Optimum Fault Current Limiter Placement

Transcription

1 Optimum aut urrent Limiter acement Jen-Hao Teng han-an Lu Abstract: Due to the difficuty in power network reinforcement and the interconnection of more distributed generations, faut current eve has become a serious probem in transmission and distribution system operations. The utzation of faut current imiters (s) in power system provides an effective way to suppress faut currents and resut in considerabe saving in the investment of high capacity circuit breakers. In a oop power system, the advantages woud depend on the numbers and ocations of instaations. This paper presents a method to determine optimum numbers and ocations for pacement in terms of instaing smaest parameters to restrain short-circuit currents under circuit breakers interrupting ratings. In the proposed approach, sensitivity factors of bus faut current reduction due to changes in the branch parameters are derived and used to choose candidates for instaations. A genetic-agorithm-based method is then designed to incude the sensitivity information in searching for best ocations and parameters of to meet the requirements. Test resuts demonstrate the efficiency and accuracy of the proposed method.. eywords: Short-ircuit urrent, ircuit Breaker, aut urrent Limiter, Sensitivity Anaysis, Genetic Agorithm W I. ITRODUTIO ith the increasing demand for power, eectric power systems have become greater and are interconnected. Generation units of independent power producers (Is) and renewabe energy have been interconnected to power systems to support the rising demands. As a resut, fauts in power networks incur arge short-circuit currents fowing in the network and in some cases may exceed the ratings of existing circuit breakers (B) and damage system equipment The probems of inadequate B short-circuit ratings have become more serious than before since in many ocations, the highest rating of the B avaiabe in the market has been used. To dea with the probem, faut current imiters (s) are often used in the situations where insufficient faut current interrupting capabty exists [-0]. Active is a variabe-impedance device connected in series with a B to imit the current under faut conditions. It has very ow impedance under norma operating conditions and high impedance under faut conditions. Active s with different operation mechanism such as based on superconductor, power eectronics, poymer positive temperature coefficient resistors and techniques of arc contro [-0] have been introduced. Depending on the ocation of instaation, coud offer other advantages such as ) increasing the interconnection of renewabe energy and independent power units; ) increasing the energy transmission This work was sponsored by Taiwan ower ompany under contract T Jen-Hao Teng is with Department of Eectrica Engineering, I-Shou University, aohsiung, Taiwan. han-an Lu is with Department of Eectrica Engineering, ationa Sun Yat-Sen University, aohsiung, Taiwan. capacity over onger distances; 3) reducing the votage sag caused by the faut; 4) improving the system stabty, and 5) improving the system security and reiabty. In radia power systems, the pacement of is not difficut, but in oop power system, pacement becomes much more compex when more than one ocation that have high faut current probems. In such a system, short-circuit currents coud come from many directions and are not easiy bocked by a singe. Therefore, from power system operation and panning points of view, a technique that can choose optimum number and ocations for pacement with smaest circuit parameters changes to constrain faut currents under B rating is becoming necessary. or this purpose, rectifier-type superconducting mode has been incuded in short-circuit current anaysis and a method to find ocations suitabe for short-circuit current reduction was proposed in []. Refs. [, 3] used a hierarchica genetic agorithm combined with a micro-genetic agorithm to search for the optima ocations and smaest circuit parameters simutaneousy. This paper proposes a new method to find the optimum numbers and ocations for pacement. or arge oop system appications, in order to reduce the search space in finding the optimum ocations, a sensitivity anaysis is first conducted to find better candidate ocations for pacement. A genetic-agorithm-based method is then designed and used to sove the optimum pacement probem. Test resuts demonstrate the efficiency and accuracy of the proposed method. II. AULT URRET REDUTIO AD IMEDAE REQUIRED Athough, most power system fauts are unsymmetrica, baanced three-phase fauts are often the worst and are used to determine the B capacity. or a baanced three-phase faut at bus the short-circuit current can be cacuated by Ei I i = * Ib () where I i is the three phase short-circuit current at bus i. E i is the votage before the faut at bus i. ommony, E i can be set as.0 p.u. is the Thevenin impedance at bus it can be obtained from diagona entries of the impedance matrix ( bus ). I b is the base current. In the bus buiding agorithm, when adding a ine with impedance b between bus j and k, the origina eement of xy wi be modified as

2 new xy = xy ( xj jj + xk kk )( jy jk ky + ) b () Vi Vi Ii, = (5) + new where xy and xy are the modified and origina eements of bus, respectivey. Substituting (4) into (5), (5) can be rewritten as Vi I = (6) ( + ) + If the is used to constrain the faut current from origina I i, to I i,, then required can be easiy cacuated by (6) and expressed as [7] I = (7) I I Substituting (7) into (3), the impedance required is ig. : Thevenin equivaent circuit of adding a ine between two existing buses = + (8) ig. shows the Thevenin equivaent circuit by ooking into the system from two existing buses. If a with impedance were instaed on ine between bus k and j and fired after the fauts, then Thevenin equivaent circuit can be expressed as ig.. ig. : Thevenin equivaent circuit with fired up The tota effect of inserting into the system can be considered as adding a new branch with the foowing impedance to the system: b ( b + ) = ( b ) //( b + ) = (3) Therefore, the modification to the diagona entries of bus after is fired up at a branch between bus j and k is = jj ( + ij kk ik ) + jk = + (4) The faut current deviation at a bus after is fired up can be written as III. ROBLEM ORMULATIO If the ocation for pacement has been decided, the impedance required to constrain the faut current to acceptabe eve coud be easiy cacuated by (8). However, in a arge power system, it coud be difficut to determine optima number, ocations and parameters when faut currents cacuated at severa ocations are approaching and/or have exceeded the ratings of existing Bs. Therefore, the objective is to find a minimum number of s and/or the smaest circuit parameters that are more economica whie keeping faut currents within Bs ratings. The probem can be formuated as foows: min J = s. t. I min j I i=, j + w j = L B * (9a) i = L (9b) where i, is the impedance of the i-th. is the number of instaed. w is the weighting factor for trading off between the number of required and the summation of circuit parameters of s. w is used to make sure that the minimum numbers of can be achieved. min and are the minimum and imum impedance aowabe for the, i-th, respectivey. I j and I j is the short-circuit current and imum aowabe B rating for bus j, respectivey. B is the number of buses that have dangerous faut current eves. To minimize the soution time, in this paper, a sensitivity anaysis technique is used to find the better candidate ocations for pacement. Eqs. (3)-(5) are

3 used to buid the sensitivity reation of bus faut current reductions with respect to impedance addition. or sa a with impedance that is added to branch between bus j and k, the faut current reduction for each bus after the is activated can be expressed in vector form as [ I L I I ] I = (0) I, B, B where B is the number of bus in the power system. It is assumed that sa is.0 p.u. in the foowing derivation. rom (0), for each bus, the argest bus faut current reductions achieved due to branch impedance changes can be obtained. If ony buses are required for faut eve mitigation, buses are arranged into a vector based on decreasing order of the faut current eve reduction and expressed as S = [( I ( I,, c, B()), B( ( I, )), B()) ( I, c L, B( () ))] where B (i) is the bus number for the i-th argest short-circuit current reduction. I, i is the current reduction due to impedance change at branch. Therefore, the sensitivity matrix between pacement and bus faut current reduction can be expressed as S [ ] T L L S S S S = L () where L is the number of ine in the power system. The best candidate ocations for pacement can be sought for by using S. ine 5 and ine 7 are better choices for pacement. (0.98,) (0.04,) (0.03,4) (0.9.) (0.09,4) (0.00,5) (0.97,) (0.063,5) (0.035,4) 3 (0.76,3) (0.3,) (0.046,4) 4 (0.54,4) (0.57,) (0.055,6) 5 S = (3) (0.0,5) (0.080,) (0.00,4) 6 (0.5,6) (0.86,) (0.066,4) 7 (0.47,3) (0.38,5) (0.08,6) 8 (0.490,3) (0.4,6) (0.00,5) 9 (0.076,4) (0.060,5) (0.005,) 0 (0.0,5) (0.8,6) (0.0,3) or a arge oop power system the probem formuation becomes a combinatoria constrained probem with a non-inear and non-differentia objective function. In this study a genetic agorithm (GA) is used to sove the probem. Main steps of the GA used in this study are:. oding: representing the probem by bit strings. Each possibe parameters and candidate ocations for pacement needs to be integrated into each popuation. or each candidate ocation, the parameters or types shoud be coded. or exampe, if we have six types of that are avaiabe in the market; three bits can be used to code type choices. In this case, 000 means no wi be instaed in this ocation and has no meaning. parameters are aso coded. If imum avaiabe parameter for is and the variation between two adjacent parameter is, the reation between and can be expressed as = (4) n n bits can be used to code parameters. ig. 3: A six-bus test system [5] Using the six-bus system shown in ig. 3 as an exampe [5], the S is shown in (3), in this case is 3. rom (3), for exampe, if bus faut current has exceeded B rating, then it can be found that ine 5 is the best ocation to insta. If the system panner intends to find two candidate ocations for bus, then. Initiaization: initiaizing the popuation. GA operates with a set of popuations. The popuations go through the process of evauation to produce new generation. To begin with, the initia popuations coud be seeded with heuristicay chosen strings or at random. In our test systems, a initia popuations are randomy generated. 3. Evauation: determining which popuation is better and deciding who mates. The evauation is a procedure to determine the fitness vaue of each popuation and is very much appication oriented. Since the GA proceeds in the direction of better-fit strings and the fitness vaue is the ony information avaiabe to the GA agorithm, the performance of the agorithm is highy sensitive to the fitness vaue. In the proposed

4 optimization probem, the fitness vaue is the objective function as deribed in (9). The fitness function with constraints can be expressed as Mutation Rate: 0.05 ig. 4 shows the fowchart of the proposed procedure. f = i= i=, + w * +, +, (5) i i p B j = j q IV. TEST RESULTS where i, p and j q are defined in (6)., are the penaty vaues and if if then ese I then ese min j p p I j, q j, q = 0 = 500, i = 0 = 000 (6) 4. rossover: exchanging information between two mates. Mating is a probabstic seection process in which popuations are seected to produce offspring based on their fitness vaues. opuations with high fitness vaues shoud have a higher probabty of generating offspring and are simpy copied into the next generation. 5. Mutation: integrating random information into GA. Mutation is the process of randomy modifying the vaue of a string position with a sma probabty. It ensures that the probabty of searching any region in the probem space is never zero and prevents compete oss of genetic materia through mate and crossover. ig. 4: owchart of the roposed Optimum acement Genetic parameters are the entities that hep to tune the performance of the pacement. The foowing parameters are used in this study: opuation Size: 90 rossover Rate: 0.5 ig. 5: The IEEE 30-bus Test System [8] The proposed agorithm was impemented with Borand ++ on a Windows based. IEEE 30-bus [8] as shown in ig. 5 is used in the foowing tests. The ine data for IEEE 30-bus test system is isted in the Appendix; other data used in the test can be found in [8]. The S/ transition-type superconducting s are used in the foowing test. Using the proposed sensitivity technique, S can be buit and Tabe shows the bus numbers correspond to entries in S. In this case is 5. rom Tabe, it can be seen that if a is instaed in ine, then the five argest bus faut current reductions in decreasing order are at buses, 3,, 4 and. These buses are marked in ig. 5. Thus, the candidate ocations for pacement can be arranged and is shown in Tabe. Using the information shown in Tabe, if the bus 6 faut current exceeds or near its B rating; good ocations for instaing in order to constrain the bus faut current woud be at ine 9, and 6. Tabe : Bus umber of S whie is 3 Line Bus umber umber

5 To show the effectiveness of the proposed method for soving more compex probems, in the foowing exampe, three buses faut currents aready exceed their B ratings, they are Bus 0 with short-circuit current 0.55kA; Bus with short-circuit current 5.895kA; Bus 3 with short-circuit current kA. The B rating in this test case is assumed to be 0 ka. rom Tabe, the candidate ocations for pacement are for bus 0, good candidate ocations are ines,, 3, 4, 9,, 4, 5, 6, 7, 8, 3; for bus, good candidate ocations are ines, 3, 4; and for bus 3 good candidate ocations are ines 5, 6, 7, 9. With the hep from sensitivity anaysis the tota number of candidate ocation is reduced from 4 to 5. This minimizes the computationa efforts in searching for optima ocations and parameters to resove simutaneousy the faut current probems at buses 0, and ig. 6: The andidate Locations for Bus 6 Tabe : The andidate Locations for acement Bus andidate Locations (Line umber) umber,,3,4,5,6,,3,4,5,6 3,,3,4,5,7,5 4,,3,4,5,7,0,3,5,6 5 5,8,9 6 3,4,6,7,8,9,0,,,3,6,34,37,38,39 7 8,9 8 6,7,8,9,0,40 9,3,4 0,,3,4,9,,4,5,6,7,8,3,3,4,,5,6,7,8,9,,,3,30,3 3 5,6,7,9 4 7,0,30 5 5,6,7,8,0,,3,4,30,3 6 9,,6 7,9,,6,7,8 8 8,0,,3,4,5 9 8,0,,3,4,5 0,3,4,5,,4,,5,6,7,8,9,3,4,6,7,8,9,3,3 3 7,8,0,9,30,3,3 4 7,8,9,30,3,3,33,34,35 5 9,33,34,35,36,40,4 6 33,34,35 7 0,33,34,35,36,37,38,39,40,4 8 6,7,8,9,0,36,37,38,39,40,4 9 33,35,36,37,38,39,40, ,37,38,39,4 itness Vaue Iteration o. ig. 7: itness Vaue for Each Iteration ig. 7 shows the fitness vaue variations of GA iterations. The optima soution obtained for this case is A with an impedance of p.u. shoud be instaed on ine 3; A with an impedance of p.u. shoud be instaed on ine 6. The short-circuit currents at buses 0, and 3 after s instaations are reduced to kA, kA and 9.783kA, respectivey. ote that ony two s are required to suppress faut currents at three buses. Using the proposed GA technique to sove the optimization probem, the computationa times required when with and without the proposed sensitivity anaysis are 43s and 3599s, respectivey. V. OLUSIOS AD DISUSSIOS The integration of s into power system provides an effective way to suppress arge faut currents

6 and may bring to considerabe reduction in investment on higher capacity Bs. or a arge oop system, its effectiveness woud depend on the proper choice of the impedance and ocation of. Sensitivity anaysis technique proposed in this paper was found effective in minimizing computationa efforts for searching the optima soution. Test resuts have demonstrated the efficiency and accuracy of the proposed method. It can be used to find the minimum number of s and seect the possibe smaest circuit parameters of s to ensure that bus faut currents are within B interrupting ratings. VI. AEDIX Line Data of IEEE 30-Bus Test System Line rom Bus End Bus umber VII. REEREES [] igre Report 39, aut current imiters in eectrica medium and high votage systems, igre Dec [] ower, A.J., An overview of transmission faut current imiters, aut urrent Limiters - A Look at Tomorrow, IEE ooquium on 8 Jun 995, pp. / - /5. [3] ovasky, L., Yuan, X., Teketsadik,., er A., Bock, J. and Breuer,., Appications of superconducting faut current imiters in eectric power transmission systems, IEEE Trans. on Appied Superconductivity, Vo. 5, o., June 005. [4] Yasuda,., Ichinose, A., imura, A., Inoue,., Mori H., Tokunaga, Y., Tori S., Yazawa, T., Hahakura, S., Shimohata,., and ubota, H., Research & deveopment of superconducting faut current imiter in Japan, IEEE Transactions on Appied Superconductivity, Vo. 5, Issue, art, Jun 005, pp [5] H. ameda and H. Taniguch Setting method of specific parameters of a superconducting faut current imiter considering the operation of power system protection, IEEE Trans. on Appied Superconductivity, Vo. 9, o., June 999, pp [6] RWE Energy, aut current imiter in medium and high votage grids, [7] Seungje Lee, hanjoo Lee, Tae uk o, and Okbae Hyun, Stabty anaysis of a power system with superconducting faut current imiter instaed, IEEE Transactions on Appied Superconductivity, Voume, Issue, art, March 00, pp [8] Das, J.., Limitations of faut-current imiters for expansion of eectrica distribution systems, IEEE Transactions on Industry Appications, Voume 33, Issue 4, Juy-Aug. 997, pp [9] Duggan,., Integration issues for faut current imiters and other new technoogies, IEEE ower Engineering Society Genera Meeting, 006. Vo., 6-0 June 006, pp [0] eumann,., Superconducting faut current imiter (S) in the medium and high votage grid, ower Engineering Society Genera Meeting, 006. IEEE, Vo., 6-0 June 006, pp [] agata, M., Tanaka,. and Taniguch H., ocation seection in arge ae power system, IEEE Transactions on Appied Superconductivity, Voume, Issue, art, March 00, pp [] omsan Hongesombut, en urusawa, Yasunori Mitan and chiro Tsuj "Aocation and circuit parameter design of superconducting faut current imiters in oop power system by a genetic agorithm," Transaction of the Institute of Eectrica Engineers of Japan, Vo. 3 (9), pp [3] Hongesombut,.; Mitan Y.; Tsuj.; "Optima ocation assignment and design of superconducting faut current imiters appied to oop power systems," IEEE Transactions on Appied Superconductivity, Voume 3, Issue, art, June 003, pp [4] J. J. Grainger and W. D. Stevenson, ower System Anaysis, McGraw-Hi Internationa Editions, 994. [5] A. H. Wood and B.. Woenberg, ower Generation Operation & ontro, John Wiey & Sons, ew York [6] G. B. Shebe and. Brittig, Refined genetic agorithm-economic dispatch exampe, IEEE Transactions on ower Systems, Vo. 0, o., pp.7-3, ebruary 995 [7] D. E. Godberg, Genetic agorithms: search, optimization and machine earning. Addison-Wesey, 989 [8] ower Systems Test ase Archive, VIII BIOGRAHIES Jen-Hao Teng received his BS, MS and h.d. degrees in eectrica engineering from the ationa Sun Yat-Sen University in 99, 993 and 996 respectivey. He has been with the I-Shou University, Taiwan, since 998. His current research interests are Distribution Automation, ower Quaity and ower System Dereguation. han-an Lu received BS degree from ationa Taiwan University in 98, MS degree from Rensseaer oytechnic Institute in 983, and h.d. degree from urdue University in 987. He hed positions at Genera Eectric o., and Harris orp. ontro Division. He has been with ationa Sun Yat-Sen University since 989.