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Power electronics converters are equipped with current controls that protect the converter from over-currents. This protection introduces non-differentiable equations into the power flow problem. The conventional Newton's method is not suitable in that conditions. This letter proposes a fixed-point iteration to overcome this difficulty. The technique is derivative-free, and hence, it can naturally include the saturation given by the converters' current protection. Exact conditions for convergence and uniqueness of the solution are demonstrated using Banach's fixed point theorem. Numerical experiments in Matlab complement the analysis

This paper addresses the problem of determining the optimal location and operation of distribution static synchronous compensators (D-STATCOMs) in power distribution networks. Metaheuristic algorithms have been conventionally used to solve this mixed-integer nonlinear programming problem. In contrast, we propose a mixed-integer second-order cone programming (MI-SOCP) model that guarantees global optimum and fast convergence of the algorithms in optimization solvers. The model seeks to minimize the annual installation cost and the operating cost, subject to active and reactive power balance constraints, voltage regulation bounds, devices capabilities, and the number of D-STATCOMs available to be connected. The multiobjective nature of the problem is also analyzed and solved using the proposed MI-SOCP model. An extensive set of simulations on the IEEE-33 nodes test system demonstrate the advantages of this approach compared to conventional heuristic algorithms and with solutions given by algebraic modeling software.

In this paper, the control problem of microgrids (MGs)operating in islanded mode is approached from a passivity-based control perspective. A control scheme is proposed that, relying only on local measurements for the power converters included in the network representation, achieves both voltage regulation and power balance in the network through the generation of grid-forming and grid-following nodes. From the mathematical perspective, the importance of the contribution lies in the feature that, exploiting a port-controlled Hamiltonian representation of the MG, the closed-loop system’s stability properties are formally proved using arguments from the theory of non-linear dynamical systems. Fundamental for this achievement is the decomposition of the system into subsystems that require a control law and another whose variables can evolve in a free way. From the practical viewpoint, the advantage of the proposed controller lies in the feature that the power demanded by the loads is satisfied without neither computing its specific value nor solving the non-linear algebraic equations given by the power flow, avoiding the computational burden associated with this task. The usefulness of the scheme is illustrated via a numerical simulation that includes practical considerations.

This paper proposes an interconnection and damping assignment passivity-based control (IDA-PBC) for multimachine power systems including hydro-turbine governing systems (HTGS) with surge tank. The main objective is to stabilize the rotor speed and regulate the terminal voltage of each synchronous machine in a power system. The proposed control is decentralized, thus avoiding challenges of communication between generators. Passivity theory is used since the open-loop of the HTGS presents a port-Hamiltonian structure. IDA-PBC allows a control law that maintains the passive structure in closed-loop, guaranteeing its asymptotic stability using Lyapunov's theory. The dynamics of each HTGS are described by an eleventh-order model, which can be reduced to a tenth-order. The proposed control is tested in a 12-bus test system and compared to a standard control, which considers a voltage regulator and exciter based on the IEEE type ST1A excitation system model and power system stabilizer IEEE-PSS1A. The governing system based on a PID control with static and transient droop is also employed. Additionally, the proposed controller is compared to a sliding mode controller. Time-domain simulations demonstrate the robustness and appropriate performance of the proposed decentralized control under different large disturbances.sliding mode controller. Time-domain simulations demonstrate the robustness and appropriate performance of the proposed decentralized control under different large disturbances. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

This paper deals with an application of the nested convex programming to the optimal power flow (OPF) in multi-terminal high-voltage direct-current grids (MT-HVDC). The real-world optimization problem under consideration is non-convex. This fact implies some possible inconsistencies of the conventional numerical minimization algorithms (such as interior point method). Moreover, the constructive numerical treatment of this problem is usually based on some approximative approaches, namely, on the suitable linearizations and problem relaxations. The resulting convex programming model constitutes an approximated model and can naturally involve the significant (approximation) errors. In difference to the strongly approximate computational approaches mentioned above, the numerical scheme we propose takes into account the specific bi-linear structure of the problem and operates with the originally given non-convex formulation of the problem. We implement the proposed nested optimization approach and study the numerical consistency of the resulting optimal design. The Python based numerical experiments demonstrate the imlementability of the proposed methodology. Optimization problem of the modified version of the CIGRE MT-HVDC is next used as a benchmark test for the approach we developed.

The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.

This brief presents a general form of designing passivity-based controllers for electrical energy storage systems (EESS) in three-phase microgrids (TP-MGs) under time-domain reference frame. The control strategy proposed in this brief use the Clark's transformation known as αβ reference frame, avoiding to use phase-locked loop systems, which allows improving the dynamical performance in the energy storage devices. Passivity-based control guarantees stable operating conditions in the sense of Lyapunov for each EESS for different grid operation scenarios in the TP-MG. The design of the controllers is made by using passivity-based control (PBC) theory in conjunction to the dynamics of the error approach. A comparison to classical proportional-integral control method is used to show the applicability of the PBC approach presented in this brief. Simulation results are conducted via MATLAB/Simulink software. © 2004-2012 IEEE. Departamento Administrativo de Ciencia, Tecnología e Innovación (COLCIENCIAS), COLCIENCIAS Department of Science, Information Technology and Innovation, Queensland Government, DSITI Manuscript received December 7, 2018; accepted January 14, 2019. Date of publication January 18, 2019; date of current version December 6, 2019. This work was supported by the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS) through the National Scholarship Program under Grant 727-2015. This brief was recommended by Associate Editor D. Giaouris. (Corresponding author: Oscar Danilo Montoya.) O. D. Montoya is with the Program of Electric and Electronic Engineering, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia (e-mail: o.d.montoyagiraldo@ieee.org).

This paper addresses the problem of the power flow analysis of bipolar direct current (DC) networks considering unbalanced loads and the effect of a neutral wire, which may be solidly grounded or non-grounded. The power flow problem is formulated using the nodal admittance representation of the system and the hyperbolic relations between power loads and voltages in the demand nodes. Using Taylor series expansion with linear terms, a recursive power flow method with quadratic convergence is proposed. The main advantage of the hyperbolic approximation in dealing with power flow problems in DC bipolar networks is that this method can analyze radial and meshed configurations without any modifications to the power flow formula. The numerical results in three test feeders composed of 4, 21, and 85 bus systems show the efficiency of the proposed power flow method. All of the simulations were conducted in MATLAB for a comparison of the proposed approach with the well-established successive approximation method for power flow studies in distribution networks.

This paper presents a unified Hamiltonian formulation for controlling distributed energy resources (DERs)in ac single-phase microgrids (SP-MGs)via proportional-integral passivity-based control (PI-PBC), and interconnection and damping assignment passivity-based control (IDA-PBC). The proposed Hamiltonian formulation allows us to consider both pulse-width modulated voltage source converters (PWM-VSC)and pulse-width modulated current source converters (PWM-CSC)under a unified model. Renewable generation and supercapacitor energy storage systems are integrated via PWM-VSC technologies, while superconducting coils are integrated through PWM-CSC technologies. IDA-PBC and PI-PBC theories enable us to design control strategies begin that consider Lyapunov's stability theory combined with the well-known advantages of proportional and integral control actions. Our simulation's results corroborate the applicability of the proposed control approaches under stability paradigm. MATLAB/Simulink is employed for computational implementations via begin the SimPowerSystems toolbox. © 2019 Elsevier Ltd Universidad Tecnológica de Pereira: Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS Department of Science, Information Technology and Innovation, Queensland Government Universidad Tecnológica de Pereira This work was supported in part by the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS) through the National Scholarship Program under Grant 727-2015 during the development of the doctoral thesis ”Passivity-based analysis and control of AC microgrids: Integration, operation and control of energy storage systems” in the Universidad Tecnológica de Pereira, and in part by the Universidad Tecnológica de Bolívar under Project C2018P020 .

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.

To determine sensitivity and specificity of the “duct-interrupted,” “corona,” and “attraction” signs on MR cholangio-pancreatography (MRCP) in distinguishing pancreatic head ductal adenocarcinoma (PDAC) from inflammatory pancreatic pseudomass (IPP). This study included 53 adults (33 men and 20 women, mean age, 55 years; range, 17–87 years) with a pancreatic head mass who underwent MRCP. Three blinded radiologists independently reviewed each MRCP exam and three signs were assessed: (1) the “duct-interrupted” sign, deemed positive for PDAC if the duct within the mass demonstrated complete interruption with upstream dilation; (2) the “corona” sign, considered positive for PDAC if dilated side-branches were located exclusively outside the mass; and (3) the “attraction” sign, deemed positive for IPP if the dilated common bile duct showed attraction and angulation towards the mass. Sensitivity, specificity, and positive and negative predictive values of the signs were calculated, as well as interobserver agreement. Out of 53 masses, 17 (32%) were PDAC and 36 (68%) were IPP. Sensitivity, specificity, and positive and negative predictive values of the “duct-interrupted” sign to differentiate between PDAC from IPP for the three readers were 29–53%, 89–95%, 56–82% and 73–81%, respectively (κ = 0.41); for the “corona” sign, they were 29–53%, 81–100%, 56–100%, and 75–78%, respectively (κ = 0.4), and for the “attraction” sign, they were 20–25%, 71–82%, 64–75%, and 31–34%, respectively (κ = 0.54). The “duct-interrupted” and “corona” MRCP signs have high specificity for diagnosing PDAC, while the “attraction” sign has good specificity for identifying IPP.

This express brief shows a convex quadratic approximation for the optimal power flow (OPF) in direct-current microgrids (dc-μ Grid) via Taylor's series expansion. This approach can be used for solving OPF problems on radial and meshed dc-μ Grids with multiple constant power terminals, allowing to cover a wide range of configurations. Two test dc-μ Grids with 10 and 21 nodes were used to validate the proposed model. Nonlinear large-scale solvers were employed to compare the proposed linearization with the conventional nonlinear nonconvex model. © 2004-2012 IEEE. Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS: 727-2015 Department of Science, Information Technology and Innovation, Queensland Government Manuscript received June 20, 2018; revised August 10, 2018; accepted September 7, 2018. Date of publication September 20, 2018; date of current version May 28, 2019. This work was supported by the National Scholarship Program Doctorates of the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS) under Grant 727-2015. This brief was recommended by Associate Editor Y.-M. Chen. (Corresponding author: Oscar Danilo Montoya.) O. D. Montoya is with the Program of Electric and Electronic Engineering, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia (e-mail: o.d.montoyagiraldo@ieee.org).

Low-frequency oscillations can occur in hydropower systems under in the new context of power system and the classical controller for hydro-turbine governing systems need to be enhanced with the purpose of improving its stability. We propose a controller based on passivity theory with the aim of damping oscillations in a power system. Passivity-based control arises as a natural choice for hydro-turbine governing system since its open-loop dynamic has a port-Hamiltonian structure, which allows designing a controller that preserves the passive structure in closed-loop via interconnection and damping reassignment. The proposed controller considers the complete non-linear model of the system and guarantees global asymptotic stability in the sense of Lyapunov. Time-domain simulations demonstrate the robustness and proper performance of the proposed methodology under different operative conditions when is compared with the classical controllers.

Contexto: El flujo de potencia es un problema clásico para la operación de redes de distribución de energía. Es un problema desafiante debido a la gran cantidad de nodos, la alta relación $r/x$ típica de las redes de baja tensión y la naturaleza desequilibrada de la carga. Métodos: Este documento revisa cuatro métodos para el análisis de flujo de potencia, a saber: el método de Newton convencional, el método de Newton en un dominio complejo, el algoritmo de punto fijo que utiliza la representación de admitancia nodal ($Y_\text{bus$) y el algoritmo de barrido hacia atrás y hacia adelante. Se presenta la convergencia de estos métodos en teoría y práctica. Es bien sabido que el método de Newton tiene convergencia cuadrática, mientras que el algoritmo de barrido hacia atrás y adelante tiene convergencia lineal. Sin embargo, el análisis formal de esta tasa de convergencia es menos conocido en la literatura de ingeniería. Resultados: se desarrolla una caja de herramientas de Matlab para realizar simulaciones numéricas tanto en el caso estático como en una simulación cuasi-dinámica usando el sistema de pruebe IEEE de 900 nodos. Conclusiones: Los algoritmos de punto fijo resultaron más rápidos. No obstante, los algoritmos basados en Newton requirieron menor número de iteraciones.

This article presents a small-signal study, based on a sensitivity analysis, of a voltage source converter (VSC) operating as a grid-following device. This type of operation is standard for integrating distributed energy resources directly into a primary grid without considering the control over specific variables (e.g., voltage and frequency), thus maximizing the amount of injected active power. The present study adopted the classical vector-oriented control based on the linearization method of the averaged model; hence, this analysis is limited to linear controls. The main objective of this study is to evaluate how each controller parameter influences the system’s stability. To conduct the sensitivity analysis, an averaged model in the dq reference frame of the VSC was employed to describe the system dynamics in the equivalent state-space model. Afterward, the stability was analyzed through a sensitivity analysis of the eigenvalues of the corresponding state matrix. The numerical results demonstrate that the main problems for the stability of VSCs operating as grid-following converters are threefold: a high value of the filter inductance, a non-ideal impedance that appears depending on the connection point, and poor coordination of the parameters of the Kp controllers. These results are compared to a simple bifurcation analysis of the state matrix, which consists of a diagram that describes the variation in eigenvalues when a parameter changes, thus proving their validity.

To evaluate clarity, completeness, and impact on surgical planning of MRI reporting of perianal fistulizing disease using a structured disease-specific template versus narrative reporting for planning of disease treatment by colorectal surgeons. In this HIPAA-compliant, IRB-approved study with waiver of informed consent, a structured reporting template for perianal fistulizing disease MRIs was developed based on collaboration between colorectal surgeons and abdominal radiologists. The study population included 45 consecutive patients who underwent pelvic MRI for perianal fistulizing disease prior to implementation of structured reporting, and 60 consecutive patients who underwent pelvic MRI for perianal fistulizing disease after implementation of structured reporting. Objective evaluation of the reports for the presence of 12 key features was performed, as also subjective evaluation regarding the clarity and completeness of reports, and impact on surgical planning. Significantly more key features were absent in narrative reports [mean: 6.3 ± 1.8 (range 3–11)] than in structured reports [mean: 0.3 ± 0.9 (range 1–5)] (p ≤ 0.001). The use of structured reporting also increased the percentage of completeness (72.5–88.3% for surgeon 1, and 61.2–81.3% for surgeon 2; p = 0.05 and 0.03, respectively), helpfulness in surgical planning (7.1 ± 1.5–7.6 ± 1.5 for surgeon 1, and 5.8 ± 1.4–7.1 ± 1.1 for surgeon 2; p = 0.05 and p

The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver.

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., Comment: Paper submitted to Electric Power Systems Research

This paper proposes a proportional-integral passivity-based controller (PI-PBC) for supporting voltage in linear loads integrated with Cuk converters. An adaptive load estimator is also employed to avoid current measurements at the load point. This estimator permits an on-line estimation of the load conductance for maintaining the output voltage as constant as possible independent of its variations. The proposed PI-PBC allows guaranteeing stability conditions in Lyapunov's sense for a closed-loop operation by exploiting the port-Hamiltonian structure of the Cuk converter model. Numerical simulations evidence the advantages of using PI actions for PBC designs compared with the classical interconnection and damping (IDA-PBC) approach. All numerical simulations are conducted via MATLAB/Simulink software.

This study addresses the power-flow-analysis problem for direct-current (DC) grids from a numerical perspective. Classical and emerging algorithms for power flow solutions in DC networks such as Gauss--Seidel, successive approximations, Newton--Raphson, and Taylor-based methods are reviewed herein in detail by providing their mathematical derivations and algorithmic implementations. All these numerical methods can be applied to high-voltage DC and low-voltage DC networks irrespective of their topologies and the number of voltage-controlled nodes. The MATLAB programming environment is used to implement these power flow algorithms using DC networks with 6, 21, 33, and 69 nodes. The simulation results show that these power flow methods are equivalent in terms of voltage estimation and power losses and only differ from one another in terms of processing time. 1. Introduction 2. Mathematical formulation 3. Numerical methods for power flow analysis 4. Test systems 5. Numerical results 6. Conclusions and future works Declaration of Competing Interest References

This paper addresses the problems of power flow and optimal power flow a nalysis c onsidering voltage-dependent load models from the convex point of view. First, Taylor series expansion method is employed for linearizing the power flow equations generating a set of affine h yperplanes. S econd, the sequential quadratic programming (SQP) approach is employed for adjusting the linearization point to eliminate the voltage estimation error between the exact and proposed convex models recursively. Two voltage-dependent load models are considered in our power flow a nd o ptimal p ower fl ow pr oposals wh ich based on the exponential and polynomial models. General algebraic modeling system (GAMS) and its nonlinear optimization packages are employed for comparison purposes. Two DC-test systems with 6 and 21 nodes are used to validate the performance of the SQP proposed. The proposed SQP approach is implemented in MATLAB software with quadprog toolbox.

This paper presents a sequential convex-optimization method for the optimal power flow in dc-grids under island operation. The proposed method is general for both high and low power applications. The former refers to multi-terminal high voltage direct current transmission and the latter include dc-distribution and dc-microgrids. Our analysis is based on the characteristics of the power flow equations, represented as an n-dimensional manifold embedded in \(\mathbb {R}^n\). This formalism allows a geometric representation for each step in the optimization process as well as a geometric interpretation of the results. The problem is divided into several convex optimization problems defined on the tangent space. Then, results are projected to the manifold defining a new tangent space. Simulations results in Matlab complement the theoretical analysis for the CIGRE-multiterminal HVDC and the a microgrid test systems.

Phase balancing is an optimization problem which can reduce power losses in modern power distribution grids. The problem consists on phase swapping of the loads at the feeder level in order to reduce the unbalance of the grid. Despite being a classic problem, it is still relevant since unbalance is a common phenomena in power distribution grids and can be intensified by the uncoordinated use of distributed resources such as renewable energies and electric vehicles, among other single phase loads. Being a combinatorial problem, phase balancing requires heuristic algorithms whose codification must be carefully designed. In addition, high penetration of renewable energies makes the problem stochastic. This chapter shows a genetic algorithm which solves efficiently the problem, considering a detailed model of the power flow. A novel codification is proposed based on the identification of symmetries on the intrinsic structure of the problem by using the concept of group, an algebraic structure that can be easily combined with the conventional genetic algorithm. Simulations results on the IEEE test systems demonstrate the efficiency of the proposed method.

Most of renewable energy technologies and energy storage devices are operated in dc. Indeed, solar photovoltaic generation and batteries require a dc/ac converter in order to be integrated into a conventional ac distribution grid. Dc distribution emerges a suitable alternative that reduces the losses and increases reliability in modern smartgrids. Classical methodologies such as the optimal power flow require to be adapted to this new scenario. However, just as in the case of ac grids, the power flow in dc distribution grids is non-linear non-convex. Therefore, convex approximations are required in order to guarantee convergence and global optimality. Several approximations can be proposed including second order cone optimization, semidefinite programming and linealization. These approximations are analyzed theoretically and numerically in this chapter.

This paper proposes an optimization model for the secondary control of islanded microgrids. It considers the action of the primary control and the references given by the tertiary control. The model is solved in each step, based on a linear approximation of the frequency-dependent power flow equations. The main objective of the model is to carry out frequency and voltages to suitable values, considering the capacity limits of renewable sources and energy-storage devices. Numerical experiments on the CIGRE low-voltage benchmark test system demonstrate the frequency achieve nominal values taking into account the main constraints of the system.

This paper presents a reformulation of the power flow problem in low-voltage dc (LVDC) power grids via Taylor's series expansion. The solution of the original nonlinear quadratic model is achieved with this proposed formulation with minimal error when the dc network has a well defined operative conditions. The proposed approach provides an explicit solution of the power flow equations system, which avoids the use of iterative methods. Such a characteristic enables to provide accurate results with very short processing times when real operating scenarios of dc power grids are analyzed. Simulation results verify the precision and speed of the proposed method in comparison to classical numerical methods for both radial and mesh configurations. Those simulations were performed using C++ and MATLAB, which are programming environments commonly adopted to solve power flows. © 2018 Elsevier B.V. Universidad Nacional de Colombia Universidad Tecnológica Nacional Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS: P-17211, UNAL-ITM-39823 This work was supported by Universidad Tecnológica de Bolivar , Universidad Tecnológica de Pereira , Instituto Tecnológico Metropolitano , Universidad Nacional de Colombia and COLCIENCIAS under the research projects P-17211 and UNAL-ITM-39823 and the Doctoral Scholarship 727-2015. Moreover, this work was also supported by the PhD program in Engineering of the Universidad Tecnológica de Pereira and the Ph.D. program “Doctorado en Ingeniería – Línea de Investigación en Automática” of the Universidad Nacional de Colombia.

The power flow is a nonlinear problem that requires a Newton's method to be solved in dc microgrids with constant power terminals. This paper presents sufficient conditions for the quadratic convergence of the Newton's method in this type of grids. The classic Newton's method as well as an approximated Newton's method are analyzed in both master–slave and island operation with droop controls. Requirements for the convergence as well as for the existence and uniqueness of the solution starting from voltages close to 1 pu are presented. Computational results complement this theoretical analysis.

To review the clinical, multimodality imaging, and pathologic characteristics of abdominal wall endometriosis (AWE), the most common type of extra-pelvic endometriosis. 116 women with histopathologically confirmed extragenital endometriosis diagnosed between 2/2014 and 6/2017 were evaluated retrospectively. Of these, 26 (22.4%) were found to have AWE and 18/26 met inclusion criteria for imaging. Available imaging studies were re-reviewed by two expert radiologists. Data regarding clinical features, histopathologic findings, and management were collected through medical record review. 21 pathology-proven AWE deposits were identified by imaging in 18 women [mean age at diagnosis of 38.5 years (range 31–48)]. Prior C-section was present in 15/18 (83.3%) and pelvic endometriosis in 3/18 (16.7%) patients. Patients presented with abdominal pain in 14/18 (77.8%) cases, which was cyclical in 8/14; palpable mass in 12/18 (66.7%); fluid discharge in 2/18 (11.1%); and local skin discoloration in 2/18 (11.1%). Of the 21 lesions, 15 were evaluated with US, 10 with CT, and 5 with MRI. Mean lesion dimensions were 2.5 × 2.2 × 2.6 cm, and deposits were predominantly located at midline or left hemiabdomen [22/30 (73.3%)], were either stellate [15/30 (50%)] or round [15/30 (50%)] in shape, had ill-defined margins [21/30 (70%)], were heterogenous in appearance [27/30 (90%)], and involved both deep and superficial abdominal wall layers [17/30 (56.7%)]. On US, lesions were mainly isoechoic/hyperechoic [7/15 (46.7%)], and scarcely vascular [8/15 (53.3%)] with a peripheral vascular pattern [8/13 (61.5%)]. On CT, AWEs were hypervascular and homogeneous [8/10 (80%)], superiorly located to scar tissue, and on MRI lesions appeared hyperintense [4/5 (80%)] to muscle with T2 cystic and T1 hemorrhagic foci [4/5 (80%)]. In 23/27 (85.1%) original reports, there was at least one known mass prior to imaging; AWE was correctly diagnosed in only 7/23 (30.4%) cases. In those with no prior knowledge of a mass, the lesion was detected in 3/4 (75%), but AWE was only diagnosed in a single case. Median time between onset of symptoms and histopathology was 24.41 moths (IQR 15.18–47.33). AWE is a challenging clinical entity frequently diagnosed with a significant delay and easily misinterpreted despite multimodality imaging. Familiarity with its radiologic features holds the potential for positively impacting diagnosis.