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This 20-minute presentation will highlight uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements.
This work discusses recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a study on a monoethanolamine (MEA)-based CO2 absorption flowsheet is presented. (Near-)robust feasible designs for CO2 absorption flowsheet at high carbon capture are obtained with the PyROS solver. The results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.
Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.
Severe geomagnetic disturbances (GMDs) increase the magnitude of the electric field on the Earth’s surface (E-field) and drive geomagnetically-induced currents (GICs) along the transmission lines in electric grids. These additional currents can pose severe risks, such as current distortions, transformer saturation and increased reactive power losses, each of which can lead to system unreliability. Today several mitigation actions (e.g., changing grid topology) exist that can reduce the harmful GIC effects on the grids. Making such decisions can be challenging, however, because the magnitude and direction of the E-field are uncertain and non-stationary. In this paper, we model uncertain E-fields using the distributionally robust optimization (DRO) approach that determines optimal transmission grid operations such that the worst-case expectation of the system cost is minimized. We also capture the effect of GICs on the nonlinear AC power flow equations. For solution approaches, we develop an accelerated column-and-constraint generation (CCG) algorithm by exploiting a special structure of the support set of uncertain parameters representing the E-field. Extensive numerical experiments based on “epri-21” and “uiuc-150” systems, designed for GMD studies, demonstrate (i) the computational performance of the accelerated CCG algorithm, (ii) the superior performance of distributionally robust grid operations that satisfy nonlinear, nonconvex AC power flow equations and GIC constraints, in comparison with standard stochastic programming-based methods during the out-of-sample testing.
The integration of large-scale uncertain and uncontrollable wind and solar power generation has brought new challenges to the operations of modern power systems. In a power system with abundant water resources, hydroelectric generation with high operational flexibility is a powerful tool to promote a higher penetration of wind and solar power generation. In this paper, we study the day-ahead scheduling of a thermal-hydro-wind-solar power system. The uncertainties of renewable energy generation, including uncertain natural water inflow and wind/solar power output, are taken into consideration. We explore how the operational flexibility of hydroelectric generation and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under a multistage robust optimization (MRO) framework. To address the computational issue, mixed decision rules are employed to reformulate the original MRO model with a multi-level structure into a bi-level one. Column-and-constraint generation (C &CG) algorithm is extended into the MRO case to solve the bi-level model. The proposed optimization approach is tested in three real-world cases. Furthermore, the computational results demonstrate the capability of hydroelectric generation to promote the accommodation of uncertain wind and solar power.
This 20-minute presentation highlights uncertainty and technical risk reduction capabilities in CCSI2, especially intrusive methods: model-based design of experiment and robust optimization.
Critical energy infrastructure are constantly under stress due to the ever increasing disruptions caused by wildfires, hurricanes, other weather related extreme events and cyber-attacks. Hence it becomes important to make critical infrastructure resilient to threats from such cyber-physical events. However, such events are hard to predict and numerous in nature and type and it becomes infeasible to make a system resilient to every possible such cyber-physical event. Such an approach can make the system operation overly conservative and impractical to operate. Furthermore, distributions of such events are hard to predict and historical data available on such events can be very sparse, making the problem even harder to solve. To deal with these issues, in this paper we present a policy-mode framework that enumerates and predicts the probability of various cyber-physical events and then a distributionally robust optimization (DRO) formulation that is robust to the sparsity of the available historical data. The proposed algorithm is illustrated on an islanded microgrid example: a modified IEEE 123-node feeder with distributed energy resources (DERs) and energy storage. Simulations are carried to validate the resiliency metrics under the sampled disruption events.
Three optimality criteria for convolutional codes are considered in this correspondence: namely, free distance, minimum distance, and distance profile. Here we report the results of computer searches for rate one-half binary convolutional codes that are 'robustly optimal' in the sense of being optimal for one criterion and optimal or near-optimal for the other two criteria. Comparisons with previously known codes are made. The results of a computer simulation are reported to show the importance of the distance profile to computational performance with sequential decoding.
Recent microstructure characterization techniques combined with Symbolic Regression(SR)analysis has been proven to generate white box plasticity models well suited for incorporation into FEA software.The current work builds upon those efforts and demonstrates the applicability of Sequential Monte-Carlo (SMC) methods within SR analysis to condense model development and robust optimization into a single, co-dependent process. In this project, SMC methods provide a mechanism through which the observed microstructure features and associated variability can be incorporated into the discovery phase of model development and simultaneously recover approximate parameter distributions through SR analysis. The demonstration utilized a data set consisting of tensile test results from a limited number of sample specimens with corresponding EBSD data from which microstructure features were characterized.The maximum threshold stress model in the Visco-Plastic Self-Consistent (VPSC) code developed by Los Alamos National Laboratories was calibrated using mechanical test data.Synthetic volume elements with statistically equivalent microstructure were generated with DREAM3Dbased on the observed EBSD data. VPSC was used to simulate the corresponding tensile test response for each of the synthetic volume elements. The simulated microstructure and tensile test data was used astraining datafor SMC-SR algorithm and the resulting model was validated with data from the original empirical data set.
All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables. The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties. In this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection. A procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness. This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.
Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k B T c ≈ 6.5 (where Δ is the pairing gap and T c is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N0 and the height of the jump δγ(T c ) in the coefficient γ of the fermionic specific heat at T c are strongly peaked. In the cuprates, δγ(T c ) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T c ) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T c .
The robustness of an atomic fountain interferometer with respect to variations in the initial velocity of the atoms and deviations from the optimal pulse amplitude is examined. We numerically simulate the dynamics of an interferometer in momentum space with a maximum separation of and map out the expected signal contrast depending on the variance of the initial velocity distribution and the value of the laser field amplitude. We show that an excitation scheme based on rapid adiabatic passage significantly enhances the expected signal contrast, compared to the commonly used scheme consisting of a series of and pulses. We demonstrate further substantial increase of the robustness by using optimal control theory to identify splitting and swapping pulses that perform well on an ensemble average of pulse amplitudes and velocities. Our results demonstrate the ability of optimal control to significantly enhance future implementations of atomic fountain interferometry.
Traveling-wave tubes (TWTs), such as the Ka-band (26-GHz) model recently developed for the Lunar Reconnaissance Orbiter, are essential as communication amplifiers in spacecraft for virtually all near- and deep-space missions. This innovation is a computational design algorithm that, for the first time, optimizes the efficiency and output power of a TWT while taking into account the effects of dimensional tolerance variations. Because they are primary power consumers and power generation is very expensive in space, much effort has been exerted over the last 30 years to increase the power efficiency of TWTs. However, at frequencies higher than about 60 GHz, efficiencies of TWTs are still quite low. A major reason is that at higher frequencies, dimensional tolerance variations from conventional micromachining techniques become relatively large with respect to the circuit dimensions. When this is the case, conventional design- optimization procedures, which ignore dimensional variations, provide inaccurate designs for which the actual amplifier performance substantially under-performs that of the design. Thus, this new, robust TWT optimization design algorithm was created to take account of and ameliorate the deleterious effects of dimensional variations and to increase efficiency, power, and yield of high-frequency TWTs. This design algorithm can help extend the use of TWTs into the terahertz frequency regime of 300-3000 GHz. Currently, these frequencies are under-utilized because of the lack of efficient amplifiers, thus this regime is known as the "terahertz gap." The development of an efficient terahertz TWT amplifier could enable breakthrough applications in space science molecular spectroscopy, remote sensing, nondestructive testing, high-resolution "through-the-wall" imaging, biomedical imaging, and detection of explosives and toxic biochemical agents.
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.
A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.
In this paper, we propose and solve a robust control problem for inverter-based resources under grid-forming operation to regulate the voltage and frequency. One major challenge is to mitigate the effect of unmeasurable load current disturbance, grid and load parametric uncertainties. Moreover, strong coupling between the state variables on both the AC and DC sides, as well as between the modulating control input and the frequency impose additional challenges. To address these challenges, first, a robust control problem is solved at the high level via transformation into an equivalent, but more tractable, optimal control problem. Then, in the middle layer a voltage control law is designed on the one side, and a frequency control law on the other side. Finally, an inverter filter current controller is designed to complete the controller design. Theoretical results are derived to provide stability guarantees for the resulting closed-loop system. Specifically, we show that the inverter current injection error is dissipative, the frequency error is semi-globally asymptotically stable, and the inverter terminal voltage error is globally asymptotically stable, all with provided sufficient conditions. Here, numerical simulation experiments are used to validate the theoretical claims. Furthermore, the developed controller is compared with existing work in literature to show the efficacy of the proposed approach.
This paper provides major contributions in expanding the literature for membrane process design with critical mineral recovery applications and showcasing the importance of robust design techniques for reducing risks of underperformance in such systems. Here, a membrane process flowsheet featuring PrOMMiS membrane models for recovering lithium/cobalt from spent batteries is showcased, uncertainty in membrane sieving and localized fouling are considered, and robust designs are obtained using the PyROS toolset. This paper is intended for a general audience of researchers working in critical minerals, membranes, and optimization related areas.
The verification of quantum entanglement is essential for quality control in quantum communication. In this work we propose an efficient protocol to directly verify the two-qubit entanglement of a known target state through a single-expectation-value measurement. Our method provides exact entanglement quantification using the concurrence measure without performing quantum state tomography. We prove the existence of a unitary transformation that drives a known initial state of a two-qubit system to a designated final state, where the trace over a chosen observable directly yields the concurrence of the initial state. Furthermore, we implement an optimal control process of that transformation and demonstrate its effectiveness through numerical simulations. We also show that this process is robust to environmental noise. Our approach offers advantages in directly verifying entanglement with low circuit depth, making it suitable for industrial-scale quality control of entanglement generation. Our results presented here provide mathematical justification for our earlier computational experiments.