Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Optimization Under Uncertainty”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Co-optimized trading of hybrid wind power plant with retired EV batteries in energy and reserve markets under uncertainties

To be competitive in the electricity markets, various technologies have been reported to increase profits of wind farm owners. Combining battery storage system, wind farms can be operated as conventional power plants which promotes the integration of wind power into the power grid. However, high expenses on batteries keep investors away. Retired EV batteries, fortunately, still have enough capacity to be reused and could be obtained at a low price. In this work, a two-stage optimization of a wind energy retired EV battery-storage system is proposed. The economic performance of the proposed system is examined concerning its participation in the frequency containment normal operation reserve (FCR-N) market and the spot market simultaneously. To account uncertainties in the wind farm output, various electricity market prices, and up/down regulation status, a scenario-based stochastic programming method is used. The sizing of the equipment is optimized on top of daily operations of the hybrid system which formulates a mixed-integer linear programming (MILP) problem. Scenarios are generated with the Monte Carlo simulation (MCS) and Roulette Wheel Mechanism (RWM), which are further reduced with the simultaneous backward method (SBM) to increase computational efficiency. A 21 MW wind farm is selected as a case study. Here, the optimization results show that by integrating with a retired EV battery-storage system (RESS) and a bi-directional inverter, the wind farm can increase its profits significantly when forwarding bids in both of the aforementioned electricity markets.

17 WIND ENERGY↗
DOE OSTI2026

Uncertainty quantification for inverse problems with application to ptychographic reconstruction

Inverse problems in imaging are commonly solved by optimization or learned surrogates that return a single reconstruction, while uncertainty information is often unavailable. In many experimental settings, however, uncertainty is required to assess reliability, guide downstream analysis, and prioritize additional measurements. In this note, we present a compact uncertainty-quantification framework based on local objective curvature, and then specialize it to ptychographic reconstruction. We further show how repeated reconstructions can be aggregated in a statistically principled way, including a practical implementation path for PtychoNN.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Uncertainty Estimation for SMAP Level-1 Brightness Temperature Assimilation at Different Timescales

In this study, we assimilate Soil Moisture Active Passive (SMAP) mission brightness temperature (Tb) observations into NASA’s Catchment Land Surface Model using an Ensemble Kalman filter to update surface and root-zone soil moisture simulations. Different time series components of the Tb observations are assimilated including anomalies, inter-annual variations, and high-frequency variations. To optimize the weights that the data assimilation (DA) puts on the observations, the ratio between the un-certainties of modeled and observed Tb is approximated using modeled and observed soil moisture uncertainties estimated using triple collocation analysis. Results are compared to a benchmark experiment that mimics the operational SMAP Level-4 algorithm, which assimilates Tb observations using a spatially-constant 4 Kelvin (K) observation uncertainty. All DA experiments exhibit notable skill improvements in most regions. Improvements are greatest for the inter-annual variations in the simulations of both surface and root-zone soil moisture (mean improvements in terms of Pearson correlation (-) are 0.08 and 0.06, respectively). Anomaly simulations improve similarly (0.07), and improvements in the high-frequency variations are only observed for sur-face soil moisture simulations (0.06). Strikingly, however, no notable difference in skill—neither improvement nor deterioration—is observed between the experiments that use optimized observation uncertainty parameters and the 4 K benchmark experiment. We show, analytically, that this may be explained by the presence of large observation operator errors, which have the potential to render post-update uncertainty insensitive to inaccuracies in the Kalman gain.

Alexander Gruber↗
DOE OSTI2016

SU-F-T-208: An Efficient Planning Approach to Posterior Fossa Tumor Bed Boosts Using Proton Pencil Beam Scanning in Fixed-Beam Room

Purpose: A fixed-beam room could be underutilized in a multi-room proton center. We investigated the use of proton pencil beam scanning (PBS) on a fixed-beam as an alternative for posterior fossa tumor bed (PF-TB) boost treatments which were usually treating on a gantry with uniform scanning. Methods: Five patients were treated with craniospinal irradiation (CSI, 23.4 or 36.0 Gy(RBE)) followed by a PF-TB boost to 54 Gy(RBE) with proton beams. Three PF-TB boost plans were generated for each patient: (1) a uniform scanning (US) gantry plan with 4–7 posterior fields shaped with apertures and compensators (2) a PBS plan using bi-lateral and vertex fields with a 3-mm planning organ-at-risk volume (PRV) expansion around the brainstem and (3) PBS fields using same beam arrangement but replacing the PRV with robust optimization considering a 3-mm setup uncertainty. Results: A concave 54-Gy(RBE) isodose line surrounding the brainstem could be achieved using all three techniques. The mean V95% of the PTV was 99.7% (range: 97.6% to 100%) while the V100% of the PTV ranged from 56.3% to 93.1% depending on the involvement of the brainstem with the PTV. The mean doses received by 0.05 cm{sup 3} of the brainstem were effectively identical: 54.0 Gy(RBE), 53.4 Gy(RBE) and 53.3 Gy(RBE) for US, PBS optimized with PRV, and PBS optimized with robustness plans respectively. The cochlea mean dose increased by 23% of the prescribed boost dose in average from the bi-lateral fields used in the PBS plan. Planning time for the PBS plan with PRV was 5–10 times less than the US plan and the robustly optimized PBS plan. Conclusion: We have demonstrated that a fixed-beam with PBS can deliver a dose distribution comparable to a gantry plan using uniform scanning. Planning time can be reduced substantially using a PRV around the brainstem instead of robust optimization.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

The optimal cosmic epoch for precision cosmology

The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time and diminishes per Hubble volume in the distant past or future of the standard cosmological model. We show that the best constraints on the initial power spectrum of linear density perturbations are accessible (e.g. through 21-cm intensity mapping) at redshifts z ∼ 10, and that the ability to constrain the cosmological initial conditions will deteriorate quickly in our cosmic future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Validation of transport models using additive flux minimization technique

A new additive flux minimization technique is proposed for carrying out the verification and validation (V and V) of anomalous transport models. In this approach, the plasma profiles are computed in time dependent predictive simulations in which an additional effective diffusivity is varied. The goal is to obtain an optimal match between the computed and experimental profile. This new technique has several advantages over traditional V and V methods for transport models in tokamaks and takes advantage of uncertainty quantification methods developed by the applied math community. As a demonstration of its efficiency, the technique is applied to the hypothesis that the paleoclassical density transport dominates in the plasma edge region in DIII-D tokamak discharges. A simplified version of the paleoclassical model that utilizes the Spitzer resistivity for the parallel neoclassical resistivity and neglects the trapped particle effects is tested in this paper. It is shown that a contribution to density transport, in addition to the paleoclassical density transport, is needed in order to describe the experimental profiles. It is found that more additional diffusivity is needed at the top of the H-mode pedestal, and almost no additional diffusivity is needed at the pedestal bottom. The implementation of this V and V technique uses the FACETS::Core transport solver and the DAKOTA toolkit for design optimization and uncertainty quantification. The FACETS::Core solver is used for advancing the plasma density profiles. The DAKOTA toolkit is used for the optimization of plasma profiles and the computation of the additional diffusivity that is required for the predicted density profile to match the experimental profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

An Analysis of Plan Robustness for Esophageal Tumors: Comparing Volumetric Modulated Arc Therapy Plans and Spot Scanning Proton Planning

Purpose: Planning studies to compare x-ray and proton techniques and to select the most suitable technique for each patient have been hampered by the nonequivalence of several aspects of treatment planning and delivery. A fair comparison should compare similarly advanced delivery techniques from current clinical practice and also assess the robustness of each technique. The present study therefore compared volumetric modulated arc therapy (VMAT) and single-field optimization (SFO) spot scanning proton therapy plans created using a simultaneous integrated boost (SIB) for dose escalation in midesophageal cancer and analyzed the effect of setup and range uncertainties on these plans. Methods and Materials: For 21 patients, SIB plans with a physical dose prescription of 2 Gy or 2.5 Gy/fraction in 25 fractions to planning target volume (PTV){sub 50Gy} or PTV{sub 62.5Gy} (primary tumor with 0.5 cm margins) were created and evaluated for robustness to random setup errors and proton range errors. Dose–volume metrics were compared for the optimal and uncertainty plans, with P<.05 (Wilcoxon) considered significant. Results: SFO reduced the mean lung dose by 51.4% (range 35.1%-76.1%) and the mean heart dose by 40.9% (range 15.0%-57.4%) compared with VMAT. Proton plan robustness to a 3.5% range error was acceptable. For all patients, the clinical target volume D{sub 98} was 95.0% to 100.4% of the prescribed dose and gross tumor volume (GTV) D{sub 98} was 98.8% to 101%. Setup error robustness was patient anatomy dependent, and the potential minimum dose per fraction was always lower with SFO than with VMAT. The clinical target volume D{sub 98} was lower by 0.6% to 7.8% of the prescribed dose, and the GTV D{sub 98} was lower by 0.3% to 2.2% of the prescribed GTV dose. Conclusions: The SFO plans achieved significant sparing of normal tissue compared with the VMAT plans for midesophageal cancer. The target dose coverage in the SIB proton plans was less robust to random setup errors and might be unacceptable for certain patients. Robust optimization to ensure adequate target coverage of SIB proton plans might be beneficial.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Shortest path network interdiction with asymmetric uncertainty

Abstract This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed‐integer semi‐infinite bilevel program and show that it can be converted into a mixed‐integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst‐case possibilities.

Punla‐Green, She'ifa Z.↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Optimization Through Multi-Fidelity Modeling

We present a novel method for optimizing parameter selection for simulations with an evaluation budget. We start with an existing method for building a multi-fidelity model out of many low-fidelity simulations and few high-fidelity simulations. We propose a novel method to simplify parameter selection without sacrificing performance. We verify these results and compare with existing literature. Next, we propose a novel algorithm which uses this difference model to suggest new points in the parameter design space to simulate. We add each point we simulate to the model to improve its quality for the next iteration. The algorithm trades off reducing the uncertainty of the existing model with optimization of the objective. The first is more useful when a large fraction of the computation budget remains. The second is more useful when a small fraction of the computation budget remains. Our method converges to the optimum by using a high-fidelity evaluation for just 16 of the 427 points. Our method is general enough to work if there is no low-fidelity model. Furthermore, it is agnostic to the underlying physics of the problem. Therefore, both the low-fidelity and high-fidelity models can be generated by any arbitrary function, including simulations and physical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Measurement of the muon neutrino charged-current mesonless cross section in the NOvA near detector

NOvA is a long-baseline accelerator neutrino experiment at Fermilab. Its physics goals include precision neutrino oscillation measurements, neutrino interaction cross-section measurements and beyond Standard Model explorations. We present a measurement of muon neutrino charged-current cross section with zero mesons in the final state at the NOvA near detector. This measurement is performed as a function of the kinematics of the final state muon. Our chosen interaction channel is especially sensitive to quasielastic and meson exchange current interactions and it provides handles for constraining the cross section systematic uncertainties in oscillation analyses in present and future experiments. For particle identification, we use a convolutional neural network (CNN) trained on individual particles simulated in the NOvA Near detector. This allows us to select the desired signal while reducing the potential bias from neutrino interaction modeling. We study strategies for constraining the remaining charged-pion background via Michel electron information in a template fitting approach. The main experimental result is a two-dimensional differential cross section as a function of final-state muon kinetic energy and polar angle. The parameters of this measurement, including binning and unfolding, were optimized to reduce the expected systematic uncertainty in the total cross section. The final result shows good agreement with the main GENIE-based simulation framework that was independently fine-tuned in NOvA. We finally propose improvements and subsequent steps that build on this analysis and further dissect the final states of neutrino interactions. This work has been supported by US DOE grant DE-SC0015684.

Sánchez Falero, Sebastián Jesús [Iowa State U.]↗
NASA NTRS2004

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗
NASA NTRS2006

Strict Constraint Feasibility in Analysis and Design of Uncertain Systems

This paper proposes a methodology for the analysis and design optimization of models subject to parametric uncertainty, where hard inequality constraints are present. Hard constraints are those that must be satisfied for all parameter realizations prescribed by the uncertainty model. Emphasis is given to uncertainty models prescribed by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles. These models make it possible to consider sets of parameters having comparable as well as dissimilar levels of uncertainty. Two alternative formulations for hyper-rectangular sets are proposed, one based on a transformation of variables and another based on an infinity norm approach. The suite of tools developed enable us to determine if the satisfaction of hard constraints is feasible by identifying critical combinations of uncertain parameters. Since this practice is performed without sampling or partitioning the parameter space, the resulting assessments of robustness are analytically verifiable. Strategies that enable the comparison of the robustness of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness characteristics are also proposed. Since the problem formulation is generic and the solution methods only require standard optimization algorithms for their implementation, the tools developed are applicable to a broad range of problems in several disciplines.

Crespo, Luis G.↗
DOE OSTI2011

FUNDAMENTAL PERFORMANCE OF A DISPERSED FIXED DELAY INTERFEROMETER IN SEARCHING FOR PLANETS AROUND M DWARFS

We present a new method to calculate fundamental Doppler measurement limits with a dispersed fixed delay interferometer (DFDI) in the near-infrared (NIR) wavelength region for searching for exoplanets around M dwarfs in the coming decade. It is based on calculating the Q factor, a measure of flux-normalized Doppler sensitivity in the fringing spectra created with DFDI. We calculate the Q factor as a function of spectral resolution R, stellar-projected rotational velocity Vsin i, stellar effective temperature T{sub eff}, and optical path difference (OPD) of the interferometer. We also compare the DFDI Q factor to that for the popular cross-dispersed echelle spectrograph method (the direct echelle (DE) method). We find that (1) Q{sub DFDI} is a factor of 1.5-3 higher than Q{sub DE} at R ranging from 5000 to 20,000; (2) Q{sub DFDI} and Q{sub DE} converge at a very high R (R {>=} 100,000); (3) Q{sub DFDI} increases as R increases and Vsin i deceases; (4) for a given R, Q{sub DFDI} increases as T{sub eff} drops from 3100 K to 2400 K (M4V to M9V). We also investigate how Q{sub DFDI} is affected by OPD and find that a 5 mm deviation from the optimal OPD does not significantly affect Q{sub DFDI} (10% or less) for a wide range of R. Given that the NIR Doppler measurement is likely to be detector-limited for a while, we introduce new merit functions, which is directly related to photon-limited radial velocity (RV) uncertainty, to evaluate Doppler performance with the DFDI and DE methods. We find that DFDI has strength in wavelength coverage and multi-object capability over the DE for a limited detector resource. We simulate the performance of the InfraRed Exoplanet Tracker (IRET) based on the DFDI design, being considered for the next generation IR Doppler measurements. The predicted photon-limited RV uncertainty suggests that IRET is capable of detecting Earth-like exoplanets in habitable zone around nearby bright M dwarfs if they exist. A new method is developed to quantitatively estimate the influence of telluric lines on RV uncertainty. Our study shows that photon-limited RV uncertainty can be reached if 99% of the strength of telluric lines can be removed from the measured stellar spectra. At low to moderate levels of telluric line strength removal (50%-90%), the optimal RV uncertainty is typically a factor of two to three times larger than photon-limited RV uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2012

Influence of robust optimization in intensity-modulated proton therapy with different dose delivery techniques

Purpose: The distal edge tracking (DET) technique in intensity-modulated proton therapy (IMPT) allows for high energy efficiency, fast and simple delivery, and simple inverse treatment planning; however, it is highly sensitive to uncertainties. In this study, the authors explored the application of DET in IMPT (IMPT-DET) and conducted robust optimization of IMPT-DET to see if the planning technique's sensitivity to uncertainties was reduced. They also compared conventional and robust optimization of IMPT-DET with three-dimensional IMPT (IMPT-3D) to gain understanding about how plan robustness is achieved. Methods: They compared the robustness of IMPT-DET and IMPT-3D plans to uncertainties by analyzing plans created for a typical prostate cancer case and a base of skull (BOS) cancer case (using data for patients who had undergone proton therapy at our institution). Spots with the highest and second highest energy layers were chosen so that the Bragg peak would be at the distal edge of the targets in IMPT-DET using 36 equally spaced angle beams; in IMPT-3D, 3 beams with angles chosen by a beam angle optimization algorithm were planned. Dose contributions for a number of range and setup uncertainties were calculated, and a worst-case robust optimization was performed. A robust quantification technique was used to evaluate the plans' sensitivity to uncertainties. Results: With no uncertainties considered, the DET is less robust to uncertainties than is the 3D method but offers better normal tissue protection. With robust optimization to account for range and setup uncertainties, robust optimization can improve the robustness of IMPT plans to uncertainties; however, our findings show the extent of improvement varies. Conclusions: IMPT's sensitivity to uncertainties can be improved by using robust optimization. They found two possible mechanisms that made improvements possible: (1) a localized single-field uniform dose distribution (LSFUD) mechanism, in which the optimization algorithm attempts to produce a single-field uniform dose distribution while minimizing the patching field as much as possible; and (2) perturbed dose distribution, which follows the change in anatomical geometry. Multiple-instance optimization has more knowledge of the influence matrices; this greater knowledge improves IMPT plans' ability to retain robustness despite the presence of uncertainties.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗