A double Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2, 3} 2 with the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for 3 which f(v) = 3 or two vertices v1 and v2 for which f(v1) = f(v2) = 2, and every vertex u for which 4 f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. The weight of a double Roman dominating function f is the value w(f) = ∑u∈V(G) 5 f(u). The minimum weight over all double 6 Roman dominating functions on a graph G is called the double Roman domination number γdR(G) 7 of G. In this paper we determine the exact value of the double Roman domination number of the 8 generalized Petersen graphs P(n, 2) by using a discharging approach.

The automobile industry is often believed to be moving towards electric vehicles. Hybrid electric vehicles (HEVs) and electric vehicles (EVs) are anticipated to dominate the automotive industry. Regenerative braking is one of the modern approaches that recharge the battery by extracting the kinetic energy from the braking thus improving the vehicle range. However, the rate of current supplied by regenerative braking to the battery is a major concern as lithium-ion (Li-ion) is susceptible to failure due to the intensity of the charging-discharging rate, and operating temperature. So, this review article focuses on the effect of regenerative braking on the life of the battery and measures being taken to protect the battery from higher charging during regenerative braking. Various research articles are considered for observing the effect of regenerative braking on battery life. It is found that longer duration charging current obtained from regenerative braking that is irrespective of current intensity is the prominent factor of battery deterioration. If the SOC and the temperature are not in the optimal range, the Lithium plating rate increases. However, a higher level of regenerative braking increases the battery life even at high SOC and temperature by reducing the Depth of Discharge (DOD) and by using shorter recharging periods.

This paper presented a method for calculating daily load curves by considering charging and discharging locations of electric vehicles to help to understand the impact of loads generated by charging and discharging of electric vehicles on the power grid. Based on the estimated PEVs’ share, the PEVs discharge power was calculated to reflect both the characteristics of the arriving vehicle in the morning and the SMP plan after establishing a assumption that the electric vehicle arrived at work in the morning and the electric vehicle arrived at home in the afternoon for each of the charging/discharging locations, that is, work and home, of electric vehicles in the city. After calculating the daily load curve for each charging/discharging power type for the PEVs charging strategy, which takes into account both the characteristics of the vehicle arriving at home in the afternoon and the TOU fare system and the characteristics of the vehicle arriving at work in the morning and the SMP fare system, it was analyzed by comparing the impact assessment on the grid by adding the existing load. The results of this paper provide an accurate understanding of the impact of PEVs charging and discharging loads on the power grid. The results should help to establish PEVs charging and discharging load management plans to prevent overloading the power grids with appropriate SMP and TOU tariffs while curbing the reinforcement and expansion of power grids as much as possible.

This paper presents a V2G strategy to flatten the daily load curve by considering the charging and discharging location of the electric vehicle to help understand the effect of the load generated by charging and discharging of the electric vehicle on the power grid. Based on the estimated share of electric vehicles, the assumption that electric vehicles go to work in the morning and leave in the afternoon was set, and the electric vehicle discharge power was calculated by reflecting both the characteristics of vehicles that go to work in the morning and the SMP1 and SMP2 plans. In addition, the electric vehicle charging power was calculated by reflecting the characteristics of vehicles returning home from work in the afternoon and the TOU rate system. In other words, in order to establish an efficient V2G strategy, a charging/discharging type-specific modeling was developed that considered all the characteristics of an electric vehicle commuting vehicle, and charging and discharging daily load using SMP1 and SMP2 rate plans for morning discharge and TOU1 and TOU2 rate plans for afternoon charging were applied. After calculating the curve, this value was compared and analyzed to evaluate the effect on grid leveling by adding the existing load. The analysis provides an accurate understanding of the impact of EV charging and discharging loads on the power grid according to V2G strategies. In this paper, it is helpful to apply EV charge and discharge management technology to avoid grid overload and minimize grid expansion by leveling the grid daily load curve by applying appropriate SMP and TOU rates through the establishment of an efficient V2G strategy by charge and discharge modeling.