Branch Outage Simulation for Contingency Studies. Dr.Aydogan OZDEMIR, Visiting Associate Professor Department of Electrical Engineering, Texas A&M University, College Station TX 77843 Tel : (979) 862 88 97 , Fax : (979) 845 62 59 E-mail : [email protected]
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Aydoğan Özdemir was born in Artvin, Turkey, on January 1957. He received the B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from Istanbul Technical University, Istanbul, Turkey 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 Turkish Electrical Engineering and IEEE.
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
operation of protective devices
and switching of the unit(s)
partial or total loss of load
security constrained opf
Monitoring : Data collection and state estimation
The 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.
SET SYSTEM MODEL TO INITIAL CONDITIONS
SIMULATE AN OUTAGE OF A GENERATOR OR A BRANCH
SELECT A NEW OUTAGE
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.
Full AC power flow for each outage
not feasible for real-time applications.
Check the limit violations
approximate methods to quickly identify conceivable contingencies
AC power flows only for critical contingencies.
Check the limit violations
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.
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
MW line flow overloads
voltage magnitude violations
involves more complicated models
and better computation algorithms
DC load flows
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
Modification of ZBUS is required for each outage
LINE OUTAGE SIMULATION
An outage of a line can either be simulated by setting its impedance, yij = 0 or by injecting hypothetical powers at both ends of the line. The latter method is preferred to preserve the original base case bus admittance matrix.
DC LOAD FLOW :
outage of a line connected between busses i and j
The new real power flow through the line connected between busses n and m can be derived and approximated as,
See “Power Generation, Operation and Control by Wood and Wollenberg” for details
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
Can be split up into two parts,
Transferring reactive power
assumed to flow through the line
Loss reactive power
assumed to allocated
at the busses
Line outage simulation by hypothetical reactive power sources
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.
Transferring 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. Therefore, 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 DQi and DQj. This in turn, will result in a change in system state variables with respect to pre-outage values. This 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. Therefore, part of the fictitious reactive generation flows through the neighboring paths instead circulating through the outaged branch. These reactive power mismatches can mathematically be expressed as,
where Qi and QDi are the net reactive power and the reactive demand at load bus i, is the complex voltage at bus i and Yik is the element of bus admittance matrix. The 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.
This 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=2,3,…, NB
where X is the inverse of the bus suseptance matrix, Pij is the pre-outage active power flow through the line and xk 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,
reactive power flows through the outaged line
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
with respect to . 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
SOLUTION BY GENETIC ALGORITHMS
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. This process leads to the evolution of populations of individuals that are better suited to their environment than the individuals that they were created from.
Generate initial population
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.
BASE CASE LOAD FLOW
SELECT AN OUTAGE
CALCULATE BUS VOLTAGE PHASE ANGLES
CALCULATE THE REMAINING QUANTITIES
IEEE 14-Bus test System
Base case control variables :
PG2 = 0.4 p.u.
PG3 = PG6 = PG8 = 0.0 p.u.
V1 = 1.06 p.u.
V2 = 1.045 p.u.
V3 = 1.01 p.u.
V6 = 1.07 p.u.
V8 = 1.09 p.u.
B9 = 0.19 p.u.
t4-7 = 0.978
t4-9 = 0.969
t5-6 = 0.932
Q7-9 = 27.24 Mvar
Q5-6 = 12.42 MVar
First one is the outage of the line connected between bus-12 and bus-13, whose pre-outage 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