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The rapid increase in the number of PV installations in current low voltage (LV) distribution networks brings many technical operational challenges. This claims for the deployment of control strategies to deal with these concerns, especially those related to overvoltage issues. Based on this, this paper presents a comprehensive assessment of the performance of PV inverters operating with droop control for overvoltage mitigation using a stochastic methodology based on a Monte Carlo approach. The uncertainty related to the PV generation and the users’ consumption behavior is fully considered through advanced statistical modeling techniques. Voltage magnitude and loading indexes are used as key metrics to assess the technical performance of the distribution network, simulated using OpenDSS, under two droop-based control strategies: Active Power Control (APC) and coordinated Reactive and Active Power Control (RPC-APC). The effects of curtailed energy on the PV users’ revenue is also analyzed. A case of study based on real smart meter data from The Netherlands is used. According to the obtained results, both control strategies are effective to mitigate voltage violations. Nevertheless, for the case of 100% PV penetration, the droop-based coordinated RPC-APC allowed an 18% more of exported energy than the droop-based APC control strategy.

Hierarchical schemes are widely used for the design of inverter-based AC microgrids control strategies. To ensure a reliable operation, hierarchical control must consider together all the functionalities that allow the regulation of key variables and guarantee a safe transition between operation modes. Conventionally, in the literature are proposed three-layer schemes which present relevant drawbacks: they include limited functionalities and they use droop method for the primary layer which, despite its decentralized nature, suffers from issues that have motivated the development of alternative strategies. Considering this, the contribution of this paper is twofold. First, a droop-free hierarchical control strategy that satisfy a proper operation of AC microgrids is proposed. Control objectives such as power-sharing, frequency regulation, optimal power dispatch, and voltage regulation are considered. Second, a closed-loop small-signal model, which facilitates the control parameters design and fills a gap in the literature is presented. Differences between the proposal and previous controls are discussed. Selected tests are carried out in a laboratory microgrid under different conditions, including normal operation and the response to failures in the central controller and to communication impairments. The experimental results show a good performance of the proposal even in adverse conditions.

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.

This paper introduces an adaptive sequential droop control strategy for PV inverters to mitigate voltage rise problems in PV-rich LV distribution networks. To facilitate the effective coordination of sequential ( Q − V and P − V ) droop control of PV inverters, multiple control areas with the strong coupling nature of PV systems are identified based on the e -decomposition technique. The droop control parameters are tuned and adapted, based on a consensus among PV inverters within each control area. This proposed control strategy inherits the autonomous feature of the droop control for coping with voltage rise issues while being able to avoid curtailing a significant amount of PV production. To evaluate the effectiveness of the proposed control strategy, simulations using MATLAB/Simulink are performed on a real European LV distribution network, considering a PV penetration level of about 150%. The obtained results highlight that the proposed control strategy successfully mitigates voltage rise problems while significantly reducing the amount of curtailed PV generation by approximately 35.6% and 76.2% when compared with the static sequential droop control and the static Q − V droop control and adaptive P − V droop control, respectively. Simultaneously, the effective contribution among all the PV systems towards voltage rise mitigation is obtained.

To realize the goals of energy transition, becoming energy-neutral at the neighborhood level by sharing energy among clusters of heterogeneous buildings with local distributed energy resources (DERs), will play a vital role. However, uncertainties related to demand and renewable sources pose a major operational challenge to schedule the DERs. In this paper, a scenario-based mixed-integer linear programming (MILP) model is proposed for an energy management system (EMS) of a local energy community. The proposed EMS executes a stochastic day-ahead scheduling operation of multi-energy systems (MES). A set of scenarios are generated with the Gaussian mixture model (GMM) to consider uncertainties of demand and renewable sources. Moreover, Monte Carlo simulations (MCS) are performed to assess the effectiveness of the proposed EMS compared to the deterministic one. The proposed method is validated by using a real-world case study of a generic Dutch university medical campus in Amsterdam, the Netherlands. Two types of analysis are performed: one-day analysis and seasonal analysis. In both cases, in an average, the stochastic process outperforms the deterministic process considerably, in terms of cost, CO 2 emission, imported electricity from grid and usage of local energy resources.

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.

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.

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.

The proliferation of PV generation systems connected to electrical distribution systems (EDSs) brings many operational challenges, and within them, over-voltage issues are regarded as the most critical. Among all the strategies available to handle these over-voltage issues, those implemented locally at the PV inverters seem to be the more promising, considering their distributed and easy-to-implement features. In this paper, the feasibility and performance assessment of a commercial PV inverter for mitigating over-voltage events in an EDS is presented. To do this, an active and reactive droop-based voltage control strategy is implemented in a commercial inverter. Realtime power hardware-in-the-loop (PHIL) laboratory tests were performed to assess the PV inverter's efficiency when absorbing reactive power, as well as its interaction with the distribution grid. According to the obtained results, the PV inverter's efficiency was not noticeably affected by the changes in reactive power. Additionally, the PV inverter responded accordingly, following the voltage control strategy implemented, providing successfully the expected voltage support services.

This paper proposes a two-stage stochastic market clearing (SMC) model based on a semidefinite programming (SDP) relaxation. The SMC model aims at determining the day-ahead schedule (DA) and the real-time (RT) balance settlement that minimize the total expected production cost. The network capacity constraints are considered in the proposed model through an AC power flow formulation, while the uncertainty in the renewable-based generation is taking into account using a set of stochastic scenarios. In order to solve the proposed non-linear programming model, a SDP relaxation is used. An illustrative example (3-bus test system) and the IEEE Reliability 24-bus test system are used to show the effectiveness and accuracy of the proposed model. Results shown that the proposed SDP relaxation introduce a negligible error, when compared with the solution after solving the original non-linear model.

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.

This paper presents a mixed integer non-linear programming (MINLP) 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 (HVAC) units, lighting appliances, photovoltaic generation (PV) and energy storage system (ESS) 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 (MILP) 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 (RH) strategy is proposed with the aim of addressing the uncertainty of the data, as well as reducing the amount of forecasting data required.

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.

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, mixed-integer linear approximations, and nonlinear approaches, as well as software tools for implementing models and simulations.

This chapter introduces concepts to understand, formulate, and solve a microgrid design and optimal sizing problem. First, basic concepts of energy potential assessment are introduced, in order to determine if a location is suitable for PV and wind generation systems implementation. Second, different modeling approaches are presented and the required characteristics for the optimal microgrid sizing problem are discussed. Third, basic concepts about load estimation for the design and sizing of microgrids are introduced. Fourth, the most common microgrid sizing criteria are presented and classified according to the type of analysis. Fifth, basic concepts related to multi-objective optimization are introduced and some common design approaches and optimization algorithms are presented, emphasizing into multi-objective genetic algorithms. In addition, microgrids design commercial software is reviewed. Sixth, some IEEE standards related to the design, operation, and implementation of microgrids are presented. Finally, the chapter concludes with key remarks on microgrid design and sizing problem.

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.

Local control strategies that operate without relying on communication systems enhance flexibility and reliability of AC industrial microgrids. Based on a previous work in which a secondary switched control was proposed, this paper presents a complementary strategy to improve the frequency regulation by reducing the maximum error. To this end, a dynamic-gain droop method driven by a time protocol is used. With this proposal, the maximum frequency error is effectively reduced without relying on complex techniques and maintaining the simplicity of the basis strategy and the non-use of communications. Experimental results obtained on a laboratory microgrid are presented to validate the performance of the proposed complementary control strategy.

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.

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.

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.

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.