Semidefinite relaxations in optimal experiment design with application to substrate injection for hyperpolarized MRI

We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this problem as the maximization of a (non-concave) quadratic function over the space of inputs, and use semidefinite relaxation techniques to efficiently find the global solution or to provide an upper bound. This investigation is motivated by a problem in medical imaging, specifically designing a substrate injection profile for in vivo metabolic parameter mapping using magnetic resonance imaging (MRI) with hyperpolarized carbon-13 pyruvate. In the l2-norm-constrained case, we show that the relaxation is tight, allowing us to efficiently compute a globally optimal injection profile. In the l1-norm-constrained case the relaxation is no longer tight, but can be used to prove that the boxcar injection currently used in practice achieves at least 98.7% of the global optimum.Comment: 6 pages, Accepted to ACC 201

Optimal active and reactive power dispatch in a distribution network with high PV penetration

Includes bibliographical references.2019 Summer.Integration of rooftop photovoltaic (PV) panels at the distribution network is on the rise. This trend is in part due to the global concerns for climate change as well as the need to find an alternative source of energy. However, if not properly coordinated, deploying renewable energy resources such as solar energy in the power grid can introduce challenges of its own. For instance, high penetration levels of PV may lead to overvoltage conditions, which can in turn cause additional stress on electrical components. In order to cope with such challenges, the operation of the distribution system has to be optimized while considering PV resources. Since irradiance at the ground level and daily load variations are stochastic in nature, a probabilistic approach is needed in order to provide a complete picture. This is what has been proposed in the current document. In this proposal, PV panels are assumed to contribute to reactive power support of the power grid, in addition to active power injection. Also, a centralized control of the distribution system is adopted. The controllable elements considered are voltage regulating transformers (voltage regulators), switching capacitors, load curtailment (or demand response), and the active and reactive powers provided by PV panels. The objective is to control the above devices in order to achieve operational goals such as improving system losses and the voltage profile, to name a few. A metaheuristic approach is used first to solve the problem. However, in order to improve the accuracy and reduce the convergence time, an analytical alternative is then proposed to optimize the performance of distribution system while considering photovoltaic integration