Simulation of Line Outage Distribution Factors (L.O.D.F) Calculation for N-Buses System

Transcription

1 Simulatin f Line Outage Distributin Factrs (L.O.D.F) Calculatin fr N-Buses System Rashid H. AL-Rubayi Department f Electrical Engineering, University f Technlgy Afaneen A. Abd Department f Electrical Engineering, University f Technlgy Mhammed R. Saeed Alhendawi Department f Electrical Engineering, University f Technlgy ABSTRACT System security invlves practices designed t keep the system perating when cmpnents fail. A transmissin line may be damage by a strm lead t taken ut by autmatic relaying. If, in cmmitting and dispatching generatin, prper regard fr transmissin flws are maintain, the remaining transmissin lines can take the increased lading with still remain within limit. Because the specific times at which initiating events that cause cmpnents t fail are unpredictable, the system must be perated at all times in such a way that the system will nt be left in a dangerus cnditin shuld any credible initiating event ccur. Pwer system equipment are designed t be perate within certain limits mst pieces f equipment are prtected by autmatic devices that can cause equipment t be switched ut f the system if these limits are vilated. If any event ccurs n a system that leaves it perating with limits vilated, the event may be fllw by a series f further actins that switch ther equipment ut f service. If this prcess f cascading failures cntinues, the entire system r large parts f it may cmpletely cllapse. In this paper, it has been building simulatin prgram t study the cases utage lines f the netwrk system. Three cases adpted fr the purpses f the study. Where study and discuss thse cases in detail and its impact n netwrk perfrmance. It was diagnsed lines, which causes increased pwer flw ver the limit in additin t the reflectin f the ther feeding lines. Keywrds Cntingency analysis; dc pwer flw; pwer system security 1. INTRODUCTION The dc pwer flw simplifies the pwer flw by making a number f apprximatins including 1) cmpletely ignring the reactive pwer balance equatins, 2) assuming all vltage magnitudes are identically ne per unit, 3) ignring line lsses and 4) ignring tap dependence in the transfrmer reactance. Hence, the dc pwer flw reduces the pwer flw prblem t a set f linear equatins. The dc slutin lad value has increased t match the ttal ac lad plus lsses, a manner t make cmparisn between the ac and dc slutin results pssible. The effectiveness f the methd develped is identified thrugh its applicatin t a 6 buses test system [1]. 2. DC POWER FLOW AC pwer flw algrithms have high calculatin precisin but d nt have fast speed. In real pwer dispatch r pwer market analysis, the requirement f calculatin precisin is nt very high, but the requirement f calculatin speed is f mst cncern, especially fr a large - scale pwer system. Mre simplificatin pwer flw algrithms than fast decupled pwer flw algrithms are used. One algrithm is called MW Only. In this methd, the Q - V equatin in the fast decupled pwer flw mdel is cmpletely drpped. Only the fllwing P θ equatin is used t crrect the angle accrding t the real pwer mismatch [2]. P 1 V 1 P 2 V 2 P n 1 V n 1 = B 11 B 12 B 13 B 21 B 22 B 23 B n 1,1 B n 1,2 B n 1,n 1 θ 1 θ 2 θ n 1 In the MW - nly pwer flw calculatin, the vltage magnitude can be handled either as cnstant r as 1.0 during each P θ iteratin. Fr the cnvergence, nly real pwer mismatch is checked n matter what the reactive pwer mismatch is. Anther mst simplified pwer flw algrithm is DC pwer flw. It is als an MW - nly methd but has the fllwing assumptins: 1. All the vltage magnitudes are equal t Ignre the resistance f the branch; i.e., the susceptance f the branch is B ij = 1 (2) 3. The angle difference n the tw ends f the branch is very small, s that we sinθ ij = θ i θ j csθ ij = 1 (4) Ignre all grund branches; that is, B i0 = B j0 = 0 csθ ij = 1 Therefre, the DC pwer flw mdel will be Or P 1 P 2 P n 1 = B θ 1 θ 2 θ n 1.. (3) (1) 1

2 P = B θ.. (4) Where: B matrix are the same as thse in the XB versin f fast decupled pwer flw but we ignre the matrix B. That is, B ij = 1 (5) B ij = j i B ij (6) The DC pwer flw is a purely linear equatin, s nly ne iteratin calculatin is needed t btain the pwer flw slutin. Hwever, it is nly gd fr calculating real pwer flws n transmissin lines and transfrmers. The pwer flwing n each line using the DC pwer flw is then P ij = B ij θ i θ j = θ i θ j (7) 3. SENSITIVITY CALCULATION The sensitivity analyses are becming mre and mre imprtant in practical pwer system peratins including in pwer market peratins. These are analyzes and discusses all kinds f sensitivity factrs such as lss sensitivity factr, generatr shift factr (GSF), cnstraint shift factr, line utage distributin factr (LODF) and respnse factr fr the transfer path. It als addresses the practical applicatin f these sensitivity factrs including a practical methd t cnvert the sensitivities with different references. The pwer peratr uses these t study and mnitr market and system behavir and detect pssible prblems in the peratin. These sensitivity calculatins are als used t determine whether the nline capacity as indicated in the resurce plan is lcated in the right place in the netwrk t serve the frecasted demand. If cngestin r vilatin exists, the generatin scheduling based n the sensitivity calculatins can determine whether r nt a different allcatin f the available resurces culd reslve the cngestin r vilatin prblem [3]. The prblem f studying thusands f pssible utages becmes very difficult t slve if it is desired t present the results quickly. One f the easiest ways t prvide a quick calculatin f pssible verlads is t use linear sensitivity factrs. These factrs shw the apprximate change in line flws fr changes in generatin n the netwrk cnfiguratin and are derived frm the DC lad flw presented in the flwing steps. These factrs can be derived in a variety f ways and basically cme dwn t tw types [3]: 1. Generatin shift factrs. 2. Line utage distributin factrs. Setp1:- Nw calculate the Y bus frm impedance as equatin We gets y ij = 1 y ii = n j =1 y ij i j (8)..(9) Y bus = y 11 y 12 y 1n y 21 y 2n (10) y n1 y n2 y nn Step2:- Since bus ne is a slack bus and eliminate (1st rw & the 1st clumn) frm matrix in equatin (10). We get y 22 y 23 y 2n y 32 y 3n Y eliminate =.(11) y n2 y n3 y nn Step3:- Find the inverse f Y eliminate, we gets 1 M = Y eliminate.(12) Step4:- Determine the sensitivity matrix by : X = M (13) Step5:- Determine the generatin shift sensitivity factr by perfrming the utage f the generatin cnnected t selected bus (k) with cnnected line (ll) frm the fllwing equatin: a ll,k = 1 x l X nk X mk (14) Step6:- Determine f the line utage distributin sensitivity factr by perfrming the utage f the line cnnected t bus is called (kk) that affected n the line in bus anther line is called (ll) frm the fllwing equatin: d ll,kk = x kk X x in X jn X im +X jm ll x kk X ii +X jj 2X ij. (15) The generatin shift factrs are designated (a ll,i ) and have the fllwing definitin: Where: a ll,i = f ll P i.. (16) ll = line index. i = bus index. f ll = change in megawatt pwer flw n line ll when a change in generatin, P i ccurs at bus i. P i = change in generatin at bus i. It is assumed in this definitin that the change in generatin, P i, is exactly cmpensated by an ppsite change in generatin at the reference bus, and that all ther generatrs remain fixed. The a ll,i factr then represents the sensitivity f the flw n line ll t a change in generatin at bus i. Suppse ne wanted t study the utage f a large generating unit and it was assumed that all the generatin lst wuld be made up by the reference generatin (we will deal with the case where the generatin is picked up by many machines shrtly). If the generatr in questin was generating P i MW and it was lst, we wuld represent P i, as [4]: P i = -P i (17) And the new pwer flw n each line in the netwrk culd be calculated using a pre calculated set f a factrs as fllws: 2

3 f ll = f ll + a ll,i P i fr ll = 1... LL.(18) Where: fails. f ll = flw n line ll after the generatr n bus i f ll = flw befre the failure. The utage flw, f ll n each line can be cmpared t its limit and thse exceeding their limit flagged fr alarming. This wuld tell the peratins persnnel that the lss f the generatr n bus i wuld result in an verlad n line ll. The line utage distributin factrs are used in a similar manner; nly hey apply t the testing fr verlads when transmissin circuits are lst. By definitin, the line utage distributin factr has the fllwing meaning: d ll,k = f ll f k (19) d ll,k = line utage distributin factr when mnitring line l after an utage n line k. f ll = change in MW flw n line l. f k = riginal flw n line k befre it was utaged (pened). 3 Gen Lad Lad Lad Table 3: The MW Limits n The Transmissin Line. Line MW Limit The simulatin prgram figures (1 & 2) was used t study multi cases f line utage netwrk as fllws: If ne knws the pwer n line ll and line k, the flw n line ll with line k ut can be determined using "d" factrs. Where: f ll = f ll + d ll,k f k (20) f ll, f k = preutage flws n lines ll and k, respectively. f ll = flw n line ll with line k ut. 4. RESULT AND DISCUSSION The line and bus data f the IEEE-6 Bus test system. The system input data is shws in tables (1, 2, & 3). Table 1: Line Data [5]. Frm T Bus Bus R (pu) X (pu) Figure 1: Test System Six-bus netwrk. Bus Number Bus Type Table 2: Bus Data [5]. Vltage Schedule (pu V) P gen. (pu MW) P lad (pu MW) 1 Swing Gen

4 start Input line number.x,r, Thermal limits Equatin 8 Fr i=1,branch Fr j=1,branch Equatin 8 Equatin 11 Equatin 12 Equatin 14 Equatin 15 Equatin 16 Print shift factr and line utage End Figure 2: Flw chart multi cases f line utage netwrk. Case 1: (1-2) utage line. Figures (3 & 4), it shws that the effect f pwer flw f the line due t effects f line utage (1-2). This affects leads t redistributing the pwer flw n the lines f the netwrk system, see table (4).Therefre we see increment and discernment in pwer flw lines t make that peratin f netwrk system. Line (1-4) increase (39.15%), line (1-5) increase (32.67%). Thse lines are directly affected by the wrks t cmpensate fr the netwrk t take advantage f the generatr at Bus1. Other lines affected indirectly where the line (2-3) reflected a decrease in the directin f the frce f the ability t read (52 kw). Decreasing pwer flw lines (2-4, 2-5, 2-6, and 3-5) by (51%, 34.71%, 13.3.%, and 17.64%), respectively, at the same time increasing pwer flw lines (3-6, 4-5, and 5-6) by (0.01%, 4.63%, and 191%), respectively. Case 2: (1-4) utage line. In the event f a defect in the line (1-4), that causes a change in the pwer flw t the lines f the netwrk, as shwn in the table (4). Figures(5 & 6) shws an increase in the pwer flw lines (1-2, 1-5, 3-6, and 5-6) by (96.5%, 44.7%, 0.46%, and 91.25%) respectively, while the decrease happen applicability capacity f lines (2-3, 2-5, 2-6, and 3-5) by (48.6%, 16.58%, 6.33%, and 8.43%), respectively. The privacy f the line (4-5) was reflected feed directin t becme (6.16 MW). There is a prblem in the line (2-4), where the amunt f the increase f the pwer flw is higher than the thermal limits by (132.88%). Case 3: (3-6) utage line. The utage line (3-6) fr technical reasns lead t an increase in the pwer flw is higher than the thermal limit in tw lines, the first (3-5) be increase (133%) The secnd line (2-3) which becme cunterprductive by feeding (20.11 MW), see table (4). In the ther hand are increase in lines (1-2, 1-4, 2-6, and 5-6) by (2%, 0.4% %, and 113%), respectively. In the same time decrease in lines (1-5, 2-5, 2-4, and 4-5) by (2.13%, 7.48%, 2.5%, and 16.1%), respectively, see figures (7 & 8). Line Table 4: variatin in Pwer Flw fr multi cases. MW Limit nrmal state (1-2) utage line (1-4) utage line (3-6) utage line verlad verlad verlad

5 Figure 3: Pwer Flw fr netwrk lines system under utage line (1-2). Figure 4: Value f pwer flw lines fr netwrk lines (case 1). Figure 5: Pwer Flw fr netwrk lines system under utage line (1-4). 5

6 Figure 6: Value f pwer flw lines fr netwrk lines (case 2). Figure 7: Pwer Flw fr netwrk lines system under utage line (3-6). 5. CONCLUSION Thrugh study and discussin ut pwer flw lines fr ensuring the netwrk system, we suggest the fllwing: 1. Cntrl thrugh regeneratin rganizatin in Buses. Figure 8: Value f pwer flw lines fr netwrk lines (case 3). 2. Taking int cnsideratin when designing the netwrk system t the limits Permitted t lines f pwer flw t avid a cllapse in the netwrk system. 3. Add lines t pwer flw in parallel-diagnsed lines, which happens rise in the pwer flw utside the 6

7 limit t avid weaknesses in the design f system netwrk. 4. Add secndary line f pwer flw parallel t the main lines f pwer flw t avid the utage ccur frequently in sme lines. 6. REFERENCES [1] J.Z. Zhu, Pwer System Optimal Operatin, Tutrial f Chngqing University, [2] Y. He, Z.Y. Wen, F.Y. Wang, and Q.H. Zhu, Pwer Systems Analysis, Huazhng Plytechnic University Press, [3] A. Keyhani, A. Abur, and S. Ha, Evaluatin f Pwer Flw Techniques fr Persnal Cmputers, IEEE Trans. n Pwer System, Vl. 4, N. 2, 1989, pp [4] O. Alsac and B. Sttt, Fast Decupled pwer flw, IEEE Trans. n Pwer System, Vl. 93, 1974, pp [5] Wd, A.J. and B.F. Wllenberg, Pwer Generatin, Operatin, And Cntrl: Jhn Willey & Sns. INC., Publicatin, p73, [6] R.A.M. Van Amerngen, A General Purpse Versin f the Fast Decupled pwer flw, IEEE Summer Meeting, [7] A. Mnticelli, A. Garcia, and O.R. Saavedra, Decupled pwer flw,: Hypthesis, Derivatins, and Testing, IEEE Trans. n Pwer System, Vl. 5, N. 4, 1990, pp [8] A. Kls, A. Kerner, "The nn-uniqueness f the lad flw slutin," in Prc PSCC-5, vl. pp , Cambridge, UK. [9] C.L. DeMarc, T.J. Overbye, Lw vltage pwer flw slutins and their rle in exit time based security measures fr vltage cllapse, in Prc. 27th Cnf. Decisin & Cntrl, Dec. 1988, Austin, TX. [10] J.S. Thrp, S.A. Naqavi, Lad flw fractals, in Prc. 28th Cnf. Decisin and Cntrl, Dec 1989, Tampa, FL. [11] J.S. Thrp, S.A. Naqavi, Lad-flw fractals draw clues t erratic behavir, IEEE Cmputer Applicatins in Pwer, pp , Jan IJCA TM : 7