A Mixed-Integer Linear Programming Model for the Electric Vehicle Charging Coordination Problem in Unbalanced Electrical Distribution Systems

Abstract

This paper presents a novel mixed-integer linear programming (MILP) model for the electric vehicle charging coordination (EVCC) problem in unbalanced electrical distribution systems (EDSs). Linearization techniques are applied over a mixed-integer nonlinear programming model to obtain the proposed MILP formulation based on current injections. The expressions used to represent the steady-state operation of the EDS take into account a three-phase representation of the circuits, as well as the imbalance of the loads, leading to a more realistic model. Additionally, the proposed formulation considers the presence of distributed generators and operational constraints such as voltage and current magnitude limits. The optimal solution for the mathematical model was found using commercial MILP solvers. The proposed formulation was tested in a distribution system used in the specialized literature. The results show the efficiency and the robustness of the methodology, and also demonstrate that the model can be used in the solution of the EVCC problem in EDSs. Index Terms-Electric vehicles charging coordination (EVCC), mixed integer linear programming (MILP), unbalanced electrical distribution systems (EDSs). NOMENCLATURE SetsF Sets of phases {A,B,C}. L Sets of circuits. N Sets of nodes. T Sets of time intervals. Constants α G n,tEnergy cost at node n in time period t. βElectric vehicle (EV) energy curtailment cost. t

Adaptive Asymptotic Tracking Control of Uncertain Time-Driven Switched Linear Systems

“…short planning horizons): as a consequence approximations or decompositions must be carried out so as to make the problem tractable. For example: in [20] linearization techniques are applied to reduce a mixedinteger nonlinear programming model to a mixed-integer linear programming: in [21] the charging problem is split into hierarchical subproblems to better handle complexity; in [22] a two-stage energy exchange scheduling strategy is presented where at the first stage the electricity cost of a microgrid is minimized and at the second stage the aggregate charging/discharging power is allocated to each EV. The openloop nature of these strategies arises from the formulation of the charging problem as an optimal control problem 'a la Pontryagin', involving open-loop control candidates.…”

Smart Charging of EVs in Residential Distribution Systems Using the Extended Iterative Method

“…(1) Compared with the optimization results in [15], the developed method had much higher calculation efficiency. (2) This developed method could avoid the risk of the node voltage exceeding the lower limit, and provided reliable and economic operation of the distribution system when massive numbers of EVs penetrate into the grid.…”

“…Clearly, the calculation efficiency of the proposed method is much higher than the method described in [15]. This is because at each iteration, optimization variables only consist of the charging power of EVs, which greatly reduce the number of optimization variables.…”

“…The optimization results of the proposed method compared with the method in [15] are shown as Table 3. Clearly, the calculation efficiency of the proposed method is much higher than the method described in [15].…”

“…This is because at each iteration, optimization variables only consist of the charging power of EVs, which greatly reduce the number of optimization variables. Whereas, in [15] nodal voltages are included in the optimization variables. Although linearization techniques are applied and mixed integer linear programming is formulated, because the number of optimization variables is large, the calculation time increases greatly.…”