Inventory and Modelling of Different Objective Functions and their Impact on Optimal Design of an Offshore Wind Farm

Abstract

The design of an offshore wind farm (OWF) is multidisciplinary in nature as it involves the design of many disciplines such as the wake effects, support structure, electrical cables etc. For the optimal design of an OWF, an optimization procedure is required where all the disciplines are optimized simultaneously. The objective function plays a significant role in optimization as it expresses the main aim of the model which is to be either minimized or maximized. So far, cost of energy (COE) and annual energy production (AEP) are one of the commonly used objective functions for OWF optimization as far as the author is aware. However, there might be other objective functions that may influence the optimal design of an OWF as well. This may include maximizing the profit, minimizing the environmental impact, reducing their carbon emissions etc. Hence, this thesis investigates the overview of different objective functions and understand its impact on the optimal design of an OWF.

An inventory of different objective functions is prepared, and relevant ones are selected for further study. It is observed that even though some objectives are dissimilar, they still depend on the same wind farm parameters and are therefore expected to give similar design results. From the list of objective functions, net present value (NPV) and risk management objectives are chosen for further research.

The selected objective functions are then formulated in a metric for optimization. The price of electricity plays a significant role in determining the NPV. It is learnt that electricity price varies with the power supply depending on the site conditions. The electricity price is low if the supply of power is high in a region where there are many OWF’s and vice versa. Moreover, OWF investors value constant power output without any fluctuations. Hence, taking all these aspects into consideration, the electricity price in the NPV function is modelled for a constant value, wind variability and wind power predictability.
The risk management function, on the other hand, aims at minimizing the uncertainty associated with an OWF project. The risk here refers to the uncertainty associated with the profit obtained from the OWF. A set of annual average wind speeds is computed using monte carlo simulations and the AEP and NPV are estimated. The mean( NPV_mean) and standard deviation ( NPV_std ) of NPV are then calculated. NPV_std represents the uncertainty in this scenario and is minimized to reduce the risk.

A suitable method is then identified to deal with multiple objectives. The NPV function is maximized for maximum profit and this objective is evaluated using a single objective optimization technique. The risk management objective involves the calculation of NPV_mean and NPV_std. Both objectives are contrasting in nature as a significant reduction in NPV_std corresponds to an undesirable reduction in NPV_mean. A tradeoff between both these objectives is the best possible solution. Therefore, a multi- objective optimization technique is used, and a list of solutions is obtained by generating a pareto front.

The new approach is then evaluated by implementing different case studies. It is observed that optimum rotor diameter and number of turbines for the single objective optimization technique are influenced by economic indicators such as the real interest rate and lifetime. However, they are not influenced by variation in the electricity price. Nevertheless, the NPV function is sensitive to the economic indicators and variation in the electricity price.

For the multi - objective optimization technique, multi criteria analysis was used to determine the weight to the objective functions while moving along the pareto curve. It was observed that the improvement of one objective led to the deterioration of the other objective. Hence, the pareto front provides opportunities to investors to negotiate and decide on the weight they want to specify for their objectives.