This paper presents a mixed-integer second-order cone programing (MISOCP) model to solve the optimal operation problem of radial distribution networks (DNs) with energy storage. The control variables are the active and reactive generated power of dispatchable distributed generators (DGs), the number of switchable capacitor bank units in operation, the tap position of the voltage regulators and on-load tap-changers, and the operation state of the energy storage devices. The objective is to minimize the total cost of energy purchased from the distribution substation and the dispatchable DGs. The steady-state operation of the DN is modeled using linear and second-order cone programing. The use of an MISOCP model guarantees convergence to optimality using existing optimization software. A mixed-integer linear programing (MILP) formulation for the original model is also presented in order to show the accuracy of the proposed MISOCP model. An 11-node test system and a 42-node real system were used to demonstrate the effectiveness of the proposed MISOCP and MILP models. Index Terms-Distributed generation, energy storage, mixed-integer linear programing (MILP), mixed-integer second-order cone programing (MISOCP), optimal operation of radial distribution networks, smart grid. ACRONYMS The abbreviations of common terms used in this paper are presented below. CB Fixed capacitor bank. DG Distributed generator. DN Distribution network. DSS Distribution substation. ESD Energy storage device. MILP Mixed-integer linear programing. MINLP Mixed-integer nonlinear programing. MISOCP Mixed-integer second-order cone programing. OLTC On-load tap-changer. OODN Optimal operation of DNs. OPF Optimal power flow. RS Renewable source.

This study presents a mixed-integer linear programming (MILP) model to solve the simultaneous transmission network expansion planning (TNEP) and reactive power planning (RPP) problem. The proposed model considers reactive power, off-nominal bus voltage magnitudes, power losses, multistage expansion, and security constraints. The use of an MILP model guarantees convergence to optimality by using existing classical optimisation methods. In order to validate the approximation performed, the steady-state operation points were compared with those obtained using an AC load flow method. Garver's 6-bus system and a modified IEEE 118-bus system were used to show the precision and efficiency of the methodology. The results indicate that better expansion and generation plans are found by considering RPP simultaneously with the AC TNEP, when the solutions were compared with the plans of the TNEP using the AC model without RPP and the TNEP considering the DC model, with RPP conducted at a subsequent stage. Continuous variables ΔP ij,y,l,t,k , ΔQ ij,y,l,t,k values of the lth block associated with active and reactive power flows in corridor ij, equivalent line y, at stage t, in condition k θ i,t,k voltage phase angle at bus i, at stage t, in condition k f u ij,t,k slack variable of the voltage phase angle calculation equation of corridor ij, at stage t, in condition k f V ij,t,k slack variable of the voltage drop equation of corridor ij, at stage t, in condition k I ij,y,t,k current flow magnitude on equivalent line y, in corridor ij, at stage t, in condition k

This paper presents a variable neighborhood search (VNS) optimization algorithm for the design of the parameters of supplementary damping controllers: power system stabilizers (PSS) and the interline power flow controller-power oscillation damping (IPFC-POD) set. The objective is to insert damping to local and inter-area oscillation modes in multimachine power systems. The electric power system dynamics is represented by the current sensitivity model. Simulations were carried out using three systems: a test system known as Two-Area Symmetrical and two real systems, the New England and the Reduced Southern Brazilian. The VNS method was compared with a multi-start algorithm in terms of performance, showing better convergence rates. The proposal was also able to obtain solutions with high damping levels, that showed to be robust when changes on the operating point of the power system were considered. Finally, it has been verified that the PSS controllers were effective for damping the local mode oscillations, while the IPFC-POD set operated mainly damping the inter-area modes.

This paper proposes a new method to solve the multistage security-constrained transmission expansion planning problem, incorporating lines based on high-voltage alternating current (HVAC) and high-voltage direct current (HVDC) alternatives. A novel mixed-integer linear programming model, which incorporates transmission losses using a piecewise linearization, is presented. An efficient method to reduce the search space of the problem is developed to help in the solution process. Garver's 6-bus system and a modified Southern Brazilian system are used to show the precision and efficiency of the proposed approach. The tests are performed for cases with and without HVDC links and transmission losses. The results indicate that better expansion plans can be found by considering HVDC proposals in the expansion process. The promising trend of using HVDC lines in future networks to improve the reliability in the system is demonstrated. Index Terms-HVDC lines, mixed-integer linear programming, multistage transmission expansion planning, power losses, security constraints. NOMENCLATURE The notation used throughout this paper is reproduced below for quick reference. Indices: c Index for a contingency scenario i, j, k Indices for buses ki, ij Indices for corridors l The lth block of the piecewise linearization t Index for a decision stage y Index for a candidate line option Sets: Ω ac , Ω dc Set of HVAC/HVDC transmission corridors Ω B

This paper presents a Specialized Chu-Beasley's Genetic Algorithm (SCBGA) to perform coordinated tuning of the parameters of proportional-integral and supplementary damping controllers (power system stabilizers and interline power flow controller-power oscillation damping) in multi-machine electric power systems. The objective is to insert additional damping to low frequency electromechanical oscillations. The current sensitivity model was used to represent the system, therefore all of its devices and components were modeled by current injection. A novel current injection model for the interline power flow controller is presented and a static analysis is considered to validate it. The New England test system-consisting of 10 generators, 39 buses, and 46 transmission lines, divided into two areas with both local and inter-area oscillation modes-was used for the simulations. The SCBGA was compared to other five algorithms: a Random Search, a Local Search, a Simulated Annealing, a Genetic Algorithm, and a Particle Swarm Optimization method, in terms of performance for the tuning of the parameters of the controllers. The results demonstrated that the SCBGA was more efficient than these other techniques. In addition, the obtained solutions proved to be robust when variation of the loads was considered.