Optimal Agc of Deregulated Interconnected Power System with Parallel Ac/Dc Link

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1 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: Optimal Ac of Dereulate Interconnecte ower System with arallel Ac/Dc Link Naimul Hasan Department of Electrical Enineerin Jamia Millia Islamia New Delhi-5, Inia Abstract : his paper presents optimal AGC reulator esin of ereulate power system base on the full state feeback control stratey. he two-area interconnecte power system of ientical nature consistin of non-reheat turbine is consiere for the investiations. he areainterconnection of the power system via parallel EHVAC/HVDC transmission link is consiere. he propose controller is applie to two-area interconnecte power system an its feasibility is emonstrate by investiatin the ynamic response plots obtaine various system states of the power system moels uner consieration. he patterns of close-loop eienvalues are obtaine to analyze the stability of the power system moels. eywors- AGC, Dereulate power system, interconnecte power system, parallel EHVAC/HVDC. I. INRODUCION he electric power inustry is in transitional phase movin from centrally reulate utilities to ereulate environment that will inject competition in the power sector amon all the companies to sale the unbunle power at very reasonable rates to the istribution companies. he restructurin an ereulation of power sector is to create a competitive environment where eneration an transmission services are bouht an sol uner eman an supply market conitions. his has unbunle the electric utility services into its basic components an offerin each component separately for the sale with separate rates. he unbunlin of the vertical entity creates the separate entity for eneration, transmission an istribution for the transaction of electric power. efore ereulation ancillary services were provie by a sinle entity possessin owns eneratin resources, transmission an istribution capacities locate within its territories. he ereulate power system will have the eneratin power station separate from transmission an istribution entities. All the power eneratin stations will be reconize as inepenent power proucers (I). hese will be known as GENCOs which will have a free market to compete each other to sell the electrical power. he retail consumers are suppose to buy the electrical power from the istribution companies known as DISCOs. here is also a thir player between the GENCOs an DISCOs for wheelin the between them which is esinate as RANSCOs. So in the ereulate power system instea of havin sinle vertical entity it will have three players as GENCOs, DISCOs an RANSCOs operatin separately with their own set functionalities. o supply the reulation between Disco an Genco, a contract will be establishe between these entities. In the ereulate power system structure, a istribution company has the freeom to have a contract with any eneration companies for purpose of transaction of power. he ifferent companies may have the bilateral transactions an these will have to be monitore throuh an inepenent system operator which will control the number of ancillary services. he main task of automatic eneration control is to maintain the reliability of the system at the esire frequency even to the varyin loa eman. he eneration companies in ereulate environment may or may not participate in the AGC task. As far as the optimal AGC schemes for interconnecte power systems operatin in ereulate environment are concerne, a consierable work has been reporte in literature [-5]. V. Done et al. in [5] have presente an AGC of interconnecte power systems in ereulate environment. he istribution companies may contract for the transaction of power with eneration companies in its area or other areas. his transaction of power amon the eneration an istribution companies is one uner the supervision of the inepenent system operators. he frame work of the ereulate power system is as follows:. Unbunlin of electrical power system separatin Vertically Interate Utility into GENCOs, RANSCOs an DISCOs as inepenent entities.. Annullin of exclusive rihts. hir party shall et access to transmission or supply ris. However, in all the above articles power system moels interconnecte via EHV AC transmission links only. ut ue to the obvious of merits of HVDC transmission line, the interconnection with HVDC link has been utilize for the power system moel uner consieration. One of the most useful applications of HVDC link is its operation in parallel with EHVAC transmission line between two power networks. his makes the system makes the more stable. he HVDC transmission link an area interconnection has also been emonstrate as a viable tool to improve ynamic performance of the system [6-9]. In the work presente in this paper, optimal controllers are esine an compare base on the interconnecte between the two areas. In one power system moel the AC tie-line is consiere an in the secon power system moel a parallel AC/DC tie line is consiere. he ynamic performance of the power system moels consiere is analyze for the esine reulators. II. ower System Moel A two-area interconnecte power system operatin uner ereulate environment with parallel EHVAC/HVDC for exchanin of power between control areas is consiere for investiation. he structure of power system moel consists of two ientical non-reheat thermal 789 a e

2 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: power plants as GENCOs an two istribution system as For power system moel uner investiation, the system DISCOs. state, control an isturbance vectors are selecte as follows: he transfer function moel of power system moel State vector uner investiation is evelope an presente in Fi. 8. In X=[ f, f, tie,, X,, X,, this moel, the actual an scheule steay state power X,, X, ACE, ACE] flows on the tie line are iven by; Control vector tie scheule (Deman of DISCOs in area- from u [ C C ] GENCOs in area-) - (Deman of DISCOs in area- from Disturbance vector GENCOs in area-) () () L L L L UC UC ] tie, scheule ij Lj ij Lj System Matrices i j i j he structure of system matrices A,, Γ an C can be he tie line power error ( tie, error ) is efine by; obtaine from the transfer function moel shown in fi8. tie tie tie (), error, actual, scheule IV. Desin of Optimal AGC Reulator he area control errors (ACEs) in ereulate he esin of optimal AGC reulators reporte in environment in both areas are efine as; literature []. he continuous time ynamic moel in the ACE f tie (), error state variable form is iven as; ACE f tie (5), error x Ax u (6) As there may be many GENCOs in each area, the ACE sinal is bein istribute amon them an their ACE participation factor () for automatic eneration control an also sum of all s in a particular area shoul be unity. In steay state, the eman of DISCOs in contract with GENCOs eneration must be matche an expresse as: (8) L, Loc L L (9) L, Loc L L, L (9) L Loc L, L () L Loc L L L L () L L L L () L L L L () L UC an UC are isturbance sinal for un-contracte loa in case of contract violation. In case un-contracte loas are absent, UC an UC are zero... Case Stuy In the present work, two ifferent power system moels are ientifie as follows: ower system Moel-I: wo- area interconnecte power system consistin of non-reheat turbine via EHVAC tie-line only. ower system Moel-II: wo area interconnecte power system of non-reheat turbine via parallel EHVAC/HVDC tie-line. III. State Variable Moel he two-area power system moel operatin uner ereulate environment is shown in Fi. 8 can be escribe by the followin controllable an observable linear timeinvariant state space representation; x Ax u () Y Cx (5) y Cx (7) Where, x, u, an y are state, control, isturbance an output vector respectively. A,, C an Г are system, control, output an isturbance matrices of compatible imensions. In the application of optimal control theory, the term in equation (6) is eliminate by reefinin the states an controls in terms of their steay-state values occurrin after the isturbance. It can be rewritten as; x Ax u, x( ) x (8) Moreover eq. (7) will remain the same. he control sinal u is such that to minimize the performance inex (J): J [x Qx u Ru] (9) Where, Q an R are weihtin matrices for the state variables an the input variables. his optimal control problem is referre to as the linear quaratic reulator esin problem. o solve this LQ optimal control problem, let us first construct a Hamiltonian function. J [x Qx u Ru] [ Ax u] () When there is no constraint on the input sinal, the optimal (in this case, the minimum) value can be solve by takin the erivative of H with respect to u an then solvin the followin equation; H Ru () u Denote by u* the optimal control sinal u. hen, u* can be explicitly written in the followin form: u* R () On the other han Laranian Multiplier (λ) can be written as; S x () Where, S is the symmetrical solution of the well known DRE. S -SA - A S SR S Q () 79 a e

3 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: able- Optimal Gains of AGC Reulator.S Moel- I he solution matrix S will ten to a constant matrix i.e. S/=, In this case DRE reuce to so calle alebraic Riccatti Equation: SA A S SR S Q (5) Now () can be written as; u* R S x (6) With a full state vector feeback control problem, a control law is state as; u * Ψ * x (7) Usin (6) an (7), the esire optimal feeback ain matrix (Ψ*) is iven by; Ψ * R S (8) How to etermine the feeback ain matrix [Ψ*], which minimizes the values of J is an important optimization problem. he value of [Ψ*] is usually obtaine from the solution of matrix Riccati equation [] V. Simulation Results he optimal ains of AGC reulators are obtaine by usin MALA software. he patterns of close loop eienvalues is reporte in able- where as the optimal ains of AGC reulators esine an performance inex obtaine are presente in able- an able- respectively. he ynamic response plots with the implementation of optimal AGC reulators are shown by Fis. (-7). VI. Discussion of Results he MALA software is use to obtain pattern of close-loop eienvalues, optimal ains of AGC reulators, performance inex an ynamic response plots for both the moels. he inspection of close-loop eienvalues as shown in ables- inferre that all the eienvalues have neative real part, thereby ensurin the system stability in close-loop fashion. he response curves of Fis. (-) represent frequency eviations of respective areas. Observations carrie out from these plots reveal that the propose optimal AGC reulators are capable to mitiate the eviations in frequency of both areas cause ue to instantaneous loa emans from DISCOs. he tie line power eviation settles to a zero value. he propose AGC reulators are foun to emonstrate their ability to brin the system state eviation as per the esire ones in an effective manner. he response curves in Fis. (-7) show the eviations in power eneration by GENCOs of respective areas. From the inspection of these Fis., it has been inferre that the propose optimal AGC reulators are effective in settlin the chane in power eneration to the require value in reasonably small time. able- attern of Close-loop Eienvalues ower system moel-i ower system moel-ii.s. Moel- II able- erformance Inex Moel-I.7 Moel-II 8.97 VII. Conclusions In this paper, the ains of optimal AGC reulators are obtaine usin moern control theory throuh state space moel technique. he patterns of close-loop eienvalues are obtaine for power system moels in ereulate environment an their investiation reveals that system is stable. he responses are associate with more number of oscillations couple with larer settlin time erae the system ynamic response in case of power system moel-i havin AC tie line only are reuce tremenously in the power system moel-ii with AC/DC parallel tie lines. f f Fi. Chane in Frequency ( F) ower System Moel- ower System Moel Fi. Chane in Frequency ( F) 5 x - ower System Moel- ower System Moel- ower System Moel- ower System Moel ±.987i ±.i ±.596i ±.8i -.5 ± 7.668i ±.i -.96 ±.9i -.8 tie Fi. 5 Chane in ie-line power ( tie) 79 a e

4 Fi. 6 Fi. 7 Fi. 8 Fi. 9 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: ower System Moel- ower System Moel- 5 Chane in ower enerate () ower System Moel- ower System Moel- 5 7 x Chane in ower enerate () ower System Moel- ower System Moel- - 5 Chane in ower enerate () ower System Moel- ower System Moel- 5 Chane in ower enerate () References: []. umar, S. A. azmi an N. Yasmeen, Comparative stuy of automatic eneration control in traitional an ereulate power environment, Worl Journal of Moellin an Simulation, vol. 6, no.,, pp []. yai an S.C. Srivastava, A LQG base loa frequency controller in a competitive electricity markets, Int. Journal of Emerin Electric ower Systems, vol., no., 5, pp. -. [] S.. Sinha, R.N. atel an R. rasa, Desin of optimal controller for AGC in a restructure power systems, roc. National Conf. Recent Avances in Electrical an Electronics Enineerin, Hamirpur, Inia, 9, pp [] E. Rakhshani an J. Saeh, Loa frequency control of multi-area restructure power system, roc. IEEE Int. Conf. ower Systems echnoloy, New Delhi, Inia, 8, pp. -7. [5] V. Done, M. A. ai an I. A. Hiskens, Simulation an optimization in a AGC system after ereulation, IEEE rans. on ower System, vol. 6, no., pp. 8-89,. [6]. umar an Ibraheem, Dynamic performance evaluation of -area interconnecte power systems: a comparative stuy, Journal of Institution of Enineers (Inia), vol. EL-, no. 78, pp. 99 9, 997. [7] C. Srinivasa Rao, S. Siva Naaraju an. Sanameswara Raju, Improvement of ynamic performance of AGC uner open market scenario employin CS an AC-DC parallel tie line, Int. J. of Recent rens in Enineerin, vol., no., May 9. [8] Ibraheem,. umar an S. Ahma, Dynamic performance enhancement of hyro-power systems with asynchronous tie-lines, Journal of Institution of Enineers (Inia), vol. 85, June, pp. -. [9] Ibraheem an. umar, Stuy of ynamic performance of power systems with asynchronous tielines consierin parameter uncertainties, Journal of Institution of Enineers (Inia), vol. 85, June, pp. 5-. [] Ibraheem,. umar an D.. othari, Recent philosophies of automatic eneration control strateies in power systems, IEEE rans. on ower Systems, vol., no., 5, pp [] M. Athans an. Falb, Optimal Control: An application to the theory an its application, Mc Graw-Hill, New York, 966. Numerical Data: L=.;L=.;L=.;L=.; M=; L=; W=; OL=.; alpha=.5;=.867; b=.9;b=.9; a=- ;p=;p=;p=;p=;c=;c=.; t=.6; =.; r=5;r=.;r=.;t=.6; =.; r=5; r=.; R=.;t=.6; =.; r=5; r=.; R=.;t=.6; =.; r=5; r=.; R=.;=.5; =.5;=.5;=.5;=.;=.;=. ; =.6; =.; =.; =.; =.; =.7;=.;=.;=.;=.; =; =.; =.; 79 a e

5 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: a e Fi.. ransfer function moel of two-area interconnecte power system uner ereulate environment System Matrix A b b R R R R ps ps ps ps ps ps ps ps A

6 International Journal of Moern Enineerin Research (IJMER) Vol., Issue., July-Au pp ISSN: a e Control Matrix Disturbance Matrix F F