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Robust and Distributed Approaches to Power System Optimization


J. Warrington


This dissertation describes optimization-based approaches to improving the short- run efficiency of electrical power systems that operate under uncertainty, in particular uncertainty arising from large quantities of intermittent renewable energy. Its contributions fall into two categories. First, robust optimization and control principles are used to define a new approach to the provision of electrical reserves, which maintain power system integrity under uncertainty. This approach relies on commitments referred to as affine reserve policies, which are planned multi-stage responses to uncertainty, chosen by solving an optimization problem based on the current system state and forecast information. For each participating device (such as a generator, energy storage unit, deferrable load, or curtailable wind farm) the policy consists of a nominal schedule plus a system of time-coupled adjustments that act when the values of uncertain variables are discovered in future time steps. These uncertain variables may model any random parameter affecting system operation, but may most usefully model poorly- predicted intermittent renewable energy infeeds, and the optimization framework exploits the fact that these uncertainties are typically correlated in time. The resulting reserve policies are guaranteed to be feasible for every realization of the uncertainty (within some assumed bounds) that could arise. Affine reserve policies are shown via numerical experiments to have two key benefits. The first is that they are able to reduce the dynamic component of system costs, such as those associated with generator ramping, by planning more systematically how the sequence of operating points will be adjusted when uncertainties are discovered. The result of this is that the total cost of making the power system robust to disturbances is reduced. The second benefit is obtained when the policy optimization is coupled with a unit commitment (generator switching decision) problem. In this case it is found that the use of expensive peaking generators may often be reduced, owing to the fact that time-coupled policies make the control of conventional generators and energy storage less conservative. In addition, it is reported that the reserve policy optimization problem can be solved for large problem instances by using distributed optimization approaches. This is facilitated by the linear structure of the constraints, which allow the interests of individual participating devices to be separated from those of the network operator via a price-like function. Second, distributed optimization principles are used to propose price clearing mech- anisms which are able to solve Optimal Power Flow (OPF) problems efficiently over a finite planning horizon. The pricing mechanisms are based on dual ascent algo- rithms, which have the interpretation of a price negotiation between the various market participants coordinated by a market operator, who adjusts prices until an optimal utilization of the generation and storage assets is obtained. Convergence of the method is guaranteed by ensuring that the characteristics of the participants adhere to the generic convexity assumptions upon which convergence proofs of subgradient algorithms are based. The market model is characterized by an arbitrary number of independent, profit- or utility-maximizing, price-taking participants. These are constrained by an alternating-current (AC) transmission network of arbitrary topology, in which real and reactive power flows, voltages, and power flows must satisfy various constraints. The algorithm makes use of a recently- discovered tight semidefinite relaxation of the static OPF problem, and heuristic approaches are used to improve the convergence speed significantly. A market operation mode based on a receding horizon (also known as rolling win- dow) principle is then described, as a logical extension of existing electricity markets that increasingly resort to intra-day trading in order to accommodate fluctuating renewable infeeds. This mechanism enables adjustments to the schedules of market participants to be made in the light of constantly-updating nominal forecasts of these infeeds, by conducting a re-negotiation of their actions. Such an approach can reduce system costs by allowing generator ramping actions and the operation of energy storage to be re-planned more effectively than under existing redispatch mechanisms.

Further Information

Type of Publication:

(03)Ph.D. Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2013:IFA_4997,
    author={J. Warrington},
    title={{Robust and Distributed Approaches to Power System
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