Probabilistic Assessment of Total Transfer Capability Using SQP and Weather Effects

Transcription

1 J Eectr Eng Techno Vo. 9, No. 5: , 24 ISSN(Print) ISSN(Onine) Probabiistic Assessment of Tota Transfer Capabiity Using SQP and Weather Effects Kyu-Ho Kim*, Jin-Wook Park**, Sang-Bong Rhee, Sungwoo Bae***, Kyung-Bin Song, Junmin Cha and Kwang Y. Lee Abstract This paper presents a probabiistic method to evauate the tota transfer capabiity (TTC) by considering the sequentia quadratic programming and the uncertainty of weather conditions. After the initia TTC is cacuated by sequentia quadratic programming (SQP), the transient stabiity is checked by time simuation. Aso because power systems are exposed to a variety of weather conditions the outage probabiity is increased due to the weather condition. The probabiistic approach is necessary to evauate the TTC, and the Monte Caro Simuation (MCS) is used to accompish the probabiistic cacuation of TTC by considering the various weather conditions. Keywords: Tota transfer capabiity, Sequentia Quadratic Programming (SQP), Transient stabiity, Probabiistic approach, Weather condition. Introduction Tota transfer capabiity (TTC) is the argest quantity of eectric power that can be transferred over the interconnected transmission networks in a reiabe manner whie meeting a of the pre- and post-contingency system conditions []. The reationship of the TTC and avaiabe transfer capabiity (ATC) is described in the North American Eectric Reiabiity Counci (NERC) definition []. At the present time, there are two techniques of methods for cacuating the TTC, deterministic and probabiistic. The deterministic approaches mainy use the methods such as security constrained optima power fow (SCOPF), continuation power fow (CPF), inear programming (LP) and repeated power fow (RPF), and have some difficuties in handing the uncertainties of power systems such as the possibiity of fauts and weather prediction [2-4]. LP is one of fast methods to search the soution for the initia TTC. In order to reduce inearization errors, oad fows shoud be performed periodicay. Probabiistic methods have considered the uncertainties of the system performance that coud not be addressed in a deterministic way, and have been impemented to evauate the TTC for various outages [5-7]. As a power system networks and the system components are exposed to nature, they are affected by the weather condition consideraby, and the Corresponding Author: Dept. of Eectrica Engineering, Yeungnam University, Korea. (rrsd@yu.ac.kr) * Dept. of Eectrica Engineering, Hankyong University, Korea. (kyuho@hknu.ac.kr) ** LG eectronics Co. LTD. Korea. *** Dept. of Eectrica Engineering, Yeungnam University, Korea. Dept. of Eectrica Engineering, Soongsi University, Korea. Dept. of Eectrica Engineering, Daein University, Korea. Dept. of Eectrica and Computer Engineering., Bayor University, USA Received: November 22, 23; Accepted: June 2, 24 faiure rates of transmission ines are increased due to weather conditions. Therefore, the operation of power system coud be addressed in a probabiistic approach [8]. This paper presents a probabiistic method to evauate the TTC by considering the uncertainty of weather conditions. In the TTC evauation, unike the previous study of the author [8], optimization method such as SQP is used to cacuate the initia TTC. The weather conditions are divided into norma and adverse weather. Because the faiure rate in adverse weather condition is consideraby arger than that in norma weather, the contingency in power system infuences TTC assessment. 2. Determination of TTC Using Deterministic Approach 2. Probem formuation In order to determine the TTC by deterministic method, the mathematica formuation for the TTC evauation can be expressed as foows: Maximize subect to n () P - P - V V ( G cosd + B sin d ) = (2) Gi Li i i i i i = n Q - Q - V V ( G cosd - B sin d ) = (3) Gi Li i i i i i = V V V (4) i min i i S i max i max S (5) d - (6) Gi( t) dg ( t) dg max 52

2 Kyu-Ho Kim, Jin-Wook Park Sang-Bong Rhee, Sungwoo Bae, Kyung-Bin Song, Junmin Cha and Kwang Y. Lee where, : incrementa factor of oad & generation in outage P ( ) Gi = PGi + kgi : rea power generation at bus i P ( ) Li = PLi + kli : rea power demand at bus i Q ( ) Li = QLi + kli : reactive power demand at bus i Q Gi : reactive power generation at bus i P Gi : origina rea power generation at bus i P, Li QLi : origina rea/reactive power oad at bus i kgi, k Li : constants specifying the rate of change in generation and oad V : votage magnitude at bus V, V : ower and upper imits of votage min max magnitude at bus i S i : apparent power fow in ine i S i : therma imit of ine i max dgi ( t), d G ( t) : rotor anges of generator i, d : maximum secure reative swing ange G max For cacuating the TTC, the inection rea and reactive power at source and sink buses are functions of the incrementa factor of oad and generation in outage,. The obective is to maximize incrementa factor of oad and generation in (). The active and reactive power baance equations can be shown in (2) and (3). Inequaity constraints such as votage magnitude of buses and therma imits can be written in (4) and (5). Eq. (6) means the difference between the critica energy and the transient energy as transient stabiity constraint. The optimization method enabes transfers by increasing the compex oad with uniform power factor at every oad in the sink areas and increasing the inected rea power at the generation buses in the source area in incrementa steps unti imits are incurred. The process of transient stabiity anaysis in Eq. (6) is i = i + N Seect Outage Case Power Fow Optimize Eq. () - (5) using SQP Determine Initia TTC Leve TTC, Stabe of Transient Stabiity Limit Eq. (6)? Y Determine TTC Leve TTC, Last? Determine Deterministic TTC, Y Decrease and Repeated Power Fow (RPF) N Fig.. Deterministic TTC cacuation. very time consuming. Therefore the processes to cacuate the deterministic TTC divide into two steps as shown in Fig.. The first step is to cacuate the initia TTC eve TTC satisfying votage and therma imits by using optimization such sequentia quadratic programming (SQP). The next step is to perform transient stabiity anaysis based on the initia TTC eve TTC cacuated in the first step. If there is no imit vioation on transient stabiity, then each TTC eve TTC is determined. If there is unstabe in the transient stabiity, the incrementa factor is decreased and the RPF is performed unti the transient stabiity is stabe. The deterministic TTC is determined by considering a factors that infuence in transfer capabiity with above [9]. 2.2 Sequentia quadratic programming Sequentia quadratic programming (SQP) is the optimization method for the minimization of the maximum of a set of smooth obective functions subect to equaity and inequaity constraints and simpe bounds on the variabes [7]. In order to get the optima soutions the SQP generates a point satisfying these constraints by soving a stricty convex quadratic program (QP) using a positive definite estimate H of the Lagrangian. And an Armio-type arc search or ine search (monotone, nonmonotone) are used to compute the direction of descent the obective function. Generaized the SQP agorithms are impemented as foows: Step Initiaization i) Initia vaue of variabes x, step size t and search directions d. If x is infeasibe for some constraint, substitute a feasibe point. Step 2 Computation of search ~ i) Compute d k, the soution of the stricty convex QP ii) Compute the step size t Step 3 Updates ~ k i) Update Hessian matrix of Lagrangian using the Powe modification. 2 ~ ii) Set x = k x + k tkd + + k tk dk iii) Sove the unconstrained QP probem in m, eq. (3). Increase k by. min z Ñ f ( x ) + x + Ñg ( x ) k, k + k k, k + + m Ñ h ( x ) + m Ñh ( x ) k, k + k, k + where the z k,, xk, m k, and k, are the K-T mutipiers associated with QP for the obective functions, variabe bounds, equaity constraints, and inequaity constraints respectivey. 2 (3) 52

3 Probabiistic Assessment of Tota Transfer Capabiity Using SQP and Weather Effects 3. Determination of TTC using Probabiistic Approach 3. Weather mode with uncertainty Because power systems are exposed to various weather conditions the faiure rate of outdoor components can be increased very significanty during adverse weather periods such as gaes, ighting storms, etc. Usuay the components that receive the most effects of the weather are transmission ines in the power system. The transmission ine can be defined to be in two states that are infuenced by weather conditions, norma and adverse weather conditions [2]. 3.2 Probabiistic TTC using monte caro simuation The sequentia Monte Caro Simuation (MCS) is used to appy the probabiistic approach. The operating characteristic of each component in the system is represented by the two-state mode described by up- and down-states, and the operating state of the whoe power system can be obtained by considering the state of a components in the system and the uncertainty of weather Up Down Norma Weather Read TTC Leve TTC, Monte Caro Simuation Adverse Weather Determine Probabiistic TTC, Fig. 2. Probabiistic TTC cacuation. Component conditions as shown in Fig. 2. The operating time in the up-state is caed time to faiure (TTF) and repair time in the down state is caed time to repair (TTR). The TTF and the TTR can be expressed by the exponentia distribution [2]. TTFi = - n( - U ) (7) i TTRi = - n( - U ) (8) m where i : faiure rate of component i m i : repair rate of component i U : uniformy distributed random number i 4. Numerica Anaysis 4. Deterministic Assessment of TTC In order to show the effectiveness of the proposed agorithm, it has been tested on a 6-bus 7-ine system, which is shown in Fig. 4. In order to show the effectiveness of the proposed method the case is tested as foows: Case A: Constraints in votage magnitudes at buses and therma imits at transmissions not incuding transient stabiity Case B: Constraints in votage magnitudes at buses and therma imits at transmissions incuding transient stabiity The sequentia quadratic programming (SQP) is used to determine the TTC of each case. Tabe and Fig. 5 show the resut of the TTC and the transient stabiity in each faut. In tabe the TTC eve of base case, MW, means the maximum power that can be transferred from source area to sink area in the base case that no outage happens to the system. When the transient stabiity is Component 2 M Component n System state Adverse Norma Time Fig. 3. State of a components using sequentia MCS. Fig. 4. IEEE 6-bus 7-ine system. 522

4 Kyu-Ho Kim, Jin-Wook Park Sang-Bong Rhee, Sungwoo Bae, Kyung-Bin Song, Junmin Cha and Kwang Y. Lee checked in Case A, the TTC eve of ine *3-4 faut is equa to 4.98 MW but transient stabiity is not satisfied in Fig. 5 (b). In Case B, the TTC eve of ine *3-4 faut is reduced to 7.92 MW whie transient stabiity is satisfied in Fig. 5 (e). It is seen that the TTC eve can be determined by the transient stabiity as we as bus votage magnitude and ine therma imits. As a resut, in case of ine faut 4-5 the initia TTC eve is equa to MW. It is seen that the TTC of the test system not incuding transient stabiity is equa to MW, the smaest vaue of TTC eves. The TTC of this test system is determined not by transient stabiity but by therma imits in deterministic assessment of TTC. uncertainty of weather, the weather data are divided into norma and adverse weather for year from Korea Meteoroogica Administration (KMA), which is in 22 year. Fig. 6 shows that the weather is divided into the norma and adverse weather states for about 876 hours, where the number and represent the norma weather and adverse weather conditions, respectivey. In adverse weather conditions, the faiure rate of a component can be consideraby arger than the norma weather condition. This paper assumes that faiure rate in the adverse weather is ten times higher than that in the norma weather [8]. Using sequentia MCS, The operating state of the system in the norma condition ony and the condition that incude 4.2 Probabiistic assessment of TTC In order to appy the probabiistic approach considering Tabe. TTC eve with and without transient stabiity Base case Faut Line *2-3 faut Line *3-4 faut Line *4-5 faut Line *2-5 faut TTC Leve [MW] Case A Transient Stabiity TTC Leve [MW] Case B Transient Stabiity satisfied (a) not satisfied (b) satisfied (c) satisfied (d) satisfied (a) satisfied (e) satisfied (c) satisfied (d) Ange[deg.] Line Faut *3-4(cearing time.4[sec.]) (c) Line Faut *2-3(cearing time.4[sec.]) Line Faut *2-5(cearing time.4[sec.]) Ange[deg.] (a) Ange[deg.] (d) 5 Line Faut *4-5(cearing time.4[sec.]) 2 5 Line Faut *3-4(cearing time.4[sec.]) Ange[deg.] 5 Ange[deg.] (b) - Fig. 5. Transient stabiity. (e) 523

5 Probabiistic Assessment of Tota Transfer Capabiity Using SQP and Weather Effects Fig. 6. Division of norma and adverse weather. Fig. 9. PDF of TTC with the ony norma weather. Fig. 7. System state data when year is ony norma weather. Fig. 8. System state data incuding adverse weather for year. adverse weather condition for year is shown in Fig. 7 and Fig. 8, respectivey. The horizonta axis is the operating state of the system for 876 hour and the vertica axis is the number of surviving components; for exampe, the number 5 means that two components are fauted among the six 7 components [8]. From Fig. 8, it is seen that the frequency of outage in the condition that incude adverse weather is higher than for the norma weather condition. The sequentia MCS can be taken to provide the probabiity distribution function (PDF) of TTC. Considering the norma weather condition, Fig. 9 shows the system can withstand most transient fauts in the range between 3 and 4 MW in probabiity. Because the outages spread widey without specia trend in Fig. 7, the more the TTC vaue in Fig. 9 moved to arge vaue side, the higher the probabiity of the outages is. On the other hand, considering adverse weather in Fig., surviving probabiity of system is ower than of norma weather. Because many outages occurred at the period affected by adverse weather in Fig. 8, the probabiity of the Fig.. PDF of TTC with incuding adverse weather. outages is high in ower portion of TTC vaue in Fig.. If system is operating under the certain adverse weather condition, it is desirabe to determine the TTC vaue in the range between 65 and 7 MW in probabiity in order to make the system stabe. The reason is that the probabiity of TTC about 66 MW for the case with adverse weather is much higher than compared with the vaue in the norma weather for year. Especiay, it is seen that it is possibe to operate power systems at ower TTC during the period such as a specia weather statement, if the weather condition is considered in advance. 5. Concusion This paper presents a probabiistic method to evauate the tota transfer capabiity (TTC) by considering the energy margin and the uncertainty of weather conditions. In TTC determination the repeated power fow (RPF) method is used to maximize the incrementa factor of oad and generation and the transient energy margin method instead of the time simuation such as Runge-Kutta is used 524

6 Kyu-Ho Kim, Jin-Wook Park Sang-Bong Rhee, Sungwoo Bae, Kyung-Bin Song, Junmin Cha and Kwang Y. Lee to check the transient stabiity. The weather condition that affects the system reiabiity is considered. As a resut of considering weather effect and using probabiistic approach, the TTC for the adverse weather condition is ower than that of the norma weather condition. Especiay, it is seen that it is possibe to operate power systems at ower TTC during the period such as a specia weather statement, if the weather condition is considered in advance. transient stabiity energy margin improvement, IEEE PES Winter Meeting, pp , Jan. 22. [2] R. Biinton and R. N. Aan, Reiabiity Evauation of Power System, Penum Press, New York, 996. [3] K. -H. Kim, S. -N. Kim, S. -B. Rhee, S. -K. Lee, and K. -B. Song, Assessment of tota transfer capabiity subect to transient stabiity energy margin, IEEE Transmission and Distribution Asia, September, pp , 28. Acknowedgements This work was supported by the Nationa Research Foundation of Korea Grant funded by the Korean Government (NRF-2-3-D4). References [] North American Eectric Reiabiity Counci, Avaiabe Transfer Capabiity Definitions and Determination, NERC Report, June 996. [2] W. Rosehart, C. Canizares, and V. Quintana, Optima power fow incorporating votage coapse constraints, IEEE PES Summer Meeting, Vo. 2, 8-22, Juy 999, pp [3] V. Aarapu and C. Christy, The Continuation Power Fow: A Too for Steady State Votage Stabiity Anaysis, IEEE T-PS, Vo. 7, No., Feb 992. [4] X. Yu and C. Singh, Probabiistic Anaysis of Tota Transfer Capabiity Considering Security Constraints, 8th Internationa Conference on PMAPS, Iowa State University, September 2-6, 24. [5] X. Yu, C. Singh, S. Jakovevic, D. Ristanovic, and G. Huang, Tota transfer capabiity considering FACTS and security constraints, in Proc. 23 IEEE PES Transmission and Distribution Conf. And Expo., Sep. 23, vo., pp [6] K. Audomvongseree and A. Yokoyama, Consideration of an Appropriate TTC by probabiistic Approach, IEEE Transaction on Power System, Vo. 9, No,, Feb 24. [7] A. Berizzi, C. Bovo, M. Defanti, M. Mero, M. Savino, A Monte Caro Approach for TTC Evauation, IEEE Transaction on Power System, Vo. 22, No, 2, May 27. [8] J. -W. Park, K. -H. Kim, H. -S. Lee, J. -O. Kim, D. -J. Shin, Assessment of Tota Transfer Capabiity Considering Uncertainty of Weather, Internationa Conference on Eectrica Engineering, Kunming, China, Juy, 25. [9] M. A. Pai, Energy Function Anaysis for Power System Stabiity, Kuwer Academic Pubishers, 989. [] A. A. Fouad and V. Vitta, Power System Transient Stabiity Anaysis Using The Transient Energy Function Methods, Prentice Ha, 992, p.38. [] S. -N. Kim, K. -H. Kim, S. -K. You, Rea-time estimation of mutipe series capacitor quantity for Kyu-Ho Kim received his B.S., M.S. and Ph.D. degrees from Hanyang University, Korea, in 988, 99 and 996, respectivey. He is an Associate Professor in the Department of Eectrica Engineering at Hankyong University, Korea. He was a Visiting Schoar at Bayor University for His research interests incude power system contro and operation, optima power fow and evoutionary computation. Jin-Wook Park received his B.S. degree in Eectrica Engineering in 2 from Se-myung University, M.S. degrees from Hanyang University, Korea, in 26. He is currenty a Manger in the LG eectronics, Korea. His research interests incude Power system, distribution power system anaysis and soar system. Sang-Bong Rhee received his B.S., M.S. and Ph.D. degrees from Hanyang University, Korea, in 994, 999 and 24, respectivey. He is currenty an Assistant Professor in the Department of Eectrica Engineering at Yeungnam University, Korea. His research interests incude artificia inteigence appications, distribution power system anaysis, operation, and contro. Sungwoo Bae received the B.S. degree from Hanyang University, Korea, and the M.S.E. and Ph.D. degrees from the University of Texas at Austin, USA, a in eectrica engineering, in 26, 29, and 2, respectivey. From 22 to 23, he was a senior research engineer with Power Center at Samsung 525

7 Probabiistic Assessment of Tota Transfer Capabiity Using SQP and Weather Effects Advanced Institute of Technoogy. He is currenty an Assistant Professor in the Department of Eectrica Engineering, Yeungnam University. Kyung-Bin Song received his B.S. and M.S. degrees in Eectrica Engineering from Yonsei University, Korea, in 986 and 988, respectivey. He received his Ph.D. degree in Eectrica Engineering from Texas A&M University, Coege Station, Texas in 995. He is currenty an Associate Professor in Eectrica Engineering at Soongsi University, Seou, Korea. His research interests incude power system operation and contro, power system economics, the optimization of the arge scae systems, and the fuzzy system and its appications. Junmin Cha received his B.Sc., M.Sc. and Ph.D. degrees from Korea University in 989, 99 and 996 respectivey. His research interest incudes Fuzzy Appications, Probabiistic Production Cost Simuation, Reiabiity Evauation, Outage Cost Assessment of Power Systems and Operation and Panning of Dereguated Power Market. Since 996, he has been a facuty of Daein University in Korea, where is now a professor. Kwang Y. Lee received the B.S. degree in Eectrica Engineering in 964 from Seou Nationa University, M.S. degree in Eectrica Engineering in 968 from North Dakota State University, and Ph. D. degree in Systems Science in 97 from Michigan State University. He was eected as a Feow of IEEE in the January 2 for his contributions to the deveopment and impementation of inteigent system techniques for power pants and power systems contro and as a Life Feow of IEEE since January 28. He has been working in the area of power pants and power systems contro for over thirty years at Michigan State, Oregon State, University of Houston, the Pennsyvania State University, and the Bayor University, where he is Professor and Chairman of the Department of Eectrica and Computer Engineering. His research interests incude contro, operation, and panning of power and energy systems; computationa inteigence, inteigent contro and their appications to power and energy systems, and modeing, simuation and contro of micro-grids with renewabe and distributed energy sources. 526