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.

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.

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 CO $_2$ emissions reduction levels during an operating strategy.