Optimal restoration of distribution systems using the Lagrangian dual relaxation

This thesis concerns the restoration of electric power distribution systems after a total blackout. The restoration process returns the system back to normal operation after any combination of system components have been lost due to an outage. During restoration, the system operator executes a set of actions that progressively mitigate the outage. These actions aim at minimizing the impact of the outage on the final user without compromising the security and operability of the system.; The approach taken is to describe the restoration problem as an optimization process with the objective of minimizing the outage impact (e.g. cost) subject to suitable constraints. Two optimization methods are discussed along with the presentation of examples of these methods. The optimization approaches taken include Lagrangian relaxation and dynamic programming. The proposed algorithms provide a step-by-step restoration plan for radial distribution systems after a blackout. The dynamic programming solution gives excellent results in an exhaustive solution but may not be suitable for large systems. The unsuitability of dynamic programming is related to the 'curse of dimensionality' which causes dynamic programming solutions to require excessive execution time. The intent is to perform the restoration in operational real time, and therefore a second optimization method is used. This is the method of Lagrangian relaxation. Lagrangian relaxation is similar to the method of Lagrange multipliers, except that special cases of the values of the control variables are used. The method requires some skill in programming, and this thesis gives the details of this skill.; The Lagrangian relaxation method uses the subgradient method to calculate the Lagrange multipliers. The LR formulation is found to render the approach suitable for large problems. The restoration algorithm is an operator permissive approach and is intended to assist the operator during restoration. A restoration index is also shown. The restoration index may be very useful in restoring the system as it gives a rapid indication of the feeder status during restoration. The subgradient based LR solution is found to have favorably fast computation speed and low storage requirements. In contrast, the subgradient may present convergence problems in some cases.