Adaptive neuro-fuzzy optimization of wind farm project net profit
Introduction
The world’s fastest growing renewable energy source is the wind energy. Wind turbines are machines which convert the wind energy to the electricity [1], [2]. A wind farm contains a number of horizontal wind turbines [3], [4]. These wind turbines are positioned and aligned in clusters facing the wind direction. Optimal wind turbine placement on a selected wind farm site is of major importance, since it can lead to a remarkable increase in the produced power and therefore the overall net profit of the wind farm [5], [6], [7].
Besides the optimal wind turbine placement, the number of wind turbines installed in the wind farm can also be of major importance to achieve the maximal produced power and net profit of the wind farm. In this article the main focus will be on number of turbines modifying by taking economic aspects into account [8]. Conceptual design of a new wind farm involves the evaluation of alternative farm configurations to determine physical and economic feasibilities [9]. In testing alternatives, designers require both an absolute economic measure and a normalized economic measure in order to make a definitive evaluation [10], [11]. In recent years NPV (Net Present Value) [12], [13], [14], [15], [16] has often been chosen as the absolute metric and IRR (Internal Rate of Return) [17], [18], [19] as the normalized one.
The NPV and IRR are two of the most important criteria for choosing among investment projects [20], [21]. In many circumstances investment projects are ranked in the same order by both criteria. In [22] was consider the NPV and IRR as indexes to evaluate the investment risk of wind power project. Paper [23] presented an alternative approach to conceptual design where a compound objective function based on the NPV and IRR aggregate performance metrics. In some situations, however, the two criteria provide different rankings [24]. In [25], [26] a sensitivity analysis of the IRR to some economic factors has been carried out.
In an uncertain economic environment, it is usually difficult to predict accurately the investment outlays and annual net cash flows of a project [27]. In addition, available investment capital sometimes cannot be accurately given either [28]. In [29] was addressed the maximization of a project’s expected NPV when the activity durations and cash flows are described by a discrete set of alternative scenarios with associated occurrence probabilities. Article [30] presented the concept of NPV curve to estimate the best investment time for the investor, where the curve is constructed by calculating the NPVs resulting from the investment in successive years.
Optimal performance (maximal net profit) of the wind farm can be obtained if the number of turbines installed in the wind farm is optimal. The aim of the investigation is to change the number of turbines in the wind farm at different interest rates per year and unit sale price of electricity so that the farm may be kept running at maximum profit level or to maximize NPV.
To improve the operations of the wind farm, application of fuzzy logic (FL) [31], [32], [33], [34], [35], [36] or artificial neural network (ANN) has attracted much attention in recent years [37], [38], [39], [40], [41], [42], [43]. As a soft computing [44], non-linear function, ANNs can be used for identifying the extremely non-linear system parameters with high accuracy. Neural networks can learn from data. However, understanding the knowledge learned by neural networks has been difficult. In contrast, fuzzy rule based models are easy to understand because they use linguistic terms and the structure of IF-THEN rules. Unlike neural networks, however, fuzzy logic by itself cannot learn. Since neural networks can learn, it is natural to merge these two techniques. This merged technique of the learning power of the ANNs with the knowledge representation of FL has created a new hybrid technique, called neuro-fuzzy networks or adaptive neuro-fuzzy inference system (ANFIS) [45]. ANFIS, as a hybrid intelligent system that enhances the ability to automatically learn and adapt, was used by researchers for modeling [46], [47], [48], [49], predictions [50], [51], [52], [53], [54] and control [55], [56], [57], [58], [59] in various engineering systems. ANFIS can be used with systems handling more complex parameters than neural networks or fuzzy logic. Another advantage of ANFIS is its speed of operation, which is much faster than in other control strategies like fuzzy control or neural network control. The basic idea behind these neuro-adaptive learning techniques is to provide a method for the fuzzy modeling procedure to learn information about data [60], [61], [62], [63], [64], [65], [66], [67].
In this paper, the application of ANFIS is proposed to optimize the number of turbines installed in the wind farm to extract the maximal net profit throughout determined working period of the wind farm. As inputs in the optimization scheme, interest rate per year and unit sale price of electricity are used. The output should be the optimal number of turbines in the wind farm which generates the maximal net profit or NPV. The objective function of the NPV and IRR for the total relevant costs considered in our model is mathematically formulated. A complete search procedure is provided to find the optimal solution by employing the properties derived in this paper and the ANFIS algorithm. The aim of this paper is to develop a model to determine economically optimal number of wind turbines for wind farms, which include the aerodynamic interactions between the turbines (wake effect) and the various cost factors.
Section snippets
Wind farm power production model
Since a wind turbine generates electricity from the energy in the wind, the wind leaving the turbine has less energy content than the wind arriving in front of the turbine. Therefore a wind turbine in a wind farm will always cast a wind shadow in the downwind direction. This is described as the wake behind the turbine, which is quite turbulent and has an average down wind speed slower than the wind arriving in front of the turbine.
For the present study analytical wake model named as Jensen’s
Definition of NPV and IRR
Capital budgeting is finance terminology for the process of deciding whether or not to undertake an investment project. There are two standard concepts used in capital budgeting: net present value (NPV) and interest rate of return (IRR) [16], [17].
The purpose of the NPV is to represent the value, or worth, of a stream of payments in a single number, recognizing the fact that the same nominal payment, made at different times, will have different worth. The NPV of a stream of payments is defined
NPV for wind farm project investment
Net present value, NPV, of the profit to be derived from the wind farm iswhere CF0 represents total investment in the wind farm (cost of turbines, installations and land cost), CFt is the net revenue from selling electricity from the wind farm, r is the appropriate financial interest rate, T is total operating time per period, n is the number of years for project investment, PT is the total extracted power from all wind
Adaptive neuro-fuzzy inference system
Fuzzy Inference System (FIS) is the main core of ANFIS [45]. FIS is based on expertise expressed in terms of ‘IF–THEN’ rules and can thus be employed to predict the behavior of many uncertain systems. FIS advantage is that it does not require knowledge of the underlying physical process as a pre-condition for its application. Thus ANFIS integrates the fuzzy inference system with a back-propagation learning algorithm of neural network. The basic structure of a FIS consists of three conceptual
Results
At the beginning the ANFIS network was trained. The training data is shown in Fig. 9 where x-axis represents experimental training data samples (250) and the output or y-axis in the Fig. 9 depicts the optimal number of wind turbines installed in wind farm. These training data are acquired by above presented mathematical procedure. The other 250 experimental data samples are used for testing of the proposed model.
Fig. 10 shows training procedure for the ANFIS network. It can be seen that the
Conclusion
The deregulation of the energy sector resulted in a new economic environment, due to the daily operations of the electric markets, and this new environment needs to be considered with the economics of investment in new facilities. The long-term horizon with the sequence of appropriate decisions adds to the complexity of the problem. A future investor in transmission assets must have a tool to decide when and where to invest in new assets. One of the most important and frequent decisions
Acknowledgments
This paper is financially supported by the Malaysian Ministry of Education under the University of Malaya High Impact Research Grant – UM.C/HIR/MOHE/FCSIT/12. This paper is also supported by Project Grant ТР35005 “Research and development of new generation wind turbines of high-energy efficiency” (2011–2014) financed by Ministry of Education, Science and Technological Development, Republic of Serbia.
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