Branch Outage Simulation for Contingency Studies Dr.Aydogan OZDEMIR, Visiting Associate Professor Department of Electrical Engineering, exas A&M University, College Station X 77843 el : (979) 862 88 97, Fax : (979) 845 62 59 E-mail : ozdemir@ee.tamu.edu
Aydoğan Özdemir was born in Artvin, urkey, on January 1957. He received the B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from Istanbul echnical University, Istanbul, urkey in 1980, 1982 and 1990, respectively. He is an associate professor at the same University. His current research interests are in the area of electric power system with emphasis on reliability analysis, modern tools (neural networks, fuzzy logic, genetic algorithms etc.) for power system modeling, analysis and control and high-voltage engineering. He is a member of National Chamber of urkish Electrical Engineering and IEEE.
Power System Security Power system security is the ability of the system to withstand one or more component outages with the minimal disruption of service or its quality. Outages of component(s) Overstress on the other components No limit violation limit violation(s) operation of protective devices and switching of the unit(s) partial or total loss of load
POWER SYSEM SECURIY monitoring contingency analysis security constrained opf Monitoring : Data collection and state estimation he objective of steady state contingency analysis is to investigate the effects of generation and transmission unit outages on MW line flows and bus voltage magnitudes.
SAR SE SYSEM MODEL O INIIAL CONDIIONS SIMULAE AN OUAGE OF A GENERAOR OR A BRANCH SELEC A NEW OUAGE LIMI VIOLAION Y ALARM MESSAGE N N LAS OUAGE END Y
Real-time applications require fast and reliable computation methods due to the high number of possible outages in a moderate power system. However, there is a well-known conflict between the accuracy of the method applied and the calculation speed. Exact solution Full AC power flow for each outage Check the limit violations not feasible for real-time applications. approximate methods to quickly identify conceivable contingencies real-time applications AC power flows only for critical contingencies. Check the limit violations
APPROXIMAE CONINGENCY ANALYSIS Contingency ranking contingencies are ranked in an approximate order of a scalar performance index, PI. contingencies are tested beginning with the most severe one and proceeding down to the less severe ones up to a threshold value. Masking effect causes false orderings and misclassifications. Contingency screening Explicit contingency screening is performed for all contingencies, following an approximate solution (DC load flow, one iteration load flow, linear distribution or sensitivity factors etc.) Contingency screening is performed in the near vicinity of the outages (local solutions) Hybrid methods utilizing both the ranking and the screening
outage of a branch or a generation unit MW line flow overloads voltage magnitude violations both DC load flows Sensitivity factors involves more complicated models and better computation algorithms
LINE OUAGE SIMULAION An outage of a line can either be simulated by setting its impedance, y ij = 0 or by injecting hypothetical powers at both ends of the line. he latter method is preferred to preserve the original base case bus admittance matrix. i S ij =0 S ji =0 j i S ij 0 y ij 0 S ji 0 j i S ij 0 y ij S ji j 0 y i 0 0 y j 0 0 y S i 0 y j 0 si S sj Z-Matrix techniques Modification of Z BUS is required for each outage Determination of the hypothetical sources so that all the reactive power circulates through the outaged line while maintaining the same voltage magnitude changes in the system
SIMULAION FOR MW LINE FLOW PROBLEM DC LOAD FLOW : ΔP B Δδ, [ B' ] ij 1 / x ij, [ B' ] ii 1 / x ik, x ij Re al {1 / y ij } k outage of a line connected between busses i and j ΔP [ 0 0.. 0 Psi 0... Psi 0..0] ; Psi Re al { S si } Δδ X [0 0.. 0 1 0 0.. 1.. 0 0 ] P si, X 1 [ B ] he new real power flow through the line connected between busses n and m can be derived and approximated as, ~ P nm Pnm Pnm Pnm 1 x lm ([X] nn [X] mm - 2[X] nm ) P si See Power Generation, Operation and Control by Wood and Wollenberg for details
SIMULAION FOR VOLAGE MAGNIUDE PROBLEM Linear models are not sufficient for most outages Reactive power flows can not be isolated from bus voltage phase angles Involves more complicated models and better computation algorithms i ij ij ji ji j Li Lj * 2 2 bi 0 Im ag { V i. y ij. V } [ V i V iv j cos ji ] bij V iv j g ij sin ij j ji V i 2 ransferring reactive power ij ji 2 [ V i ij 2 V j ] bij / 2 V iv j g ij sin ji assumed to flow through the line Can be split up into two parts, Loss reactive power 2 2 [ V Li i V j 2V iv j cos b ij ji ] 2 2 ( V i V 2 b i 0 j ) 4 assumed to allocated at the busses Lj Li
Line outage simulation by hypothetical reactive power sources i ij 0 ij ij ji 0 j si ij Li Li Li si ij Li For a tap changing transformer, cross flow through the equivalent impedance is considered to be the transferring reactive power, where shunt flows can be considered as the loss reactive powers. bus i a :1 b ij bus j bus i ij b ij ji bus j 1 a 1 ( a 1) b ij Li Lj ( 1 1 ) bij a ransferring reactive power is sensitive both to bus voltage magnitudes and bus voltage phase angles. However, loss reactive power is dominantly determined by bus voltage phase angles and has a weak coupling with bus voltage magnitudes. herefore, transferring reactive powers are enough for a reasonable accuracy.
Hypothetical reactive power injections to bus i and bus j, will result in a change in net reactive bus powers i and j. his in turn, will result in a change in system state variables with respect to pre-outage values. his change must be equivalent to the changes when the line is outaged. Load bus reactive powers do not satisfy the nodal power balance equation due to the errors in load bus voltage magnitudes calculated from linear models. herefore, part of the fictitious reactive generation flows through the neighboring paths instead circulating through the outaged branch. hese reactive power mismatches can mathematically be expressed as, i Im ag * V i k Y ik V k k ik j ij si Di j Im ag V * j k Y jk V k k i jk ji sj Dj where i and Di are the net reactive power and the reactive demand at load bus i, is the complex voltage at bus i and Y ik is the element of bus admittance matrix. he superscript * denotes the conjugate of a complex quantity. Calculated load bus voltage magnitudes need to be modified in a way to minimize the bus reactive power mismatches at both ends of the outaged line. his can be accomplished a local optimization formulation
1. Select an outage of a branch, numbered k and connected between busses i and j. 2. Calculate bus voltage phase angles by using linearized MW flows. l ( X X ) P l li lj k, l=2,3,, NB Pk Pij 1 ( X ii X jj 2 X ij ) / x k where X is the inverse of the bus suseptance matrix, P ij is the pre-outage active power flow through the line and x k is the reactance of the line. ~ ~ 3. Calculate intermediate loss reactive powers, 4. Minimize reactive power mismatches at busses i and j, while satisfying linear reactive power flow equations. Mathematically, this corresponds to a constrained optimization process as, Li Lj Minimize wrt ij ( i ij Di ) ( j ji Dj ) Subject to g q ( V ) B V ~ ij ij Li ~ ji ij Li reactive power flows through the outaged line
SOLUION OF HE CONSRAINED OPIMIZAION PROBLEM After having formulated the outage simulation as a constrained optimization problem, minimization can be achieved by solution of the partial differential equations of the augmented Lagrangian function L ( ij i ij Di j ji Dj 2 2 1, V, ( ) ( ) [ B V] with respect to ij, V and. Note that V does not need to include all the load bus voltage magnitudes; instead only busses i, j and their first order neighbors are enough for optimization cycle. Drawback : Convergence to local maximum Single direction search
SOLUION BY GENEIC ALGORIHMS Evolutionary algorithms are stochastic search methods that mimic the metaphor of natural biological evolution. Genetic Algorithms (GAs) are perhaps the most widely known types of evolutionary computation methods today. GAs operate on a population of potential solutions applying the principle of survival of the fittest procedure better and better approximation to a solution. At each generation, a new set of better approximations is created by selecting individuals according to their fitness in the problem domain. his process leads to the evolution of populations of individuals that are better suited to their environment than the individuals that they were created from. GENERAE NEW POPULAION selection crossover mutation N Generate initial population evaluate objective function optimization criteria met Y best individuals For the details of the processes see Cheng, Genetic Algorithms&Engineering Optimization by M. Gen, R., New York: Wiley, 2000. Such a single population GA is powerful and performs well on a broad class of optimization problems. result
BASE CASE LOAD FLOW bounded network SELEC AN OUAGE CALCULAE BUS VOLAGE PHASE ANGLES i j Minimize ij ji outaged branch wrt ij subject to V X CALCULAE HE REMAINING UANIIES END
NUMERICAL EXAMPLES IEEE 14-Bus test System G 1 G G 6 2 3 5 4 G 8 7 11 10 9 G Base case control variables : P G2 = 0.4 p.u. P G3 = P G6 = P G8 = 0.0 p.u. V 1 = 1.06 p.u. V 2 = 1.045 p.u. V 3 = 1.01 p.u. V 6 = 1.07 p.u. V 8 = 1.09 p.u. B 9 = 0.19 p.u. t 4-7 = 0.978 t 4-9 = 0.969 t 5-6 = 0.932 12 13 14 7-9 = 27.24 Mvar 5-6 = 12.42 MVar
P o s t-o u ta g e V o lta g e M a g n itu d e s fo r I E E E -1 4 B u s e s t S y s te m B u s O u ta g e o f L in e 7-9 O u ta g e o f tra n s fo rm e r 5-6 N o V LF [p u ] V PF [p u ] V [% ] V LF [p u ] V PF [p u ] V [% ] 1 1.0 6 0 1.0 6 0 0.0 1.0 6 0 1.0 6 0 0.0 2 1.0 4 5 1.0 4 5 0.0 1.0 4 5 1.0 4 5 0.0 3 1.0 1 0 1.0 1 0 0.0 1.0 1 0 1.0 1 0 0.0 4 1.0 1 5 1.0 1 5 0.0 1.0 1 5 1.0 2 3 0.8 5 1.0 1 6 1.0 1 8 0.2 1.0 2 5 1.0 3 2 0.7 6 1.0 7 0 1.0 7 0 0.0 1.0 7 0 1.0 7 0 0.0 7 1.0 6 6 1.0 6 8 0.1 1.0 5 5 1.0 5 5 0.0 8 1.0 9 0 1.0 9 0 0.0 1.0 9 0 1.0 9 0 0.0 9 0.9 8 8 0.9 9 3 0.5 1.0 4 6 1.0 3 8 0.8 10 0.9 9 4 0.9 9 9 0.5 1.0 4 3 1.0 3 6 0.7 11 1.0 2 7 1.0 3 0 0.3 1.0 5 3 1.0 4 9 0.4 12 1.0 5 0 1.0 51 0.1 1.0 5 2 1.0 5 4 0.2 13 1.0 4 0 1.0 4 1 0.1 1.0 4 9 1.0 4 8 0.1 14 0.9 9 2 0.9 9 6 0.4 1.0 2 8 1.0 2 4 0.4 M a x im u m e rro r: 0.5 % M a x im u m e rro r: 0.8 %
Post-outage reactive power flows for IEEE-14 Bus est Systems Line Outage of Line 7-9 Outage of transformer 5-6 l=m PF DF PF DF [MVa [Mvar r] ] [Mvar] [MVar] [Mvar] [Mvar] 1-2 -20.3-20.2 0.07-21.6-21.1 0.53 1-5 5.4 4.4 0.98 1.3-1.3 2.64 2-3 3.6 3.6 0.02 3.3 3.3 0.03 2-4 0.2-0.1 0.27-1.6-5.8 4.15 2-5 2.8 1.7 1.15-1.3-4.2 2.90 3-4 5.3 5.0 0.33 3.7-0.1 3.81 4-5 12.0 9.0 3.02 8.6 14.0 5.35 4-7 -14.1-14.8 0.70-5.1-0.8 4.31 4-9 13.2 12.9 0.32 3.0 6.4 3.35 5-6 12.8 13.8 0.97 42.6 6-11 14.6 12.9 1.73 19.5 19.9 0.41 6-12 3.7 3.5 0.20 5.1 4.7 0.36 6-13 13.0 12.0 0.96 15.1 15.5 0.42 7-9 86.7 9.6 17.7 8.12 9-10 -5.5-4.8 0.71-8.2-8.9 0.66 9-14 -2.6-1.9 0.70-4.6-5.5 0.88 10-11 -11.3-10.2 1.11-14.9-15.5 0.64 12-13 1.9 1.6 0.34 3.4 3.5 0.06 13-14 8.3 7.4 0.85 12.4 12.2 0.24 7-8 -14.5-13.3 1.21-21.2-21.2 0.04
IEEE 57-Bus est System 5 4 G 3 G 2 G 1 16 2 G 6 18 19 20 21 45 15 17 14 13 12 46 G 47 44 48 50 26 24 49 2 25 23 22 37 36 38 39 40 56 57 41 11 27 30 33 35 42 43 28 31 32 34 7 29 52 53 54 55 G 8 9 G 10 51
First one is the outage of the line connected between bus-12 and bus-13, whose preoutage reactive power flow is 60.27 Mvar. Second case is the outage of a transformer with turns ratio 0.895 connected between bus-13 and bus-49, whose pre-outage reactive power flows is 33.7 Mvar. Post-Outage Voltage Magnitudes for outage of the line connected between bus 12 and bus Voltage magnitudes [p.u.] Bus No pre-outage VPF V DF V 13 0.979 0.955 0.953 0.0019 14 0.970 0.953 0.951 0.0018 20 0.964 0.955 0.953 0.0016 46 1.060 1.042 1.040 0.0023 47 1.033 1.016 1.014 0.0016 48 1.028 1.011 1.009 0.0020 49 1.036 1.019 1.017 0.0024 threshold error = 0.0015 p.u.
Post-Outage Reactive Power Flows for outage of the line connected between bus 12 and bus 13 Reactive Power Flow [MVar] Line pre-outage PF DF l-m lm ml lm ml lm [MVar] ml 1-2 75.00-84.12 74.84-83.94 75.01 84.14 0.17 0.20 1-15 33.74-23.95 45.29-34.96 46.26 35.22 0.97 0.26 3-15 -18.26 13.73 0.54-5.15 0.87-5.26 0.33 0.11 50-51 -4.16 6.51-9.43 9.92-9.23 9.78 0.20 0.14 threshold error = 0.2 MVar.
Post-Outage Voltage Magnitudes for outage of the transformer connected between bus 13 and bus 49 Bus No Voltage magnitudes [p.u.] V pre-outage V PF V DF 11 0.974 0.976 0.977 0.0011 13 0.979 0.985 0.987 0.0016 21 1.009 0.982 0.980 0.0017 48 1.028 0.997 0.995 0.0016 49 1.036 0.978 0.972 0.0056 50 1.024 0.980 0.977 0.0032 51 1.052 1.038 1.036 0.0018 threshold error = 0.0015 p.u. Post-Outage Reactive Power Flows for outage of the transformer connected between bus 12 and bus 13 Reactive Power Flow [MVar] Line pre-outage PF DF l-m lm ml lm ml lm [MVar] ml 3-15 -18.26 13.73-15.59 11.01-17.09 12.53 1.50 1.52 12-13 60.27-64.01 52.49-56.76 50.06-54.46 2.43 2.30 15-45 -0.79 2.15 7.67-5.67 9.33-7.36 1.66 1.69 14-46 27.32-25.39 42.82-39.29 45.93-42.24 3.11 2.95 47-48 12.36-12.26 24.76-24.41 22.71-22.27 2.05 2.14 48-49 -7.40 6.95 5.93-6.10 4.31-4.20 1.62 1.90 50-51 -6.16 6.51-13.25 14.53-11.84 13.35 1.41 1.18 10-51 12.47-11.81 21.06-19.83 23.24-21.98 2.18 2.15 threshold error = 1.0 MVar.