Automatic Voltage Controllers for South Korean Power System

Transcription

1 Automatc Voltage lers for South Korean Power System Xng Lu Vathanathan Man Venkatasubramanan Tae-Kyun Km Washngton State Unversty Korea Electrc Power Research nsttute Pullman, WA Seoul, South Korea Emals: and Emal: Abstract The paper proposes two automatc voltage controllers for the South Korean power system. Smulaton results from detaled Korean power-flow models show that the controllers can provde sgnfcant mprovements n securty, qualty and effcency of power system voltage montorng and control. Operatng wthn a tme scale rangng from tens of seconds to a few mnutes, the controllers can act upon voltage alarms and voltage nsecure condtons to mantan prescrbed voltage profle and adequate VAR margns. The control actons nclude contnuous adjustment of generator VAR outputs as well as swtchng of dscrete VAR support devces such as shunt capactor banks. Ths paper extends an earler dscrete verson of the controller developed at Washngton State Unversty and tested at Bonnevlle Power Admnstraton nto a hybrd voltage controller. Ths paper tests the mplementaton and applcaton of the prevously developed dscrete as well as the proposed hybrd controllers n Korean power system models.. ntroducton Automatc voltage control of transmsson network can provde sgnfcant mprovements n operatonal securty, qualty, effcency and economy of power system operaton. n Europe, voltage control s tradtonally organzed n a three levels herarchcal structure. At the second level, the secondary voltage control dvdes the network nto multple control regons based on the plot node concept where all generators wthn a regon are operated n a coordnated fashon. n North Amerca, transmsson grd voltage control s mostly operated through manual swtchng of capactor/reactor banks and Load Tap-Changng (LTC) transformers and generator voltage schedules by system operators n the respectve control centers. n earler work [], a slow voltage dscrete controller has been developed that treated capactor/reactor and LTC transformers as voltage control canddates and t recommended the best devce by optmzng a sutable objectve functon that mnmzed voltage volatons and related control costs. A prototype verson of ths controller was mplemented at Bonnevlle Power Admnstraton (BPA) by Natonal Systems Research (NSR) nc. Recent thess [2] proposed an advanced hybrd voltage controller as an extenson of the slow voltage controller. The hybrd voltage control (HVC) ncludes three phases n the control formulaton. Phase can regulate contnuously the reference voltages of generators n ther reactve power output reserves. The functon of Phase s smlar to the dscrete controller. When the controller exhausts Phase and Phase yet there s no effectve way to keep good voltage profles, Phase wll be appled. The thrd phase s meant to be for stressed operatng condtons and n ths phase, HVC controller wll exhaust all avalable control devces and controls to mnmze the voltage volatons. n a recent research project, Korean power system engneers have been explorng optons of automatc voltage control schemes and ther relatve advantages. n the Korean system, many operatonal factors can lead to bus voltage volatons and voltage stress scenaros, such as from heavy loads and large transfers across long dstance transmsson lnes. Broadly speakng, the types of control devces and ther operatng rules are smlar to the control problems at BPA. However, Korean system specfcs are qute dfferent from those of BPA. Ths paper dscusses the modfed desgns of the dscrete controller and HVC for the Korean system so that they can sut the needs of the Korean power system models. One beneft that both the dscrete controller and HVC have s that they can automatcally separate the whole power system nto several problematc areas n term of related bus voltage volatons. Ths s done n a dynamc fashon for every control teraton and the problem areas are not pre-defned. Ths s essentally problem-orented and s local. Therefore, the two controllers are nherently suted towards parallel computatons. We show that the two controllers can be appled for even very large power systems /09 $ EEE

2 Meanwhle, the control decsons that both controllers make can meet some economcal requrements as well as practcal constrants such as control prortes. For example, n BPA practce, t was noted that the mantenance of LTC costs much more than capactor/reactor banks and that we can not change taps of LTC transformers frequently. Accordngly, capactor and reactor banks were set wth hgher prortes than LTCs. Addtonal detals are presented n the paper. Ths paper s organzed as follows. n secton 2, the desgn and formulaton of the dscrete controller and HVC are dscussed. We wll demonstrate the feasblty of two controllers. For llustratng the control process, a standard example of a 39-bus test system s dscussed n secton 3. We wll demonstrate the feasblty of two controllers by three cases n Korean power system data n secton Automatc voltage controllers Frst, we wll dscuss the dscrete voltage controller. The proposed controller confguraton s shown n Fgure. The dscrete controller prmarly acts upon SCADA measurements for checkng the acceptablty of the system voltage profle. The state estmate power-flow model wll be used only for calculatng the ncremental changes n bus voltages after swtchng the control devces and these ncremental changes wll be assessed wth respect to actual SCADA measurements to compute the expected voltage profle after the swtchng events. Load forecastng estmates for ndvdual loads n the area wll be computed by consderng the system total load forecast avalable from the some load forecastng program n order to reduce the number of swtchng durng perods of rapd load growths and declnes (for nstance, durng mornng and evenng pckups). n cases when a state estmator model system becomes unavalable or unrelable (for nstance because of topology errors), HVC can stll compute control actons snce HVC only uses SCADA measurements, devce status and voltage alarms drectly. Both controllers can work ndependently, or one s the backup of the other. Normally, consderng the mplementaton cost, the dscrete controller may be the prmary controller. separate the whole system nto several problematc areas frst and then choose one best devce from the canddates we have gven n each area n terms of some optmal crterons, such as best voltage profle after control, mnmal swtchng cost, mnmal crcular VAR flow [3], maxmum reactve power reserve of generators and so on. canddates used by ths dscrete controller are capactor banks, reactor banks and LTC transformer banks n Korean power system. Besdes the above three knds of control devces, the avalable generators n Korean Power System are treated as contnuous control canddates n HVC. Here, the knowledge about local system n [2] s appled. And the local power flows are defned and computed. The basc assumpton s that an outage or voltage control acton only has a lmted geographcal effect. For the reactve power problem, ths s a vald assumpton snce a VAR devce usually has a lmted geographc effect. Hence, we can form a subsystem (local system) around devces or the problematc bus that s much smaller than the whole system and has only tens or hundreds of buses. The computaton s fast and n most of cases, they are accurate enough. Of course, the dfferent network could have dfferent local systems (number of the buses n local system), we need to set the dfferent parameters and do tests for each power system. Snce we do not focus on local power system ssues and local power-flow computatons n ths paper, we wll postpone detaled dscussons to a future paper. 2.. Formulaton of dscrete controller The man purpose of the controller s to fnd the mnmum swtchng cost and crcular VAR flow [3] that keeps all the voltages wthn the operatng lmts (or some knd of nterval gven by standards). Meanwhle, by usng the load forecastng, the controller should mnmze the number of swtchng actons. That s, the controller should be robust n some sense. We can formulate ths optmal problem as the followng form []: Each of two controllers can check system voltage profles. f some bus voltage volatons occur, t can 2

3 for dfferent control devces to reflect on sutable control prortes. Then, by changng the value of cost of each devce, we can easly set and choose the reasonable control devces. But t heavly depends on the real stuaton. Addtonally, some mnor but practcal rules can be added nto objectve functon by modfyng C. For example, we prefer to swtch out a devce n servce before swtchng n another so that maxmum number of control devces s avalable for control purposes at a future tme. Accordngly, we set hgher costs for swtchng n devces as compared to swtchng out the same. The functon F means a knd of penalty functon under { k, =,, n}. As we know, the acton of some devces cant make all bus voltages satsfy the demands (n the lmts). Then, t s necessary to defne a penalty functon to ndcate how far the soluton s away from the feasblty regon. An nstance s shown n Fgure 2. Fgure. Framework of slow voltage controller n Mn k C = + p [ F ( k,, k ) + λ g ( k, k )] n = M m = st.. k N m m n cr, m n sw k {,0,} () f the voltage at a bus s wthn lmt, the penalty term s zero. f t s too hgh or too low (hgher than avmax, a > or lower than bv, b < mn ) then a very large value f m s set to the penalty term. n between ( V, av max max ) or ( bv, V mn mn ), t s lnear. The penalty cost s set to be the norm of the voltage-volatng vector. Here we use the summaton of all the absolute value of the voltage volaton, say F ( norm ). Here k represents the acton of the control devce. For capactor and reactor banks, -, 0, means swtchng out, no acton and swtchng n, respectvely. For LTC transformer, they mply tap down, no acton or tap up, respectvely. C s the cost of each devce n such a way that ts value would ncrease sgnfcantly after each swtchng. Mantenance costs for transformer banks are hgher than those for capactor banks. n general, tap changes should be avoded whenever the voltages can be mantaned by swtchng of capactor/reactor banks alone. f tap changes have to be mplemented n some cases, only one tap change s allowed n each teraton. Ths procedure s followed n many utltes ncludng BPA. From operatng experence, dfferent cost values can be set Fgure 2. A penalty functon formulaton Smlarly, g cr s the total crcular VAR flow under { k, =,, n}. λ can be the weght of crcular VAR flow n the objectve functon and p s the weght of the system propertes. The subscrpt m th corresponds to the m load forecastng. Assume there are totally M power flows. The objectve functon wll consder all M stuatons when swtchng devces. N sw defnes the maxmum number of control actons, 3

4 whch are permtted n any of the teraton of the controller. Snce the operators usually hestate to swtch a large number of devces smultaneouly, the procedure for swtchng one devce at a tme or N sw = s dscussed n ths paper. Of course, we can set t to be any number. But the bgger t s, the more complcated the optmzaton Formulaton of HVC Ths subsecton summarzes the three phase formulaton of the hybrd voltage control from [2], [6] Phase. n Phase, the controller tres to mantan prescrbed voltage profles by adjustng the reference voltages of generators wthn a certan local problematc area, whle keepng the generator VAR outputs wthn ther reserved lmts. And, Phase treats generators as contnuous control devces. Hence, ths optmzaton of generators s related to lnear programmng. The formulaton s shown as follows: NG Mn α Δ V + ( α) ΔQ G s.. t pq Q pq ; =,..., N V V V ; j =,..., N G mn G G max G jmn j jmax NG G (2) Where, α s a weghtng factor between 0 to. p s the percentage of full reactve power lmt as reserve lmt for Phase. Δ VG and Δ QG are voltage settng and reactve power output change of th generator. V j mn and V j max are the j th lower and upper bound. Smlarly, Q Gmn and Q G max are the th lower and upper reserved lmts of ths generator. N and N G denote total number of buses and generators respectvely. Snce we assume the changes are lnear wthn small ntervals, we can rewrte equaton (2) nto (3). NG α + α β ΔVG r r G mn βδ G G max = G NG jmn j, βδ G jmax ; =,..., = Mn : [ ( ) ] s. t.: pq V pq ;,..., N V s V V j N (3) ΔQG where, β = Δ V and Δ V = sj, ΔQG. s j, G = th means the j row and th column element of nverse of Jacoban whch s only related to a certan local power system Phase. Phase s essentally smlar to the dscrete controller but smpler than that controller. t doesnt consder requrements as many as the dscrete controller does such as load forecastng. n M n k [ C ( k ) + λ F ( k ) + g ( k )] cr = j= n sw = st.. k N (4) k {,0,} Note that after swtchng of the dscrete control devces, the nearby generators wll be releved from the reactve power demand and thus the total reactve power outputs may come back to be wthn the reactve power reserve lmts, and the controller may go back to operate n Phase agan Phase. When the total reactve power outputs ht the generator reactve power reserve lmts and no more dscrete control devces are avalable to provde supplemental reactve support, the controller wll operate n Phase. n ths phase, the system s under much stress and the full generator reactve capacty wll be utlzed n an algned mode to restore the system voltages or at least mtgate the voltage volatons. The lnear programmng formulaton s dfferent from that n Phase, wth the objectve of mnmzng voltage volatons under the constrants of full generator reactve power lmts. The formulaton s wrtten as: N N N G 0 exp j j + j, βδ G j= = r r Gmn βδ G G max = G Mn V V s V N G (5) s.. t Q V Q ;,..., N where the denotatons have the same defntons as those n (2), (3) and (4) bus system example 39-bus New England system studed n ths secton s a standard test system. For showng the control process clearly, we set a stressed scenaro on ths system, and then try to use the dscrete controller and HVC to control some devces so that all the bus 4

5 voltages are rendered wthn ther lmts whle the soluton s optmal. There are totally 28 load buses. We ncrease 5 buses of them by 20%. Table shows the amount of loads before and after changes. The acceptable bus voltage range s arbtrarly assumed to be [0.985p.u..060p.u.] at each bus. Table. The buses wth 20% ncreased loads NO Bus Name ntal load 20% ncreasng BUS3 345 P=322.0 Q=2.4 P=386.4 Q=2.9 2 BUS4 345 P=500.0 Q=84.0 P=600.0 Q= BUS7 345 P=233.8 Q=84.0 P=280.6 Q= BUS8 345 P=522.0 Q=74.0 P=626.4 Q=2. 5 BUS2 345 P=8.5 Q=88.0 P=0.2 Q=5.6 6 BUS5 345 P=320.0 Q=53.0 P=384.0 Q= BUS P=329.4 Q=32.3 P=395.3 Q= BUS8 345 P=58.0 Q=30.0 P=89.6 Q= BUS20 0 P=680.0 Q=03.0 P=86.0 Q= BUS2 345 P=274.0 Q=5.0 P=328.8 Q=38.0 BUS P=247.5 Q=84.6 P=297.0 Q=0.5 2 BUS P=224.0 Q=47.2 P=268.8 Q= BUS P=39.0 Q=7.0 P=66.8 Q= BUS P=28.0 Q=75.5 P=337.2 Q= BUS P=206.0 Q=27.6 P=247.2 Q=33. The parameters of the controllers are set as: (a). For LTC tap change: cos t cos t (b). For swtchng n capactor/reactor: cos t cost + 00 (c). For swtchng out capactor/reactor: cos t cost + 0 (d). After each swtchng: cos t cos t + 0 (e). The ntal cost s for all devces. Snce there s no control devce nformaton n the orgnal data, we could assume some shunt devces. Table 2 gves the avalable shunt control devces: Table 2. Avalable shunt devces Bus Name Type Amount per Amount Status Bank of Bank BUS7 C 30 OFF BUS8 C 30 OFF BUS9 C 30 OFF BUS0 C 5 3 OFF BUS C 50 OFF BUS2 C 50 OFF BUS3 C 50 OFF BUS4 C 50 OFF BUS20 R 50 BUS2 R 50 All generators except swng bus can be modeled as the contnuous control devces for HVC. The system one-lne dagram wth bus voltage volatons and control devce nformaton s shown n Fgure 3. The buses n the ellpses experence voltage volatons. Among them, BUS8 s the worst one. So a local system s formed. Due to ths test system beng a small system, all buses are ncluded n one local system. The control devces n the damonds are effectve among those n the Table 2 and among all generators (BUS3 s swng bus) f we use HVC to control ths stuaton. All the control actons of dscrete ler are shown n Table 3. And all the control actons of HVC are shown n Table 4. The dscrete ler almost uses all avalable shunt control devces to brng the bus voltages to acceptable values above p.u. HVC uses a combnaton of three generators and three capactors. The fnal results of both controllers appear reasonable and are as expected. Table 3. actons of Dscrete ler on 39-bus system Before Worst volaton and Total number of volatons BUS p.u. 8 volatons BUS p.u. 7 volatons BUS p.u. 6 volatons BUS p.u. BUS p.u. 4 volatons BUS p.u. 3 volatons BUS p.u. BUS p.u. BUS p.u. ce Step Acton BUS2 Step 2 BUS Step 3 BUS4 Step 4 BUS3 Step 5 BUS7 30 Mvar Step 6 BUS20 Step7 BUS2 Step 8 BUS8 30 Mvar Step 9 BUS0 45 Mvar OFF OFF After Worst volaton and Total number of volatons BUS p.u. 7 volatons BUS p.u. 6 volatons BUS p.u. 6 volatons BUS p.u. 4 volatons BUS p.u. 3 volatons BUS p.u. BUS p.u. BUS p.u. No volatons 5

6 starts n Phase frst by swtchng 50 MVAR at Bus Study cases for Korean power system Before we show the cases, some knd of prorty of control devces needs to be represented. Here, swtchng off has hgher order than swtchng on, whch can always make us keep the maxmum number of control devces. Capactors and Reactors are cheaper to swtch than LTC. And, t s assumed that only one tap of LTC can be adjusted at one tme. 4.. Case of dscrete controller Assume that several buses have load ncreasng gven n Table 5: Fgure bus system wth voltage volatons and control devce nformaton Table 4. Actons of HVC on 39-bus system Before Worst volaton and Total number of volatons ce: Cap or Gen Step Acton After Worst volaton and Total number of volatons Table 5. The buses wth 20% ncreased loads NO Bus Name ntal load 20% ncreasng ULKWANG54 P=62.00 Q=30.03 P=74.4 Q= MOBAL54 P=73.00 Q=35.36 P=87.6 Q= DANGNR54 P=66.0 Q=32.0 P=79.3 Q= P=2.0 Q=54.24 P=34.4 Q=65. 5 JOGBU54 P=44.0 Q=24.36 P=52.9 Q= MOSAN54 P=92.30 Q=44.7 P=0.8 Q= MOBG54 P=5.40 Q=24.89 P=6.7 Q= SHNDUK P=4.90 Q=7.22 P=7.9 Q=8.7 9 SANGAM P=20.30 Q=9.83 P=24.4 Q=.8 0 NEUNGGOK P=94.70 Q=45.87 P=3.6 Q=55 BUS p.u. 8 volatons BUS p.u. 7 volatons BUS p.u. BUS2 BUS30: Vref BUS32: Vref BUS39: Vref Step 2 Step 3 BUS0 45 Mvar Step to to to.046 BUS p.u. 7 volatons BUS p.u. BUS p.u. Now, we let the controller consder all the dscrete control devces n the whole system as the canddates. Maybe, ths process s tme-consumng snce many devces are obvously far away from the problematc bus. But, for test purpose, we smply apply ths condton. n the real system, operators may know whch devces could be effectve and only these devces can be the canddates. Moreover, we set 8 ters as the upper bound of local power system centered around the worst bus voltage volaton. That s, the local system can only be n 8 ters around the problematc bus. The settng of cost s the same of those n Secton 3. BUS p.u. BUS7 30 Mvar Nao volatons Before control, there are three buses wth bus voltage volatons whch are shown n Table 6. For HVC, please recall that f there are no feasble solutons for Vref adjustments n Phase, HVC wll transton nto Phase. n Table 4, HVC accordngly 6

7 Table 6. Buses wth voltage volatons NO. Bus Name V(PU) Vmax(PU) Vmn(PU) GMHAE EOBANG DKMHAE The dscrete controller takes several steps to make control decson. n every step, t selects the devces whch may be effectve for the current voltage volatons from the canddates. Then, the controller can consder the status of these control devces, the effect on the bus voltages and operaton costs f one of them would be used. By comparng the total costs (the value of objectve functon), the controller can gve us an optmal devce n every step. For example, after we ncrease the buses load n terms of the presentaton n Table 5, there are 6 control devces chosen by the controller from all canddates n the local system whch s centered by the worst voltage volaton, whch nclude 3 capactors and 3 LTCs. Table 7 shows the decson made by the dscrete controller n each step, meanwhle, we can fnd the changes of the worst bus voltages before and after control. Table 7. decsons of dscrete controller Before control (PU) acton After control (PU) GMHAE EOBANG DKMHAE GMHAE 54 DKMHAE GMHAE 54 DKMHAE GMHAE 54 DKMHAE GMHAE EOBANG DKMHAE Acton SANGN54 5 Mvar On (Cap) Acton 2 SHNUL3345 to SB8740 (LTC): Tap 3 to 2 Acton 3 SHNUL3345 to SB874 (LTC): Tap 3 to 2 Acton 4 SHNUL3345 to SB8742 (LTC): Tap 3 to 2 Acton 5 SANGN54 20 Mvar On (Cap) GMHAE 54 DKMHAE GMHAE 54 DKMHAE54 GMHAE 54 DKMHAE54 GMHAE EOBANG DKMHAE GMHAE DKMHAE As mentoned earler, the controller can detect crcular VAR flows and try to delete t. n step 2 (Acton 2), LTC n SHNUL3 345 s the cheapest one snce ths LTC can elmnate some crcular VAR flow through tself, however, ths decson cant make voltage profle better. The reason why controller dd that s we set bgger weght for crcular VAR flow. Although, there are two buses whose voltages are stll lower than the lower bound, they can be accepted n real system. And the controller s able to mprove the voltage profles by choosng the best control devces. Another reason s that we use the peak load data of Korean power system and only a lttle amount of shunt compensators left Case of HVC Snce we want to show the feasblty of ths controller, HVC can be set to work alone. Now, we have more control devces (generators), then we can employ the worse stuaton n ths case. The 50% load ncreasng n the same buses as those n Table 8 s assumed from ntal load and one transmsson lne s set to off servce. Table 8 shows ths knd of scenaro. Table 8. Worse scenaro for HVC test NO Bus Name ntal load 20% ncreasng ULKWANG54 P=62.00 Q=30.03 P=93.0 Q= MOBAL54 P=73.00 Q=35.36 P=09.5 Q= DANGNR54 P=66.0 Q=32.0 P=99.2 Q= P=2.0 Q=54.24 P=68 Q=8.4 5 JOGBU54 P=44.0 Q=24.36 P=66.2 Q= MOSAN54 P=92.30 Q=44.7 P=38.5 Q=67. 7 MOBG54 P=5.40 Q=24.89 P=77. Q= SHNDUK P=4.90 Q=7.22 P=22.4 Q=0.8 9 SANGAM P=20.30 Q=9.83 P=30.4 Q=4.7 0 NEUNGGOK P=94.70 Q=45.87 P=42. Q=68.8 JOGBU DANGNR 54 Servce off Even though ths appears to be a stressed case, HVC only uses Phase and so that all bus voltages are n the lmts. All the parameters are set lke those as the case of dscrete controller. And we set the smaller ters (6) to show the controller can deal wth problems smultaneously. There are two regons. One s centered by GMHAE 54 wth p.u. bus voltage, and the other s centered by DUNPO 54 wth p.u. bus voltage. We can assume they are 7

8 ndependently. But n the practcal system, some devces chosen n one regon wll affect the choce n the other one n the future. n ths case, we wll see ths pont. HVC also evaluates the control effect on the bus voltages, operaton costs and the other targets from those control devces whch could be avalable and effectve for the current scenaro. The devce wth mnmal value of objectve functon wll be the soluton. All control decsons are shown n Table 9. n the table, the buses lsted n the column before control are the worst ones. That s, there could be many buses experencng voltage volaton but one of them has the maxmum value. So a knd of local system s formed around ths worst one. f there are stll some buses whch have voltage volaton are out of ths local system, another local system s formed. Ths process wll go on untl all buses havng voltage volaton are n some local systems. Thus, the control of HVC s knd of parallel process, whch s another hghlght of our desgn. n the next case, HVC need Phase to control the bus voltages. That s, HVC has exhausted all generators wthn ther reactve reserved lmts and all shunt compensaton devces, but bus voltage volatons stll exst. HVC wll utlze the full reactve power capacty of generators to restore the voltage as close as possble to the prescrbed values. We use the same scenaro as the shown n Table 8, but here the control objectve s to mantan all bus voltages wthn.5% band around the normal voltage profles (n the prevous two case, [0.985p.u..060p.u.] s set to the acceptable range for all bus voltage profles). All control decsons are shown n Table 0. Apparently, snce we change ths mportant condton for HVC, the worst voltage volate could be dfferent and then the local system would be dfferent, whch results n the dfferent control decsons. After control, all bus voltages are rendered wthn ther acceptable lmts at last. Regon & Phase 2 2 Table 9. decsons of HVC Step Before ces Acton SAMCHU 22.0 Vref.0 SAMCHU Vref.0 GMHAE p.u. SAMCHU Vref.0 SAMCHU Vref.0 SAMCHU Vref.0 DUNPO p.u. ces ces Step 2 SAMCHU 22.0 Vref.0.02 SAMCHU Vref.02 SAMCHU3.0 GMHAE p.u Vref SAMCHU Vref.02 SAMCHU Vref.02 DUNPO p.u. DUNPO p.u. 5. Conclusons Step 3 YANG54 (Cap) 5Mvar After GMHAE p.u. MHAE p.u. DUNPO p.u. The paper proposes and llustrates two automatc controller schemes for the South Korean power system. Dscrete voltage controller s prmarly amed at mantanng voltage schedules. Hybrd voltage controller mantans adequate VAR reserves as well as voltage vablty by controllng generator VAR resources and dscrete VAR devces n a three layered control formulaton. nternal algorthms of both controllers are desgned to be extremely fast by utlzng the local nature of the reactve power-flow problem. 8

9 Table 0. decsons of HVC wth.5% varaton range Step Regon & Phase Before 54.0 p.u. (.03 p.u.) p.u. (.03 p.u.) p.u. (.03 p.u.) ces WOCHUN 54 (Cap) Step 2 KEUMOH 54 (Cap) Step 3 LSA#GT 3.8 Vref LSA#2GT 3.8 Vref LSA#3GT 3.8 Vref LSA#4GT 3.8 Vref LSA#5GT 3.8 Vref LSA#6GT 3.8 Vref LSA#ST 20.0 Vref SHNGT 8.0 Vref SHNGT2 8.0 Vref SHNGT3 8.0 Vref SHNGT4 8.0 Vref SHNGT5 8.0 Vref SHNGT5 8.0 Vref Acton 20Mvar On 5Mvar On After p.u. (.03 p.u.) p.u. (.03 p.u.) p.u. (.03 p.u.). Notce: the value shown wthn the brackets s the nomnal voltage.. students for helpng us wth South Korean power system data and ts operatonal detals. References [] Y. Chen, elopment of Automatc Slow Voltage for Large Power Systems, Ph.D. dssertaton, School of Electrcal Engneerng And Computer Scence, Washngton State Unversty, Pullman, WA, August 200 [2] J. Su. A heurstc Slow Voltage Scheme for Large Power System, Ph.D. dssertaton, School of Electrcal Engneerng And Computer Scence, Washngton State Unversty, Pullman, WA, May [3] Y. Chen, X. Lu, V. Venkatasubramanan Fast Algorthms for Detectng Crcular VAR Flows n Large Power-Flow Models, Proceedngs of HCSS, Hawa, Januray [4] P. Lagonotte, J.C. Sabonnadere, J.Y. Leost and J.P. Paul (EDF), Structural Analyss of the Electrcal System: Applcaton to the Secondary Voltage n France, EEE Trans. on Power Systems, pp , May 989. [5] J.P. Paul, J.T. Leost, J.M. Tesseron, Survey of the Secondary Voltage n France: Present Realzaton and nvestgatons, EEE Transactons on Power Systems, vol. PWRS-2, no.2, pp , 987. [6] J. Su and V. Venkatasubramanan, A Hybrd On-lne Slow Voltage Scheme for Large Power Systems, Proceedngs of REP Symposum on Bulk Power System Phenomena, Charleston, SC, August Acknowledgements The authors gratefully acknowledge fundng of ths research by Korea Rural Economc nsttute, Seoul, South Korea. We also thank Prof. Byongjun Lee (Korea Unversty, Seoul, South Korea) and hs 9