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This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language. • Bipolar DC networks can operate with balanced and unbalanced conditions as a function of the demands connected between poles. • A convex approximation can be applied to bipolar DC networks via second order cone programming. • A simplification based on expected balanced operation ca be reached to obtain a relaxed convex model with low estimation errors. • Dispersed generators and battery energy storage systems can be added to bipolar DC networks using a optimal power flow formulation. [ABSTRACT FROM AUTHOR]

• An entire dynamic model of a synchronous machine with hydro-turbine systems is shown. • A decentralized controller of a hydro-turbine systems with surge tank based on Euler–Lagrange representation is proposed. • The proposed controller is based on standard passivity-based control. • A comparison of the proposed controller with a standard cascade PID controller and sliding-mode controller is presented. This paper addresses the problem of control design for hydro-turbine governing systems with surge tanks from the perspective of standard passivity-based control. The dynamic model of a synchronous machine is considered in conjunction with a model of the hydro-turbine to generate an eleventh-order nonlinear set of differential equations. An Euler–Lagrange representati of the system and its open-loop dynamics is developed. Then, the standard passivity-based control is applied to design a global and asymptotically stable controller in closed-loop operation. The proposed control is decentralized to avoid challenges of communication between the hydro-turbine governing systems. The proposed standard passivity-based control approach is compared with two control approaches. First, a classical standard cascade proportional-integral-derivative controller is applied for the governing system, the automatic voltage regulator, and the excitation system. Second, a sliding mode control is also implemented in the governing system. Two test systems were used to validate the performance of the proposed controller. The first test system is a single machine connected to an infinite bus, and the second test system is the well-known Western System Coordinating Council's multimachine system. Overall, simulation results show that the proposed controller exhibits a better dynamic response with shorter stabilization times and lower peaks during the transient periods. [ABSTRACT FROM AUTHOR]

• Passivity-based controllers for PWM-VSCs and PWM-CSCs were presented. • Asymptotic stability via Hamiltonian paradigm was guaranteed by implementing PBCs. • Active and reactive power control in single-phase MGs were proposed without PLLs. • Renewable and energy storage devices were integrated in MGs with CSC and VSCs. 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. [ABSTRACT FROM AUTHOR]

Highlights • A mathematical model for a two-terminal VSC-HVDC system based on DPC is presented. • A passivity-based PI controller for a two-terminal VSC-HVDC system is described. • The performance of the PI-PBC for the VSC-HVDC system under conditions is tested. Abstract This paper proposes a direct power control (DPC) for a high-voltage direct-current system using voltage source converters (VSC-HVDC) by applying passivity-based control theory. This system allows doing an efficient and reliable integration of electrical network from renewable energy sources. The DPC model permits instantaneous control of the active and reactive power without employing the conventional inner-loop current regulator and the phase-locked loop, thus diminishing investment costs and increasing the reliability of the system. The proportional-integral passivity-based control (PI-PBC) is chosen to control the direct power model of the VSC-HVDC system since this system exhibits a port-Hamiltonian formulation in open-loop and as PI-PBC can exploit this formulation to design a PI controller, which guarantees asymptotically stable in closed-loop based on Lyapunov's theory. Passivity-based control is an active research subject in the control community which has gained a reputation of being a very theoretical subject. Nevertheless, it can have advantages from a practical point of view including an implementation similar to the conventional controls for power systems applications. The paper is oriented to the power & energy systems community, taking into account this practical approach. The proposed controller is assessed by simulations in a two-terminal VSC-HVDC system and compared with a PI direct power controller. Four simulation conditions using MATLAB/SIMULINK were conducted to verify the effectiveness of PI-PBC against a PI controller and a perturbation observer-based adaptive passive control under various operating conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal pole-swapping problem in bipolar asymmetric distribution networks by proposing a mixed-integer conic approximation (MICA) model to minimize the total grid power losses for a particular load condition. The non-convex relation between voltage and power in the constant power loads is relaxed through equivalent cones. The effect of the neutral wire's connection is considered in the proposed MICA model via an auxiliary variable associated with the total current drained to the earth in the case of a solidly grounded connection. Numerical comparisons with three combinatorial optimization methods (black-hole optimization, sine-cosine algorithm, and the Chu & Beasley genetic algorithm) and a mixed-integer quadratic approximation in two test feeders composed of 21 and 85 buses demonstrate the effectiveness of the proposed MICA model. Reductions of about 3.9411 and 10.1706% were obtained after applying the MICA model to the optimal pole-swapping problem. All numerical validations were carried out in the MATLAB programming environment, using the convex disciplined tool known as CVX with the Gurobi solver. • Optimal load balancing in bipolar asymmetric DC networks minimizes its power losses. • The mixed-integer nonlinear model of the pole-swapping is transformed as a convex one. • The neutral floating connection presents the worst scenario for power losses. • Combinatorial methods find local solutions as the number of network nodes increases. [ABSTRACT FROM AUTHOR]

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]

• Power flow analysis is a fundamental toolbox for DC planning and operation. • Classical methods such as Gauss-Seidel, Newton-Raphson and Taylor-based methods are analyzed. • Four classical DC test feeders are employed for verifying the applicability and robustness of power flow methods in DC grids. 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. [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]

This paper focuses on the problems of optimal operation of battery energy storage systems (BESSs) in distributed networks from a nonlinear programming (NLP) point of view. This proposal contains the active and reactive power capabilities of the voltage source converters that interface with the BESS independently, which implies that the BESSs have the possibility to work as dynamic energy compensators over all the four quadrants. Two radial distribution networks have been used to validate the proposed NLP model. This model has been arrived at by using the general algebraic modeling system (GAMS) optimization package. Artificial neural networks (ANN) are also employed for short-term forecasting of renewable generation based on wind and photo-voltaic sources. Numerical results show that the inclusion of reactive power capabilities of batteries reduces the daily operational cost of the network as compared to the classical unity power factor operation approach. All the simulations are made considering Colombian utility typical curves. [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 relaxed convex model for the optimal location and sizing of constant power sources in dc grids is presented. • A convex relaxation by using Taylor's series expansion is proposed. • A sequential quadratic programming to solve the convex model is described. This report addresses the problem of optimal location and sizing of constant power sources (distributed generators (DGs)) in direct current (DC) networks for improving network performance in terms of voltage profiles and energy efficiency. An exact mixed-integer nonlinear programming (MINLP) method is proposed to represent this problem, considering the minimization of total power losses as the objective function. Furthermore, the power balance per node, voltage regulation limits, DG capabilities, and maximum penetration of the DG are considered as constraints. To solve the MINLP model, a convex relaxation is proposed using a Taylor series expansion, in conjunction with the transformation of the binary variables into continuous variables. The solution of the relaxed convex model is constructed using a sequential quadratic programming approach to minimize the linearization error using the Taylor series method. The solution of the relaxed convex model is used as the input for a heuristic random hyperplane method that facilitates the recovery of binary variables that solve the original MINLP model. Two DC distribution feeders, one having 21 and the other having 69 nodes, were used as test systems. Simulation results were obtained using the MATLAB/quadprog package and contrasted with the large-scale nonlinear solvers available for General algebraic modeling system (GAMS) software metaheuristic optimization approaches to demonstrate the robustness and effectiveness of our proposed methodology. [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]