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-Abstract – From the results of previous my paper [10] in 2015
year of economic and electrical power storage research conference in Naju, this paper describes an application of autoregressive and moving average (ARMA) model to forecast hourly average wind
speed (HAWS) in Jeju island. The models are used to build up
short-term forecast of hourly average wind speed by the weighted sum of previous wind speed values.
1. INTRODUCTION
Nowaday, the penetration of wind power continues to increase in
power system. Wind is considered as an energy credit but it is also fluctuation. It motivated a need to develop methodologies for assessing the real benefits and risks of including wind turbines to conventional generating systems. The study of wind power forecast, comprehensive reliability and cost evaluation of the system is as answer. An essential step in the study is to model the wind speed of specific site. The wind speed model is used to reproduce accurately actual wind speed. The analysis of historical wind speed data is to determine the necessary parameters for model
2. SIMULATION RESULTS
The ARMA model is mix of autoregressive and moving average process. Where autoregressive process models the time series by taking into account the past values of the data and moving average process defines the random change of the data by using the random
or white noise process at. By applying ARMA process, the HAWS
at present time t of time series of given month is expressed [2]:
where , qj, p and q are autoregressive, moving average parameters,
and their orders respectively. at is white noise, which is random
normality distribution with zero mean and
is variance. The fitted ARMA(2,1) model is estimated in [10] with following parameters
<TABLE I> The Parameter Estimates of ARMA(2,1) Models
The fitted ARMA(2,1) model for wind speeds is employed to
generate a time series of simulated HAWS. Firstly, a sequence of
independent random variables, denoted by at, having normal
distribution with zero mean and
variance is generated for every month. Then, the time series of month is generated by (4). The simulated hourly wind speeds, denoted by , , … , are
obtained as follows:
where µt = µ(h,m) is the mean of hourly wind speed in the hour h of
given month and is the standard deviation of hourly
wind speed in the hour h of given month.
<Fig. 1> The comparison of wind speeds simulation and observation of 24h of all day in a given month
The comparison of hourly average wind speed simulations and
제주도에서의 ARMA 모델을 기반으로한 단기 풍속 예측
도응우엔대풍*, 임진택*, 이연찬*, 오웅진*, 최재석+
경상대학교*+
SHORT-TERM WIND SPEED FORECAST BASED ON ARMA MODEL IN JEJU ISLAND
Duy Phuong N. Do*, Jintaek Lim*, Yeonchan Lee*, Ungjin Oh*, Jaeseok Choi+
Gyeongsang National University*+
Months q1
Jan 1.263 -0.309 0.701 0.447 Feb 1.200 -0.263 0.597 0.405 Mar 1.178 -0.254 0.555 0.410 Apr 1.304 -0.360 0.626 0.359 May 1.347 -0.388 0.653 0.306 Jun 1.236 -0.281 0.620 0.335 Jul 1.152 -0.204 0.550 0.320 Aug 1.086 -0.132 0.437 0.221 Sep 1.148 -0.200 0.514 0.284 Oct 1.340 -0.376 0.729 0.393 Nov 1.187 -0.255 0.582 0.408 Dec 1.166 -0.229 0.599 0.418 Jan Apr Jul Oct 2015년도 대한전기학회 하계학술대회 논문집 2015. 7. 15 - 17330
-observations of 24 hours periods of all day in a given month and their standard deviations is as in Fig. 1. The simulated wind speed approximately revealed the daily variation characteristic and standard deviation of observed wind speed. It is also considered an error of hourly average wind speed of 24 hours periods between the observation and simulation values in a given month.
3. APPLICATION ARMA MODEL to WIND SPEED FORECAST The fitted ARMA(2,1) model is also used to predict hourly average wind speed in Jeju island by the weighted sum of previous wind speed values [2]. The predicted wind speed is expressed as
where p weights are obtained by an inverted form of the ARMA(2,1) model
The predicted HAWS is shown in Fig. 2. But the p weights series is declined sharply [2], the accuracy of predicted values is sufficient in moderate n previous values. The predicted wind speed with 24 lead time hours is showed in Fig. 1, as example for
March 7th, 2015. The wind speed forecast decays exponentially to
mean value in long lead time. The error of wind speed forecast
is randomly fluctuation in acceptable range, exception of
too low and suddenly varied values. Almost actual wind speed is on 95% probability limits of , which is a variation of the wind
speed forecast errors.
However, the un-correlated wind speeds forecast errors are decayed at longer lead times l. It is need to use y weights series for updating the old predicted values at origin time t and lead
time l+k by new ones at origin time t+k and lead timel [2]
where , forl < 0 and forl > 1.In this case, the predicted wind speed is updated in every hour
. The updated wind speeds forecast sticks to the actual wind speed well (Fig. 2).
<Fig. 2> The wind speed forecast in March 7th,2015
4. CONCLUSION
The comparison of main statistical characteristics of the observed HAWS and simulated time series demonstrates the fitness of the models to wind speed in Jeju island. These ARMA(2,1) models are used to generate reference monthly data which close to the actual
statistical characteristics of the 3 year (from 2010 to 2012) time series of wind speed data on Jeju island. These models are also developed to build up a forecast model of wind speed in Jeju island. In the short-term, the wind speed forecast values are acceptable and keep on the main characteristics of the models. It is a useful tool for studying more in the reliability analysis of power system including wind power on Jeju island, Korea.
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