M.Sc Student Feldman Raz Optimal Power Flow Solution Using Clustered Networks Department of Electrical Engineering Assistant Professor Yoash Levron Abstract

The changes in the power grid, such as a new network structure containing more distributed energy sources as well as the increase in power demand, have made the complexity of the power systems increase dramatically. Therefore, new optimization algorithms that are more efficient and robust are needed to handle the emerging problems of the smart grid. One such problem is concerned with the optimal transfer of power throughout a network, i.e., the optimal power flow (OPF) problem.

The OPF problem is an optimization problem in which different elements in the system are controlled, e.g., generators and loads, in order to bring some cost function to a minimum while keeping all the different constraints of the problem, e.g., maximum power transferred via a power line, generators capacity, etc. The cost function may combine several objectives, e.g., reducing cost, saving energy, etc. The OPF problem is generally nonlinear, non-convex, contains several different objectives, and may consists of thousands of nodes, thus, making it a large scale, multi-objective optimization problem which is hard to solve efficiently for the general case. Consequently, recent studies have focused on radial networks, since they are usually a good characterization of a practical distribution network and have qualities which make the OPF problem efficiently solvable. Therefore, power network analysis or design algorithms may profit from adopting dedicated algorithms for this type of networks.

In this research thesis, a novel algorithm is proposed in order to solve the OPF problem over radial networks. The proposed algorithm attempts to achieve a globally optimal solution by simplifying the network at hand in order to reduce calculation complexity and solving the simplified problem.

The algorithm utilizes backward/forward sweep methodology which is comprised of the following steps:

1.      One backward sweep where the network is reduced into one elementary node. In order to utilize the network reduction, the clustering technique is used. This method works without the need for approximations, specific data modulations or assumptions about the problem, and performs an exact reduction, i.e., no information about the original system is lost.

2.      Solution of the new optimization problem at the elementary node. The new optimization problem can be solved using a variety of dedicated algorithms, and the proposed algorithm is unbound to a specific solver. Moreover, the algorithm does not require any assumptions concerning the cost function to be optimized, i.e., any arbitrary cost function is acceptable.

3.      One forward sweep where the newfound solution is spread throughout the system as the network expands back to its original configuration.

The algorithm was partially implemented and was compared to Matpower using six radial networks. The proposed algorithm was found to be more reliable than Matpower, where the percentage of times where the algorithm succeeds to find a solution while Matpower fails, have reached above 39%. In addition, the proposed algorithm was found to yield equal or better results than Matpower, where the typical improvement is of 2%-5%. However, in fatal cases the improvement may reach over 500%.