change continuously for which there exists a
variation in cell working temperature, as well as in
solar irradiance. Because of changes in
atmospheric conditions, the output voltage,
current, and power of the PV unit changes
significantly. For example, if a single module of a
series string is partially shaded, and then its
output current will be reduced, which will change
the operating point of the whole string. Since the
amount of the PV generation depends on solar
irradiation that is uncertain, there are
uncertainties in ipv which in turn causes
uncertainties in the current (in the dq-frame, Id
and Iq ) injected into the grid. Moreover, as the
values of the parameters used in the PV model are
not exactly known, there are also parametric
uncertainties. The PV system model as shown by
(10) cannot capture these uncertainties. Therefore,
it is essential to consider these uncertainties within
the PV system model. In the presence of
uncertainties, the nonlinear mathematical model of
the three-phase grid-connected PV system, as

shown in (13), can be represented by the following
equation:
(16)
The uncertainties need to be modeled in such a
way that the controller will robustly stabilize the
original system despite the uncertainties Δf(x) and
Δg(x), i.e., the robust controller will attenuate the
influence of system uncertainties. In order to
achieve the control objective of robust stabilization,
the structure of uncertainties and the locations of
unknown parameters should satisfy the following
conditions:
(17)
which is known as the matching condition [24]. If
this matching condition holds, the following
condition is true:
(18)
where r is the total relative degree of the nominal
system, which is 2 [18], w is the relative degree of
uncertainty Δg(x), and ρ is the relative degree of
uncertainty Δf(x). In order to match the
uncertainties with the PV system model, the
relative degree of the uncertainty Δf should be 2 as
it needs to equal to the relative degree of the
nominal system in (10), which is 2. The relative
degree of the uncertainty Δf can be calculated from
the following equation:
(19)
If the relative degree of Δf corresponding to the
outputs h1 and h2 is 1, then the total relative
degree of Δf will be 2, which will happen if Δf1 and
Δf3 are not equal to zero. To match the uncertainty
Δg, the relative degree of Δg should be equal to or
greater than the relative degree of the nominal
system and will be 2 if the following conditions
hold:
(20)
Where Δg11 must not be zero and either Δg31 or
Δg32 can be zero, to match the uncertainty with
the structure of the PV system. Since the proposed
uncertainty modeling scheme considers the upper
bound of the uncertainties, it is important to set
these bounds, and the controller needs to be
designed based on these
bounds. If the maximum allowable changes in the
system parameters is 30% and the variations in
solar irradiation and environmental temperature
are considered up to 80% of their nominal values.
The partial feedback linearizing scheme as
presented in [18] cannot stabilize the PV system
appropriate if the aforementioned uncertainties are
considered within the PV system model as the
controller is designed to stabilize only the nominal
system. However, in the robust partial feedback
linearizing scheme, the aforementioned
uncertainties need to be included to achieve the
robust stabilization of the grid-connected PV
system. The robust controller design by
considering the aforementioned uncertainties
within the grid-connected PV system model is
shown in the following section.
V. ROBUST CONTROLLER DESIGN
This section aims the derivation of the robust
control law that robustly stabilizes a
grid-connected PV system with uncertainties
whose structures are already discussed in the
previous section. The following steps are followed
to design the robust controller for a three-phase
grid-connected PV system.
1) Step 1 (Partial feedback linearization of grid
connected PV systems): In this case, the partial
feedback linearization for the system with
uncertainties, as shown by (16), can be obtained as
For the PV system, the partially linearized system
can written as

(21)
If v1 and v2 are linear control inputs for the
aforementioned partially feedback linearized
system, (21) can be written as
(22)
Which can be obtained using any linear control
technique, and in this paper, two PI controllers are
used. However,
Fig. 4. Implementation block diagram.
before designing and implementing the controller
based on partial feedback linearizing scheme, it is
essential to check the stability of the internal
dynamics that is similar to that described in [18].
2) Step 2 (Derivation of robust control law): From
(22), the robust control law can be obtained as
follows:
(23)
Equation (23) is the final robust control law for a
three grid connected PV system, and the control
law contains the modeled uncertainties. The main
difference between the designed robust control law
(23) and the control law (15) is the inclusion of
uncertainties within the PV system model. The
performance of the designed robust stabilization
scheme is evaluated and compared in the following
section with our previously published partial
feedback linearizing scheme with no uncertainties
[18]. The performance of the controller is evaluated
in the following section.
VI. INDUCTION MOTOR
An induction motor is an example of
asynchronous AC machine, which consists of a
stator and a rotor. This motor is widely used
because of its strong features and reasonable cost.
A sinusoidal voltage is applied to the stator, in the
induction motor, which results in an induced
electromagnetic field. A current in the rotor is
induced due to this field, which creates another
field that tries to align with the stator field, causing
the rotor to spin. A slip is created between these
fields, when a load is applied to the motor.
Compared to the synchronous speed, the rotor
speed decreases, at higher slip values. The
frequency of the stator voltage controls the
synchronous speed. The frequency of the voltage is
applied to the stator through power electronic
devices, which allows the control of the speed of the
motor. The research is using techniques, which
implement a constant voltage to frequency ratio.
Finally, the torque begins to fall when the motor
reaches the synchronous speed. Thus, induction
motor synchronous speed is defined by following
equation,
(24)
Where f is the frequency of AC supply, n, is the
speed of rotor; p is the number of poles per phase of
the motor. By varying the frequency of control
circuit through AC supply, the rotor speed will
change.
A. Control Strategy of Induction Motor
Power electronics interface such as three-phase
SPWM inverter using constant closed loop Volts l

Hertz control scheme is used to control the motor.
According to the desired output speed, the
amplitude and frequency of the reference
(sinusoidal) signals will change. In order to
maintain constant magnetic flux in the motor, the
ratio of the voltage amplitude to voltage frequency
will be kept constant. Hence a closed loop
Proportional Integral (PI) controller is implemented
to regulate the motor speed to the desired set point.
The closed loop speed control is characterized by
the measurement of the actual motor speed, which
is compared to the reference speed while the error
signal is generated. The magnitude and polarity of
the error signal correspond to the difference
between the actual and required speed. The PI
controller generates the corrected motor stator
frequency to compensate for the error, based on the
speed error.
VII. SIMULATION RESULTS
Fig 5 Matlab/simulation circuit of Adaptive Control Scheme
for Pv Based system
Fig 6 Performance under standard atmospheric conditions
(Blue line—grid voltage, red line—grid current with the
RPFBLSS, and green line—grid current with the PFBLS)
Fig 7 Performance under changing atmospheric conditions
(Blue line—grid voltage, red line-grid current with the
RPFBLSS, and green line—grid current with the PFBLS).
Fig 8 Performance under a three-phase short-circuit fault
(Red line—grid current with the RPFBLSS, and green
line—grid current with the PFBLS).
Fig 9 Matlab/simulation circuit of Adaptive Control Scheme
for Pv Based system with Induction Motor
Fig 10 simulation wave form of line output voltage with IM
Fig 11 simulation wave form of line output current with IM
Fig 12 simulation wave form of phase voltage with IM

Fig 13 simulation wave form of stator current, speed and
torque
VIII. CONCLUSION
In this paper, a robust stabilization scheme is
considered by modeling the uncertainties of a three
phase grid-connected PV system based on the
satisfaction of matching conditions to ensure the
operation of the system at unity power factor. In
order to design the robust scheme, the partial
feedback linearization approach is used, and with
the designed scheme, only the upper bounds of the
PV systems’ parameters and states need to be
known rather than network parameters, system
operating points, or nature of the faults. The
resulting robust scheme enhances the overall
stability of a three-phase grid connected PV
system, considering admissible network
uncertainties. Thus, this stabilization scheme has
good robustness against the PV system parameter
variations, irrespective of the network parameters
and configuration. Future work will include the
implementation of the proposed scheme on a
Induction machine system to study the
characteristics of speed, torque.
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