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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]

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

limit violation(s)

operation of protective devices

and switching of the unit(s)

partial or total loss of load

contingency analysis

security constrained opf

POWER SYSTEM

SECURITY

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.

START

SET SYSTEM MODEL TO INITIAL CONDITIONS

SIMULATE AN OUTAGE OF A GENERATOR OR A BRANCH

N

SELECT A NEW OUTAGE

Y

ALARM MESSAGE

N

LAST OUTAGE

Y

END

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

Exact solution

not feasible for real-time applications.

Check the limit violations

approximate methods to quickly identify conceivable contingencies

real-time applications

AC power flows only for critical contingencies.

Check the limit violations

APPROXIMATE CONTINGENCY ANALYSIS

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 ranking

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

both

MW line flow overloads

voltage magnitude violations

involves more complicated models

and better computation algorithms

DC load flows

Sensitivity factors

j

j

i

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

Z-Matrix techniques

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.

i

Sij=0

Sji=0

j

SIMULATION FOR MW LINE FLOW PROBLEM

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

SIMULATION FOR VOLTAGE MAGNITUDE 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

j

i

Qij

Qji

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

bij

bus j

bus i

bus j

bij

Line outage simulation by hypothetical reactive power sources

i

j

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

SOLUTION OF THE CONSTRAINED OPTIMIZATION 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

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

selection

crossover

mutation

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.

evaluate objective

function

N

optimization

criteria

met

Y

best

individuals

result

i

outaged branch

BASE CASE LOAD FLOW

SELECT AN OUTAGE

bounded network

CALCULATE BUS VOLTAGE PHASE ANGLES

CALCULATE THE REMAINING QUANTITIES

END

G

3

2

G

1

5

4

G

8

7

G

6

11

10

9

12

13

14

NUMERICAL EXAMPLES

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

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