Data Analysis and Physical Modeling for Short Term Wind Speed Forecasting at Four Locations in Ireland

Transcription

1 Data Aalysis ad Physical Modelig for Short Term Wid Speed Forecastig at Four Locatios i Irelad Prof. Parikshit G. Jamdade Departmet of Electrical Egieerig, PVG s College of Egieerig & Techology, Pue Shri. Aurag V Chava UG Studet, Departmet of Electrical Egieerig, PVG s College of Egieerig & Techology, Pue Shri. Jagruti J Soawae UG Studet, Departmet of Electrical Egieerig, PVG s College of Egieerig & Techology, Pue Shri. Komal A Padalkar UG Studet, Departmet of Electrical Egieerig, PVG s College of Egieerig & Techology, Pue Shri. Rahul Shivshara UG Studet, Departmet of Electrical Egieerig, PVG s College of Egieerig & Techology, Pue Prof. Shriivas G. Jamdade Departmet of Physics, Nowrosjee Wadia College, Pue 1

2 Problem statemet Wid eergy has the lower cost of electricity productio ad it is available i ample amout. Therefore, larger umbers of coutries are takig steps forward for wid power productio as source for future power geeratio. Power demad is havig varyig ature because of various ucertaities, icludig populatio growth, chagig techology, ecoomic coditios, weather coditios, ad geeral radomess i idividual usage etc. It is also affected by kow caledar effects due to the time of day, day of week, time of year, local evet, festivals ad public holidays. To satisfy the power demad we have to do resource forecastig. Wid power forecastig is oe of the parts of the resource forecastig. As wid is radom i ature wid speed forecastig became mai cosideratio. Accurate forecastig is a ecessary for maager to pla effectively. Iaccurate forecastig may lead to iaccurate decisios that may lead to ieffective maagemet i overall operatios. Wid power predictio is also a eed process for Wid farms uit s maiteace Optimal power flow betwee covetioal uits ad wid farms Electricity marketig biddig Power system geerators schedulig Eergy reserves ad storages plaig ad schedulig May factors affect wid power predictio, icludes Forecastig model for wid speed Directio at the farm site Historical data Farm layout 2

3 Problem statemet This paper is presets the methods used for the short term load forecastig rages up to four weeks (oe moth) ahead based o relatig the forecasted value to their correspodig historical value i previous years withi the same time period. A predictio model is developed usig historical data. The developed model is the used to predict the correspodig wid speed ad the results are checked with the actual values. The proposed models are characterized by Very simple Effective for few hours ahead ad day a head predictio Idepedet o collected data from other sites 3

4 Approach used to solve the problem For short term wid speed forecastig five methods are used ad they are Movig average method (MAM) Liear regressio method (LRM) Polyomial regressio method (PRM) Trascedetal regressio method (TRM) Auto-regressive itegrated movig average (ARIMA) Method I experimetatio, forecasted values are obtaied for year 2014 from data s of years ad they are compared with the actual wid speed values of 2014 for checkig the accuracy of the results. Tools used MATLAB Software for Code Buildig ad Graph Aalysis Results achieved Results obtaied are highly accurate. From the aalysis of these results we foud that ARIMA is the most suitable method for short term wid speed forecastig. These results are used for further study to have accurate desigs of wid power istallatios ad to develop wid power plat. 4

5 Abstract I a log-term plaig, power system plaers are usig probabilistic method to access wid power geeratio while short term wid speed forecastig plays a importat role i load maagemet. For short term wid speed forecastig sythesis methods are used. I this paper for modelig ad data aalysis, sythesis methods used are movig average method (MAM), liear regressio method (LRM), polyomial regressio method (PRM), trascedetal regressio method (TRM), auto-regressive itegrated movig average (ARIMA) Method. I experimetatio, forecasted values are obtaied for year 2014 from data s of years ad they are compared with the actual wid speed values of 2014 for checkig the accuracy of results. From aalysis of these results we foud that ARIMA is the most suitable method for short term wid speed forecastig. Keywords Movig Average Method (MAM); Liear Regressio Method (LRM); Polyomial Regressio Method (PRM); Trascedetal Regressio Method (TRM); Auto Regressive Itegrated Movig Average (ARIMA) Method. 5/15/2017 5

6 I this study, data set of years 1995 to 2014 are obtaied cotaiig mea wid speed of each moth i a year with observatio height of 50 m above groud level. The chose statios from Irelad are Locatio Latitude N Logitude W Mali Head Co. Doegal 55 23'N 07 23'W Dubli Airport Co. Dubli 53 21'N 06 15'W Belmullet Co. Mayo 54 14'N 09 58'W Mulligar Co. Westmeath 53 31'N 07 21'W Locatio Table 1 Mea Wid Speed Mali Head Co. Doegal Dubli Airport Co. Dubli 10.6 Belmullet Co. Mayo Mulligar Co. Westmeath Table 2 For aalysis, forecasted values are obtaied from the data spaig from years 1995 to 2013 which is easily available o Irish meteorological website ad they are compared with the actual wid speed values of 2014 for scrutiizig the accuracy of results. 6

7 Figures are showig the relative variatio i wid speed of Dubli Airport, Belmullet ad Mulligar sites with respect to wid speed for locatios Mali Head, respectively for 20 years. Relative Variatio i Wid Speed of Dubli Airport with the Wid Speed of Mali Head Relative Variatio i Wid Speed of Belmullet with the Wid Speed of Mali Head Relative Variatio i Wid Speed of Mulligar with the Wid Speed of Mali Head 7

8 Movig Average Method (MAM) Sometimes, use of old data might o loger be relevat so we are usig this method. This method uses the average of the data to predict ext value called as forecasted value, i.e. we calculate the mea usig oly k latest observatios as F t 1 1 k t Y i itk1 As the ew data becomes available, the oldest observatio is dropped ad the latest icluded. Here forecast is easily updated from period to period. A disadvatage of this method is that it places as much weight o X t(-1) as o X t. Liear Regressio Method (LRM) Here we assume a liear relatioship exist betwee Y ad X. so that Y a bx ei Where a is itercept, b is the slope of the lie ad e is error due to deviatio of the observatio from the liear relatioship. This is the ordiary least-squares estimatio. Where b a (X i - X) (Y i - Y) i1 - X) 2 (Xi i1 Y - bx Let the vertical deviatio (errors) be deoted by ei Yi - Y 8

9 Polyomial Regressio Method (PRM) PRM is most suitable for o-liear data values. The least squares techique ca be readily used to fit the data to a polyomial. Cosider a polyomial of degree m-1 Y a a m-1 1 a 2 X a 3 X 2... X Y f(x) If the data is havig m sets of X ad Y values, the the sum of squares of the errors is give by Q i0 Where f(x) is a polyomial cotaiig coefficiets a 1, a 2, a 3, etc, we have to calculate all the coefficiets. So we have to solve equatios to get these coefficiets Q a1 0 Cosider a geeral term, Q a j Thus, we have Yi - f Q 2 Yi-f k0 Xi 0 2 Q a m a 0 Xi j1 f Xi a j i1 X i Y j1 0 i - f X i X i f Xi a j 0 9

10 Polyomial Regressio Method (PRM) j-1 Yi X i j-1 - X i f Substitutig for f (X i ) 0 X i j1 Xi a1 a2xi... amxim1 i0 j1 YiXi i0 These are equatios (j = 1, 2.m) ad each summatio is for i = 1 to The set of m equatios ca be represeted i matrix otatio as follows Where, The elemet of matrix C is a a 2 X i a 3 X i... a m X i Yi a 2 3 m 1 X i a 2 X i a 3 X i... a m X i Y i X i m1 m m1 a1 Xi a2 Xi a3 Xi m-2 m1 am Xi Yi Xi CA B C j,k X jk-2 i i0 Similarly, B j Yi X j 1 i i 10

11 Trascedetal Regressio Method (TRM) The relatioship betwee the depedet ad idepedet variables is ot always liear. The oliear relatioship betwee data poits ca be represeted i the form of trascedetal equatios (or higher order polyomials). Here oliear model is used for wid speed forecastig which is give as p a X b Where p are the wid speed values for correspodig variable wid speed values (v), we ca the calculate the parameters a ad b. Usig least square method, the sum of the squares of all errors ca be writte as Q p i i0 - a X b i To miimize Q, we have Q a 0 Q b We ca prove that b a Y b pixi i p i X i b l X i a b 2 Y l Xi i This equatios ca be solved for a ad b. But sice b appears uder the summatio sig, a iterative procedure is used for obtaiig a ad b. The equatio usig the covetioal variables X ad Y as Y b a X 11

12 Trascedetal Regressio Method (TRM) Takig logarithm o both the sides, we get l Y l a b l X This equatio is similar i form to the liear equatio ad, therefore, usig the same procedure we ca calculate the parameters a ad b b l Xi l Yi - l Xi l Yi l 2 l 2 Xi Xi l a R a R e 1 l Y i b l Xi Similarly, we ca liearize the expoetial model by takig logarithm o both the sides. This would yield l p l p 0 kt l e Sice, l e 1 We have l p l p 0 kt This is similar to the liear equatio Y a bx Where Y l p a l p0 b = k, X = t We ca easily calculate a ad b ad the p 0 ad k 12

13 Auto Regressive Itegrated Movig Average (ARIMA) Method The forecasted variables are depeds o the past observatios the we ca write the relatioship as Yt b0 b1yt-1 b2yt-2... byt-p et The RHS of eq. cotais time-lagged values of the forecasted variable. Differecig ca remove o-statioary i a series of forecasted values. The first order differece is give by Y 1 t Yt - Yt-1 Results The results preseted i table 3, table 4, table 5 ad table 6 shows the actual value (AV) ad forecasted value of wid speed for differet methods for locatios Mali Head, Dubli Airport, Belmullet ad Mulligar sites respectively. From these tables error i wid speed for each moth was calculated which shows that the error differece is lesser i the values give by ARIMA method as compared to the others. This idicates that, due to the presece of mathematical iteratios i calculatig forecasted values, the accuracy of ARIMA method is better as compared to other methods. Figures are showig the error i wid speed for each moth usig differet methods for locatios Mali Head, Dubli Airport, Belmullet ad Mulligar sites respectively. These figures are showig additive tred with seasoal effect. Time series models are fairly accurate for wid speed forecastig applicatios. These are used for log term forecasts as well as for very short term forecasts. Oe of the disadvatage of these methods for short term forecast is that they are uable to predict accurately the oliear characteristics betwee wid speed ad time duratio. This paper suggests that ARIMA method is most suitable for short term wid speed forecastig as it gives error values, while movig average method (MAM) is the secod best method. 13

14 Error i Wid Speed for Locatio Mali Head with Moths Error i Forecasted Wid Speed for Locatio Dubli Airport with Moths Error i Wid Speed for Locatio Belmullet with Moths Error i Wid Speed for Locatio Mulligar with Moths 14

15 Moth AV MAM SRM PRM TRM ARIMA Ja Feb Mar Apr May Ju Jul Aug Sep Oct Nov Dec Moth AV MAM SRM PRM TRM ARIMA Ja Feb Mar Apr May Ju Jul Aug Sep Oct Nov Dec Table 3 Table 4 Moth AV MAM SRM PRM TRM ARIMA Ja Feb Mar Apr May Ju Jul Aug Sep Oct Nov Dec Moth AV MAM SRM PRM TRM ARIMA Ja Feb Mar Apr May Ju Jul Aug Sep Oct Nov Dec Table 5 Table 6 15

16 Refereces M. A. Matos ad R. J. Bessa, Settig the operatig reserve usig probabilistic wid power forecasts, IEEE Tras. Power Syst., 26 (2),pp , E. Erdem ad J. Shi, ARMA based approaches for forecastig the tuple of wid speed ad directio, Appl. Eergy, vol. 88, o. 4, pp , Apr Corbera-Vallet, A., Bermudez, J. D., ad Vercher, E., Forecastig correlated time series with expoetial smoothig Models. Iteratioal Joural of Forecastig, Vol. 27, pp , R. J. Bessa, V. Mirada, A. Botterud, Z. Zhou ad J. Wag, Time-adaptive quatile copula for wid power probabilistic forecastig, Reew. Eergy, 40 (1), pp , S. G. Jamdade ad P. G. Jamdade, Extreme Value Distributio Model for Aalysis of Wid Speed Data for Four Locatios i Irelad, Iteratioal Joural of Advaced Reewable Eergy Research, 1 (5), pp , A. M. Foley, P.G. Leahy, A. Marvuglia, E. J. McKeogh, Curret Methods ad Advaces i Forecastig of Wid Power Geeratio, Reewable Eergy, 37(1), pp. 1-8, A. Khosravi, S. Nahavadi ad D. Creighto, Predictio itervals for short-term wid farm power geeratio forecasts, IEEE Tras. Sustai. Eergy, 4 (3), pp , S. M. Weekes ad A. S. Tomli, Low-cost wid resource assessmet for small-scale turbie istallatios usig site pre-screeig ad short-term wid measuremets, Reewable Power Geeratio, IET, 8 (4), pp , P. G. Jamdade ad S. G. Jamdade, Evaluatio of wid eergy potetial for four sites i Irelad usig Weibull distributio model, J. Power Techol, 1(95), pp , Balagurusamy, Numerical Methods, Tata McGraw Hill Publicatio,1999. P. G. Jamdade ad S. G. Jamdade, Power System Plaig ad Reliability, TechMax Publicatio, ISBN , Ja