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NREL researcher Peter Graf discusses distributed reinforcement learning with ADMM-RL as part of the Innovative Optimization and Control Methods for Highly Distributed Autonomous Systems workshop. NREL hosted the workshop to exchange ideas on state-of-the-art control and optimization strategies as well as get feedback on work being done at NREL.
As large electricity consumers, water distribution system (WDS) pumping stations have the potential to become meaningful participants in demand response (DR) programs. The authors propose an optimization framework for assessing the DR capacity of a WDS and identifying the optimal bidding strategy for maximizing WDS revenue in the DR spot market. The proposed mixed integer linear programming (MILP) model overcomes computational constraints of previous DR optimization models by adopting a preprocessing procedure to minimize the number of binary variables and implementing a convex relaxation technique to linearize the hydraulic equations. The proposed MILP model also explicitly accounts for varying levels of risk tolerance of WDS operators by varying the recovery period over which pumping returns to business-as-usual operation. The optimization framework is implemented on a skeletonized 48-node WDS model that includes 7 pumps, 6 tanks, and 39 pipes. Using a simulated DR event and water consumption profile, the authors derive the optimal DR supply curves (i.e., compensation price versus load curtailment quantity) and revenue potential of the WDS under six scenarios for DR participation.
Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.
A self-healing power grid can mitigate the impact of power outages and recover the affected area swiftly. To properly size the optimal amount and location of de-energized loads in the presence of both conventional and renewable sources, a precise optimization-based load recovery tool is proposed herein. The steady-state and transient behaviors of loads have been taken into account. The proposed tool contains three separate problems that interact with each other during the restoration period. The first-level problem determines the dispatching of generation units. The second-level problem comprises the non-linear algebraic equations, whose task is to provide the initial conditions for the third-level problem. Finally, the third-level problem intends to determine the optimal location and amount of load pickup through modeling the governor of generators as well as loads' dynamic behaviors. To examine the effectiveness of the proposed tool, a modified IEEE 39-system under a partial blackout condition has been tested. The results are verified by a commercial time-domain simulation software (PSS/E) to demonstrate the accuracy of the proposed approach. Ultimately, the impact of wind turbine frequency control on the load recovery process has been studied under different penetration levels.
Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. Additionally, we then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.
This paper studies the joint fleet sizing and charging system planning problem for a company operating a fleet of autonomous electric vehicles (AEVs) for passenger and goods transportation. Most of the relevant published papers focus on intracity scenarios and adopt heuristic approaches, e.g., agent based simulation, which do not guarantee optimality. In contrast, we propose a mixed integer linear programming model for intercity scenarios. This model incorporates comprehensive considerations of 1) limited AEV driving range; 2) optimal AEV routing and relocating operations; 3) time-varying origin-destination transport demands; and 4) differentiated operation cost structure of passenger and goods transportation. The proposed model can be computational expensive when the scale of the transportation network is large. We then exploit the structure of this program to expedite its solution. Numerical experiments are conducted to validate the proposed method. Our experimental results show that AEVs in passenger and goods transportation have remarkable planning and operation differences. We also demonstrate that intelligent routing and relocating operations, charging system and vehicle parameters, e.g., charging power, battery capacity, driving speed etc., can significantly affect the economic efficiency and the planning results of an AEV fleet.
Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO2 emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO2 processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from 15% to 0% is observed to lead to an 83.7% reduction in CO2 processing capacity and a 77.1% decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions.
Idaho National Laboratory (INL) is developing a first-of-a-kind leadout instrumented capsule experiment design to enable in-situ measurement capabilities in the Advanced Test Reactor (ATR) core. The Ceramic Advanced Thermal Evolution Research (CRATER) experiment supports the aLEU program objective to accelerate fuel performance irradiation testing for identifying alternative high-assay, low enriched uranium (HALEU) fuel systems. CRATER is a fueled, instrumented capsule experiment to measure in-situ temperature and thermal conductivity of ceramic fuels. Two ceramic fuel types will be used, uranium mono-nitride (UN) and uranium mono-carbide (UC), with a third metallic fuel used for comparison (UMo). The three fuel specimens will use a stainless-steel cladding. Programmatic objectives include linear heat generation rates (LHGR) of 210 ± 25 Watts per cm. and an inner clad temperature of 300-450 °C. The evolution of fuel thermal conductivity during irradiation has never been successfully measured in-situ for these systems and this experiment is designed to use advances in measurement sciences to characterize how thermal transport properties evolve while in reactor. Neutronic simulations of the experiment and its surrounding reactor environment were conducted using the Monte Carlo N-Particle Transport code (MCNP) and result in optimized fuel enrichment to meet target linear heat generation rates (LHGRs) influencing fuel temperatures, and fuel burnup requirements. Fabrication research and development (R&D) efforts are underway to produce annular right cylinder UC and UN pellets using carbothermic reduction and nitridation (or hydride-dehydride-nitride) synthesis methods, followed double-action die cold isostatic pressing.
Robust optimization (RO) has attracted great attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.
Recent severe outages highlight the urgency of improving grid resiliency in the U.S. Microgrid formation schemes are proposed to restore critical loads after outages occur. Most distribution networks have unbalanced configurations that are not represented in sufficient detail by single-phase models. This study provides a microgrid formation plan that adopts a three-phase network model to represent unbalanced distribution networks. The problem formulation has a quadratic objective function with mixed-integer linear constraints. The three-phase network model enables us to examine the three-phase power outputs of distributed generators (DGs), preventing unbalanced operation that might trip DGs. Because the DG unbalanced operation constraint is non-convex, an iterative process is presented that checks whether the unbalanced operation limits for DGs are satisfied after each iteration of optimization. We also develop a relatively conservative linear approximation on the unbalanced operation constraint to handle larger networks. Compared with the iterative solution process, the conservative linear approximation is able to accelerate the solution process at the cost of sacrificing optimality to a limited extent. Simulation in the IEEE 34 node and IEEE 123 test feeders indicate that the proposed method yields more practical microgrid formations results. In addition, this paper explores the coordinated operation of DGs and energy storage (ES) installations. The unbalanced three-phase outputs of ESs combined with the relatively balanced outputs of DGs could supply unbalanced loads. In conclusion, the case study also validates the DG-ES coordination.
This Technical Report presents work completed by The Applied Research Laboratory at The Pennsylvania State University, in conjunction with Sandia National Labs, on the optimization of the power conversion chain (PCC) design to maximize the Average Annual Electric Power (AAEP) output of an Oscillating Water Column (OWC) device. The design consists of two independent stages. First, the design of a floating OWC, a Backward Bent Duct Buoy (BBDB), and second the design of the PCC. The pneumatic power output of the BBDB in random waves is optimized through the use of a hydrodynamically coupled, linear, frequency-domain, performance model that links the oscillating structure to internal air-pressure fluctuations. The PCC optimization is centered on the selection and sizing of a Wells Turbine and electric power generation equipment. The optimization of the PCC involves the following variables: the type of Wells Turbine (fixed or variable pitched, with and without guide vanes), the radius of the turbine, the optimal vent pressure, the sizing of the power electronics, and number of turbines. Also included in this Technical Report are further details on how rotor thrust and torque are estimated, along with further details on the type of variable frequency drive selected.
The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. Here, in this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing.
The addition of a compressible degree of freedom (CDOF) to a wave energy converter (WEC)-which results in a compressible WEC-has been shown to significantly increase power absorption compared to a rigid WEC of the same shape and mass for a variety of architectures. This study demonstrates that a compressible point absorber, with a passive power-take-off (PTO) and optimized damping, can also achieve equal or better performance levels than an optimally controlled rigid point absorber (with the same shape and mass) using reactive power from the PTO. Wave energy is converted to mechanical energy in both cases using a linear damper PTO, with the PTO coefficient optimized for each resonance frequency and compressible volume. The large compressible volume required to tune the compressible point absorber to the desired frequency is a practical limitation that needs to be addressed with further research, especially for low frequencies. While realistic, these auxiliary units would increase the CapEx and OpEx costs, potentially reducing the aforementioned benefits gained by CDOF. However, alternative approaches can be developed to implement CDOF without the large compressible volume requirements, including the development of flexible surface panels tuned with mechanical springs.
In this paper, we present the new discrete optimization-based interface-aware sub-scale dynamics (IA-SSD) closure model for multimaterial cells for Lagrangian cell-centered hydrodynamics. For the multimaterial cell, the kinematic and thermodynamic properties (e.g., velocity, density, pressure and internal energy) will typically vary between the materials. The discrete closure model is responsible for an accurate update of the thermodynamic states of the individual material components in the multimaterial cell, and for determining the nodal forces that move the vertices of the cell. The IA-SSD closure model consists of two stages — a bulk stage followed by a sub-scale stage. During the bulk stage, the total change in the volume of the cell, total force applied to the cell, and total work done on the cell are distributed between the materials to update their volume, velocity and total energy. This distribution is performed using volume fractions of the materials. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is used, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and are limited using physically justified constraints: positivity of volume, positivity of internal energy, and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. It is a first-of-its kind application of constrained optimization to develop discrete closure models in a more rigorous fashion. The pair-wise interaction between materials is essentially one dimensional in the direction that is normal to interface. Finally, for this reason, we demonstrate in this paper the performance of our new model on one dimensional numerical examples.
This paper outlines a novel sensor selection and observer design algorithm for linear time-invariant systems with both process and measurement noise based on H 2 optimization to optimize the tradeoff between the observer error and the number of required sensors. The optimization problem is relaxed to a sequence of convex optimization problems that minimize the cost function consisting of the H 2 norm of the observer error and the weighted l 1 norm of the observer gain. An LMI formulation allows for efficient solution via semi-definite programing. The approach is applied here, for the first time, to a turbo-charged spark-ignited engine using exhaust gas circulation to determine the optimal sensor sets for real-time intake manifold burnt gas mass fraction estimation. Simulation with the candidate estimator embedded in a high fidelity engine GT-Power model demonstrates that the optimal sensor sets selected using this algorithm have the best H 2 estimation performance. Sensor redundancy is also analyzed based on the algorithm results. This algorithm is applicable for any type of modern internal combustion engines to reduce system design time and experimental efforts typically required for selecting optimal sensor sets.
In this paper, a multivariable model-based non-linear controller for Warm Compression Stations (WCS) is proposed. The strategy is to replace all the PID loops controlling the WCS with an optimally designed model-based multivariable loop. This new strategy leads to high stability and fast disturbance rejection such as those induced by a turbine or a compressor stop, a key-aspect in the case of large scale cryogenic refrigeration. The proposed control scheme can be used to have precise control of every pressure in normal operation or to stabilize and control the cryoplant under high variation of thermal loads (such as a pulsed heat load expected to take place in future fusion reactors such as those expected in the cryogenic cooling systems of the International Thermonuclear Experimental Reactor ITER or the Japan Torus-60 Super Advanced fusion experiment JT-60SA). The paper details how to set the WCS model up to synthesize the Linear Quadratic Optimal feedback gain and how to use it. After preliminary tuning at CEA-Grenoble on the 400W@1.8K helium test facility, the controller has been implemented on a Schneider PLC and fully tested first on the CERN's real-time simulator. Then, it was experimentally validated on a real CERN cryoplant. The efficiency of the solution is experimentally assessed using a reasonable operating scenario of start and stop of compressors and cryogenic turbines. This work is partially supported through the European Fusion Development Agreement (EFDA) Goal Oriented Training Program, task agreement WP10-GOT-GIRO.
Dynamic reactive power sources can be used to effectively mitigate the fault-induced delayed voltage recovery and transient voltage instability issues. When many var sources need to be installed at planned locations, optimisation of their sizes is a complicated non-linear optimisation problem due to its non-convexity and the dependence of the constraint on time-series trajectories of post-fault voltages. Solving this optimal sizing problem needs to utilise both a non-linear optimisation solver and a power system differential-algebraic equation solver. This study proposes a new approach for solving this problem under both a single contingency and multiple contingencies by using the mesh adaptive direct search algorithm interfaced with a power system simulator. The proposed approach is validated by case studies on a North American Eastern Interconnection model to optimise the sizes of planned STATCOMs against critical contingencies.
In order to achieve stringent greenhouse gas emission reductions, a transition of our entire energy system from fossil to renewable resources needs to be designed. Such an energy transition brings two main challenges: most renewables generate variable electric energy, yet most demand is currently not electric (carrier mismatch) and does not always manifest at the same time as supply (temporal mismatch). Integrating multiple energy infrastructures can address both challenges by using the synergy between different energy carriers; building on existing infrastructure, while allowing a robust and flexible integration of the new. This paper proposes an optimization framework for long-term, multi-period investment planning of urban energy systems in an integrated manner. We formulate it as a mixed-integer linear program, combining a capacitated facility location with a multi-dimensional, capacitated network design problem. It includes generation and network expansion planning as well as interconnections between networks and storage infrastructure for each energy system. It can incorporate pathway effects like techno-economic developments, policy measures, and weather variations. The intended use is to support urban decision makers with long-term investment planning, though it can be tailored to fit other geographical or temporal scales. We demonstrate the model using two cases based on an average city in The Netherlands, which wants to reduce its CO 2 -emissions with 95% by 2050. In the first case, we include explicit carbon-emission constraints to study the effects of the carrier mismatch. In the second case, we implement interannual weather variations to analyze the temporal mismatch. The results give valuable insights into the energy transition design strategy for urban decision makers. They also show the future potential, as well as the computational challenges of the optimization framework.