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The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l 1 -norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3 × 3 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively. [ABSTRACT FROM AUTHOR]

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software. [ABSTRACT FROM AUTHOR]

In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of the optimal location and sizing of photovoltaic (PV) sources in direct current (DC) electrical networks considering time-varying load and renewable generation curves. To represent this problem, a mixed-integer nonlinear programming (MINLP) model is developed. The main idea of including PV sources in the DC grid is minimizing the total greenhouse emissions produced by diesel generators in isolated areas. An artificial neural network is employed for short-term forecasting to deal with uncertainties in the PV power generation. The general algebraic modeling system (GAMS) package is employed to solve the MINLP model by using the CONOPT solver that works with mixed and integer variables. Numerical results demonstrate important reductions of harmful gas emissions to the atmosphere when PV sources are optimally integrated (size and location) to the DC grid. [ABSTRACT FROM AUTHOR]

This paper discusses the power loss minimization problem in asymmetric distribution systems (ADS) based on phase swapping. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage consists of an improved version of the crow search algorithm. This stage is based on the generation of candidate solutions using a normal Gaussian probability distribution. The master stage is responsible for providing the connection settings for the system loads using integer coding. The slave stage uses a power flow for ADSs based on the three-phase version of the iterative sweep method, which is used to determine the network power losses for each load connection supplied by the master stage. Numerical results on the 8-, 25-, and 37-node test systems show the efficiency of the proposed approach when compared to the classical version of the crow search algorithm, the Chu and Beasley genetic algorithm, and the vortex search algorithm. All simulations were obtained using MATLAB and validated in the DigSILENT power system analysis software. [ABSTRACT FROM AUTHOR]

Here, we explore the possibility of employing proportional-integral passivity-based control (PI-PBC) to support active and reactive power in alternating current (AC) distribution networks by using a supercapacitor energy storage system. A direct power control approach is proposed by taking advantage of the Park's reference frame transform direct and quadrature currents ( i d and i q ) into active and reactive powers (p and q). Based on the open-loop Hamiltonian model of the system, we propose a closed-loop PI-PBC controller that takes advantage of Lyapunov's stability to design a global tracking controller. Numerical simulations in MATLAB/Simulink demonstrate the efficiency and robustness of the proposed controller, especially for parametric uncertainties. [ABSTRACT FROM AUTHOR]