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his paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newtonlike iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch 𝑅����∕𝑋���� ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm.

To guarantee a successful deployment of a droop-based control strategy to mitigate overvoltage problems caused by solar photovoltaic (PV) generation, Distribution System Operators (DSOs) will need to estimate the amount of active power curtailed by the PV inverters for billing purposes. This paper provides a structural elaboration on the development of data-driven approaches in Python to estimate the PV curtailed power as a provision of voltage support services by residential users using droop-based voltage control strategies. The use of the total input data, available for a DSO, would be impractical for an all-regression approach for the estimation of the PV curtailed power. Since in the majority of the data no active power is curtailed, the data-driven models would in this case partly be trained and fitted for situations where there is no active power curtailment. The regression models for the curtailed power prediction are therefore preceded by a classification model. The developed combined classification-regression model was able to estimate the PV curtailed power with an error of less than 4%, for test data from the network on which the model was trained.

In this paper, a Reinforcement Learning (RL)-based approach to optimally dispatch PV inverters in unbalanced distribution systems is presented. The proposed approach exploits a decentralized architecture in which PV inverters are operated by agents that perform all computational processes locally; while communicating with a central agent to guarantee voltage magnitude regulation within the distribution system. The dispatch problem of PV inverters is modeled as a Markov Decision Process (MDP), enabling the use of RL algorithms. A rolling horizon strategy is used to avoid the computational burden usually associated with continuous state and action spaces, coupled with a computationally efficient learning algorithm to model the action-value function for each PV inverter. The effectiveness of the proposed decentralized RL approach is compared with the optimal solution provided by a centralized nonlinear programming (NLP) formulation. Results showed that within several executions, the proposed approach converges either to the optimal solution or to solutions with a PV curtailment excess of less than 2.5% while still enforcing voltage magnitude regulation.

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.

Autonomous microgrids are a suitable solution for off-grid electrification in terms of costs and reliability. The correct sizing of its generation and storage systems ensures efficient utilization of the available energy resources. Generally, many sizing approaches assume optimized energy management strategies that rely on central control architectures. However, these architectures are not always available, especially in limited investment microgrid projects. For this reason, the study of operation scenarios based on decentralized control strategy such as droop control is relevant. Based on this, this paper aims to evaluate the impact of the droop control over the sizing results of a solar/wind/battery/diesel microgrid. For this purpose, a case study of a sizing problem is presented, including the formulation and modelling. Results are presented comparing an hourly optimized energy management scenario with multiple values of the droop control parameters. Simulations results indicate that a competitive total cost can be obtained if the droop parameters are calculated considering the microgrid sizing results. Based on this, a generalizable design methodology for this purpose is presented.

The operation of a community energy storage system (CESS) is challenging due to the volatility of photovoltaic distributed generation, electricity consumption, and energy prices. Selecting the optimal CESS setpoints during the day is a sequential decision problem under uncertainty, which can be solved using dynamic learning methods. This paper proposes a reinforcement learning (RL) technique based on temporal difference learning with eligibility traces (ET). It aims to minimize the day-ahead energy costs while maintaining the technical limits at the grid coupling point. The performance of the RL is compared against an oracle based on a deterministic mixed-integer second-order constraint program (MISOCP). The use of ET boosts the RL agent learning rate for the CESS operation problem. The ET effectively assigns credit to the action sequences that bring the CESS to a high state of charge before the peak prices, reducing the training time. The case study shows that the proposed method learns to operate the CESS effectively and ten times faster than common RL algorithms applied to energy systems such as Tabular Q-learning and Fitted-Q. Also, the RL agent operates the CESS 94% near the optimal, reducing the energy costs for the end-user up to 12%.

The development of thorough probability models for highly volatile load profiles based on smart meter data is crucial to obtain accurate results when developing grid planning and operational frameworks. This paper proposes a new top-down modeling approach for residential load profiles (RLPs) based on multivariate elliptical copulas that can capture the complex correlation between time steps. This model can be used to generate individual and aggregated daily RLPs to simulate the operation of medium and low voltage distribution networks in flexible time horizons. Additionally, the proposed model can simulate RLPs conditioned to an annual energy consumption and daily weather profiles such as solar irradiance and temperature. The simulated daily profiles accurately capture the seasonal, weekends, and weekdays power consumption trends. Five databases with actual smart meter measurements at different time resolutions have been used for the model's validation. Results show that the proposed model can successfully replicate statistical properties such as autocorrelation of the time series, and load consumption probability densities for different seasons. The proposed model outperforms other multivariate state-of-the-art methods, such as Gaussian Mixture Models, by one order of magnitude in two different distance metrics for probability distributions.

This paper proposes an algorithm for the optimal operation of community energy storage systems (ESSs) using a machine learning (ML) model by solving a nonlinear programming (NLP) problem iteratively to obtain synthetic data. The NLP model minimizes the network's total energy losses by setting the community ESS's operation points. The optimization model is solved recursively by Monte Carlo simulations in a distribution system with high PV penetration, considering uncertainty in exogenous parameters. Obtained optimal solutions provide the training dataset for a stochastic gradient boosting trees (SGBT) ML algorithm following an imitation learning approach. The predictions obtained from the ML model have been compared to the optimal ESS operation to assess the model's accuracy. Furthermore, the ML model's sensitivity has been tested considering the sampling size and the number of predictors. Results showed a 98% of accuracy for the SGBT model compared to optimal solutions. This accuracy was obtained even after a reduction of 83% in the number of predictors.

In this paper, a co-simulation framework is presented to assess the impact on the distribution network of provision of support services (i.e. voltage support) by smart residential users. Such users are capable of providing flexibility by increasing/decreasing generation/consumption controlling the operation of an available set of flexible assets. The control of assets such as PV systems, electrical vehicles (EVs), heat storage and micro combined heat and power (mCHP) units is done by a Customer Energy Manager (CEM) after receiving flexibility requests as a result of an Aggregator-Distribution System Operator (DSO) interaction. In the presented framework, the distribution system is modeled in OpenDSS while the aggregator-flexible asset interaction, including the market-clearing procedure, is modeled using the Energy System Simulator (ESSIM). Results from several simulated scenarios are presented. According to the presented results, in summer, where over-voltage issues are expected due to the high PV penetration, a solution rate of 90% is estimated. For winter, in which under-voltage issues are more predominant, the solution rate is found to be around 70%.

This paper presents a distributed strategy for the optimal dispatch of islanded microgrids, modeled as unbalanced three-phase electrical distribution systems (EDS). 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 (VCM), with an active droop control loop, and a power control mode (PCM), 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.

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.

This chapter presents a stochastic mixed-integer second-order cone programming model for the operation of grid-connected (GC) and standalone (SA) three-phase microgrids. The proposed formulation minimizes the imported energy cost from the main grid in GC mode, as well as the unserved energy during a certain period of time during planned disconnection from the main grid due to intermittent supply or planned outages. It takes into account consumers’ priorities and guarantees the operational limits of the system, including voltage limits, branch current ratings, and operational limits of the devices, among others. Controllable components such as dispatchable distributed generation units, energy storage systems, and demand-side response are considered in the model along with renewable energy sources (RES) like wind turbines and photovoltaic generation units. The model presented in this chapter has been tested for a defined time horizon on a 25-bus microgrid, while considering uncertainty on conventional demands and RES. The effect of the obtained decisions on the operational points of the microgrid will be assessed on a second stage by analyzing a probabilistic power flow using the Monte Carlo simulation method.

Linear optimal power flow (OPF) formulations are powerful tools applied to a large number of problems in power systems, e.g., economic dispatch, expansion planning, state estimation, congestion management, electricity markets, among others. This article proposes a novel mixed-integer linear programming formulation for the ac-OPF of three-phase unbalanced distribution networks. The model aims to minimize the total energy production cost while guaranteeing the network's voltage and current magnitude operational limits. New approximations of the Euclidean norm, which is present in the calculation of nodal voltage and branch current magnitudes, are introduced by applying a linear transformation of weighted norms and a set of intersecting planes. The accuracy, optimality, feasibility, and scalability of the proposed linearizations are compared with common linear approximations in the literature using two unbalanced distribution test systems. The obtained results show that the proposed formulation is computationally more efficient (almost twice) while being as accurate and more conservative than the benchmarked approaches with maximum errors lower than 0.1%. Thus, its potential application in a variety of distribution systems operation and planning optimization problems is endorsed.

This paper proposes an algorithm for the optimal operation of community energy storage systems (ESSs) using a machine learning (ML) model, by solving a nonlinear programming (NLP) problem iteratively to obtain synthetic data. The NLP model minimizes the network's total energy losses by setting the operation points of a community ESS. The optimization model is solved recursively by Monte Carlo simulations in a distribution system with high PV penetration, considering uncertainty in exogenous parameters. Obtained optimal solutions provide the training dataset for a stochastic gradient boosting trees (SGBT) ML algorithm. The predictions obtained from the ML model have been compared to the optimal ESS operation to assess the model's accuracy. Furthermore, the sensitivity of the ML model has been tested considering the sampling size and the number of predictors. Results showed an accuracy of 98% for the SGBT model compared to optimal solutions, even after a reduction of 83% in the number of predictors.

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.

A short literature review on optimal restoration methods applied to electrical distribution systems (EDS) was presented in chapter one. On that context, this chapter presents a mixed-integer linear programming (MILP) model for the optimal restoration of electrical distribution systems, considering switching sequence. After a permanent fault has been identified, the optimal service restoration determines the status of the remote-controlled switches and the operation of the dispatchable distributed generation (DG) units, in order to isolate the faulty zone and supply as many customers as possible. The proposed mathematical approach considers the switching sequence over a horizon of S discrete steps, guaranteeing that the operational constraints of the system are not violated in every step. By considering the switching sequence in the optimization model, the restoration time and the number of switching operations can be controlled. Thus, the reliability and the power quality of the system are enhanced. The use of a MILP model guarantees convergence to the optimal solution by applying convex optimization techniques. Tests are run using a 136-node distribution system with 28 remote controlled switches, and dispatchable DG. Finally, a comparative analysis is used to establish the relationship between the total un-supplied demand and the number of switching actions along the sequence horizon.

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.

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.