Renewable energy, such as wave energy, plays a significant role in sustainable energy development. Wave energy represents a large untapped source of energy worldwide and potentially offers a vast source of sustainable energy. We present models and a heuristic algorithm for choosing optimal locations of wave energy conversion (WEC) devices within an array, or wave farm. The location problem can have a significant impact on the total power of the farm due to the interactions among the incident ocean waves and the scattered and radiated waves produced by the WECs. Depending on the nature of the interference (constructive or destructive) among these waves, the wave energy entering multiple devices, and thus the power output of the farm, may be significantly larger or smaller than the energy that would be seen if the devices were operating in isolation. Our algorithm chooses WEC locations to maximize the performance of a wave farm as measured by a well known performance measure called the q-factor, which is the ratio of the power from an array of N WECs to the power from N WECs operating independently, under the point absorber approximation. We prove an analytical optimal solution for the 2-WEC problem and, based on the properties of the 2-WEC solution, we propose an iterative heuristic optimization algorithm for the general problem.

The inherent uncertainty of renewable energy sources (RES) makes the solution to the electricity network's associated economical dispatch (ED) problem with network constraints challenging. In particular, the uncertainty in the power output of RES requires conventional generation units to ramp up and down more frequently to maintain the power balance and the reliability of the system. Typically, the RES power output uncertainty is modeled in ED problems by considering its potential future scenarios. However, this leads to an optimization problem that is difficult to solve for real-sized networks. Here, we propose an alternative way of considering the uncertainty of RES and the consequent ramping of conventional generation via a robust reformulation of the problem. In particular, we show that in typical real-world instances of the ED problem, the associated deterministic formulation of the robust problem can be solved efficiently for larger scale constrained electricity networks even when the underlying uncertainty distribution is not normal. Moreover, we show that our approach results on dispatch solutions that require less ramping than scenario-based solutions, with little trade-off on the long-term expected costs of the network dispatch. These results also provide insights about how RES penetration affects cost and dispatch policies in the electricity network. To illustrate our results, we present relevant numerical experiments on IEEE test networks.

We present methods for optimizing generation and storage decisions in an electricity network with multiple unreliable generators, each colocated with one energy storage unit (e.g., battery), and multiple loads under power flow constraints. Our model chooses the amount of energy produced by each generator and the amount of energy stored in each battery in every time period in order to minimize power generation and storage costs when each generator faces stochastic Markovian supply disruptions. This problem cannot be optimized easily using stochastic programming and/or dynamic programming approaches. Therefore, in this study, we present several heuristic methods to find an approximate optimal solution for this system. Each heuristic involves decomposing the network into several single‐generator, single‐battery, multiload systems and solving them optimally using dynamic programming, then obtaining a solution for the original problem by recombining. We discuss the computational performance of the proposed heuristics as well as insights gained from the models. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 493–511, 2015

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