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Records with Subject: Optimization
593. LAPSE:2023.23320
Flexibility Assessment of Multi-Energy Residential and Commercial Buildings
March 27, 2023 (v1)
Subject: Optimization
Keywords: CO2 emissions, commercial buildings, flexibility optimization, flexibility quantification, HVAC systems, multi-energy systems, network operation, residential buildings
With the growing concern about decreasing CO 2 emissions, renewable energy sources are being vastly integrated in the energy systems worldwide. This will bring new challenges to the network operators, which will need to find sources of flexibility to cope with the variable-output nature of these technologies. Demand response and multi-energy systems are being widely studied and considered as a promising solution to mitigate possible problems that may occur in the energy systems due to the large-scale integration of renewables. In this work, an optimal model to manage the resources and loads within residential and commercial buildings was developed, considering consumers preferences, electrical network restrictions and CO 2 emissions. The flexibility that these buildings can provide was analyzed and quantified. Additionally, it was shown how this model can be used to solve technical problems in electrical networks, comparing the performance of two scenarios of flexibilit... [more]
594. LAPSE:2023.23319
Practical Energy Retrofit of Heat Exchanger Network Not Containing Utility Path
March 27, 2023 (v1)
Subject: Optimization
Keywords: commercial software, heat exchanger design, heat exchanger network retrofit, heat transfer enhancement, linear programming, practical hybrid method, retrofit superstructure grid diagram, utility path, utility savings
The paper presents a method developed for the energy retrofit of specific Heat Exchanger Networks not containing Utility Paths. This useful and highly practically oriented method involves a systematic approach to obtaining the most efficient minimal modification topology of a Heat Exchanger Network, which brings the greatest benefits in terms of energy savings of the modified process. In principle, it is focused on finding the most suitable location for a new heat exchanger insertion to create the most efficient Utility Path. The next step of the developed retrofit method is the detailed design of the newly integrated heat exchanger using commercial software in combination with several heuristic rules regarding the cost-free investment and maintenance cost minimization of a new heat exchanger and considering heat transfer enhancement within the available exchanger type, space, and fluids pressure drop constraints. The detail design stage of the method also includes observation and reas... [more]
595. LAPSE:2023.23249
Optimal Operation Control of PV-Biomass Gasifier-Diesel-Hybrid Systems Using Reinforcement Learning Techniques
March 27, 2023 (v1)
Subject: Optimization
Keywords: Biomass, CO2 reduction, Machine Learning, microgrids, mixed integer linear programming, operations research, Optimization, reinforcement learning
The importance of efficient utilization of biomass as renewable energy in terms of global warming and resource shortages are well known and documented. Biomass gasification is a promising power technology especially for decentralized energy systems. Decisive progress has been made in the gasification technologies development during the last decade. This paper deals with the control and optimization problems for an isolated microgrid combining the renewable energy sources (solar energy and biomass gasification) with a diesel power plant. The control problem of an isolated microgrid is formulated as a Markov decision process and we studied how reinforcement learning can be employed to address this problem to minimize the total system cost. The most economic microgrid configuration was found, and it uses biomass gasification units with an internal combustion engine operating both in single-fuel mode (producer gas) and in dual-fuel mode (diesel fuel and producer gas).
596. LAPSE:2023.23228
A Dynamic Multi-Swarm Particle Swarm Optimizer for Multi-Objective Optimization of Machining Operations Considering Efficiency and Energy Consumption
March 27, 2023 (v1)
Subject: Optimization
Keywords: Energy Efficiency, fuzzy comprehensive evaluation, machining operation, multi-objective optimization, particle swarm optimizer
Facing energy shortage and severe environmental pollution, manufacturing companies need to urgently energy consumption, make rational use of resources and improve economic benefits. This paper formulates a multi-objective optimization model for lathe turning operations which aims to simultaneously minimize energy consumption, machining cost and cutting time. A dynamic multi-swarm particle swarm optimizer (DMS-PSO) is proposed to solve the formulation. A case study is provided to illustrate the effectiveness of the proposed algorithm. The results show that the DMS-PSO approach can ensure good convergence and diversity of the solution set. Additionally, the optimal machining parameters are identified by fuzzy comprehensive evaluation (FCE) and compared with empirical parameters. It is discovered that the optimal parameters obtained from the proposed algorithm outperform the empirical parameters in all three objectives. The research findings shed new light on energy conservation of machin... [more]
597. LAPSE:2023.23196
A Stepped-Segmentation Method for the High-Speed Theoretical Elevator Car Air Pressure Curve Adjustment
March 27, 2023 (v1)
Subject: Optimization
Keywords: air pressure curve adjustment, high-speed elevator, multi-performance optimization, stepped-segmentation, theoretical air pressure curve
As the demand for high-speed elevators grows, the requirements of elevator performance have also increased. Most of these are single variables that do not consider the comprehensive impact of multiple variables on performance, especially comfort. To overcome this problem, a stepped segmentation method for a theoretical high-speed elevator car air pressure curve (THEC-APC) adjustment is proposed that could actively help to select a suitable theoretical elevator car air pressure adjustment curve. By utilizing the proposed Particle Swarm Optimization (PSO) algorithm, the theoretical elevator car air pressure curve is optimized for multiple performances (including passenger comfort, energy consumption, and aerodynamic characteristics). In addition, the THEC-APC is smoothed by the Bezier curve for the variable destination floor. To verify the proposed method, the KLK2 (Canny Elevator Co., Ltd., 2015, Suzhou) high-speed elevator design process is applied. The numerical experiment results sho... [more]
598. LAPSE:2023.23156
Optimal Energy Management of Plug-In Hybrid Electric Vehicles Concerning the Entire Lifespan of Lithium-Ion Batteries
March 27, 2023 (v1)
Subject: Optimization
Keywords: battery aging, energy management, Genetic Algorithm, global optimization, particle swarm algorithm, plug-in electric vehicles, state of health
The performance of lithium-ion batteries will inevitably degrade during the high frequently charging/discharging load applied in electric vehicles. For hybrid electric vehicles, battery aging not only declines the performance and reliability of the battery itself, but it also affects the whole energy efficiency of the vehicle since the engine has to participate more. Therefore, the energy management strategy is required to be adjusted during the entire lifespan of lithium-ion batteries to maintain the optimality of energy economy. In this study, tests of the battery performances under thirteen different aging stages are involved and a parameters-varying battery model that represents the battery degradation is established. The influences of battery aging on energy consumption of a given plug-in hybrid electric vehicle (PHEV) are analyzed quantitatively. The results indicate that the variations of capacity and internal resistance are the main factors while the polarization and open circu... [more]
599. LAPSE:2023.23146
Analysis of Magnetic Field and Torque Features of Improved Permanent Magnet Rotor Deflection Type Three-Degree-of-Freedom Motor
March 27, 2023 (v1)
Subject: Optimization
Keywords: deflection, magnetic field and torque, permanent magnet motor, three-degree-of-freedom
This paper proposes a novel layered permanent magnet motor (N-LPM), which is based on a three-degree-of-freedom (3-DOF) permanent magnet motor. Compared with the former, the improved N-LPM air gap magnetic density, torque and structure stability have been significantly improved. The proposed N-LPM has three layers of stator along the axis direction, and each layer of stator has three-phase winding. In order to calculate the magnetic field and torque distribution of the N-LPM, an analytical method (AM) is proposed. For performance verification and accurate calculation, finite-element analysis (FEA) is adopted. The two kinds of motors before and after the improvement are compared, and their magnetic field, torque and stability are analyzed. The optimization rate is defined to evaluate the performance of the motor before and after improvement. The results show that the radial flux density, rotation torque, deflection torque and the volume optimization rate of the permanent magnet of the i... [more]
600. LAPSE:2023.23126
A Two-Stage Algorithm of Locational Marginal Price Calculation Subject to Carbon Emission Allowance
March 27, 2023 (v1)
Subject: Optimization
Keywords: carbon emission allowance, day-ahead electricity market, multi-objective optimization, two-stage algorithm
To analyze the effect of carbon emission quota allocation on the locational marginal price (LMP) of day-ahead electricity markets, this paper proposes a two-stage algorithm. For the first stage of the algorithm, a multi-objective optimization model is established to simultaneously minimize the total costs and carbon emission costs of power systems. Hence, an evenly distributed Pareto optimal solution can be solved effectively by means of the normalized normal constraint method. For the second stage, a tracing model is built with the goal of minimizing the total costs of power systems and satisfying the constraints generated based on the Pareto optimal solution obtained from the first stage. Furthermore, the influence of carbon emission quota allocation on the LMP of electricity markets is analyzed, and different schemes to allocate carbon emission quotas are evaluated on a real 1560-bus and 52-unit system.
601. LAPSE:2023.23121
Multi-Objective Sizing Optimization of a Grid-Connected Solar−Wind Hybrid System Using Climate Classification: A Case Study of Four Locations in Southern Taiwan
March 27, 2023 (v1)
Subject: Optimization
Keywords: climate classification, constrained optimization, decomposition, differential evolutionary algorithm, hybrid power systems, multi-objective optimization, power grid, solar energy, wind energy
Increased concerns over global warming and air pollution has pushed governments to consider renewable energy as an alternative to meet the required energy demands of countries. Many government policies are deployed in Taiwan to promote solar and wind energy to cope with air pollution and self-dependency for energy generation. However, the residential sector contribution is not significant despite higher feed-in tariff rates set by government. This study analyzes wind and solar power availability of four different locations of southern Taiwan, based on the Köppen−Geiger climate classification system. The solar−wind hybrid system (SWHS) considered in this study consists of multi-crystalline photovoltaic (PV) modules, vertical wind turbines, inverters and batteries. Global reanalysis weather data and a climate-based electricity load profile at a 1-h resolution was used for the simulation. A general framework for multi-objective optimization using this simulation technique is proposed for... [more]
602. LAPSE:2023.23115
Opportunities and Challenges of Future District Heating Portfolios of an Austrian Utility
March 27, 2023 (v1)
Subject: Optimization
Keywords: dispatch optimization, district heating, economic framework conditions, portfolio options
In this paper, opportunities and challenges of concrete portfolio options of an Austrian district heating (DH) supplier are assessed against the background of current challenges of the DH sector. The following steps are performed: (1) analysis of status quo; (2) analysis of current and possible future economic framework conditions; (3) definition of four concrete future portfolio options for investment planning until the year 2030; (4) modeling of status quo and future portfolios together with the respective framework conditions in a linear dispatch optimization model; and (5) perform techno-economic analysis for each portfolio under the different possible future framework conditions. The expected increase in renewable power generation capacity is likely to increase volatility in future electricity prices with hours of both very low and very high prices. This higher volatility results in higher technical flexibility requirements for the heat generation plants and a need for heat genera... [more]
603. LAPSE:2023.23048
Electric Powertrain Topology Analysis and Design for Heavy-Duty Trucks
March 27, 2023 (v1)
Subject: Optimization
Keywords: electric vehicles, Optimization, powertrains, topology design
Powertrain system design optimization is an unexplored territory for battery electric trucks, which only recently have been seen as a feasible solution for sustainable road transport. To investigate the potential of these vehicles, in this paper, a variety of new battery electric powertrain topologies for heavy-duty trucks is studied. Thereby, topological design considerations are analyzed related to having: (a) a central or distributed drive system (individually-driven wheels); (b) a single or a multi-speed gearbox; and finally, (c) a single or multiple electric machines. For reasons of comparison, each concurrent powertrain topology is optimized using a bilevel optimization framework, incorporating both powertrain components and control design. The results show that the combined choice of powertrain topology and number of gears in the gearbox can result in a 5.6% total-cost-of-ownership variation of the vehicle and can, significantly, influence the optimal sizing of the electric mach... [more]
604. LAPSE:2023.23026
Optimization of Operating Parameters for Stable and High Operating Performance of a GDI Fuel Injector System
March 27, 2023 (v1)
Subject: Optimization
Keywords: fuel injection quantity, injector driving circuit, Optimization, Taguchi method
In this study, a novel injector driving circuit was developed to achieve the regulation of fuel injection quantity and to work with the engine control system in a vehicle. The main purpose of the proposed injector driving circuit is to control the quantity and timing of fuel injection within the gasoline direct injection (GDI) fuel injector system. In this paper, a mathematical state model of a high-pressure (H.P.) fuel injector system is derived and the improved Taguchi method is proposed to define the optimal operating parameter settings of a fuel injector system. The experiments on fuel injection quantity were performed to achieve the requirements of the injector driving circuit. The fuel quantity sprayed from a fuel injector system under these control parameters was analyzed by leading the design of experiments. The S/N and β slopes were analyzed to determine their optimal control settings. The H.P. injector driving circuit developed was designed to drive the fuel injector and spra... [more]
605. LAPSE:2023.22998
Selected Aspects of Combustion Optimization of Coal in Power Plants
March 24, 2023 (v1)
Subject: Optimization
Keywords: Coal, combustion, economy, Optimization, Poland, power plant
Growing ecological standards force the implementation of solutions that will contribute to reducing greenhouse gas (GHG) emissions to the atmosphere. This is particularly important in Poland, whose energy system is almost 80% based on coal. In the interest of low carbon development it is worth considering the optimization of existing old coal-based power plants. The main goal of the research was to present the benefits of modernization of existing boiler equipment and to analyze the combustion process of various types of coal sorts that have a significant impact on the optimization of the production processes of energy media. An analysis of the processes occurring in boiler devices during the combustion of fuel was carried out, which had a significant impact on the quality of generated heat and electricity. The conducted research defined technological solutions for boiler structures that have a significant impact on improving the efficiency of the technological process in heating plant... [more]
606. LAPSE:2023.22916
Distribution Power Loss Reduction of Standalone DC Microgrids Using Adaptive Differential Evolution-Based Control for Distributed Battery Systems
March 24, 2023 (v1)
Subject: Optimization
Keywords: Adaptive Differential Evolution (ADE), bus voltage regulation, DC microgrid, distributed battery system (DBS), distribution power loss, hierarchical control
With high penetrations of renewable energy sources (RES), distributed battery systems (DBS) are widely adopted in standalone DC microgrids to stabilize the bus voltages by balancing the active power. This paper presents an Adaptive Differential Evolution (ADE)-based hierarchical control for DBS to achieve online distribution power loss mitigation as well as bus voltage regulations in standalone DC microgrids. The hierarchical control comprises two layers, i.e., ADE for the secondary layer and local proportional-integral (PI) control for the primary layer. The secondary layer control provides the bus voltage references for the primary control by optimizing the fitness function, which contains the parameters of the bus voltage deviations and the power loss on the distribution lines. Simultaneously, the state-of-charge (SoC) of the battery packs are controlled by local controllers to prevent over-charge and deep-discharge. Case studies using a Real-Time Digital Simulator (RTDS) validate t... [more]
607. LAPSE:2023.22897
Energy Consumption and Lifecycle Cost Analysis of Electric City Buses with Multispeed Gearboxes
March 24, 2023 (v1)
Subject: Optimization
Keywords: city bus, electric vehicle, Energy Efficiency, gearbox, Optimization, transmission
This study investigates the potential of improving the energy efficiency and reducing the lifecycle costs of electric city buses with multispeed gearboxes. A two-speed dual clutch gearbox and a continuously variable transmission were studied and compared to a reference fixed gear ratio powertrain. A novel two-level optimization model was introduced. The top level involves an exhaustive search algorithm and quasi-static vehicle dynamic model for optimizing the two-speed gearbox gear ratios, utilizing efficiency maps for the electric motor and the inverter. The second level is an integer programming model, which finds an optimal gear shifting policy subject to constraints on hysteresis and gear shifting induced losses. The model was applied with a standard driving cycle and additionally with three measured cycles acquired from a prototype battery electric city bus operating on a daily schedule on a suburban route in Espoo, Finland. The results showed that a two-speed gearbox reduced ener... [more]
608. LAPSE:2023.22877
Implementation of Particle Swarm Optimization (PSO) Algorithm for Tuning of Power System Stabilizers in Multimachine Electric Power Systems
March 24, 2023 (v1)
Subject: Optimization
Keywords: multimachine system, Particle Swarm Optimization, power system, power system stabilizer
The application of artificial intelligence-based techniques has covered a wide range of applications related to electric power systems (EPS). Particularly, a metaheuristic technique known as Particle Swarm Optimization (PSO) has been chosen for the tuning of parameters for Power System Stabilizers (PSS) with success for relatively small systems. This article proposes a tuning methodology for PSSs based on the use of PSO that works for systems with ten or even more machines. Our new methodology was implemented using the source language of the commercial simulation software DigSilent PowerFactory. Therefore, it can be translated into current practice directly. Our methodology was applied to different test systems showing the effectiveness and potential of the proposed technique.
609. LAPSE:2023.22865
Minimizing Power Consumption of an Experimental HVAC System Based on Parallel Grid Searching
March 24, 2023 (v1)
Subject: Optimization
Keywords: graphics processing unit, HVAC systems, parallel computing, power consumption optimization
This paper proposes a parallel grid search algorithm to find an optimal operating point for minimizing the power consumption of an experimental heating, ventilating and air conditioning (HVAC) system. First, a multidimensional, nonlinear and non-convex optimization problem subject to constraints is formulated based on a semi-physical model of the experimental HVAC system. Second, the optimization problem is parallelized based on Graphics Processing Units to simultaneously compute optimization loss functions for different solutions in a searching grid, and to find the optimal solution as the one having the minimum loss function. The proposed algorithm has an advantage that the optimal solution is known with evidence as to the best one subject to current resolutions of the searching grid. Experimental studies are provided to support the proposed algorithm.
610. LAPSE:2023.22847
Prospect Prediction of Terminal Clean Power Consumption in China via LSSVM Algorithm Based on Improved Evolutionary Game Theory
March 24, 2023 (v1)
Subject: Optimization
Keywords: adaptive differential evolution, evolutionary game theory, grey relevance theory, least squares support vector machine, terminal clean power consumption forecast
In recent years, China’s terminal clean power replacement construction has experienced rapid development, and China’s installed photovoltaic and wind energy capacity has soared to become the highest in the world. Precise and effective prediction of the scale of terminal clean power replacement can not only help make reasonable adjustments to the proportion of clean power capacity, but also promote the reduction of carbon emissions and enhance environmental benefits. In order to predict the prospects of China’s terminal clean energy consumption, first of all, the main factors affecting the clean power of the terminal are screened by using the grey revelance theory. Then, an evolutionary game theory (EGT) optimized least squares support vector machine (LSSVM) machine intelligence algorithm and an adaptive differential evolution (ADE) algorithm are applied in the example analysis, and empirical analysis shows that this model has a strong generalization ability, and that the prediction res... [more]
611. LAPSE:2023.22843
On Obtaining Energy-Optimal Trajectories for Landing of UAVs
March 24, 2023 (v1)
Subject: Optimization
Keywords: Energy, landing, Optimization, unmanned aerial vehicle
The optimization issues connected to a landing task of an unmanned aerial vehicle are discussed in the paper, based on a model of a mini-class drone. Three landing scenarios are considered, including minimum-time landing, landing with minimum energy consumption, and planned landing. With the use of classical dynamic programming techniques, including the minimum principle of Pontryagin, as well as the calculus of variations, the optimal altitude reference trajectories are found, to form the altitude control system in such a way as to mimic the profile of the reference trajectory by the actual altitude of the UAV. The simulation results conducted with the use of the Simulink Support Package for Parrot Minidrones verify the correctness and effectiveness of the method, and open the research directions for further analysis, especially to tune altitude controller in a way, as to track the reference profile. Up to this point, optimization tasks considered in the literature, with respect to th... [more]
612. LAPSE:2023.22836
An Algorithm for Optimization of Recharging Stops: A Case Study of Electric Vehicle Charging Stations on Canadian’s Ontario Highway 401
March 24, 2023 (v1)
Subject: Optimization
Keywords: charging stations (CSs), electric vehicles (EVs), highway, Optimization, type of charging station
Electric vehicles (EVs), which have become a fundamental part of the automotive industry, were developed as part of concerted worldwide efforts to reduce dependency on fossil fuels due to their devastating effects on the environment. The aim of this study was to analyse a complete trip using an EV from Toronto to Ottawa (Canada) along Ontario’s Highway 401, considering that use of conventional vehicles powered by petrol or diesel allow one to make this trip without stops; using EVs, it is necessary to recharge the vehicle. For this purpose, an algorithm was developed for optimizing recharging stops during a complete trip. In particular, the simulations analysed the number of stops and specifically where it is possible to recharge taking into account the actual charging stations (CSs) located along the trip and the time of recharge during the stops as a function of the state of charge (SoC) of the vehicle. Using this approach, it was possible to evaluate the suitable coverage of the CSs... [more]
613. LAPSE:2023.22826
A Deep-Learning-Based Oil-Well-Testing Stage Interpretation Model Integrating Multi-Feature Extraction Methods
March 24, 2023 (v1)
Subject: Optimization
Keywords: data interpretation, deep belief network, integrated interpretation model, well testing
The interpretation of well-testing data is a key means of decision-making support for oil and gas field development. However, conventional processing methods have many problems, such as the stochastic nature of the data, feature redundancies, the randomness of the initial weights or thresholds, and fluctuations in the generalization ability with slight changes in the network parameters. These result in a poor ability to characterize data features and a low generalization ability of the interpretation models. We propose a new integrated well-testing interpretation model based on a multi-feature extraction method and deep mutual information classifiers (MFE-DMIC). This model can avoid the low model classification accuracy caused by the simple training structures, lacking of redundancy elimination, and the non-optimal classifier configuration parameters. First, we obtained the initial features according to four classical feature extraction methods. Then, we eliminated feature redundancies... [more]
614. LAPSE:2023.22819
Improved PSO: A Comparative Study in MPPT Algorithm for PV System Control under Partial Shading Conditions
March 24, 2023 (v1)
Subject: Optimization
Keywords: maximum power point tracking (MPPT), particle swarm optimization algorithm (PSO), photovoltaic (PV)
This paper deals with the implementation and analysis of a new maximum power point tracking (MPPT) control method, which is tested under variable climatic conditions. This new MPPT strategy has been created for photovoltaic systems based on Particle Swarm Optimization (PSO). The novel Improved Particle Swarm Optimization (IPSO) algorithm is tested in several simulations which have been implemented in view of the various system responses such as: voltage, current, and power. The performances of the proposed IPSO algorithm have been completed and compared with results of well-established methods adopted in the literature showing a higher accuracy.
615. LAPSE:2023.22761
A Novel Topology Optimization Approach for Flow Power Loss Minimization Across Fin Arrays
March 24, 2023 (v1)
Subject: Optimization
Keywords: Brinkman penalization, fin array, hydrodynamic power loss minimization, periodic flow, pseudo-spectral, topology optimization
Fin arrays are widely utilized in many engineering applications, such as heat exchangers and micro-post reactors, for higher level of fluid−solid contacts. However, high fluid pressure loss is reportedly the major drawback of fin arrays and a challenge for pumping supply, particularly at micro-scales. Previous studies also indicate that fin shapes, spacing and alignment play an important role on the overall pressure losses. Therefore, we present a numerical tool to minimize pressure losses, considering the geometrical aspects related to fin arrays. In this regard, a density-based topology optimization approach is developed based on the pseudo-spectral scheme and Brinkman penalization in 2D periodic domains. Discrete sensitives are derived analytically and computed at relatively low cost using a factorization technique. We study different test cases to demonstrate the flexibility, robustness and accuracy of the present tool. In-line and staggered arrays are considered at various Reynold... [more]
616. LAPSE:2023.22746
A FACTS Devices Allocation Procedure Attending to Load Share
March 24, 2023 (v1)
Subject: Optimization
Keywords: FACTS allocation, index-based optimization, load share, power grids, voltage stability
Power system stability is a topic which is attracting considerable interest due to the increase of both electrical demand and distributed variable generation. Since Flexible AC Transmission Systems (FACTS) devices are an increasingly widespread solution to these issues, it is important to study how their allocation procedure should be done. This paper seeks to assess the influence of load share in FACTS devices allocation. Despite this interest, researchers, as well as system planners, have mainly focused on studying single power system configuration rather than using a wider approach. Keeping this in mind, we have iteratively created several load share scenarios based on an IEEE 14-bus test system. Subsequently, we have applied an heuristic procedure in order to demonstrate how load share may affect the results of the FACTS devices allocation procedure. Additionally, we have compared results from two different objective functions so as to evaluate our proposal. Finally, we have propos... [more]
617. LAPSE:2023.22741
On the Sensitivity of Local Flexibility Markets to Forecast Error: A Bi-Level Optimization Approach
March 24, 2023 (v1)
Subject: Optimization
Keywords: bi-level optimization, optimal flexibility dispatch, sensitivity analysis, transactive energy
The large-scale integration of intermittent distributed energy resources has led to increased uncertainty in the planning and operation of distribution networks. The optimal flexibility dispatch is a recently introduced, power flow-based method that a distribution system operator can use to effectively determine the amount of flexibility it needs to procure from the controllable resources available on the demand side. However, the drawback of this method is that the optimal flexibility dispatch is inexact due to the relaxation error inherent in the second-order cone formulation. In this paper we propose a novel bi-level optimization problem, where the upper level problem seeks to minimize the relaxation error and the lower level solves the earlier introduced convex second-order cone optimal flexibility dispatch (SOC-OFD) problem. To make the problem tractable, we introduce an innovative reformulation to recast the bi-level problem as a non-linear, single level optimization problem whic... [more]
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