Network slicing markets have the potential to increase significantly the utilization of virtualized network resources and facilitate the low-cost deployment of over-the-top services. However, their success is conditioned on the service providers (SPs) being able to bid effectively for the virtualized resources. In this paper, we consider a hybrid advance-reservation and spot slice market and study how the SPs should reserve resources to maximize their services' performance while not violating a time-average budget threshold. We consider this problem in its general form where the SP demand and slice prices are time-varying and revealed only after the reservations are decided. We develop a learning-based framework, using the theory of online convex optimization, that allows the SP to employ a no-regret reservation policy, i.e., achieve the same performance with an oracle that has full access to all future demand and prices. We extend the framework to the scenario where the SP decides dynamically its slice orchestration and hence needs to learn the performance-maximizing resource composition; and we further develop a mixed-time scale scheme that allows the SP to leverage spot-market information that is revealed between successive reservations. The proposed learning framework is evaluated using representative simulation scenarios that highlight its efficacy as well as the impact of key system and algorithm parameters.

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This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.@en

In this paper, a new and generalized model for the optimal operation of microgrids is presented. The proposed mathematical model considers both the grid-connected (GC) and islanded (IS) operational modes. First, a mixed integer non-linear programming (MINLP) formulation is introduced, modeling the microgrid as an unbalanced ac three-phase electrical distribution system, comprising distributed generator (DG) units, battery systems and wind turbines. In GC mode, the frequency and the voltage magnitude references are imposed by the main grid at the point of common couple, while in IS mode, it is assumed that the DG units operate with droop control. Additionally, a set of convexification procedures are introduced in order to approximate the original MINLP model into a new convex formulation that can be solved using commercial solvers. The proposed model has been tested in a 25-bus microgrid for different scenarios, including one where a degradation of the voltage magnitude reference is observed. Results show that the proposed model is able to properly define the operational mode of the microgrid, based on the technical constraints of the system.

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In this paper, the economic impact of the active power droop gain in droop-based microgrids has been studied. To accomplish this, a theoretical analysis is presented first. This analysis is used to study a simple case in which the solution of the economic dispatch problem is compared with the dispatch obtained after applying the standard definition of the droop gains for the droop-controlled DGs, given by the Standard IEEE 1547.7. Then, the mathematical model for the optimal power flow of droop-based islanded microgrids is used to simulate and study a real unbalanced three-phase system. Results have shown that the standard definition guarantees a proper active power sharing among all the DG units, independent of the load level. However, as shown by the simulations, the standard definition does not necessarily correspond to the solution with minimum active power losses and can have a significant economic impact when compared with the optimal economic dispatch solution.

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This paper presents a distributed strategy for the optimal dispatch of islanded microgrids, modeled as unbalanced three-phase electrical distribution systems. To set the dispatch of the distributed generation (DG) units, an optimal generation problem is stated and solved distributively based on primal-dual constrained decomposition and a first-order consensus protocol, where units can communicate only with their neighbors. Thus, convergence is guaranteed under the common convexity assumptions. The islanded microgrid operates with the standard hierarchical control scheme, where two control modes are considered for the DG units: a voltage control mode, with an active droop control loop, and a power control mode, which allows setting the output power in advance. To assess the effectiveness and flexibility of the proposed approach, simulations were performed in a 25-bus unbalanced three-phase microgrid. According to the obtained results, the proposed strategy achieves a lower cost solution when compared with a centralized approach based on a static droop framework, with a considerable reduction on the communication system complexity. Additionally, it corrects the mismatch between generation and consumption even during the execution of the optimization process, responding to changes in the load consumption, renewable generation, and unexpected faults in units.

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This paper presents a mixed integer non-linear programming model to optimize, in a centralized fashion, the operation of multiple buildings in a microgrid. The proposed model aims to minimize the total cost of the energy imported from the main grid at the interconnection point, managing the power demand and generation of buildings, while operational constraints of the electrical grid are guaranteed. This approach considers the management of heating, ventilation, and air conditioning units, lighting appliances, photovoltaic generation and energy storage system of each building. Comfortable indoor conditions for the occupants are kept by a set of mathematical constraints. Additionally, a strategy that simplifies the original model is presented, based on a set of linearization techniques and equivalent representations, obtained through a pre-processing stage executed in EnergyPlus software. This strategy allows approximating the proposed model into a mixed integer linear programming formulation that can be solved using commercial solvers. The proposed model was tested in a 13-bus microgrid for different deterministic cases of study with non-manageable loads and smart buildings. A large-size test case is also considered. Finally, a rolling horizon strategy is proposed with the aim of addressing the uncertainty of the data, as well as reducing the amount of forecasting data required.

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This paper presents a new mixed-integer nonlinear programming (MINLP) model for the optimal operation of unbalanced three-phase droop-based microgrids. The proposed MINLP model can be seen as an extension of an optimal power flow for microgrids operating in islanded mode, that aims to minimize the total amount of unsupplied demand and the total distributed generator (DG) generation cost. Since the slack bus concept is not longer valid, the proposed model considers the frequency and voltage magnitude reference as variables. In this case, DGs units operate with droop control to balance the system and provide a frequency and voltage magnitude reference. Additionally, a set of efficient linearizations are introduced in order to approximate the original MINLP problem into a mixed-integer linear programming (MILP) model that can be solved using commercial solvers. The proposed model has been tested in a 25-bus unbalanced three-phase microgrid and a large 124-node grid, considering different operational and time-coupling constraints for the DGs and the battery systems (BSs). Load curtailment and different modes of operation for the wind turbines have also been tested. Finally, an error assessment between the original MINLP and the approximated MILP model has been conducted.

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In this chapter the most significant characteristics and functionalities of an energy management system (EMS) for microgrids are introduced. For this, the definitions of hierarchical control layers are considered. First, the main concepts and modules of the hierarchical control structure of a generalized EMS are presented. Then, energy management function is represented as an optimization problem, described as the simultaneous solution of both, a unit commitment problem and an economic load dispatch problem. An extension of the energy management problem is also formulated based on an optimal power flow. Second, the advantages and disadvantages of using either a centralized or a decentralized EMS approach are discussed. Finally, since the energy management problem is represented as an optimization problem, the most common methodologies and solution algorithms used in the specialized literature are discussed, including metaheuristics, mixedinteger linear approximations, and nonlinear approaches, as well as software tools for implementing models and simulations.

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An extended dynamic programming (EDP) approach is developed to optimize the ac steady-state operation of radial electrical distribution systems (EDS). Based on the optimality principle of the recursive Hamilton-Jacobi-Bellman equations, the proposed EDP approach determines the optimal operation of the EDS by setting the values of the controllable variables at each time period. A suitable definition for the stages of the problem makes it possible to represent the optimal ac power flow of radial EDS as a dynamic programming problem, wherein the 'curse of dimensionality' is a minor concern, since the number of state and control variables at each stage is low and the time complexity of the algorithm grows linearly with the number of nodes of the EDS. The proposed EDP is applied to solve the economic dispatch of the DG units installed in a radial EDS. The effectiveness and the scalability of the EDP approach is illustrated using real-scale systems and comparisons with commercial programming solvers. Finally, generalizations to consider other EDS operation problems are also discussed.

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In this paper, an optimal distributed approach is presented to solve the economic dispatch (ED) problem in an islanded microgrid. Active and reactive resources are taken into account in the optimization problem aiming to consider the operational requirements of the electrical system. The optimization framework is based on primal-dual constrained decomposition. Additionally, two consensus algorithms are develop to be executed in parallel by each unit, aiming to estimate locally the value of the dual variables. Convergence is guaranteed under the common convexity assumptions. Simulations were performed on the standard IEEE 30-bus system considering dispatchable and renewable generation units. The capability of the algorithm to responds in variations in load consumption, renewable generation and faults in units were assessed. Result shows the flexibility and effectiveness of the proposed approach.

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In this paper, a generalization of the λ-Method for the economic dispatch (ED) problem in an islanded electrical distribution system (EDS) is presented. The proposed approach is based on primal-dual constrained decomposition, which allows decomposing the centralized problem into small-scale problems that can be solved in parallel and independently by each unit. Active and reactive resources are taken into account in order to consider the technical operation of the EDS. A technical implementation based on the classic droop control is also proposed, in order to reduce the communication needs of the units and the leader unit. To assess the performance of the proposed approach, simulations were performed on the IEEE 118-bus system. The capability of the algorithm to respond to unexpected changes in load consumption, non-dispatchable generation, and faults in units were assessed. Finally, the flexibility and model independence characteristics of this approach are also shown considering prohibited operational zones (POZ) for some units.

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This paper presents a mixed-integer linear programming (MILP) model for the optimal energy management of residential microgrids, modeled as unbalanced, three-phase, electrical distribution system (EDS). Initially, the problem is formulated as a mixed-integer nonlinear programming (MINLP) problem. Then, a set of linear approximations and equivalent mathematical representations are used to obtain a precise MILP model. The proposed formulation considers three-phase generation units (GU), single-phase photovoltaic (PV) resources, and single-phase energy storage systems (ESS), as well as load management. The aim of the proposed model is to minimize the final operational costs of the microgrid while considering operational constraints of the EDS and an unexpected outage of the main grid through a security-constrained set of equations. The optimal solution of the MILP model is found using commercial convex optimization solvers. The proposed model was tested in a residential, three-phase EDS. Results show that the proposed linearizations and approximations produce accurate solutions when compared with a nonlinear three-phase OPF formulation, with an error in the objective function near to 2% and a maximum error in the voltage near to 1%. Efficiency and flexibility of the proposed methodology are also discussed.@en

This paper presents a new mixed integer linear programing (MILP) model for the management of energy consumption and comfort in smart buildings. Initially, a detailed mixed integer non-linear programming (MINLP) model is formulated. The approach considers the management of heating, ventilation and air conditioning (HVAC) units, lighting appliances, photovoltaic generation (PV) and energy storage system (ESS). Then, a set of linear and equivalent representations are used to approximate the problem by an MILP model. The aims of the proposed model is to minimize the electricity bill by managing the loads, as well as the schedule of the ESS, meanwhile comfortable indoor conditions are ensured by a set of mathematical constraints. A commercial MILP solver was used to guarantee optimality. The strategy was tested in an university building with multiple zones. Comparisons between the proposed MILP model and simulations in EnergyPlus were used to validate the results.

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Reliability analyses are essential for the design of hybrid photovoltaic/wind/battery systems. The selection of design criteria is an important task and has to ensure proper reliability and optimal configuration. In the literature, loss of power supply probability (LPSP) and loss of load hours (LOLH) are the most common reliability criteria used for this matter. This study presents a comparative analysis on LPSP and LOLH design criteria based on a Monte Carlo simulation, taking into consideration uncertainties in the variables involved in the design process. Moreover, two new statistical design criteria are proposed, aiming to avoid over-sizing of the optimal configuration. According to the obtained results, LOLH is a stricter design criterion compared with LPSP, leading to a more reliable energy system. In addition, the optimal configuration selected by using the proposed statistical design criteria showed better performance when compared with the solution based on LPSP or LOLH.

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In this paper, the optimal schedule of dispatchable distributed generation (DG) units connected to radial electrical distribution systems (EDS) is solved using an extended dynamic programming approach. The objective of the optimal DG scheduling problem is to determine the hour-by-hour active generation output of each dispatchable DG unit, in order to minimize the total active power losses of the EDS and the generation costs. The proposed extended dynamic programming (EDP) is an advantageous approach because convexity is not required to obtain a global optimal solution, and the 'curse of dimensionality' is not a concern since the computational complexity of the algorithm grows linearly with the size of the network. Besides, the state variables have only two dimensions, one to represent the active power flows and the other to represent the nodal voltages. A 56-nodes MV distribution system with two dispatchable DG units is used to evaluate the performance of the proposed EDP approach, considering a deterministic and a stochastic case. A set of Monte Carlo simulations is used to analyze the influence of uncertainties. Results confirm that the proposed methodology is a suitable approach to unveil the best operation schedule for dispatchable DG units.

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Distributed Generation (DG) can provide multiple benefits in MV/LV distribution networks. However, high penetration levels may cause technical issues to the grid, as already observed in some countries. Thus, Distribution Network Operators (DNOs) have to consider alternative solutions to guarantee normal operation, even under high penetration levels. In this paper, a time-series based probabilistic methodology is used to estimate the maximum PV hosting capacity of LV distribution networks. The proposed method is applied to assess a real rural Brazilian distribution system. According to the obtained results, voltage regulation and overloads in distribution transformers limit the PV hosting capacity. Therefore, aiming to increase this capacity, the use of PV VAr absorption and OLTC transformers was technically evaluated.

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This paper proposes a real-time Energy Management System (EMS) for a low voltage (LV) Microgrid (MG). The system operation consists in solving the Unit Commitment (UC) and Economic Load Dispatch (ELD) simultaneously for 24 hours ahead at every 15-minute period. This operation is formulated as a multi-objective optimization problem where the minimization of operational cost, total emissions and power losses is simultaneously pursued using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). In this algorithm, crossover and mutation operators were improved with respect to existing approaches to achieve an adequate characterization of the energy management problem and a good algorithm performance. Simulation studies have outlined that, in fact, the NSGA-II can be used as a real-time optimization tool providing a good-quality Pareto front to operate optimally the MG in a limited time of 15 minutes.

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