nsga-ii algorithm

Although significant private investment is absorbed in different sectors of power systems, transmission sector is still suffering from appropriate private investment. This is because of the pricing policies of transmission services, tariffs, and especially for investment risks. Investment risks are due to the uncertain behaviour of power systems that discourage investors to invest in the transmission sectors. In uncertain environment of power systems, a proper method is needed to find investment attractive transmission lines with high investment return and low risk. Nowadays, wind power generation has a significant portion in total generation of most power systems. However, its uncontrollable and variable nature has turned it as a main source of uncertainty in power systems. Accordingly, the wind power generation can play a fundamental role in increasing investment risk in the transmission networks. In this paper, impact of this type of generation on investment risk and returned investment cost in transmission network is investigated. With different levels of wind power penetration, the recovered values of investment cost and risk cost in transmission network are calculated and compared. This is a simple method to find investment attractive lines in presence of uncertainties. Wherein, transmission network expansion planning (TNEP) is formulated as a multi-objective optimization problem with objectives of minimizing the investment cost, maximizing the recovered investment cost and network reliability. The point estimation method (PEM) is used to address wind speed variations at wind farms sites in the optimization problem, and the NSGA II algorithm is applied to determine the trade-off regions between the TNEP objective functions. The fuzzy satisfying method is used to decide about the final optimal plan. The proposed methodology is applied on the IEEE 24-bus RTS and simplified Iran 400 kV network.

Ski jump is one of the most e ective structures in energy dissipation over spillways. Spillways have long been of practical importance to safety of dams. The major criteria in hydraulic design are based on the analytical and empirical methods. In the current study, in order to increase chute spillway eciency, a multi-objective evolutionary algorithm known as the Non-dominated Sorting Genetic Algorithm II (NSGA-II) has been utilized to design the optimal triangular bucket angle and chute width. In design method, two separate objective functions have been used. In the rst objective function, equations of dynamic pressure of the bucket, the jet length after bucket, and the scour depth have been used. The second objective function is related to construction volume of chute spillway. For calibrating the rst objective function, characteristics of Karoon III dam have been used as a case study. The di erence between design parameters of Karoon III spillway and those from NSGA-II algorithm method is less than 12 percent. According to the results, if the jet length is considered as the most impressive parameter in the rst objective function, design of the spillway becomes frugal.