This paper presents a mixed integer linear programming model to optimize the costs of maintenance and extra hours for scheduling a fleet of battery electric vehicles (BEVs) so that the products are delivered to prespecified delivery points along a route. On this route, each BEV must have an efficient charging strategy at the prespecified charging points. The proposed model considers the average speed of the BEVs, the battery states of charge, and a set of deliveries allocated to each BEV. The charging points are located on urban roads and differ according to their charging rate (fast or ultra-fast). Constraints that guarantee the performance of the fleet's batteries are also taken into consideration. Uncertainties in the navigation of urban roads are modeled using the probability of delay due to the presence of traffic signals, schools, and public works. The routes and the intersections of these routes are modeled as a predefined graph. The results and the evaluation of the model, with and without considering the extra hours, show the effectiveness of this type of transport technology. The models were implemented in AMPL and solved using the commercial solver CPLEX.

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In this paper, a mixed-integer linear programming (MILP) model is proposed to optimize hybrid electric vehicle (HEV) navigation modes on the city map, namely the problem of the optimal selection of navigation modes (OSNMs). The OSNMs problem of the HEV as part of the operating strategy is obtained considering a constraint set related to CO2 emissions reduction, efficient battery charging, and the optimal scheduling of deliveries. Uncertainties in the HEV navigation on urban roads are modeled using probability values assigned to an established set of traffic density values according to the levels of service (LOS). The model is implemented in AMPL and solved using the commercial solver CPLEX. The case study considers real data related to the Prius Prime technology and shows the effectiveness of automating the HEV navigation modes considering CO2 emissions reduction levels during an operating strategy. Index Terms-Efficient battery charging, optimal selection navigation modes, optimal scheduling of deliveries, operating strategy. NOMENCLATURE A. Sets , Average speed value in the navigation of the HEV in urban road ki for delivery d (km/h).

Optimal power flow (OPF), a mathematical programming problem extending power flow relationships, is one of the essential tools in the operation and control of power grids. To name but a few, the primary goals of OPF are to meet system demand at minimum production cost, minimum emission, and minimum voltage deviation. Being at the heart of power system problems for half a century, the OPF can be split into two significant categories, namely optimal active power flow (OAPF) and optimal reactive power flow (ORPF). The OPF is spontaneously a complicated non-linear and non-convex problem; however, it becomes more complex by considering different constraints and restrictions having to do with real power grids. Furthermore, power system operators in the modern-day power networks implement new limitations to the problem. Consequently, the OPF problem becomes more and more complex which can exacerbate the situation from mathematical and computational standpoints. Thus, it is crucially important to decipher the most appropriate methods to solve different types of OPF problems. Although a copious number of mathematical-based methods have been employed to handle the problem over the years, there exist some counterpoints, which prevent them from being a universal solver for different versions of the OPF problem. To address such issues, innovative alternatives, namely heuristic algorithms, have been introduced by many researchers. Inasmuch as these state-of-the-art algorithms show a significant degree of convenience in dealing with a variety of optimization problems irrespective of their complexities, they have been under the spotlight for more than a decade. This paper provides an extensive review of the latest applications of heuristic-based optimization algorithms so as to solve different versions of the OPF problem. In addition, a comprehensive review of the available methods from various dimensions is presented. Reviewing about 200 works is the most significant characteristic of this paper that adds significant value to its exhaustiveness.

An influential factor in enhancing the attendance services, mainly in commercial and emergency sectors, is the vehicular technology used to transport people, goods, or equipment. Although hybrid electric vehicles (HEVs) represent a sustainable transport alternative, the existing technical limitations such as battery and fuel capacities, and autonomy, among others, highlight the provision of an efficient automation tool. The tool can serve to enhance the operational performance of the HEV by selecting the proper driving mode (on fuel or electricity), and the navigation strategies to the delivery and charging points in urban areas. This paper proposes a two-stage methodology that allows the HEVs operators to automate the operational performance of a heterogeneous HEV fleet on a city map. Each stage is handled by its corresponding optimization model. In the first stage, the total navigation time and the battery lifetime of the fleet during the operation are optimized. In this stage, constraints related to charge-sustaining/charge-depleting modes, state of charge (SoC) of the HEVs battery, and deliveries schedules are taken into account. To this end, operating strategies related to the performance of different types of existing HEV technologies are anonymously considered. In the second stage, the best operating strategy among all the operating strategies is selected while considering the capacity of HEVs to deliver a given quantity of goods. Moreover, uncertainties during the HEV navigation are simulated considering the change in traffic density of the urban roads as a function of the levels of service (LOS). Results show that the proposed methodology establishes an efficient operational scheme for a HEVs fleet, ensuring a significant reduction of energy usage as well as mitigating the CO2 emissions.

This paper presents a mixed integer linear programming (MILP) model to optimizing the maintenance costs during the operation of the hybrid electric vehicles (HEVs) aiming at reducing CO2 emissions during operating along of the day. This target is obtained by an appropriate selection of navigation modes and the optimal scheduling of deliveries. The proposed model considers the average speed, battery state of charge (SOC), and the set of deliveries to be made by each type of HEV. A set of constraints that ensures the performance of the HEVs is considers while the uncertainties of the trip on each urban road are modeled using the traffic density values according to the levels of service (LOS). The proposed model is implemented in AMPL and solved using the solver CPLEX showed the effectiveness in the evaluation of each type of HEV technology. Index Terms-Battery state of charge, navigation modes, scheduling of deliveries, performance of the HEVs. NOMENCLATURE A. Sets Set of intersections i. Set of urban roads ki. Set of density values u. B. Parameters Autonomy value (km). Length of urban road ki (km). Traffic density in each urban road ki (veh/km). Value of the traffic density of element u (veh/km). Saturation density (veh/km). Optimal density related to (veh/km). CO2 emissions (gCO2/km). Maximum traffic flow (veh/h). Battery energy capacity (kWh). Tank fuel capacity (L). Big value used in the linearization process. , Matrix of possible routes. Number of deliveries. Total number of periods. Number of possible routes. , Upper and lower battery charge limits (kW). Location of the charging station (0/1: intersection i without/with charging station). Initial state of charge of the battery of HEV (kWh). , Type of intersection i in delivery d (1: starting; 0: intermediate; 1: arrival). Type of urban road ki (1: main; 0: secondary). Maximum average speed in urban road ki (km/h).

In prosumers’ communities, the use of storage batteries (SBs) as support for photovoltaic (PV) sources combined with coordination in household appliances usage guarantees several gains. Although these technologies increase the reliability of the electricity supply, the large-scale use of home appliances in periods of lower solar radiation and low electricity tariff can impair the performance of the electrical system. The appearance of new consumption peaks can lead to disturbances. Moreover, the repetition of these events in the short term can cause rapid fatigue of the assets. To address these concerns, this research proposes a mixed-integer linear programming (MILP) model aiming at the optimal operation of the SBs and the appliance usage of each prosumer, as well as a PV plant within a community to achieve the maximum load factor (LF) increase. Constraints related to the household appliances, including the electric vehicle (EV), shared PV plant, and the SBs, are considered. Uncertainties in consumption habits are simulated using a Monte Carlo algorithm. The proposed model was solved using the CPLEX solver. The effectiveness of our proposed model is evaluated with/without the LF improvement. Results corroborate the efficient performance of the proposed tool. Financial benefits are obtained for both prosumers and the energy company.

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