Synchronous Generator Excitation System for a Ship Based

Research ArticleSynchronous Generator Excitation System for a Ship Based onActive Disturbance Rejection Control

Rongjie Wang12 Xiangyu Liu1 and Yuyuan Huang 12

1Marine Engineering Institute Jimei University Xiamen 361021 China2Fujian Provincial Key Laboratory of Naval Architecture and Ocean Engineering Xiamen 361021 China

Correspondence should be addressed to Yuyuan Huang yyhuang2504163com

Received 17 December 2020 Revised 24 March 2021 Accepted 7 April 2021 Published 28 April 2021

Academic Editor Qiuye Sun

Copyright copy 2021 RongjieWang et al-is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To solve synchronous generator oscillations in marine power systems which cannot be effectively suppressed according to thenonlinearity and time variability of the ship power system a method of synchronous generator excitation control for a ship basedon active disturbance rejection control (ADRC) is proposed Under different working conditions three methods are automaticvoltage regulator (AVR) automatic voltage regulator with power system stabilizer (PSS) and ADRC methods which are appliedto the two-generator parallel-running excitation system of a ship in simulations -e simulation results show that the excitationcontrol system based on ADRC is faster and has better anti-interference ability and has a better restraining effect on synchronousgenerator oscillation

1 Introduction

A ship power system is an islanded power system When therunning conditions change or the load changes suddenlydue to the inertial action of the synchronous generator rotorthe power angle cannot be instantaneously maintained at anew stable value and adjustment of the near the steady-statevalue under the action of the excitation control system isrequired that is synchronous generator oscillation occurs[1 2] -is phenomenon reduces the stability of the syn-chronous generator set and generator instability can occurthereby affecting the safe and stable running of the entireship power system [3] -erefore the generator excitationsystem of a ship has always been a popular research topic Torestrain synchronous generator oscillation a generator ex-citation system in the ldquoX+AVR (automatic voltage regu-lator)rdquo mode where ldquoXrdquo is the control method is used onland At present the studies that have been carried out oncontrol methods mainly focus on single variable controlmultivariable control and nonlinear control [4ndash13] How-ever the generator excitation system in the ldquoX+AVRrdquo modehas shortcomings such as unreasonable error examplesdifficulty with realizing differential signals which must be

improved and unreasonable linear combinations of errorsignals which cannot resolve the contradiction betweenrapidity and overshooting In connection with the syn-chronous generator oscillation of a ship power system anexcitation system in the ldquoAVR+PSS (power system stabi-lizer)rdquo mode is mainly used [14 15] When the disturbance itis subjected to is relatively small the system can maintainapproximate linearization characteristics however whenthe disturbance the system is subjected to is relatively largeleading to deviation from the normal working point theapproximate linearization characteristics cannot be main-tained thereby leading to a decrease in the performance ofthe control system Due to the unique nature of the runningof the ship power system the existing excitation system inthe ldquoX+AVRrdquo and ldquoAVR+PSSrdquo modes presents a negativedamping effect [16 17] thus synchronous generator os-cillations cannot be effectively restrained -e active dis-turbance rejection control (ADRC) in [18] regards theinternal and external disturbances of the system as a totaldisturbance ADRC combines the advantages of moderncontrol theory and nonlinear theory [19] and has a goodcontrol effect even for nonlinear systems that are difficult toestablish accurate mathematical models Because the

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 6638370 17 pageshttpsdoiorg10115520216638370

algorithm does not depend on the specific model of thecontrol object [20] it has the advantages of high controlaccuracy and strong anti-interference ability so it has beenwidely used in important fields such as national defense andscientific research [21] -e total disturbance of the system isestimated in real time through an extended state observerand then the feedback loop of the system is quickly com-pensated in with this estimated value of the total distur-bance which is a control method suitable for use innonlinear systems and is based on the proportional-integral-derivative principle [22 23] -erefore this paper attemptsto apply ADRC to the synchronous generator excitationsystem of a ship from the perspective of compensating thedamping of the AVR for the ship power system

2 Analysis of theNegativeDampingEffect of theSynchronous Generator Oscillation of a ShipPower System

When the generator is disturbed in the running processdeviations are generated in its various electrical parameters-e electromagnetic torque no-load electromotive forcegenerator voltage and rotor angle of the synchronousgenerator are recorded as Me Eq Ut and δ respectively andthe corresponding amounts of change are ΔMe ΔEq ΔUtand Δδ respectively -eir Heffron-Phillips model isexpressed in

ΔMe K1Δδ + K2ΔEqprime

ΔEqprime

K3

1 + Td0prime K3sΔEfd minus

K3K4

1 + Td0prime K3sΔδ

ΔUt K5Δδ + K6ΔEqprime

Δδ ω0

TJs2 ΔMm minus ΔMe( 1113857

(1)

-e structural block diagram corresponding to equation(1) is shown in Figure 1

As seen in Figure 1 the excitation system changes ΔMe2by changing ΔEq

prime -e transfer function of the entire open-loop system is obtained by moving the K4 summing pointforward

ΔMe2(s)

Δδ(s)

K2G3 K4 + K5GE( 1113857

1 + GEG3K6 (2)

-en

G3 K3

1 + K3Td0prime s (3)

For the rapid excitation system the transfer function GEis

GE(s) KA

1 + TEs (4)

Substituting equations (3) and (4) into equation (2) wecan obtain

ΔMe2

Δδ minus

K2K3K4 1 + TEs( 1113857 + K2K3K5KA

1 + K3Td0prime s( 1113857 1 + TEs( 1113857 + K3K6KA

(5)

Since in the rapid excitation system TEasymp 0K3K6KA is farlarger than 1 so we let s jωd Equation (5) is simplified toobtain

ΔMe2

Δδ

K2K6( 1113857 K4KA + K5( 1113857

1 + jωdTd0prime KAK6 (6)

Setting TEQ Td0prime (KAK6) we have

ΔMe2

Δδ

K2 K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873

+ jωd

K2TEQ K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873

(7)

Equation (7) can be rewritten as

ΔMe2 ΔMsΔδ + ΔMdsΔδ (8)

Equation (8) shows that two torque components can begenerated due to flux linkage changes that is the syn-chronous torque ΔMsΔδ and the damping torque ΔMDsΔδwhere

ΔMs K2 K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873asymp

K2K5

K6 1 + ω2T2EQ1113872 1113873

(9)

ΔMd K2TEQ K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873asymp

K2K5TEQ

K6 1 + ω2T2EQ1113872 1113873

(10)

Considering the inherent damping torque DSΔδ and thesynchronous torque K1Δδ of the synchronous generator theconditions necessary for oscillation instability and non-periodic instability not to occur to the synchronous gen-erator are expressed in

D + ΔMd gt 0 (11)

K1 + ΔMs gt 0 (12)

-e ship power system is often in a state of heavy load Inthis case δ is relatively large and K5lt 0 From equation (9)ΔMsgt 0 is obtained that is the AVR causes the synchronousability of the system to increase from equation (10)ΔMDlt 0is obtained that is the AVR causes the total damping torqueof the system to decrease With increasing voltage ampli-fication coefficient KA TEQ decreases and |ΔMD| increasesBecause the AVR uses voltage as the control variable thephase of the additional flux linkage it provides lags behindΔδ and has a component that is a reversed-phase quantitywith respect to Δω When the negative damping torque itgenerates causes the total damping torque coefficient tosatisfy D+ΔMDlt 0 Δδ becomes large leading to a decreasein the stability of the system and it is impossible to effec-tively restrain the oscillation phenomenon -is type ofphenomenon in which the AVR worsens the damping of thegenerator set can be expressed in Figure 2

When the system is in an equilibrium state because it issubjected to external disturbance the δ angle generates

2 Mathematical Problems in Engineering

oscillations which is expressed as Δδ Let K5lt 0 then thefirst component of the voltage deviation ΔUt1 is the reverseof Δδ Afterwards ΔEfd is input into the excitation systemand the output ΔErsquoq is proportional to ΔMe2 When the AVRamplification multiple is relatively large K4 can be ignoredas it is approximately equal to 0 -en the block diagram ofthe excitation system control is shown in Figure 3 -etransfer function of Figure 3 isΔMe2

ΔUt1 minus

K2K3KA

K3K6KA + 1 + K3Td0prime s( 1113857 1 + TEs( 1113857 (13)

Because TEltlt 1 and K3K6KAgtgt 1 equation (13) issimplified as

ΔMe2

ΔUt1 minus

K2K6

1 + Td0prime K6KAs (14)

As seen from equation (14) the part from -ΔUt1 to ΔMe2is equivalent to an inertia link which generates a phase lag ofΦx 0ndash90deg Figure 2 shows that the component of ΔMe2 onthe Δω axis is a negative value that is the damping torque isnegative In the oscillation process if δ increases the ter-minal voltage Ut1 decreases and the excitation voltage isincreased after AVR regulation however due to the inertialaction the flux linkage still increases when the rotationalspeed Δω is a negative value which causes the electro-magnetic torque of braking to increase that is the so-calledldquonegative dampingrdquo effect If a device is added to the ex-citation it can generate a positive damping torque largeenough to make the position of the combined torque of thistorque with ΔMe2 positive which can compensate for thephase lag of the excitation system and restrain the oscillationof the system

∆Mm ∆ω

∆Eprimeq

∆Me1

∆Efd

∆δω0s

∆Me2

ndash

ndash

ndash+

+ +

+

+ndash

K1

sum

sum sum sum

1TJs

D

K2

K4

V1

Vref

K31 + K3Tprimed0s

K6

K5

Excitationsystem

Figure 1 Heffron-Phillips model of the synchronous generator

∆Ut1 = K5∆δ

∆ω

∆Ms ndash∆Ut1 ∆δ

Φx

∆Me2 = K2∆Eprimeq∆MD

Figure 2 Torque vector diagram

Mathematical Problems in Engineering 3

3 ADRC-Based Control Methods for theSynchronous Generator Excitation System ofa Ship

31 Principle of the Active Disturbance Rejection Controller-e ADRC is mainly composed of three parts the trackingdifferentiator (TD) the extended state observer (ESO) andthe nonlinear state error feedback (NLSEF) control law Itsstructural block diagram is shown in Figure 4 v(t) inFigure 4 is the system input signal After v(t) enters the TDthe TD carries out rapid tracking of v(t) and obtains the twooutput signals v1 and v2 where v1 is the tracking signal ofv(t) and v2 is the differential signal of v(t) -e output signalof ESO is the output signal of the controlled object and threeoutput signalsmdashz1 z2 and z3mdashare given after state esti-mation z1 and z2 are the estimated values of the statevariables by the ESO for an uncertain model z3 is the totaldisturbance estimate by the ESO for an uncertain modelAfterwards v1 and z1 as well as v2 and z2 are compared toobtain two sets of error signals e1 and e2 NLSEF carries outnonlinear combination of the two sets of error signals toobtain the control signal u0(t) the control signal is multi-plied by the ESO-estimated total disturbance state variable z3and the coefficient 1b and the final control value u(t) isobtained

32 Design of the Active Disturbance Rejection Controller forthe Synchronous Generator Excitation System of a ShipEach part of the ADRC can be independently designedaccording to the ldquoseparation principlerdquo and then combinedinto a complete closed-loop controller -e steps for thedesign of the active disturbance rejection controller for thesynchronous generator excitation system of a ship are asfollows

321 Modeling of the Controlled Object -e ADRC con-troller does not require an accurate mathematical model anapproximate model suffices -e approximate mathematicalmodel of the synchronous generator excitation system is

δbull

ω minus ω0

_ω ωH

Pm minus Pe( 1113857 minusD

Hω minus ω0( 1113857

Eqprime minus

1Td0

Eq +1

Td0Ef

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)

322 Arranging the Transition Process -e purpose ofarranging the transition process is to quickly and accuratelytrack the input signal and the differential of the input signalIn this paper the terminal voltage rating taken by the ADRCfor the synchronous generator is the TD input voltage v andthe fastest comprehensive function of the transition processis fhan -e TD transition process is arranged as

_v1 v1 + hv2

_v2 v2 + hfhan v1 minus v2 r h( 11138571113896 (16)

where r is an adjustable parameter and h is the integrationstep size

323 Design of the ESO -e functional relationship be-tween the terminal voltage and the excitation voltage of thesynchronous generator is regarded as an unknown functionf(x) then the state spatial equation of the excitation systemcan be expressed as

_x1 x2

_x2 f x1 x2( 1113857 + bu

y x1

⎧⎪⎪⎨

⎪⎪⎩(17)

Expanding f(x1 x2) into a new state variable we have

_x1 x2

_x2 x3 + bu

_x3 w

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)

K2

K6

K5

∆Uref KA1 + TEs K31 + K3Tprimed0sndash

ndash+

∆δ

∆Me2∆Eprimeq

Figure 3 Block diagram of the generator excitation system that ignores K4


By introducing the fal function we can design the fol-lowing third-order state observer -rough this state ob-server the total disturbance of the excitation system and theterminal voltage Ut of the synchronous generator areestimated

e z1 minus y1

z1 z1 + h z2 minus β01e minus u1( 1113857

z2 z2 minus hβ02 minus hfal e α1 h( 1113857

z3 z3 minus hβ03fal e α2 δ( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(19)

where β01 β02 and β03 are adjustable parameters and h is theintegration step size

324 Design of the Nonlinear Error Feedback -e design ofthe nonlinear error feedback is shown in the followingequation

e1 v1 minus z1

e2 v2 minus z2

u0 k1fal e1 α1 δ( 1113857 + k2fal e2 α2 δ( 1113857

u u0 minusz3

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(20)

where u is the control variable Uf b is the control variablecoefficient and k1 and k2 are adjustable parameters

After the three core links of ADRC that is the TD theESO and the nonlinear error feedback have been designedthey are connected in accordance with the input of thecontrolled object the output and the input and output ofeach module according to the logical relationship and anADRC-based synchronous generator excitation controlsystem for a ship is constructed -e structural block dia-gram of control is shown in Figure 5

Figure 5 shows that the system input is the referencevoltage Uref After going through the TD and NLSEF linksthe initial control voltage u0(t) is output Afterwards the

ESO carries out disturbance compensation for -z3b toobtain the control voltage u(t) -e control voltage u(t)undergoes limiting and the excitation voltage Uf is outputafter the exciter starts the excitation Afterwards the voltageof the synchronous generator is measured to obtain theoutput terminal voltage Ut and it is fed back to the ESO tocomplete closed-loop control

325 Parameter Tuning Methods -ere are currently nospecific methods for ADRC parameter tuning Manualadjustment of parameters can be carried out only accordingto empirical methods In this paper parameter adjustment iscarried out according to the order of TD ESO and NLSEFand actual simulation experience is combined with datafrom relevant literature -e following is a summary of theexperience in ADRC parameter tuning

According to the TD principle described in the abovetext the TD is a system that contains linear and nonlinearparts and the selection of its nonlinear function and pa-rameters greatly affects the performance of the TD-emainparameters of the TD are r and h According to experience rmainly determines the speed in tracking the signal and hmainly affects the filtering effect of the TD and the quality ofthe differential signal -e parameter r cannot take on anoverly large value to ensure the tracking speed otherwisethe quality of the output signal is reduced the TD outputsignal is the same as the input signal the function ofarranging the transition process is lost and the contradictionbetween speed and overshooting cannot be resolved -eparameter h should not take on an overly small valueotherwise the quality of the differential signal cannot beensured -is parameter is generally between 0001 and 001

-e role of the ESO as the core of ADRC is to accuratelyestimate the state variables and disturbances and compen-sate for the control signal u0 If the parameters of the ESO arenot regulated properly the entire closed-loop control isgreatly affected β01 β02 and β03 are the three main pa-rameters of the ESO A large amount of simulation expe-rience and data show the following -e larger β01 is thefaster z1 tracks a given signal y and the faster z2 tracks thederivative of y However when β01 is too large an oscillation

v (t)TD v1

v2

e2

e1+

+ndash

ndashndash

NLSEFu0 (t) u (t)

W (t)

y (t)+ Controlledplant

1b

z3

z2

z1

ESO

b

Figure 4 Structural block diagram of the active disturbance rejection controller


phenomenon appears in z2 and z3 when β01 is too small adivergence phenomenon appears in the three state variables-e parameter β02 does not have too great of an effect on thestate variable x1 with increasingβ02 the estimation effect ofESO on the disturbance x3 worsens and high-frequencynoise appears leading to a failure to track the disturbance ifβ02 is too small then a divergence phenomenon appears in z1and z2 -e parameter β03 has a greater effect on z1 and z2and an increase in the value of β03 causes z1 and z2 to divergeDecreasing the value of β03 generates a large error in theestimated value of x1z1 and the estimated value of thedisturbance z3 becomes very poor We can see from theabove experience that only by fully considering the con-straint relationship between the three parameters of β01 β02and β03 can a more ideal simulation result be obtained

According to the principle of nonlinear state errorfeedback the role of the two parameters k1 and k2 is similarto that of kp and kd in proportional-integral-derivative (PID)control Increasing the parameter k1 can improve the ra-pidity of system regulation but the amount of overshootingincreases the rapidity of the system is reduced by decreasingthe parameter k1 and the amount of overshooting decreases-e role of the parameter k2 is opposite to that of k1 in-creasing k2 decreases the amount of overshooting and thesystem regulation time increases Decreasing k2 increases thespeed of the system and the amount of overshootingChanges in the parameter b greatly change the controlvariable u As seen from the logical relationships inFigures 5ndash8 increasing b can increase the control variable ubut decreasing b decreases the compensation for the dis-turbance Selecting an appropriate value for the parameter bis very important for the disturbance compensation effect

4 Simulation Verification

41 ADRC Simulation Model First the simulation modelsfor the three core partsmdashTD ESO and NLSEFmdashareestablished

411 TD Simulation Model -e TD simulation modelestablished in accordance with equation (16) is shown inFigure 6

To verify the effectiveness of the TD simulation modelbuilt a simple verification simulation is carried out Giventhe input of a sinusoidal signal of sin(t) the initial inputsignal of the TD is v(t) sin(t) -e simulation parametersettings are an integration step size h 0005 and r 100-esimulation curves are shown in Figure 7

-e TD parameters are changed to an integration stepsize h 0005 and r 200 and the simulation curves areshown in Figure 8


As seen from the above three simulation diagrams theestablished TD simulation model has a relatively goodtracking effect on the input signal and can obtain a good-quality differential signal Comparison of Figures 7 and 8shows that when the value of the parameter r is increasedthe signal tracking is better but the fluctuations in thedifferential signal increase Comparison of Figures 8 and 9shows that increasing the value of h can obviously improvethe tracking result but reduces the quality of the differentialsignal

412 ESO Simulation Model -e established ESO simu-lation model is shown in Figure 10

In the figure the two fal modules arem files written withthe S-function

Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+

Limit ExcitationUf Ut

W (t)

1b

z3

z2

z1

ESO

b

Synchronousgenerator

Figure 5 Structural block diagram of the ADRC-based synchronous generator excitation control system of a ship

1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h

Figure 6 TD simulation model


413 NLSEF SimulationModel According to equation (20)the m files are written with the S-function -e establishedNLSEF simulation model is shown in Figure 11

In Figure 11 the initial control variable u can be outputby carrying out nonlinear feedback regulation on the twoerrors of e1 and e2 and carrying out reasonable parameterregulation

-e simulation models of the above three modules arepackaged and connected to form a complete ADRC simu-lation model shown in Figure 12

To verify the effectiveness of the established ADRCsimulation model a simple verification simulation experi-ment is carried out -e controlled object is assumed to be

G(s) 1

s2

+ 3s + 1 (21)

-e simulation parameter settings are as follows TDparameters r 100 and h 0005 ESO parameters β01 50β02 300 and β03 10 compensation coefficient b 05nonlinear state feedback parameters α1 05 α2 075 andδ 01 -e TD input is a sinusoidal signal and the simu-lation curve is shown in Figure 13

-e above simulation curve shows that the establishmentof the ADRC controller simulation model is successfulMoreover Figure 13 shows that the ESO can very accuratelyestimate state x1 Figure 14 shows that the ESO can carry outmore accurate estimation for state x2 but that the estimationis not as good as the estimation for x1 which may be relatedto the settings for the three parameters of β01 β02 and β03

42 Sudden Loading and Sudden Unloading Simulation Test-e ADRC simulation model in Figure 12 and the two-generator parallel-running simulationmodel of a ship powersystem are combined to establish an ADRC-based two-generator parallel-running simulationmodel of a ship powersystem -e simulation model is shown in Figure 15

To verify the effectiveness of the ADRC-based two-generator parallel-running simulationmodel of a ship powersystem established in Figure 15 and to verify the restrainingeffect of the ADRC-based synchronous generator excitationcontrol system of a ship on the synchronous generatoroscillation shown in Figure 15 the three excitation controlmethods (AVR AVR+PSS2B and ADRC) are used to carryout simulation experiments under different working con-ditions to verify the effectiveness of the proposed method

-e following parameters of the synchronous generatorfrom a certain real ship are used -e parameters of thesynchronous generators G1 and G2 are as followsPn 3125times106 VA Un 450V fn 60Hz Xd 156Xdrsquo 0296 Xdrsquorsquo 0177 Xqrsquo 106 Xqrsquorsquo 0177 X1 0052Tdrsquo 37 Tdrsquorsquo 005 and Tq0 005 -e parameters of theTD are as follows r 100 h 0005 those of ESO are asfollows β01 80 β02 50 β03 10 h 01 α1 075 andα2 075 and those of the nonlinear state feedback are asfollows k1 35 k2 150 α1 05 and α2 125

0 1 2 3 4 5 6 7 8 9 10ts

Tracking signalOriginal signalDifferential signal

Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15

Figure 7 Simulation curves with r 100 and h 0005

0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15



In this test the simulation time is 35 s -e synchronousgenerators G1 and G2 start running in parallel with no loadat 0 s are suddenly loaded with Load 1 at 5 s are suddenlyloaded with Load 2 at 15 s and are suddenly unloaded ofLoad 2 at 25 s -e load parameter settings of Load 1 andLoad 2 are P 15times103 kW andQ 12times103 kW-e curvesof the changes in each parameter of the synchronous gen-erator are shown in Figure 16

Figure 16 shows that when the synchronous generatorstarts with no load at 0 s in the cases where the excitationsystem uses the control methods of AVR and AVR+PSS2Bthe generator can quickly start and in the case where ADRCis usedUt has an adjustment process with a large amplitudewhich shows that under no disturbances the regulationeffect of AVR and AVR+PSS2B is better than that of ADRCWith the sudden loading at 5 s and 15 s the use of ADRC forapproximately 03 s can restore Ut to a stable value andalmost no overshooting occurs in the regulation process

whereas the regulation time using AVR+PSS2B is ap-proximately 1 s and the voltage slightly overshoots in theregulation process In the case where only AVR is used theamount of overshooting in voltage is the largest and theregulation time is the longest With the sudden unloading at25 s after the maximum voltage is increased to 102 with theuse of ADRC and the voltage is restored to 1 after 02 s themaximum voltage is increased to 105 with the use ofAVR+PSS2B and AVR the voltage tends to stabilize afterapproximately 3 s23 and the voltage fluctuation is smaller inthe AVR+PSS2B regulation process

Figure 17 shows that with the sudden loading at 5 s and15 s as well as the sudden unloading at 25 s in the case wherethe excitation system is using AVR control the fluctuation inthe rotational speed of the synchronous generator is thegreatest and the regulation time is the longest whenAVR+PSS2B is used the maximum value and theminimumvalue of the rotational speed fluctuation are both reduced

[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn

Figure 10 ESO simulation model

1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn

Figure 11 NLSEF simulation model


V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF

Figure 12 ADRC controller simulation model

Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1

Figure 13 State (x)1 estimation curve

0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1

Figure 15 ADRC-based two-generator parallel-running simulation model of a ship power system

04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC

Figure 16 Comparison of the terminal voltages of the synchronous generator under sudden loading and sudden unloading workingconditions

0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC

Figure 17 Comparison of the rotational speeds of the synchronous generator under sudden loading and sudden unloading workingconditions


and the time needed for restoration to a stable value isshorter After ADRC is used the rotational speed fluctuationof the synchronous generator reaches the minimum

As seen in Figure 18 after sudden loading with Load 1 at5 s the active power is increased to 02 and after suddenloading with Load 2 at 15 s the active power is increased totwo times the original value Under the two control modes ofAVR and AVR+PSS2B after the active power is restored toa stable value there is a slight fluctuation and after ADRC isused the active power exhibits a large fluctuation only for aninstant at sudden loading afterwards this parameter isquickly restored to the stable value and does not oscillateafter restoration to the stable value At 25 s when half of theload is suddenly unloaded after a slight fluctuation theactive power drops to half of the original and the ADRCrestores the steady-state value the fastest

Figure 19 shows that the mechanical power of thesynchronous generator running with no load from 0 to 5 s is0 the mechanical power increases after sudden loading at 5 sand 15 s and the mechanical power drops to half of theoriginal after the sudden unloading of half the load at 25 s Inthis process under the three cases of AVR AVR+PSS2Band ADRC the ADRC regulation time is the shortest withthe smallest amplitude fluctuation in the active power fol-lowed by AVR+PSS2B and the AVR regulation time is thelongest with the largest amplitude fluctuation in the activepower

-e above simulation results show that under suddenloading and sudden unloading working conditions for theship power system compared with the control methods ofAVR and AVR+PSS2B when the excitation system uses theADRC method the oscillation amplitudes of the parametersof the synchronous generator are the smallest and the timeof restoration to stability is the fastest

43 Sudden Loading and Single-Phase Short-Circuit FaultSimulation Test In this test the simulation time is 25 s thesynchronous generators G1 and G2 start running parallellywith no load at 0 s the heavy load of Load 3 is suddenlyadded at 5 s and a single-phase short-circuit fault occurssuddenly at 15 s with a fault duration of 01 s -e loadparameter settings of Load 3 are P 31times 103 kW andQ 25times103 kvar -e curves of the changes of each pa-rameter of the synchronous generator are shown inFigure 20

As seen from Figure 20 when a heavier load is suddenlyloaded at 5 s the results are still the same as the analysis ofthe previous scenario the control effect of the ADRC is thebest followed by that of AVR+PSS2B and the control effectof AVR is the worst When a single-phase short-circuit faultoccurs at 15 s an obvious drop appears in the terminalvoltage of the synchronous generator under the three controlmodes of AVR AVR+PSS2B and ADRC and the ampli-tudes of the drops are basically the same however under thetwo control modes of AVR and AVR+PSS2B the voltageneeds to undergo approximately 25 s of regulation before itis restored to stability and the voltage oscillation amplitudein the AVR regulation process is greater than that of

AVR+PSS2B Under ADRC the voltage needs to gothrough only approximately 1 s of restoration it can berestored to the stable value and the voltage oscillationamplitude in the regulation process is very small

Figure 21 shows that when the heavy load is suddenlyadded at 5 s the differences in the curves of the rotationalspeed for the three control modes are relatively large withthe control effect of ADRC being the best when the short-circuit fault suddenly occurs at 15 s a slight drop appears inthe rotational speed of the synchronous generator droppingto 0996 under all three control modes and then the voltageis restored to a stable value after undergoing 3-4 s [23] ofregulation In the regulation process the oscillation in therotational speed of the AVR control mode is somewhat largeand the curves for the two control methods of AVR+PSS2Band ADRC are almost the same

Figure 22 shows that when the heavy load is suddenlyadded at 5 s the active power increases to 05 after under-going transient oscillation the oscillation amplitude withADRC is the smallest and its time for restoration to a steadystate is the shortest -e control effect of AVR+PSS2B is thesecond best followed by that of AVRWhen the single-phaseshort-circuit fault occurs at 15 s a sudden change occurs inthe active power which increases to 14 at the maximum anddrops to 03 at the minimum the curves of the three controlmodes are almost the same

Figure 23 shows that when the heavy load is suddenlyadded at 5 s the mechanical power quickly rises and sta-bilizes at 045 after undergoing transient regulation -eoscillation amplitude is the greatest under the AVR controlmode and the increase in the oscillation amplitude is thesmallest with ADRC After the short-circuit fault occurs at15 s a slight sudden increase occurs in the mechanicalpower which is restored to stability after undergoing ap-proximately 3 s of regulation the effects of the three controlmodes are almost the same

-e above analysis shows that when small disturbancessuch as single-phase short-circuit faults occur in the shippower system the restraining effect of ADRC on the os-cillation of various parameters of the synchronous generatoris slightly better than those of the other two control methods

44 ree-phase Short-Circuit Fault Simulation Test In thistest the simulation time setting is 20 s -e synchronousgenerators G1 and G2 start at 0 s with Load 3 and a three-phase short-circuit fault occurs in the system at 10 s with afault duration of 01 s -e curves of the changes in eachparameter of the synchronous generator are shown inFigure 24

As seen from Figure 24 when the three-phase short-circuit fault occurs in the system at 10 s a large drop occursin the terminal voltage of the synchronous generator andthen the terminal voltage quickly rallies and is restored tostability Under AVR control the terminal voltage drops to aminimum of 02 increases to a maximum of 1185 and isrestored to stability after approximately 5 s UnderAVR+PSS2B control the terminal voltage drops to aminimum of 02 increases to a maximum of 118 and is


restored to stability after approximately 3 s Under ADRCthe terminal voltage drops to a minimum of 02 increases toa maximum of 115 and is restored to stability after ap-proximately 2 s

Figure 25 shows that after the three-phase short-circuitfault occurs in the system at 10 s an obvious drop appears inthe rotational speed of the synchronous generator and therotational speed is restored to stability after undergoing ashort period of oscillation regulation Under AVR controlthe rotational speed drops to a minimum of 0987 increasesto a maximum of 1009 and is restored to stability afterundergoing approximately 6 s of regulation Under

AVR+PSS2B control the rotational speed drops to aminimum of 0987 increases to a maximum of 1007 and isrestored to stability after undergoing approximately 5 s ofregulation Under ADRC the rotational speed drops to aminimum of 0987 increases to a maximum of 1005 and isrestored to stability after undergoing approximately 4 s ofregulation

Figure 26 shows that after the three-phase short-circuitfault occurs in the system at 10 s a large oscillation appearsinstantaneously in the active power of the synchronousgenerator and the active power is restored to stability afterundergoing a short period of oscillation regulation Under

ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC

Figure 18 Comparison of the active powers of the synchronous generator under sudden loading and sudden unloading working conditions

0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC

Figure 19 Comparison of the mechanical powers of the synchronous generator under sudden loading and sudden unloading workingconditions


AVR control the active power drops to a minimum of 0increases to a maximum of 33 and is restored to stabilityafter undergoing approximately 25 s of regulation UnderAVR+PSS2B control the active power drops to a minimumof 0 increases to a maximum of 33 and is restored tostability after undergoing approximately 22 s of regulationUnder ADRC the active power drops to a minimum of 0

increases to a maximum of 32 and is restored to stabilityafter undergoing approximately 15 s of regulation

Figure 27 shows that after the three-phase short-circuitfault occurs in the system at 10 s the mechanical power ofthe synchronous generator increases instantaneously fallsback and is restored to stability after undergoing a shortperiod of oscillation regulation Under AVR control the

04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC

Figure 20 Comparison of the terminal voltages of the synchronous generator under sudden loading and single-phase short-circuit faultworking conditions

098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC

Figure 21 Comparison of the rotational speeds of the synchronous generator under sudden loading and single-phase short-circuit faultworking conditions


mechanical power drops to a minimum of 035 increases toa maximum of 088 and is restored to stability after un-dergoing approximately 6 s of regulation UnderAVR+PSS2B control the mechanical power drops to aminimum of 037 increases to a maximum of 088 and isrestored to stability after undergoing approximately 45 s ofregulation Under ADRC the mechanical power drops to a

minimum of 04 increases to a maximum of 088 and isrestored to stability after undergoing approximately 3 s ofregulation

-e above simulation analysis in this section shows thatwhen larger disturbances such as three-phase short-circuitfaults occur in the ship power system compared with thecontrol methods of AVR and AVR+PSS2B the ADRC

ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC

Figure 22 Comparison of the active powers of the synchronous generator under sudden loading and single-phase short-circuit faultworking conditions

0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC

Figure 23 Comparison of the mechanical powers of the synchronous generator under sudden loading and single-phase short-circuit faultworking conditions


0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC

Figure 24 Comparison of the terminal voltages of the synchronous generator under three-phase short-circuit fault working condition

098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC

Figure 25 Curves comparing the rotational speed of the synchronous generator under three-phase short-circuit fault working conditions


method has a better restraining and regulating effect onsynchronous generator oscillations caused by largedisturbances

5 Conclusion

In this paper the negative damping effect of the excitationsystem is first analyzed from the perspective of synchronoustorque and damping torque in accordance with the Heffron-Phillips model of the synchronous generator and the ap-plication of ADRC to the synchronous generator excitationsystem of a ship is proposed Finally simulation experiments

of the two-generator parallel-running system of the syn-chronous generator of a ship are carried out under differentworking conditions comparative simulation tests are carriedout under different working conditions for the three exci-tation control methods of AVR AVR+PSS2B and ADRCand the simulation results show the effectiveness of theproposed method Notably when the system is subjected todisturbances under different working conditions therestraining effect of ADRC on the oscillations of variousparameters of the synchronous generator is the best ADRCreplaces the PID control in the traditional marine syn-chronous generator and constructs an ADRC-based marine

0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC

Figure 26 Comparison of the active powers of the synchronous generator under three-phase short-circuit fault working conditions

0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC

Figure 27 Comparison of the mechanical powers of the synchronous generator under three-phase short-circuit fault working conditions


synchronous generator excitation control system in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported in part by the National NaturalScience Foundation of China under Grant nos 51879118 and51779102 the High-Level Talent Training Project in theTransportation Industry under Grant no 2019-014 the FujianProvince Office of Science and Technology Support for Armyunder Grant no B19101 the Foundation of Fujian EducationCommittee of China for New Century Distinguished Scholarsunder Grant no B17159 the Scientific Research Foundationof Key Laboratory of Fishery Equipment and EngineeringMinistry of Agriculture of the Peoplersquos Republic of Chinaunder Grant nos 2016002 and 2018001 the Scientific Re-search Foundation of Artificial Intelligence Key Laboratory ofSichuan Province under Grant no 2017RYJ02 and the Sci-entific Research Foundation of Jiangsu Key Laboratory ofPower Transmission amp Distribution Equipment Technologyunder Grant no 2017JSSPD01

References

[1] T H Tang Ship Electric Propulsion System China MachinePress Beijing China 2015

[2] R J Wang Y J Zhan and H F Zhou ldquoResearch on optimalsizing of stand-alone diesel-based hybrid energy systemsrdquoActa Energiae Solaris Sinica vol 40 no 2 pp 348ndash355 2019

[3] H Jun J Sun and H Hofmann ldquoMitigating power fluctu-ations in electric ship propulsion with hybrid energy storagesystem design and analysisrdquo IEEE Journal of Oceanic Engi-neering vol 43 no 1 pp 93ndash107 2018

[4] S Lalit-Chandra ldquoPerformance of coordinated interlinepower flow controller and power system stabilizer in com-bined multiarea restructured ALFC and AVR systemrdquo In-ternational Transactions on Electrical Energy Systems vol 29no 3 pp 2822ndash2839 2019

[5] H Reza ldquoPower system stabilizer design based on optimalmodel reference adaptive systemrdquo Ain Shams EngineeringJournal vol 9 no 2 pp 311ndash318 2016

[6] M Luan W Lu and D C Liu ldquoCoordination excitationcontroller design based on disturbance tracking Terminalsliding mode and multi-objective zero dynamics controlrdquoPower System Protect and Control vol 43 no 4 pp 311ndash3182015

[7] Y Jiang and Z-P Jiang ldquoRobust adaptive dynamic pro-gramming for large-scale systems with an application tomultimachine power systemsrdquo IEEE Transactions on Circuitsand Systems II Express Briefs vol 59 no 10 pp 693ndash6972012

[8] B J Lei S M Fei and J Y Zhai ldquoCoordinated control ofautomatic voltage regulator and SVC in multi-machine power

systemrdquo Transactions of China Electrotechnical Societyvol 30 no 18 pp 131ndash139 2015

[9] X W Zhan H Xie and S X Lv ldquoParameter setting and on-site test of power system stabilizer ndashPSS4Brdquo Power SystemTechnology vol 40 no 2 pp 508ndash513 2016

[10] H Wang W Wei and Y F Pan ldquoA bilevel programmingbased method for tuning parameters of nonlinear robustpower system stabilizerrdquo Automation of Electric Power Sys-tem vol 38 no 14 pp 42ndash48 2014

[11] Z Ilias and X Wang ldquoWide-Area damping control forinterarea oscillations in power grids based on PMU mea-surementsrdquo IEEE Control Systems Letters vol 2 no 4pp 719ndash724 2018

[12] X Y Liu e Research on Methods of Suppressing Oscillationof Synchronous Generator in Ship Power System Jimei Uni-versity Xiamen China 2020

[13] C Yan G K Venayagamoorthy and K Corzine ldquoAIS-basedcoordinated and adaptive control of generator excitationsystems for an electric shiprdquo IEEE Transactions on IndustrialElectronics vol 59 no 8 pp 3102ndash3112 2012

[14] H Shayeghi and Y Hashemi ldquoProfit enhancement by a set ofperformance and robustness indices based design of dual-dimensional PODC and PSS2B in smart gridsrdquo EnergyConversion and Management vol 83 no 7 pp 99ndash109 2014

[15] H Shayeghi and Y Hashemi ldquoPecuniary evaluation of pro-vided service by local and global based dual-dimensional SDCand PSS2B in the context of deregulated power marketsrdquoEnergy Conversion and Management vol 76 no 7pp 753ndash763 2013

[16] G Sulligoi A Vicenzutti V Arcidiacono and Y KhersonskyldquoVoltage stability in large marine-integrated electrical andelectronic power systemsrdquo IEEE Transactions on IndustryApplications vol 52 no 4 pp 3584ndash3594 2016

[17] Q Sun R Han H Zhang J Zhou and J M Guerrero ldquoAmultiagent-based consensus algorithm for distributed coor-dinated control of distributed generators in the energy in-ternetrdquo IEEE Transactions on Smart Grid vol 6 no 6pp 3006ndash3019 2015

[18] R Wang Q Sun W Hu Y Li D Ma and P Wang ldquoSoC-based droop coefficients stability region analysis of the batteryfor stand-alone supply systems with constant power loadsrdquoIEEE Transactions on Power Electronics vol 36 no 7pp 7866ndash7879 2021

[19] W Hu C Ruan H Nian and D Sun ldquoZero-sequence currentsuppression strategy with common mode voltage control foropen-end winding PMSM drives with common DC busrdquoIEEE Transactions on Industrial Electronics vol 68 no 6pp 4691ndash4702 2020

[20] D Ma X Hu H Zhang Q Sun and X Xie ldquoA hierarchicalevent detection method based on spectral theory of multi-dimensional matrix for power systemrdquo IEEE Transactions onSystems Man and Cybernetics Systems vol 51 no 4pp 2173ndash2186 2019

[21] X Hu H Zhang D Ma and R Wang ldquoA tnGAN-based leakdetection method for pipeline network considering incom-plete sensor datardquo IEEE Transactions on Instrumentation andMeasurement vol 70 pp 1ndash10 2020

[22] J Q Han ldquoAuto disturbances rejection control techniquerdquoFrontier Science vol 98 no 1 pp 24ndash31 2007

[23] B Payvand and S M H Hosseini ldquoA new method formitigating frequency fluctuations in ships with electricalpropulsionrdquo ISA Transactions vol 92 no 1 pp 241ndash2562019


algorithm does not depend on the specific model of thecontrol object [20] it has the advantages of high controlaccuracy and strong anti-interference ability so it has beenwidely used in important fields such as national defense andscientific research [21] -e total disturbance of the system isestimated in real time through an extended state observerand then the feedback loop of the system is quickly com-pensated in with this estimated value of the total distur-bance which is a control method suitable for use innonlinear systems and is based on the proportional-integral-derivative principle [22 23] -erefore this paper attemptsto apply ADRC to the synchronous generator excitationsystem of a ship from the perspective of compensating thedamping of the AVR for the ship power system

2 Analysis of theNegativeDampingEffect of theSynchronous Generator Oscillation of a ShipPower System

When the generator is disturbed in the running processdeviations are generated in its various electrical parameters-e electromagnetic torque no-load electromotive forcegenerator voltage and rotor angle of the synchronousgenerator are recorded as Me Eq Ut and δ respectively andthe corresponding amounts of change are ΔMe ΔEq ΔUtand Δδ respectively -eir Heffron-Phillips model isexpressed in

ΔMe K1Δδ + K2ΔEqprime

ΔEqprime

K3

1 + Td0prime K3sΔEfd minus

K3K4

1 + Td0prime K3sΔδ

ΔUt K5Δδ + K6ΔEqprime

Δδ ω0

TJs2 ΔMm minus ΔMe( 1113857

(1)

-e structural block diagram corresponding to equation(1) is shown in Figure 1

As seen in Figure 1 the excitation system changes ΔMe2by changing ΔEq

prime -e transfer function of the entire open-loop system is obtained by moving the K4 summing pointforward

ΔMe2(s)

Δδ(s)

K2G3 K4 + K5GE( 1113857

1 + GEG3K6 (2)

-en

G3 K3

1 + K3Td0prime s (3)

For the rapid excitation system the transfer function GEis

GE(s) KA

1 + TEs (4)

Substituting equations (3) and (4) into equation (2) wecan obtain

ΔMe2

Δδ minus

K2K3K4 1 + TEs( 1113857 + K2K3K5KA

1 + K3Td0prime s( 1113857 1 + TEs( 1113857 + K3K6KA

(5)

Since in the rapid excitation system TEasymp 0K3K6KA is farlarger than 1 so we let s jωd Equation (5) is simplified toobtain

ΔMe2

Δδ

K2K6( 1113857 K4KA + K5( 1113857

1 + jωdTd0prime KAK6 (6)

Setting TEQ Td0prime (KAK6) we have

ΔMe2

Δδ

K2 K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873

+ jωd

K2TEQ K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873

(7)

Equation (7) can be rewritten as

ΔMe2 ΔMsΔδ + ΔMdsΔδ (8)

Equation (8) shows that two torque components can begenerated due to flux linkage changes that is the syn-chronous torque ΔMsΔδ and the damping torque ΔMDsΔδwhere

ΔMs K2 K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873asymp

K2K5

K6 1 + ω2T2EQ1113872 1113873

(9)

ΔMd K2TEQ K4KA + K5( 1113857

K6 1 + ω2T2EQ1113872 1113873asymp

K2K5TEQ

K6 1 + ω2T2EQ1113872 1113873

(10)

Considering the inherent damping torque DSΔδ and thesynchronous torque K1Δδ of the synchronous generator theconditions necessary for oscillation instability and non-periodic instability not to occur to the synchronous gen-erator are expressed in

D + ΔMd gt 0 (11)

K1 + ΔMs gt 0 (12)

-e ship power system is often in a state of heavy load Inthis case δ is relatively large and K5lt 0 From equation (9)ΔMsgt 0 is obtained that is the AVR causes the synchronousability of the system to increase from equation (10)ΔMDlt 0is obtained that is the AVR causes the total damping torqueof the system to decrease With increasing voltage ampli-fication coefficient KA TEQ decreases and |ΔMD| increasesBecause the AVR uses voltage as the control variable thephase of the additional flux linkage it provides lags behindΔδ and has a component that is a reversed-phase quantitywith respect to Δω When the negative damping torque itgenerates causes the total damping torque coefficient tosatisfy D+ΔMDlt 0 Δδ becomes large leading to a decreasein the stability of the system and it is impossible to effec-tively restrain the oscillation phenomenon -is type ofphenomenon in which the AVR worsens the damping of thegenerator set can be expressed in Figure 2

When the system is in an equilibrium state because it issubjected to external disturbance the δ angle generates



ΔUt1 minus

K2K3KA



ΔMe2

ΔUt1 minus

K2K6



∆Mm ∆ω

∆Eprimeq

∆Me1

∆Efd

∆δω0s

∆Me2

ndash

ndash

ndash+

+ +

+

+ndash

K1

sum

sum sum sum

1TJs

D

K2

K4

V1

Vref

K31 + K3Tprimed0s

K6

K5

Excitationsystem


∆Ut1 = K5∆δ

∆ω


Φx








δbull

ω minus ω0

_ω ωH



Eqprime minus

1Td0

Eq +1

Td0Ef

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)


_v1 v1 + hv2




_x1 x2

_x2 f x1 x2( 1113857 + bu

y x1

⎧⎪⎪⎨

⎪⎪⎩(17)


_x1 x2

_x2 x3 + bu

_x3 w

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)

K2

K6

K5


ndash+

∆δ

∆Me2∆Eprimeq




e z1 minus y1




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(19)



e1 v1 minus z1

e2 v2 minus z2


u u0 minusz3

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(20)








v (t)TD v1

v2

e2

e1+

+ndash

ndashndash

NLSEFu0 (t) u (t)

W (t)


1b

z3

z2

z1

ESO

b














Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+


W (t)

1b

z3

z2

z1

ESO

b



1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h







G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References



























ΔUt1 minus

K2K3KA



ΔMe2

ΔUt1 minus

K2K6



∆Mm ∆ω

∆Eprimeq

∆Me1

∆Efd

∆δω0s

∆Me2

ndash

ndash

ndash+

+ +

+

+ndash

K1

sum

sum sum sum

1TJs

D

K2

K4

V1

Vref

K31 + K3Tprimed0s

K6

K5

Excitationsystem


∆Ut1 = K5∆δ

∆ω


Φx








δbull

ω minus ω0

_ω ωH



Eqprime minus

1Td0

Eq +1

Td0Ef

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)


_v1 v1 + hv2




_x1 x2

_x2 f x1 x2( 1113857 + bu

y x1

⎧⎪⎪⎨

⎪⎪⎩(17)


_x1 x2

_x2 x3 + bu

_x3 w

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)

K2

K6

K5


ndash+

∆δ

∆Me2∆Eprimeq




e z1 minus y1




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(19)



e1 v1 minus z1

e2 v2 minus z2


u u0 minusz3

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(20)








v (t)TD v1

v2

e2

e1+

+ndash

ndashndash

NLSEFu0 (t) u (t)

W (t)


1b

z3

z2

z1

ESO

b














Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+


W (t)

1b

z3

z2

z1

ESO

b



1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h







G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References






























δbull

ω minus ω0

_ω ωH



Eqprime minus

1Td0

Eq +1

Td0Ef

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(15)


_v1 v1 + hv2




_x1 x2

_x2 f x1 x2( 1113857 + bu

y x1

⎧⎪⎪⎨

⎪⎪⎩(17)


_x1 x2

_x2 x3 + bu

_x3 w

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(18)

K2

K6

K5


ndash+

∆δ

∆Me2∆Eprimeq




e z1 minus y1




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(19)



e1 v1 minus z1

e2 v2 minus z2


u u0 minusz3

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(20)








v (t)TD v1

v2

e2

e1+

+ndash

ndashndash

NLSEFu0 (t) u (t)

W (t)


1b

z3

z2

z1

ESO

b














Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+


W (t)

1b

z3

z2

z1

ESO

b



1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h







G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References



























e z1 minus y1




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(19)



e1 v1 minus z1

e2 v2 minus z2


u u0 minusz3

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(20)








v (t)TD v1

v2

e2

e1+

+ndash

ndashndash

NLSEFu0 (t) u (t)

W (t)


1b

z3

z2

z1

ESO

b














Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+


W (t)

1b

z3

z2

z1

ESO

b



1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h







G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References





































Uref TD v1

e1

e2

v2

+

+ndash

ndashndash

NLSEFu0 (t) u (t)+


W (t)

1b

z3

z2

z1

ESO

b



1z++

++

+ndash

1V1

2V2

1Uref

x1x2 fhan

fhan

h







G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References






























G(s) 1

s2

+ 3s + 1 (21)






0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15


0 1 2 3 4 5 6 7 8 9 10ts


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash15







[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References






























[z1]

[y]

[h]

+ndash

[B01]

[B02]

[B03]

ndashμ

ndashμ

ndashμ

times

times

times

times

+

+

+++

K Tsz-1

K Tsz-1

K Tsz-1

[z1]

075

e0

a0

delta

e0

a0

delta

y

fal

fal1

[u]

[b]

[z2]

01

[h]

y

[z3]

fcn

fcn


1

3

5

e1

a1

delta0

2

4

6

e2

a2

delta2

e1

a1

delta

y

e2

a2

delta

y

K1

K2

fal

fal2

+

+1u

fcn

fcn



V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References


























V

V1

V2

td

+ndash

+ndash+ndash

a2 a1 delta0 delta2

e1e2a1

delta0delta2

a2 u

1bb

num (s)den (s)

h

B01

B02

B03

b

yz1

z2

z3

u

h

B01

B02

B03

b

ESO

NLSEF


Am

plitu

de

15

1

05

ndash05

0

ndash1

ndash150 1 2 3 4 5 6 7 8 9 10

ts

Z1X1


0 1 2 3 4 5 6 7 8 9 10ts

215

105

0ndash05

ndash1

ndash15

Am

plitu

de

Z2X2



Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References


























Uref

Ut1Ut1

Ut2

Vf1

Uref

Ut2Vf2

Vf1

Vf2

ADRC

ADRC1ship

1

1


04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0992

0994

0996

0998

1

1002

1004

1006

1008

ωpu

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC





















ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References












































ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References






























ndash02

0

02

04

06

08

1

Pep

u

0 5 10 15 20 25 30 35ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25 30 35ts

0

01

02

03

04

05

06

Pmp

u

AVRAVR + PSS2BADRC






04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References





























04

05

06

07

08

09

1

11

12

Utp

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC






ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References





























ndash02

0

02

04

06

08

1

12

14

16

Pep

u

0 5 10 15 20 25ts

AVRAVR + PSS2BADRC


0 5 10 15 20 25ts

0

01

02

03

04

05

06

07

Pmp

u

AVRAVR + PSS2BADRC



0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References


























0

02

04

06

08

1

12

Utp

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


098

0985

099

0995

1

1005

101

ωpu

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC




5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References



























5 Conclusion



0

05

1

15

2

25

3

35

Pep

u

0 2 4 6 8 10 12 14 16 18 20ts

AVRAVR + PSS2BADRC


0 2 4 6 8 10 12 14 16 18 20ts

0

01

02

03

04

05

06

07

08

09

Pmp

u

AVRAVR + PSS2BADRC




Data Availability




Acknowledgments


References



























Data Availability




Acknowledgments


References


























Documents

Synchronous Generator Excitation System for a Ship Based