009 Amercan Control Conference Hyatt Regency Rverfront, St. Lou, MO, USA June -1, 009 hb03. CPS Complant Fuzzy Neural Network Load Frequency Control X.J. Lu and J.W. Zhang Abtract Power ytem are characterzed by non-lnearty and uncertanty. A neural network predctve fuzzy control propoed for load frequency control. Recurrent neural network employed to forecat controller and ytem future output, baed on the current Area Control Error (ACE) and the predcted change-of-ace. he Control Performance Standard (CPS) crteron ntroduced nto the fuzzy controller degn, thu mprove the dynamc qualty of ytem. Smulaton on a two-area power ytem that take nto account load dturbance demontrate the effectvene of the propoed methodologe. M I. INRODUCION ODERN power ytem are normally compoed of nterconnected ubytem or control area. he contant change of load n a gven power ytem can affect the ytem frequency. Controllng of the power ytem frequency wthn a certan cope realzed through mantanng the total power nput of the parallel operaton unt equal to the effectve power conumpton of the ytem load. he proce known a the power grd load frequency control(lfc). he te-lne ba control of power ytem ha been acheved ung conventonal PI control conderng Area Control Error (ACE). A the frequency and te-power devate from the cheduled value, accumulaton of tme error and nadvertent nterchange may occur. Paper [1] deal wth dcrete-tme automatc generaton control(agc) of an nterconnected reheat thermal ytem conderng a new area control error (ACEN) baed on te-power devaton, frequency devaton, tme error and nadvertent nterchange. h controller can effectvely regulate tme error ξ and nadvertent nterchange accumulaton I. However, t dd not conder the generaton rate contrant (GRC) and the nonlnear effect of dead zone. he nherent non-lnearty n ytem component and ynchronou machne ha led reearcher to conder artfcal neural network(ann) and fuzzy logc technque to buld a non-lnear controller wth hgh effcency. In [], a feed forward neural network ha been traned by back propagaton-through-tme algorthm to control the team Manucrpt receved September 0, 008. h work wa upported n part by Program for New Century Excellent alent n Unverty under Grant NCE-06-007, Natural Scence Foundaton of Bejng under Grant 406030, Natonal 863 plan under Grant 007AA04Z163 X.J. Lu wth the Department of Automaton, North Chna Electrc Power Unverty, Bejng, 06, P.R. Chna (correpondng author. el: 86--80798549; e-mal: luxj@ncepu.edu.cn). J.W. Zhang wth the Department of Automaton, North Chna Electrc Power Unverty, Bejng, 06, P.R. Chna (e-mal: zhang168@163.com). turbne admon valve. he ANN baed controller on a four area nterconnected ytem whch cont of reheat turbne and generaton contrant ha been tuded n [3]. he nput of the propoed ANN controller are ytem tate varable and dturbance vector. Back propagaton-through-tme algorthm ha been ued to cope wth the contnuou tme dynamc a the learnng rule. In ung neural network for dynamc power ytem control, nce t contan large number of parallel nput vector, the total ytem may be too complcated. Paper [4] ntally degned a fuzzy logc controller for automatc generaton control. he reult how advantage over clacal ntegral controller. Paper [5] preented fuzzy gan chedulng PI controller. h cheme ha been degned for a four area nterconnected power ytem wth control dead zone and generaton rate contrant. Paper [6] developed a combned fuzzy logc, GA and ANN baed controller for LFC. A mult layered feed-forward neural network wth nput from GA baed fuzzy controller traned by back propagaton ha been ued to develop the propoed controller. Control Performance Crtera (CPC) ha been formerly ued to evaluate AGC performance. h ha been dffcult to meet the requrement of today' hgh power qualty control. he Control Performance Standard (CPS) pecfcally degned to comply wth the performance tandard mpoed by the North Amercan Electrc Relablty Councl (NERC) for equtable operaton of an nterconnected ytem. Fuzzy logc ytem uually degned to aure that the control performance n complance wth NERC control performance tandard [7]. Conderng the power ytem load frequency control, th paper etablhe a recurrent neural network model to predct the future frequency of the target object, thu forecatng the ACE and the CPS tandard ndex. Baed on th predcton, the optmzed controller degned, whch follow the CPS performance tandard through the fuzzy logc. Smulaton reult how the effectvene of the propoed method. II. INERCONNECED ELECRICAL POWER SYSEMS Interconnected power ytem cont of many control area connected by te-lne. he block cheme of a two-area power ytem hown n Fg. 1. g, t and p repreent the tme contant of the governor, the tme contant of the turbne and the tme contant of the power ytem repectvely. R (herenafter area = 1, = ) the governor peed regulaton parameter; β the frequency ba; K p 978-1-444-454-0/09/$5.00 009 AACC 755
the power ytem gan; Δ Pg the ncremental generaton change; Δ Xe the ncremental change for the poton of the governor valve; Δ Pc the ncremental change of the governor; U the output value of the controller; dpl the local demand; df the frequency devaton from nomnal value; dp te the error n chedule te flow; 1 the ynchronzng coeffcent between 1t and nd Area. Fg. 1.he block cheme of a two-area power ytem he overall ytem can be modeled a a mult-varable ytem n the followng form:. X=AX+BU+FΔP d X(0)=0 (1) where A the ytem matrx, B and F are nput and dturbance dtrbuton matrce, x(t), u(t) and d(t) are tate, control and load change dturbance vector, repectvely. X=[X 1, X ], U=[U 1, U ], ΔP d=[δp d1, ΔP d] ; X, U and ΔP d repreent tate varable vector, control varable vector and dturbance load vector of the 1 t or nd ubytem repectvely. X=[Δf, ΔP, ΔP, ΔX, ΔP, g c e te ACEdt, ACEN dt, ACEN ] he output of the ytem baed on ACEN: Y1 ACEN1 Y= = =CX () Y ACEN n whch ACEN =ACE +γ ACEdt, ACE = ΔP te+βδ f. In the extng lterature, nce a normally operated power ytem only expoed to mall change n the vcnty of the load demand, the above lneared model uually ued to expre the dynamc behavor of the ytem around the operatng pont. However, when a udden large change n the load demand occur by deregulated operaton, frequent on off control of large capacty load unt may caue large amount of overhoot or long-latng ocllaton on the valve poton of the governor [4].he nonlnearty of the ytematcal model manly ext n: 1) he mpact of the generator rate contrant on LFC. h contrant to avod damage to the equpment a a reult of exceve change of the varable uch a temperature and preure. ) he nfluence of the governor dead zone on LFC. III. HE NEURAL NEWORK FUZZY CONROL In the control cheme, neural network choen to create the real-tme dynamc model of the power ytem. In accordance wth the current controller output u(r), the te-lne power devaton dpte(r) and the frequency devaton df(r), the neural network ued to predct the next moment frequency devaton df (r+1), thu calculate the ACE, the ACEN a well a CPS. he predcted CPS1 and CPS are ued a nput varable to the fuzzy controller that offer optmal PI parameter. A. he recurrent neural network LFC model Elman network a typcal dynamc recurrent neural network. It feedback cont of a group of connected module and ued to record the mplct memory. Meanwhle, the feedback, along wth the network nput, act a the mport to hdden unt n the next moment. h nature render recurrent neural network wth dynamc memory and thu the capacty to predct future output, whch qute ftful to power ytem load frequency control. Fg..he Elman neural network tructure n the load frequent control he network tructure hown n Fg.. α(0 α 1) the feedback lnk gan. he external nput to the network are the fuzzy controller output u(r) R, the te-lne power devaton dpte(r) R and frequency devaton df(r) R. he network output the predcted frequency devaton for the next moment df (r+1) R, n whch r the amplng ntant. Let the hdden layer output be x(r+1) R 5, then: 756
x(r+1)=f(w1x c(r)+wu(r)+w3dpte(r)+w4df(r)) x c(r)=x(r)+αx c(r-1) (3) df(r+1)=g(w5 x(r+1)) where W1, W, W3, W4 and W5 are the weght matrx of connected unt to the hdden unt, nput unt to hdden unt and hdden unt to the output unt repectvely. f ( ) and g ( ) are the non-lnear vector functon of the actvaton functon of the hdden layer neural cell and output layer neural cell; x c (r+1) repreent the tate at r+1 moment. Here, x(r+1) the total tate of the power ytem dynamc. Genetc algorthm ued to tran the feed-forward and the feedback connecton weght. In th way, the connecton weght wll be n a bnary encoded trng form. Aume that the connecton weght have the rght to pre-defne the cope of the change. he relatonhp between the network connecton weght and the actual weght could be expreed a: (w t(,j,m,k)) w t(,j,m,k)=w mn(,j,m,k)+ l -1 [w (,j,m,k)-w (,j,m,k)] max where t repreent amplng tme; k repreent the number of learnng tme; [w max (,j,m,k),w mn (,j,m,k)] the changng cope of thee connecton weght; w(,j,m,k) t repreent the connecton weght between the th neuron of the (m-1)th layer to the jth neuron of the (m)th layer at that amplng tme t; (w t(,j,m,k)) repreent the correpondng bnary trng of w(,j,m,k). t he optmzng genetc algorthm can be ummarzed a: (1) Generate a et of randomly bnary trng, each trng repreent a collecton of all network collecton weght. () ranlate the bnary trng nto network connecton weght accordng to (4), and evaluate the performance by runnng the network. Make the ndvdual choce of the network accordng to the followng probablty expreon: fl P= (5) N f =1 l where P the electon probablty; f l repreent adapter value of ung one bt of bnary code n ndvdual. Here the adapter value the countdown of the quadratc quare of the dfference between the network output and the actual output. Obvouly, the greater the adapter value, the greater the genetc probablty. For the elected network, make croover and mutaton under pre-determned value of the probablty P c and P m to generate the next network. Repeat equaton (4) and (5) untl the dfference between the network output and the dered value reache the requred condton. At th tme, decode the optmal ndvdual n the fnalzed group to fnd out the network connecton properte. mn (4) B. Fuzzy logc degn baed on CPS optmzaton 1) CPS performance tandard For equtable operaton of the nterconnected ytem, control area have to comply wth the North Amercan Electrc Relablty Councl control performance tandard CPS1 and CPS, whch were adopted n February 1997. CPS1 aee the mpact of ACE on frequency over a certan perod wndow or horzon and t defned a follow: over a ldng perod, the average of the clock-mnute average of a control area ACE dvded by tme t area frequency ba tme the correpondng clock-mnute average of the nterconnecton frequency error hall be le than the quare of a gven contant, ε 1, repreentng a target frequency bound. h expreed by: ACE AVG perod 1 Δf 1 =ε1 Δf=fa-f (6) -β where Δf 1 the nterconnecton frequency error, β the frequency ba of the th control area, ε 1 the targeted frequency bound for CPS1 and 1 the clock-1-mn average. o calculate CPS1 ( K CPS1 ), a complance factor ( K CF ) defned a: ACE 1 Δf 1 -β K CF = (7) nε1 CPS1 then obtaned from the followng equaton: K CPS1 =(-K CF ) 0% (8) hu, 1) When KCPS1 00%, whch mean KCF 0, there (ACE1 Δf 1) 0. Under th condton, ACE facltate the frequency qualty. ) When0% K CPS1<00%, whch mean 0<KCF 1, ACE there 0 1 Δf 1 nε1. he CPS1 tandard -β atfed. 3) When K CPS1<0%, whch mean K CF >1, there ACE 1 Δf 1 >nε1. ACE ha exceeded the permtted -β range o that t ha a bad effect on the frequency and qualty of power grd. he econd performance tandard, CPS ( K CPS ), lmt the magntude of hort-term ACE value. It requre the -mn average of a control area ACE be le than a gven contant ( L ), a n the equaton below: 757
AVG mn (ACE ) L (9) Where, L =1.65ε (-β )(-β ). Note that β the ummaton of the frequency ba ettng of all control area n the condered nterconnecton, and ε the target frequency bound for CPS. o comply wth th tandard, each control area mut have t complance no le than 90%. A complance percentage calculated from the followng equaton: AVG mn (ACE ) K CPS = () L In order to meet the requrement of the power grd frequency qualty, the average ACE value durng mn n each control regon hould be n the normal dtrbuton a: σ=ε (-β )(-β ). (11) ) Optmzaton rule baed on CPS tandard Suppoe CPS1 0% and CPS 90% to be the goal of the AGC control trategy. able 1 how AGC optmzaton rule baed on CPS ABLE I AGC OPIMIZAION RULES BASED ON CPS condton he tate of AGC unt CPS1 0% and CPS 90% No optmzaton adjutng CPS1< 0% and ACE Δ f > 0 optmzaton adjutng CPS 90% ACE Δ f < 0 No optmzaton adjutng CPS1 0% and CPS < 90% optmzaton adjutng CPS1< 0% CPS < 90% optmzaton adjutng 3) Fuzzy PI controller baed on CPS Fuzzy logc rule are degned to manpulate the conventonal PI-type load frequency control. he propoed control tructure hown n Fg.3. he controller ue nformaton that reflect complance wth CPS1 and CPS a the nput to the fuzzy logc rule. Parameter Kp and K are fuzzy rule output. Fg. 4.Memberhp functon for the nput varable(cps1, CPS) Fg. 5.Memberhp functon for the controller output (Kp, K) CPS CPS1 PS PM PB ABLE II C. he control algorthm FUZZY LOGIC RULES PS PM PB Kp=PB K=ZE Kp=PB K=PS Kp=PS K=PB Kp=ZE K=ZE K=ZE K=PM Kp=ZE K=PB Kp=NS K=PS K=NS K=PM Kp=NB K=PV B he propoed algorthm baed on fuzzy neural network predctve method can be ummarzed a follow: (1) Set the ntal value of the dered frequency devaton df(r), dered ACE(r) and dered ACEN(r) to 0; () Forecat the frequency devaton df(r+1) at the (r+1) moment ung recurrent neural network a hown n Fg., reultng the forecatng of ACE(r+1); (3) Forecat CPS1(r+1) and CPS(r+1) at the (r+1) moment baed on ACE(r+1) and the CPS; (4) Get control output Kp(r+1) and K(r+1)at the (r+1) moment by CPS1(r+1) and CPS(r+1) from fuzzy rule n able 1, return to (). Here, the upercrp repreent the predcted value. Fg. 3.Fuzzy PI controller for CPS Accordng to the optmzed rule from the able 1, the memberhp functon of CPS1, CPS, Kp, and K could be defned a Fg. 4 and Fg. 5. Fuzzy rule are ummarzed n able. IV. CASE SUDY Smulaton conducted on the two regonal load frequency model hown n Fg. 1. he ytem parameter are choen a: g = 0.08; t =0.3; p =0; R =.4; β =0.45; K p =Hz/pu; j =0.086; a j =-1; ε 1 =5.40mHz; ε =0.56mHz, ( = 1,; j = 1,, where j ). Kp=0.8, K=0.6, γ= 0.5. Correlaton coeffcent of frequency 758
ε 1, ε have a drect mpact on CPS1 and CPS ndcator. Here ε 1. to be Δ P =5.40mHz, ε g =0.56mHz. Conder turbne GRC λ=0.03mw/, the dead zone of governor to be 0.00. Add random ource wth magntude of 0.003 and frequency of 0.5 to mulate the uncertanty of parameter. Genetc algorthm are ued to tran the Elman neural network that model the plant. After a ere of tral and error, the ANN archtecture choen to be 3 6 1. he actvaton functon of the network neuron hyperbolc tangent, 1-exp(-0.8) 1-exp(-0.6) f()=, g()= 1+exp(-0.8) 1+exp(-0.6) Feedback gan α = 0.65, amplng perod = 0.01. Fg. 6 how the output of the Elman neural network. It can be een that the propoed ANN could effectvely predct the power output. Fg. 7.Frequent devaton n area 1 Fg. 8.Frequent devaton n area Fg. 6.he predctve output of the Elman neural network Fg. 9.Power generaton output n area 1 Smulaton made under the condton that the two regon are added dfferent load dturbance, wth 0.005 p.u.mw to the frt regon and 0.013 p.u.mw to the econd regon. From Fg. 7 and Fg. 8, the propoed method offer a much better frequency repone to both area than that of the tradton fuzzy control wth the ettlng tme of 15 n area1 and 13 n area. he maxmum frequency overhoot are -0.05 and -0.0 repectvely. Due to the mpact of a random ource, the frequency output baed on the tradtonal fuzzy control ocllate contantly wth the maxmum overhoot beng -0.04 and -0.03 repectvely. From Fg. 9 and Fg., the power output under the ANN predcton fuzzy control more table than that of tradtonal fuzzy control n both area. From Fg. 11 and Fg. 1, the control effort under the ANN predctve fuzzy control much le than that of tradtonal fuzzy control, whch mean wear and tear of generatng unt equpment are qute reduced. From Fg.13 and Fg. 14, the ACEN quckly drven to zero and have maller overhoot ung the propoed method. From Fg.15-Fg.18, the ANN predcton fuzzy control can better meet the CPS performance tandard. Fg..Power generaton output n area Fg. 11.Control effort n area 1 Fg. 1.Control effort n area 759
Fg. 13.ACEN n area 1 Fg. 14.ACEN n area V. CONCLUSIONS In th paper, Elman network propoed to model the load frequency control of a two-area power ytem. Fuzzy control trategy wa choen to comply wth the North Amercan Electrc Relablty Councl control performance tandard, CPS1 and CPS. o demontrate the effectvene of the propoed method, the control trategy teted under load perturbaton. he mulaton reult how that the propoed ANN controller ha better control performance compared to the conventonal fuzzy controller even n the preence of GRC. In addton, t effectve and can enure the tablty of the overall ytem for all admble uncertante and load change. he mulaton reult obtaned alo how that the performance of ANN controller better than conventonal fuzzy controller agant the load perturbaton at any area. Epecally t can reduce wear and tear of generatng unt equpment, and thu offer a feable control tructure for AGC. Fg. 15.Output of CPS1 n area 1 Fg. 16.Output of CPS1 n area REFERENCES [1] M. L. Kothar, J. Nanda, D. P. Koathar, and D. Da, Dcrete mode automatc generaton control of a two-area reheat thermal ytem wth new area control error, IEEE ran. on Power Sytem, vol. 4, no., pp. 730 738, 1989. [] F. Beaufay, Y. Abdel-Magd, and B. Wdrow, Applcaton of neural network to load frequency control n power ytem, IEEE ran. Neural Network, vol. 7, no. 1, pp. 183 194, 1994. [3] H. L. Zeynelgl, A. Demroren, and N. S. Sengor, he applcaton of ANN technque to automatc generaton control for mult-area power ytem, Internatonal Journal of Electrcal Power & Energy Sytem, vol. 4, no. 5, pp. 345 354, 00. [4] C. S. Indulkar and Baldev Raj, Applcaton of fuzzy controller to automatc generaton control, Electrc machne and power ytem, vol. 3, no., pp. 09 0, 1995. [5] C. S. Chang and W. Fu, Area load frequency control ung fuzzy gan chedulng of PI controller, Electrc power ytem reearch, vol. 4, pp. 145 15, 1997. [6] Y. L. Karnava and D. P. Papadopoulo, AGC for autonomou power ytem ung combned ntellgent technque, Electrc Power Sytem Reearch, vol. 6, no. 3, pp. 5 39, 00. [7] M. J. Yao, R. R. Shoult and R. Kelm, AGC Logc Baed on NERC New Control Performance Standard and Dturbance Control Standard, IEEE ran. on Power Sytem,, vol. 15, no., pp. 85 857, 000. Fg. 17.Output of CPS n area 1 Fg. 18.Output of CPS n area 760