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Performance analysis is challenging in modern power distribution networks due to the increasing penetration of distributed energy resources (DERs) interfaced by voltage source converters (VSCs). Parameter uncertainty, black-box models of the components, and low inertia are some of the issues that must be addressed. The latter can represent high vulnerabilities to sudden load changes in a microgrid (MG). Additionally, the islanded operation represents a challenge for inverter-based (DERs), where secondary control must regulate the microgrid frequency and voltage to its nominal values. When a secondary control strategy is implemented, it is necessary to validate its performance under several conditions. Most existing research papers focus on the microgrid's small-signal and transient stability. At the same time, little has been done on the influence of the load model on voltage stability. This type of analysis is required to ensure an adequate transition between the grid-connected and stand-alone modes. This paper provides a voltage stability analysis of a microgrid, considering secondary control based on receding horizon and frequency-dependent load models. Simulation results demonstrate the robust performance of the secondary control and validate the importance of considering or adapting voltage stability indices to ensure adequate microgrid performance. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a general model for microgrids in the 0dq reference frame for stationary state and small dynamic variations. The proposed model considers the dynamics of the distribution lines, including mutual coupling and unbalanced loads, and the dynamics of the converters required to integrate renewable sources and energy storage devices (eg, batteries and/or supercapacitors). A fixed‐point algorithm is proposed for finding the equilibrium point. This algorithm constitutes a load flow in the 0dq reference frame used to develop an average model of the grid. Finally, a small‐signal stability analysis is presented. Simulations results on the CIGRE low‐voltage benchmark microgrid demonstrate the performance of the model in terms of accuracy and fast computation compared to simulations in the ABC reference frame. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear stability analysis for DC-microgrids in both, interconnected and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient system generated by a strongly convex function. The stability analysis is thus reduced to a series of convex optimization problems. The proposed method allows to: (i) demonstrate the existence and uniqueness of the equilibrium, (ii) calculate this equilibrium, (iii) give conditions for global stability using a Lyapunov function and (iv) estimate the region of attraction. Previous works only address one of these aspects. Numeric calculations performed in CVX and simulation results in MATLAB complement the analysis and demonstrate how to use this theoretical results in practical problems. [ABSTRACT FROM AUTHOR]

The power flow equations in DC microgrids are nonlinear due to the presence of constant power terminals. In this context, a rigorous demonstration of the convergence and uniqueness of the solution for Newton's method is required. This problem is particularly important in islanded microgrids, where the power flow method determines the equilibrium point, which in turn is used for other analyses such as stability, optimal operation, and reliability. In this paper, we present a new concept associated with power flow equations, namely the potential function of the power flow. This function allows transforming the power flow problem into an optimization model and uses convex analysis for determining its convergence and the uniqueness of the solution. Being a scalar function, the potential of the power flow can give valuable geometrical insights on the problem. In addition, the optimization approach can be used to solve the power flow problem considering inequality constraints. Simulation results demonstrate the applicability of this approach in practice. [ABSTRACT FROM AUTHOR]

This paper presents a generalized model for small signal stability in DC microgrids considering electric vehicles. The proposed model considers four types of terminals, namely: constant power, constant voltage, constant current and constant impedance. A Newton-Raphson methodology is used to calculate the operation point of the microgrid and a sensitivity analysis is also presented. Some general features of the DC microgrid based on the intrinsic characteristics of the model are presented. Simulation results on different type of microgrids show the proposed small signal model is accurate compared to dynamical simulations. [ABSTRACT FROM AUTHOR]

• An OPF algorithm taylored for tertiary control in microgrids is proposed. • This model considers 24h operation and includes renewable energy sources, energy storage devices, and grid code limitations. • Power flow equations are simplified using a recently developed approximation based on Wirtinger's calculus • Simulation results demonstrate the algorithm is suitable for tertiary control. This article presents an optimization model for tertiary control in three-phase unbalanced microgrids. This model considers 24h operation and includes renewable energy sources, energy storage devices, and grid code limitations. Power flow equations are simplified using a recently developed approximation based on Wirtinger's calculus. The proposed model is evaluated both theoretically and practically. From the theoretical point of view, the model is suitable for tertiary control since it is convex; hence, global optimum, uniqueness of the solution, and convergence of the interior point method are guaranteed. From the practical point of view, the model is simple enough to be implemented in a small single-board computer with low time calculation. The latter is evaluated by implementing the model in a Raspberry-Pi board with the CIGRE low voltage benchmark; the model is also evaluated in the IEEE 123-nodes test system for power distribution networks. [ABSTRACT FROM AUTHOR]

As multi-microgrids become readily available, some limited models have been proposed that study operational and power quality constraints with local energy markets independently. This paper proposes a convex optimization model of an energy management system with operational and power quality constraints and interactions in a Local Energy Market (LEM) for unbalanced microgrids (MGs). The LEM consists of a pre-dispatch step and an energy transactions step (ETS). The ETS combines the MGs' objectives while considering two strategies: minimize the cost of buyers or maximize the revenue of sellers. Our proposed model considers harmonic distortion and voltage limit power quality constraints in both steps. Moreover, we model operational constraints such as power flow, power balance, and distributed energy resources behaviors and capacities. We numerically evaluate the proposed model using three unbalanced MGs with residential, industrial, and commercial load profiles, where each microgrid manages its resources locally. Furthermore, we create two groups of cases to analyze the interactions in the local energy market. In the first group, the price of the DSO energy and the surplus from MGs to DSO are the same. The numerical results show that using the increasing revenue strategy promotes MGs to interact more while encouraging them to have high energy prices. When the reducing cost strategy is used, fewer energy interactions occur, and the price of MGs energy is encouraged to be lower. • Local Energy Market for energy transactions among unbalanced microgrids and DSO. • Multi-microgrids energy management with operational and power quality constraints. • Unbalanced linear power flow and first-principal-based harmonic power flow modeling. [ABSTRACT FROM AUTHOR]