Publications

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In this work, we show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. In conclusion, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone.

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This document summarizes research performed under the Laboratory Directed Research and Development (LDRD) project titled Developing Fugitive Emissions Sensor Networks: New Optimization Algorithms for Monitoring, Measurement and Verification. The purpose of this project is to develop methods and software to enhance detection programs through optimal design of the sensor network. This project includes both software development and field work. While this project is focused on methane emissions, the sensor placement optimization framework can be applied to a wide range of applications, including the placement of water quality sensors, surveillance cameras, fire and chemical detectors. This research has the potential to improve national security by improving the way sensors are deployed in the field.

We present novel stochastic optimization models to improve power systems resilience to extreme weather events. We consider proactive redispatch, transmission line hardening, and transmission line capacity increases as alternatives for mitigating expected load shed due to extreme weather. Our model is based on linearized or "DC" optimal power flow, similar to models in widespread use by independent system operators (ISOs) and regional transmission operators (RTOs). Our computational experiments indicate that proactive redispatch alone can reduce the expected load shed by as much as 25% relative to standard economic dispatch. This resiliency enhancement strategy requires no capital investments and is implementable by ISOs and RTOs solely through operational adjustments. We additionally demonstrate that transmission line hardening and increases in transmission capacity can, in limited quantities, be effective strategies to further enhance power grid resiliency, although at significant capital investment cost. We perform a cross validation analysis to demonstrate the robustness of proposed recommendations. Our proposed model can be augmented to incorporate a variety of other operational and investment resilience strategies, or combination of such strategies.

Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. Furthermore, this approach opens the door for global solution of MINLP problems with AC power flow equations.

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State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. To improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding–blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.

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The solution of the Optimal Power Flow (OPF) and Unit Commitment (UC) problems (i.e., determining generator schedules and set points that satisfy demands) is critical for efficient and reliable operation of the electricity grid. For computational efficiency, the alternating current OPF (ACOPF) problem is usually formulated with a linearized transmission model, often referred to as the DCOPF problem. However, these linear approximations do not guarantee global optimality or even feasibility for the true nonlinear alternating current (AC) system. Nonlinear AC power flow models can and should be used to improve model fidelity, but successful global solution of problems with these models requires the availability of strong relaxations of the AC optimal power flow constraints. In this paper, we use McCormick envelopes to strengthen the well-known second-order cone (SOC) relaxation of the ACOPF problem. With this improved relaxation, we can further include tight bounds on the voltages at the reference bus, and this paper demonstrates the effectiveness of this for improved bounds tightening. We present results on the optimality gap of both the base SOC relaxation and our Strengthened SOC (SSOC) relaxation for the National Information and Communications Technology Australia (NICTA) Energy System Test Case Archive (NESTA). For the cases where the SOC relaxation yields an optimality gap more than 0.1 %, the SSOC relaxation with bounds tightening further reduces the optimality gap by an average of 67 % and ultimately reduces the optimality gap to less than 0.1 % for 58 % of all the NESTA cases considered. Stronger relaxations enable more efficient global solution of the ACOPF problem and can improve computational efficiency of MINLP problems with AC power flow constraints, e.g., unit commitment.