Lqr Baed Load Frequency Control By Introducing Demand Repone P.Venkateh Department of Electrical and Electronic Engineering, V.R iddhartha Engineering College, Vijayawada, AP, 520007, India K.rikanth Department of Electrical and Electronic Engineering, V.R iddhartha Engineering College, Vijayawada, AP, 520007, India V.Hari Vami Department of Electrical and Electronic Engineering, V.R iddhartha Engineering College, Vijayawada, AP, 520007, India Abtract he trong inpiration for raie of renewable energy in power ytem, mainly at the demand ide, reult in novel change in frequency and voltage regulation. In power ytem operation, wide area monitoring application will focu heavily on Demand Repone (DR), particularly in the mart grid area, where two-way communication and conumer haring are involved. Load Frequency Control (LFC) model play a ignificant role in electric power ytem deign and operation. hi paper preent an idea of incorporating a DR loop in conventional LFC known a LFC-DR, for a inglearea power ytem uing Intelligent Controller. In the controller deign DR communication delay latency i conidered which linearized uing Pade approximation. he DR control loop in LFC improve tability of the overall cloed-loop ytem, efficiently increae the dynamic performance of the ytem. he imulation reult how that the LQR controller baed propoed power ytem model (LFC-DR) for ingle-area give better performance than the traditional controller under any operating cenario. Index erm Demand Repone (DR), Load Frequency Control (LFC), Linear Quadratic Regulator (LQR), Pade approximation, tability I. INRODUCION Conventionally, frequency parameter in power ytem i maintained by balancing generation and demand via load i.e., pinning and non-pinning reerve [1]. Now a day power generation, i mainly focu on renewable energy (RE) which are highly changeable. In thi cae, torage device and reponive load how huge pledge for balancing generation and demand, a they ait to neglect the uage of the common generation cheme, which are cotly and/or environmentally ditant. From the literature tudy it i known that, the idea of LFC model ha determined only on the generation part, DR ha not explained anywhere. he idea of the paper i to change common mall-ignal model of ytem utilized in LFC tudie by incorporating DR control loop in traditional LFC (known a LFC-DR). Demand repone (DR) play a ignificant role in power market by adjuting load rather than adjuting at generation ide, to maintain balance between upply and demand. By the latet, mart grid technologie higher the integration of DR i achieved. Other idea of the paper i to contruct the model a general a potential, to incorporate communication latency coupled with DR between the load aggregator companie (Lagco) and the end-uer cutomer device. DR option i elected by the ytem operator baed on the real-time electricity price. II. YEM MODEL For frequency control analyi, generalized mall-order linearized power ytem model i given by the power balance equation in the frequency-domain [5], [8]: P ( ) P ( ) 2 H.. f ( ) D. f ( ) L Where P ( ) P ( ) Incremental power mimatch L (1) Volume 8 Iue 3 June 2017 189 IN: 2319-1058
f ( ) Frequency deviation 2H D Equivalent inertia contant Load damping coefficient Laplace tranform operator Fig.1. Propoed model of ingle area power ytem. he cutomized block diagram for ingle area power ytem (hermal) with Demand Repone (DR) control loop for LFC with communication latency i hown in Fig.1. DR preent pinning reerve in magnitude and power flow path i.e., if frequency difference become negative (poitive), it i neceary to turn OFF (ON) a ection of reponive load for ancillary ervice, Equation (1) i change a: P ( ) P L( ) P DR ( ) 2 H.. f ( ) D. f ( ) (2) he power utilization of controllable load can be varied immediately by the demand ignal they accept. he only difficulty for DR i communication delay, identified a latency, which affect the dynamic behavior of the ytem. here are different method fort linearization variou problem with delay. In order to linearize the communication delay, Pade approximation i ued in thi tudy which i explained in the ection IV. III. AE-PACE DYNAMICAL MODEL OF LFC-DR tate-pace repreentation i a helpful method for the purpoe of the modern/robut control theory. For deigning a common tructure of LFC in dynamic frequency analyi thi kind of repreentation can be eaily changed and applied to any ize of power ytem. he tate-pace model for LFC-DR i repreented to how the impact of DR in LFC and controller deign. he tate-pace repreentation of propoed model (hown in Fig.1) i known by, ( t) A. ( t) B. u( t). ( t) Where A ytem matrix, C Obervation matrix B Control input matrix Diturbance matrix ( t) Diturbance variable u( t ) Input vector Diturbance matrix y( t ) ytem output X tate vector y( t) C. ( t) )o obtain the tate-pace model of the ytem, it i neceary to have the linear ytem. From Fig.1 it i oberved that the model a a non-linear element that i time delay propoed model. he time delay i linearized by the approximation known a Pade approximation. IV. PADE APPROXIMAION In turn, to linearize the time delay in control engineering the Pade approximation i commonly ued. Pade approximation i one of the frequently ued method to approximate a dead-time by rational function, but with the numerator and denominator with ame degree i mot widely uggeted. [7] he pade function for the time delay i defined by,. e d Rpq (. d ) (3) Volume 8 Iue 3 June 2017 190 IN: 2319-1058
It i a follow:. d. d 1. d R ( e ) D ( e ). N ( e ) pq pq pq Where N e ( p q k)! p! p. d k pq ( ).(. d ) k 0 ( p q)! k!( p q)! q. ( p q k)! q! d k pq ( ).(. d ) k0 ( p q)! k!( q k)! D e (6) N pq and D pq are the polynomial of order p and q repectively. It i common to ue ame order of numerator and denominator for the approximation and the order generally varie between 1 to 10. In thi tudy 5 th order Pade approximation i ued, becaue the low-pa filter i.e., peed-governor and turbine, in the model i le than 15 rad/ec. V. ANALYICAL EVALUAION OF HE MODEL a) teady-tate Error: he primary control loop in Fig.1 i the fatet propoed control action in a ytem but it i not adequate to make the frequency deviation to zero at teady-tate. o overcome thee, the upplementary frequency control loop hown in Fig.1. By adding DR, it i eential to examine the effect of DR loop on the teady-tate error hown in Fig.1. he optimal ditribution between DR and upplementary control loop i calculated from the teady tate error etimation for controller deign. he equation of conventional LFC at teady-tate are well recognized from [8]. By DR control loop the ytem frequency deviation can be expreed a follow: 1 f ( ) P ( ) P L( ) G( ). P DR ( ) 2 H. D (7) Where, 1 P ( ) H ( ). P ( ). f ( ) R (8) 1 H ( ) (1. g )(1. t ) (9) 5 30 4 420 3 3360 2 15120 30240.... 2 3 4 5 d d d d d G( ) 5 30 4 420 3 3360 2 15120 30240.... 2 3 4 5 d d d d d (10) Baed on the final value theorem, the teady-tate frequency deviation can be obtained a follow [8]. P, PDR, PL f 1 D R (11) From equation (11) the following concluion can be oberved Not dependent on the delay and the approximation order. he high reliability of frequency regulation can be achieved with DR. he control effort i plit between upplementary and DR loop for zero frequency deviation at teady-tate. By taking above concluion into account: with DR in the LFC, the control effort can be hared a follow baed on cot of electricity in the real market. P ( ). Control effort (12) P ( ) (1 ). Control effort (13) DR On by plitting control effort between two loop the ytem i modified and i governed by the, (1 ). G( ). H ( ) (14) Where varie between 0 to 1. For alpha =1, the total reerve i provided by uual regulation ervice. For alpha = 0, the total control i guaranteed by DR. he alpha value i determined by IO/ RO, depend on the cot of DR and uual regulatory (4) (5) Volume 8 Iue 3 June 2017 191 IN: 2319-1058
ervice in the real time market [2]. he imulation tudie are paed with two different value of alpha for frequency deviation on the ytem. b) enitivity Analyi with and without DR: A ytematic way i ued to know the effect of DR loop on the overall enitivity of the cloed-loop ytem w.r.t the open- Loop ytem. econd analyi i the enitivity of the cloed-loop ytem w.r.t alpha. For thi analyi Fig.1 i lightly changed with ingle integral controller (with gain K) for both control loop hown in Fig.2. hi change permit to hare the neceary control effort between two loop a dicu earlier. Fig.2 Propoed ytem with integral controller. he enitivity analyi of the cloed-loop ytem w.r.t the open-loop ytem, for the ytem with and without DR i written a follow [8], DR 1 DR OL ( OL ( )) OL DR 1 K K ( OL ( )).. H ( ).(1 ). G ( ) OL 1 ( ( ) ) 1 K ( ( )). H ( ) (15) From equation (15) the relation of enitivity function can be derived a, 1 K D R ( ( )). H ( ) 1 K K ( ( )).. H ( ) (1 ). G ( ) (16) A the alpha alo play an important role in the LFC-DR it i eential to check the enitivity function of the cloed-loop ytem w.r.t alpha. he enitivity function w.r.t to alpha i given by, ) DR K. H ( ) G ( ) DR DR 1 K K ( OL ( )).. H ( ).(1 ). G ( ) (17) he imulation reult are compared with different alpha value and are dicued in ection VII c) tability Analyi with and without DR: In control ytem tability play an important role. In thi ection, the gain and phae margin for two different value of alpha are explained. he open loop and cloed loop tranfer function with load diturbance i given by, H( ). M( ) K K 1.. H( ). M( ).(1 ). G( ). M( ) 0 R DR H ( ). M ( ) K 1. H ( ). M ( ) 0 R he imulation reult are compared with different alpha value and are dicued in the ection VII (18) VI. CONROLLER DEIGN Variou modern control theorie have been ued for the LFC model. he general controller deign (LQR) method for the Volume 8 Iue 3 June 2017 192 IN: 2319-1058
LFC-DR model i preented in thi ection. he optimal controller Linear- Quadratic regulator (LQR) theory deal with minimizing cot function of a dynamic ytem. he Optimal control in tate-pace i related with Riccati Equation with tate variable function which are olved by the control law. he baic deign of the LQR controller i to minimized the performance index of the ytem given in equation (3) 0 x. Q. x. u. R. u ]. dt Where, i weighting factor choen by deigner Q i n n emi definite ymmetric tate cot matrix R i m m poitive definite ymmetric control cot matrix x [ f, P, P, x, x, x, x, x ] g 4 5 6 7 8 t 4 5 6 7 8 x, x, x, x, x are the tate aociated with pade Approximation From equation (12) & (13) the control input to the upplementary and DR controller i given by, 1 u1. u 2 u2. u1 (20) 1 (Or) he two input are unified a ingle input, all the matrice remain ame except B matrix in tate-pace, the modified B matrix by including unified control input u2 F( u1) i given by, 1 1 16(1 ) B 0 0 0 0 0 (21) 2 H. g he imulation reult are carried out for two cae of unified input which are hown in Fig.7 o make zero teady-tate error for frequency deviation, the traditional full-tate feedback cannot achieve. o, integral control i required to overcome the above problem. With the modified tate pace equation enuring the ytem matrix i controllable [9]. A 0 Bˆ.. u ˆ. C 0 x I 0 0 x I y C 0. x I (22) he control law for tate feedback i defined only if the ytem matrix i controllable, given by uˆ K K 1. K. (23) x 1 o ue the LQR method, Q and R are the tate and control weighting matrice (calar quantitie) to be known. Q and R elected baed on the frequency repone requirement. In thi tudy, MALAB command i ued for LQR implementation. K = lqr [A, B, Q, R] for finding the feedback gain value. V11. IMUAION REUL he parameter utilized in the imulation tudie for the propoed model (LFC-DR) for ingle-area i given in able. I ABLE.I PARAMEER FOR HE IMULAION UDY (19) g R 2H D t d P K L 0.08 ec 0.4 ec 3.0 Hz/p.u 0.1667 pu.ec 0.015 p.u/ Hz 0.1 ec 0.01 ec 0.2 Fig.3 how the effect of DR loop for two different value of alpha. For alpha=0.1, the ytem i le enitive to the cloed-loop ytem w.r.t the open-loop ytem, i.e., 10% from traditional regulation and 90% from DR reource. When, alpha= 0.8, the Volume 8 Iue 3 June 2017 193 IN: 2319-1058
ytem i highly enitive to the cloed-loop ytem w.r.t the open-loop ytem, here 80% if from traditional reerve and 20% from DR reerve. Fig.3 enitivity of cloed loop ytem w.r.t to open-loop ytem Fig.4 how the enitivity analyi of cloed-loop ytem w.r.t the alpha. For alpha = 0.1, the cloed-loop ytem i le enitive to alpha, the higher hare in frequency regulation i provided by DR control loop. Fig.4 enitivity of cloed-loop ytem w.r.t alpha Bode plot of the ytem with and without DR i hown in Fig.5. he gain and phae margin i hown in able. II. It i oberved that maller the alpha value (alpha =0.1) higher the gain and phae margin i obtained, reult in table ytem. Fig. 5 Bode plot for LFC with and without DR ABLE. II PHAE AND GAIN MARGIN FOR YEM (LFC) WIH AND WIHOU DR Gain margin, db Phaemargin, degree Cloed-loop ytem for alpha= 0.1 Cloed-loop ytem for alpha= 0.8 Cloed-loop ytem without DR 14.1 11.3 10.3 83.5 74.8 72.2 Volume 8 Iue 3 June 2017 194 IN: 2319-1058
he imulation wa carried out in MALAB/ Control ytem toolbox for the propoed ytem for ignificant explanation. For the comparion, LQR deign i employed i ued for both ytem with and without to how the effectivene of the ytem. In the firt imulation tudy, 0.01 p.u load diturbance i applied for the traditional LFC and LFC-DR. It i oberved, when alpha=0.1 it i noticed that LFC-DR model give uperior performance than the traditional LFC throughout tranient period. he ame proce i repeated for alpha= 0.8. Fig.6 Frequency deviation for LFC and LFC-DR A dicued in ection.6, the control input are unified a the function of alpha. he unification i made in two way: u1 F( u2) or u2 F( u1 ).o how the impact of unification imulation wa carried out to evaluate the behavior of the ytem for both cae, which i hown in Fig.7. It i noticed that the variation between two unifying approache i mall. Fig.7 Unified input on LFC-DR he communication delay in DR loop play an important role in LFC-DR for frequency tabilization. he imulation i performed to know the impact of different value of latency for different value of alpha, hown in Fig.8 Fig.8 Impact of latency on the LFC-DR he propoed model give improved performance when compared to the traditional LFC when communication delay i le than 0.2 ec. With the time delay more than 0.2 ec the repone i mot horrible than the conventional LFC. ABLE.III Volume 8 Iue 3 June 2017 195 IN: 2319-1058
ype of the ytem EADY-AE VALUE upplementary loop DR loop LFC-DR for alpha= 0.8 0.008 p.u 0.002 p.u LFC-DR for alpha= 0.1 0.001 p.u 0.009 p.u ABLE.IV NUMERICAL ANALYI FOR CHANGE IN FREQUENCY ype of the ytem ettling time (ec) Underhoot (p.u) Conventional LFC >10 0.0333 LFC-DR for alpha= 0.8 >8 0.018 LFC-DR for alpha= 0.1 7 0.011 From the above dicued imulation tudie, it i oberved that the propoed method give better reult and robut. It can alo be practical and reult are een at different perturbation uing different traditional controller a well a the propoed controller for LFC-DR model. VIII. CONCLUION In thi paper, LFC-DR problem i olved by uing the optimal LQR controller. he DR communication latency i conidered which i linearized by pade approximation. he ettling time and underhoot value are conidered to explain the robutne of the propoed controller. REFERENCE [1] R. Doherty and M. O Malley, A new approach to quantify reerve demand in ytem with ignificant intalled wind capacity, IEEE ran. Power yt., vol. 20, no. 2, pp. 587 595, May 2005 [2].A.Pourmouavi and M.H.Nehrir, Real-time central demand repone for primary frequency regulation in microgrid, IEEE ran.mart Grid, Vol.3, No.4,Dec.2012, pp.1988-1996. [3] Mahdi Behrangrad, Hideharu ugihara and uyohi Funaki, Analyi of optimal pinning procurement with demand repone reource under ocial cot minimization, IEEJ ran. Electrical and Electronic Enginnering, Vol.6, iue 3, May 2011, pp 211-220 [4] U. Department of energy, mart Grid, ep 28, 2011 [online] http://energy.gov/oe/technology-development/mart-grid [5] P. Kundur, Power ytem tability and control. New York, NY, UA: McGraw-Hill, 1994, ch.11. [6] Mohyi ed-dm Azzam, An optimal Approach to Robut Controller for Load-Frequency Control, IEEE 2002 [7] G.H.Golub and C.F. Van Loan, Matrix Computation 3 rd edition Baltimore, MD, UA: John Hopkin Unverity, Pre, 1996, pp.572-574 [8] H. Bevarani, Robut Power ytem Frequency Control, New York, NY, UA: pringer, 2009, ch.1-3 [9] R.C. Dorf and R.H.Bihop, Modern Control ytem, 7 th edition. New York, NY, UA: Addition-Weley, 1995, pp.807 [10].Ali Pourmouavi, M.Hahem Nehir, Introducing Dynamic Demand Repone in the LFC model, IEEE ran. Power yy., Vol.29, No.4, July 2014, pp.1562-1572 Volume 8 Iue 3 June 2017 196 IN: 2319-1058