Abstract-We consider a static wind model for a three-bladed, horizontal-axis, pitch-controlled wind turbine. When placed in a wind field, the turbine experiences several mechanical loads, which generate power but also create structural fatigue. We address the problem of finding blade pitch profiles for maximizing power production while simultaneously minimizing fatigue loads. In this paper, we show how this problem can be approximately solved using convex optimization. When there is full knowledge of the wind field, numerical simulations show that force and torque RMS variation can be reduced by over 96% compared to any constant pitch profile while sacrificing at most 7% of the maximum attainable output power. Using iterative learning, we show that very similar performance can be achieved by using only load measurements, with no knowledge of the wind field or wind turbine model.

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SUMMARYThis work considers a portfolio of units for electrical power production and the problem of utilizing it to maintain power balance in the electrical grid. We treat the portfolio as a graph in which the nodes are distributed generators and the links are communication paths. We present a distributed optimization scheme for power balancing, where communication is allowed only between units that are linked in the graph. We include consumers with controllable consumption as an active part of the portfolio. We show that a suboptimal, but arbitrarily good power balancing, can be obtained in an uncoordinated, distributed optimization framework, and we argue that the scheme will work even if the computation time is limited. We further show that our approach can tolerate changes in the portfolio, in the sense that increasing or reducing the number of units in the portfolio requires only local updates. This ensures that units experiencing faults or need for maintenance can be removed from the graph without affecting the overall performance or convergence of the optimization. The results are illustrated by numerical case studies. Copyright © 2014 John Wiley & Sons, Ltd.

In this work, we address the problem of optimizing the electrical consumption patterns for a community of closely located households, with a large degree of flexible consumption, and further some degree of local electricity production from solar panels. We describe optimization methods for coordinating consumption of electrical energy within the community, with the purpose of reducing grid loading and active power losses. For this we present a simplified model of the electrical grid, including system losses and capacity constraints. Coordination is performed in a distributed fashion, where each consumer optimizes his or her own consumption pattern, taking into account both private objectives, specific to each individual consumer, as well as objectives common to all consumers. In our work, the common objective is to minimize active losses in the grid, and ensure that grid capacity limits are obeyed. These objectives are enforced by coordinating consumers through a nonlinear penalty on power consumption. We present simulation test-cases, illustrating that significant reduction of active losses, can be obtained by such coordination. The distributed optimization algorithm employs the alternating directions method of multipliers.Index Terms-Alternating direction method of multipliers (ADMM), consumer behavior, distributed networks, energy management, smart grid.

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