Structure-exploiting interior point methods for security constrained optimal power flow problems
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The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods (IPM). Firstly, we consider a DC-SCOPF model, which is a linearized version of AC-SCOPF. One new reformulation of the DC-SCOPF model is suggested, in which most matrices that need to be factorized are constant. Consequently, most numerical factorizations and a large number of back-solve operations only need to be performed once throughout the entire IPM process. In the framework of the structure-exploiting IPM implementation, one of the major computational efforts consists of forming the Schur complement matrix, which is very computationally expensive if no further measure is applied. One remedy is to apply a preconditioned iterative method to solve the corresponding linear systems which appear in assembling the Schur complement matrix. We suggest two main schemes to pick a good and robust preconditioner for SCOPF problems based on combining different “active” contingency scenarios. The numerical results show that our new approaches are much faster than the default structure-exploiting method in OOPS, and also that it requires less memory. The second part of this thesis goes to the standard AC-SCOPF problem, which is a nonlinear and nonconvex optimization problem. We present a new contingency generation algorithm: it starts with solving the basic OPF problem, which is a much smaller problem of the same structure, and then generates contingency scenarios dynamically when needed. Some theoretical analysis of this algorithm is shown for the linear case, while the numerical results are exciting, as this new algorithm works for both AC and DC cases. It can find all the active scenarios and significantly reduce the number of scenarios one needs to contain in the model. As a result, it speeds up the solving process and may require less IPM iterations. Also, some heuristic algorithms are designed and presented to predict the active contingencies for the standard AC-SCOPF, based on the use of AC-OPF or DC-SCOPF. We test our heuristic algorithms on the modified IEEE 24-bus system, and also present their corresponding numerical results in the thesis.