Optimization in electrical distribution systems: Discrete Ascent Optimal Programming
This dissertation presents a new algorithm for optimal power flow in distribution systems. The new algorithm, Discrete Ascent Optimal Programming (DAOP), will converge to the same solution as the Lagrange multiplier approach as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. Because no partial derivatives, solutions of simultaneous equations, or matrix operations are required, the DAOP algorithm is simple to apply and program. DAOP is especially suited for programming with pointers. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required to reach a solution.
In addition to optimal power flow, the algorithm, heuristic in nature, can be applied to switch placement design, reconfiguration, and economic dispatch. The basic principles of the algorithm have been used to devise a phase balancing routine which has been implemented in the Distribution Engineering Workstation (DEWorkstation) software package sponsored by the Electric Power Research Institute (EPRI).
The new algorithm presented in this dissertation works toward a solution by performing a series of calculations within a finite number of steps. At the start of the algorithm, the assumption is made that no power is flowing in the system. Each step adds a discrete unit of load to the system in such a fashion as to minimize loss. As progress toward the solution is made, more and more load is satisfied and the losses in the system continue to increase. The algorithm is terminated when all system load is satisfied. When the algorithm is finished, the sources which should supply each load have been identified along with the amount of power delivered by each source. Discussion will show that the method will converge to a solution that is within the discrete step size of the optimum.
The algorithm can be thought of as an ascent method because the cost (losses) continually increases as more and more load is satisfied. Hence, the name Discrete Ascent Optimal Programming (DAOP) has been given to the algorithm.
The new algorithm uses the topology of the power system such that the entire system is not considered at each step. Therefore, DAOP is not an exhaustive state enumeration scheme. Only those portions of the system containing loads most closely connected (via least loss paths) to the sources are first considered. As loads become supplied during the course of the solution, other loads are considered and supplied until the system is fully loaded.