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.

This article presents a novel mixed-integer second-order cone programming model to increase the photovoltaic (PV) hosting capacity and optimize the operation of distribution networks. The problem considers voltage and reactive (Volt/VAr) control through the optimal operation of capacitors banks, substations’ on-load tap changers, voltage regulators, and network reconfiguration with radial and closed-loop operation topologies. The proposed formulation considers voltage-dependent models for loads and capacitor banks. The objective function maximizes the PV hosting capacity of the network. Numerical experiments are carried out using the 33-node and the 85-node networks. Results demonstrate the effectiveness of the proposed formulation to increase the penetration of PV sources, especially when the closed-loop operation is allowed, together with network reconfiguration and Volt/VAr control.

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.

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.

This work proposes a novel mixed-integer linear programming model for the medium-term multistage planning of active distribution systems and electric vehicle charging stations (EVCSs). Investment alternatives include the installation of conductors, capacitor banks, voltage regulators, dispatchable and nondispatchable distributed generation, energy storage units, and EVCSs. Hence, the model identifies the best size, location, and installation time for the candidate assets under the uncertainty associated with electricity demand, energy prices, renewable energy sources, and EVCSs’ load profiles. Unlike classical planning approaches, conventional load is modeled as voltage-dependent. Besides, EVCSs are planned by zones to optimize the coverage of the service provided to users of electric vehicles and to reduce the discrepancy between the geographical requirements and the optimal locations for the installation of EVCSs in the system. EVCSs’ load profiles are calculated using a travel simulation algorithm based on real travel patterns that consider fast, slow, and residential chargers. Moreover, as another salient feature, constraints for CO ₂ emissions are incorporated into the model. The resulting model is formulated as a stochastic scenario-based program, which is driven by the minimization of the total expected cost. Tests are conducted using a 69-node system to demonstrate the effectiveness of the proposed model.

This article presents a new mixed-integer linear programming model for the optimal restoration of active distribution networks during permanent fault events considering not only network reconfiguration but also the islanded operation of distributed generation, thereby giving rise to the formation of microgrids. To that end, the proposed approach accounts for both the black-start capacity of generators and the connection of multiple generators to the same microgrid. Moreover, voltage control devices such as substations’ on-load tap changers, voltage regulators, and capacitor banks are also considered in the formulation. The model is driven by the minimization of the out-of-service load after single or multiple faults in the network using the minimum number of switching operations and modifications in the statuses of the voltage control devices. The proposed model is implemented in the mathematical modeling language AMPL and solved with the CPLEX solver. Tests are conducted using a 53-node distribution system considering different fault locations. Numerical results show the relevant effect of microgrid formation and voltage control in the restoration process. Simulations also prove the effective performance of the proposed approach in terms of computation time.