A Majorization-Minimization Approach to Design of Power Transmission Networks

We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network efficiency (low power dissipation within the transmission network) and the cost to build the network. We begin with a convex optimization method based on the paper ``Minimizing Effective Resistance of a Graph'' [Ghosh, Boyd \& Saberi]. We show that this (DC) resistive network method can be adapted to the context of AC power flow. However, that does not address the combinatorial aspect of selecting network structure. We approach this problem as selecting a subgraph within an over-complete network, posed as minimizing the (convex) network power dissipation plus a non-convex cost on line conductances that encourages sparse networks where many line conductances are set to zero. We develop a heuristic approach to solve this non-convex optimization problem using: (1) a continuation method to interpolate from the smooth, convex problem to the (non-smooth, non-convex) combinatorial problem, (2) the majorization-minimization algorithm to perform the necessary intermediate smooth but non-convex optimization steps. Ultimately, this involves solving a sequence of convex optimization problems in which we iteratively reweight a linear cost on line conductances to fit the actual non-convex cost. Several examples are presented which suggest that the overall method is a good heuristic for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators.Comment: 8 pages, 3 figures. To appear in Proc. 49th IEEE Conference on Decision and Control (CDC '10

A Multi-Objective Planning Framework for Optimal Integration of Distributed Generations

This paper presents an evolutionary algorithm for analyzing the best mix of distributed generations (DG) in a distribution network. The multi-objective optimization aims at minimizing the total cost of real power generation, line losses and CO2 emissions, and maximizing the benefits from the DG over a 20 years planning horizon. The method assesses the fault current constraint imposed on the distribution network by the existing and new DG in order not to violate the short circuit capacity of existing switchgear. The analysis utilizes one of the highly regarded evolutionary algorithm, the Strength Pareto Evolutionary Algorithm 2 (SPEA2) for multi-objective optimization and MATPOWER for solving the optimal power flow problems

Phase transitions in project scheduling.

The analysis of the complexity of combinatorial optimization problems has led to the distinction between problems which are solvable in a polynomially bounded amount of time (classified in P) and problems which are not (classified in NP). This implies that the problems in NP are hard to solve whereas the problems in P are not. However, this analysis is based on worst-case scenarios. The fact that a decision problem is shown to be NP-complete or the fact that an optimization problem is shown to be NP-hard implies that, in the worst case, solving it is very hard. Recent computational results obtained with a well known NP-hard problem, namely the resource-constrained project scheduling problem, indicate that many instances are actually easy to solve. These results are in line with those recently obtained by researchers in the area of artificial intelligence, which show that many NP-complete problemsexhibit so-called phase transitions, resulting in a sudden and dramatic change of computational complexity based on one or more order parameters that are characteristic of the system as a whole. In this paper we provide evidence for the existence of phase transitions in various resource-constrained project scheduling problems. We discuss the use of network complexity measures and resource parameters as potential order parameters. We show that while the network complexity measures seem to reveal continuous easy-hard or hard-easy phase-transitions, the resource parameters exhibit an easy-hard-easy transition behaviour.Networks; Problems; Scheduling; Algorithms;

Cost Forecasting Model of Transmission Project based on the PSO-BP Method

In order to solve being sensitive to the initial weights, slow convergence, being easy to fall into local minimum and other problems of the BP neural network, this paper introduces the Particle Swarm Optimization (PSO) algorithm into the Artificial Neural Network training, and construct a BP neural network model optimized by the particle swarm optimization. This method can speed up the convergence and improve the prediction accuracy. Through the analysis of the main factors on the cost of transmission line project, dig out the path and lead factors, topography and meteorological factors, the tower and the tower base materials and other factors. Use the PSO-BP model for the cost forecasting of transmission line project based on historical project data. The result shows that the method can predict the cost effectively. Compared with the traditional BP neural network, the method can predict with higher accuracy, and can be generalized and applied in cost forecasting of actual projects