Aurelio Oliveira – UNICAMP Silvia Maria S. Carvalho - UFSCar Silvia Maria S. Carvalho - UFSCar Christiano Lyra- UNICAMP

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MPI Aplicados ao Problema de Pr-Despacho com Manobras

Interior Point Methods Applied to Predispatch with Network Topology Manipulation Covering Bus and Transmission Lines SimultaneouslyAurelio Oliveira UNICAMP Silvia Maria S. Carvalho - UFSCarChristiano Lyra- UNICAMP

1Brazilian SystemInterconnected SystemPredominantly HydroelectricLarge ReservoirsIsolated Systems 300 isolated locationsPredominantly Thermoelectric2National Interconnected System Interconnections with about 84,000 kilometers of power lines;Long transmission lines

3Why IPM?Good performance on large problemsRobust method;Fast convergence.

Primal-Dual IPMit is more efficient;Starting Point need not be feasible.

4PredispatchOperational ProblemShort-Term;Meet demands and targets;

ModelMinimization of a quadratic function;Linear Constraints5Dynamic Primal Model

6 Dual

7Optimality ConditionsPrimal Feasibility

Dual Feasibility

Complementarity conditions

8 Newton MethodApplying Newton's method:Jd=r

Where9The directions from NewtonVariable substitution

10System to be solved

11Matrix structure study for the problem with modification in the network topologyAssuming that there were pre-programmed modification in the network topology i;

The matrix B is no longer constant;

Each modification performed, one row and one column of the matrix B are removed (inserted);

ModificationsThe modifications are conducted in an attempt to adapt the transmission network to the load change

They are usually held four to six modifications per day for the Brazilian System

13Types of ModificationsLines Modification;

Bus Modification;

Line and Bus Modifications.

14Lines ModificationsA branch is removed from the system

The network topology is modifiedIncidence and reactance matrix are modifiedManeuvers BarsShutdown of a plant

Shutdown of a consumer center;

Change in demand.

Simultaneous Bus and Lines ManipulatonsThe bus and line manipulations executed simultaneously characterize more complex changes in the network.

A greater number of rows and columns from the incidence matrix and their respective reactances are removed.ImplementationManipulations are given data;

studied networks IEEE30 and IEEE118BRAZIL1993 and BRAZIL351118Data from experimentsVariable Number of ManipulationsDeveloped in MatlabAccuracy 10-3Intel centrino core 2 duo4 GB of RAMSpeed 2.13GHZ19Initial Point

20 IEEE30 System

21Sistema IEEE118

BRAZIL 1993 System

23 Brazil 3511 System Real brazilian system

24Bus and Lines Modifications IEEE30 System

Bars and Lines Manipulations IEEE118 System

Bars and Lines Manipulations Brazil 1993 System

ConclusionsFrom the computational point of view, the effort to solve a problem with or without such modifications on the network topology is similar;

B matrix can be factored before the interior point methods application; The results obtained showed the adequacy of the methodology. .