Distribution System Optimization on Graphics Processing Unit

Power distribution networks operate in a radial topology, but also include extra tie switches to allow for their reconfiguration in case of scheduled maintenance or unexpected failure. With the implementation of the smart grid and the development of fast high power switching devices, it is now possible to automatize this reconfiguration to also adjust to demand fluctuation and always operate the network in the optimal topology, minimizing power transmission losses. This automation requires the development of highly efficient and powerful optimization algorithms that can compute the optimal configuration with minimum delay. This paper presents a parallel genetic algorithm on graphics processing unit for distribution feeder reconfiguration. By exploiting the massively parallel architecture of graphics processors, the execution time of the solver is reduced by a factor of 66.2×, resulting in a very fast solver. Moreover, the metaheuristic uses a unique solution encoding based on the minimum spanning tree to maintain the radial structure of the candidate topologies. This novel encoding drastically improves the effectiveness of the genetic algorithm and allows for the optimal reconfiguration of networks up to 4400 buses; five times larger than any of the references surveyed.

I. Introduction

The power distribution network is the last stage in the delivery of electricity. It connects the distribution substations to the customers. Typically arranged in a radial topology, distribution networks include additional tie switches to allow for the reconfiguration of the network in case of planned maintenance, unexpected failure or demand fluctuation. An example of a 16-bus distribution network in shown in Figure 1. With the upgrade of the power infrastructure and the implementation of the smart grid, it is possible to automatize the network reconfiguration in order to always operate in a highly optimal topology minimizing outage time, power transmission losses and ultimately, operating costs. As explained in [1], this motivates the development of algorithms capable of calculating the network reconfiguration in real-time in order to quickly react to changes, especially following a hardware fault in order to minimize down time. Yet, calculating this optimal topology is not trivial. In fact, the distribution feeder reconfiguration (DFR) problem is a large-scale, non-convex, non-linear, combinatorial optimization problem. It can be formulated as finding the radial topology that:

$$\begin{align}&{\mathrm{ minimizes}}\notag \\&\qquad \qquad \qquad f\left ({\bar {x}}\right )=\mathop {\sum }\nolimits _{i=1}^{N_{branches}} P_{loss~i} \\&{\mathrm{ subject~to}}\notag \\&\left |{V_{i} }\right |_{min} \le \left |{V_{i} }\right |\le \left |{V_{i} }\right |_{max} \quad {\mathrm{ for}}~ i=1toN_{buses} \\&\quad ~ \left |{S_{i} }\right |\le \left |{S_{i~max} }\right | \qquad \quad ~~ {\mathrm{ for}}~ i=1,\ldots ,N_{branches} \end{align}$$ where is the solution vector (topology of the network), are the real power losses on branch , is the voltage magnitude at bus and is the apparent power on branch . , and are the limits on the bus voltage and the branch rating. The biggest challenge in solving the DFR problem is to maintain the radial topology of the network when generating potential solutions. Fig. 1.

16-bus system (dash lines represent open switches).