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Highlights • Two convex optimal power flow reformulations are proposed. • Sequential quadratic programming allows global convergence. • Radial and mesh dc grids with multiple generation nodes are included. • Nonlinear model does not guarantee reaching the optimal solution. • SQP proposed models are faster than the exact non-convex OPF model. Abstract In this paper, we address the optimal power flow problem in dc grids (OPF-DC). Our approach is based on sequential quadratic programming which solves the problem associated with non-convexity of the model. We propose two different linearizations and compare them to a non-linear algorithm. The first model is a Newton-based linearization which takes the Jacobian of the power flow as a linearization for the optimization stage, and the second model uses the nodal currents as auxiliary variables to linearize over the inequality constraints. Simulation results in radial and meshed grids demonstrate the efficiency of the proposed methodology and allow finding the same solution given by the exact nonlinear representation of the OPF-DC problem. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. • D-STACOMs permit annual operative costs reduction in distribution grids. • MI-SOCP formulation allows finding the global optimal solution of the exact MINLP model through solution space convexification. • The proposed optimization model does not require statistical evaluation to validate its efficiency since it is mixed-integer convex in nature. [ABSTRACT FROM AUTHOR]

This 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 Newton-like 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. • Two novel efficient power flow algorithms for distribution systems. • Linearization using Laurent series expansion. • Convergence and stability analysis using Banach fixed-point theorem. • Proposed algorithms are at least three times faster than the backward–forward sweep. [ABSTRACT FROM AUTHOR]

This paper deals with the power flow problem in bipolar direct current distribution networks with unbalanced constant power loads. The effect of the neutral wire is considered in two prominent cases: (i) when the system is solidly grounded at each load point and (ii) when the neutral terminal is only grounded at the substation bus. The problem is solved using the successive approximation power flow method. Numerical results in two test feeders composed of 4 and 25 nodes demonstrate that the successive approximation power flow approach is adequate to solve the problem. It is also demonstrated that it is equivalent to the backward/forward power flow in matrix form. The main advantage of both power flow approaches is that they can work with radial and meshed distribution networks. Additionally, they do not require inverting matrices at each iteration, making them efficient in terms of computational processing times requirements. All the simulations are carried out in the MATLAB programming environment. • Bipolar DC networks have the double transference capability of their monopolar DC networks. • Convergence of the successive approximation power is ensured through the application of the Banach fixed point theorem. • Power losses increase for the topology with non-grounded neutral wire. • Monopolar unbalanced loads produce voltage imbalances between the positive and negative poles. [ABSTRACT FROM AUTHOR]

• This paper addresses the stabilization of DC resistive networks with multiple RERs. • A port-Hamiltonian model and PBC theory are used for designing nonlinear controllers. • The proposed controller does not require cross measures (the main paper contribution). • The operative point is obtained by a convex reformulation of the optimal power flow. • The proposed model is solved via semidefinite programming approach. This paper presents a model for stabilizing multi-terminal high voltage direct-current (MT-HVDC) networks with constant power terminals (CPTs) interfaced with power electronic converters. A hierarchical structure of hierarchical control is developed, which guarantees a stable operation under load variations. This structure includes a port-Hamiltonian formulation representing the network dynamics and a passivity-based control (PBC) for the primary control. This control guarantees stability according to Lyapunov's theory. Next, a convex optimal power flow formulation based on semidefinite programming (SDP) defines the control's set point in the secondary/tertiary control. The proposed stabilization scheme is general for both point-to-point HVDC systems and MT-HVDC grids. Simulation results in MATLAB/Simulink demonstrate the stability of the primary control and the optimal performance of the secondary/tertiary control, considering three simulation scenarios on a reduced version of the CIGRE MT-HVDC test system: (i) variation of generation and load, (ii) short-circuit events with different fault resistances and (iii) grid topology variation. These simulations prove the applicability and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

• The optimal selection of calibers allows reducing investments and energy losses costs. • Non-convexities in the problem of the selection of calibers make necessary powerful solution methods. • The optimal selection of calibers requires an incidence node-to-branch matrix for being adequately represented. This paper addresses the problem of optimal conductor selection in direct current (DC) distribution networks with radial topology. A nonlinear mixed-integer programming model (MINLP) is developed through a branch-to-node incidence matrix. An important contribution is that the proposed MINLP model integrates a set of constraints related to the telescopic structure of the network, which allows reducing installation costs. The proposed model also includes a time-domain dependency that helps analyze the DC network under different load conditions, including renewable generation and battery energy storage systems, and different voltage regulation operative consigns. The objective function of the proposed model is made up of the total investment in conductors and the total cost of energy losses in one year of operation. These components of the objective function show multi-objective behavior. For this reason, different simulation scenarios are performed to identify their effects on the final grid configuration. An illustrative 10-nodes medium-voltage DC grid with 9 lines is used to carry out all the simulations through the General Algebraic Modeling System known as GAMS. [ABSTRACT FROM AUTHOR]

• Convergence validation in power flow allows ensuring the correct operation of the grid. • The proposed power flow methods permit analyzing radial and meshed grids. • Multiple slack nodes can be included in the successive approximation approach. The convergence analysis of the power flow methodologies for direct current (dc) electrical networks is addressed in this paper. The Banach fixed-point theorem is employed to prove the convergence and uniqueness in the power flow solution for two different alternatives based on graph theory named successive approximations and triangular-based power flow. The successive approximation method works with radial and mesh grids, including multiple voltage-controlled sources. The triangular-based method only deals with radial structures and one slack node. A six-nodes high-voltage dc system is used to illustrate the convergence of the graph-based methods under study. Three test feeders composed of 33, 35, and 69 nodes are used to validate the effectiveness of the proposed approaches when compared with classical methods such as Newton-Raphson and Gauss-Seidel. In addition, large-scale radial distribution networks are generated randomly with 50 to 200 nodes to demonstrate the scalability of studied power flow methods regarding processing time and the number of iterations. All the simulations have been conducted in MATLAB software. [ABSTRACT FROM AUTHOR]

• A power flow formulation for alternating-current distribution networks was proposed. • The proposed power flow can apply to AC grids with radial- and mesh-topology. • The proposed power flow is a compact design of a modified Gauss-Seidel method. • Numerical comparisons of the proposed power flow with classical methods are shown. This paper proposes a new power flow formulation for alternating-current distribution networks for radial and mesh topologies. This formulation corresponds to a successive approximation based on a modification of the conventional Gauss-Seidel numerical method by using a successive approximation approach. This power flow method allows working with complex variables by reducing the number of required calculations and avoiding the transformation of the power flow model into polar coordinates. Additionally, it does not use derivatives for approximating the problem as it occurs with Taylor-based approaches. Simulation results confirm that the proposed method is faster concerning computational time, as well as in the total number of iterations required. Numerical comparisons with classical methods such as Gauss-Seidel, Newton-Raphson, Levenberg-Marquardt, graph-based methods, and linear approximations have been made and implemented in MATLAB software to demonstrate the effectiveness of the proposed approach regarding power flow solutions in radial and mesh distribution networks. [ABSTRACT FROM AUTHOR]

• Nonlinear dynamic model of a small hydro-power plant is shown. • A controller of a small hydro-power plant based on passivity theory is developed. • The electrical, mechanical and hydraulic dynamics for small hydro-power are considered. • A small hydro-power plant is connected to DC microgrid. This paper presents the modeling and control of a small hydro-power plant (SHP) for a DC microgrid based on passivity theory. The SHP is made up of a turbine, a permanent magnet synchronous generator (PMSG), a voltage source converter and a DC microgrid. The electrical, mechanical and hydraulic dynamics in the mathematical model of the SHP are considered. We employ a nonlinear controller based on passivity, whose stability is guaranteed under practically reasonable assumptions. Our simulation results show better performance of the proposed controller when compared with a PI controller in all of the scenarios that were considered. [ABSTRACT FROM AUTHOR]

• A linear power flow of dc grids via a logarithmic transformation is presented. • Linear power flow methods allow improving convergence times in repetitive routines. • Logarithmic transformation of voltage magnitudes (LTVM) provides a graphical interpretation of the Taylor-based methods for power flow analysis. • Radial and meshed networks with multiple generation sources can be analyzed in the LTVM approach. • Power flow analysis is an essential tool for planning and operating electrical networks. This paper proposes a logarithmic transformation of voltages (LTVM) for the power flow in DC grids. This problem is non-linear due to the presence of constant power loads (CPLs), which also introduce a negative resistance effect that can create numerical instability for conventional algorithms. The proposed methodology is applied to dc-microgrids, dc-distribution and multi-terminal high voltage DC transmission (MT-HVDC). Two main approximations are presented and compared in terms of computational performance and the accuracy of the solution. Simulation results performed in Matlab/Octave demonstrate the advantages of the proposed methodology using a complete set of test systems, from low to high voltage applications. The proposed methodology does not require any consideration about the topology of the grid (radial or meshed) or the number of constant power loads. [ABSTRACT FROM AUTHOR]

• A mathematical model for electrical energy storage systems based on direct power control is presented. • A PI controller design based on passivity theory for electrical energy storage systems is described. • An evaluation of the performance of the PI–PBC for electrical energy storage systems is done. This paper proposes a direct power control for electrical energy storage systems (EESS) in ac microgrids. This strategy allows managing instantaneous active and reactive power without using a conventional inner-loop current regulator and without a phase-locked loop, increasing the reliability of the system while reducing investment costs. PI passivity-based control (PI-PBC) is selected to control the direct power model of EESS. This is because their models exhibit a port-Hamiltonian formulation in open-loop, and PI-PBC exploits this formulation to design a PI controller, which guarantees global asymptotically stability in closed-loop in the sense of Lyapunov. Simulations tested the proposed model in a microgrid and compared with conventional vector oriented controls in a dq reference frame and a direct power model controlled via feedback linearization (FL). PI-PBC has a better performance than other two controllers in all considered scenarios. Simulation results have conducted through MATLAB/SIMULINK software by using the SimPowerSystem toolbox. [ABSTRACT FROM AUTHOR]

• A fault location method for transmission lines which does not depend on the HIF model, considering the distributed parameter model. • The proposed formulation can be applied to both high and low impedance fault location. • An adjustable HIF model that allows generating synthetic high impedance faults to reproduce specific behaviors in fault current features, such as number of shoulders and current magnitudes, among others. A fault in a power system generates economic losses, security problems, social problems and can even take human lives. Therefore, it is necessary to have an efficient fault location strategy to reduce the exposure time and recurrence of the fault. This paper presents an impedance-based method to estimate the fault location in transmission lines. The mathematical formulation considers the distributed parameters transmission line model for the estimation of the fault distance, and it is obtained by the application of Gauss-Newton method. Said method considers available voltage and current measurements at both terminals of the transmission line as well as the line parameters. Moreover, the method can be used for locating high and low impedance faults. Additionally, it is proposed an adjustable HIF model to validate its performance, which allows to generate synthetic high impedance faults by setting specific features of a HIF from simple input parameters. The error in fault location accuracy is under 0.1% for more than 90% of the performance test cases. The easy implementation of this method and encouraging test results indicate its potential for real-life applications. [ABSTRACT FROM AUTHOR]