Flow Constraints Research Articles

Differential Game-Based Deep Reinforcement Learning in Underwater Target Hunting Task.

To meet requirements for real-time trajectory scheduling and distributed coordination, underwater target hunting task is challenging in terms of turbulent ocean environments and dynamic adversarial environment. Despite the existing research in game-based target hunting area, few approaches have considered dynamic environmental factors, such as sea currents, winds, and communication delay. In this article, we focus on a target hunting system consisted of multiple unmanned underwater vehicles (UUVs) and a target with high maneuverability. Besides, differential game theory is leveraged to analyze adversarial behaviors between hunters and the escapee. However, it is intractable that UUVs have to deploy an adaptive scheme to guarantee the consistency and avoid the escape of the target without collision. Therefore, we conceive the Hamiltonian function with Leibniz's formula to obtain feedback control policies. In addition, it proves that the target hunting system is asymptotically stable in the mean, and the system can satisfy Nash equilibrium relying on the proposed control policies. Furthermore, we design a modified multiagent reinforcement learning (MARL) to facilitate the underwater target hunting task under the constraints of energetic flows and acoustic propagation delay. Simulation results show that the proposed scheme is superior to the typical MARL algorithm in terms of reward and success rate.

Two-stage robust programming model for active distribution network with a high proportion of renewable energy

To reduce operating costs and obtain the optimal location and capacity of renewable energy access, a two-stage robust planning model is studied for active distribution networks with a high proportion of renewable energy access. To build a function to minimize annual comprehensive costs, the constraints of power flow, branch power, and node voltage of the active distribution network are studied. Considering the characteristics and properties of power flow safety constraints, the mixed integer second-order cone transformation is used to construct a mixed integer convex programming model, which is convenient for efficiently obtaining the global optimal solution. To avoid the influence of uncertainty, a two-stage robust model is constructed. The explicit maximum value method is used to obtain the solution results that satisfy the planning model of all uncertain problems. Experiments show that the model can obtain the optimal access position and capacity of renewable energy. After application, it can reduce the annual comprehensive cost of the distribution network and ensure the stable and safe operation of the active distribution network.

Distributed Model Predictive Consensus Control for Stable Operation of Integrated Energy System

The stable operation of the integrated energy system (IES) is affected by the fluctuation of heat or electricity loads, energy or communication problems, and the interaction of different energy networks. To overcome above challenges, firstly, the integrated dynamic models with three-time scales are established for control design, fully considering dynamic behaviors, energy coupling, and constraints of power flow including electrical, heat and gas on network stability. Then, a novel distributed model predictive control (DMPC) consensus algorithm with process control and trajectory control is proposed to achieve stable operation for IES based on second-order cone programming (SOCP). A unified distributed cooperative control mode is formed in IES by implementing the proposed stability control method, which is suitable for different forms of energy. The control design takes into account the different dynamic characteristics of energy equipment and the energy coupling feature, which realizes the multi-scale time cooperation and dynamic process control for IES by tuning the control parameters. The optimal solution is obtained by rolling optimization for achieving frequency/voltage/temperature/pressure/flow regulation and consensus objectives. Finally, the proposed model and method are validated in various simulation scenarios, such as load variation, energy flow variation, nodes removed, and topology change.

Admissible Control Laws for Constrained Linear Power Flow: The General Case

Linearized power flow with line flow and voltage constraints can be modeled as a system of linear inequalities depending on the power injections. When some injections are controlled by the grid operator while others are determined exogenously, robust control aims at determining grid operator's actions under imperfect system observability such that the grid state is feasible for all possible realizations of the exogenous actions. It was shown how to design and analyze such admissible control policies efficiently for the subclass of affine control laws, but this paper shows that there are important cases that require more general control policies. We show that, for the constrained linear power flow setting, general admissible control policies can always be chosen as piecewise affine (PWA) mappings. The PWA mapping can be explicitly characterized offline or control actions can be computed online by solving an optimization problem given a current observation. For the latter setup, we provide an algorithm that verifies offline that the online control scheme is admissible. This verification step is a crucial precondition to apply the online control scheme in real, safety-critical power grids. The proposed framework is demonstrated with applications to voltage regulation in active distribution grids subject to uncertain prosumers and low observability.

An optimization approach for assembly job shop order release based on clearing functions

As an integral part of production planning control, order release management is critical to enhance the competitiveness and production efficiency of companies. Previous literature shows limited application of optimization-based models in assembly job shops, primarily due to the intricate nature of product structures and assembly operations. Therefore, based on the idea of the allocated clearing function (ACF) model, we introduce material flow constraints and complex assembly structure constraints during the assembly stage, proposing the assembly job shop allocated clearing function (AACF) model. The performance of the AACF model and the rule-based mechanisms in terms of cost and timing measures are compared through experiments containing 6 factors and 96 scenarios. The results show that the AACF model performs better in terms of cost management, service level and order due date deviation. In addition, a sensitivity analysis of the objective function parameters is performed to confirm the robustness of the AACF model. Finally, a case application in a real assembly shop illustrates the feasibility and validity of the proposed AACF model.

Fiber reorientation due to obstacles in open channel flow

A model along with experimental validation is presented for fiber re-orientation within the flow of a thin fluid layer down an inclined plane. Unlike the usual approach (Jeffery), the model accommodates the fast-changing velocity gradient defying linearization and the flow constraints due to the thin thickness of the fluid film. Model equations are formulated, and the algorithm for the fiber rotation is developed. The velocity field within the channel is obtained, using COMSOLTM multiphase simulation. The formulated model equations are used to track the orientation of a single fiber. The spatial fiber orientation state is described in terms of the second order tensor by tracking multiple individual fibers with different initial orientations. To validate the model's predictions, an experimental setup was fabricated to record individual fiber kinematics during the flow and to describe the orientation of fibers in the open channel. A novel benchmark for assessing fiber re-orientation models is presented, wherein the dynamics of fiber orientation is observed in response to a semicircular obstacle within the fluid flow. The experimental results are compared to model predictions and are in reasonable agreement. Despite the simplified approach, both the dynamic of single fiber and the development of fiber orientation distribution due to the obstacle can be reasonably predicted.

Corrections to “Uncovering Bugs in Code Coverage Profilers via Control Flow Constraint Solving”

Corrections to “Uncovering Bugs in Code Coverage Profilers via Control Flow Constraint Solving”

Shear thickening in suspensions of particles with dynamic brush layers.

Control of frictional interactions among liquid-suspended particles has led to tunable, strikingly non-Newtonian rheology via the formation of strong flow constraints as particles come into close proximity under shear. Typically, these frictional interactions have been in the form of physical contact, controllable via particle shape and surface roughness. We investigate a different route, where molecular bridging between nearby particle surfaces generates a controllable constraint to relative particle movement. This is achieved with surface-functionalized colloidal particles capable of forming dynamic covalent bonds with telechelic polymers that comprise the suspending fluid. At low shear stress this results in particles coated with a uniform polymer brush layer. Beyond an onset stress σ* the telechelic polymers become capable of bridging and generate shear thickening. Over the size range investigated, we find that the dynamic brush layer leads to dependence of σ* on particle diameter that closely follows a power law with exponent -1.76. In the shear thickening regime, we observe an enhanced dilation in measurements of the first normal stress difference N1 and reduction in the extrapolated volume fraction required for jamming, both consistent with an effective particle friction that increases with decreasing particle diameter. These results are discussed in light of predictions for suspensions of hard spheres and of polymer-grafted particles.

Efficient Constraint Learning for Data-Driven Active Distribution Network Operation

Scheduling flexible sources to promote the integration of renewable generation is one fundamental problem for operating active distribution networks (ADNs). However, existing works are usually based on power flow models, which require network parameters (e.g., topology and line impedance) that may be unavailable in practice. To address this issue, we propose an efficient constraint learning method to operate ADNs. This method first trains multilayer perceptrons (MLPs) based on historical data to learn the mappings from decisions to constraint violations and power loss. Then, power flow constraints can be replicated by these MLPs without network parameters. We further prove that MLPs learn constraints by formulating a union of disjoint polytopes to approximate the corresponding feasible region. Thus, the proposed method can be interpreted as a piecewise linearization method, which also explains its desirable ability to replicate complex constraints. Finally, a novel pruning method is developed to remove the useless binary variable solutions in advance, which can enhance the solution's reliability and reduce the computational complexity. Numerical experiments based on the IEEE 33- and 123-bus test systems validate that the proposed method can achieve desirable optimality, feasibility, and computational efficiency simultaneously.

An AC-Feasible Linear Model in Distribution Networks With Energy Storage

With the increasing deployment of distributed energy resources (DERs), dispatching DERs subject to operational constraints in distribution networks draws much attention. One challenge is the non-convexities in 1) system-wide AC power flow constraints and 2) the individual complementarity constraint of energy storage. To resolve this challenge, this paper studies an AC-feasible linear model in distribution networks with energy storage, including its formulation, analysis, and applications. First, an AC-feasible linear model is formulated as a set of linear constraints on controllable DERs and uncontrollable power demand by 1) converting the non-convex system-wide constraints into linear constraints based on the Brouwer's fixed-point theorem and the second-order Taylor expansion, and 2) replacing the non-convex individual complementarity constraint of energy storage with one properly designed linear constraint. Furthermore, to analyze the power demand level at which the proposed linear model can provide a solution, this paper proposes an examination-based projection method under the Monte Carlo framework to handle projections of thousands of dimensions from linear constraints over time periods. Finally, the potential applications of our AC-feasible linear model are discussed. Numerical experiments are conducted in the IEEE 33-bus and 136-bus test systems to demonstrate the effectiveness of the proposed methods.

Economic Dispatch between Distribution Grids and Virtual Power Plants under Voltage Security Constraints

Due to the high penetration of virtual power plants (VPPs), the bi-directional power flow between VPPs and active distribution grids makes the grid operation complex. Without congestion management, the operation schedule only considers the economic benefits, and power flow constraints might be violated. Hence, it is necessary to conduct power interaction within the operation constraints. This paper proposes a coordinated economic dispatch method under voltage security constraints. The linear expressions were derived by simplifying the AC power flow equations to reduce the computation complicity. Then, optimal economic dispatch models with voltage security constraints were established for the active distribution grid and VPPs, respectively. Meanwhile, the transacted power and clearing price were set as the communication variables, and a coordinated strategy was proposed for the overall optimal goal. The modified IEEE 33-node and PG&E-node distribution grids were utilized for the simulations, and the results affirmed the validity of the proposed method.

Research on optimal allocation of flow and head in cascade pumping stations based on Harris hawks optimization

Abstract To address the problems of massive energy consumption and low operating efficiency in cascade pumping stations (CPSs), an optimized scheduling model for CPSs with water flow and head constraints was constructed in this study. The Harris hawks optimization (HHO) algorithm was employed to solve this model owing to its excellent performance in the field of engineering majorization. Based on this model, an optimal scheduling method for CPSs was proposed and applied to the three-stage pumping station system. The results demonstrate that the optimization schemes based on the HHO algorithm can improve the operational efficiency and annual cost savings under three different pumping flow conditions by 0.16, 0.55, and 0.56%, reducing the annual operating cost by ¥22,703, ¥74,581, and ¥75,356, respectively, relative to the currently used schemes. These results are better than those obtained by the particle swarm optimization (PSO) algorithm and genetic algorithm (GA). Furthermore, in terms of computational time, the optimization method with the HHO algorithm can show an improvement of 8.94–29.74% compared with those of PSO and GA, verifying the feasibility and efficiency of the HHO algorithm in the optimal scheduling for CPSs. Therefore, the proposed method is effective at solving the scheduling problem of CPSs.

A Parabolic Flow with MHD, the Dufour and Rotational Effects of Uniform Temperature and Mass Diffusion through an Accelerating Vertical Plate in the Presence of Chemical Reaction

A study that was carried out to analyses the movement and behavior of a vertically infinite plate with a parabolic beginning velocity profile in an unsteady flow scenario, taking into account numerous elements such as rotation, chemical reaction, and the Dufour effect. The investigation included evaluating heat readings from the plate as well as accumulation levels in its surroundings. The inverse Laplace technique was used to solve the governing equations. The research looked at two fundamental governing flow constraints: rotation and diffusion, velocity, temperature (Dufour), and how they affect the speed, temperature, and accumulation of a vertically oriented plate. These flow parameters' effects on mass and heat transfer proportions were also graphically represented using Matlab R 2020a. The study's findings were supported by referencing and aligning with earlier research.

Physics-informed surrogate modeling for supporting climate resilience at groundwater contamination sites

Contamination of soil and groundwater presents a widespread global problem, significantly impacting both human well-being and environmental stability. Conventional models employed for estimating pollutant concentrations under varying climatic conditions demand extensive computational power and high-performance computing resources. In response to this issue, we have devised an innovative method utilizing a physics-informed machine learning technique, known as the U-Net Enhanced Fourier Neural Operator (U-FNO), to generate rapid surrogate models for flow and transport. These models are capable of forecasting groundwater pollution levels under diverse climatic situations and subsurface characteristics without necessitating a supercomputer. In our research, we centered our attention on the Department of Energy’s Savannah River Site (SRS) F-Area and established two time-dependent structures: U-FNOB and U-FNOB-R. Both frameworks incorporate a tailored loss function, including specific physical constraints of groundwater flow and transport such as spatial derivatives, and contaminant boundary conditions. The findings of our study indicate that the U-FNO models can consistently foresee spatialtemporal fluctuations in groundwater flow and pollutant transportation properties, such as contaminant concentration, hydraulic head, and Darcy’s velocity. Our research reveals that the U-FNOB-R architecture is especially adept at predicting the effects of alterations in recharge rates on groundwater contamination sites, delivering superior time-dependent forecasts compared to the U-FNOB structure. Our novel approach holds the potential to revolutionize environmental monitoring and remediation efforts by providing rapid, precise, and cost-efficient estimations of groundwater pollution levels under uncertain climate conditions.

Battery energy storage system planning for promoting renewable energy consumption using a constraint boundarization technique

AbstractThe battery energy storage system (EES) deployed in power system can effectively counteract the power fluctuation of renewable energy source. In the planning and operation process of grid side EES, however, the incorporation of power flow constraints into the optimization problem will strongly affect the solving efficiency. Therefore, a bi‐level planning and operation co‐optimization model for EES is proposed based on a constraint boundarization technique. Firstly, a constraint boundarization method for considering power flow constraints is proposed to solve the efficiency problem of the optimization model. Secondly, in terms of the upper and lower bounds of storage's operation curve obtained by the constraint boundarization method, an operation risk evaluation index is defined to describe the potential risk of storage planning scheme. Thirdly, this paper establishes a bi‐level planning and operation co‐optimization model for EES, in which the planning problem with a goal of minimizing total cost is taken as an outer layer and the operation problem for pursuing renewable energy consumption and reducing the load curtailment is taken as an inner layer. Finally, case studies are carried out, and results demonstrate the feasibility and effectiveness of the proposed model and method.

Environmental–Economic Analysis of Multi-Node Community Microgrid Operation in Normal and Abnormal Conditions—A Case Study of Indonesia

This paper presents a comprehensive analysis of the operation management of a multi-node community microgrid (MG), emphasizing power flow constraints and the integration of photovoltaic (PV) and battery systems. This study formulates MG operation management as a multi-objective optimal power flow problem, aiming to minimize costs (maximize profits) and emissions simultaneously. The multi-objective particle swarm optimization (MPSO) method is employed to tackle this complex optimization challenge, yielding a Pareto optimal front that represents the trade-offs between these conflicting objectives. In addition to the normative operation scenarios, this research investigates the robustness of the MG system in the face of abnormal situations. These abnormal scenarios include damage to the PV system, sudden increases in the MG load, and the loss of connection to the main electricity grid. This study focuses on Lombok Island, Indonesia as a practical case study, acknowledging the ongoing efforts to implement the community MG concept in this region. It is observed that when the access to the electricity grid is limited, the energy not served (ENS) increases to 2.88 MWh. During the fault scenario in which there is a 20% increase in the hourly load of each MG, a total of 4.5 MWh ENS is obtained. It is concluded that a resilient operation management system is required to ensure a consistent and reliable energy supply in community MGs in the face of disruptions.

Graph Neural Network-Based Distribution System State Estimators

State estimation is an essential tool for situational awareness and control to ensure safe operation. While current state-of-the-art techniques, such as model-based sparsity-aware state estimators, provide superior performance over conventional approaches, they have poor scalability and require large computational times. These limitations can be overcome by utilizing deep learning models such as deep neural networks (DNNs). However, DNNs are prone to over-fitting and cannot incorporate structural information of networks. Furthermore, current model-based approaches require detailed knowledge of network parameters that may be unavailable in large systems. Therefore, new models with comparable performance are desired that either do not require network parameters or that can work using partial knowledge of these parameters. Recently, graph neural networks (GNNs) have become popular deep learning models that extend neural models to graph structures and incorporate structural information of the networks through graph structures. Therefore, this article proposes GNN-based state estimators by modeling the state estimation problem in distribution systems as node-level prediction problems on their graph representations with state measurement matrices and tensors as input features. Feature scaling and pseudo-measurement generation phases are introduced to enhance their performance. These approaches are evaluated on the IEEE 33, 37-node systems, and an unbalanced three-phase 559-node system. The proposed approaches provide comparable performance to sparsity-aware state estimators while using significantly lower computational times. The GNN-based approaches produce state estimates conforming to the power flow constraints without prior knowledge of the network parameters, thus suggesting that the proposed models can learn the system's underlying physical flows.

Emergency frequency control strategy of distribution system based on the coordination of multi-resource

Introduction: The urban distribution system plays a crucial role in efficient power distribution within urban areas. The increasing frequency and intensity of extreme events in recent years pose significant challenges to the reliable operation of urban distribution systems. While extensive research focuses on emergency frequency control strategies for large-scale power grids, there is a need for targeted attention to address the emergency frequency control challenges arising when the urban distribution system becomes isolated from the superior power grid due to extreme events.Methods: This paper aims to enhance the system's resilience to extreme events by investigating the coordinated regulation of various resources within the urban distribution system. The studied resources include synchronous generators, wind farms, battery energy storage systems, temperature control loads, and conventional load resources. A reduced-order model for the multi-resource system’s frequency response is established. Analytical expressions for key parameters, including the lowest system frequency, lowest point time, and quasi-steady state frequency, are derived.Results: To address the challenge of multi-resource coordinated regulation, an emergency frequency control strategy is proposed. This strategy takes into account the system safety frequency constraint, resource control amount constraint, and line power flow constraint. Simulations are conducted using the MATLAB/Simulink platform, considering IEEE 13 bus and IEEE 33 bus distribution systems as test cases.Discussion: Simulation results demonstrate the effectiveness of the proposed method in regulating the distribution system's resources, ensuring that the lowest frequency remains within the safety threshold of 49.8 Hz. Moreover, the proposed method minimizes control costs and limits load shedding, thereby fully leveraging the capabilities of diverse resources in the urban distribution system. This research contributes valuable insights into addressing emergency frequency control challenges in urban distribution systems during extreme events.

A Fully-Decentralized Transactive Energy Management Under Distribution Network Constraints via Peer-to-Peer Energy Trading

Peer-to-peer (P2P) energy trading is seen as a promising method for distributed transactive energy (TE) management. Since distribution network is used for electricity transfer, physical constraints should be imposed during the P2P trading. In this paper, we propose a P2P-based distributed TE management approach considering distribution network constraints and product differentiation for P2P energy trading between different buses. A multi-period AC optimal power flow (OPF) model is used to monitor power flow in distribution system, and the exactness of second-order cone relaxation is recovered by the convex-concave procedure, making sure that P2P transactions do not violate network constraints. Moreover, we propose a fully-decentralized variant of alternating direction method of multipliers for clearing P2P transactions in a fully-decentralized manner under AC power flow constraints. Our proposed variant does not need any interactions with the central supervisor in comparison with the traditional one. Finally, numerical results on IEEE 33-bus and 141-bus distribution systems verify the effectiveness of our proposed method in ensuring physical feasibility, lowering data communication and protecting data privacy during P2P energy trading.

Fixed-Index-Set Based Approach for Solving a Bilevel Fuzzy Relation Programming With Addition-Min Composition

In recent years, the addition-min fuzzy relation inequalities have been adopted to describe the flow constraint in a P2P network system. Each solution of the inequalities represents a feasible flow control scheme. Motivated by some different managerial objectives, several optimization problems subject to the addition-min inequalities have been recently studied. For example, considering the total efficiency for decreasing the network congestion, the linear objective function was adopted. While considering the fairness among the terminals, the min-max objective function was employed. In this work, combining these two objectives, we establish a corresponding bi-level fuzzy relation programming subject to the addition-min inequalities. For solving the bi-level programming, we first investigate some properties of the first-level programming, using the concept of fixed index set. Based on the properties of the first-level programming, our studied bi-level programming could be equivalently converted into a single-level programming and then solved by the existing linear programming approach. Our resolution approach is carried out by the fixed-index-set based algorithm and illustrated by some numerical examples.