Potential Interaction between VSC HVDC an STATCOM. Shen, M. Barne, Jovica V. Milanović, The Univerity of Mancheter, UK li.hen@tuent.mancheter.ac.uk K.R.W. Bell, an M. Belivani The Univerity of Strathclye, UK Abtract Thi paper analye the ynamic behaviour of a power ytem with both FACTS an VSC HVDC, in particular, poible potential interaction between a STATCOM an a VSC in a point-to-point HVDC link. The invetigation conier ifferent STATCOM location an VSC control trategie. A generic linearize mathematic moel i firtly evelope, where a combine metho involving relative gain array (RGA) an moal analyi i applie to ientify the interaction within the plant moel an the outer controller. The interaction ientifie are further analye by creating a et of cenario integrating both the STATCOM an VSC HVDC into a ynamic equivalent realitic AC ytem. Reult how a collaborative operation between the STATCOM an the cloely locate VSC with reaonably tune controller. Keywor: VSC HVDC, STATCOM, Interaction, Relative Gain Array, Moal Analyi, Dynamic GB ytem 1 INTRODUCTION Power ytem are now being operate cloer to their tability limit ue to economic an environmental contraint. Maintaining a table an ecure operation of a power ytem i therefore becoming more challenging. Particularly the integration of large amount of offhore win power will poe a challenge. DC tranmiion interconnection have been propoe both to connect win turbine ite far offhore an for reinforcement of the onhore network via unerea DC cable link. Self-commutating Voltage Source Converter (VSC) HVDC technology i coniere uperior to claical line commutate converter (CC) HVDC tranmiion a a mean of effective bulk power tranmiion, if an offhore DC ubtation i require. Meanwhile, a the amount of win farm intallation increae, FACTS evice like STATCOM will be ue to help win power generation to achieve gri coe compliance [1]. STATCOM alo have a potential ynergy with CC bae HVDC link for reactive power upply. A natural conequence of increaing quantitie of actively fat controlle evice i that thee component might be locate in the electrical proximity to each other, epecially for a multi-terminal VSC HVDC in the future. It i therefore important to unertan their control interaction. Thi paper conier the particular cae of a STACOM, intalle perhap a part of a win farm, locate cloe to a VSC-bae HVDC link. Valuable work regaring interaction tuie ha been carrie out in many apect: 1. Stuie regaring concurrent operation of multiple FACTS evice or FACTS evice an conventional CC HVDC link inicate that there o exit potential interaction [-4]. Many metho have been propoe an applie to tuy thee. The concept of inuce torque i introuce in [] to tuy the interaction between power ytem tabilizer an FACTS tabilizer. Furthermore, the relative gain array (RGA) [5] metho ha been hown in [3, 6] to be uite to quantify the interaction in power ytem teay tate an ynamic tuie.. It wa alo uggete in [4] that moal analyi can be ue to highlight how moification in one FACTS controller can affect another. Several factor incluing the electrical itance between the evice an the AC ytem hort circuit ratio have been ientifie a influencing the egree of interaction. However, the interaction between VSC bae HVDC link, which ue ubtantially ifferent control to CC HVDC, an FACTS evice have not yet been thoroughly invetigate. The cacae control tructure in a VSC HVDC mean interaction with a STATCOM can occur through multiple control tructure an cannot completely be ientifie through a ingle conventional metho. Thi paper propoe a metho that combine a RGA to quantify the plant moel interaction an moal analyi to illutrate the outer controller interaction. Different type of VSC control trategie are alo coniere ince thi may affect the egree of controller interaction. Controller interaction i initially tuie uing a mall tet ytem to facilitate phyical unertaning of interaction. Following thi a et of cenario i then create uing ynamic equivalent moel of realitic AC ytem, to valiate initial fining. STATCOM AND VSC MODE FOR STABIITY STUDIES.1 STATCOM A STATCOM i a VSC bae hunt evice which regulate it terminal voltage via reactive power compenation. The voltage ource i create from a DC capacitor in thi cae an thu the STATCOM ha very little inherent active power capability. A typical tructure i illutrate in Figure 1, howing alo the coupling tranformer an reactor. Figure 1 preent a typical control tructure for a STATCOM: A control of the phae angle ( ) an the
V AC ytem Bu V c * V* V c V δ 0 0 Tc R jx or G jb (a) I β δ 0 m ao moulation inex (m a ) [7]. The AC bu voltage magnitue i controlle through the moulation inex a thi affect the VSC output voltage irectly. The phae angle i ue to etermine the active power flowing into the VSC an hence charging an icharging the DC capacitor to maintain contant DC voltage. For power ytem voltage an angle tability tuie, the STATCOM moel can be expree by the power balance an voltage converion equation. After linearization [8], the equation are: ΔV Δ V = Δ + Δ c A Vc B V0 = Δδ V G VV0( G co( δ δ0) + B in( δ δ0) ΔV CV c V δ GV V δ δ δ δ 0G co( 0) V 0B in( 0) CVc ΔV VG co( δ δ δ δ 0) VB in( 0) + Δ V0 CVc Δ δ VV G δ δ VV B δ δ 0 in( 0) 0 co( 0) CVc 3 V = V m 8 c a c T (1) Where the parameter are a pecifie in Figure 1. The controller limit are efine bae on the controller current limit (e.g. IGBT current limit) an the effect of tranient performance nee to be factore into the controller tuning. However, the limit of the phae angle an the moulation inex o not necearily limit the actual current. Accoring to the V-I characteritic, the moulation inex limit m a_max an m a_min can be calculate a: m a V DC_min δ V + K I ref lope max m = a _max 3 Vc _ ref V + K I ref lope min m = a _min 3 Vc _ ref V K lope C V c Vref I Aborb Q I min I max Inject Q (b) Figure 1: STATCOM moel (a) with δ-ma control (b) V-I characteritic. () (3) The phae hift limit δ max an δ min nee to be erive by calculating the teay tate equation for the control ytem at I max an I min [7].. Point to point VSC HVDC A typical point to point VSC HVDC link i the baic tructure unerlying future multi-terminal DC gri an wa ue in the tuy. Thi capture key moe without obcuring interaction with exceive etail. Normally, one of the VSC will be configure to maintain a contant DC voltage ince DC voltage variation inicate unbalance AC/DC power exchange. Figure how a control tructure for the DC voltage regulating converter. A cacae control tructure i ue in the VSC bae on an inner q current control loop. Thi q tranformation proce contain the Clarke an Park tranform. The latter require a phae-locke loop (P) to be applie to the network reference voltage, to obtain a reference phae angle for the VSC control. Figure 3 how the tructure of a P where an inquarature phae etector i ue. Auming an input voltage v θ an the controlle output phae angle of P θ, the error ignal for the controller i: e = v inθco θ' v coθin θ' = v in( θ θ'). (4) Once the P i locke to the input ignal, the ifference between the input voltage angle an the output angle woul become zero an thu no ocillatory term will be preente in the teay tate. After ecoupling an linearization, the reulting q omain converter plant moel without outer controller can be expree by the following equation: Δe R ω 0 Δ i Δ Δ i e q Δi Δ R iq = A Δ iq + B Δv = ω 0 Δiq Δ Δ Δ Δ Vc Vc v q + Vc e e q ( ei eqiq) Δ I c CeqVc CeqVc CeqVc 1 1 0 0 0 Δ e 1 1 Δ eq + 0 0 0 Δv i i Δ v q q 1 0 0 Δ CeqVc CeqV I c c C eq Cacae outer voltage an power loop can alo be ae. A feeback DC voltage control together with a contant fee forwar reactive power outer control loop i alo illutrate in Figure. The fee forwar reactive power loop irectly link the converter power repone to the actual current in the q omain reulting in le ynamic in theory an ha fater repone in comparion with feeback loop. However, thi type of control may be affecte by the inaccuracy in P uring ytem fault or unbalance conition [9]. With one VSC regulating the DC voltage, the other VSC in a point-to-point link can be ue for AC voltage/power control. In thi paper, 3 ifferent outer control loop are inclue an hown in Figure 4. (5)
θ θ kp + ki kp + ki ω kp + ki Figure : Feeback V c an fee forwar Q (V c -Q) control for VSC. kp + ki v θ Figure 3: General P tructure. co( x ) v in( θ θ ') kp + ki ω in( x ) Figure 4(a) how a feeback real an reactive power control ae to the inner current loop that enable the VSC to control it output real an reactive power to reference value inepenently. Meaurement of real an reactive power at the controlle point are require. In comparion with fee forwar control, extra ynamic are introuce a the power repone are not irectly relate to the q current but through a PI controller. However, for to the ame reaon, it i le affecte by P failure. A lightly varie control i hown in Figure 4(b) where the feeback reactive power loop i replace by a feeback AC voltage loop. By oing o, the VSC i mae enitive to the voltage variation at the controlle point. Intea of proviing contant reactive power in Figure 4(a), it trie to maintain a contant AC voltage at the controlle point by proviing the neee amount of reactive power compenation. DC voltage roop control Figure 4(c) [10] i ifferent from the previou two outer control loop an i normally ue for multi-terminal DC gri operation. Since it i unwie to rely on only one converter to regulate the DC voltage for the whole DC gri, thi type of outer control loop allow limite variation in the DC voltage an thu there can be multiple converter controlling the DC voltage imultaneouly. A roop characteritic (roop gain k) i ue between the converter active power an the DC voltage o that the converter active power reference can be ajute accoring to the actual DC voltage. When the limit of power are reache, the converter will work in contant ω 0 θ ' Figure 4: 3 ifferent control trategie for VSC (a) Feeback PQ control (b) Feeback P-Vac control (c) V c -P roop an fee forwar Q control. power moe at the limit. Thi control alo fulfill the requirement that the DC voltage operating point are ifferent for each converter in a multi-terminal DC gri ue to line loe. In thi paper, the DC voltage roop cacae to a fee forwar power loop i alo coniere for interaction tuie. 3 GENERIC INTERACTION STUDY In orer to quantify the interaction between a STATCOM an a VSC in the HVDC link, a reuce tet ytem wa etablihe with only a VSC an a STATCOM interconnecte through a line with ajutable impeance (Figure 5). Thi remove unneceary etail which coul clutter an obcure reult. The plant moel an the control trategie ecribe in the previou ection are ue for the VSC an the STATCOM. A voltage ource behin impeance i ue to repreent an AC network. The VSC control it injection current to the ytem while in turn the ytem provie the reference bu voltage (bu ) to the P an the VSC. The STATCOM communicate with the AC ytem through voltage exchange. The intention of uing a reuce ytem moel i to obtain general interaction before applying the moel to a large an pecific tet ytem. RGA wa ue to analye the interaction in the plant moel a it oe not epen on the controller. Outer controller interaction can be invetigate through moal analyi technique. 3.1 RGA for Plant Moel Since firtly propoe by Britol [5], RGA provie a meaure of interaction an i normally ue a a tool for multi-input multi-output (MIMO) ytem optimal input-output pairing. However, here it i poible to conier it a way to quantify the egree of interaction between the plant moel of the STATCOM an VSC.
θ i σ v θ e θ i σ v θ v δ 3 0 E δ E δ V δ 0 δ E δ v ref 0 Figure 5: Reuce ytem moel. One way to calculate the RGA of a MIMO ytem i to ue the teay-tate gain matrix obtaine from ytem moel equation. et u j an y i enote an inputoutput pair of a plant G(), the relative gain can be expree a the ratio of two extreme cae [11]: all other loop open y i u j g uk = 0, k j ij 1 λ = = = [ G] G ˆ y gij i u ij all other loop cloe ij ji j yk = 0, k i λ11... 1 T RGA = = ( ) λ G G... 44 P P P P * * i δ iq ma v v v v * * (7) i iq δ ma where G = V c Vc Vc Vc * * i iq δ ma v3 v3 v3 v3 * * δ i iq ma The RGA element λ ij meaure the influence of all other variable on the gain between input u j an output y i. If λ ij =1, all the other control loop have no impact on the control pair u j an y i an thi i the cae where no interaction exit. Thu λ ij 1 inicate there are interaction between the other control loop an the electe control pair. The cloer the value of λ ij i to the unity, the maller the interaction i. Some important propertie of RGA (ummarize in [6, 11]) are ue in thi paper. (6) To tuy the interaction within the plant moel, the outer control loop of the STATCOM an the VSC houl be remove. The plant manipulate input an output are efine a hown in Figure 6. By linearizing the ytem moel at an operating point, the ytem teay tate gain matrix can be calculate for the efine input an output. Thi will be a 4 4 matrix G() with each element repreenting a tranfer function between the correponing input an output (e.g. g 1 tan for the tranfer function between input 1 an output ). Accoring to the efinition in equation (6), Figure 6: RGA plant moel with electe input an output. Input output ine: (1+0j)Ω ine: (0.5+10j) Ω i * i q * δ m a i * i q * δ m a y 1 :P 1 0 0 0 1 0 0 0 y :v 0 1.4 0-0.4 0 1.96 0-0.96 y 3 :V c 0 0 1 0 0 0 1 0 y 4 :v 3 0-0.4 0 1.4 0-0.96 0 1.96 Table 1: RGA reult for electe input an output. the RGA of the 4 input 4 output ytem can be erive a hown in equation (7). Calculating the RGA from the teay tate gain matrix (frequency 0 ), the reulting RGA for two ifferent length of the interconnecting line i given in Table 1. The iagonal element in bol how the correponing control pair where the input ha ominant effect on the output. The RGA element value of 1 for the control pair of u 1 -y 1 an u 3 -y 3 how thee two control pair are not affecte by any other control loop in the ytem. Interaction are mainly etecte between the VSC q-axi current control loop i q *-v an the STATCOM moulation inex control loop m a -v 3. Thi interaction become larger a the electrical itance between the VSC an the STATCOM ecreae (RGA number 1.4 to 1.96). The RGA analyi ugget interaction between VSC i q *-v an STATCOM m a -v 3 in the plant moel without outer control loop. To further how how VSC an STATCOM affecte each other through outer control, a parametric analyi bae on the ytem tate pace moel an eigenvalue wa performe. 3. Moal Analyi for Outer Control oop To analye the outer controller interaction, two type of outer control are invetigate here: (1) the feeback PQ control loop an () the feeback P-V ac control loop. The other two type of VSC control (V c -Q an roop control) focu on controlling the DC ie voltage rather than the AC ytem parameter an are not likely to have interaction with the STATCOM control in the AC ytem, hence are not inclue here. For the ame ytem moel (Figure 5), the VSC i now ae with either PQ or P-V ac outer control loop an the STATCOM i equippe with it δ-m a control. The ytem moe are monitore when the PI controller in the STATCOM m a control i moifie. By tracing an plotting the ytem eigenvalue a increaing the banwith of the STATCOM m a control, the reulting
HVDC Figure 7: Sytem eigenvalue trajectory trajectory of ome ytem moe uner conition (1) VSC with PQ control an () VSC with P-V ac control i preente in Figure 7. The line impeance i kept at a lower value of (0.5+10j)Ω for more clear interaction. The arrow in Figure 7 inicate the irection of hifting. Increaing the banwith of the STATCOM m a control caue the relate moe to hift left ue to a fater repone. Since the STATCOM m a control require feeback voltage from the AC ytem, it i much lower than the VSC PQ an the STATCOM DC voltage control loop, where meaurement can be taken within the VSC or the STATCOM. Therefore, the moe relate to thoe fat control loop are not ignificantly affecte by the change in the STATCOM m a control. A illutrate in Figure 7(a), no ignificant movement i etecte in other ytem moe. However, when P-V ac control i aopte in the VSC, it alo require a meaurement of the controlle bu voltage in the AC ytem, making the frequency of thi control loop imilar to the STATCOM m a control. Uner thi circumtance, variation in the STATCOM m a control not only affect it own moe but alo ignificantly affect the moe relate to VSC AC voltage control, a illutrate in Figure 7(b). A fat change in the STATCOM voltage reference point may eteriorate the performance of the VSC HVDC control. 4 TEST SYSTEM AND CASE STUDY To verify the interaction ientifie in the reuce moel, the STATCOM an VSC moel are applie to a large multi-machine ytem. A et of cenario regaring ifferent electrical itance an control trategie wa create for teting. The influence brought by the STATCOM an the VSC HVDC on the AC ytem ynamic are alo invetigate. 4.1 Tet Sytem The tet AC ytem moel, a hown in Figure 8, i obtaine by moifying a repreentative reuce GB network bae on a real reference loa flow cae [1, 13] with generic generator an control ynamic inclue. The evelope ytem moel contain 9 bue an 4 generator of ifferent type. Each generator i an aggregate moel that repreent all the generation unit of a particular area. The etaile 6th orer ynchronou generator moel i ue for the aggregate unit except the win generator which i moele a a win farm connecte through a converter to the gri. They are alo equippe with tanar excitation ytem an power ytem tabilizer. The Figure 8: Dynamic GB ytem with VSC HVDC link an FACTS. reulting ynamic GB moel ha a total intalle generation of approximately 75 GW, wherea the peak eman i aroun 60 GW. A 1 GW VSC HVDC line i integrate to the AC ytem connecting bu an bu 10, carrying 500MW onhore power flow. VSC1 i configure to regulate the DC voltage an the ifferent control trategie ecribe in ection are aopte by VSC. A 5 MVA STATCOM i alo ae to the ytem at the location illutrate in Figure 8. The invetigation i carrie out by coniering three ifferent STATCOM location an three VSC HVDC control trategie. 4. Cae Stuy 1 -Different STATCOM ocation The electe location are likely to have win power injection or CC HVDC terminal where a STATCOM might be intalle. The STATCOM attempt to maintain a contant voltage of 1 p.u. at it connecte bu. The converter at the receiving en of the DC link (VSC) i in the feeback PQ control moe that eliver a contant 500 MW active power from bu to bu 10 while keeping the reactive power to zero. The STATCOM i connecte equentially to three bue (10, 1, an 6). For the firt location, the STATCOM i cloely couple with the receiving en VSC a they are both trying to control either the voltage or the power of bu 10. The econ an the thir location are coniere a looely couple conition for the VSC an the STATCOM. A elf-clearing 100m three phae hort circuit fault i applie at bu 1 in the AC gri an the ytem repone are monitore for ifferent STATCOM location. The comparion of the repone i preente in Figure 9. In Figure 9(a), for the tie line 10-15 power flow, it i emontrate that the STATCOM ha a lightly better amping effect when it i locate at bu 10. In Figure 9(b), the voltage variation at bu 10 are ignificantly better ampe when the STATCOM i connecte to the bu 10. When the STATCOM i place at the other two looely couple location, it effect on the bu 10
STATCOM at bu 10 STATCOM at bu 1 STATCOM at bu 6 (a) (b) () (c) Figure 9: Sytem fault repone for ifferent STATCOM location. (a) line 8-10 power (b) DC injection bu (bu 10) voltage (c) VSC reactive power () VSC active power Control Strategy VSC1 VSC CS1 Feeback V DC an Fee forwar Q Feeback P an Q CS Feeback V DC an Fee forwar Q Feeback P an V ac CS3 Droop V DC-P an Droop V DC-P an Contant Q Contant Q Table : it of VSC control trategie. voltage become much maller in comparion with the firt location. A hown in Figure 9(c) an 9(), the VSC controlle real an reactive power repone are only affecte ignificantly by the STATCOM when it i cloely couple to VSC (bu 10) ue to their plant interaction. With the STATCOM at bu 10 the ocillation in the VSC controlle real an reactive power become maller. Thi tet verifie that the STATCOM ha the larget effect on the VSC HVDC connecte bu voltage when it i place at the location nearet to the VSC HVDC link. It alo how that it ha better power ocillation amping performance when it i locate cloer to the fault location. Hence the STATCOM will be kept at the cloely couple location an the focu will be on the control trategie ue in VSC HVDC link in the following cae tuy. 4.3 Cae Stuy - Outer Control oop Interaction (ifferent VSC control trategie) The STATCOM i kept at bu 10 in thi cae. Three ifferent type of control trategie a epicte in Figure 4 were aopte in the VSC. Thee control trategie are lite in Table where VSC outer control loop are mainly varie. Among the three control trategie, only CS i enitive to the AC ytem voltage variation an attempt to maintain it at a contant level. Bu 10 will be referre to a the common coupling bu (CCB). The elf-clearing 100m 3 phae hort circuit at bu 1 i applie an the integrate ytem repone are recore an preente in Figure 10. The cae with no HVDC i alo inclue in the reult for comparion purpoe. The STATCOM i trying to maintain a contant voltage level at the CCB uring the fault. Thi voltage control i affecte when the 500 MW VSC HVDC link i ae. The voltage ocillation at bu 10 i improve by aing VSC HVDC an i further ampe when CS i aopte in the VSC HVDC link, a hown in Figure 10(a). Thi i expecte a the moal analyi for the reuce ytem inicate larger control interaction when AC voltage control i aopte in VSC. However, here they act in a collaborative way a the voltage etpoint for the STATCOM an VSC are the ame. CS1 an CS3 aopte for the HVDC link reult in imilar CCB voltage repone a they both have maller interaction with the STATCOM. The ame phenomenon can alo be oberve from Figure 10(b) which how the amount of reactive power upplie by the STATCOM in ifferent conition. Figure 10(c) emontrate that when an only when CS i ue, VSC will provie reactive power compenation to upport the ytem. Thi proce again how the potential control interaction between the STATCOM an VSC a they are both trying to control the bu voltage. If ifferent voltage control etpoint are configure in the STATCOM an VSC, an avere interaction effect woul occur.
(a) (b) (c) STATCOM only STATCOM an HVDC with CS1 STATCOM an HVDC with CS STATCOM an HVDC with CS3 Figure 10: Sytem fault repone for ifferent VSC control. (a) DC injection bu (bu 10) voltage (b) STATCOM reactive power (c) VSC reactive power 5 CONCUSIONS The potential interaction between a STATCOM an a VSC HVDC operating imultaneouly in the AC network are analyze in thi paper. Interaction are ientifie both in the plant moel of the VSC an the STATCOM an in their outer controller loop uing a generic mathematical methoology. The ientifie interaction are then valiate by imulation reult. It ha been emontrate that the egree of interaction increae a the electrical itance between two plant ecreae. It i mot noticeable when STATCOM an VSC are connecte to the ame bu. For ifferent VSC control trategie the AC voltage control in a VSC interact mot with the STATCOM moulation inex, m a control (lower). The reult of moal analyi how the control etting in one evice woul affect the performance of the other evice ignificantly. Avere interaction may occur if the controller are not properly parameterize. However, imulation in thi paper how a collaborative operation of the STATCOM an the VSC with well-tune controller. ACKNOWEDGEMENTS The author woul like to thank National Gri for upporting thi work REFERENCES [1] Z. Saa-Saou, M.. iboa, J. B. Ekanayake, N. Jenkin, an G. Strbac, "Application of STATCOM to win farm," Generation, Tranmiion an Ditribution, IEE Proceeing-, vol. 145, pp. 511-516, 1998. [] M. J. Gibbar, D. J. Vowle, an P. Pourbeik, "Interaction between, an effectivene of, power ytem tabilizer an FACTS evice tabilizer in multimachine ytem," Power Sytem, IEEE Tranaction on, vol. 15, pp. 748-755, 000. [3] X. iange, D. Ping, an. Mingbo, "A comparative analyi of the interaction between ifferent FACTS an HVDC," in Power an Energy Society General Meeting, 01 IEEE, 01, pp. 1-5. [4] EPRI, "Analyi of Control Interaction on FACTS- Aite Power Sytem," 1998. [5] E. Britol, "On a new meaure of interaction for multivariable proce control," Automatic Control, IEEE Tranaction on, vol. 11, pp. 133-134, 1966. [6] Milanovic J. V., an A. C. S. Duque, "Ientification of electromechanical moe an placement of PSS uing relative gain array," Power Sytem, IEEE Tranaction on, vol. 19, pp. 410-417, 004. [7] C. A. Cañizare, M. Pozzi, S. Cori, an E. Uzunovic, "STATCOM moeling for voltage an angle tability tuie," International Journal of Electrical Power & Energy Sytem, vol. 5, pp. 431-441, 003. [8] G. O. Kalcon, G. P. Aam, O. Anaya-ara, S. o, an K. Uhlen, "Small-Signal Stability Analyi of Multi-Terminal VSC-Bae DC Tranmiion Sytem," Power Sytem, IEEE Tranaction on, vol. 7, pp. 1818-1830, 01. [9] Z. iong,. Harnefor, an H. P. Nee, "Power- Synchronization Control of Gri-Connecte Voltage- Source Converter," Power Sytem, IEEE Tranaction on, vol. 5, pp. 809-80, 010. [10] T. M. Haileelaie an K. Uhlen, "Impact of DC ine Voltage Drop on Power Flow of MTDC Uing Droop Control," Power Sytem, IEEE Tranaction on, vol. 7, pp. 1441-1449, Aug 01. [11] S. Skogeta an I. Potlethwaite, Multivariable Feeback Control: Analyi an Deign, n e.: WIEY, 005. [1] M. Belivani an K. R. W. Bell, "Repreentative GB Network Moel," Dep.of Electronic an Electrical Engineering, Univerity of Strathclye, Glagow, Report, Apr 011. [13] K. R. W. Bell an A. N. D. Tlei, "Tet ytem requirement for moelling future power ytem," in Power an Energy Society General Meeting, 010 IEEE, 010, pp. 1-8.