A geometric approach for three-phase load balancing in distribution networks

In the proposed method, each loop in a network is represented as a circle, which is derived from the relationship between the change of load balancing due to the branch-exchange and the power-flows in the branches. If there is no change of load balancing in the system, then all the circles touch each other at the (0,0) coordinate. The circles with no load balancing are called zero load balancing change circles. The maximum load balancing loop in the network is identified by comparing the radii of all the modified zero load balancing change circles. The corresponding loop of the largest one gives the maximum improvement of load balancing in the network. Then the possible branch exchanges in the maximum load balancing loop are investigated by comparing the size of the circle for every branch-exchange. If the loads are balanced due to a branch exchange, the size of the circle diminishes and hence the smallest circle gives the maximum improvement in load balancing and the corresponding branch-exchange is considered to be the best candidate for maximum improvement in load balancing. To show the efficiency and performance of the proposed method for the solution of computationally complex and large dimensionality problems, a system with 69-bus and 7 laterals has been considered as the test system. Test results have shown that the proposed method can identify the most effective branch-exchange operations for load balancing with less computational effort and time. The number of load flow solutions has been reduced to a greater extent in the proposed method