Journal of Engineering Science and Technology Review 11 (4) (2018) Research Article

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1 Jestr Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 Research Artcle Generator Exctaton Control Method based on Iteratve Learnng Control wth Intal State Learnng and Model-free Adaptve Grey Predcton Control Jngca Ba *, Junxao Wu, Guozhu Wang and Yongtao Hu JOURNAL OF Engneerng Scence and Technology Revew Department of Automatc Control, Henan Insttute of Technology, Xnxang 4533, Chna Receved July 8; Accepted 9 September 8 Abstract In a synchronous generator exctaton control system, the dampng capacty of the system s generally weakened durng hgh-accuracy regulaton of termnal voltage, whch s aganst system stablty. In ths study, an exctaton control method based on teratve learnng control (ILC) wth ntal state learnng and model-free adaptve grey predcton control (MFAGPC) was proposed to acheve hgh-accuracy voltage regulaton and system stablty. Based on the thrd-order dynamc model of generators, an exctaton control system was constructed. The system used ILC as prmary controller and MFAGPC as secondary controller to desgn the termnal voltage and rotor speed, respectvely. Furthermore, the nfluences of ILC and MFAGPC on the regulaton accuracy of termnal voltage and system stablty were dscussed. The proposed control method was valdated by smulaton and expermentaton. The results demonstrate that under the conventonal, the overshoot and settlng tme of the termnal voltage are 3% and.6s, and the rotor speed undergoes 6 oscllatons n 4.3s before the system returns to a stable state. Due to the synergc effect of ILC and MFAGPC, the overshoot and settlng tme of the termnal voltage are 7% and.7s, and the rotor speed just undergoes 3 oscllatons n.5s before the system returns to steady state. The proposed control method assures that the system acheves adequate regulaton accuracy of termnal voltage n a short tme, overcomes nfluences of nternal and external dsturbances on the system, and enhances system stablty. Ths study provdes a reference for further studes on multgoal control problems of power systems. Keywords: Exctaton control, Iteratve learnng control, Model-free adaptve control, Grey predcton, GM (,) model. Introducton Synchronous generator exctaton control has attracted attenton n the academe n the past 5 years. The tasks of exctaton control have shfted from smple mantenance of the termnal voltage n the past to hgh-accuracy voltage regulaton at present consderng oscllaton nhbton and mprovement of system stablty. Mantanng the termnal voltage and enhancng the stablty of power system are tasks that have to be performed consstently. However, the dampng torque s nadequate to deterorate the system stablty when the termnal voltage keeps constant []. At present, addng exctaton control n the exctaton control system s an effectve measure. control [] and lnear optmal exctaton control [] are representatve methods that have approxmate lnearzaton of the power system close to the equlbrum pont. When the power system s dsturbed from ts orgnal state pont, these lnear models may generate large devatons and a sgnfcant reducton n the control effect. Thus, nonlnear exctaton control theory has been studed extensvely n the last two decades. The exctaton controller s desgned by dfferental geometry method n nonlnear exctaton control n reference [3]. In the past, drect feedback lnear method [4], Hamlton system theory [5], varable structure control [6] and backsteppng method *E-mal address: okbjc@63.com ISSN: Eastern Macedona and Thrace Insttute of Technology. All rghts reserved. do:.53/jestr.4.4 [7-8] were appled n nonlnear exctaton control successvely. However, these nonlnear exctaton control methods return the power angle of a recoverng generator to the orgnal angle before dsturbance. System parameters and control method may change upon dsturbance. Although the system can realze the fnte stablzaton of dsturbance, ths may cause the termnal voltage to deflect from the desred value. The prncpal tasks of the generator exctaton system are to enhance system stablty and satsfy the regulaton accuracy of termnal voltage. These two tasks are often contradctory. The goal of the control focuses ether on the power angle or on the termnal voltage to mprove the stablty of power system or satsfy the regulaton accuracy of voltage, whch has dsadvantages. Voltage should be desgned as an ndependent and master control to ensure the regulaton accuracy. Thus, a new exctaton control method s proposed by studyng the mult-objectve control problem. Ths method takes the termnal voltage as the master control varable that can enhance the system stablty durng hgh-accuracy regulaton of voltage.. State of the art Plenty of experts have dscussed the stablty of power system and the regulaton accuracy of termnal voltage. Mahmud [9] desgned an exctaton controller based on the partal feedback lnearzaton method and obtaned good exctaton stablzaton by combnng the observer, but the

2 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 uncertantes exstng n the power system model were gnored. Consdered the uncertantes wthn system, Su [] demonstrated the fnte stablzaton of the fault by usng the hgh-order sldng mode but faled to acheve deal stablzng termnal voltage. Zhao [] combned the sldng mode varable structure and AVR nto the exctaton system of a waste heat generator unt. The method could track the gven sgnal well but dd not elmnate the adverse effects of buffetng. Alden [] studed the power system wth feedback delay and proposed a robust control based on lnear matrx nequalty, whch acheved transent stablty effectvely. However, obtanng the boundary nformaton of the uncertan parts n the actual control system was dffcult, thereby resultng n conservaton of the robust controller desgn. Peng [8] desgned the exctaton controller by random nonlnear ntegral backsteppng method. Ths controller could partally nhbt random dsturbance n the system. Masrob[3] and Zhao[4] developed an artfcal neural network power system stablzer (PSS) and a predctve exctaton controller to mprove system stablty by reducng order n the power system model. However, the regulaton of termnal voltage was not vewed as a master control. Ghasem [5] and Kumar [] optmzed the PSS parameters by fuzzy gravty search algorthm and local nformaton of each machne n a mult-machne envronment, and solved the combnaton optmzaton problem. However, the nput constrants of the system were neglected. Zhao [6] ntroduced the model-free adaptve control (MFAC) nto the desgn of wde-area PSS, whch nhbted the nter-area low-frequency oscllaton effectvely. However, the nfluence of the wde-area PSS on termnal voltage was not analyzed. Guo [7] appled the nonlnear exctaton controller based on the devaton separaton for power system consderng model devaton and dsturbance devaton. The controller could nhbt dsturbance of the power system to a certan extent, but the deducton process of control law was complcated and the power angle was dffcult to measure. Zhang [8] appled an mproved MFAC algorthm nto the marne generator exctaton system, whch had certan fault tolerance to data dstorton and load change. However, the voltage regulaton was absent. Wang [9] ntroduced the dfferental evoluton mechansm to optmze the automatc voltage regulaton system by PID. Ln [] combned the Adams predcton model and MFAC wth the generator exctaton control system. The aforementoned two methods mproved the regulaton accuracy of termnal voltage but gnored the mult-objectve requrements of the power system. Based on the dfferental geometry and expanson state observer, Chang [] desgned a dummy controlled varable usng varable structure theory, and added the devaton control of the termnal voltage to ensure transent stablty and voltage regulaton. However, the effect n stablzng termnal voltage faled, and the process nvolved multple parameters and complex operatons. To avod measurement of the power angle, Ruan [] and Yang [3] desgned the exctaton controller by nonlnear output feedback method to ensure the transent stablty and the regulaton accuracy of termnal voltage. However, uncertanty features were neglected n the operaton. The results mentoned were based on the control goal of the termnal voltage or the power angle. Such an exctaton system desgn based on a sngle control goal cannot satsfy the performance of the power system. Moreover, the proposed algorthms were extremely complcated and had numerous parameters. Recently, teratve learnng control (ILC) and MFAC have attracted the attenton of many scholars. Independent of an accurate mathematcal model of the controlled system, ILC can search the deal control sgnal through a learnng law and a repeated tranng process based on prevous control experences and the measured trackng error sgnal. Therefore, the controlled system could output a hgh-accuracy track n lmted tme wth a smple and easy algorthm [4]. MFAC does not need to construct the precse mathematcal model of nonlnear system and could realze an adaptve control of complcated nonlnear system by usng the nput and output data n the operatng process. As MFAC s unrelated to any state n the process, t s free from external dsturbances and s robust. A few parameters n the algorthm could be easly fne-tuned [8, 5]. Consderng condtons such as nonlnearty, tme varaton, and dffculty of establshng a precse model, ILC and MFAC were combned and appled to the generator exctaton control system based on complete analyss of the tasks and characterstcs of the exctaton system. The exctaton controller had a prmary and a secondary control loop. The prmary control loop used hgh-accuracy trackng of termnal voltage by ILC, whle the secondary control loop transformed the system nto a robust structure not nfluenced by nternal and external dsturbances of the MFAC of rotor speed. Wth the advantages of grey predcton, a GM(,) model s added n the feedback loop of the MFAC, thus formng model-free adaptve grey predcton control (MFAGPC). The GM(,) model s used to predct and compensate the system n the presence of tme varyng of parameters, system delays, and overshootng to mprove the system performance. The remander of ths study s organzed as follows. Secton 3 establshes the thrd-order nonlnear model of synchronous generator and analyzes the ILC desgn of termnal voltage as well as the MFAGPC desgn of rotor speed. Secton 4 ntroduces the smulaton and expermentaton of the proposed control method. Conclusons are summarzed n Secton Methodology 3. Power system model When the equvalent dampng wndng g, D, and Q are dsregarded, only wndng f and the dynamc equaton of rotor are consdered, and the nput mechancal power are assumed constant, the thrd-order dynamc model of the th generator [6] can be wrtten as!δ = ω ω!ω = ω (P H m P e ) D (ω H ω ) E!ʹ q = ʹ U T f E ʹ (x xʹ ) d d U q d xʹ s cosδ dσ The relevant algebrac equatons durng the steady-state condtons can be wrtten as d = ʹ E q U s cosδ ʹ x dσ () 3

3 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 q = U s snδ x qσ U d = x q q U q = E q ʹ xʹ d d U t =U d +U q P e =U d d +U q q = Eʹ q U xʹ s snδ dσ () 3. Generator exctaton control system based on ILC and MFAGPC The generator exctaton control system s constructed wth the termnal voltage regulaton as the master and ndependent control (Fg. ). The output of the ILC controller drves the set pont of the MFAC controller. ILC s employed to complete the trackng of termnal voltage whle MFAC s employed to stablze the system and overcome the effects of the nternal and external dsturbances on the system. ILC and MFAC complement each other s advantages. where δ, ω,and Eʹ are state varables, whch denote the q power angle, rotor speed of rotor, and q -axs transent potental of the th generator, respectvely. U and f Ut are the exctaton voltage and termnal voltage of the th generator. U s s the nfnte bus voltage. P m s the mechancal nput power of the th generator, whch s assumed to be constant. Pe s the actve power generated by the th generator. H s the nerta constant of the th generator. D s the dampng coeffcent of the th generator. d Tʹ s the d-axs open-crcut transent tme constant of the stator n the th generator. x d and xʹ d are d-axs synchronous reactance and transent reactance of the th generator. x q s the q-axs synchronous reactance of the th generator. x T and x L are the total reactance of transformer and transmsson lne, xʹdσ = xʹd + xt + x and L x = q x + q x + Σ T x. L ω s the synchronous speed of the th generator. The unts of δ, ω, and Tʹ are rad, rad/s, and d s, respectvely. The other parameters are per-unt values. The mathematcal model by Eq. () can be rewrtten n the form of an affne nonlnear system as follows:!x (t) = f (x (t))+ g (t)u (t) y (t) = h (x (t)) where x = [ δ, ω, Eʹ ] T s the state vector of the system, q u () t = U s the th control vector, y() t = h( x()) t = U s f t the th output vector, g() t =,, s the known Tʹ d functonal matrx, and ω ω ω D f( x( t)) = ( Pm Pe) ( ω ω) s the known H H Eʹ q ( xd xʹ d) U scosδ Tʹ d Tʹ d xʹ d nonlnear functon vector. T (3) Fg.. Structure of exctaton control system As a gven value ( U ), the bus voltage s compared wth the termnal voltage ( U t ) to obtan the error ek ( ). After the closed-loop ILC operaton, a new output s obtaned, whch s the gven value rω ( k) of the MFAC controller. The devaton between rω ( k) and the predcted value µ ω ( k) of the GM(,) model s controlled by MFAC to determne the exctaton voltage. 3.3 ILC wth ntal state learnng desgn of termnal voltage After comparson between U and U t, the constant-value control s realzed by the prmary controller. The dscrete closed-loop PI-type ILC algorthm wth ntal state learnng s used as the control law, as shown n Fg.. The closedloop control not only accelerates learnng convergence but also enhances the robustness of the learnng control. At the same tme, the ntal state s learned, allowng an ntal state error to relax the requrement on ntal state postonng. The closed-loop PI-type ILC and ntal state learnng law are expressed as follows: k u ( k) = u ( k) + Pe ( k) + I e ( j) (4) n+ n c n+ c n+ j= xn+ () = xn() + Len() (5) where n s the number of teratons. kk ( =,, L, N) s the samplng tme of the dscrete system. P c and I c are bounded learnng gan matrxes of proporton and ntegral terms. L s the bounded gan of ntal state learnng law. e ( k) = y ( k) y ( k) s the trackng error at k n the n+ d n+ n + run. yd ( k ) s the desred output. y ( ) n+ k s the actual output of the n + teraton. Smlarly, u ( k ) and x ( k ) are the desred control varable and state vector. u ( ) n+ k and x ( ) n+ k are the actual control varable and state vector of the n + teraton. For the nonlnear system n Eq. (3), we assume that the functons f( x ) and gk ( ) are contnuous n the tme nterval k [, T], and hx ( ) has partal dervatves. They satsfy the followng condtons: d d 33

4 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 () f( x ) meets the Lpschtz condton. In other words, a constant l f > exsts. For x, x f( x ) f( x ) l ( x x ). f n R, we have () hx ( ) has the dervatve h ( x ) n relaton to x. h( x ) meets the global consstent Lpschtz condton and hx () x s bounded. (3)The desred trajectory yd ( k ) s expected to be contnuous on [, T ]. (4)An deal control varable u ( k ) exsts to make the state vector and output as the expected values x ( k ) and yd ( k ). (5)The ntal state at each teraton s dfferent and the ntal state of the n teraton s x n(). Fg.. Structure of ILC system For smplcty, the followng notatons are used: λt e e a = l fgpc + l fgicg g λ λ l δ x = x x n n+ n ξ = x + γδx, γ c n n n = sup h ( ξ ) x x n k [, T] ρ = ca x cl x M = ca x x d ( lf λ ) T Theorem: If system (3) satsfes the above hypotheses and the followng equaton en+ ρ en + M en() on λ λ λ [, T ] and ρ < under two learnng laws, when the selected λ s adequately large to make ca x > and M <, then lm e = when n. y ( k ) n converges at yd ( k ) on [, T ]. n λ 3.4 MFAGPC desgn of rotor speed In the exctaton control system, the system stablty should be consdered along wth the hgh-accuracy regulaton of termnal voltage. The MFAGPC of the rotor speed [8, 5] s desgned to mprove the system stablty. Grey predcton control uses the system behavor data as the samplng nformaton and constructs the grey predcton model accordng to the metabolsm prncple to predct the system behavor data n the future. Then, the predcted and gven values are compared to realze the advanced control. As the GM(,) model can reflect monotonous, nonmonotonous, and oscllatng dynamc processes, the GM(,) f d n (6) model s appled to predct the samplng sequence. rω ( k) s the gven value of MFAC, ω s the samplng value, and µ ω s the predcted value of ω Constructon steps of GM(,) model The orgnal sequence s obtaned through equal nterval samplng of ω as follows: { (), (),, ( N) } () () () () ω = ω ω L ω (7) () Preprocessng of orgnal sequence () Based on an accumulaton of ω, the accumulatve sequence s { (), (),, ( N) } () () () () ω = ω ω L ω (8) k () () where ω ( k) = ω ( j), k =,, L, N. j= () Accordng to the once accumulatve reducton of ω, the followng accumulatve reducton sequence s obtaned: { (), (3),, ( N) } () () () () () () () () α ω = α ω α ω L α ω (9) () () () () where α ω ( k) = ω ( k) ω ( k ), k =,3, L, N. ()Establshment of GM(,) model The near-mean sequence s constructed by follows: { (), (3),, ( )} () () () () Z Z Z Z N () ω as = L () () () () where ( ω ω ) s d ω dt Z ( k) =.5 ( k) + ( k ), k =,3, L, N. The albnsm dfferental equaton of the GM(,) model dω + + = () dt () () a a () b ω After dscretzaton, the followng s obtaned: α ω ( k) + aω ( k) + a Z ( k) = b, k =,3, L, N () () () () () (3)Estmaton of coeffcents a, a, and b The above three coeffcents are dentfed by the least squares method. ( ) ( ω ( ) Z ) ( ) ( ) ( ( ) ) ω 3 Z ( 3) Let B = and M M M ( ) ( ω ( N) Z ) ( N) () () α ω () () () aˆ α ω (3) Y T T =, then M aˆ = ( B B) B Y. ˆ () () b α ω ( N) (4)Quadratc estmaton of parameters 34

5 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 Estmated values a, a, and b of three parameters are! (k) + λ u(k) u(k ) J (u(k)) = rω (k) ω! () (k) s brought nto the albnsm dfferental equaton. ω solved accordng to the characterstc root. (5) Constructon of predcton formula The predcted value of ω () s! () () = ω! () () ω! () (k +) = ω! () (k +) ω! () (k),k =,,", N ω where η (,] s the step length factor and λ > s the weghtng factor. ε s the nfntely small postve real number. The lnear model s brought nto the crteron functon to calculate the extremum of Eq. (8). Based on the result, the followng control law can be wrtten: (3) u(k) = u(k ) + A new GM(,) model s obtaned based on the precedng steps, and the new sequence s predcted and controlled. (9) 4. Result Analyss and Dscusson 4. Smulaton study In ths study, the -zone 4-machne system n Fg. 3 was analyzed by the proposed exctaton control method based on ILC and MFAGPC. The proposed control method was compared wth the open-loop ILC based on the termnal voltage bas and the conventonal exctaton control method. System parameters were ntroduced n reference [6]. The nput mechancal power keeps constant durng smulaton and the ntal workng pont of the system δ =55o, Pm =.65, was chosen randomly: (4) then the compact-form lnear model of the system s Δω (k + ) = ΦT (k )Δu ( k )! (k) ρφ! (k)) (rω (k) ω! λ + Φ(k) where ρ (,] s the step length factor. The control varable obtaned from Eq. (9) s the exctaton voltage U f MFAC method MFAC performs an onlne estmaton of the pseudo-partaldervatve (PPD) by I/O data and replaces the general nonlnear system by the dynamc lnear mathematcal model n ncremental form, thereby stablzng the dsturbance of the system effectvely. As shown n Fg., ω (k ) and u (k ) are the output and nput of the system at k. Let Δω (k + ) = ω (k + ) ω (k ), Δu (k ) = u (k ) u(k ) (8) (5) where ΦT ( k ) s the PPD of the system and Φ T ( k ) a, Ut =. ; δ =37o, Pm =.85, Ut = ; δ 3 =5o, where a s the postve real number. ω (k ) s the rotor speed at k. u (k ) s the output of the MFAC controller at k. The estmaton crteron functon of PPD s defned as Pm3 =.7, Ut 3 =. ; δ 4 =5.o, Pm 4 =.8, Ut 4 = ; ω =34.6 ; U s =. For the th generator, U f = and the exctaton voltage lmt s U f 4, where =,,3,4. The subscrpt denotes the ntal value. J (Φ(k )) = ω (k ) ω (k ) ΦT (k ) Δu(k ) +! (k ) µ Φ(k) Φ (6)! (k) s the onlne estmaton value of system PPD where Φ and µ > s the penalty factor. The extremum of Eq. (6) s calculated, and the PPD estmaton algorthm of the system at k can be wrtten as! (k) = Φ! (k ) + Φ ηδu(k ) µ + Δu(k )!T Δω (k) Φ (k )Δu(k ) Fg. 3. -zone 4-machne power system Controller parameters are set before the smulaton. () In ILC, Pc = 3, I c = 6.7, and L = 7. () MFAGPC: In the GM(,) model, the modelng dmenson N=5, ntal nput value u () = u () =, and ntal output value ω () = ω () = ω (3) =. In MFAC, penalty factor µ =.65, step length factor η =.3 and ρ =.75, and weghtng factor λ =.5. The system beng tested runs from the equlbrum pont. In the smulaton, the preset fault was ntroduced as follows. The three-phase-to-ground short-crcut fault close to bus 3 of lne 3- occurred at t = s. The fault lne was cleared and lne 3- was trpped out at t =.5 s. The (7)! (k) = Φ() exsts.! (k) ε or Δu (k ) ε, then Φ If Φ To prevent the algorthm from generatng excessve control varables, thereby destroyng the exctaton system, the followng control nput crteron functon s appled: 35

6 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39 correspondng curves were studed based on the generator G. Response curves of the termnal voltage, actve power, power angle, and rotor speed of the synchronous generator under three control methods are shown n Fg. 4. The dotted lne represents the open-loop ILC algorthm, the dashed lne represents the conventonal exctaton control method, and the sold lne represents the proposed method based on ILC and MFAGPC. Fg. 4(a) demonstrates that all the three control methods can make the termnal voltage return to the steady state after a certan perod. Under the open-looped ILC, the system takes.7 s to return to the steady state wth approxmately % overshootng. Under, the settlng tme s approxmately.8 s and the overshoot s around %. Under the collaboratve effect of ILC and MFAGPC, the settlng tme and overshoot are approxmately.6 s and 8%. The proposed exctaton control method acheves flatter waveform, shorter tme, and hgher regulaton accuracy of the termnal voltage. Fg. 4(b) shows that compared wth the other two control methods, the proposed method based on ILC and MFAGPC can stablze mechancal oscllaton at transent state more quckly and acheves better dampng feature and actve power trackng performance. In addton, Fgs. 4(c) and 4(d) reveal that under the open-loop ILC, the transent process of the power angle and rotor speed takes.3 s and.8 s, respectvely. Under the conventonal, the transent process of the power angle and rotor speed takes s and.4 s, respectvely. Under the ILC and MFAGPC effect, the transent process of the power angle and rotor speed takes s and. s, respectvely. The power angle curves reach relatve stablty after 4 oscllatons under the open-loop ILC and after 3 oscllatons under the, but only after oscllaton under the ILC and MFAGPC effect. These results ndcate that the proposed exctaton control method has strong dampng ablty and can nhbt the nfluence of dsturbance on the system. The response curve of the relatve power angle δ between generators 3 and s shown n 3 Fg. 5. After the frst oscllaton of the power angle, the proposed method can recover δ to the ntal equlbrum 3 state more quckly and shows a smaller ampltude of swng than the two other methods. The proposed method effectvely mantans the transent stablty of the system. As the termnal voltage s only regulated by the open-loop ILC wthout consderng the nfluence on system stablty, the correspondng waveforms of the termnal voltage, actve power, power angle, and rotor speed fluctuate acutely wth dampng capacty as the worst performer. The method consders both the termnal voltage and system stablty; thus, t s superor to the open-looped ILC n stablty. However, the method s desgned based on a precse lnear model of the system. Therefore, ths method nvolves a sngle parameter settng and poor adaptablty and s nferor to the proposed method n terms of the voltage regulaton and system stablty. 4. Expermental study To verfy the feasblty of the proposed exctaton control method, a unt composed of a 3 kw DC motor and a 3 kw synchronous generator s used on the exctaton regulaton devce that apples TMS3F8335 chp as the nternal control core to smulate the sngle-machne nfnte bus power system. 4.. Expermental platform The expermental platform manly conssts of an exctaton regulaton control table, a DC motor, and a three-phase AC synchronous generator (Fg. 6). The DC motor s used as the prme mover. U t pu P e pu (a) () δ ω pu (b) (c) (d) Fg. 4. Dynamc curve of generator.(a) Curves of termnal voltage. (b) Curves of actve power. (c) Curves of power angle. (d) Curves of rotor speed 36

7 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) δ 3 ( ) 5 Fg. 7. Curves of termnal voltage.5.5 Fg. 5. Curves of relatve power angle δ Fg. 8. Curves of actve power Fg. 6. Expermental platform 4.. System parameters The structure of the sngle-machne nfnte-system s shown n reference [7]. Lne parameters. Double-crcut lnes are adopted between the generator and bus. Each lne s.5 Ω and the correspondng per-unt value s.55, xl =.47. Transformer parameter. The no-load voltage rato of the transformer s 4/8. The prme mover used three pars of extremely brushless DC motor. The correspondng rated power s 3 kw and the rated speed s 5 r/mn. Generator parameters. Rated power = 3 kw, rated voltage = 4 V, rated current = 5.4 A, rated exctaton voltage = 7 V, and rated exctaton current = 3 A. Fg. 9. Curves of power angle 4..3 Analyss of results The prme mover s started frst and the exctaton current s regulated to make t work under the rated state. Then, a three-phase-to-ground short-crcut fault occurs at a pont on the hgh-voltage sde close to the transformer, whch lasts for. s. Subsequently, the protectve acton s mplemented and the fault lne s cleared after. s. The comparson of the results between the proposed control method and conventonal s shown n Fgs.7-. Fg.. Curves of rotor speed The response curves of the termnal voltage and actve power of the generator are shown n Fgs. 7 and 8. Under the collaboratve effect of ILC and MFAGPC, the waveform of the termnal voltage s flat. The correspondng overshoot and settlng tme are 7% and.7 s, respectvely. Under 37

8 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) 3-39, the overshoot and settlng tme are 3% and.6 s, respectvely. Therefore, the proposed control method can help the system acheve the desred voltage more quckly wth a hgher regulaton accuracy of the termnal voltage. In addton, the actve power fluctuates sgnfcantly at the fault occurrence under and settles down after.7 s. However, the effect of ILC and MFAGPC can prevent oscllaton quckly. Overall, the control effect of the proposed method s superor to that of. The response curves of the power angle and rotor speed are shown n Fgs. 9 and. After the fault, the power angle can return to rest after 3.5 s and 4 oscllatons, and the rotor speed settles to a steady state after 4.3 s and 6 oscllatons under. However, under the effect of ILC and MFAGPC, the power angle can reach stablty only after s and oscllaton, the rotor speed can reach stablty after.5 s and 3 oscllatons. Compared wth, the proposed method based on ILC and MFAGPC has stronger dampng capacty, so that the system can reach transent stablty quckly. 5. Concluson To enhance the system robustness aganst nternal and external dsturbances durng hgh-accuracy regulaton of termnal voltage, the closed-loop ILC and MFAGPC were appled n the synchronous generator exctaton control system based on the thrd-order dynamc model of the power system. Smulaton and expermentaton were conducted. The followng conclusons could be drawn: () When the control system structure s desgned reasonably, ILC and MFAGPC can complement each other such that the system can obtan hgh-accuracy voltage regulaton to ensure adequate dampng capacty. () The closed-loop PI-type ILC algorthm not only shortens the tme for the system to reach a steady state but also allows hgh-accuracy trackng of the desred voltage. Intal state also learns to adapt to the devaton of the ntal workng pont by changes n the system parameters. (3) Grey predcton s ntroduced n the MFAC method, whch can enable advanced predcton of rotor speed to compensate the nfluences of uncertanty on the system, thereby showng robustness. (4) Only lmted parameters are consdered n ILC and MFAGPC, and few couplng effects occur among these parameters. In ths study, two major exctaton tasks, namely, meetng the regulaton characterstcs of termnal voltage and mprovng the system stablty, are consdered comprehensvely. The proposed control method based on ILC and MFAGPC mrrors the actual stuatons of the generator exctaton control system and requrements of the power system. Ths study provdes a reference for further research on the performance of exctaton systems. The experment conducted focused only on the sngle-machne nfnte-bus power system n a laboratory. Therefore, future studes can consder mult-machne system problems. Furthermore, the speed regulaton can be ntroduced to change the mechancal power of the prme mover n future studes. Acknowledgments Ths work was supported by the Key Scentfc and Technologcal Project of Henan Provnce (Grant No. 833) and the Key Scentfc Fundng Projects for Insttutons of Hgher Educaton of Henan Provnce (Grant No. 9B46). Ths s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcence References. Lu, Q., Power System Stablty and Generator Exctaton Control. Bejng: Chna Power Press, Chna, 7, pp Kumar, A., Power system stablzers desgn for multmachne power systems usng local measurements. IEEE Transactons on Power Systems, 3(3), 6, pp Isdor, A., Nonlnear control systems. Lecture Notes n Control & Informaton Scences, 4(65), 3, pp Lu, Q., Me, S. W., Sun, Y. Z., Nonlnear Control of Power System. Bejng: Tsnghua Unversty Press, Chna, 8, pp Zhou, H. Q., Ju, P., Xue, Y. S., L, H. Y., Transent stablty analyss of stochastc power system based on quas-hamltonan system theory. Automaton of Electrc Power Systems, 4(9), 6, pp Han, Y., Nonlnear varable structure control technque for power system exctaton controllers. Tsnghua Scence & Technology, (3),, pp Yang, J. H., Chen, K. Y., Wang, Q. J., Chen, S. Z., Varable structure control of voltage source converter-hgh voltage drect current system based on backsteppng. Control Theory & Applcatons, 3(), 4, pp Peng, Y. J., Han, F. M., Chen, J. H., Deng, F. Q., Synchronous generator exctaton controller for random dsturbance rejecton. Control Theory & Applcatons, 35(4), 8, pp Mahmud, M. A., Hossan, M. J., Pota, H. R., Transent stablty enhancement of multmachne power systems usng nonlnear observer-based exctaton controller. Internatonal Journal of Electrcal Power & Energy Systems, 58(), 4, pp Su, B. L., Xn, Y. H., Mult machne electrc power control system based on the hgh order of exctaton sldng mode. Control Engneerng of Chna, 5(5), 8, pp Zhao, H., Wang, Y. F., Wang, H. J., Yue, Y. J., Study of waste heat power generaton unts exctaton control based on sldng mode varable structure control. Power System Protecton and Control, 43(6), 5, pp Alden, M. J., Wang, X. Robust control of tme delayed power systems. Systems Scence & Control Engneerng, 3(), 5, pp Masrob, M. A., Rahman, M. A., George, G. H., Desgn of a neural network based power system stablzer n reduced order power system. In: 7 IEEE 3th Canadan Conference on Electrcal and Computer Engneerng, Wndsor, CAN: IEEE, 7, pp Zhao, H., Lan, X., Xue, N., Wang, B., Exctaton predcton control of mult-machne power systems usng balanced reduced model. Iet Generaton Transmsson & Dstrbuton, 8(6), 4, pp Ghasem, A., Shayegh, H., Alkhatb, H., Robust desgn of multmachne power system stablzers usng fuzzy gravtatonal search algorthm. Internatonal Journal of Electrcal Power& Energy Systems, 5(), 3, pp Zhao, Y., Lu, C., Han, Y., Men, K., Wde area power system stablzer desgn based on mproved model free adaptve control. Journal of Tsnghua Unversty, 53(), 3, pp Guo, G., Lu, J. M., Lu, W. J., Xang, Z., Nonlnear exctaton control based on devaton separaton for synchronous generator. Proceedngs of the CSU-EPSA, 6(3), 4, pp

9 Jngca Ba, Junxao Wu, Guozhu Wang and Yongtao Hu/Journal of Engneerng Scence and Technology Revew (4) (8) Zhang, W., Sh, W., Wang, G., Sun, B., An mproved model-free adaptve control of marne generator exctaton system. Internatonal Journal of Robotcs & Automaton, 3(6), 7, pp Wang, R. J., Zhan, Y. J., Zhou, H. F., Cu, B. W., PID controlled AVR system based on dfferental evoluton mechansm optmzaton. Power System Protecton and Control, 43(4), 5, pp Ln, T., Xu, Q. G., Xuan, Q. Q., Wu, M. X., Study on optmal control of stablty of synchronous generator exctaton system. Computer Smulaton, 34(6), 7, pp.-6.. Chang, X. R., Zhang, H. S., Cu, Z. J., Exctaton control based on dfferental geometry and extended state observer. Proceedngs of the CSU-EPSA, 7(8), 5, pp Ruan, Y., Yuan, R. X., Wan, L., Zhao, H. S., Nonlnear robust voltage control for synchronous generators. Transactons of Chna Electrotechncal Socety, 7(9),, pp Yang, F., Ruan, Y., Yuan, R. X., Nonlnear robust exctaton control based on output feedback for synchronous generator. Electrc Power Automaton Equpment, 3(),, pp Yan, Q. Z., Sun, M. X., L, H., Iteratve learnng control for nonlnear uncertan systems wth arbtrary ntal state. Acta Automatca Snca, 4(4), 6, pp Hou, Z. S., Hghlght and perspectve on model free adaptve control. Systems Scence and Mathematcal Scences, 34(), 4, pp Kundur, P., Power System Stablty and Control. New York: McGraw-Hll, Inc. USA,, pp Ge, B. J., Yn, J. W., Tao, D. J., Nu, Z. L., Modelng of feldcrcut-network coupled tme-steppng fnte element for one machne nfnte bus system based on exctaton and speed control. Transactons of Chna Electrotechncal Socety, 3(3), 7, pp