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# Solving optimal power flow with voltage constraints using MATLAB optimization toolbox

Mijatovic, Aaron (2013) Solving optimal power flow with voltage constraints using MATLAB optimization toolbox. Other thesis, Murdoch University.

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## Abstract

This thesis set out to build a program in MATLAB that is designed to find an optimal power flow system on that minimizes the cost of generation while satisfying prescribed voltage constraints.

Current optimal power flow solutions generally have three main issues with optimal power flow and this is the direction of most research in the area. The first issue is that the systems are not able to robustly provide a solution to the given information and are unable to find a stable solution. The second issue is that the optimal power flow may only find a local minimum solution rather than a global minimum due to the nature of the optimization routines. The third and final issue is that the solve time needs to be kept to a minimum to ensure usability in real world systems.

The system was built in MATLAB using the Optimization Toolbox, and specifically the fmincon function. The system accepted some basic input variables including a formatted numerical description of the power network, and then performed some calculations to prepare the system for solving. The system was then solved according to Economic Dispatch which determined that the sum of generation should equal the sum of the load. Losses were ignored and new starting variables for the generators where determined. These starting variables were passed into a Gauss-Seidel iterative method which solved the new bus voltages and reactive generation for each of the generators. The objective function for fmincon was set to minimise the cost of the generators, and the constraint function was set to the Gauss-Seidel iteration. Buses were given lower and upper constraints and generator constraints were set from the minimum and maximum given in initialization. Fmincon was then called and solved for minimum cost according to stable constraints.

The system was able to solve this problem the optimal power flow and provide an appropriate solution. However it was not determined whether the solution was a global minimum, or simply a local one. Stability was determined by the generators and buses being within their limits and a voltage stability index was determined. Different starting positions determined that using the economic dispatch provided the cheapest solution and produced a stable outcome.

This thesis provides strong starting point for further expansion into the field of optimal power flow. The program provides a solution and is set to certain stability constraints. Adding new constraints, or increasing the size of the system is easily possible by the user.

Item Type: Thesis (Other) School of Engineering and Information Technology Crebbin, Gregory http://researchrepository.murdoch.edu.au/id/eprint/21660
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