Igor Poljak

In this paper, stochastic sizing of a stand-alone Photovoltaic/Hydrokinetic/Hydrogen storage energy system is performed with aim of minimizing the cost of project life span (COPL) and satisfying the reliability index as probability of load shortage (POLS). The stochastic sizing is implemented using a novel framework considering two-point estimate method (2m+1 PEM) and improved gradient-based optimizer (IGBO). The 2m+1 PEM is used to evaluate the impact of uncertainties of energy resource generation and system demand on sizing problem. The 2m+1 PEM utilizes the approximate method to account for these uncertainties. In order to avoid premature convergence, the gradient-based optimizer (GBO), a meta-heuristic algorithm influenced by Newtonian concepts, is enhanced using a dynamic lens-imaging learning approach. The size of the system devices, which is determined utilizing the IGBO with the COPL minimization and optimally satisfying the POLS, is one of the optimization variables. The results of three hPV/HKT/FC, hPV/FC, and hHKT/FC configurations of the system are presented in two situations of deterministic and stochastic sizing without and with taking uncertainty into consideration. The findings showed that the hPV/HKT/FC configuration and the IGBO performed better than other configurations and techniques like conventional GBO, particle swarm optimization (PSO), and artificial electric field algorithm (AEFA) to achieve the lowest COPL and POLS (higher reliability) in various cases. Additionally, the COPL for the hPV/HKT/FC, hPV/FC, and hHKT/FC configurations increased by 7.63%, 7.57%, and 7.65%, respectively, while the POLS fell by 5.01%, 4.48%, and 4.59%, respectively, contrasted to the deterministic sizing, according to the results of stochastic sizing based on 2m+1 PEM. As a result, the findings indicate that in the deterministic sizing model, the quantity of output and energy storage is insufficient to meet demand under unknown circumstances. Applying stochastic sizing while taking into account the volatility of both supply and demand can, therefore, be an economically sound way to meet demand.

The commingling of the two types of heavy fuel oils (fuel remaining in the tanks and fuel loaded) is determined by the company’s guidance and safety management system. Remained heavy fuel oil must be distributed in the heavy fuel oil tanks before bunkering efficiently, in order to obtain maximum bunker loading. This paper proposes the use of the bisection method to calculate the distribution of the remaining fuel in heavy fuel oil tanks on the liquefied natural gas carrier. The use of this method is illustrated by three examples. The first and second examples show that the iterations converge quickly to the solution. It is found that maximum tank filling with fuel commingling is achievable if the bunker intervals satisfy the company policy of 10% as a lower limit of tank filling, and 90% to 100% as an upper limit. The third example illustrates a situation when the proposed mathematical model does not allow maximization of the total tank capacity without risk assessment. The mathematical spectrum of the possible tank filling solution is presented. Despite its limitations, the bisection method is suitable for onboard applications because it is simple and fast, and can be easily programmed.