Nonlinear Observer-Based Control for Three phase Grid … · 2019-10-30 · connected photovoltaic system. The grid-connected PV system is becoming more used to meet global demand

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

[email protected]

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)



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:



Mohammed El Malah

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


𝜕2𝑖𝑝

𝜕𝑣𝑝2)−𝑘1 1(3

𝜕2𝑖𝑝

𝜕𝑣𝑝2+𝑣𝑝

𝜕3𝑖𝑝

𝜕𝑣𝑝3)��𝑝

(2𝜕𝑖𝑝


𝜕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


𝜕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


𝜕2𝑖𝑝

𝜕𝑣𝑝2)

1

𝐶𝑝

1

𝑣𝑝

3

2𝐸𝑑𝜀1 +

(−𝑟


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


𝜕2𝑖𝑝

𝜕𝑣𝑝2)

1

𝐶𝑝

1

𝑣𝑝

3

2𝐸𝑑𝜀1 + (−

𝑟


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



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:



Mohammed El Malah

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.



Mohammed El Malah

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.



Mohammed El Malah

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).


(achievement of UPF in presence of the capacitor Cp

disturbance)


(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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Nonlinear Observer-Based Control for Three phase Grid … · 2019-10-30 · connected photovoltaic system. The grid-connected PV system is becoming more used to meet global demand