7. Remarks About the Dantzig-Wolfe Scheme

A distributed linear-programming model has been created, developed, implemented, and tested. Two standard IEEE bus systems are modeled and successfully decomposed, in multiple ways, into sub-problems. The problem is solved iteratively in each case and directly supports resource allocation in a Smart-grid environment. I have shown that the LP-based design using the Dantzig-Wolfe decomposition can execute and can quickly determine the primary resource scheduling and allocation issues if a failure occurs in the grid. The decomposition procedure can easily be managed by system operators. In the study using the 4-bus, 14-bus, and 30-bus systems, the results indicate that the computational benefits of the Dantzig-Wolfe approach enable fast responses on the order of a millisecond to a few seconds as network size increases. Although the 30-bus system is not a large bus network, the results clearly indicate a faster computation time if an appropriate Dantzig-Wolfe structure is formulated. This approach can enable system operators in the electric grid to respond to any allocation request for resources in the event of outages or line failures. The book’s key contribution is the design, development, and testing of a procedure that successfully decomposes an optimization problem that is defined over a large grid but can be solved in regional pieces.