Robust Decentralized Design of H -based Frequency Stabilizer of SMES

Transcription

1 International Energy Journal: Vol. 6, No., Part, June Robut Decentralized Deign of H -baed Frequency Stabilizer of SMES C. Vorakulpipat *, M. Leelajindakrirerk *, and I. Ngamroo ** * Electrical Engineering Department King Mongkut Intitute of echnology Ladkrabang, angkok ** Electrical Power Engineering Program Sirindhorn International Intitute of echnology hammaat Univerity, Pathumtani HAILAND ASRAC hi paper preent a new robut decentralized deign of frequency tabilizer for uperconducting magnetic energy torage (SMES) baed on an H control. A an interconnected power ytem i ubjected to load diturbance, ytem frequency may be everely diturbed and ocillate. o tabilize frequency ocillation, the active power control by SMES intalled in a power ytem can be applied. he propoed decentralized control deign tranlate interconnected power ytem intalled with SMES into a Multi-Input Multi-Output (MIMO) control ytem. he technique of overlapping decompoition i applied to extract the decoupled ubytem with Single-Input Single-Output (SISO) from an MIMO ytem. A a reult, a frequency tabilizer of SMES can be independently deigned to enhance the damping of the inter-area mode embedded in the decoupled ubytem. In addition, to guarantee the robut tability of ytem againt uncertaintie uch a ytem parameter variation etc., the multiplicative uncertainty model i alo incorporated. Conequently, H control via a mixed enitivity approach i applied to deign the robut frequency tabilizer of SMES. Study reult explicitly how that the robutne of the H -baed frequency tabilizer of SMES i uperior to that of the PID baed tabilizer under variou load diturbance and negative damping.. INRODUCION Nowaday, variou kind of apparatu with large power conumption, uch a, a magnetic levitation tranportation, a large cale accelerator, a teting plant for nuclear fuion etc., tend to increae ignificantly. When thee load are concentrated in an interconnected power ytem, they may caue a eriou problem of frequency ocillation. Epecially, if the frequency of changing load i in the vicinity of the inter-area ocillation mode ( Hz), the ocillation of ytem frequency may experience a eriou tability problem due to an inadequate damping. Under thi ituation, the conventional frequency control, i.e. a governor, may no longer be able to aborb the large frequency ocillation due to it low repone []. In order to compenate thee udden load change and tabilize frequency ocillation, an active power ource with fat repone, uch a SMES [], i expected a one of the mot effective countermeaure. In the literature [3-5], a SMES i propoed for invetigating it application to frequency control. It ha been oberved that a SMES can effectively reduce frequency and tie-line power ocillation following udden load diturbance. Neverthele, ytem uncertaintie uch a change in ytem configuration due to unpredictable diturbance, ytem parameter variation and modeling

2 -60 International Energy Journal: Vol. 6, No., Part, June 005 error, etc. have not been conidered in thee literature. he frequency tabilizer of SMES that are deigned without taking ytem uncertaintie into conideration may not guarantee a robut tability of the ytem. o olve thi problem, thi paper propoe a new robut decentralized deign of frequency tabilizer for SMES baed on an H control. he multiplicative uncertainty model i employed to repreent all poible uncertaintie in interconnected power ytem. he H control baed on mixed enitivity approach i applied to deign frequency tabilizer. he robutne of deigned frequency tabilizer i evaluated in the three-area loop interconnected ytem. he organization of thi paper i a follow. Section provide the motivation of the propoed control. Next, Section 3 explain the propoed deign method. Subequently, the imulation tudy of deigned PSS i given in Section 4. Finally, the outcome from thi paper are ummarized.. MOIVAION OF HE PROPOSED CONROL )DVW/RDG &KDQJH $5($ 60(6 $5($ )DVW/RDG &KDQJH $5($ 60(6 Fig. hree-area Loop Interconnected Power Sytem with SMES A three-area loop interconnected power ytem [6] a hown in Fig. i ued a a tudy ytem. It i aumed the large load with udden change have been intalled in area and 3. hee load change caue evere frequency ocillation in both area. o olve thi problem, SMES and SMES3 are placed in area and 3 repectively. Here, the frequency tabilizer of each SMES i deigned by the propoed control. 3. PROPOSED CONROL DESIGN 3. Coordinated Control of SMES and Governor he repone of SMES i extremely rapid when compared to the conventional frequency control ytem, i.e. a governor. he difference in repone ignifie that the SMES and governor can be coordinated. When a power ytem i ubjected to a udden load diturbance, the SMES quickly act to damp frequency ocillation in the tranient period. Subequently, the governor continue to eliminate the teady-tate error in frequency ocillation. A the period of operation for the SMES and governor do not overlap, the dynamic of governor can then be neglected in the deign of frequency tabilizer for the ake of implicity.

3 International Energy Journal: Vol. 6, No., Part, June Linearized Power Sytem Model he power ytem hown in Fig. can be repreented by a linearized power ytem model, a hown in Fig.. Note that the governor are eliminated in thi ytem. he SMES model i repreented by the active power controller [7]. he dynamic characteritic of SMES i modeled a the firt order controller with a time contant SM = 0.03 ec. he linearized tate equation of Fig. can be expreed a: Load Change in Area P L P SMES SMES P 3 M +D f P ar Power Sytem P M +D f ar 3 Power Sytem P SMES 3 M 3+D3 f 3 P L3 Load Change in Area 3 ar 3 Power Sytem 3 3 P 3 f i K SMES i SM+ P SMES i SMES LOCK DIAGRAM Fig. Linearized Model of hree Area Sytem for Control Deign Δf a a a3 a4 a5 Δf P a a a3 a4 a 5 P Δ Δ S : Δf = a a a a a Δf ΔP 3 a4 a4 a43 a44 a45 ΔP 3 Δf a 3 5 a5 a53 a54 a 55 Δf 3 b b SMES b3 b 3 P Δ SMES b4 b 4 b 5 5 b b Δ P b ()

4 -6 International Energy Journal: Vol. 6, No., Part, June 005 where, a = -D /M, a = (ar + 3 / )/M, a 4 = - 3 /M 3, a = -π, a 3 = π, a 3 = -/M, a 33 = -D /M, a 34 = -ar 3 /M, a 43 = π 3, a 45 = -π 3, a 5 = -ar 3 3 /M 3, a 54 = (+ar 3 3 / 3 )/M 3, a 55 = -D 3 /M 3, b = -/M, b 5 = -/M 3, the other are equal to 0 he variable Δ P i repreented in term of 3 Δ P and Δ P by 3 Δ P = Δ P + Δ P () hu, Δ P ha diappeared in Eq. (). hi ytem ha two conjugate pair of complex 3 eigenvalue and a negative real eigenvalue. he former correpond to two inter-area ocillation mode and the latter the inertia center mode. aed on the mode controllability matrix, the inter-area mode between area and, and area and 3 are controllable for the control input ΔP SMES and Δ P SMES 3, repectively. Accordingly, the deign purpoe of frequency tabilizer i to enhance the damping of the mentioned inter-area mode. 3.3 Overlapping Decompoition Since the ytem () i a Multi-Input Multi-Output (MIMO) ytem, it i not eay to deign both frequency tabilizer imultaneouly and directly from the ytem. o implify the deign proce, the technique of overlapping decompoition [8-9] i applied to reduce the ytem () to a ubytem embedded with only the inter-area mode of interet. he original ytem () i referred to a the ytem S. x A A A3 x S : x = A A A x 3 x 3 A3 A3 A 33 x 3 u u (3) he ub-matrice A ij and ij, ( i, j =,,3) have appropriate dimenion identical to the correponding tate and input vector. According to the proce of overlapping decompoition, the ytem S can be expreed a: S : A A 0 A3 z A A 0 A 3 z z = A 0 A A 3 z A3 0 A3 A33 u + u 3 (4)

5 Å Æ Æ International Energy Journal: Vol. 6, No., Part, June where z = x, x and z = x, x 3. Subequently, the ytem S can be decompoed into two interconnected overlapping ubytem, i.e. A A S : z = z u A A + 0 A3 + z + u 0 A 3 (5) and A A3 S : z = z u A3 A A 0 + z + u A3 0 3 (6) he tate variable x i repeatedly included in both ubytem, which implie Overlapping Decompoition. For ytem tabilization, two interconnected ubytem S and S are conidered. he term in the right hand ide of Eq. (5) and (6) can be eparated into the decoupled ubytem (a indicated in the parenthei in Eq. (5) and (6)) and the interconnected ubytem. A mentioned in [8-9], if each decoupled ubytem can be tabilized by it own input, the aymptotic tability of the interconnected overlapping ubytem and are maintained. Moreover, the aymptotic tability of the original ytem i alo guaranteed. Conequently, the interaction of the decoupled ubytem with the interconnection ubytem in Eq. (5) and (6) are regarded a perturbation. hey can be neglected during control deign. A a reult, the decoupled ubytem of Eq. (5) and (6) can be expreed a: A A S D : z = z + u A A (7) and A A3 S D : z = z + u A3 A 33 (8) 3 y regarding the power deviation between area and ( ) Δ P a the overlapped variable for deign of frequency tabilizer of SMES, the ubytem embedded with the inter-area mode between area and can be expreed a: G : ( ) f Δf D M ar + M Δ = M + Δ P SMES 0 3 ΔP π 0 ΔP (9)

6 Å Æ Æ -64 International Energy Journal: Vol. 6, No., Part, June 005 Next, by conidering the power deviation between area and 3 ( ) Δ P 3 a the overlapped variable for deign of frequency tabilizer of SMES3, the ubytem embedded with the inter-area mode between area and 3 can be expreed a: G : ΔP 0 π ΔP = 0 + ΔPSMES 3 M Δf3 + a M3 D3 M3 Δf3 (0) Eq. (9) and (0) are ued to deign SMES and SMES3, repectively. It hould be noted that after the proce of overlapping decompoition, the original MIMO ytem () are divided into two decoupled Single-Input Single-Output (SISO) ubytem (Eq. (0) and ()). Accordingly, each frequency tabilizer can be independently deigned in the decoupled ubytem. 3.4 H Control Deign W Z W Z G W W S u= P P y= f K H SMES Fig. 3 H control deign In order to deign the controller baed on H method, each decoupled ubytem can be formulated into Linear Fractional ranformation model in Fig. 3 [0]. he multificative uncertainty i ued to model all poible perturbed plant. For the ytem notation, P i the interconnected ytem which conit of nominal plant G, i.e., a tranfer function of a decoupled ubytem, performance weighting function W S and uncertaintie weighting function W, y i a meaurement plant output, u i a control ignal, w and w are diturbance at plant input and output, repectively, z and z are error ignal of W and W S weight, repectively. he H controller i repreented by controller K. It utilize the frequency deviation Δf i of the controlled area a the feedback ignal input. o achieve robutne, the controller mut be obtained atifying inequality () and () for the control ytem W S () W () where, S i the enitivity tranfer function ((I+GK) - ) and i the complementary enitivity tranfer function (GK(I+GK) - ). According to inequalitie () and (), he W S i elected in form of low pa filter a:

7 International Energy Journal: Vol. 6, No., Part, June W = (3) + 5 For all frequencie, the relation of S + = I i held. hu, W i elected in form of high pa filter a: + 3 W = (4) + 0 A a reult, the H -baed frequency tabilizer of SMES in an area i 3 K = + + SMES (5) Fig. 4 ode Plot of S and W S - Fig. 5 ode Plot of and W -

8 -66 International Energy Journal: Vol. 6, No., Part, June 005 Fig. 6 ode Plot of ubytem (9) (efore and After Applying H SMES) Fig. 4 and Fig. 5 confirm that the condition in inequalitie. () and () are atified by the deigned controller K SMES. In addition, the control effect of H -baed tabilizer i clearly hown by bode plot of deigned model in Fig. 6. he H -baed tabilizer i capable of reducing the peak reonance in the frequency of inter-area ocillation mode. he ame trategy i ued to deign the H -baed tabilizer in area 3. W S and W are elected a: + 0 w S = (6) w = (7) + 0 A a reult, the H -baed frequency tabilizer of SMES in area 3 i given by: 3 K = S + S + SMES (8) SIMULAION RESULS In imulation, the deigned H -baed tabilizer i compared to the PID-baed frequency tabilizer. aed on the ame firt overhoot of frequency ocillation againt 0.0 pu.mw tep load increae in area and 3, he PID-baed tabilizer are given a: K SMES = (9) K = SMES 3 (0) In addition, the governor i included in a linearized power model in a imulation tudy, a hown in Fig. 7.

9 International Energy Journal: Vol. 6, No., Part, June LoadChange i ia Coefficient R i Regulation Ratio P Li P g -K i Integral Controller t (Area only) + gi P gi + ti Governor i urbinei Areai, i =,, 3 GRC P t P t P ti P ij ij Synchronizing Coefficient M+D i i Power Sytemi f i i j Fig. 7 Linearized model with governor f j Simulation tudie are eparated to 3 cae a hown in Fig. 8. ieline- Area ieline-3 f Area H SMES f Area PID SMES Area Area3 Area Area3 H Area SMES 3 ieline-3 f3 Fig. 8 Cae tudie for hree Area Loop Sytem Area3 PID SMES 3 f3 Fig. 9 and 0 how the dynamic repone for 0.0 pu.mw tep load diturbance in area and 3. H -baed tabilizer provide better damping effect on frequency ocillation Δf and Δf 3 than thoe of PID-baed tabilizer. Fig. 9 Frequency Deviation of Area

10 -68 International Energy Journal: Vol. 6, No., Part, June 005 Fig. 0 Frequency Deviation of Area 3 Fig. he active power output of H - baed tabilizer Fig. he energy deviation of H - baed tabilizer Fig. how the active power output of H - baed tabilizer. he MW capacitie of SMES are evaluated from the peak value of power output of the SMES. he MW capacitie of SMES and SMES3 are and pu.mw, repectively. Fig. how the MJ energy deviation of H - baed tabilizer that evaluated from

11 International Energy Journal: Vol. 6, No., Part, June Δ E SMES = ΔP SMES dt () Neceary MJ capacity of SMES can be calculated by: MJ Capacity = ΔE ΔE () SMES( MAX ) SMES( MIN) A a reult, MJ capacitie of SMES and SMES3 are 0.06 and pu. MJ, repectively. Next, the load change appiled to area and 3 are aumed to be ΔP L = in(3t) in(6t) in(9t) and ΔP L3 = in(t) in(5t) in(7t), repectively. Suppoe that the ytem i in untable tate o that the ytem damping coefficient D and D 3 are -0.3 [pu.mw/hz]. A hown in Fig. 3 and 4, the power ytem with PID-baed tabilizer completely loe tability, frequency ocillation in area and 3 everely fluctuate and finally diverge. On the other hand, frequency ocillation are effectively tabilized by H -baed tabilizer. hee reult confirm that the robutne of the H -baed tabilizer i uperior to that of the PID-baed tabilizer. Fig. 3 Frequency Deviation of Area Fig. 4 Frequency Deviation of Area 3

12 -70 International Energy Journal: Vol. 6, No., Part, June CONCLUSIONS hi paper focue on the new robut deign of frequency tabilizer of SMES by taking ytem uncertaintie into conideration. he overlapping decompoition technique i ued to extract the SISO ubytem embedded with the inter-area ocillation mode of interet from the original MIMO ytem. A a reult, each frequency tabilizer can be independently deigned in the decoupled ubytem. y including the multiplicative uncertainty model in the decoupled ubytem, the H control via mixed enitivity approach can be applied to deign frequency tabilizer of SMES. he reulted H frequency tabilizer i low order controller. In addition, it ued only a frequency deviation of the control area a a local ignal input. Experimental tudie have confirmed the high robutne of the deigned frequency tabilizer againt variou load diturbance with changing frequency in the vicinity of inter-area mode and negative damping. 6. REFERENCES [] Jaleeli. 99. Undertanding Automatic Generation Control. IEEE ran. on Power Sytem 7(3): 06-. [] Haenzahl, W Superconducting Magnetic Energy Storage. IEEE ran. on Magnetic 5(): [3] anerjee, S.; Chatterjee, J.K.; and ripathy, S.C Application of Magnetic Energy Storage Unit a Load-Frequency Stabilizer. IEEE ran. on Energy Converion 5(): [4] ripathy, S.C. and Juengt, K.P Sampled Data Automatic Generation Control with Superconducting Magnetic Energy Storage in Power Sytem. IEEE ran. on Energy Converion (): [5] ripathy, S.C.; alaubramanian, R.; and Chandramohanan Nair, P.S. 99. Effect of Superconducting Magnetic Energy Storage on Automatic Generation Control Coniderating Governor Deadband and oiler Dynamic. IEEE ran. on Power Sytem 7(3): [6] Elgerd, O.L Electric Energy Sytem heory. An Introduction. nd edition: McGraw-Hill, 340 p. [7] Mitani, Y.; uji, K.; and Murakami, Y Application of Superconducting Magnetic Energy Storage to Improve Power Sytem Dynamic Performance. IEEE ran. On Power Sytem 3(4): [8] Singh, M.G. 98. Decentralied Control. North-Holland Sytem and Control Serie: [9] Ikeda, M. et al. 98. Decentralized control with overlapping information et. Journal of Optimization heory and Application 34(): [0] Zhou, K Eential of Robut Control: Prentice-Hall, Inc.