Optimal transmission expansion via intrinsic properties of power flow conditioning

In a period with the potential for major bulk power system transmission expansion in the U.S., many traditional transmission planning methodologies are proving insufficient to the task. The huge degree of uncertainty as to the types and geographic placement of significant new generation sources introduce tremendous scenario uncertainty into approaches that seek to optimize long time horizon production costs. Drawing on analogies to the network routing/congestion minimization problem in data networks, this work proposes a fundamentally new paradigm for optimal transmission expansion, focusing solely on properties of the transmission network itself. In particular, we adopt the condition number of the power flow Jacobian (or its dc approximation, the B susceptance matrix) as an intrinsic measure of the robustness of transmission network. Recent results regarding condition number optimization in symmetric matrices confirm that an efficient strategy should focus on successively increasing the smallest eigenvalue(s) of the bus susceptance matrix B. Exploiting the special graph-related eigenvalue/eigenvector structure of Laplacian matrices (such as B), this work will show that eigenvalue derivative techniques yield efficient heuristic algorithms for successively locating and sizing transmission addition(s) that significantly improve condition number of B. Two proposed heuristics are demonstrated on the IEEE 14 bus, 30 bus, 57 bus and 118 bus test systems.