A Survey Paper on Solar Irradiance Forecasting Methods

DOI : 10.17577/IJERTV5IS030469

Download Full-Text PDF Cite this Publication

Text Only Version

A Survey Paper on Solar Irradiance Forecasting Methods

Sanjay Kumar Prajapati Kishan Bhushan Sahay

PG Scholar

Electrical Engineering Department

Assistant Professor Electrical Engineering Department

MMMUT, Gorakhpur, India-273010 MMMUT, Gorakhpur, India-273010

Abstract Collaboration of solar energy into electricity system is becoming vital it is due to its continuous growth and usages. Photovoltaic (PV) system demand a trusted forecast data as it produce the fluctuating energy. It is fact that with the use of accurate prediction of solar irradiance this type of collaboration can offer an improved quality of service. This paper describes a depth review of various reliable method of solar irradiance forecasting according to present needs. First of all the study starts with a techniques based on cloud images with the help of statistical method. At last we provide concentration to the proposed solar radiation prediction methods.

Keywords Forecast method, solar radiation, cloud images method and statistical method.

  1. INTRODUCTION

    As the integration of electrical energy from solar radiation is growing continuously. Many utilities, company, and transmission operators are depend on variable inputs of photovoltaic energy sources. It offers a challenges deals with load profile. The variable output energy of PV system demand a trusted forecast information. Global Horizontal irradiance forecasting is the most prominent step in various PV power prediction system. With the use of input data the GHI forecasting approaches can be distributed and it is helpful in determines the prediction range.

    Statistical method depend on installed radiation measurement which is used for least duration from 4minute to 6 hours [2]. For instance time graph model is autoregressive moving average (ARMA) and autoregressive (AR) models. Irradiance forecasting can also be done by using artificial neural network. Analysis of cloud motion vectors from satellite images [3] show best result for the temporal ranges from 30 minutes up to 6 hours. There are various input data used to derive an optimized forecast based on the forecast horizon by the use of combined approaches.

    Solar irradiance forecast was measured by root average square error (RMSE) and average biases error (MBE) which are given as-

    There are various solar radiation predicting system were estimated .Basically categorized in to two groups: analytical model and numerical weather prediction model.

    Analytical methods deals with study of past value which is based on time graph methods, ANN models ancillary based methods, sky images based models, wavelet observation systems.

  2. STATISTICAL SYSTEM

    By using historical data for solar irradiance forecasting it may categorized further as- statistical and learning methods. Multiple Regressive, Exponential Smoothing, Auto Regressive Integrated Moving Average (ARIMA), are the best example of analytical system.

    1. Linear or Time series model

      In time series forecasting model the statistical method is used since several decades. Statistical method decides the relation between predictors, statistical model accepts the variable input and the predicted variable are obtained from the statistical analysis. The use of easy Auto Regressive (AR) model is used to predict directly PV power in comparison with other model.

    2. Persistence Model

      This model identify if the forecast model deliver accurate result than any other reference model. This model is very helpful in implementing to run a complex predicting tool only if it perform the accurate result from any other model. Basically persistence model give its best result in solar and PV predicting system for small duration. Its predicted model consider the global irradiance at time t is predicted value at time t-1.

    3. Process to achieve stable solar radiation time series The quantity of solar intensity over a single plane level to a certain direction of time in particular locality is governed as solar isolation .Solar zenith angle is responsible for its strong features .The impact of earlier solar figure and present environmental intention is favorably treated under statistical model,

      = 1 . (

      )2

    4. ARMA Model

      =1

      1

      ,

      ,

      The Autoregressive Moving Average is generally applicable to auto estimated to time series data. For deciding the future parameter of an accurate time series, this model perform a

      =

      . (, ,)

      =1

      remarkable role .ARMA model depend on two techniques- Autoregressive (AR), and moving average (MA) section. ARMA system has the capability to separate valuable analytical method and introduction of well-known Bon- Jenkins method [17, 15].

    5. ARIMA Model

    Auto- regressive Integrated Moving Average technique Hamilton [18] is helpful in deciding of entire radiation field. ARIMA model approaches in the calculation of non-stable series. Reikard [2] allow a technique in regard to the initial parameter of ARIMA model to forecast the solar radiation .He introduced a theory of comparison of ARIMA model with other prediction method such as ANN at different horizon. According to this theory ARIMA model gave sharp transition in solar irradiance with dur anal cycle which is more accurate than any other methods.

  3. WAVELET NEURAL SYSTEM

    Wavelet transform is a analytical approach, which is used in different application of signal to adjust signal with complicated frequency-time layout. Mallet and al. [2] discussed a structural wavelet network model for predicting hourly solar irradiance

    Fig.1 Flowchart to forecast power output of a PV system.

    In this research for calculating the hidden data problem, various layout have been investigated. The Photovoltaic (PV) data series involved different fluctuation, curves and different types of non-stationary. So this method include different neural network topology with wavelet transform attached in the missing unit. In this discussion three section of decomposition have been involved which are obtained from the actual PV time series signal. As decomposition incudes filtering parameters of Fuzzy ARTMAP network are the value of PV power for the current hour t and previous day. (t-24), PVt , PVt-24. In this section wavelet transform possess only PV data series while

    solar irradiance is passed through the fuzzy art map network. The decomposed PV signal and the solar irradiance data is then insert into fuzzy art map network and employed 60days previous data as input source before the forecast day. Therefore parameter affects the performance of forecasting significantly. Now use of firefly algorithm to optimize the parameter in fuzzy art map network.

  4. ANN AND CLASSICAL TIME ARRANGEMENT MODELS CORRELATION

    An examination of ANN and established time arrangement models has been done in Richard [2] and in Sestos and Cannock [10]. Both studies that the mistake of a straightforward relapse model can be lessened significantly by an element in the scope of 0.6 0.8 when utilizing propelled models. Richard [2] thinks about a relapse an ARIMA and the UCM system, an exchange capacity display, a neural system model and half and half system. In this analysis, the creator utilizes a supervised measurement of the information. Output is demonstrate for the resolutions of 15, 30 and 60 minutes, the ARIMA system perform an accurate output. In Cannock and Sestos [9], a food further ANN is assigned as the most fitting. So examination in Richard [] for a few location with changed weather conditions likewise demonstrates so it is a solid, enhance of the atmospheric conditions on dual conjecture precision and energy in development of the utilization of cutting edge system.

  5. SATELLITE AND CLOUD SYMBOLISM BASED SYSTEM

    1. Cloud symbolism

      Other than the deterministic day by day and yearly examples of irradiance, mists spread and in addition cloud optical profundity have the most grounded in hence on sunlight based intensity at plane level. Mists demonstrate a solid fluctuation in space and time. Subsequently, aim of mists in an assigned time is a fundamental errand of radiation gauging for displaying. To estimate skylines to a few hr., the worldly difference in cloud geometry is unequivocally in hence to cloud movement like a consequence of level shift in weather conditions. Ground- based sky and Satellites pictures, has been utilized to determine country which was anticipating nearby sun based radiation situation. In premise to this strategy depends on the goal of the cloud figure aimed in the earlier installed time stage. High range of their movement prompts a figure of cloud situation and, the outcome, to the neighbourhood radiation circumstance. Ground-based sky and Satellites pictures to the high transient and pertaining to determination of era the possibility for infer the decided data to cloud movement. By handling of ground or satellite pictures, mists could be distinguished and described, to adverted for anticipate GHI moderately precisely for 6 hours ahead of time. The time arrangement models in view of satellite information and sky pictures identify the movement of cloud structures utilizing movement vector area (Lorenz and al. [4]). Radiation to all sky geometry in addition to overcast sky might be inferred utilizing transmitted exchange system (RTM) (see Heinemann and al. [3]) needs info on the y-axis figure of cloud tangible input source, for instance, ice water and cloud substance are bead range. Analytical climate expectation (NWP) method suggest input source of transmitted exchange counts. As blunders information from and sky pictures based figures

      sustained for writing increment definitely under minimum solar heights, maximum spherical variability also minimum radiation situation. Sledge and al. [19] exhibited accomplished 18% RMSE in satellite symbolism for 32 minutes cloud record figures and 32% RMSE for 2 hr. estimate skylines. For intra- day estimates, a decrease in RMSE by 7 10% contrasted with diligence conjectures was found. Chow and al [19] displayed a procedure for intra-hour, sub-kilometre cloud images now casting and estimating utilizing a ground-based sky pictures for chose days at the UC San Diego. This procedure permits one to get sky spread, cloud movement, cloud image, radiation, and also cloud figure areas.

    2. Satellite Images

      A way to deal with figure sun oriented irradiance taking into account metaset satellite pictures like premise to Photovoltaic power estimate was sustained in Lorenz and al. [4]. Both examined for contrasted different strategies with get movement vector fields from metaset information, and connected them to estimate sun based intensity to a few next hours. In Perez and al. [3], the later effects of radiation figures taking into account the pictures from Geostationary Operational Environmental Satellite (GOES) with a comparative methodology designed further Lorenz and al. [4] are appeared.

    3. Ground-dependent sky pictures

    In accomplishment of maximum fleeting and spherical determination for next-hour estimates, satellite and NWP figures are presently deficient. Earth perceptions utilizing an aggregate sky pictures (TSI) available a chance in all these anticipating service and convey a sub-kilometre perspective of cloud pictures over a huge range of photovoltaic power plant in an urban circulation utility. Contrasted and satellite information, of earth based sky pictures of era a maximum spherical and worldly determination, in addition to the likelihood of catching immediate fluctuations in the radiation, regularly allowed like a slopes, at a fleeting size under 1 minute. The most extreme conceivable gauge skyline firmly relies on upon the cloud speed and is restricted when the observed cloud picture was entered in the area or range of hobby. So the time is dictated through the spherical expansion to the observed cloud pictures in blend together cloud speeds. In Chow and al [16], figures up to 4 minutes further was assessed for 5 incompletely overcast days. In measurement of a most extreme conceivable augmentation of the gauge skyline in reliance on the cloud scene brought about qualities running from 5 to 25 minutes. Just short deterministic figure skylines are doable utilizing a solitary TSI to a location because of minimum mists to maximum mists variability to the new spherical range considered. Catching this components decided from past is about outlandish with satellite or NWP struggle (Chow and al [16]).

  6. ANALYTICAL CLIMATE PREDICTION SYSTEM

    Numerical Weather Prediction (NWP) system is a process which is helpful in estimating the condition of air to 15 further days. For worldly improvement in the condition of environment is displayed through essential different mathematical statements that depict the physical laws administering the climate. Beginning at starting situation which are gotten for

    overall calculation, firstly, the further condition of the climate was computed to a worldwide NWP system. Worldwide NWP system is right now in process at around 20 climate administrations. Cases determined by the Global Forecast System (GFS) keep running through the European Centre for Medium-Range Weather Forecasts (ECMWF) and US National Oceanic and Atmospheric Administration (NOAA). Worldwide method typically has a test determination i.e. don't take into account an itemized mapping of little scale highlights, in spite of the fact that determination has expanded quickly amid the most recent couple of years and these days, contingent upon the system, for the scope of 1650 km. In this earlier case, various ideas might be connected in representing nearby response for determine enhanced site-selected gauges. First probability is the low measurement through Mesoscale system that are additionally allowed like territorial system. Mesoscale system catch just a portion of Earth however could be worked through a higher spherical determination. These are regularly keep running through national climate administrations and self- climate organizations. Additionally, post processing techniques, might be connected to display domestic response. They permit adjustment to efficient curve in reliance on various atmospheric phenomena. To display the radiation on the off chance that is not gave like yield source of a NWP system. So following couple of sub-division they will survey NWP description, information highlight, worldwide model illustration, meso- scale model case, NWP precision, NWP restriction and post processing techniques.

    1. Temporal determination

      The inward time range provide the duration at which the change in variables environment is portrayed by the non-static mathematical statements. Fleeting determination of inner counts in NWP models for the most part is significantly more to that of different yield. Different yields are conveyed for a determination of normally 1 hour with territorial system and up to 36 hours for worldwide system. The inward time range might be recess to 30 seconds in profoundly determined computations to mesoscale system and this is around 10 minutes for worldwide NWP method.

    2. Spatial determination

      The even determination decides the spatial degree of climate marvels that can be specifically reproduced. Matrix focuses are normally disseminated just as in the level reach. The determination of worldwide NWP models these days is in the scope of 1650 km. In mesoscale models, the even determination might be down to 1 km; climate benefits regularly work mesoscale system to a spherical determination for the scope of 520 km. The determination of y-axis plane is for the most part adjusted to the event of physical procedures that happen in specific districts of the climate. The event of physical procedures that happen in specific districts of the climate.

    3. Input information highlights

    To begin a figure, data on the present condition of the air is required. To worldwide NWP system, the data is acquired with an overall system of climatic perceptions and estimations. The different basic input required are the 3-dimensional area of air, thermal intensity, and dampness also the 2-dimensional area of ground weight. Limit different inputs as ice spread and ocean

    level heat is likewise of maximum significance. Local system in starting situation and in addition sidelong limit conditions from worldwide NWP model yield, furthermore over the likelihood of incorporating neighbourhood estimations.

  7. NUMERICAL WEATHER PREDICTION MODEL PRECISION

    Gauges past 6 hours, up to a few days ahead, are the most precise if got for NWP system. NWP system anticipate Global Horizontal Irradiance utilizing vertical (1D) illuminated exchange system (IES) (see Heinemann and al., [6]). Heinemann and al. [6] demonstrated that MM5 mesoscale system may forecast GHI in open sky without inclination. In any case, the predisposition was exceptionally subject to cloud conditions and gets to be solid in cloudy conditions. Perez and al. [13] analysed the exactness of the National Forecast Database (NFD), a subordinate of the operational NWP system distributed through the NCEP. Later a neighbourhood amendment capacity were connected, demonstrate that for 826 h gauge skylines, the NDFD had an hourly-normal GHI relative RMSE (rRMSE) of 38%. Remand and al. [14] assessed various NWP-based GHI gauges in USA, submitting rRMSE values going from 20% to 40% for a 24 h estimate skyline. Comparative results were accounted for by Perez and al. [4], assessing NWP-based irradiance estimates in a few spots in the USA. Remand and al. [14] analysed NWP inclinations contrasted with a solitary site and that ECMWF and GFS following day GHI gauges have a Mean Absolute Error or Mean Bias Error (MBE) of 20%. So MAE was observed to be roughly steady for intra-day (hour-ahead) to 3-4 days ahead gauge skylines. Lorenz and al. [16] assessed a few NWP-based GHI conjectures in Europe.

    A. NWP Limitations

    A restriction of NWP anticipating is its coarse determination. Indeed, even the 0.1°x 0.1°NAM spherical determination is insufficient to determine generally mists. Just a normal overcast spread may be determined to a decided value. According to worldwide system (ECMWF and GFS) the determination was much larger. Notwithstanding, regardless to the possibility that the spherical determination was near, the fleeting yield interims will not allow for evaluation of time based mark overcast spread differently, imperative for foreseeing slope counts and scopes of differently for sun oriented force trees. In spite of the fact that NWP system time-range are on the request of minutes, the RTM is run less oftentimes, for the yield is just hourly (NAM) or each 3hr. (ECMWF and GFS). Hence, any examples with trademark time scales not exactly an hour are uncertain. Connecting observed fleeting variability in GHI to local NWP figures will needs further analysis.

  8. SYSTEM OUTPUT STATISTIC (SOS)

    SOS relates watched climate components for fitting different indicators by means of a measurable methodology. These indicators might be NWP model conjecture, earlier perceptions, or geo-climatic information. A cutting edge MOS for sun oriented irradiance expectations in view of ECMWF conjectures has been presented in Benger and Heister [4]. Different regression is connected to alter long haul month to month mean estimations of the gauge information. Direct

    model yield of ECMWF and measurably inferred indicators are utilized to make day by day sun based power expectations exact to 24% rRMSE for found the middle value of every day figures. The SOS is worked to the premise of earth-calculated radiation points as accessible. In areas where no radiation estimations, radiation got to meet information from the Heliostat technique was utilized. A correlation to radiation gauges utilizing the SOS plan by WRF fore-throws and different methodologies is illustrated in Heinemann and al. [5] . Lorenz and al. [13] related determined sun oriented apex edge (SZA) and clear sky list to ECMWF MAE for Germany, uncovering a steady over- expectation (up to 100 W.m2) for reasonably shady weather. Utilizing a SOS adjustment capacity killed predisposition and decreased RMSE of short (hour) figures by 6% for 1 day gauges. The staircase dynamic fourth-arrange relapse is connected to infer the SOS rectification capacity. In Mathieson and Kleist

    [19] the investigation and MOS rectification of GHI fore- throws from GFS, NAM and ECMWF system inside of the mainland. They demonstrated that SOS uses to the NWP radiation yield is fruitful in reducing inclination also decreasing RMSE, however wasnt give data for predisposition inputs. SOS remedies for deliberate clear clouds administration wasnt lessen RMSE. So on account of the SOS couldn't recognize RTM mistakes (over-forecast of GHI notwithstanding for clear clouds, especially for NAM) and cloud figure blunders (wrong parameterization of RTM inputs). Thus, numerous at first exact figures were pointlessly corrected. Differentiating between the wellsprings to the blunder is critical to pointy remedy conjectures. Albeit customarily SOS plans are generally in view of direct relapse, any factual methodology relating watched different to NWP yield for the idea of SOS. Specifically, ANN was additionally utilized to enhance NWP output for irradiance forecast (Cao and Lin [9], Guarneri and al.[11]). In Guarneri and al. [11], ANN is connected to radiance figures of the NCEP Eta system process at the Brazilian Centre for Climate Forecasts and Atmosphere analysis. In assessment through estimations of two zone in the south of Brazil uncovers a solid excess estimation of the radiation with the first figures, to a significant change is accomplished through the utilization of ANN utilizing various air gauge input of the Eta system.

  9. HYBRID MODELS

    Hybrid system was acquainted with beat the lack of utilizing as a part of single system, for example, measurable strategies (ARIMA, Multiple Regression and so forth.) and AI techniques. Mixture models combine different techniques to enhance the forecast exactness. Cross breed methods may be additionally allowed like joined system or group system which is regularly utilized equally. Crossover system may be actualized through various ways; straight system, unbalanced system and both direct and unbalanced system. Through the goal to enhance estimating precision, the mix of determining methodologies was announced through numerous specialists ([20], [11], [2], [16], [2]). From their studies, they show that the coordinated determining methods beat the individual figures. Artificial knowledge systems, for example, fluffy rationale and neural systems, have been utilized for evaluating hourly worldwide sunlight based irradiance from satellite images. The outcomes appear to call attention to that fluffy rationale and neural system models are superior to anything relapse models. Cao and Cao

    in [20] and [11] added to a cross breed model for estimating sequences of aggregate every day sunlight based radiation, thats joins ANN to wavelet. Lin and Cao [14] utilize ANN through an uncommon outlined preparing calculation) consolidated with wavelets (in view of askew intermittent wavelet neural system (DRWNN))

    To anticipate following day hourly estimations for worldwide radiation. Various sorts of aerial perceptions are utilized as data to the system; among others the everyday mean worldwide radiation and day by day mean overcast front of the day are estimated. For further day and next hou gauge skyline time arrangement system were utilized. The vast amount of information (GHI) calculated on the earth errors an extensive arrangement of worldly arrangement of radiation. At that time arrangement will allow to build a measurable estimating system. According to this estimate skyline, the ARIMA system appear as the most dependable system. So it may can provide an estimate in a small amount of a next to PC. In any case, for a skyline of estimate of a couple of minutes, the ingenuity model accomplishes preferred exactness over ARIMA system. According to this the decision of the system tends basically not too far off of estimate. At longer skylines, the information are commanded by the diurnal cycle. For this situation ARIMA models work better. At higher recurrence, the information is more commanded by fleeting examples which can be gotten by ingenuity or ANN.

    will be joined to sky pictures to yield an exhaustive and more exact estimate item with different skylines of conjecture. The objective is to deal with the necessities of matrix administrators.

  10. CONCLUSION

Sunlight based irradiance anticipating is essential for the joining of photovoltaic plants into an electrical framework. Legitimate sun based irradiance anticipating helps the matrix administrators to advance their power generation and/or to decrease extra expenses by setting up a suitable methodology. Various time arrangement system and analytical climate forecast (NWP) system was inspected in above discussion. With the portrayal to the different consequences of sunlight based radiation anticipating, that keep up the decision in the selected estimating system relies upon gauge skyline to the accessible information. From figure skyline for 5 hours up to 2 days ECMWF connected to a SOS next operation demonstrates the suitable exact output. In any condition, on account of Reunion Island, the WRF system is by all accounts more germane. For a littler conjecture horizons, from 5 minutes to 4 hours ARIMA appears to display the best precision. Cloud symbolism and a cross breed model can enhance the aftereffects of anticipating when sunlight based irradiance introduces a solid variability like in a large portion of separate domains. It is important that Kostylev and Pavlov ski [1] have done broad but centricities of the exact operating system on during time range. So expressed earlier, various system are suitable at various gauge skylines. It provide the assessments of the exact RMSE parameter for each generally overcast times and the most part solved. The qualities measured from around 18% at 60 minutes, to 24% for 3 days. As the most part overcast, they run around 30% to 42% excess to the gauge scope of initial to 3 days. Sustainable task will incorporate a few components to enhance estimate precision. Sky picture procedures will be utilized to represent the procedure of cloud development. The fascinating strategies identified here (WRF, ARIMA and AR)

REFERENCES

  1. T. Hammons, Integrating renewable energy sources into European grids, in Universities Power Engineering Conference. Proceedings of the 41st International, vol. 1, Sept. 2006, pp. 142 151

  2. T. Boehme, G. Harrison, and A. Wallace, Assessment of distribution Network limits for non-firm connection of renewable generation, Renewable Power Generation, IET, vol. 4, no. 1, pp. 64 74, Jan. 2010.

  3. A. Anvari Moghaddam and A. Seifi, Study of forecasting renewable energies in smart grids using linear predictive filters and neural networks, Renewable Power Generation, IET, vol. 5, no. 6, pp. 470 480, Nov.2011

  4. G. Capizzi, C. Napoli, and F. Bonanno, Innovative second- generation wavelets construction with recurrent neural networks for solar radiation forecasting, Neural Networks and Learning Systems, IEEE Transactions on, vol. 23, no. 11, pp. 1805 1815, Nov. 2012.

  5. W. Yan, Toward automatic time-series forecasting using neural networks, Neural Networks and Learning Systems, IEEE Transactions on, vol. 23, no. 7, pp. 1028 1039, July 2012.

  6. M. Qi and G. Zhang, Trend time-series modelling and forecasting with neural networks, Neural Networks, IEEE Transactions on, vol. 19, no. 5, pp. 808 816, May 2008.

  7. S. Yilmaz and Y. Oysal, Fuzzy wavelet neural network models for Prediction and identification of dynamical systems, Neural Networks, IEEE Transactions on, vol. 21, no. 10, pp. 1599 1609, Oct. 2010.

  8. A. Haque, P. Mandal, J. Meng, M. Kaye, and L. Chang, A new strategy For wind speed forecasting using hybrid intelligent models, in Electrical and Computer Engineering (CCECE), 2012 25th Canadian Conference on, Apr.-May 2012.

  9. S. Al-Alawi and H. Al-Hinai, An ANN-based approach for predicting Global radiation in locations with no direct measurement instrumentation, Renewable Energy, vol. 14, no. 14, pp. 199 204, 1998.

  10. S.N. Kaplanis. New methodologies to estimate the hourly global solar radiation; comparisons with existing models. Renewable Energy, 31(6):781 – 790, 2006.

  11. J. Boland. Time series analysis of climatic variables. Solar Energy, 55(5):377 – 388, 1995.

  12. J. Boland. Time series and statistical modelling of solar radiation. In Recent Advances in Solar Radiation Modelling, pages 283{312. Springer-Verlag, 2008.

  13. Wu Ji and Keong Chan Chee. Prediction of hourly solar radiation using a novel hybrid model of arma and tdnn. Solar Energy, 85(5):808 – 817, 2011.

  14. George Box and Gwilym Jenkins. Time series analysis: Forecasting and control. Holden-Day, San Francisco, 1970.

  15. Jing Huang, Malgorzata Korolkiewicz, Manju Agrawal, and John Bolandl. Forecasting solar radiation on an hourly time scale using a coupled autoregressive and dynamical system (cards) model. Solar Energy, (in press), 2013.

  16. [16] K. Yap, C.P. Lim, I.Z. Abidin, A Hybrid ART-GRNN online learning neural network with a insensitive loss function, IEEE Trans. Neural Netw., vol. 19, no. 9, pp. 1641-1646, 2008.

  17. [17] P. L. Mao and R. K. Aggarwal, A novel approach to the classification of the transient phenomena in power transformers using combined wavelet transform and neural network, IEEE Trans. Power Delivery, vol. 16, no. 4, pp. 654-660, 2001.

  18. [18] Z. A. Bashir and M. E. El-Hawary, Applying wavelets to short-term load forecasting using PSO-based neural networks, IEEE Trans. Neural Netw., vol. 24, no. 1, pp. 20-27, 2009.

  19. [19] J. O. Chapa and R. M. Rao, Algorithms for designing wavelets to match a specified signal, IEEE Trans. Digital Object Identifier, vol. 48, no. 12, pp. 3395-3406, 2000.

  20. [20] Y. Bi, J. Zhao, and D. Zhang, Power load forecasting algorithm base on wavelet packet analysis, in Proc. IEEE Int. Conf. Power System Technology, pp. 987990, 2004

Leave a Reply