Risk-based approach to the Optimal Transmission Switching problem

TL;DR

This work addresses secure transmission switching under a risk-based interpretation of the $N-1$ rule, recognizing that some contingencies may necessitate temporarily de-energizing portions of the grid. It introduces a deterministic MILP that couples base-case connectivity with $N-1$ connectivity via a mirror-graph construction, and a DC power-flow-based formulation that balances energized areas while minimizing the expected load losses across contingencies expressed as $\mathfrak{p}_{c}$ and $\langle 1, d-\hat{d}_{c} \rangle$. Key contributions include the principled integration of base-case and N-1 connectivity within an MILP, a Big-M linearization strategy for Hadamard and logical constraints, and the demonstration of the preventive-openings-cascade phenomenon on the IEEE 14-bus system. The approach yields solutions that resemble real operational patterns and provides a framework for evaluating security-cost trade-offs in subtransmission where loss of service to some customers may be acceptable to prevent broader reliability issues.

Abstract

This paper deals with the secure Optimal Transmission Switching (OTS) problem in situations where the TSO is forced to accept the risk that some contingencies may result in the de-energization of parts of the grid to avoid the violation of operational limits. This operational policy, which mainly applies to subtransmission systems, is first discussed. Then, a model of that policy is proposed that complements the classical MILP model of the N-1 secure OTS problem. It comprises a connectivity and notably a partial grid loss analysis for branch outage contingencies. Finally, its application to the IEEE 14-bus system is presented. Solutions similar to those observed in operation are reached by the algorithm, notably revealing the preventive-openings-cascade phenomenon.

Figures (4)

• Figure 1: Preventive-openings-cascade. Each bubble represents a portion of a grid a) the initial pattern; b) after the tripping of $AB$, no overloading and $B$ is secured; c) the preventive opening of $CD$; d) the tripping of $AB$ now leads to an overloading of $AC$; e) the tripping of $AD$ results in an overloading on $CD$ which implies the opening of $BC$ f) final situation avoiding post-contingency overloadings.
• Figure 2: Base without OTS: There is no overflow in the base case. The security analysis reveals that numerous trippings raise an overloading on $ID$.
• Figure 3: Base case with OTS.
• Figure 4: Intermediate case the operator would needed to step into. The branch openings in the northern area solve the constraint on branch $DI$, but raises one on branch $BE$.