Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning and Operations
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24 POWER TRANSMISSION AND DISTRIBUTION↗
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Results for “Linear Optimization”
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.
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Analytical optimal pulse shapes obtained with the aid of genetic algorithms
We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding the interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
REopt: A Platform for Energy System Integration and Optimization: Preprint
REopt is NREL's energy planning platform offering concurrent, multi-technology integration and optimization capabilities to help clients meet their cost savings and energy performance goals. The REopt platform provides techno-economic decision-support analysis throughout the energy planning process, from agency-level screening and macro planning to project development to energy asset operation. REopt employs an integrated approach to optimizing a site?s energy costs by considering electricity and thermal consumption, resource availability, complex tariff structures including time-of-use, demand and sell-back rates, incentives, net-metering, and interconnection limits. Formulated as a mixed integer linear program, REopt recommends an optimally-sized mix of conventional and renewable energy, and energy storage technologies; estimates the net present value associated with implementing those technologies; and provides the cost-optimal dispatch strategy for operating them at maximum economic efficiency. The REopt platform can be customized to address a variety of energy optimization scenarios including policy, microgrid, and operational energy applications. This paper presents the REopt techno-economic model along with two examples of recently completed analysis projects.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
The triple decomposition of a fluctuating velocity field in a multiscale flow
A new method for the triple decomposition of a multiscale flow, which is based on the novel optimal mode decomposition (OMD) technique, is presented. OMD provides low order linear dynamics, which fits a given data set in an optimal way and is used to distinguish between a coherent (periodic) part of a flow and a stochastic fluctuation. The method needs no external phase indication since this information, separate for coherent structures associated with each length scale introduced into the flow, appears as the output. The proposed technique is compared against two traditional methods of the triple decomposition, i.e., bin averaging and proper orthogonal decomposition. This is done with particle image velocimetry data documenting the near wake of a multiscale bar array. It is shown that both traditional methods are unable to provide a reliable estimation for the coherent fluctuation while the proposed technique performs very well. The crucial result is that the coherence peaks are not observed within the spectral properties of the stochastic fluctuation derived with the proposed method; however, these properties remain unaltered at the residual frequencies. This proves the method’s capability of making a distinction between both types of fluctuations. The sensitivity to some prescribed parameters is checked revealing the technique’s robustness. Additionally, an example of the method application for analysis of a multiscale flow is given, i.e., the phase conditioned transverse integral length is investigated in the near wake region of the multiscale object array.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Human operator identification model and related computer programs
Four computer programs which provide computational assistance in the analysis of man/machine systems are reported. The programs are: (1) Modified Transfer Function Program (TF); (2) Time Varying Response Program (TVSR); (3) Optimal Simulation Program (TVOPT); and (4) Linear Identification Program (SCIDNT). The TV program converts the time domain state variable system representative to frequency domain transfer function system representation. The TVSR program computes time histories of the input/output responses of the human operator model. The TVOPT program is an optimal simulation program and is similar to TVSR in that it produces time histories of system states associated with an operator in the loop system. The differences between the two programs are presented. The SCIDNT program is an open loop identification code which operates on the simulated data from TVOPT (or TVSR) or real operator data from motion simulators.
Kessler, K. M.↗
Optimization Routine for Generating Medical Kits for Spaceflight Using the Integrated Medical Model
The Integrated Medical Model (IMM) is a MATLAB model that provides probabilistic assessment of the medical risk associated with human spaceflight missions.Different simulations or profiles can be run in which input conditions regarding both mission characteristics and crew characteristics may vary. For each simulation, the IMM records the total medical events that occur and “treats” each event with resources drawn from import scripts. IMM outputs include Total Medical Events (TME), Crew Health Index (CHI), probability of Evacuation (pEVAC), and probability of Loss of Crew Life (pLOCL).The Crew Health Index is determined by the amount of quality time lost (QTL). Previously, an optimization code was implemented in order to efficiently generate medical kits. The kits were optimized to have the greatest benefit possible, given amass and/or volume constraint. A 6-crew, 14-day lunar mission was chosen for the simulation and run through the IMM for 100,000 trials. A built-in MATLAB solver, mixed-integer linear programming, was used for the optimization routine. Kits were generated in 10% increments ranging from 10%-100% of the benefit constraints. Conditions wheremass alone was minimized, volume alone was minimized, and where mass and volume were minimizedjointly were tested.
Medical Kit↗
Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing
A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.
Childs, A. G.↗
Bi-Level Volt-VAR Optimization to Coordinate Smart Inverters with Voltage Control Devices
Conservation voltage reduction (CVR) uses voltage control to reduce customer power demand and help improve the operational efficiency of the electric power distribution system. With the advent of advanced distribution management systems (ADMS), the underlying data and control-rich platform can be utilized to enable a centralized Volt-VAR optimization (VVO) scheme that includes smart inverter controls along with legacy voltage control devices such as voltage regulators and capacitor banks to ensure a maximum CVR benefit. The objective of this paper to present a VVO approach that controls system’s legacy voltage control devices and coordinates their operation with smart inverter control. An optimal power flow (OPF) formulation is proposed by developing linear and nonlinear power flow approximations for a three-phase unbalanced electric power distribution system. A bi-level VVO approach is proposed where, Level-1 optimizes the control of legacy devices and smart inverters using a linear approximate three-phase power flow. In Level-2, the control parameters for smart inverters are adjusted to obtain an optimal and feasible solution by solving the approximate nonlinear OPF model. Level-1 is modeled as a Mixed Integer Linear Program (MILP) while Level-2 as a Quadratically Constrained Quadratic Program (QCQP). The proposed approach is validated using IEEE test cases and the results demonstrate the applicability of the framework in achieving the CVR objective.
Jha, Rahul Ranjan↗
Peak Power Minimization for Commercial Thermostatically Controlled Loads in Multi-Unit Grid-Interactive Efficient Buildings
The load profiles of most commercial and industrial consumers are characterized by brief periods of very high power consumption followed by intervals of lower demand. To encourage such consumers to flatten their load profiles, power utilities in and around the world often levy a monthly demand charge (DC) on the peak demand measured over brief intervals. In this work, we consider the joint optimization of energy costs (EC) and the instantaneous peak power of a multi-unit building which uses a hydronic heating, ventilation and cooling (HVAC) system and responds to a demand response (DR) program. Despite the non-linear structure of the problem, we show how optimal solutions can be obtained efficiently using linear programming. Next, we study the power demand patterns resulting from our proposed strategy for thermostatically controlled loads (TCLs), and evaluate the strategy’s performance for various climate zones in the US, under both typical and atypical weather conditions. Finally, the results show that depending on the ambient conditions and the tariff structure, our strategy can result in utility bill savings of up to nearly 19% compared to the baseline. The results also indicate that our power control strategy can significantly reduce the instantaneous peak power consumption in commercial TCLs.
HVAC↗
A homotopy algorithm for digital optimal projection control GASD-HADOC
The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.
Collins, Emmanuel G., Jr.↗
Complete Assembly of Circular and Chloroplast Genomes Based on Global Optimization
This paper focuses on the last two stages of genome assembly, namely scaffolding and gap-filling, and shows that they can be solved as part of a single optimization problem. Our approach is based on modeling genome assembly as a problem of finding a simple path in a specific graph that satisfies as many as possible of the distance constraints encoding the insert-size information. We formulate it as a mixed-integer linear programming problem and apply an optimization solver to find the exact solutions on a benchmark of chloroplasts. We show that the presence of repetitions in the set of unitigs is the main reason for the existence of multiple equivalent solutions that are associated to alternative subpaths. We also describe two sufficient conditions and we design efficient algorithms for identifying these subpaths. Comparisons of the results achieved by our tool with the ones obtained with recent assemblers are presented.
59 BASIC BIOLOGICAL SCIENCES↗
Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation
We present a classically tractable model that leads to optimized low-depth quantum circuits leveraging separable-pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms. The associated wave functions can be represented with linear memory requirement, which allows classical optimization of the circuits and naturally defines a minimum benchmark for quantum algorithms. In this work we employ directly determined pair-natural orbitals within a basis-set-free approach. This leads to accurate representation of the one- and many-body parts for weakly correlated systems and we explicitly illustrate how the model can be integrated into other quantum algorithms for stronger correlated systems.
74 ATOMIC AND MOLECULAR PHYSICS↗
An optimal discrete control strategy for interplanetary guidance.
Guiding one state of linear dynamical system to prescribed rms terminal accuracy in presence of injection, measurement and engine-mechanization error
ROOT-MEAN-SQUARE ERROR↗
On the status of optimal control and stability for stochastic systems.
Optimal control and stability for stochastic systems, viewing linear diffusion models based upon Gaussian-Markov process as finite dimensional linear system driven by white noise
SYSTEM STABILITY↗
Development and Implementation of an Optimization Model for Hydropower and Total Dissolved Gas in the Mid-Columbia River System
Managing energy, water, and environmental priorities and constraints within a cascade hydropower system is a challenging multiobjective optimization effort that requires advanced modeling and forecasting tools. Within the mid-Columbia River system, there is currently a lack of specific solutions for predicting how coordinated operational decisions can mitigate the impacts of total dissolved gas (TDG) supersaturation while satisfying multiple additional policy and hydropower generation objectives. In this study, a reduced-order TDG uptake equation is developed that predicts tailrace TDG at seven hydropower facilities on the mid-Columbia River. The equation is incorporated into a general multiobjective river, reservoir, and hydropower optimization tool as a prioritized operating goal within a broader set of system-level objectives and constraints. A test case is presented to assess the response of TDG and hydropower generation when TDG supersaturation is optimized to remain under state water-quality standards. Satisfaction of TDG as an operating goal is highly dependent on whether constraints that limit TDG uptake are implemented at a higher priority than generation requests. According to the model, an opportunity exists to reduce TDG supersaturation and meet hydropower generation requirements by shifting spillway flows to different time periods. In conclusion, a coordinated effort between all project owners is required to implement systemwide optimized solutions that satisfy the operating policies of all stakeholders.
13 HYDRO ENERGY↗
Peak Power Reduction for HVAC Operations in Multi-unit Commercial Buildings
The load profiles of most commercial consumers are characterized by brief periods of very high power consumption followed by intervals of relatively lower demand. In order to flatten commercial load profiles, several power utilities in addition to billing energy consumption, levy a demand charge (DC) on the monthly peak demand. In this work, we consider the problem of joint optimization of energy costs (EC) and DC incurred by a multi-unit building which follows a demand response (DR) program. Despite the non-linear structure of the problem, we show how the optimal solutions can be obtained efficiently using linear programming. We evaluate the performance of the proposed power control scheme for various climate zones in the US. We show that depending on the ambient conditions and the prescribed tariff structure, our strategy can result in savings of up to nearly 19% compared to the baseline.
Raza Naqvi, Syed A.↗
Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C
The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.
58 GEOSCIENCES↗
Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes
This paper deals with a mean-variance problem for finite horizon semi-Markov decision processes. The state and action spaces are Borel spaces, while the reward function may be unbounded. The goal is to seek an optimal policy with minimal finite horizon reward variance over the set of policies with a given mean. Using the theory of N-step contraction, we give a characterization of policies with a given mean and convert the second order moment of the finite horizon reward to a mean of an infinite horizon reward/cost generated by a discrete-time Markov decision processes (MDP) with a two dimension state space and a new one-step reward/cost under suitable conditions. We then establish the optimality equation and the existence of mean-variance optimal policies by employing the existing results of discrete-time MDPs. We also provide a value iteration and a policy improvement algorithms for computing the value function and mean-variance optimal policies, respectively. In addition, a linear program and the dual program are developed for solving the mean-variance problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗