Multilevel Optimization Research Articles

Sustainable power systems operations under renewable energy induced disjunctive uncertainties via machine learning-based robust optimization

For sustainable and reliable power systems operations integrating variable renewable energy, it is essential to incorporate the uncertain intermittent power outputs. A novel robust unit commitment framework with data-driven disjunctive uncertainty sets is proposed for sustainable energy systems with volatile renewable wind power, assisted by machine learning. The approach can flexibly identify the uncertainty space based on renewable power forecast error data with disjunctive structures. Specifically, the uncertainty data are grouped using K-means and density-based spatial clustering of applications with noise (DBSCAN) following the optimal cluster number determined by the Calinski-Harabasz index. Disjunctive uncertainty sets are constructed accordingly as the union of multiple basic uncertainty sets, including conventional box and budget uncertainty sets, and data-driven uncertainty sets using Dirichlet process mixture model, principal component analysis coupled with kernel density estimation, and support vector clustering. Subsequently, the problem is formulated into a two-stage adaptive robust unit commitment model with data-driven disjunctive uncertainty sets and with a multi-level optimization structure. To facilitate the solution process, a tailored decomposition-based optimization algorithm is developed. The effectiveness and scalability of the proposed framework are illustrated with two case studies investigating sustainable operations scheduling based on IEEE 39-bus and 118-bus systems, considering the integration of intermittent renewable energy. Results show that the proposed framework can reduce the price of robustness by 8–48% compared to the conventional “one-set-fits-all” robust optimization approaches. Benchmarking with stochastic programming indicates that the proposed framework can achieve the same or better economic performance for sustainable operations with over 75% less computational time.

Capacity withholding assessment of power systems considering coordinated strategies of virtual power plants and generation companies

This paper presents a multi-level optimization framework for power system operators' joint electricity markets capacity-withholding assessment. The main contribution of this research is that three capacity-withholding indices are introduced for day-ahead, intra-day, and real-time scheduling of the system that detect the capacity withholding and arbitrage opportunities of Virtual Power Plants (VPPs) and non-utility fossil-fueled GENeration COmpanies (GENCOs) in an ex-ante procedure. A three-level optimization process is used so that the system operator can estimate the coordinated bidding of VPPs/GENCOs in different energy and ancillary services markets to prevent the formation of withholding groups. The first level problem consists of two stages. The first stage estimates the optimal capacity withholding and arbitrage bidding strategy of VPPs/GENCOs, and the second stage determines the optimal system scheduling for the day-ahead horizon. A full competition algorithm is also carried out to evaluate the competition states of VPPs/GENCOs. The second and third level problems consist of two optimization stages for the intra-day and real-time optimization horizons. At the first stage of each level, the process estimates the coordinated bidding of VPPs/GENCOs, and at the second stage of each level, the system resources are optimally dispatched. The proposed method is applied to 30-bus and 118-bus IEEE test systems. The proposed algorithm reduced the maximum locational marginal prices of 30-bus and 118-bus test systems by about 57.04% and 44.73% compared to the normal and the worst-case contingency operating conditions, respectively. Furthermore, the proposed method reduced the average values of day-ahead, intra-day and real-time dynamic capacity withholding indices of the 118-bus test system by about 32.92%, 40.1%, and 46.85%, respectively.

An integrated power load point-interval forecasting system based on information entropy and multi-objective optimization

During an era of rapid growth in electricity demand throughout society, accurate forecasting of electricity loads has become increasingly important to guarantee a stable power supply. Nevertheless, historical models do not address the structure of the data itself, and a single model cannot accurately determine the nonlinear characteristics of the data. This would not allow for accurate and stable predictions. With the aim of filling this gap, this paper proposes an innovative intelligent power load point-interval forecasting system. The system discretizes the time series, then performs efficient dimensionality reduction by fuzzification, and multi-level optimization of five benchmark deep learning models by the proposed multi-objective optimization algorithm, and finally analyzes the uncertainty of the prediction results. Experiments comparing the developed prediction system with other models were conducted on three datasets, and the prediction results were discussed for validation from multiple perspectives. The simulation results show that the proposed model has superior prediction accuracy, robustness and uncertainty analysis capability, and can provide accurate deterministic prediction information and fluctuation interval analysis to ensure the long-term safety and stability and operation of the grid.

Optimising Building-to-Building and Building-for-Grid Services Under Uncertainty: A Robust Rolling Horizon Approach

Energy systems are undergoing radical changes that have resulted in buildings being regarded as proactive players with the potential to contribute positively to energy networks. This study investigates the role of active buildings (ABs) as prosumers in energy systems by introducing a building-to-building (B2B) strategy for energy exchange between residential units, as well as a building-for-grid (B4G) model by exploiting the demand flexibility of residential microgrids (RMGs). The mid-market rate mechanism is adopted to produce local market price signals at RMG level. A robust rolling horizon controller is developed for real-time energy management of a community of ABs. This control philosophy can improve the robustness of the RMG in face of real-time weather and energy price prediction errors. The proposed method is a multi-level optimisation which pursues multiple goals while making a trade-off between operational cost and occupant comfort. Finally, the repercussions of COVID-19 induced power consumption resulting from changing lifestyle and building occupancy profile is analysed by the proposed method as a case study. The results show that the proposed B2B and B4G strategy can reduce energy bills by 18.45%, while notable robust real-time control and computational efficiencies are achieved when benchmarked against conventional methods.

A framework for generalized Benders’ decomposition and its application to multilevel optimization

We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of optimization problems that fall under the umbrella of multilevel/multistage mixed integer linear optimization problems. The application of this abstract framework to this broad class of problems provides new insights and a broader interpretation of the core ideas, especially as they relate to duality and the value functions of optimization problems that arise in this context.

Interactive Multi-level planning for energy management in clustered microgrids considering flexible demands

This paper presents a novel interactive multi-level planning strategy for the energy management of distribution networks with clustered microgrids (CMGs). CMGs are a group of microgrids with multiple renewable energy resources that comprise various technologies, such as photovoltaic systems, wind turbines, micro turbines and electric vehicles. This study develops an innovative multi-level optimization framework for the energy management coordination between microgrids and CMGs in the lower level, between clusters and distribution systems, and finally between distribution systems and upstream networks in the upper level. Accordingly, an hourly optimal energy management (HOEM) system is applied to minimize the multi-objective objective function for each level. The lower level may be operated in islanded or grid-connected mode in some hours. This is decided by changing switches between MGs, clusters, and grids, while the upper level is only operated in the grid-connected mode. Moreover, a demand response program that has a great effect on the hourly planning of switches is modeled in the upper level. The proposed model is tested on CMGs and actual distribution systems. The results show the significance of this planning strategy in the techno-economic aspects and optimal power transaction in the distribution system operation.

Lightweight design method and application of MEWP bracket based on multi-level optimization

<abstract> <p>Mobile elevating work platform (MEWP) is a large-scale engineering machinery equipment that transports workers and tools to the designated height for operation. As the key supporting component of MEWP, the bracket simultaneously needs to meet the performances of high stiffness and strength. Furthermore, the mechanical performance of the bracket can be significantly influenced by its cross-sectional shape. However, the optimal cross-sectional shape of bracket is not easily to obtain owing to the lacking of lightweight design method. Thus, a lightweight design method of MEWP bracket based on multi-level optimization is proposed in this paper. Firstly, the multi-case topology optimization model of MEWP bracket is constructed by using the compromise programming method, and the optimal section configuration of MEWP bracket is obtained based on Solid Isotropic Material with Penalization (SIMP). Secondly, the parameterization of the cross-sectional shape of bracket is realized using the mesh deformation technology, and the multi-case optimization mathematical model of the MEWP bracket is established. Then, the cross-sectional shape and gauge of the bracket are optimized using multi-level optimization method. The optimized results show that weight reduction mass is 11.66 kg and the ratio is 52.4% under the premise that the stiffness of the bracket does not decrease. Furthermore, the weight of MEWP bracket optimized by the multi-level optimization method reduced by 1.27 kg compared with single gauge optimization method. Finally, a physical prototype is developed according to the optimization results.</p> </abstract>

Self-directed machine learning

Conventional machine learning (ML) relies heavily on manual design from machine learning experts to decide learning tasks, data, models, optimization algorithms, and evaluation metrics, which is labor-intensive, time-consuming, and cannot learn autonomously like humans. In education science, self-directed learning, where human learners select learning tasks and materials on their own without requiring hands-on guidance, has been shown to be more effective than passive teacher-guided learning. Inspired by the concept of self-directed human learning, we introduce the principal concept of Self-directed Machine Learning (SDML) and propose a framework for SDML. Specifically, we design SDML as a self-directed learning process guided by self-awareness, including internal awareness and external awareness. Our proposed SDML process benefits from self task selection, self data selection, self model selection, self optimization strategy selection and self evaluation metric selection through self-awareness without human guidance. Meanwhile, the learning performance of the SDML process serves as feedback to further improve self-awareness. We propose a mathematical formulation for SDML based on multi-level optimization. Furthermore, we present case studies together with potential applications of SDML, followed by discussing future research directions. We expect that SDML could enable machines to conduct human-like self-directed learning and provide a new perspective towards artificial general intelligence.

Estimation of Light Field Depth Based on Multi-Level Network Optimization

Estimation of Light Field Depth Based on Multi-Level Network Optimization

A distributionally robust approach for the optimal protection of power networks with endogenous uncertainty

Power networks are among the most important infrastructures in any society, and protecting them from a large variety of disruptive events is an essential task. Finding an optimal protection plan often takes the form of a multilevel optimization problem. Recently, approaches based on distributionally robust optimization (DRO) have gained the attention of many scholars. In fact, DRO allows protecting the decision-maker from the ambiguity arising from the imprecisely identified probability distributions of the failure scenarios. In this framework, the probability distribution of the failure scenarios is assumed to be known ambiguously, and contained in an ambiguity set defined by moment-based conditions. In practice, some decisions taken in the protection plan affect the conditions of the ambiguity set. We refer to this situation as DRO with endogenous uncertainty. In this paper, we study the impact of the endogenous uncertainty on the optimal protection plan of a power network, using a numerical example built upon the IEEE 14-bus system with a traditional moment-based ambiguity set.

Smart Energy Management in Virtual Power Plant Paradigm With a New Improved Multilevel Optimization Based Approach

A virtual power plant (VPP) is a cloud based distributed power plant that aggregates the capacities of diverse distributed energy resources (DERs) for the purpose of enhancing power generation as well as trading or selling power on the electricity market. The main issue faced while working on VPPs is energy management. Smart energy management of a VPP is a complex problem due to the coordinated operation of diverse energy resources and their associated uncertainties. This research paper proposes a real-time (RT) smart energy management model for a VPP using a multi-objective, multi-level optimization-based approach. The VPP consists of a solar, wind and thermal power unit, along with an energy storage unit and some flexible demands. The term multi-level refers to three different energy levels depicted as three homes comprising of different amounts of loads. RT operation of a VPP is enabled by exploiting the bidirectional communication infrastructure. Multi-objective RT smart energy management is implemented on a community-based dwelling system using three alternative algorithms i.e., hybrid optimal stopping rule (H-OSR), hybrid particle swarm optimization (H-PSO) and advanced multi-objective grey wolf optimization (AMO-GWO). The proposed technique focuses on achieving the objectives of optimal load scheduling, real-time pricing, efficient energy consumption, emission reduction, cost minimization and maximization of customer comfort altogether. A comparative analysis is performed among the three algorithms in which the calculated real-time prices are compared with each other. It is observed that on average H-PSO performs 7.86 % better than H-OSR whereas AMO-GWO performs 10.49% better than H-OSR and 5.7% better than H-P-SO. This paper concludes that AMO-GWO is the briskest, most economical, and efficient optimization algorithm for RT smart energy management of a VPP.

A Multi-Level Optimization Model Based Integration Scheduling Method for Flexible Job Shop with Green Lot Splitting

A Multi-Level Optimization Model Based Integration Scheduling Method for Flexible Job Shop with Green Lot Splitting

Optimization of flight test tasks allocation and sequencing using genetic algorithm

Flight test tasks arrangement is one of the most significant problems in the development of new civil aircraft. Normally, there are many factors restraining flight test tasks arrangement, including characteristics of experimental aircraft, requirements of tasks themselves, and logical relationships among them, leading to increased development period and costs. Hence, flight test tasks arrangement is generally viewed as a multi-constraint nonlinear optimization problem. To improve flight test efficiency, a multi-level optimization model of flight test tasks allocation and sequencing is introduced in this paper, where flight test period is the main optimization objective, and a penalty function evaluating tasks testing dates is the minor optimization objective. A flight test tasks sequence oriented improved genetic algorithm (FTTSOIGA) is proposed to solve the model. Firstly, a tasks allocation algorithm is designed to establish the mapping between tasks sequence and tasks arrangement result, which is independent of feasible sequence. Then, the arrangement result is optimized by optimizing the tasks sequence using the genetic algorithm. Furthermore, a tasks sequence adjustment strategy is applied to accelerate algorithm convergence. Simulation cases of 3 experimental aircraft and 80 flight test tasks demonstrate the efficiency of FTTSOIGA.

Unit Commitment under Uncertainty using Data-Driven Optimization with Clustering Techniques

This paper proposes a novel robust unit commitment (UC) framework with data-driven disjunctive uncertainty sets for volatile wind power outputs, assisted by machine learning techniques. To flexibly identify the uncertainty space based on wind power forecast error data with disjunctive structures, the uncertainty data are grouped using K-means and density-based spatial clustering of applications with noise following the optimal cluster number determined by the Calinski-Harabasz index. The disjunctive uncertainty sets are constructed accordingly as the union of multiple basic uncertainty sets, including conventional box and budget uncertainty sets, and data-driven uncertainty sets using Dirichlet process mixture model, principal component analysis coupled with kernel density estimation, and support vector clustering. The problem is formulated into a two-stage adaptive robust UC model with data-driven disjunctive uncertainty sets and with a multi-level optimization structure. To facilitate the solution process, a tailored decomposition-based optimization algorithm is developed. The effectiveness of the proposed framework is illustrated using an application on the IEEE 39-bus system. The proposed approach can reduce the price of robustness by 8-38 % compared to the conventional “one-set-fits-all” approaches. Benchmarking with stochastic programming indicates that the proposed framework can achieve the same or better economic performance with over 30 % less computational time.

Increasing Superstructure Optimization Capacity Through Self-Learning Surrogate Models

Simulation-based optimization models are widely applied to find optimal operating conditions of processes. Often, computational challenges arise from model complexity, making the generation of reliable design solutions difficult. We propose an algorithm for replacing non-linear process simulation models integrated in multi-level optimization of a process and energy system superstructure with surrogate models, applying an active learning strategy to continuously enrich the database on which the surrogate models are trained and evaluated. Surrogate models are generated and trained on an initial data set, each featuring the ability to quantify the uncertainty with which a prediction is made. Until a defined prediction quality is met, new data points are continuously labeled and added to the training set. They are selected from a pool of unlabeled data points based on the predicted uncertainty, ensuring a rapid improvement of surrogate quality. When applied in the optimization superstructure, the surrogates can only be used when the prediction quality for the given data point reaches a specified threshold, otherwise the original simulation model is called for evaluating the process performance and the newly obtained data points are used to improve the surrogates. The method is tested on three simulation models, ranging in size and complexity. The proposed approach yields mean squared errors of the test prediction below 2% for all cases. Applying the active learning approach leads to better predictions compared to random sampling for the same size of database. When integrated in the optimization framework, simpler surrogates are favored in over 60% of cases, while the more complex ones are enabled by using simulation results generated during optimization for improving the surrogates after the initial generation. Significant time savings are recorded when using complex process simulations, though the advantage gained for simpler processes is marginal. Overall, we show that the proposed method saves time and adds flexibility to complex superstructure optimization problems that involve optimizing process operating conditions. Computational time can be greatly reduced without penalizing result quality, while the continuous improvement of surrogates when simulation is used in the optimization leads to a natural refinement of the model.

Reliability‐based risk‐involved macrogrid expansion planning considering community microgrids within a market environment

In this paper, a new reliability-based risk-involved model is presented for multi-period macrogrid expansion planning (MAGEP) by amalgamating the notion of community microgrids (CoMigs) within a market environment. The main targets of the proposed model are not only to develop a holistic framework for the MAGEP problem, but also to scrutinize the impacts of the macrogrid-connected multi-CoMigs on power supply reliability enhancement. To that end, the mathematical formulation of the proposed model falls into a nonconvex mixed-integer nonlinear three-level optimization problem. The lower-level outlines a security-constrained bid-based-pool electricity market aimed at providing an efficient platform for different CoMigs and market participants—generation companies (GenCos) and distribution companies (DisCos)—to freely trade electrical power across the macrogrid. The intermediate-level represents an interactive decentralized multi-period two-stage microgrid expansion planning (MIGEP) problem in which optimal expansion plans of the CoMigs obtained in the first stage will be examined against the reliability restrictions in the second stage. The upper-level, however, addresses a centralized multi-period techno-economic MAGEP problem, while handling the risks of planning arising from severe uncertainties in forecasted price, demand, and power generation of the CoMigs through a potent envelope-bound information-gap decision theory (IGDT). Due to its proper tackling of the non-convex mixed-integer nonlinear multi-level optimization problems, the symphony orchestra search algorithm (SOSA) is widely employed for solving the proposed model. Effectiveness and capability of the newly developed model are numerically analyzed and verified using its implementation on the IEEE 30-bus and IEEE 118-bus test systems.

РОЗРАХУНОК НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ПЛАКУЮЧОГО ШАРУ ПРИ ПЛАКУВАННІ (ЗВАРЮВАННІ) ВИБУХОМ

Purpose. Development of a mathematical model of the process of elastoplastic deformation of the cladding layer of a layered workpiece during welding (cladding) by explosion with the formation of the objective function of optimal deformation and establishing a relationship between the parameters of welding (cladding) by explosion and the shear bond strength of the layers and the wear resistance of the cladding layer. Methodology. The solution to the problem of elastoplastic deformation is carried out using the equations of the flow theory and the nodal calculation scheme. The required deformation values are determined at the nodal mass points of the computational grid. At each moment of time, the positions of the nodes of the cladding workpiece, thrown under loading by a traveling pressure wave, are de-termined. Deformations and their intensity are determined by the position of the nodes. The task of determining the re-quired parameters of explosion welding (cladding) is reduced to the task of mathematical programming. The objective function is minimized on a family of curves, the arguments of which are the explosion welding (cladding) parameter and the welding gap. The interaction of the cladding workpiece with the pressure wave generated during the detonation of the explosive is determined by the dependences of the pressure of the detonation products, the mass velocity of the cladding workpiece and the shock wave velocity at the moment the shock wave reaches the free surface on the parame-ters of the explosion cladding (welding) with subsequent calculation of the stress-strain state of the workpieces. Accord-ing to the optimal parameters of explosion welding (cladding), a probabilistic assessment of the shear bond strength of the layers is carried out. If the strength is insufficient, the parameters are adjusted. Findings. As a result of numerical modeling, the calculation of the deformed state of the projectile is carried out. The parameters of explosion welding (cladding) are determined, at which the intensity of deformations of the cladding layer corresponds to the limit uniform ones. Based on the obtained parameters of explosion welding (cladding), the calculation of the shear strength of the layer joint was performed. Originality. For the first time, a model has been developed for the optimal deformation of the cladding layer during explosion welding (cladding) of wear-resistant compositions. The target function and the optimal process parameters have been established. A method is proposed for calculating the weighting coefficients of the objective function for multi-criteria multilevel optimization. Practical value. Recommendations for industrial application were developed and modes of explosion welding (cladding) were tested to obtain wear-resistant compositions of aluminum alloy with carbon steel.

Maximisation of installed net resulting force through multi-level optimisation of an ultra-high bypass ratio engine nacelle

Engine/wing interference in podded installations can introduce relevant changes to their isolated behaviour, especially for large turbofans with an ultra-high bypass ratio. With such coupled flow field, the interaction is best described by the integrated force acting on the whole aircraft. Rather than focusing on drag or thrust metrics separately, in this paper we maximise the net resulting force on the NASA CRM wing body with underwing-installed turbofans through a multi-level optimisation procedure of the engine nacelle. The first stage involves two-dimensional axisymmetric geometries for cowl and exhaust ducts shapes optimisation. The solutions are transformed into three-dimensional nacelles with pylon, featuring a non-axisymmetric inlet. The impact of the pylon on the exhaust flow is evaluated through a design of experiment and a successive surrogate-based optimisation. In the last step, nacelle/wing offset, intake angles, and engine orientation are assessed in the installed configuration at fixed lift. The final optimised design is compared with a baseline geometry initially defined, showing a significant improvement of the net vehicle thrust equal to 3% of the reference force. The result highlights a counteracting effect of individual force components, in a way that the installed resulting force can only be improved when considering them globally.

A multi-level optimization model of infrastructure-dependent technology adoption: Overcoming the chicken-and-egg problem

Policymakers seeking to promote the diffusion of infrastructure-dependent technologies are often confronted with the “chicken-and-egg” problem: consumers are reluctant to adopt the technology without adequate infrastructure available, and firms are reluctant to invest in infrastructure without a sufficient number of adopters. This chicken-and-egg problem can hinder the diffusion of new technologies and prolong the timeframe over which existing technological systems remain locked-in. In this paper, we formulate a stylized model of technology policy decision-making from the perspective of a policymaker who seeks to stimulate the market penetration of an infrastructure-dependent technology. Our model is a multi-level optimization problem in which a policymaker (first level) maximizes net social benefits by setting the levels of two incentives: a subsidy for a profit-maximizing firm (in equilibrium with two other firms, the second level) to invest in infrastructure that raises the benefit of adoption to consumers, and a direct subsidy for consumers to adopt the technology (third level). Under certain assumptions about functional forms, we solve the full multi-level problem analytically through backward induction and derive closed-form expressions for the policymaker’s optimal subsidy levels. Then, we present a case study on policies to promote battery electric vehicle (BEV) diffusion. Our results reveal three main insights: (1) the optimal policy portfolio often subsidizes charging infrastructure more than BEV purchases, (2) infrastructure and adoption subsidies tend to be substitutes rather than complements, and (3) an increase in the marginal social benefit of BEV adoption shifts the optimal policy away from infrastructure subsidies and toward BEV subsidies.

Multi-Level Optimization of an Ultra-Low Power BrainWave System for Non-Convulsive Seizure Detection.

We present a systematic evaluation and optimization of a complex bio-medical signal processing application on the BrainWave prototype system, targeted towards ambulatory EEG monitoring within a tiny power budget of 1 mW. The considered BrainWave processor is completely programmable, while maintaining energy-efficiency by means of a Coarse-Grained Reconfigurable Array (CGRA). This is demonstrated through the mapping and evaluation of a state-of-the-art non-convulsive epileptic seizure detection algorithm, while ensuring real-time operation and seizure detection accuracy. Exploiting the CGRA leads to an energy reduction of 73.1%, compared to a highly tuned software implementation (SW-only). A total of 9 complex kernels were benchmarked on the CGRA, resulting in an average 4.7 × speedup and average 4.4 × energy savings over highly tuned SW-only implementations. The BrainWave processor is implemented in 28-nm FDSOI technology with 80 kB of Foundry-provided SRAM. By exploiting near-threshold computing for the logic and voltage-stacking to minimize on-chip voltage-conversion overhead, additional 15.2% and 19.5% energy savings are obtained, respectively. At the Minimum-Energy-Point (MEP) (223 μW, 8 MHz) we report a measured state-of-the-art 90.6% system conversion efficiency, while executing the epileptic seizure detection in real-time.