附 录Solar Energy Copyright Elsevier Science DATA SAMPLING SPEED VERSUS ENERGETIC MEASUREMENT ERRORS OF IRRADIATION MONITORING IN PHOTOVOLTAIC Tokyo University of Agriculture and Technology,2-24-16,Nakamachi, Koganei-shi, Tokyo 184, Japan.(Communicated by GERARD WRIXON.)Abstract:To measure solar irradiation and photovoltaic array output energy a measuring accuracy cannot be guaranteed unless the data sampling interval is appropriately selected.From this viewpoint,actual irradiance has been measured by comparatively high speed sampling of l-4s for 44 months and the daily errors of the numerical integral have been estimated for various step sizes.Approximation formulae of the error versus the step size have been statistically obtained as well as their probability density function covering +4c.Finally, a nomograph is presented to decide an appropriate sampling interval.A concluding example shows that the deviating component of the error exceeding +1% can happen once for every 1 month or 6 months if the step size is selected as 105 or 65.5s,in each of which the total error becomes -0.0485k 1% or -0.0336&1% including an average error component according to the data measured at Tsukuba.Copyright 1996 Elsevier Science Ltd. Introduction:In a photovoltaic system the input solar energy has a basic day-and-night cycle and an uncertain, time varying factor caused by meteorological conditions.When a measurement is performed to obtain long-term performance parameters such as irradiation,the amount of generated energy,etc.,the accuracy of the measurement may not be maintained if the sampling speed of data acquisition is decided regardless of the fluctuating rate of solar radiation. Since simplified measurements may have to be adopted in the future with the spread of photovoltaic systems,some instructions must be clearly prepared as a system monitoring standard.The author presents an analysis of this need. For this purpose, actual irradiance profile has been measured by comparatively high speed sampling for 44 months at the Electro- technical Laboratory in Tsukuba Science City(Kurokawa and Mine,1989;Kurokawa,1994).By using these data, the daily errors of numerical integration have been evaluated for various time step sizes.Then,the errors for each step size have been analyzed for a certain term to obtain statistical parameters such as standard deviation 0 and average value.Approximation formulae have been also given to express relationships between these values and step sizes.In addition,the probability density function profile of the errors has been also estimated.Finally,by applying the approximation formulae and the probability density function,a nomograph is presented for determining a maximum allowable step size to assure monitoring precision.Data Acquisition:In order to know the true integral of irradiance profiles,original irradiance data were taken at a comparatively high speed sampling rate for 44 months from September 1986 to April 1990 at Tsukuba Science City.The city is located 60 km north of Tokyo and its climatic conditions seem to be ordinary as far as Japan is concerned.Measuring equipment used is illustrated in Fig.1.Noises,which may be generated in signal conditioners,were also suppressed very carefully by using an isolation amplifier and electronic filter.In addition,a digital averaging technique synchronized with the utility grid frequency was adopted and drastically decreased the noise level.More than 100 data were sampled and averaged for just 40ms,which corresponds to 2 cycles of the frequency.This becomes one sample of raw data for this study.Total data acquisition flow is illustrated in Fig.2.The normal raw data sampling period was 1s but it was made longer,up to 4s,in case of a slower fluctuating speed of the irradiance to reduce data volume.Daily data were stored in a 2HD disk for every day.By applying the trapezoidal rule to the measured irradiance data, typical examples of which are shown in Figs3(a) and 4(a),the integrated value of irradiance,i.e.irradiation, si is given by.The integrating interval is indicated by h.Iteration of eqn(1) gives as daily integral of Si until ti=sunset.The various intervals are denoted as hj for j=l-60.The sampling interval of the original data is ho.The range of hi corresponds to 10s to 2h logarithmically as shown in Table 1.S,and Sj are given as S for h=ho and h=hi,respectively.Then,per cent integration error,ej is defined by.The statistical values obtained for a comparatively short term are apt to show some irregularity in the trends of standard deviations as presented in Fig.6.However, it is observed that the overall results for the whole 44 months gave enough smoothness as shown in Fig.9.Therefore, the 44 month results are to be studied as described below.By using the data in Fig.9,approximation formulae were formed.As shown in Figs 10 and 11,the relationship showing and cs versus hj is determined by.To obtain enough p