dynamicmodelingandrobustcontrolbyadrcof grid...

Research ArticleDynamic Modeling and Robust Control by ADRC ofGrid-Connected Hybrid PV-Wind Energy Conversion System

Imad Aboudrar Soumia El Hani Mohamed Saleck Heyine and Nisrine Naseri

Energy Optimization Diagnosis and Control Centre de Recherche en Sciences et Techniques de lrsquoIngenieur et de la SanteENSET Mohammed V University Rabat Morocco

Correspondence should be addressed to Imad Aboudrar imadaboudrarum5snetma

Received 19 June 2019 Accepted 13 September 2019 Published 20 October 2019

Academic Editor Antonino Laudani

Copyright copy 2019 Imad Aboudrar et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

is work presents linear and nonlinear control strategies applied to a grid-connected multiple-source renewable energy system(wind and photovoltaic) in order to extract the maximum power and to enhance the control of the active and reactive powers Anew robust control strategy known as the active disturbance rejection control (ADRC) is proposed and applied to the hybridrenewable energy system (HRES) and it is based on the extended state observer (ESO) which allows us to estimate the internal andexternal disturbances such as modeling errors and parameter variations e studied system consists of two conversion chainswhich are linked via a common DC bus and interconnected to the grid through a voltage source inverter (VSI) the first chainconsists of a PV system and a DC-DC boost converter and the second chain consists of a direct-driven wind turbine permanentmagnetic synchronous generator (PMSG) and of a ACDC rectifier converter e extraction of maximum power from the PVsystem and the wind energy conversion system is ensured by using the voltage based perturb and observe (VPO) and the optimaltorque control (OTC)MPPT techniques respectivelye ADRC technique is utilized to control the active and reactive powers byacting on the grid currents In order to verify and validate the effectiveness of the proposed control strategy a detailedmodel of thestudied system is designed and evaluated under the MATLABSimulink softwaree simulation results prove the effectiveness ofthe MPPT techniques in terms of maximum power extraction during the variation in the environmental conditions Additionallythe regulation of active and reactive powers is ensured by ADRC and the system is operating at a unity power factor Moreover itis demonstrated that the suggested strategy is efficient in terms of fast tracking and robustness to internal and external dis-turbances compared to the classical PI controller

1 Introduction

Since the beginning of the century global energy con-sumption has been growing very strongly in all regions ofthe world It seems that on a trend basis energy con-sumption will continue to increase driven by economicgrowth on the one hand and by the increase in per capitaelectricity consumption on the other hand regardless of thescenarios considered [1] For this reason renewable ener-gies appear today and in the long term as the solution thatcovers this energy requirement by reducing the majordisadvantages of fossil fuels such as greenhouse emissions[2] ey have become an essential form of energy due totheir flexibility simplicity use and the multiplicity of fields

of activity in which they are called upon to play a role esemodes of production as well as the associated means ofdistribution are subject to deep changes over the next fewdecades [3]

Available in quantities greater than humanityrsquos currentenergy needs the resources of renewable energy also rep-resent an opportunity for more than two billion peopleliving in remote areas to have access to electricity Howeverthese renewable energy sources have a drawback that theiroutput characteristic change becomes extreme because itsignificantly depends on climatic conditions as solar irra-diance and temperature in PV systems and wind speed inthe wind turbines [4] Consequently for better operation ofthese systems maximum power point tracking (MPPT)

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 8362921 19 pageshttpsdoiorg10115520198362921

algorithms are needed to improve the energy efficiency of bothPV and wind systems In this context several research hasbeen conduct in the literature going from the utilization ofclassical algorithms such as perturb and observe (PO) in-cremental conductance (INC) and hill climbing search (HCS)[5 6] for both PV and WECS applications to those based onartificial intelligence as fuzzy logic and neural networks [7]

e grid-side converter is a necessary element in anelectrical power generation system for obtaining sinusoidalwaveforms with low total harmonic distortion Neverthe-less the performance of the system depends largely on thecontrol strategy applied by the grid-side converter [8]erefore several control techniques for the voltage in-verter have been discussed in the literature Among themin [9] the authors deals with a new nonlinear backsteppingsliding mode control for photovoltaic- (PV-) based gridinteractive voltage source converter (VSC) system and anew small signal stability phenomenon is depicted by themultivariable dynamic model of the proposed PV-basedgrid converter system where PV penetration as well asnonlinear control parameter optimization practices isconsidered in this paper In [10] the authors presenteddifferent topologies and control strategies for grid-con-nected photovoltaic systems and the following sectionsreport investigate and present control structures forsingle-phase and three-phase inverters Some solutions tocontrol the power injected into the grid and functionalstructures of each configuration are proposed Jain et al in[11] presented a review for the control strategies applied tothe grid-connected PMSG-based wind turbines a com-parative study of rotor flux-oriented control and directtorque control (DTC) techniques applied in the generator-side converter of PMSG wind turbine application for grid-side converter and various control schemes are developedmainly based on voltage-oriented control (VOC) or ondirect power control (DPC) And authors in [12] havepresented a sensorless maximum power point tracking(MPPT) method for a hybrid photovoltaic-wind systemwhich consists of photovoltaic (PV) system and doubly fedinduction generator (DFIG) wind turbine (WT) eperformance of the proposed method is demonstrated inthe simulation study and the three converters can workvery well to handle the power flow under various operationscenarios such as variations of mechanical power andirradiation changes of DC-link voltage Hence the pro-posed system can be a cost-effective alternative of the twoseparated systems

In general the most commonly used control strategy toconnect the power generation systems with the utility powergrid is based on the proportional integrator controller due toits simple structure as presented in [13 14] Considering theinternal and external disturbances of grid-connected mul-tiple-source renewable energy systems such as a hybrid PV-wind system the control objective becomes more difficultand ordinary controllers like PI and PR controllers are notsufficient erefore several researchers have proposed andinvestigated nonlinear controllers to drive this system as in

[15] A control strategy based on the sliding mode controltheory is proposed for the hybrid grid-connected PV-windsystem where the obtained results are satisfactory andnevertheless this controller presents oscillations around itsreferences due to the chattering phenomena In [16] theauthors have designed a backstepping controller for PV-wind hybrid system with grid interfacing and shunt activefiltering functionality but to ensure stability or the nega-tiveness of the derivative of the every-step Lyapunovfunction it usually requires the cancellation of the indefinitecross-coupling terms while this cancellation results in theperfect-looking of the derivative of the Lyapunov functionand it does not necessarily mean that good performance isensured To overcome these problems another controllerwas proposed in the last 10 years and it is used in severalareas for the control applicationsis controller is known asthe active disturbance rejection controller (ADRC) and it isproposed by Han in 2009 [17]

e prospective of ADRC as an effective new controlstrategy is evident in many case studies where the techniqueis used to address a number of benchmark problems indiverse industry sectors with promising results However tothe authorrsquos best knowledge very few publications areavailable in the literature documenting the issue of con-trolling the hybrid PV-wind energy conversion systems butin a separate way In [18] the authors have proposed apredictive ADRC to overcome the time delay in PMSG windturbine systems and in [19] control of active and reactivepowers in a DFIG-based WECS by the ADRC technique hasbeen discussed and in [20] the author proposed an activedisturbance rejection control to a solar PV DC-DC con-verter e main advantages of this controller lies on thereal-time rejection of internal and external disturbancesbased on an extended state observer (ESO) [21] e vari-ation of internal parameters or modeling errors as internaldisturbances and the instability of the grid as externaldisturbances are caused either by voltage dips and frequencydroops As a result this paper presents the application of anew linear ADRC to the hybrid PV-wind energy conversionsystem

Our main contribution in this work lies on the devel-opment of a new robust control strategy for the grid-con-nected hybrid PV-wind energy conversion system by ADRCin order to extract the maximum power available from thePV-wind system and to control the power delivery evoltage based perturb and observe technique is used toextract the maximum power from the PV system while theoptimal torque control technique is used for the WECS elinear ADRC is utilized to regulate the DC bus voltage and toensure the control of active and reactive powers For thispurpose this paper is structured as follows Section 2presents the overall architecture of the proposed system andits modeling components Section 3 introduces the math-ematical model of the active disturbance rejection controllerSection 4 gives the proposed control by ADRC for the hybridsystem while in Section 5 the simulation results of the windenergy conversion system are presented

2 Mathematical Problems in Engineering

2 Mathematical Modeling and Architecture ofthe Proposed System

e proposed system as demonstrated in Figure 1 consists ofa variable speed direct-driven wind turbine based on per-manent magnetic synchronous generator (PMSG) a pho-tovoltaic array a DCDC converter an ACDC converter acommonDC bus capacitor and a grid interface inverter withan RL filter e PV generator is controlled by the boostconverter to track the maximum power point by using theMPPT technique e WEC system which involves a windturbine directly connected to the PMSG and is controlled bythe ACDC converter to extract the maximum power fromthe wind ese two energy sources are connected in parallelwith a commonDC link through their individual converterswhere a voltage source inverter (VSI) is utilized to supply thetotal generated power into the grid while ensuring a unitpower factor

21Mathematical EquivalentModel of PVArray In order toset up the PV model it is necessary to establish itsequivalent electrical circuit Indeed the literature citesnumerous mathematical models [22] representing the verystrong nonlinear behavior of the PV model due to theirdesign based on semiconductor junctions ese modelsdiffer from each other depending on the number of pa-rameters involved in calculating the voltage and currentdelivered by the PV module e single- and the double-diode models are generally used to model the solar cellbehavior e double-diode model is adopted in this paper[22] and its equivalent circuit is given in Figure 2 Itconsists of two diodes (D1 D2) characterizing the P-Njunction a current source (Iph) characterizing the pho-tocurrent a series resistor (Rs) representing the losses bythe Joule effect and a shunt resistor (Rsh) characterizingthe leakage current

e cell model can then be expressed by

Icell Iph minus Id1 minus Id2 minus Ish

Id1 Isc1 expVcell + Rs middot Icell( 1113857

a1 middot Vth1113890 1113891 minus 11113888 1113889



Ish Vcell + Rs middot Icell

Rsh

(1)

where Isc1 and Isc2 are the reverse saturation current of thediodes a1 and a2 are the ideality factors of diodes and Vth isthe cell thermal voltage Vth k middot (Tq) where T is thejunction P-N temperature k is Boltzmannrsquos constant(138 times 10minus 23(JK)) and q is the electron charge (1602times

10minus 19 C)

22WindTurbineModeling In any wind energy conversionsystem the purpose of the turbine is to harness the windkinetic energy and transform it into mechanical energy thatrotates an electric generatoremodeling of a wind turbineconsists in expressing the extracted aerodynamic power Paeroas a function of the incident wind speedV and its expressionis given by

Paero Cp(λ β)PW Cp(λ β)ρsv3

2 (2)

Its aerodynamic torque Taero is given by the followingexpression

Taero 1

2Ωt

Cp(λ β)ρsv3 (3)

where ρ is the air density generally taken equal to 1225 kgm3

e wind turbine aerodynamic efficiency is representedby a power factor called Cp [23] is coefficient depends onthe turbine characteristics (speed ratio λ and pitch angle β)Figure 3 represents the Cp characteristics

Cp(λ β) minus 06175116λprime

minus 04β minus 51113874 1113875eminus 21λprime

+ 01405λ

(4)

λ ΩtR

V (5)

1λprime

1

λ + 008βminus0035β3 + 1

(6)

where Ωt is the turbine rotational speed e mechanicalequation of the turbine shaft which is rigidly connected tothe synchronous generator is given by [24]

JdΩt

dt Taero minus Tem minus fΩt (7)

where J is the system total inertia f is the friction coefficientand Tem represents the generator electromagnetic torque

23 Permanent Magnet Synchronous Generator ModelingGenerally to represent a state model we define the statevector x the input vector u and the output vector y ismodel is written in the following form

_x Ax + Bu

y Hx(8)

For the PMSG the input vector is composed of the statorvoltages e state vector consists of electrical quantities(currents) and mechanical quantities (speed and position)e nonlinear state model in the d-q frame is described bythe system below

Mathematical Problems in Engineering 3

_id

_iq

_ω

_θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

minus Rs

Ld

ωLq

Ld0 0

minus ωLd

Lq

minus Rs

Lq

ψf

Lq0

0 0 0 0

0 0 1 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

id

iq

ω

θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

+

minus 1Ld

0

0minus 1Lq

0 0

0 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

vd

vq

0

0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

or x idiqωθ1113960 1113961T

u vdvq1113960 1113961T

y idiq1113960 1113961T

H

1 0 0 0

0 1 0 0⎛⎝ ⎞⎠

(9)

where Rs represents the stator resistance Ld and Lq are thedirect and quadrature inductances id and iq are the statorcurrents in the d-q frame ψf is the permanent magnet fluxωis the PMSG speed and it is given by ω PΩt and P are thepair poles [25]

e electromagnetic torque is given by

Tem 32

P Ld minus Lq1113872 1113873idiq + iqψf1113960 1113961 (10)

24 DC Link and Filter Modeling e interconnection be-tween the hybrid energy conversion system and the utilitypower grid is carried out via an RL filter (Lf Rf ) as illustratedin Figure 4 is filter is used to prevent harmonic currentsfrom spreading through the grid [26]

Vsminus a Vfa minus Rf ifa minus Lfdifa

dt

Vsminus b Vfb minus Rf ifb minus Lfdifb

dt

Vsminus c Vfc minus Rf ifc minus Lfdifc

dt

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

PMSG

Turbine

AC

DC

DC

AC

DC

DC

PV array

PCC

Transformer

Lf Rf

Filter

Udc

Figure 1 Grid-connected variable speed wind energy conversion system based on the permanent magnet synchronous generator

Id1 Id2 Ish

RshD2D1

Rs

Iph

Icell

+

ndash

Vcell

Figure 2 Double-diode PV cell models

060504030201

00 5 10 15 20Tip speed ratio

Pow

er co

effic

ient

0 10 20 30 40Pitch angle

Figure 3 Power coefficient characteristics for various values ofpitch angle β and tip speed ratio λ


Applying Parkrsquos transformation equation (11) becomesin d-q frame as follows

Vgd Vfd minus Rf ifd minus Lfdifd

dt+ Lfωgifq

Vgq Vfq minus Rf ifq minus Lfdifq

dtminus Lfωgifd

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

where vfd and vfq are the inverter voltage components vgdand vgq are the grid voltages and ifd and ifq are the filtercurrents

e modeling of the DC-link bus is given bydUdc

dt1C

iwind + ipv minus iinv1113872 1113873 (13)

where C is the DC-link capacitor

3 Proposed Control Strategy for theHRES by ADRC

e proposed control scheme for the grid-connected hybridenergy conversion system is given as follows

(i) VPO-MPPT based on ADRC is used to enhance thephotovoltaic energy conversion system (PVECS)efficiency under irradiation changes

(ii) OTC-MPPT based on ADRC is used to enhance theWECS efficiency under wind velocity changes

(iii) VOC based on ADRC is used to control the DC-linkvoltage and to regulate the injection of the producedactive and reactive powers into the grid

31 Mathematical Model of ADRC Active disturbance re-jection control (ADRC) is a robust control strategy proposedby Han [17] e principal concept of this method is to treatthe internal and external uncertainties as a ldquogeneralizeddisturbancesrdquo try to estimate them in real time by using anextended state observer (ESO) and then use it in thefeedback control law with the objective to compensate thedisturbances rapidly A first-order ADRC configuration isshown in Figure 5 It mainly consists of three parts trackingdifferentiator (TD) extended state observer (ESO) andnonlinear state error feedback (NLSEF)

In Figure 5 v is the input signal v1 is the input trackingsignal y is the system feedback signal z1 is the estimatedtracking signal z2 is the total disturbance estimation b0 isthe compensation factor z2b0 is the internal and externaldisturbance compensation u0 is the initial control object byNLSEF and u is the final control signal after disturbancecompensation

For a first-order controlled object its mathematicalmodel of ADRC is set as [27]

ε0 v1 minus v

dv1

dt minus r fal ε0 α0 δ0( 1113857

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(14)

ε z1 minus y

dz1

dt z1 minus β01 fal(ε α δ) + bu(t)

dz2

dt β02 fal(ε α δ)

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(15)

ε1 v1 minus z1

u0 β1 fal ε1 α1 δ1( 1113857

u u0 minusz2

b0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(16)

fal(ε α δ)

|ε|αsgn(ε) |ε|gt δ

εδ1 minus α

|ε|le δ

⎧⎪⎪⎨

⎪⎪⎩(17)

Udc PCC

Rf Lf

Vf_abc

Voltage source inverter

Vs_abc

If_abc

Iinv

T13T12T11

T21 T22 T23

Iwind + Ipv

Ic

Figure 4 e connection of the hybrid energy conversion system with the utility grid

+ndash +ndashTD NLSEF System

ESO

b01b0

dyu0v v1

yADRC z1 = y

z2 = f

Figure 5 Block diagram of a first-order active disturbance re-jection controller


where the mathematical model of the TD is defined by usingequation (14) the model of ESO is given by equation (15)and for NLSEF block it is represented by equation (16) β01β02 and β1 are the output error factors fal(ε α δ) is the bestfunction which is defined by using equation (17) δ is thefiltering factor to ESO and α is a nonlinear factor

In practice the ADRC needs to adjust a large number ofparameters and adjusting these parameters is complicated Soas to reduce the model complexity and the controller com-putational a linear ADRC design method is proposed andapplied to the hybrid PV-wind energy conversion system

32 Linear ADRC Design To illustrate the principle ofADRC [28] a nonlinear and time-varying dynamic systemof n order is considered with only a single input u(t) and anoutput and it can be described by the following equation

y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873

+ d(t) + b0 middot u(t)

(18)

where f(y(t) y(1)(t) y(2)(t) y(nminus 1)(t) u(t)) repre-sents the model internal dynamics which is assumed to beunknown d(t) represents the external disturbances and b0represents the known system parameter

e following terms f(t) f(y(t) y(1)(t) y(2)(t)

y(nminus 1)(t) u(t)) + d(t) are considered as all the internal andexternal disturbances affecting the system to be controlled

erefore the system equation is rewritten in the fol-lowing form

y(n)

(t) f(t) + b0 middot u(t) (19)

Instead of looking for an explicit mathematical model off(t) ADRC offers another alternative that significantly re-duces the dependence of the control on accurate systemmodeling as the proposed strategy consists in estimating f(t)and then to cancel it in real time using an appropriate controlsignal u(t) To do so an extended state observer is used Let

z1 y

z1 _y zn y(nminus 1)

zn+1 f

(20)

Assume that f is differentiable and let _f h enequation (19) can be written as

_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)

0 1 0 middot middot middot 00 0 1 middot middot middot 0⋮ ⋮ ⋮ ⋱ ⋮0 0 0 middot middot middot 10 0 0 middot middot middot 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B(n+11) 1 0 middot middot middot 0 01113858 1113859T

E(n+11) 0 0 middot middot middot 0 11113858 1113859T

B(1n+1) 1 0 middot middot middot 0 01113858 1113859T

(22)

A full-order Luenberger state observer can be designedas

_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)

where L is the observer gain vectore error between the actual value z and the estimated

value 1113954z by the observer can be written in the following form

e(t) z minus 1113954z (24)

e dynamics of the estimation error is thereforeexpressed by

_e (A minus LC)e (25)

where

A minus LC

minus β1 1 0 middot middot middot 0


⋮ ⋮ ⋮ ⋱ ⋮

minus βn 0 0 middot middot middot 1

minus βn+1 0 0 middot middot middot 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)

In order to ensure asymptotic convergence of the esti-mation error (e⟶ 0 when t⟶infin) and therefore a goodfunctioning of the observer it is necessary that the pa-rameters of the gain matrix L are chosen in such a way that(A minus LC) forms a Hurwitz matrix that is to say the poles ofits polynomial characteristic PESO(s) are all with strictlynegative real parts

PESO(s) det sIn+1 minus (A minus LC)( 1113857 sn+1

+ β1sn

+ β2snminus 1

+ middot middot middot + βns + βn+1

(27)

eobserverrsquos gains are generally determined by the poleplacement technique A compromise must be establishedbetween the speed at which the observer follows the statesand his sensitivity to noise measurement e faster the ESOis the earlier the disturbance is estimated and cancelled bythe correctoris is achieved by placing the observerrsquos poleswell to the left of the observed system poles the P-plan ischoice leads to the adoption of a large bandwidth for theextended state observer However it should be rememberedthat toomuch bandwidth can harm the system by promotingnoise transmission [28]

Taking into account all these constraints the cutoff pulseof the extended state observer ωo is chosen to have a suitablestabilization time and its (n + 1) poles are placed to minus ωo

PESO(s) sn+1

+ β1sn

+ β2snminus 1

+ middot middot middot + βns + βn+1 s + ωo( 1113857n+1

(28)


e observerrsquos gains are then expressed as follows

βi (n + 1)

(n + 1 minus i)iωio (29)

erefore when (A minus LC) is asymptotically stable1113954z1 1113954z2 1113954zn will approximate y and its derivatives (up toorder n minus 1) and 1113954zn+1 will approximate the generalizeddisturbance f Consequently the estimated generalizeddisturbances can be applied in control to reject it morequickly

If the control law is chosen as

u(t) u0(t) minus 1113954zn+1(t)

b0 (30)

then the system equation (19) becomes

y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)

If 1113954zn+1 is a correct estimation of f(1113954zn+1 asymp f) then thesystem is reduced to an n-order integral system

y(n)

(t) u0(t) (32)

erefore the final system can be controlled by thecorresponding state-feedback control law

u0(t) k1(r(t) minus y(t)) + k2( _r(t) minus _y(t))

+ middot middot middot + kn r(nminus 1)

(t) minus y(nminus 1)

(t)1113872 1113873(33)

where r(t) is the reference signalSince 1113954z1(t) 1113954zn(t) is a correct estimation of

y(t) y(nminus 1)(t) then the final control law can beapproached as

u(t) k1 r(t) minus 1113954z1(t)( 1113857 + middot middot middot + kn r(nminus 1)(t) minus 1113954zn(t)( 1113857 minus 1113954zn+1(t)

b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)

e linear active disturbance rejection controller can besummarized and designed by

1113954z_(t) A1113954z(t) + Bu(t) + L[y(t) minus C1113954z(t)]

(A minus LC)1113954z(t) + Bu(t) + Ly(t)

u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)

e structure of the first-order LADRC is depicted inFigure 6

4 Control of the Machine-SideConverter by ADRC

e control of the machine-side converter is obtained byusing the linear ADRC and it regulates the stator currentswith its references where Isdref is set to zero and Isqref isgiven by the optimal torque control OTC-MPPT [29] blockas depicted in Figure 7

41 MPPT Analysis for the Variable Speed Wind TurbineTo ensure maximum power extraction from the wind tur-bine the rotational speed must be maintained at the

optimum value of the tip speed ratio λopt which makes theturbine operating at CP CPmax

Considering the relationship between the wind speed Vand the tip speed ratio λ in equation (5) the wind turbinepower can be expressed as a function of the rotational speedΩm

Pt 05ρπR5Cp(λ β)

λ3ω3

m (38)

Replacing λ by λopt and placing in Cp(λ β) CPmax thewind turbine maximum power can be expressed as

Ptmax Koptω3m (39)

where Kopt is a coefficient given by

Kopt 05ρπR5Cpmax

λ3opt (40)

So the torque reference Temminus ref is expressed as follows

Temminus ref Koptω2m (41)

42 Linear ADRC Design for Machine-Side Converter ezero direct axis control (ZDC) is used to obtain the refer-ences of currents used in control [29]e three-phase statorcurrents isabc are converted into d-q axis frame using Parkrsquostransformation technique and then the d-axis current a is

+ndash +ndashKp System

ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0

Figure 6 Block diagram of a first-order linear ADRC


set to be zero and the q-axis current iq is set to be equal to thestator current is

is i2d + i2q

1113969 iq (42)

Consequently for id 0 the electromagnetic torque canbe controlled by iq

Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)

e stator current regulations are achieved by twoADRC where the equations of id and iq are adapted to thecanonical from of ADRC

dy(t)

dt f(y d t) + b0u(t) (45)

For the d-axis current we have

did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

and for the q-axis we have

diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)

5 Control of the DC-DC Converter by ADRC

To obtain the optimal exploitation of the PVECS during thechange of environmental conditions a two-stage controlstrategy is proposed and adopted here [30] As illustrated inFigure 8 firstly a PO-based voltage MPPT is used to gen-erate the reference voltage Vmpp After that an improvedcascaded loop based on linear ADRC is used to track the PVvoltage and current in order to extract the maximum powerfrom the PV array

51 P and O-Based V-MPPT e main aim of the VO-MPPT is to generate the reference voltage Vmpp corre-sponding to the maximum power point For this purpose Pand O-based V-MPPT [30] technique is utilized due to itsfeaturing effectiveness and simplicity as shown in Figure 9

52 ADRC Design for the V-MPPT Because of the almostzero variation in PV voltage at the MPP under irradiationchanges V-MPPT is considered as an effectiveness alter-native However the efficiency of this method depends onthe cascaded VI control loop concept In this section arobust cascaded VI control loop based on ADRC is pro-posed and demonstrated to track the MPP under weatherchanges

V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc

115p ψ ADRCVq_refTem_ref

iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ

Figure 7 Machine-side converter control by ADRC


e outer loop of the proposed strategy consists incontrolling the Vpv voltage to its reference obtained by theV-MPPT e dynamic of the Vpv voltage is expressed asfollows

dVpv

dt

1Cpv

ic (50)

en theADRC for the outer loop canbedesigned as follows

vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl

Figure 8 Control of the DC-DC converter linear ADRC

Measurement of ipv(k)

ipv(k ndash 1)vpv(k)

vpv(k ndash 1)

Calculation ofΔvpv = vpv(k) ndash vpv(k ndash 1)Δppv = ppv(k) ndash ppv(k ndash 1)

Δppv gt 0

Δvpv gt 0 Δvpv gt 0

NoYes

Vref+incVref+inc Vrefndashinc

Start

ADRC controller

Yes YesNo No

Figure 9 P and O-based V-MPPT


f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)

For the inner loop it is used to regulate the currentacross the inductor Its dynamics is presented below

dil

dt1L

vl (52)

en the ADRC for the inner loop can be designed asfollows

f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)

6 Control of the Grid-Side Converter by ADRC

e grid-side control consists of two cascade control loops inwhich its main purpose is to stabilize the DC-link voltageand to control the active and reactive powers injected to thegrid during variation in environmental conditions einner loop will control the filter currents and the outer loopwill control the DC bus voltage e inner loop dynamics issettled to be faster than the outer one e GSC can becontrolled either by voltage-oriented control (VOC) ordirect power control (DPC) technique VOC is considered tobe more efficient due to lower energy losses and to lowercurrent distortion compared to DPC [31]

As illustrated in Figure 10 VOC is used to control theGSC and it involves a dual-loop control structure an outerloop to control the DC-link voltage and an inner loop tocontrol the grid currents

e phase-locked loop (PLL) device is used to obtain thephase angle and frequency from the grid voltages [32] ed-axis component of the synchronous reference frame isaligned with the grid voltage vdg vg and the q-axis com-ponent was set to zero vqg 0

e active and reactive powers are then given by

Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)

is shows that the active and reactive powers will becontrolled respectively by currents ifd and ifq

61DCBusVoltageControl byLADRC epower across theDC-link capacitor C can be expressed by

Pdc Udc iwind + ipv minus iinv1113872 1113873 (55)

By substituting equation (13) with equation (55) we get

Pdc CUdcdUdc

dt (56)

If all the losses in the filter the power electronics con-verters and in the capacitor are neglected the exchangedpowers on the DC bus are expressed by

Pdc Ps + Ppv minus Pg (57)

where Ps Ppv and Pg are the generator PV system and gridpowers respectively

By taking into account equations (54)ndash(56) the DC busvoltage can be expressed by

CUdcdUdc

dt Udc iwind + ipv1113872 1113873 minus

32vgdifd (58)

ordU2

dcdt

2Udc

Ciwind + ipv1113872 1113873 minus

3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)

62 Control of Filter Currents by LADRC e externalvoltage regulation loop makes it possible to maintain thevoltage across the capacitor Udc and to generate the currentreference ifdminus ref for the internal current loop

For the current ifqminus ref it is calculated by the desireddelivery of reactive power

ifqminus ref minus2

3vgdQf minus ref (62)

en similarly to the machine-side control the filtercurrents are given in canonical form of ADRC

For d-axis currentdifd

dt

1Lf

minus Rf ifd minus vgd + Lfωgifq1113872 1113873 +vfd

Lf (63)


where

f(y d t) 1Lf

minus Rf ifd minus vgd + Lfωgifq1113872 1113873

b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)

For q-axis currentdifq

dt

1Lf

minus Rf ifq minus Lfωgifd1113872 1113873 +vfq

Lf (65)

where

f(y d t) 1Lf

minus Rf ifq minus Lfωgifd1113872 1113873

b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)

7 Results and Discussion

71 Simulation Results To validate the theoretical study andthe effectiveness of the presented control strategy a com-plete structure of HRES is designed and simulated underMATLABSimulink environment e simulation parame-ters are given in appendix

e applied wind speed profile is shown in Figure 11Figures 11ndash18 present the simulations results of the pro-posed strategy for the WECS system

As can be noticed in Figures 12 and 13 the mechanicalspeed and the extracted power take the same form as thewind profile and it is also shown in Figure 14 that the powercoefficient has been maintained at its optimal value(Cpmax 043) which shows the effectiveness of the MPPTstrategy in terms of maximum power extraction

e response of the ADRC shows good tracking char-acteristics as highlighted in Figures 15 and 16 where thedirect axis current Id was maintained to be zero and thequadrature current Iq tracks its references e generatedactive power and stator currents are shown in Figures 17and 18

For the PVECS the applied profile of the irradiation isillustrated in Figure 19 and the corresponding results aredemonstrated in Figures 20ndash22

As can be noticed in Figures 20 and 21 the Vpv voltage isregulated with its references that is obtained from the VPO-MPPT and the inductor current is also regulated to itsreferences which ensures the extraction of themaximumPVpower as illustrated in Figure 22

Figure 23 shows that the DC-link voltage Vdc is main-tained at its reference with some fluctuations which are dueto the stochastic nature of wind speed Also we notice inFigures 24 and 25 that the linear ADRC regulates the gridcurrents to their references

e control of the active and reactive powers is alsoachieved as shown in Figures 26ndash28 where the extractedpower from the HECS was injected into the grid and thereactive power was set to zero to ensure a unit power factor

In order to test the robustness of the proposed controlstrategy another test was carried out in which we havechanged the internal parameters of the PMSG the statorresistance and inductance Ls by an increase of 50 of theirnominal value e results obtained by LADRC are com-pared with the classical PI controller e utilized wind

DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC

ndash2(3 lowast Vgd)

θg

θg

θgθg

Figure 10 Grid-side converter control by linear ADRC


speed profile is given in Figure 29 For the PV system theirradiation was maintained at 1000Wm2

As shown in Figure 30 both controllers regulate thecurrent Id to zero but the ADRC has a faster responsecompared to the PI controller

It can be noticed in Figure 31 that the current Iq wasregulated to its reference and that the response of LADRC isbetter than the PI one So as a closing statement the sim-ulation results have demonstrated that the proposed strategyis efficient in terms of stability rapidity accuracy and

8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

Figure 11 Wind speed profile

2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

Figure 12 Turbine mechanical power

0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

Figure 13 PMSG speed in rads

05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12

Time (seconds)14 16 18 2

Figure 14 Power coefficient Cp


0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref

Figure 15 Stator d-axis current Id

0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028

04 06 08 1 12Time (seconds)


ndash500

Isq

(A)

0

500

1000

IsqIsqref

Figure 16 Stator q-axis current Iq

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105

Figure 17 PMSG stator active power

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500

Figure 18 Generated stator currents


0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2

Figure 19 e applied irradiation profile

0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3

Figure 20 PV voltage control by ADRC

0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref

Figure 21 Inductor current control by ADRC

25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105

Figure 22 Extracted PV power by MPPT-ADRC


robustness regarding the variation of the parameters of themachine

72 Discussion Benefits and Limitations e proposedhybrid PV-wind system presents some benefits and limi-tations in terms of efficiency and control and the mainadvantages of the used structure are as follows

(i) Continuous power supply solar and wind energiesare complimentary in nature that is when there isno sun there is plenty of wind and vice versa

(ii) Reducing cost of the system the cost of the hybridsystem is reduced because the inverter and all theassociated circuits are removed

(iii) Reducing power loss the converter numbers in theproposed system are less than a separated systemerefore the power loss of the PVrsquos inverter iseliminated A two-level inverter power loss is es-timated to be around 0015 pu [33] is value isconsiderable in case of MW-level power plantsFor the system limitations we can mention thefollowing

2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06

Figure 23 DC bus voltage control by LADRC

2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref

Figure 24 Filter direct current Ifd control by LADRC

0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref

Figure 25 Filter quadrature current Ifq control by LADRC


0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106

Figure 26 Active power injected to the grid

0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104

Figure 27 Reactive power injected to the grid

ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2

Figure 28 Grid voltage Vsa and grid current Ifa

075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2

Figure 29 Wind speed prole


(i) Complicated controlling process with differenttypes of energy sources in use the systems requiresome knowledge e operation of different energysources and their interaction and coordination mustbe controlled and it can become complicated

(ii) Operations under grid faults according to the newgrid code the wind power system and the PV systemshould not disconnect from the grid in case ofvoltage dips Moreover it is required to participatein ancillary services therefore the control structureneeds to be adjusted

8 Conclusion

In this article we have studied the modeling of a hybridenergy conversion chain (wind and photovoltaic) followedby an overall control structure introducing the ADRCmethod and the extended state observer (ESO) whichconstitutes its core Its generalized mathematical theory inthe linear and nonlinear cases is discussed It is then appliedto the control of the two chains (photovoltaic and wind) inorder to extract the maximum power on the one hand andon the other hand it is applied to the control of the grid-sideconverter by ensuring the stability of the DC bus voltage and

the control of the active and reactive powers exchanged withthe utility grid To prove its robustness a simulation isestablished by applying variations to the machine parame-ters and the test results have demonstrated that the ADRC islargely independent of its variations unlike the classical PIregulator

Appendix

A PMSG Wind Turbine Parameters

(i) Radius R 24m(ii) Nominal wind speed VV 12ms(iii) Total inertia of the mechanical transmission

JT 105 kgmiddotm2

(iv) Cpmax 043(v) λoptimal 44971(vi) Nominal power Pn 750 kW(vii) Stator resistance Rs 652eminus 3Ω(viii) Stator inductance Ls Ld Lq 385eminus 3 H(ix) Flux Ψ 853(x) Pair poles P 26

6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12

Time (seconds)14 16 18

IsdPIIsdADRCIsdref

2

Figure 30 Control of d-axis stator current Id

00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2

Figure 31 Control of q-axis stator current Iq


B PV System Parameters

(i) PV array system rated power P 250 kW(ii) PV panel rated power P 255W(iii) Open circuit voltage of the PV panel

Voc 3794V(iv) Short circuit current of the PV panel Isc 876A(v) MPP voltage of the PV panel Vmpp 3071(vi) MPP current of the PV panel Impp 837A(vii) Number of series connected panels per string

Ns 10(viii) Number of PV panel strings Np 98

C Grid-Side Parameters

(i) DC bus voltage Vdc 1500V(ii) DC bus capacitor C 20000eminus 6 F(iii) Filter resistance Rf 001Ω(iv) Filter inductance Lf 1eminus 3 H

Data Availability

No data were used to support this study

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] L Bouselham M Hajji B Hajji and H Bouali ldquoA newMPPT-based ANN for photovoltaic system under partialshading conditionsrdquo Energy Procedia vol 111 pp 924ndash9332017

[2] AMohapatra B Nayak P Das and K B Mohanty ldquoA reviewon MPPT techniques of PV system under partial shadingconditionrdquo Renewable and Sustainable Energy Reviewsvol 80 pp 854ndash867 2017

[3] I Aboudrar S E Hani H Mediouni N Bennis andA Echchaachouai ldquoHybrid algorithm and active filteringdedicated to the optimization and the improvement ofphotovoltaic system connected to grid energy qualityrdquo In-ternational Journal of Renewable Energy Research-IJRERvol 7 no 2 2017

[4] H Yang Z Wei and L Chengzhi ldquoOptimal design andtechno-economic analysis of a hybrid solar-wind powergeneration systemrdquo Applied Energy vol 86 no 2 pp 163ndash169 2009

[5] M A Abdullah A H M Yatim C W Tan and R Saidur ldquoAreview of maximum power point tracking algorithms for windenergy systemsrdquo Renewable and Sustainable Energy Reviewsvol 16 no 5 pp 3220ndash3227 2012

[6] F L Tofoli D de Castro Pereira and W J de PaulaldquoComparative study of maximum power point trackingtechniques for photovoltaic systemsrdquo International Journal ofPhotoenergy vol 2015 Article ID 812582 10 pages 2015

[7] A E Yaakoubi A Asselman A Djebli and E H AroudamldquoA MPPT strategy based on Fuzzy control for a wind energyconversion systemrdquo Procedia Technology vol 22 pp 697ndash704 2016

[8] E Rokrok M Shafie-khah and J P S Catalatildeo ldquoReview ofprimary voltage and frequency control methods for inverter-based islanded microgrids with distributed generationrdquo Re-newable and Sustainable Energy Reviews vol 82 pp 3225ndash3235 2018

[9] S Dhar and P K Dash ldquoAdaptive backstepping sliding modecontrol of a grid interactive PV-VSC system with LCL filterrdquoSustainable Energy Grids and Networks vol 6 pp 109ndash1242016

[10] L Hassaine E OLias J Quintero and V Salas ldquoOverview ofpower inverter topologies and control structures for gridconnected photovoltaic systemsrdquo Renewable and SustainableEnergy Reviews vol 30 pp 796ndash807 2014

[11] B Jain S Jain and R K Nema ldquoControl strategies of gridinterfaced wind energy conversion system an overviewrdquoRenewable and Sustainable Energy Reviews vol 47 pp 983ndash996 2015

[12] D Nguyen and G Fujita ldquoAnalysis of sensorless MPPTmethod for hybrid PV-wind system using DFIG wind tur-binesrdquo Sustainable Energy Grids and Networks vol 5pp 50ndash57 2016

[13] S M Tripathi A N Tiwari and D Singh ldquoOptimum designof proportional-integral controllers in grid-integrated PMSG-based wind energy conversion systemrdquo International Trans-actions on Electrical Energy Systems vol 26 no 5pp 1006ndash1031 2016

[14] H-W Kim S-S Kim andH-S Ko ldquoModeling and control ofPMSG-based variable-speed wind turbinerdquo Electric PowerSystems Research vol 80 no 1 pp 46ndash52 2010

[15] H Laabidi H Jouini and A Mami ldquoSliding mode control forPV-wind hybrid system connected to gridrdquo EnvironmentalEngineering in Proceedings of the 5th International Confer-ence on Green Energy and Environmental Engineering (GEEE-2018) vol 6 Sousse Tunisia April 2018

[16] V N Jayasankar and U Vinatha ldquoDesign of backsteppingcontroller for PV-wind hybrid system with grid-interfacingand shunt active filtering functionalityrdquo International Journalof Power Electronics vol 9 no 2 pp 167ndash188 2018

[17] J Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3pp 900ndash906 2009

[18] S Li and J Li ldquoOutput predictor-based active disturbancerejection control for a wind energy conversion system withPMSGrdquo IEEE Access vol 5 pp 5205ndash5214 2017

[19] M Arbaoui A Essadki T Nasser and H ChalawaneldquoComparative analysis of ADRCamp PI controllers used in windturbine system driving a DFIGrdquo International Journal ofRenewable Energy Research-IJRER vol 7 no 4 2017

[20] H Yang Q Jiang and Y Zhong ldquoActive-disturbance re-jection control and its application to solar PV DC-DC con-verterrdquo in Proceedings of the 2010 3rd InternationalConference on Advanced Computer Jeory and Engineering(ICACTE) IEEE Chengdu China August 2010

[21] X Yang and Y Huang ldquoCapabilities of extended state ob-server for estimating uncertaintiesrdquo in Proceedings of the 2009American Control Conference pp 3700ndash3705 St Louis MOUSA June 2009

[22] M Hejri H Mokhtari M R Azizian M Ghandhari andL Soder ldquoOn the parameter extraction of a five-parameterdouble-diode model of photovoltaic cells and modulesrdquo IEEEJournal of Photovoltaics vol 4 no 3 pp 915ndash923 2014

[23] A Imad S E Hani A Echchaachouai and A A EnergyldquoRobust Active disturbance Rejection Control of a directdriven PMSG wind turbinerdquo in Proceedings of the 2017


International Renewable and Sustainable Energy Conference(IRSEC) pp 1ndash6 Tangier Morocco December 2017

[24] A Katkout and A Essadki ldquoNonlinear power control strat-egies for variable-speed wind turbinesrdquo International Journalof Renewable Energy Research (IJRER) vol 7 no 4pp 1998ndash2003 2017

[25] A Echchaachouai S E Hani A Hammouch andI Aboudrar ldquoA two-level sensorless MPPT strategy usingSRF-PLL on a PMSG wind energy conversion systemrdquo Ad-vances in Electrical and Electronic Engineering vol 15 no 3pp 383ndash390 2017

[26] H Laghridat A Essadki and T Nasser ldquoComparativeanalysis between PI and linear-ADRC control of a gridconnected variable speed wind energy conversion systembased on a squirrel cage induction generatorrdquo MathematicalProblems in Engineering vol 2019 Article ID 852718316 pages 2019

[27] I Aboudrar S El Hani H Mediouni and A AghmadildquoModeling and robust control of a grid connected directdriven PMSG wind turbine by ADRCrdquo Advances in Electricaland Electronic Engineering vol 16 no 4

[28] G Herbst ldquoA simulative study on active disturbance rejectioncontrol (ADRC) as a control tool for practitionersrdquo Elec-tronics vol 2 no 4 pp 246ndash279 2013

[29] S S Kumar K Jayanthi and N S Kumar ldquoMaximum powerpoint tracking for a PMSG based variable speed wind energyconversion system using optimal torque controlrdquo in Pro-ceedings of the 2016 International Conference on AdvancedCommunication Control and Computing Technologies(ICACCCT) pp 347ndash352 Ramanathapuram India May2016

[30] A Kihal F Krim B Talbi A Laib and A Sahli ldquoA robustcontrol of two-stage grid-tied PV systems employing integralsliding mode theoryrdquo Energies vol 11 no 10 p 2791 2018

[31] M H Nehrir C Wang K Strunz et al ldquoA review of hybridrenewablealternative energy systems for electric powergeneration configurations control and applicationsrdquo IEEETransactions on Sustainable Energy vol 2 no 4 pp 392ndash4032011

[32] S Mishra I Hussain G Pathak and B Singh ldquodPLL-basedcontrol of a hybrid wind-solar grid connected inverter in thedistribution systemrdquo IET Power Electronics vol 11 no 5pp 952ndash960 2018

[33] J-I I Daisuke Sato ldquoTotal loss comparison of inverter circuittopologies with interior permanent magnet synchronousmotor drive systemrdquo in Proceedings of the 2013 IEEE ECCEAsia Downunder (ECCE) pp 1ndash6 Melbourne Australia June2013


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algorithms are needed to improve the energy efficiency of bothPV and wind systems In this context several research hasbeen conduct in the literature going from the utilization ofclassical algorithms such as perturb and observe (PO) in-cremental conductance (INC) and hill climbing search (HCS)[5 6] for both PV and WECS applications to those based onartificial intelligence as fuzzy logic and neural networks [7]

e grid-side converter is a necessary element in anelectrical power generation system for obtaining sinusoidalwaveforms with low total harmonic distortion Neverthe-less the performance of the system depends largely on thecontrol strategy applied by the grid-side converter [8]erefore several control techniques for the voltage in-verter have been discussed in the literature Among themin [9] the authors deals with a new nonlinear backsteppingsliding mode control for photovoltaic- (PV-) based gridinteractive voltage source converter (VSC) system and anew small signal stability phenomenon is depicted by themultivariable dynamic model of the proposed PV-basedgrid converter system where PV penetration as well asnonlinear control parameter optimization practices isconsidered in this paper In [10] the authors presenteddifferent topologies and control strategies for grid-con-nected photovoltaic systems and the following sectionsreport investigate and present control structures forsingle-phase and three-phase inverters Some solutions tocontrol the power injected into the grid and functionalstructures of each configuration are proposed Jain et al in[11] presented a review for the control strategies applied tothe grid-connected PMSG-based wind turbines a com-parative study of rotor flux-oriented control and directtorque control (DTC) techniques applied in the generator-side converter of PMSG wind turbine application for grid-side converter and various control schemes are developedmainly based on voltage-oriented control (VOC) or ondirect power control (DPC) And authors in [12] havepresented a sensorless maximum power point tracking(MPPT) method for a hybrid photovoltaic-wind systemwhich consists of photovoltaic (PV) system and doubly fedinduction generator (DFIG) wind turbine (WT) eperformance of the proposed method is demonstrated inthe simulation study and the three converters can workvery well to handle the power flow under various operationscenarios such as variations of mechanical power andirradiation changes of DC-link voltage Hence the pro-posed system can be a cost-effective alternative of the twoseparated systems

In general the most commonly used control strategy toconnect the power generation systems with the utility powergrid is based on the proportional integrator controller due toits simple structure as presented in [13 14] Considering theinternal and external disturbances of grid-connected mul-tiple-source renewable energy systems such as a hybrid PV-wind system the control objective becomes more difficultand ordinary controllers like PI and PR controllers are notsufficient erefore several researchers have proposed andinvestigated nonlinear controllers to drive this system as in

[15] A control strategy based on the sliding mode controltheory is proposed for the hybrid grid-connected PV-windsystem where the obtained results are satisfactory andnevertheless this controller presents oscillations around itsreferences due to the chattering phenomena In [16] theauthors have designed a backstepping controller for PV-wind hybrid system with grid interfacing and shunt activefiltering functionality but to ensure stability or the nega-tiveness of the derivative of the every-step Lyapunovfunction it usually requires the cancellation of the indefinitecross-coupling terms while this cancellation results in theperfect-looking of the derivative of the Lyapunov functionand it does not necessarily mean that good performance isensured To overcome these problems another controllerwas proposed in the last 10 years and it is used in severalareas for the control applicationsis controller is known asthe active disturbance rejection controller (ADRC) and it isproposed by Han in 2009 [17]

e prospective of ADRC as an effective new controlstrategy is evident in many case studies where the techniqueis used to address a number of benchmark problems indiverse industry sectors with promising results However tothe authorrsquos best knowledge very few publications areavailable in the literature documenting the issue of con-trolling the hybrid PV-wind energy conversion systems butin a separate way In [18] the authors have proposed apredictive ADRC to overcome the time delay in PMSG windturbine systems and in [19] control of active and reactivepowers in a DFIG-based WECS by the ADRC technique hasbeen discussed and in [20] the author proposed an activedisturbance rejection control to a solar PV DC-DC con-verter e main advantages of this controller lies on thereal-time rejection of internal and external disturbancesbased on an extended state observer (ESO) [21] e vari-ation of internal parameters or modeling errors as internaldisturbances and the instability of the grid as externaldisturbances are caused either by voltage dips and frequencydroops As a result this paper presents the application of anew linear ADRC to the hybrid PV-wind energy conversionsystem

Our main contribution in this work lies on the devel-opment of a new robust control strategy for the grid-con-nected hybrid PV-wind energy conversion system by ADRCin order to extract the maximum power available from thePV-wind system and to control the power delivery evoltage based perturb and observe technique is used toextract the maximum power from the PV system while theoptimal torque control technique is used for the WECS elinear ADRC is utilized to regulate the DC bus voltage and toensure the control of active and reactive powers For thispurpose this paper is structured as follows Section 2presents the overall architecture of the proposed system andits modeling components Section 3 introduces the math-ematical model of the active disturbance rejection controllerSection 4 gives the proposed control by ADRC for the hybridsystem while in Section 5 the simulation results of the windenergy conversion system are presented












Rsh

(1)


10minus 19 C)



2 (2)


Taero 1

2Ωt

Cp(λ β)ρsv3 (3)





+ 01405λ

(4)

λ ΩtR

V (5)

1λprime

1

λ + 008βminus0035β3 + 1

(6)


JdΩt




_x Ax + Bu

y Hx(8)



_id

_iq

_ω

_θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

minus Rs

Ld

ωLq

Ld0 0

minus ωLd

Lq

minus Rs

Lq

ψf

Lq0

0 0 0 0

0 0 1 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

id

iq

ω

θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

+

minus 1Ld

0

0minus 1Lq

0 0

0 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

vd

vq

0

0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

or x idiqωθ1113960 1113961T

u vdvq1113960 1113961T

y idiq1113960 1113961T

H

1 0 0 0

0 1 0 0⎛⎝ ⎞⎠

(9)



Tem 32




dt


dt


dt

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

PMSG

Turbine

AC

DC

DC

AC

DC

DC

PV array

PCC

Transformer

Lf Rf

Filter

Udc


Id1 Id2 Ish

RshD2D1

Rs

Iph

Icell

+

ndash

Vcell


060504030201


Pow

er co

effic

ient






dt+ Lfωgifq


dtminus Lfωgifd

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)



dt1C











ε0 v1 minus v

dv1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(14)

ε z1 minus y

dz1


dz2


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(15)

ε1 v1 minus z1

u0 β1 fal ε1 α1 δ1( 1113857

u u0 minusz2

b0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(16)

fal(ε α δ)


εδ1 minus α

|ε|le δ

⎧⎪⎪⎨

⎪⎪⎩(17)

Udc PCC

Rf Lf

Vf_abc


Vs_abc

If_abc

Iinv

T13T12T11

T21 T22 T23

Iwind + Ipv

Ic



ESO

b01b0

dyu0v v1

yADRC z1 = y

z2 = f






y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873


(18)





y(n)



z1 y


zn+1 f

(20)


_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦




(22)


_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)



e(t) z minus 1113954z (24)



where

A minus LC



⋮ ⋮ ⋮ ⋱ ⋮



⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)



+ β1sn

+ β2snminus 1


(27)



PESO(s) sn+1

+ β1sn

+ β2snminus 1


(28)



βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018


















Rsh

(1)


10minus 19 C)



2 (2)


Taero 1

2Ωt

Cp(λ β)ρsv3 (3)





+ 01405λ

(4)

λ ΩtR

V (5)

1λprime

1

λ + 008βminus0035β3 + 1

(6)


JdΩt




_x Ax + Bu

y Hx(8)



_id

_iq

_ω

_θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

minus Rs

Ld

ωLq

Ld0 0

minus ωLd

Lq

minus Rs

Lq

ψf

Lq0

0 0 0 0

0 0 1 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

id

iq

ω

θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

+

minus 1Ld

0

0minus 1Lq

0 0

0 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

vd

vq

0

0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

or x idiqωθ1113960 1113961T

u vdvq1113960 1113961T

y idiq1113960 1113961T

H

1 0 0 0

0 1 0 0⎛⎝ ⎞⎠

(9)



Tem 32




dt


dt


dt

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

PMSG

Turbine

AC

DC

DC

AC

DC

DC

PV array

PCC

Transformer

Lf Rf

Filter

Udc


Id1 Id2 Ish

RshD2D1

Rs

Iph

Icell

+

ndash

Vcell


060504030201


Pow

er co

effic

ient






dt+ Lfωgifq


dtminus Lfωgifd

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)



dt1C











ε0 v1 minus v

dv1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(14)

ε z1 minus y

dz1


dz2


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(15)

ε1 v1 minus z1

u0 β1 fal ε1 α1 δ1( 1113857

u u0 minusz2

b0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(16)

fal(ε α δ)


εδ1 minus α

|ε|le δ

⎧⎪⎪⎨

⎪⎪⎩(17)

Udc PCC

Rf Lf

Vf_abc


Vs_abc

If_abc

Iinv

T13T12T11

T21 T22 T23

Iwind + Ipv

Ic



ESO

b01b0

dyu0v v1

yADRC z1 = y

z2 = f






y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873


(18)





y(n)



z1 y


zn+1 f

(20)


_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦




(22)


_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)



e(t) z minus 1113954z (24)



where

A minus LC



⋮ ⋮ ⋮ ⋱ ⋮



⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)



+ β1sn

+ β2snminus 1


(27)



PESO(s) sn+1

+ β1sn

+ β2snminus 1


(28)



βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








_id

_iq

_ω

_θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

minus Rs

Ld

ωLq

Ld0 0

minus ωLd

Lq

minus Rs

Lq

ψf

Lq0

0 0 0 0

0 0 1 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

id

iq

ω

θ

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

+

minus 1Ld

0

0minus 1Lq

0 0

0 0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

vd

vq

0

0

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

or x idiqωθ1113960 1113961T

u vdvq1113960 1113961T

y idiq1113960 1113961T

H

1 0 0 0

0 1 0 0⎛⎝ ⎞⎠

(9)



Tem 32




dt


dt


dt

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

PMSG

Turbine

AC

DC

DC

AC

DC

DC

PV array

PCC

Transformer

Lf Rf

Filter

Udc


Id1 Id2 Ish

RshD2D1

Rs

Iph

Icell

+

ndash

Vcell


060504030201


Pow

er co

effic

ient






dt+ Lfωgifq


dtminus Lfωgifd

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)



dt1C











ε0 v1 minus v

dv1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(14)

ε z1 minus y

dz1


dz2


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(15)

ε1 v1 minus z1

u0 β1 fal ε1 α1 δ1( 1113857

u u0 minusz2

b0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(16)

fal(ε α δ)


εδ1 minus α

|ε|le δ

⎧⎪⎪⎨

⎪⎪⎩(17)

Udc PCC

Rf Lf

Vf_abc


Vs_abc

If_abc

Iinv

T13T12T11

T21 T22 T23

Iwind + Ipv

Ic



ESO

b01b0

dyu0v v1

yADRC z1 = y

z2 = f






y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873


(18)





y(n)



z1 y


zn+1 f

(20)


_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦




(22)


_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)



e(t) z minus 1113954z (24)



where

A minus LC



⋮ ⋮ ⋮ ⋱ ⋮



⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)



+ β1sn

+ β2snminus 1


(27)



PESO(s) sn+1

+ β1sn

+ β2snminus 1


(28)



βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018










dt+ Lfωgifq


dtminus Lfωgifd

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)



dt1C











ε0 v1 minus v

dv1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(14)

ε z1 minus y

dz1


dz2


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(15)

ε1 v1 minus z1

u0 β1 fal ε1 α1 δ1( 1113857

u u0 minusz2

b0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(16)

fal(ε α δ)


εδ1 minus α

|ε|le δ

⎧⎪⎪⎨

⎪⎪⎩(17)

Udc PCC

Rf Lf

Vf_abc


Vs_abc

If_abc

Iinv

T13T12T11

T21 T22 T23

Iwind + Ipv

Ic



ESO

b01b0

dyu0v v1

yADRC z1 = y

z2 = f






y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873


(18)





y(n)



z1 y


zn+1 f

(20)


_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦




(22)


_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)



e(t) z minus 1113954z (24)



where

A minus LC



⋮ ⋮ ⋮ ⋱ ⋮



⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)



+ β1sn

+ β2snminus 1


(27)



PESO(s) sn+1

+ β1sn

+ β2snminus 1


(28)



βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018











y(n)

(t) f y(t) y(1)

(t) y(2)

(t) y(nminus 1)

(t) u(t)1113872 1113873


(18)





y(n)



z1 y


zn+1 f

(20)


_z Az + Bu + Eh

y Cz1113896 (21)

where

z z1 z2 zn zn+11113858 1113859T

A(n+1n+1)


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦




(22)


_1113954z(t) A1113954z + Bu + L(y minus 1113954y)

1113954y C1113954z

⎧⎨

⎩ (23)



e(t) z minus 1113954z (24)



where

A minus LC



⋮ ⋮ ⋮ ⋱ ⋮



⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(26)



+ β1sn

+ β2snminus 1


(27)



PESO(s) sn+1

+ β1sn

+ β2snminus 1


(28)



βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018









βi (n + 1)




u(t) u0(t) minus 1113954zn+1(t)

b0 (30)


y(n)

(t) f(t) minus 1113954zn+1(t) + u0(t) (31)


y(n)

(t) u0(t) (32)





(t)1113872 1113873(33)




b0 K0(1113954r(t) minus 1113954z(t)) (34)

where

1113954r(t) r(t) _r(t) r(nminus 1)

(t)01113960 1113961T (35)

K0 k1 k2 kn11113858 1113859

b0 (36)




u(t) K0[1113954r(t) minus 1113954z(t)]

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(37)








λ3ω3

m (38)


Ptmax Koptω3m (39)


Kopt 05ρπR5Cpmax

λ3opt (40)





ESO

dyr

y LADRC

u

z1 = yz2 = y

b0

u0 1b0




is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018









is i2d + i2q

1113969 iq (42)


Tem 32

Pψfiq (43)

Hence

Temminus ref 32

Pψf iqref

iqref 2

3PψfTemminus ref

(44)


dy(t)

dt f(y d t) + b0u(t) (45)


did(t)

dt minus

Rs

Ld

id + ωeiqLq

Ld

+vd

Ld

(46)

where

f(y d t) minusRs

Ld

id + ωeiqLq

Ld

b0 1

Ld

u vd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)


diq(t)

dt minus

Rs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

+vq

Lq

(48)

f(y d t) minusRs

Lq

iq minus ωeidLd

Lq

minusψf

Lq

b0 1Lq

u vq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(49)





V

AC

DC

Im_abc

PMSG

Turbine

MSC

1sP

wm

we

dq

abc

MPPT dq

abc


iq_ref

iq

ADRCVd_ref

id_ref = 0

idPWM

6

Iwind

Ic

Udc

θ

θ




dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018









dVpv

dt

1Cpv

ic (50)


vpv

vlowastpv

vpv

+

vlowastmMPPT

ipv

ipv

ipv

PWM

+ndash ADRC +ndash

il

+ilowastc

ndash ADRC

vdc

ndash

Dlowast

Ta (degC)Lpv

Cpv

ic

il

vdcki

ilowastl vlowastl

Dvl




vpv(k ndash 1)


Δppv gt 0


NoYes


Start

ADRC controller

Yes YesNo No



f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








f(y d t) ΔCpv

b0 1

Cpv

u ic

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(51)


dil

dt1L

vl (52)


f(y d t) ΔL

b0 1L

u vl

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(53)






Pg 32vgdifd

Qg minus32vgdifq

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(54)





Pdc CUdcdUdc

dt (56)





CUdcdUdc


32vgdifd (58)

ordU2

dcdt

2Udc


3vgd

Cifd (59)

and we put X U2dc

dX

dt2

X

radic


3vgd

Cifd (60)

so we obtain

f(y d t) 2

X

radic

Ciwind + ipv1113872 1113873

b0 minus3vgd

C

u ifd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(61)



ifqminus ref minus2




dt

1Lf


Lf (63)


where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








where

f(y d t) 1Lf


b0 1Lf

u vfd

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(64)


dt

1Lf


Lf (65)

where

f(y d t) 1Lf


b0 1Lf

u vfq

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(66)











DC

AC Grid

Rf Lf

Vf_abc

If_abc

Vs_abc

Irec Iinv

Udc

GSC

g1 g6

g1 g6

Ic

dq

abc

PLL

dq

abc

Wg

Vgq

Vgd

IfdIfq

dq

abc

ADRCVd_refIfd_ref

Ifd

ADRCVq_ref

Ifq_ref

IfqPWM

Udc

Udc_ref

Q_ref

ADRC


θg

θg

θgθg






8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018











8

7

9

10V v

(ms

)11

12

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


2

0

4

6

8

P t (W

)

times105

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


0

05

1

15

2

25

Wm

(rad

s)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2


05

043

04295

042902 04 06 08 1 12 14

C p

04

03

02

01

00 02 04 06 08 1 12




0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








0ndash20

ndash10

0

10

20

Isd

(A)

02 04 06 08 1 12Time (seconds)

14 16 18 2

IsdIsdref


0 02

520500480460440420

008 01 012 014 016 018 02 022 024 026 028



ndash500

Isq

(A)

0

500

1000

IsqIsqref


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

8

6

4

2

0

P s (W

)

times105


0 02 04 06 08 1 12Time (seconds)

14 16 18 2

500

Imab

c (A

)

0

ndash500



0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








0700

800

I r (W

m2 )

900

1000

1100

02 04 06 08 1 12Time (seconds)

14 16 18 2


0 02

Vpv

Vpvref


14 16 18 20

100

200

V pv (

V)

300

400

02

220

240

260

280

300

04 06 08 1 12 14 16 18 2 22times10ndash3


0

600

07505 0751 07515 0752075

650

700

750

800

0

500

1000

IL (A

)

1500

02 04 06 08 1 12Time (seconds)

14 16 18 2

ILILref


25

2

15

1

05

0

P pv (

W)

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

times105








2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018













2000

1500

1000

500

0

V dc (

V)

VdcVdcref

0 02 04 06 08 1 12Time (seconds)

14 16 18 2

01

1460

1480

1500

1520

02 03 04 05 06


2000

1000

Igd

(A)

0

ndash1000

ndash20000 02 04 06 08 1 12


01

400500600700800

015 02 025 03 035 04 045 05 055 06

IgdIgdref


0ndash20

0

20

40

Igq

(A)

05 1 15 2 25 3Time (seconds)

35 4 45

IfqIfq-ref



0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018








0 02 04 06 08 1 12Time (seconds)

14 16 18 2ndash1

0

ndash05

05

1

Act

ive p

ower

(W)

PgPpvPs

times106


0 05 1 15 2 25 3Time (seconds)

35 4 45

ndash05

ndash1

05

0

1

15

Reac

tive p

ower

(VA

R)

times104


ndash1000

Va (

V)

la (A

)

0

ndash500

500

1000

0 02

04

ndash500

0

500

041 042 043 044 045 046 047 048 049 05


14 16 18

Vala

2


075

V v (m

s)

8

85

9

95

10

105

02 04 06 08 1 12Time (seconds)

14 16 18 2





8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018










8 Conclusion



Appendix



JT 105 kgmiddotm2


6

4

2

0Isd

(A)

ndash2

ndash40 02 04 06 08 1 12


IsdPIIsdADRCIsdref

2


00

200

400

Isq

(A)

600

800

02

02410415420425430435

640

09 1 11 12 13 14 15

650

660

670

680

03 04 05 06 07


14 16 18

IsqPIIsqADRCIsqref

2









Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018














Data Availability




References












































Journal of












Journal of







Volume 2018






Volume 2018



























Journal of












Journal of







Volume 2018






Volume 2018








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