Nonlinear Observer-Based Control for Three phase Grid Connected
Photovoltaic System
Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon
Adekanle, Mohammed El Malah
Department of Applied Physics
University hassan 1
ASTI Laboratory
Morocco
Abstract: - This paper presents a nonlinear observer-based control strategy for a photovoltaic system. This last
consists of a photovoltaic generator PVG coupled to a three phase load and three phase grid by a three phase
voltage source inverter VSI without DC-DC converter. The controller is developed by using Backstepping
method based on d-q transformation of a new model of the global system. Then, to minimize the number of
sensors used for the implantation of the controller, a nonlinear state observer is proposed for estimate the
inverter current. The main objectives of this control strategy are to extract maximum power from the PV array
with very good effectiveness and to achieve the unity power factor and low harmonic distortion in the level of
the grid power flow. The simulation results proved that the observer-based control method has been achieved
all the objectives with high dynamic performance under different operating conditions such as atmospheric
conditions changes and system disturbance.
Key-Words: - Voltage source Inverter; Maximum Power Point; Unity power factor; Photovoltaic Generator;
Power Conversion Harmonics; Pulse Width Modulation Converters; Reactive Power compensation; Nonlinear
load; Bakstepping; State observer.
1 Introduction The Global Energy demand is increasing due to
Technological development, Industrial growth and
rising population density [1]. At the same time, pollution
from the use of fossil fuels urges for a need to find an
alternate source of energy. In this way, photovoltaic
energy is one of the most important sources of renewable
energy, and the photovoltaic system is one of the most
important energy solutions; the energy generated by
photovoltaic system represents a large part of the total
amount of solar energy produced [2]. We find two types
of photovoltaic systems, the autonomous system and grid
connected photovoltaic system. The grid-connected PV
system is becoming more used to meet global demand for
electrical energy [3].
This paper presents an advanced control strategy
using Backstepping method and nonlinear state observer
of a three phase grid single stage connected photovoltaic
system feeding non-linear load. The main objectives of
this observer-based control are:
• Minimizing the number of the sensors used
in the global PV system
• Extracting maximum output power from the
PV array.
• Operation with a unity power factor UPF
and low harmonic distortion.
• Controlling the power flow between the grid
and the rest of grid connected PV system.
There are some research efforts to realize these goals
[3]-[5]. The above works have not been able to achieve
these objectives with a good performance and they
haven’t considered all the constraints of the photovoltaic
system. Moreover, these researches don’t try to minimize
the number of sensors used in the implementation of the
controller which have some effects. Indeed, the
integration of large number of both voltage and current
sensors decreases the controller efficiency and increases
system complexity, cost, space, and reduces system
reliability. Hence, the necessity of using an observer in
the control loops to complete the information about the
state variables. A few works have been realized in order
to reduce the current sensors for older categories of PV
system [6], [7], [8]. The work presented in [8] proposed a
simplify method to control a single-phase single-stage
grid-connected PV inverter with a low number of sensors.
The direct MPPT developed in this work has been
achieved the MPPT with a best efficiency than the
performance of the controller developed in [9 10 11 12].
But the work proposed by [8] presents also some
drawbacks. Indeed, the controlled PV system track the
MPPT with bad response time more than 2s and it
oscillates around the PVG MPP. This fact is not normal,
because the system output PV power can’t exceed the
normal MPP of the PVG. Furthermore, the research
described in [8] don’t try to achieve the UPF; Knowing
that in single stage PV grid connected system the MPPT
WSEAS TRANSACTIONS on SYSTEMS
Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon Adekanle,
Mohammed El Malah
E-ISSN: 2224-2678 235 Volume 18, 2019
and UPF must be controlled simultaneously, a task that is
quite complex[13]. So, we can see that the work [8] is
limited and incomplete even if the experimentation
validation has been carried out. In this paper the nonlinear state observer is proposed
to minimize the number of sensors used by the
Backstepping controller. This observer is designed to
directly estimate the dq0 transformation components of
the inverter current [14]. That permits to eliminate the
inverter current sensor and the dq0 transformation block
applied to convert the three phase current to double phase
current. The elimination of this sensor reduces de
complexity of the global PV system installation and
enhances the robustness of the Backstepping controller in
front of noise measurement. Furthermore, this control
strategy can operate independently of sensor calibration
and accuracy failures, data acquisition and processing
errors.
The elaborated state observer has correctly estimated
the inverter current with a very good precision and fast
response time less than the dynamic behavior variation of
the system. Using the information generated by the
observer, the Backestepping controller has achieved the
MPPT with very good performances during sudden
atmospheric conditions changes. The observer-based
control has controlled also the inverter to compensate
with a good precision the reactive power caused by the
load, which assures the unity power factor operation of
the system. Moreover, this strategy has demonstrated a very good robustness in the presence of the system
disturbance. Mathematical analyses and simulation
results have proved the high performance of this control
strategy. The rest of the paper is organized as follows: the
system description and mathematical model of the global
system are present in Section II. The controller design for
the global system is illustrated in Section III. In Section
IV, a high gain state observer is developed to estimate the
inverter current. Section V shows the simulation results
.Finally, a short conclusion will be presented.
2 System Description and Modelling Fig. 1 shows a PVG connected to the grid. It
consists of a PVG coupled to a three phase grid by
an input capacitor Cp, Voltage Source Inverter VSI
and low pass filter (L,r). Moreover, a three phase
load is also coupled to the system; this load can be
supplied by the PVG power if it is sufficient, if it
isn’t enough the load will be supplied by the PVG
and the grid. But when there is no sunlight, the load
will be provided by the grid and the inverter will
just compensate the Reactive Power caused by this
load. The input capacitor Cp is used to store the
energy extracted from the PVG and smooth the
inverter input voltage ripple. The filter is integrated
to filter out harmonic distortion provoked by the
inverter switching.
Fig.1. PVG connected to a three phase grid and nonlinear
load.
The PVG power equation is given by:
Pv = vp × ip (1)
Where vp and ip are the PVG voltage and current
respectively.
The mathematical model of the global system is given
by:
{
dvp
dt=
1
Cp
Pv
vp−
1
Cp
Pi
vp
dia
dt= −
r
Lia −
1
Lea +
1
Lva
dib
dt= −
r
Lib −
1
Leb +
1
Lvb
dic
dt= −
r
Lic −
1
Lec +
1
Lvc
(2)
Where Pi is the inverter Active Power, (ia, ib, ic) and
(va, vb, vc) are the inverter currents and
voltages,(va, vb, vc) represents also the PWM references
of the inverter,(ea, eb, ec)are the three grid voltages, Cp
is the input capacitor, L is the filter’s inductance and r is
the filter‘s resistance.
The model of the global system in the park axes is
given by the following equation:
{
dvp
dt= vp =
1
Cp
Pv
vp−
1
Cp
1
vp
3
2EdId
dId
dt= Id = −
r
LId + wIq −
1
LEd +
1
LVd
dIq
dt= Iq = −
r
LIq − wId −
1
LEq +
1
LVq
(3)
Where:
(
EdEqE0
) = Pabcdq0
(
eaebec);(
IdIqI0
) = Pabcdq0
(
iaibic
);(
VdVqV0
) = (
vavbvc).
(Id, Iq), (Vd, Vq) and (Ed, Eq)are respectively the
coordinates in the d-q axis of the inverter current, the
PWM references and the grid voltages, 𝑤 is the
gridpulsation. With Pabcdq0
is the Park transformation
matrix which is given below [14]:
Pabcdq0
=
2
3
(
sin (θ) sin (θ−
2π
3) sin (θ−
4π
3)
cos (θ) cos (θ−2π
3) cos (θ−
4π
3)
1
2
1
2
1
2 )
(4)
WSEAS TRANSACTIONS on SYSTEMS
Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon Adekanle,
Mohammed El Malah
E-ISSN: 2224-2678 236 Volume 18, 2019
θ represents the phase angle of the grid
calculated by the PLL technique [15].
After having modelled the system, the next
section will illustrate the design of the control
strategy.
3 Nonlinear observer and Control
Strategy
3.1 Nonlinear State Observer Design To estimate unmeasured state variables or replace
high priced sensors the observers are designed. An
observer can estimate also the full state using
knowledge of the available measurements output
and input of the system. In this work, the nonlinear
observer is used to estimate the d-q components of
the inverter current (𝐼𝑑, 𝐼𝑞 ).
The model of the global system in the Park axes
(3) can be represented in a general form which
belong to the class of state affine systems uniformly
observable allowing the synthesis of the state
observer [16], [17], [18], [19], [20].
{
(
��𝐼��𝐼��
) = (0 −
1
𝐶𝑃
3
2𝐸𝑑 0
0 0 𝑤0 0 0
)(
𝑍𝐼𝑑𝐼𝑞
)
+
(
−1
𝐶𝑃𝐼𝑝√2𝑍
−𝑟
𝐿𝐼𝑑 −
𝐸𝑑
𝐿+𝑉𝑑
𝐿
−𝑟
𝐿𝐼𝑞 −𝑤𝐼𝑑 −
1
𝐿𝐸𝑞 +
1
𝐿𝑉𝑞)
𝑦𝑚 = 𝑍
(5)
With 𝑍 =𝑉𝑝
2
2,
We define also the following variables:
𝑈 = (𝑉𝑑, 𝑉𝑞)is theinput controlvector, 𝑥 =
(𝑍, 𝐼𝑑 , 𝐼𝑞)𝑇 is the state variables vector, 𝑦𝑚 is the
measured output that represents the PVG voltage
state and 𝑠 = (𝐼𝑝, 𝐸𝑑 , 𝐸𝑞)is a known signal.
The global system (5) can be represented in a
more general observable canonical form given by:
{�� = 𝐴(𝑈)𝑥 + 𝜑(𝑥, 𝑈, 𝑠)
𝑦𝑚 = 𝐶𝑥 (6)
Where:
𝜑(𝑥, 𝑈, 𝑠) =
(
−1
𝐶𝑃𝐼𝑝√2 × 𝑍
−𝑟
𝐿𝐼𝑑 −
𝐸𝑑𝐿+𝑉𝑑𝐿
−𝑟
𝐿𝐼𝑞 −𝑤𝐼𝑑 −
1
𝐿𝐸𝑞 +
1
𝐿𝑉𝑞)
And:
𝐶 = [1 0 0], 𝐴 = (0 −
1
𝐶𝑃
3
2𝐸𝑑 0
0 0 𝑤0 0 0
)
𝜑(𝑥, 𝑈, 𝑠) is a locally Lipschitz function [20].
The control input 𝑈is assumed to be regularly
persistent [21].
The following form is estimating states by the
high-gain nonlinear observer:
{
�� = 𝐴(𝑈)𝑥 + 𝜑(𝑥, 𝑈, 𝑠) − 𝑆−1𝐶𝑇(��𝑚 − 𝑦𝑚)
�� = −𝛽𝑆 − 𝐴𝑇(𝑈)𝑆 − 𝑆𝐴(𝑈) + 𝐶𝑇𝐶��𝑚 = 𝐶𝑥
(7)
Where:
𝑆 is a symmetric positive definite matrix and a
solution of the differential Lyapunov equation, 𝛽 is
the setting parameter of the observer which must be
positive and sufficiently large, 𝑥 = (��, 𝐼𝑑 , 𝐼𝑞) is the
estimation of the full state vector.
Applying this observer method the estimation
error ��𝑚 − 𝑦𝑚 converge exponentially to zero in
function of the setting parametervalue 𝛽.Which
means that the estimation vector 𝑥 tracks with a
good effectiveness the real state vector𝑥 of the PV
system if 𝛽 is sufficiently large. 𝑥 Will be used by
the Backstepping control laws developed after.
3.2 Nonlinear observer based control
strategy The control strategy has been design by the
Backstepping method [22] in order to realize the
following objectives under climatic condition
changes and system perturbation with a very good
performance and high robustness:
• Extract maximum output power from the
PVG and convert all this power on Active Power.
• Compensate Reactive Power and harmonic
distortion caused by any kind of load.
3.2.1 MPPT and Active Power Controller The output selected to control the MPPT is the derivative
of the PVG power with respect to the PVG voltage. Its
form is defined by: 𝛿𝑃𝑣
𝛿𝑣𝑝= 𝑖𝑝 + 𝑣𝑝
𝜕𝑖𝑝
𝜕𝑣𝑝 (8)
This output must converge to zero in order to
extract the MPP from the PVG with a very good
precision [23], [24].
The Backstepping control of the first output is
designed as follows: Defining the first tracking error between the output and
its reference as:
WSEAS TRANSACTIONS on SYSTEMS
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E-ISSN: 2224-2678 237 Volume 18, 2019
𝜀1 =𝛿𝑃𝑣
𝛿𝑣𝑝− 0=𝑖𝑝 + 𝑣𝑝
𝜕𝑖𝑝
𝜕𝑣𝑝 (9)
Using model (3), the derivative of 𝜀1 can be
developed as:
ε1 = (2∂ip
∂vp+ vp
∂2ip
∂vp2) (
1
Cp
Pv
vp−
1
Cp
1
vp
3
2Ed𝐼𝑑) (10)
The candidate Lyapunov function is chosen as:
𝑉1 =1
2𝜀12 (11)
Its derivative is as follows:
V1 = 𝜀1𝜀1 = 𝜀1 (2𝜕𝑖𝑝
𝜕𝑣𝑝+ 𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2) (
1
𝐶𝑝
𝑃𝑣
𝑣𝑝−
1
𝐶𝑝
1
𝑣𝑝
3
2𝐸𝑑𝐼𝑑)(12)
This derivative must be negative. For that a
virtual control law 𝛼 is chosen to get the following
equation:
(2∂ip
∂vp+ vp
∂2ip
∂vp2) (
1
Cp
Pv
vp−
1
Cp
1
vp
3
2Edα) = −k1ε1
(13)
Where:
α = (𝐼𝑑)desired (14)
k1 is a positive setting parameter of the
controller.
Using equation (13), the expression of 𝛼is
developed as:
α =−11
Cp
3
2Edvp (
−k1ε1
(2∂ip
∂vp+vp
∂2ip
∂vp2)
−1
Cp
Pv
vp)
(15)
It’s derivate is calculated as follows: �� =
−11
𝐶𝑝
3
2𝐸𝑑��𝑝 (
−𝑘1 1
(2𝜕𝑖𝑝
𝜕𝑣𝑝+𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)
−1
𝐶𝑝
𝑃𝑣
𝑣𝑝) −
−11
𝐶𝑝
3
2𝐸𝑑𝑣𝑝 (
−𝑘1 1(2𝜕𝑖𝑝
𝜕𝑣𝑝+𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)−𝑘1 1(3
𝜕2𝑖𝑝
𝜕𝑣𝑝2+𝑣𝑝
𝜕3𝑖𝑝
𝜕𝑣𝑝3)��𝑝
(2𝜕𝑖𝑝
𝜕𝑣𝑝+𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)
2 −
1
𝐶𝑝
𝑃��𝑣𝑝−𝑃𝑣��𝑝
𝑣𝑝2 ) (16)
With the above choice, the derivative of the
Lyapunov function becomes necessarily negative.
Its expression is given by using (12), (13) and (14):
V1 = −𝑘1𝜀12 (17)
Equation (15) assumes that the virtual control
lawα is equal to the estimateddirect current
component𝐼𝑑. Moreover, in reality there is an error
between them. This error is defined as:
𝜀2 = 𝐼𝑑 − 𝛼 (18)
So,
𝐼𝑑 = 𝜀2 + 𝛼 (19)
Substituting (19) in (12) and using (13), the
novel expression of ��1 is given by:
V1 = −𝑘1𝜀12 − (2
𝜕𝑖𝑝
𝜕𝑣𝑝+ 𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)
1
𝐶𝑝
1
𝑣𝑝
3
2𝐸𝑑𝜀1𝜀2
(20)
Therefore, ��1 is no longer necessarily negative.
For that a second Lyapunov function is proposed
which is defined by:
𝑉2 = 𝑉1 +1
2𝜀22 (21)
Its derivative is given by:
��2 = ��1 + 𝜀2𝜀2 (22)
By using (19), the derivative of ε2 is given by:
𝜀2 = 𝐼�� − ��=−𝑟
𝐿𝐼𝑑 + 𝑤𝐼𝑞 −
1
𝐿𝐸𝑑 +
1
𝐿𝑉𝑑 − ��
(23)
Substituting (20) and (23) in (22) the final
expression of V2 is as follows:
��2 = −𝑘1𝜀12 − ⌊(2
𝜕𝑖𝑝
𝜕𝑣𝑝+ 𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)
1
𝐶𝑝
1
𝑣𝑝
3
2𝐸𝑑𝜀1 +
(−𝑟
𝐿𝐼𝑑 + 𝑤𝐼𝑞 −
1
𝐿𝐸𝑑 +
1
𝐿𝑉𝑑 − ��)⌋ 𝜀2
(24)
In order to stabilize 𝜀1 and 𝜀2 to zero,V2 must be
strictly negative. For this reason, the following
equality is imposed:
−(2𝜕𝑖𝑝
𝜕𝑣𝑝+ 𝑣𝑝
𝜕2𝑖𝑝
𝜕𝑣𝑝2)
1
𝐶𝑝
1
𝑣𝑝
3
2𝐸𝑑𝜀1 + (−
𝑟
𝐿𝐼𝑑 + 𝑤𝐼𝑞 −
1
𝐿𝐸𝑑 +
1
𝐿𝑉𝑑 − ��) = −𝑘2𝜀2 (25)
Where 𝑘2 is a positive control parameter.
By substituting (25) into (24), the desired form
of V2 is obtained as:
V2 = −𝑘1𝜀12 − 𝑘2𝜀2
2 (26)
Using (25) and replacing the d-q components of
the inverter current (𝐼𝑑 , 𝐼𝑞) with their
estimatedvalues(Id, Iq), the expression of real
control law which guarantees the desired form of V2
is as follows:
Vd = L [−k2ε2 + (2∂ip
∂vp+ vp
∂2ip
∂vp2)
1
Cp
1
vp
3
2Edε1 −
(−r
LId + wIq −
1
LEd − α)] (27)
By applying this control law, V2 become
obligatory strictly negative and ε1 converge
asymptotically to zero, which guarantees the pursuit
of the MPP with a very good precision and fast
response time. Moreover, the input voltage is
WSEAS TRANSACTIONS on SYSTEMS
Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon Adekanle,
Mohammed El Malah
E-ISSN: 2224-2678 238 Volume 18, 2019
constant; consequently all the PVG power will be
converted by the inverter to active power which
means that the Active Power delivered by the
inverter is maximized.
In this part, the maximization of the inverter
Active Power output has been realized; the next part
consists of controlling the inverter Reactive Power.
3.2.2 Reactive Power Controller The objective in this subsection is to
compensate the Reactive Power and harmonic
distortion caused by the load, in order to
achieve the Unity Power Factor in the level of
the power exchange between the grid and the
PVG system. For that, the inverter must inject
Reactive Power Qiequal to the Reactive Power
caused by the load QL. The load and the inverter
Reactive Power are given by using the
mathematical expressions in dq0 frame as
follows [25]:
𝑄𝐿 = −3
2𝐸𝑑𝐼𝑞𝑙 (28)
𝑄𝑖 = −3
2𝐸𝑑𝐼𝑞 (29)
Where:
(
𝐼𝑑𝑙𝐼𝑞𝑙𝐼𝑙0
) = 𝑀𝑎𝑏𝑐𝑑𝑞0
(
𝑖𝑙𝑎𝑖𝑙𝑏𝑖𝑙𝑐
)
Knowing that the relation below must be realized
𝑄𝑖 = 𝑄𝐿 (30)
So, the reference 𝐼𝑞𝑟𝑒𝑓 of the second output 𝐼𝑞
can be calculated by using (29) and (30) as follows:
𝐼𝑞𝑟𝑒𝑓 = −2
3𝐸𝑑𝑄𝐿 (31)
The Backstepping control law linked to the
second output is developed as follows: Let’s define the tracking error:
𝜀3 = −𝐼𝑞𝑟𝑒𝑓 (32)
Its Lyapunov function is defined as:
𝑉3 =1
2𝜀32 (33)
Its derivative with respect to time and using (32)
and (33):
��3 = 𝜀3𝜀3 = 𝜀3(𝐼�� − 𝐼��𝑟𝑒𝑓) (34)
By using (3) of Iq, this expression can be
developed as:
��3 = 𝜀3𝜀3 = 𝜀3 (−𝑟
𝐿𝐼𝑞 − 𝑤𝐼𝑑 −
1
𝐿𝐸𝑞 +
1
𝐿𝑉𝑞 −
I𝑞𝑟𝑒𝑓)(35)
The derivative of V3must be negative. For that
the following condition is proposed:
−𝑟
𝐿𝐼𝑞 − 𝑤𝐼𝑑 −
1
𝐿𝐸𝑞 +
1
𝐿𝑉𝑞 − 𝐼��𝑟𝑒𝑓 = −𝑘3𝜀3
(36)
With k3 is a positive setting parameter.
Therefore, the new expression of ��3 is given by
using (35) and (36) as follows:
��3 = −𝑘3𝜀32 (37)
Therefore, V3 is negative
By using (36) and introducing estimated values
(Id, Iq) of the d-q components of the inverter
current (𝐼𝑑, 𝐼𝑞), the control law 𝑉𝑞 is given by:
𝑉𝑞 = 𝐿 [−𝑘3𝜀3 + 𝑤Id +𝑟
𝐿Iq +
1
𝐿𝐸𝑞 + 𝐼��𝑟𝑒𝑓]
(38)
The quadratic control law Vq forces the
Lyapunov function V3 to be negative and the
tracking error ε3 to converge to zero, which
guarantees the asymptotic convergence of the
quadratic component estimates 𝐼𝑞 to its reference
Iqref. Finally, the Reactive Power and harmonic
component caused by the load have been
compensated with a very good performance.
The fig. 2 illustrates the block diagram of the PV system with the High-gain nonlinear observer and the Backstepping controller.
Fig.2. Block diagram of the PV system and the nonlinear
observer based Backstepping controller.
The PWM references Ra, Rb and Rc are generated by
the inverse dq0 transformation of the control laws Vd and
Vq. The PWM outputs μ1, μ
2 and μ
3 are used to generate
the switching signals of the inverter G1∓, G2∓, G3∓ able to
achieve the controller objectives with a very good
efficiency.
Where:
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Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon Adekanle,
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E-ISSN: 2224-2678 239 Volume 18, 2019
μi=1..3
= {1 → Gi+: on; Si−: off
0 → Si+: off; Si−: on
All the performances of the nonlinear observer-based
Backstepping controller will be illustrated in the next
section by using the simulation results under
MATLAB/SIMULINK.
4 Simulation Results and Analysis In order to verify the performance and robustness of
the proposed observer and control strategy, a PVG
system and the nonlinear observer based
Backstepping control is built in Simulink/Matlab.
The parameters of both the PV system and the
observer-based controller are summarized in Table
1. The scenarios used in this simulation are shown
in Figure 3. It considers a solar irradiation changes
from 600W/m2 to 100W/m
2 at 0.5s and from 100
W/m2 to 1000W/m
2 at 1s. It considers also a
temperature changes from 25°C to 50°C at 1.5s. At
2s the disturbance of the input capacitor Cp by 40%
of its nominal value is introduced. In the end of the
scenarios, the load current harmonic pollution by
6% of its fundamental value is applied from 2.5s to
3s.
The maximum power of the simulated PVG is
about 55,94KW under the standard atmospheric
conditions.
The nonlinear load can be any kind of load; In
fact, the observer based Backstepping controller is
designed independently of the kind of load. In this
simulation we considered an inductive load.
Table 1: The parameters of the PV system and
the controller
System Parameters Controller and observer
parameters
Input capacity: Cp=4700 μF k1=50
k2=5000
Filter inductance: L=3 mH
Filter resistance: r=0.002Ω k3=1100
Load inductance: LC=20 mH
Load resistance: Rc=10Ω PWM frequency: 10 KHz
Grid voltage: 380V
Grid frequency: 50 Hz Ө=50000
Figs. 4 to 6 represent, respectively 𝑉p, ��𝑑 and ��𝑞
which are the estimated values of the GPV voltage, the
inverter direct and quadratic currents generated by the
nonlinear High Gain Observer. These simulation results
show that the state variables estimated converge rapidly
with a very good precision to the real state variables of
the PV system. The estimated states are used by the
control strategy, which minimizes the number of sensors
used.
The PWM references are shown in Fig. 7. The notice
is that the waveform of these references doesn’t contain
distortion or fluctuation. These last can saturate the
inverter by producing a high frequency PWM switching
signal.
Fig. 8 shows the controlled first output 𝛿𝑃𝑣
𝛿𝑣𝑝 that
represents the derivative of PVG power with respect to
its voltage. This output converge asymptotically to zero
under the scenarios conditions, which guarantees the
achievement of the MPPT with excellent performance;
precision and fast response time and high robustness in
the presence of system disturbance as shows in fig. 9.
Fig. 10 shows that the totality of the PVG power has
been converted to Active Power by the inverter.
Effectively, the inverter Active Power converges
precisely and rapidly to the PVG power despite the hard
scenario conditions.
Fig. 11 illustrates the Active Power flow between
the inverter, the load and the grid. We remark that
the load Active Power is stable. The load is supplied
by the inverter Active Power in case if it is
sufficient and the rest of the inverter Active Power
is injected in to the grid. If the inverter active power
is not enough, the load is supplied by both the
inverter Active Powers and the grid.
The curve of the second output 𝐼𝑞 is shown in
fig. 12.It converges very quickly to its reference
with very good precision. This realization
compensates the harmonic distortion and Reactive
Power caused by the load under any condition as
shown in fig. 13. From fig. 14 it’s clear that the
Reactive Power in the level of grid power flow is
null.
Fig. 15, fig. 16 and fig. 17 show the high
performances of the UPF achievement under
atmospheric condition changes, system parameters
disturbance and load current harmonic pollution.
Indeed, the grid current is in phase with the grid
voltage during the simulation conditions.
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Hicham Bahri, Khadija Oualifi, Mohamed Aboulfatah, M’hammed Guisser, Oluwaseun Simon Adekanle,
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E-ISSN: 2224-2678 240 Volume 18, 2019
Fig.3. Simulation scenarios.
Fig.4. Real and estimated voltage.
Fig.5. Real and estimated direct component of the
inverter current.
Fig.6. Real and estimated quadratic component of the
inverter current.
Fig. 7. The inverter PWM references.
Fig.8. The curve of the derivative of the PVG power with
respect to PVG voltage 𝛿𝑃𝑣
𝛿𝑣𝑝.
Fig. 9. MPPT achievement under the scenarios conditions.
Fig.10. The behavior of the inverter Active Power in function
of the fast variation of the PVG power
Fig. 11. Active Power exchanges between the inverter, the grid
and the load.
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E-ISSN: 2224-2678 241 Volume 18, 2019
Fig. 12.The curve of the quadratic component current of the
inverter Iq.
Fig. 13. Compensation of the load Reactive Power by the
inverter Reactive Power
Fig. 14. Grid Reactive Power
Fig.15. Phase ‘a’ of the grid voltage and current
(achievement of UPF under sudden changes of the PVG
output power with very fast response time).
Fig.16. Phase ‘a’ of the grid voltage and current
(achievement of UPF in presence of the capacitor Cp
disturbance)
Fig.17. Phase ‘a’ of the grid voltage and current
(achievement of UPF in presence of the load current
harmonic pollution).
4 Conclusion This paper presented a nonlinear observer-based
control strategy for a three phase load and grid
connected PV system. The nonlinear observer
proposed in order to estimate the inverter current
allows to minimize the number of sensors used in
the PV installation, which decreases mainly system
cost and reduces instability of the controller by
elimination of measurement noise. A Backstepping
method based on Lyapunov stability approach and
dq0 transformation of the PV system model is
employed to design the controller. The main focus
of this control strategy is to achieve the UPF and
MPPT under different conditions by controlling the
power switches of DC/AC inverter. The best
advantage of this controller with less sensors is its
robustness in the presence of system disturbance
and abrupt climatic condition changes.
Mathematical studied has been demonstrated the
Lyapunov stability of the global system and
simulation results proved that the proposed control
strategy has realized the MPPT and the UPF with a
very good precision and fast response time in
presence of any operation conditions, which
demonstrates the Efficiency and robustness of this
strategy. The next step will be devoted to
experimental validation of the nonlinear observer-
based controller.
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Mohammed El Malah
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