Energy output estimation for small-scale wind power generators using Weibull-representative wind data

Abstract

Estimation of energy output for small-scale wind power generators is the subject of this article. Monthly wind energy production is estimated using the Weibull-representative wind data for a total of 96 months, from 5 different locations in the world. The Weibull parameters are determined based on the wind distribution statistics calculated from the measured data, using the gamma function. The wind data in relative frequency format is obtained from these calculated Weibull parameters. The wind speed data in time-series format and the Weibull-representative wind speed data are used to calculate the wind energy output of a specific wind turbine. The monthly energy outputs calculated from the time-series and the Weibull-representative data are compared. It is shown that the Weibull-representative data estimate the wind energy output very accurately. The overall error in estimation of monthly energy outputs for the total 96 months is 2.79%.

Introduction

Large-scale wind turbines have already proved themselves as cost competitive electricity generators in locations where wind resource is good enough. Improved turbine designs and plant utilisation have contributed to a decline in large-scale wind energy generation costs from 35 cents per kWh in 1980 to less than 5 cents per kWh in 1997 in favourable locations [1]. At this price, wind energy has become one of the least-cost power sources. Wind electricity by medium-scale wind turbines is preferable in remote locations and in small islands for being socially valuable and economically competitive. For example, as the Aegean Archipelago has excellent wind potential, the Greek State is strongly subsidising private investments in the area of wind energy applications. Kaldellis and Gavras [2] state that the mean electricity production cost of autonomous power stations, used to fulfil the electricity demands for most of the Aegean Sea islands, is extremely high, three times higher than the corresponding marginal cost of Greek Power Production Company (PPC). After a complete cost-benefit method and an extensive sensitivity analysis, they conclude that the vast majority of wind energy applications in Greece is one of the most promising investments in the energy production sector. Besides, wind power stations can fulfil the energy requirements for almost all islands of the Aegean Archipelago. The most appropriate wind farm in Greece includes about 10 wind turbines in the range of 300–500 kW each, according to Kaldellis and Gavras's experience.

Small-scale wind turbines (as small as 50 W nominal power) produce more costly electricity than large and medium-scale wind turbines, especially in poor wind sites and in autonomous applications that require a high level of reliability. However, when sized properly and used at optimal working conditions, small-scale wind turbines could be a reliable energy source and produce socio-economically valuable energy not only in developing countries but also in autonomous applications in locations that are far away from the grid power in developed countries. Small-scale wind turbines are in fact becoming an increasingly promising way to supply electricity in developing countries. Lew [3] states that the number of people in China who do not have access to the national electricity grid is approximately 72 million. By 1995, a total of 150 000 small-scale (typically 50–300 W) wind turbines had already been disseminated within a national program in China. Today, approximately 140 000 small wind turbines are located only in Imar, an autonomous region in northern China, contributing over 17 MW to installed capacity. It is also worth noting that China produces more wind turbines than any other country in the world and now has 40 manufacturers of small-scale wind turbines. The future of this continuing growth of small-scale wind turbines largely depends on the cost: namely, initial cost per W power and the unit-cost per kWh they produce. If an autonomous wind system is to supply reliable electricity at a reasonable cost in a given location, an accurate wind potential and wind energy assessment have to be carried out beforehand. It is however the lack of such assessment tools, providing an accurate and a simple assessment of wind speed and wind energy output, especially for small-scale systems, that prevents small-scale wind generators from becoming techno-economically successful in operation. Daoo et al. [4] relate the finding of a study in which it is shown that only about 40% of all installed wind mills in India were located in areas having sufficient wind speed for movement of the wind mills. This poor judgement of the wind potential and of the energy output leads to either over or under-sizing of such autonomous wind energy systems. This means a poorly designed system in terms of techno-economics. Therefore over or under-sized systems, which are mostly due to the misjudgement of the resource, should be avoided if such renewable energy systems are to become an alternative way for providing electricity. This is exceptionally crucial for developing countries where millions of people do not have access to conventional electricity services.