Load Allocation Problem Research Articles

Scenario-Based Uncertainty Modeling for Power Management in Islanded Microgrid Using the Mixed-Integer Distributed Ant Colony Optimization

Reliable droop-controlled islanded microgrids are necessary to expand coverage and maximize renewables potential. Nonetheless, due to uncertainties surrounding renewable generation and load forecast, substantial power mismatch is expected at off-peak hours. Existing energy management systems such as storage and demand response are not equipped to handle a large power mismatch. Hence, utilizing dump loads to consume excess power is a promising solution to keep frequency and voltage within permissible limits during low-load hours. Considering the uncertainty in wind generation and demand forecast during off-peak hours, the dump load allocation problem was modeled within a scenario-based stochastic framework. The multi-objective optimization with uncertainty was formulated to minimize total microgrid cost, maximum voltage error, frequency deviation, and total energy loss. The mixed-integer distributed ant colony optimization was utilized in a massive parallelization framework for the first time in microgrids to solve the decomposed deterministic problem of the most probable scenarios. Moreover, a flexible and robust load-flow method called general backward/forward sweep was used to obtain the load-flow solution. The optimization problem was applied to the IEEE 69-bus and 118-bus systems. Furthermore, a cost benefit analysis was provided to highlight the proposed method’s advantage over battery-based power management solutions. Lastly, the obtained results further demonstrate the fundamental role of dump load as power management solution while minimizing costs and energy losses.

Impact of Stochastic Generation/Load Variations on Distributed Optimal Energy Management in DC Microgrids for Transportation Electrification

This paper studies the impact of stochastic load variations on distributed optimal load tracking and allocation (OLTA) problems in cyber-physical DC microgrids (MGs) for transportation electrification. Without load variations, the distributed optimization strategies developed in our earlier work can achieve convergence to global optimal solutions in a multi-objective optimization that balances fair load allocation and power loss reduction. Under persistent stochastic load variations, this paper develops distributed optimal strategies to track time-varying loads under noisy observations and establishes their convergence properties and error bounds. The limiting behavior of the errors characterizes the fundamental impact of the step size on irreducible errors due to conflict between attenuating observation noises and tracking load changes. Optimality conditions and algorithms for selecting the optimal step size are introduced to guide step size selection in practical applications. Simulation studies on real-world systems demonstrate the effectiveness of the proposed algorithms and validate the theoretical results.

Complex Energy Networks Optimization: Part I—Development and Validation of a Software for Optimal Load Allocation

Abstract The growing diffusion of the distributed generation systems, due to the European and national legislations which impose the fossil fuel and greenhouse gas emissions reduction and the renewable sources exploitation, have led to an increase in the complexity of the existing energy networks. The main issue of the complex energy grids is their management, which consists in the resolution and optimization of the load allocation problem by minimizing the primary energy consumption and, thus, improving the overall efficiency. In this context, the aim of this paper is to develop and validate a nonlinear algorithm suitable for the resolution of the load allocation problem. In detail, the software combo, which has been developed by the University of Bologna, is based on a nonheuristic algorithm and allows to optimize a complex energy network—characterized by electrical, thermal, cooling and fuel fluxes—by evaluating all the possible combinations of solutions. The objective function of the software consists in the minimization of the total cost of energy production, including not only the variable costs, but also the costs related to the environmental impact of the energy systems. In this paper the mathematical model of the algorithm at the basis of the software combo is presented and described in detail. Furthermore, the software has been validated by its application to a case study and comparing the results with the ones obtained with a previously developed software based on a genetic algorithm (heuristic nonlinear method).

Equilibrium strategy based waste load allocation using simulated annealing optimization algorithm.

This study focuses on development of equilibrium strategy based on simulated annealing (SA) algorithm for balancing economic and environmental concerns in waste load allocation (WLA) problem. To resolve conflicts among various stakeholders, including Iran Department of Environment (DoE) as governmental authority and industrial and municipal dischargers, Stackelberg and Nash bargaining games have been applied in this WLA problem and the results have been compared. SA algorithm has been coupled to QUAL2Kw model to derive optimal WLA program and the environmental penalty tariff (EPT) in Nash bargaining and Stackelberg games. The proposed tools and methodologies were illustrated in a case study of multi-stakeholders WLA problem in Gheshlagh River, Sanandaj, Kordestan, Iran. The results indicate that lower BOD removal rates are allocated to the pollutant dischargers in the Stackelberg game compared to the Nash bargaining game. Furthermore, the EPT assigned by Iran DoE in Stackelberg and Nash bargaining games are 11.25 and 3.6 Rials/(gr/month), respectively. The estimated EPT in the Stackelberg game is close to the current tariff (10 Rials/(gr/month)) specified by Iran DoE on impermissible BOD discharges.

Allocation of unequally-weighted wastewater discharge loads using a simulation-optimization approach

In this study, a new simulation–optimization approach is proposed to solve the multi-pollutant waste load allocation (WLA) problems in surface water systems. The proposed approach simulates the fate and transport of multiple pollutants utilizing the AQUATOX model. Since AQUATOX is an independent model and its integration into the optimization process is computationally not efficient, a multi-pollutant concentration–response matrix (mpCRM) is developed by using the results of the AQUATOX model. This mpCRM is then integrated into an optimization model where a nonlinear generalized reduced gradient (GRG) optimization method is used. Unlike in previously conducted studies, a new optimization formulation is proposed wherein the multiple pollutant loads are allocated among the source locations depending on their pre-assigned load allocation weights. This formulation allows for an equal or variable pollutant load allocation plan among source locations depending on the water management strategy for the watershed. The applicability of the proposed approach is evaluated on a sub-watershed of the Küçük Menderes River Basin (KMRB) in Turkey by considering different load allocation scenarios. Furthermore, a detailed sensitivity analysis is conducted to evaluate the model results for different problem parameters. Identified results suggest that the proposed simulation–optimization approach is an effective way to solve the multi-pollutant WLA problem.

Coded Computation Over Heterogeneous Clusters

In large-scale distributed computing clusters, such as Amazon EC2, there are several types of “system noise” that can result in major degradation of performance: system failures, bottlenecks due to limited communication bandwidth, latency due to straggler nodes, and so on. There have been recent results that demonstrate the impact of coding for efficient utilization of computation and storage redundancy to alleviate the effect of stragglers and communication bottlenecks in homogeneous clusters. In this paper, we focus on general heterogeneous distributed computing clusters consist of a variety of computing machines with different capabilities. We propose a coding framework for speeding up distributed computing in heterogeneous clusters by trading redundancy for reducing the latency of computation. In particular, we propose heterogeneous coded matrix multiplication (HCMM) algorithm for performing distributed matrix multiplication over heterogeneous clusters that are provably asymptotically optimal for a broad class of processing time distributions. Moreover, we show that HCMM is unboundedly faster than any uncoded scheme that partitions the total workload among the workers. To demonstrate how the proposed HCMM scheme can be applied in practice, we provide results from numerical studies and Amazon EC2 experiments comparing HCMM with three benchmark load allocation schemes—uniform uncoded, load-balanced uncoded, and uniform coded. In particular, in our numerical studies, HCMM achieves speedups of up to 73%, 56%, and 42%, respectively, over the three benchmark schemes mentioned earlier. Furthermore, we carry out experiments over Amazon EC2 clusters and demonstrate how HCMM can be combined with rateless codes with nearly linear decoding complexity. In particular, we show that HCMM combined with the Luby transform codes can significantly reduce the overall execution time. HCMM is found to be up to 61%, 46%, and 36% faster than the aforementioned three benchmark schemes, respectively. Additionally, we provide a generalization to the problem of optimal load allocation in heterogeneous settings, where we take into account the monetary costs associated with distributed computing clusters. We argue that HCMM is asymptotically optimal for budget-constrained scenarios as well. In particular, we characterize the minimum possible expected cost associated with a computation task over a given cluster of machines. Furthermore, we develop a heuristic algorithm for (HCMM) load allocation for the distributed implementation of budget-limited computation tasks.

Multi-objective multi-pollutant waste load allocation model for rivers using coupled archived simulated annealing algorithm with QUAL2Kw

Abstract A simulation-optimization approach is a suitable tool in waste load allocation problems when considering competing objectives and complex pollutant fate and transport processes in water bodies. Here, an archived multi-objective simulated annealing (AMOSA) algorithm is developed to determine various decision variables related to multi-pollutant waste load allocation (MPWLA) problems. The developed AMOSA algorithm has been coupled to QUAL2Kw in order to derive optimal MPWLA programs in Gheshlagh River, Kordestan, Iran. Minimizing wastewater treatment plant (WWTP) costs, improving the EquityMeasure, and enhancing water quality index (WQI) of the river have been considered as objective functions of MPWLA problems. The applied WQI integrates various water quality parameters (biochemical oxygen demand (BOD), dissolved oxygen (DO), NH4-N, NO3-N, PO4-P, total suspended solids (TSS), and Coliform) in monitoring stations along the river. Results show in the scenario with the best EquityMeasure, higher pollutant removal rates have been allocated to Sanandaj WWTP effluent and pollutant point source No. 7 (creek of landfill leachate) due to their greater contributions to Gheshlagh River contamination. Owing to high pollutant load effluents and unsuitable background conditions in Gheshlagh River, more specific studies show that the water quality index may not be improved over 0.22, no matter how much cost is incurred or equity is sacrificed.

Apoyo a la toma de decisión en una red de evaporadores industriales

<p>La planificación de la producción y tareas de mantenimiento en una red de equipos es una tarea cuya complejidad aumenta exponencialmente con el número de productos, equipos y tareas. Encontrar soluciones óptimas económicas o de eficiencia de recursos) se hace especialmente difícil para un planificador humano, más aún cuando se requiere tomar decisiones en breves periodos de tiempo. Este trabajo aborda el problema de distribución de carga en tiempo real y programación de limpiezas en una red de evaporadores industriales mediante herramientas de ayuda a la decisión basadas en optimización mixta entera con modelos. Las herramientas propuestas tienen en cuenta las preferencias de visualización de los operarios y están integradas con el sistema de supervisión de la planta. Además de proporcionar recomendaciones para la operación óptima de la red, se incluye un sistema semiautomático de actualización de modelos basado en datos históricos de operación.</p>

Planning for agricultural return flow allocation: application of info-gap decision theory and a nonlinear CVaR-based optimization model.

A new methodology is proposed for sizing the required infrastructures for water and waste load allocation in river systems receiving return flow from agricultural networks. A nonlinear optimization model with a constraint based on conditional value at risk (CVaR) is developed to provide water and waste load allocation policies. The CVaR-based constraint limits the probabilistic losses due to existing uncertainties in available surface water. The deep uncertainties of return flow simulation model parameters, which have significant impacts on the simulated quantity and quality of agricultural return flows, are handled by using the info-gap theory. Total dissolved solid (TDS) is selected as water quality indicator and diverting a fraction of return flows to evaporation ponds is considered to control the TDS load of agricultural waste load dischargers. Quantity and TDS load of agricultural return flows over a 1-year cultivation period are simulated by using a calibrated SWAP agro-hydrological model. The results of many runs of SWAP model for different combinations of important uncertain parameters in their ranges of variations provide some response (impact) matrixes which are used in optimization model. The applicability of the proposed methodology is illustrated by applying it to the PayePol region in the Karkheh River catchment, southwest Iran. The selected strategy for water and waste load allocation in the study area is expected to provide total annual benefit of 48.64 million US dollars, while 7.84 million m3 of total return flow should be diverted to evaporation ponds. The results support the effectiveness of the methodology in incorporating existing deep uncertainties associated with agricultural water and waste load allocation problems.

Dayahead Electricity Pricing for a Heterogeneous Microgrid Under Arbitrary Utility and Cost Structures

In this paper, we consider the dayahead load and supply allocation problem in an electrical microgrid, which consists of a system manager, consumers, and suppliers. We do not impose any mathematical, operational, and economic assumptions on the consumers and suppliers other than restricting them to have a finite number of load and supply schedules. For example, a consumer can have arbitrary forms of flexibilities in its demand, such as deferrability or intermittence, and the user can choose from a set of predetermined load allocations that represent these flexibilities. Thus, our system model can accommodate heterogeneous user requirements and constraints in the same problem formulation. Under this system model, we formulate a welfare maximization problem, and derive a distributed primal–dual pricing algorithm. In our algorithm, the system manager generates prices for the load and supply allocations of the users, and given these prices, the users independently choose the schedules to their best operational and economic interests. Furthermore, the pricing algorithm incentivizes the users so that their decisions benefit the system performance, and it achieves the optimal load and supply allocation. Finally, we study the algorithm’s performance via simulations and demonstrate how the demand-side flexibilities are utilized for the system’s benefit.

Robust integrated production-maintenance scheduling for an evaporation network

This work aims to reduce the global resource consumption in an industrial evaporation network by better tasks management and coordination. The network works in continuous, processing some products in several evaporation plants, so optimal load allocation and product-plant assignment problems appear. The plants have different features (capacity, equipment, etc.) and their performance is affected by fouling inside the heat exchangers and external factors. Hereby, the optimizer has to decide when maintenance operations have to be triggered. Therefore, a mixed production/maintenance scheduling problem arises. The plant behavior is approximated by surrogate linear models obtained experimentally, allowing thus the use of mixed-integer linear optimization routines to obtain solutions in acceptable time. Furthermore, uncertainty in the weather forecast and in the production plan is also considered via a two-stage stochastic programming approach. Finally, a trade-off analysis between other objectives of interest is given to support the decision maker.

An improved risk-explicit interval linear programming model for pollution load allocation for watershed management.

Although the risk-explicit interval linear programming (REILP) model has solved the problem of having interval solutions, it has an equity problem, which can lead to unbalanced allocation between different decision variables. Therefore, an improved REILP model is proposed. This model adds an equity objective function and three constraint conditions to overcome this equity problem. In this case, pollution reduction is in proportion to pollutant load, which supports balanced development between different regional economies. The model is used to solve the problem of pollution load allocation in a small transboundary watershed. Compared with the REILP original model result, our model achieves equity between the upstream and downstream pollutant loads; it also overcomes the problem of greatest pollution reduction, where sources are nearest to the control section. The model provides a better solution to the problem of pollution load allocation than previous versions.

Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China.

This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.

A decision-making framework for river water quality management under uncertainty: Application of social choice rules

An important issue in river water quality management is taking into account the role played by wastewater dischargers in the decision-making process and in the implementation of any proposed waste load allocation program in a given region. In this study, a new decision-making methodology, called ‘stochastic social choice rules’ (SSCR), was developed for modeling the bargaining process among different wastewater dischargers into shared environments. For this purpose, the costs associated with each treatment strategy were initially calculated as the sum of treatment cost and the fines incurred due to violation of water quality standards. The qualitative simulation model (QUAL2Kw) was then used to determine the penalty function. The uncertainty associated with the implementation of strategies under the economic costs (i.e., the sum of treatment and penalty costs) was dealt with by a Monte-Carlo selection method. This method was coupled with different social choice methods to identify the best solution for the waste load allocation problem. Finally, using the extended trading-ratio system (ETRS), the most preferred treatment strategy was exchanged among dischargers as the initial set of discharge permits aimed at reducing the costs and encouraging dischargers to participate in the river water quality protection scheme. The proposed model was finally applied to the Zarjoub River in Gilan Province, northern Iran, as a case study. Results showed the efficiency of the proposed model in developing waste load allocation strategies for rivers.

Optimal load allocation of complex ship power plants

In a world with increased pressure on reducing fuel consumption and carbon dioxide emissions, the cruise industry is growing in size and impact. In this context, further effort is required for improving the energy efficiency of cruise ship energy systems.In this paper, we propose a generic method for modelling the power plant of an isolated system with mechanical, electric and thermal power demands and for the optimal load allocation of the different components that are able to fulfil the demand.The optimisation problem is presented in the form of a mixed integer linear programming (MINLP) problem, where the number of engines and/or boilers running is represented by the integer variables, while their respective load is represented by the non-integer variables. The individual components are modelled using a combination of first-principle models and polynomial regressions, thus making the system nonlinear.The proposed method is applied to the load-allocation problem of a cruise ship sailing in the Baltic Sea, and used to compare the existing power plant with a hybrid propulsion plant. The results show the benefits brought by using the proposing method, which allow estimating the performance of the hybrid system (for which the load allocation is a non-trivial problem) while also including the contribution of the heat demand. This allows showing that, based on a reference round voyage, up to 3% savings could be achieved by installing the proposed system, compared to the existing one, and that a NPV of 11kUSD could be achieved already 5years after the installation of the system.

Hybrid Nested Particle Swarm Optimization for a Waste Load Allocation Problem in River System

AbstractThe aim of this article is to develop a hybrid nested particle swarm optimization to solve a Pigovian tax-based waste load allocation problem for river systems. The river system at the Tuojiang River basin is the prototype which is then extended to a generalized waste load allocation problem. The responsible environmental protection agency (EPA), as the leader, sets the pollution tax standards at a given checkpoint to resolve the conflict between the dischargers, and each discharger, as the follower, makes biological oxygen demand (BOD) removal decisions to minimize their own pollution costs under the specified pollution and pollution tax standards. A cooperative bilevel multifollower decision-making model is established that takes into account the objectives and constraints. The particular nature of this model requires the development of a nested particle swarm optimization algorithm. Instead of using a traditional particle performance measurement method, an exact algorithm for solving the lower-...

TSC-based Method to Enhance Asset Utilization of Interconnected Distribution Systems

This paper proposes a new planning method for interconnected smart distribution networks based on total supply capability (TSC), which provides better utilization of existing assets. The specific five steps of the proposed TSC-based planning are: 1) analysis of the power supply problem; 2) calculation of the TSC value; 3) verification and adjustment of TSC and total load; 4) verification between distributed TSC and each feeder load; and 5) ${N-1}$ simulation. The load allocation problem is solved with a model that is capable of searching optimized load allocation considering ${N-1}$ security constraints. Two planning cases are presented to illustrate this method and to compare it with traditional substation-network two-step planning. It is shown that the TSC-based planning can exploit existing networks efficiently and save money. The proposed planning approach is suitable for urban smart distribution networks featured by distribution automation and large-scale interconnection.

Multi-objectiveWaste LoadAllocation in RiverSystembyMOPSOAlgorithm

This paper explores the capabilities of Multi-objective Particle Swarm Optimization algorithmin a simulation-optimization model for solving waste load allocation problems. The main goals are totaltreatment costs, violation of the water quality standards and equity. In this research, the water qualitysimulation model is coupled with a multi-objective optimization model, MOPSO. In order to derive nondominatedsolutions, two different optimization models are used. The first is referred to as the cost versusquality model and the second one also consider minimizing cost and inequity. For the each case, the trade-offcurve (Pareto front) is derived and the best non-dominated solution on the trade-off could be selected bystakeholders and decision makers. The proposed model has been developed for Haraz River in the northernpart of Iran which represented scenarios considering different interests and answered questions to modifyscenarios according to the decision makers’ideas. Solutions were compared with NSGA-II, and the resultsdemonstrate a suitable convergence and diversity of proposed algorithm.

Load allocation problem for optimal design of aircraft electrical power system

More and more electric systems are embedded in today aircraft. As a result, the complexity of electrical power system design is increasing and the need of generic and efficient design methods is today required. Among numerous design tasks, the allocation of electric systems on the busbars of the electrical power system is considered as an important one since it has a direct impact on the aircraft mass. But due to the high number of possible allocations and regarding the large diversity of potential sizing cases for the equipments, finding the optimal allocation of electric loads is a hard task. In this paper, the problem is formalized mathematically. Then, four stochastic optimization methods are assessed on complex load allocation problems. Based on this assessment, a genetic algorithm using niching method is considered as the most appropriate algorithm for solving this aircraft design problem

Fast and reliable distribution load and state estimator

A new methodology to solve load allocation and state estimation problems for medium voltage systems is presented. The main innovation of the proposed solution involves iterating between load allocation and state estimation solutions, and the consideration of a sliding window to update input data. The use of daily load curves is also a key feature of the proposed solution and determinant in the final solution. Not only does the detailed and thorough analysis through numerous tests demonstrate the good performance of the proposed procedure, but they also confirm the accuracy of the results.