energies

Article Solar Radiation Estimation Algorithm and Field Verification in

Ping-Huan Kuo 1 ID , Hsin-Chuan Chen 2 and Chiou-Jye Huang 3,* ID

1 Computer and Intelligent Robot Program for Bachelor Degree, National Pingtung University, Pingtung 90004, Taiwan; [email protected] 2 School of Computer Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China; [email protected] 3 School of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou 341000, China * Correspondence: [email protected]

 Received: 5 May 2018; Accepted: 22 May 2018; Published: 29 May 2018 

Abstract: The power generation potential of a solar photovoltaic (PV) power generation system is closely related to the on-site solar radiation, and sunshine conditions are an important reference index for evaluating the installation of a solar PV system. Meanwhile, the long-term operation and maintenance of a PV system needs solar radiation information as a reference for system performance evaluation. Obtaining solar radiation information through the installation of irradiation monitoring stations is often very costly, and the cost of sustaining the reliability of the monitoring system, Internet stability and subsequent operation and maintenance can often be alarming. Therefore, the establishment of a solar radiation estimation model can reduce the installation of monitoring stations and decrease the cost of obtaining solar radiation information. In this study, we use an inverse distance weighting algorithm to establish the solar radiation estimation model. The model was built by obtaining information from 20 solar radiation monitoring stations in central and southern Taiwan, and field verification was implemented at Yuan Chang town hall and the Liujia campus. Furthermore, a full comparison between Inverse Distance Weighting (IDW) and the Kriging method is also given in this paper. The estimation results demonstrate the performance of the IDW method. In the experiment, the performance of the IDW method is better than the Ordinary Kriging (OK) method. The Mean Absolute Percentage Error (MAPE) values of the solar radiation estimation model by IDW at the two field verifications were 4.30% and 3.71%, respectively.

Keywords: solar PV system; solar radiation; inverse distance weighting algorithm

1. Introduction As global warming is worsening and human dependence on energy is on the rise, global growth in solar PV system development is accelerating. From global installed capacity statistics, solar energy installation capacity reached 79.4 GW in 2016, compared to 55.4 GW installed capacity in 2015; the annual growth rate is 43%, exceeding 30% annual growth for the second consecutive year. This figure is much higher than the original forecast, with the main difference coming from China’s installation volume of 34 GW, which is significantly higher than expected [1,2]. Moreover, in recent years there have been many studies on photovoltaic power generation. Jurasz and Ciapała proposed a new method of smoothing the energy exchange with the grid based on fixed volumes of energy [3]. In addition, such a method can also be applied to deal with the problem of larger-scale hydropower plants. The literature [4] indicates that a combination of the cost–benefit calculation and the nesting model can be used to optimize the PV plant size. Furthermore, it can be integrated into other renewable

Energies 2018, 11, 1374; doi:10.3390/en11061374 www.mdpi.com/journal/energies Energies 2018, 11, 1374 2 of 12 energy sources to improve performance. As increasingly high amounts of solar PV power are connected to the grid, solar power output volatility and randomness are presenting greater challenges for the stability and economical operation of the central power system. Solar radiation is the main factor affecting solar PV output; by measuring solar radiation we could more accurately calculate energy output from centralized and distributed solar PV systems. The most direct way to detect solar radiation is to set up solar radiation monitoring stations; however, this is costly and requires huge manpower, so the density of solar radiation monitoring stations is often insufficient. With government promotion of solar PV systems in recent years, there is increasing public demand to understand and acquire solar radiation and insolation values in areas without monitoring stations, and various statistical methods and interpolation and extrapolation algorithms have emerged. The following is a literature review of the common calculation methods. IDW [5–11] interpolation applies a linear combination of weights to a set of sample points to determine the estimate. Weighting is an inverse distance function, so inverse distance weighting is the simplest interpolation method. Kriging [12] is an interpolation method similar to inverse distance weighting; it is based on a simplified minimum self-forming algorithm, and uses a variogram as a weight function. The method is named after South African mining geologist D. G. Krige, who developed the fundamental version of this method. At present, there are many variations on the Kriging method for general use, including simple kriging, ordinary kriging, universal kriging, local kriging, co-kriging, and disjunctive kriging. The kriging tool could determine the output value of each position by fitting mathematical functions to a certain number of points or to all points within a specified radius. The kriging method is a multi-step calculation process; it includes exploratory statistical analysis of data, variogram modeling, and creating surfaces. When there are spatial distances or directional deviations in data, the kriging method is often considered the most suitable method. The most commonly used algorithm [13–15], Ordinary Kriging, is used for solar radiation estimation in this study; regression function and geographic parameters (latitude, longitude, and altitude) are also used to determine the correlation between solar radiation and measured climate variables and geographic indicators. Behrang and Rumbayan [16,17] proposed using latitude, longitude, altitude, monthly mean temperature, average sunshine hours, and relative humidity as independent variables to develop an Artificial Neural Network (ANN) model to estimate solar radiation. Mohamed [18] proposed the Particle Swarm Optimization algorithm to train a Neural Network (PSO-NN) to develop a solar radiation estimation model. The input information used include month, sunshine hours, latitude, longitude, and altitude. Cambodian scholar Janjai [19] proposed using satellite cloud imagery to estimate the Monthly Average Daily Solar Radiation (MADSR) model, whose Root-Mean-Square Deviation (RMSD) is 6.3%. Chinese scholar Wu [20] uses the Support Vector Machines method to estimate MADSR, using highest temperature, lowest temperature, and average temperature as independent variables. The Root-Mean-Square Error (RMSE) value and Nash–Sutcliffe coefficient of this model are 1.637 MJm-2 and 0.813 MJm-2, respectively. In general, the ANN algorithm has most often used in previous studies, as this method has a high predictive accuracy, but its estimation process is a “black box,” making it difficult to interpret the predictions. Therefore, the inverse distance weight algorithm is applied in this paper to estimate solar radiation through a simple distance concept. The major contributions of this paper are as follows: (1) a high-precision inverse distance weighting algorithm is designed to solve the problem of solar radiation estimation; (2) the field test of the IDW algorithm in solar radiation estimation is demonstrated; (3) comparisons with other solar radiation estimation methods are provided; (4) the advantages and the performance analysis of the proposed verification method are also discussed. The remainder of the paper is organized as follows. The horizontal solar radiation monitoring sites are introduced in Section2. In Section3, the algorithm of the inverse distance weighting is described. The experimental results are presented in Section4. The discussion are mentioned in Section5. Finally, the conclusions are given in Section6. Energies 2018, 11, 1374 3 of 12

Energies 2018, 11, x FOR PEER REVIEW 3 of 12 2. Horizontal Solar Radiation Monitoring Sites Taiwan2. Horizontal is about Solar 395 Radiation km in lengthMonitoring from Sites north to south, and about 144 km in width from east to west. TheTaiwan geographical is about 39 scope5 km ofin thislength experiment from north isto insou centralth, and andabout southern 144 km in Taiwan, width from the east maximum to distancewest. between The geographical monitoring scope stations of this from experiment north to is south in central is about and 212southern km, andTaiwan, the maximumthe maximum distance betweendistance monitoring between stations monitoring from stations east to from west northis about to 66south km. is The about monitoring 212 km, and stations the maximum selected are in centraldistance and southern between monitoringTaiwan, and stations the Solmetric from eastSun to west Eye is is about used to66 evaluate km. The monitoring shading to stations ensure that selected are in central and southern Taiwan, and the Solmetric Sun Eye is used to evaluate shading the solar gauges installed at the monitoring stations would not be affected by shade from external to ensure that the solar gauges installed at the monitoring stations would not be affected by shade environment factors such as buildings or trees. On-site survey and installation of horizontal solar from external environment factors such as buildings or trees. On-site survey and installation of radiationhorizontal monitoring solar radiation stations monitoring are done in stations 22 sites. are The done locations in 22 sites. of the The monitoring locations of stations the monitoring are displayed in Figurestations1. are displayed in Figure 1.

Dajia Office Office

Shan Yang Elementary School City Love Home Township First-Class Community Fang Yuan Elementary School Puli Township Administration Chung Hsing Junior High School Shijou Township Administration

Mailiau Township Administration TransWorld University

Yuanchang Township Office Wun-Guang Elementary School Hu-Kou Branch Chih-Hang Elementary School

Budai Township Office

Tainan Liujia Campus

Jiading District Office

PingPei Senior High School.

Dashu District Office National Science and Technology Museum Junior High School

DungLung Elementary School

FigureFigure 1. Global 1. Global horizontal horizontal irradiation irradiation monitoring station station installed installed locations locations map. map.

The computer monitoring system collects solar radiation intensity data through an A/D signal Theconverter computer (I-7188XA monitoring, ICP DAS system, collects, Taiwan solar) by radiation a solar radi intensityometer complying data through with an ISO A/D 9060 signal converterClass (I-7188XA, 2 certifications. ICP At DAS, least Hsinchu, one datum Taiwan) is recorded by a solar every radiometer minute and complying stored in the with Internet ISO 9060

Class 2 certifications. At least one datum is recorded every minute and stored in the Internet gateway storage media. Data are transmitted through File Transfer Protocol (FTP) from the data Energies 2018, 11, x FOR PEER REVIEW 4 of 12 Energies 20182018,, 11,, x 1374 FOR PEER REVIEW 44 of of 12 12 gateway storage media. Data are transmitted through File Transfer Protocol (FTP) from the data gateway storage media. Data are transmitted through File Transfer Protocol (FTP) from the data gatewaygateway to to the the backend backend network network serv serverer through through an an I Internetnternet connection connection.. The The data data are are supplemented supplemented gateway to the backend network server through an Internet connection. The data are supplemented throughthrough data synchronization synchronization and and inspection inspection function, function, and and subsequently subsequently processed processed through through the solar the through data synchronization and inspection function, and subsequently processed through the solarradiation radiation estimation estimation model. model. Among Among the the various various monitoring monitoring stations, stations, those those thatthat dodo not have have an an solar radiation estimation model. Among the various monitoring stations, those that do not have an IInternetnternet connection resolve resolve the the data data transmission transmission issue issue through through a 3G a network. 3G network. The monitoring The monitoring system Internet connection resolve the data transmission issue through a 3G network. The monitoring systemarchitecture architecture is detailed is detailed in Figure in2 Figure. 2. system architecture is detailed in Figure 2. Front-end Front-end monitoring equipment monitoring equipment Web server Web server Internet gateway Internet gateway Receiving Receiving TXT file software TXT file File Transfer Protocol software File Transfer Protocol A/D signal A/D signal converter Solar radiation estimation converter Solar radiation estimation Data synchronization check model and algorithm Data synchronization check model and algorithm ISO 9060 Class 2 ISO 9060 Class 2 solar radiometer solar radiometer

Figure 2. Horizontal solar radiation monitoring system architecture. FigureFigure 2. 2. HorizontalHorizontal solar solar radiation radiation monitoring monitoring system system architecture. The 22 horizontal solar radiation monitoring systems collect local horizontal solar radiation The 22 horizontal solar radiation monitoring systems collect local horizontal solar radiation information and establish a solar radiation data bank. The longitude and latitude information of the informationinformation and and establish establish a a solar solar radiation radiation data data bank. bank. The The longitude longitude and and latitude latitude information information of of the the monitoring systems is detailed in Table A1. monitoringmonitoring systems is detailed in Table A1A1.. Some installed monitoring stations are shown in Figures 3 and 4. The red circle in the picture on Some installed monitoring stations are s shownhown in Figure Figuress 33 andand4 4.. The The red red circle circle in in the the picture picture on on the left indicates the installed location of the solar radiometer; the red circle in the picture on the thethe left indicatesindicates thethe installed installed location location of of the the solar solar radiometer; radiometer the; the red red circle circle in the in picturethe picture on the on right the right indicates the monitoring system box, which includes an Internet gateway and an A/D signal rightindicates indicate the monitorings the monitoring system system box, which box, includeswhich includes an Internet an gatewayInternet gateway and an A/D and signal an A/D converter. signal converter. The longitude and latitude information of the 22 monitoring systems is detailed in Table A1. converter.The longitude The andlongitude latitude and information latitude information of the 22 of monitoring the 22 monitoring systems systems is detailed is detailed in Table in A1 Table. A1.

Figure 3. Tainan Liujia Campus monitoring equipment installation location. FigureFigure 3. 3. TainanTainan Liujia Liujia Campus Campus monitoring equipment installation location location..

Energies 2018, 11, x FOR PEER REVIEW 5 of 12

Energies 2018, 11, 1374 5 of 12 Energies 2018, 11, x FOR PEER REVIEW 5 of 12

Figure 4. Wuwang Elementary School monitoring system location. FigureFigure 4. Wuwang4. Wuwang Elementary Elementary SchoolSchool monitoring monitoring system system location location.. 3. Inverse Distance Weighting Algorithm 3. Inverse Distance Weighting Algorithm 3. Inverse Distance Weighting Algorithm The studyThe study uses uses horizontal horizontal solar solar radiation radiation datadata from monitoringmonitoring stations stations 1– 20,1– 20,and and applies applies the the inverseTheinverse distance study distance uses weighting horizontal weighting algorithm solar algorithm radiation to to establish establish data from aa zonalzonal monitoring solar solar radiation stations radiation estimation 1–20, estimation and appliesmodel. model. the inverseMeanwhile,Meanwhile, distance the weightingstudythe study uses uses algorithm sola solar radiationr radiation to establish data data afromfrom zonal stationstation solarsradiation s21 21 and and 22 estimation22to toverify verify the model. theresult results Meanwhile, of thes of the theestimation studyestimation uses model. solarmodel. The radiation The inverse inverse data distance distance from stationsweighting weighting 21 andalgorithm 22 to verifyis is shown shown the in results inEquation Equation of the(1): (1) estimation: model. The inverse distance weighting algorithm is shownss1 in Equation s s 1 1 (1): SI0  SIi k/ k , (1) SI0   SIi k/   k , (1) i1s d1i i s 1 d d1 i SI =i1SI i i  1 i 0 ∑ i k /∑ k , (1) where SI0 is the estimate value of Point 0, SIii =is1 the valuedi i= of1 dknowni Point i, di is the distance between where SI0 is the estimate value of Point 0, SIi is the value of known Point i, di is the distance between Point i and Point 0, s is the known point used for estimation, and k is the self-determined weight Point i and Point 0, s is the known point used for estimation, and k is the self-determined weight wherevalue.SI0 is the estimate value of Point 0, SIi is the value of known Point i, di is the distance between Pointvalue.i andThe Point solar 0, radiations is the known values collected point used at the for 22 estimation, horizontal and solark isradiation the self-determined monitoring stations weight are value. Thedisplayed solar inradiation radiation Table A2, values valuesand the collected collectedchart of peak at at the sum the 22 22hours horizontal horizontal at 22 monitoring solar solar radiation radiationstations monito is shown monitoringring in Figure stations stations 5. are aredisplayed displayedSolar energyin Table in is Table A2,generally andA2, the calculated and chart the of chartbased peak ofon sum peaka unit hours sumof 1000 at hours 22 W/m monitoring2 at and 22 converted monitoring stations to isequivalent stationsshown in daily is Figure shown 5. inSolar Figure Peakenergy5 Sum. Solar is Hours generally energy (PHS). calculated is This generally represen based calculatedts the on total a unit number based of 1000 on of effective aW/m unit2 ofand hours 1000 converted per W/m unit in 2to andwhich equivalent converted the sun daily to equivalentPeak releasesSum Hours daily energy. Peak (PHS). PSH Sum Thisis defined Hours represen (PHS).as follows:ts the This totalsolar represents numberradiation the of(PSH)total effective = number daily hours accumulated of effectiveper unit radiation hoursin which per/1000 the unit sun in (W/m2). whichreleases the energy. sun releases PSH is energy.defined PSH as follows: is defined solar as radiation follows: solar(PSH) radiation = daily accumulated (PSH) = daily radiation accumulated/1000 radiation/1000(W/m2). (W/m2). Peak Sum Hours Peak Sum Hours Hours Hours

11/1 11/2 11/3 11/4 11/5 11/6 11/7 Figure 5. The chart of peak sum hours at 22 monitoring stations.

11/1 11/2 11/3 11/4 11/5 11/6 11/7 Figure 5. The chart of peak sum hours at 22 monitoringmonitoring stations.

Energies 2018, 11, x FOR PEER REVIEW 6 of 12 Energies 2018, 11, 1374 6 of 12 4. Verification Results

4. VerificationThe Mean Results Absolute Percentage Error (MAPE) is often used as an indicator of estimation error and is defined as follows: The Mean Absolute Percentage Error (MAPE) is often used as an indicator of estimation error and N is defined as follows: 1 yynn ˆ MAPE= N (2) 1  yn − yˆn, Ny MAPE = ∑n 1 n , (2) N n=1 yn where yn is the actual value, yˆ represents the estimated value, N is the number of estimations where yn is the actual value, yˆn representsn the estimated value, N is the number of estimations within thewithin evaluation the evaluation period. period. This paper This paper selected selected two monitoringtwo monitoring stations stations to verify to verify the accuracythe accuracy of the of estimationthe estimation results results and and used used the the inverse inverse distance distance weighting weighting algorithm algorithm to to establish establish thethe zonalzonal solar radiationradiation estimationestimation model.model. The paper compares and verifiesverifies the actual irradiation value against thethe estimatedestimated value at Yuan ChangChang TownshipTownship AdministrationAdministration andand thethe TainanTainan LiujiaLiujia Campus.Campus. Figure6 6 representsrepresents the the comparison comparison results results in Yuan in Yuan Chang Chang Township Township Administration Administration and Tainan and Liujia Tainan Campus Liujia byCampus IDW andby IDW OK method.and OK Themethod. comparison The comparison results show results that show the performance that the performance is better thanis better with than the Krigingwith the method. Kriging Table method.1 shows Table the 1 verification shows the results verification for Yuan results Chang for Township Yuan Chang Administration; Township withAdministration; respect to the with IDW respect method, to the we IDW find thatmethod, during wethe find verification that during period the verification the maximum period MAPE the ismaximum 9.50% and MAPE the minimum is 9.50% and MAPE the isminimum 1.15%. Table MAPE2 shows is 1.15%. the Tab verificationle 2 shows results the verification for Tainan results Liujia Campus;for Tainan with Liujia respect Campus; to the with IDW re method,spect to we the find IDW that method, during the we verification find that during period the the verification maximum MAPEperiod isthe 9.26%, maximum and the MAPE minimum is 9.26%, MAPE and is 0.72%.the minimum During theMAPE verification is 0.72%. period, During the the average verification MAPE ofperiod, solar radiationthe average estimation MAPE of of solar Yuan Changradiation Township estimation Administration of Yuan Chang and Township Tainan Liujia Administration Campus was 4.30%and Tainan and 3.71%, Liujia respectively.Campus was The 4.30% detailed and 3.71% results, respectively. shown in Tables The 1detail and2ed also results demonstrate shown in that Table thes 1 performanceand 2 also demonstrate of the IDW method that the is betterperformance than that of ofthe the IDW OK method. method The is better current than verification that of datathe OK do notmethod. provide The a current sufficient verification explanation data for do such not differences; provide a sufficient this is an issueexplanation that should for such be addressed differences; in thethis future. is an issue that should be addressed in the future.

11/1 11/2 11/3 11/4 11/5 11/6 11/7 (a)

11/1 11/2 11/3 11/4 11/5 11/6 11/7 (b)

Figure 6.6. The comparisoncomparison results:results: ( a(a)) Yuan Yuan Chang Chang Township Township Administration; Administration; (b )(b Tainan) Tainan Liujia Campus. Liujia Campus.

Energies 2018, 11, x FOR PEER REVIEW 7 of 12 Energies 2018, 11, 1374 7 of 12 According to studies completed in 2000, Lee et al. proposed a MAPE accuracy classification to assessAccording the estimation to studies accuracy completed of proposed in 2000, models. Lee et In al. this proposed experiment, a MAPE the IDW accuracy algorithm classification proposed to assessin this thepaper estimation was compared accuracy with of proposedthe OK algorithm models. In(redesign this experiment, simulation) the, IDWwhich algorithm is commonly proposed used in thissolar paper radiation was comparedestimation. with The thecomparison OK algorithm showed (redesign that the simulation), performance which of the is commonlyIDW is better used than in solarthat of radiation the OK estimation.algorithm; Thenamely comparison, IDW had showed the lowest that the MAPE performance value. The of the classification IDW is better criteria than thatare ofdescribed the OK algorithm; in Table 3.namely, According IDW had to the the lowestclassification, MAPE value. the proposed The classification model of criteria this study are described on the inestimation Table3. According of solar radiation to the classification, has very good the accuracy. proposed The model geographic of this study research on the scope estimation of this study of solar is radiationconcentrated has veryin the good central accuracy. and southern The geographic part of researchthe country; scope the of research this study results is concentrated propose a insolar the centralradiation and estimation southern partmodel ofthe and country; verification the research for cen resultstral and propose southern a solar counties. radiation It is estimation hoped that model this andsolar verification radiation estimation for central andmodel southern could be counties. promoted It is hopedrapidly that to other this solar counties radiation in Taiwan estimation in order model to couldestablish be promoted a national rapidly solar radiationto other counties distribution in Taiwan map. in Hopefully order to establish a central a national and southern solar radiation Taiwan distributioncontour map map. could Hopefully be drawn a central according and southern to actual Taiwan data collected contour map from could horizontal be drawn solar according radiation to actualstations, data and collected estimated from values horizontal calculated solar radiation with the stations, inverse and distance estimated weighting values algorithm. calculated Figure with the 7 inverseshows the distance central weighting and southern algorithm. Taiwan Figure solar7 shows radiation the centraldistribution and southern map; with Taiwan this solarmap radiationwe could distributionobserve fluctuation map; with trends this inmap solar we radiation could observe resources fluctuation in different trends counties, in solar radiation which can resources serve as ina differentreference counties, for investment which can in serve solar as PV a reference system for installation, investment system in solar performance PV system installation, evaluation, system and performancelong-term operation evaluation, and andmaintenance. long-term operation and maintenance.

FigureFigure 7. 7.Central Central and and southern southern Taiwan Taiwan solar solar radiation radiation distribution distribution map for map Inverse for Distance InverseWeighting Distance 2 (IDW)Weighting (kWh/m (IDW).) (kWh/m2).

Energies 2018, 11, 1374 8 of 12

Table 1. Solar radiation estimation model verification—Yuan Chang Township Administration.

Estimated Value MAPE Estimated Value MAPE Date Actual Value (IDW) (IDW) (OK) (OK) 11/1 2.93 2.90 1.15% 2.67 8.79% 11/2 5.01 4.83 3.53% 4.90 2.17% 11/3 4.76 4.47 6.17% 4.32 9.03% 11/4 3.82 3.74 2.01% 3.93 2.94% 11/5 2.95 3.23 9.50% 3.56 20.7% 11/6 3.91 4.05 3.65% 3.71 5.02% 11/7 4.90 4.70 4.04% 4.50 8.03% Average 3.78 3.99 4.30% 3.94 8.10%

Table 2. Solar radiation estimation model verification—Tainan Liujia campus.

Estimated Value MAPE Estimated Value MAPE Date Actual Value (IDW) (IDW) (OK) (OK) 11/1 3.36 3.05 9.26% 2.57 23.28% 11/2 4.29 4.22 1.63% 4.42 3.24% 11/3 4.83 4.54 6.06% 4.80 0.42% 11/4 3.73 3.76 0.72% 4.21 13.00% 11/5 3.22 3.31 2.65% 3.31 2.94% 11/6 3.87 3.98 2.88% 3.88 0.38% 11/7 4.82 4.69 2.76% 4.86 1.01% Average 4.02 3.94 3.71% 4.01 6.32%

Table 3. Mean Absolute Percentage Error (MAPE) estimation accuracy classification.

MAPE Value Model Accuracy MAPE < 10% Very Good (The closer to 0 the better) 10% < MAPE < 20% Good 20% < MAPE < 50% Reasonable 50% < MAPE False

5. Discussion Despite the fact that satellite-derived irradiation is quite easy and can be done at low cost, ground measurements from stations are still important for the solar radiation estimation process. In general, irradiation data from satellites cover the whole planet and have a reasonably good spatial and temporal resolution. In Africa, Europe, China, etc., the spatial and temporal resolution provided by satellites is sufficient. However, in some special cases with small land area, such as Taiwan, a much higher spatial resolution for solar radiation monitoring is needed. Furthermore, the information derived from the satellite may be influenced by the current atmospheric and cloud conditions. Therefore, data verified by ground monitoring stations are also important and cannot be ignored. Moreover, PV power generators are also built on the ground. The information from the monitoring stations is closest to the actual situation. We included data from a large number of monitoring stations in Taiwan in this paper, and the estimations of the generated PV power can also be improved by the setting of the ground monitoring stations. Energies 2018, 11, 1374 9 of 12

According to the characteristics of the IDW method, the distances between the monitoring stations and the locations of where we want to estimate are the main factors determining the estimation results. Monitoring stations closer to the estimation points have higher influence during the estimation process. Therefore, input stations with minimal distance played the most important role in simulating irradiation in stations 21 and 22. In our experience, monitoring stations within 30 km of the estimation point may have a great influence on the estimation result. In other words, the decreasing number of input stations may impact the irradiation modeling precision, but the degree of impact depends on the distance between the estimation point and the removed monitoring stations. The closer the referencing monitoring station, the greater the impact on the estimation results, and vice versa. The selection criteria for stations 21 and 22 as verification stations are simply that they are located in the central and southern region of Taiwan, respectively. We have carefully considered various sensitive influence factors; if other stations were selected and their distance between other reference stations was within 30 km, there would be little effect on our research results. The geographical scope of this experiment is central and southern Taiwan; the maximum distance between monitoring stations from north to south is about 212 km, and the maximum distance between monitoring stations from east to west is about 66 km. In the paper, the distance is very short so that the self-determined k parameter value was established to equal 1. The solar radiation estimation employed the IDW algorithm on the input dataset, which is PSH data from monitoring stations 1–20. Then, monitoring stations 21 and 22 are verification stations. Finally, the verification period in this article is the experimental verification period from 1 November to 7 November.

6. Conclusions This paper presents a simple method for establishing a solar radiation estimation model by setting up 22 horizontal solar radiation computer monitoring systems to collect solar radiation data, and applying inverse distance weighting algorithm to 20 locations to establish the estimation model. The paper compares the actual solar radiation data of Yuan Chang Township Administration and Liujia Sewage Treatment Plant with the estimated values calculated by the proposed model to verify the hypothesis. The experiments compare the estimation results done by the IDW and Ordinary Kriging methods. The comparison results show that IDW has better performance than the Kriging method. The MAPE of the IDW solar radiation estimation model applied at Liujia Sewage Treatment Plant and Wuwang Elementary School are 4.30% and 3.71%, respectively, confirming that this model has very good estimation accuracy. The experimental results also validate the feasibility and practicality of the IDW method. In the future we hope to make these experimental results more widely available in Taiwan, and, as more data are collected in the horizontal solar radiation monitoring database, longer verification periods could be applied. As the climate in Taiwan has four distinct seasons, the solar radiation estimation model could also be broken down into four models for more in-depth research to improve the accuracy of future estimates.

Author Contributions: P.-H.K. wrote the program and designed the solar radiation estimation model. C.-J.H. planned this study and collected the solar radiation dataset. P.-H.K., H.-C.C. and C.-J.H. contributed to the realization and revision of the manuscript. Acknowledgments: This work was supported by the Ministry of Science and Technology, Taiwan, Republic of China, under Grants MOST 106-2218-E-153-001-MY3. Conflicts of Interest: The authors declare no conflict of interest. Energies 2018, 11, 1374 10 of 12

Appendix A

Table A1. Geographic locations of the 22 horizontal solar radiation computer monitoring systems.

Longitude and Longitude and No. Location Name No. Location Name Latitude Latitude 24.131594, Wun-Guang Elementary 23.534850, 1 Taichung City Love Home 12 120.653725 School Hu-Kou Branch 120.165990 24.349143, 23.376099, 2 Dajia District Office 13 Budai Township Office 120.622465 120.169879 24.304839, 23.462219, 3 Houli District Office 14 Chih-Hang Elementary School 120.710660 120.445861 Shan Yang Elementary 24.159267, 22.905872, 4 15 Jiading District Office School 120.544885 120.180293 Hemei Township 24.105946, National Science and 22.641431, 5 16 First-Class Community 120.497144 Technology Museum 120.322551 Shijou Township 23.851281, 22.693476, 6 17 Office Administration 120.499099 120.432831 Fang Yuan 23.924819, PingPei Senior 22.759382, 7 18 Elementary School 120.319233 High School. 120.543578 Chung Hsing Junior High 23.931503, WanLuan Junior 22.571429, 8 19 School 120.693683 High School 120.574788 Puli Township 23.966574, DungLung 22.464138, 9 20 Administration 120.969214 Elementary School 120.451289 Mailiau Township 23.753435, Yuanchang 23.649667, 10 21 Administration 120.252098 Township Office 120.314859 TransWorld 23.680371, Tainan 23.225857, 11 22 University 120.555737 Liujia Campus 120.366523

Table A2. Solar radiation (PSH) of 22 horizontal solar radiation monitoring stations in central and southern Taiwan.

PSH (Unit: Hours) No. Station Name 11/1 11/2 11/3 11/4 11/5 11/6 11/7 1 Shijou Township Administration 2.55 4.64 4.39 3.74 3.41 3.76 4.64 2 Mailiau Township Administration 2.98 4.90 4.33 3.44 3.43 4.18 4.65 3 Puli Township Administration 1.22 5.10 4.50 3.60 4.42 4.96 4.82 4 Jiading District Office 2.69 4.79 4.73 4.65 3.37 4.42 4.88 5 Houli District Office 1.28 4.20 3.61 2.67 3.34 3.57 4.25 6 Budai Township Administration 3.03 4.87 4.67 4.51 3.84 4.22 4.73 7 Shan Yang Elementary School 2.63 5.00 4.34 3.22 3.32 3.83 4.45 8 Dajia District Office 1.87 3.72 4.38 3.69 3.76 3.42 4.32 9 Taichung City Love Home 1.59 4.63 3.77 3.48 3.18 3.72 4.19 10 Fang Yuan Elementary School 2.91 4.69 3.95 3.66 3.29 3.40 4.26 11 Hemei First Class Community 2.40 4.67 4.23 3.55 3.43 3.83 4.50 12 Chung Hsing Junior High School 1.89 4.55 4.12 3.53 4.08 4.35 4.54 13 TransWorld University 2.30 3.80 4.98 3.97 3.18 4.65 5.42 14 Wun Guang Elementary School 2.99 5.78 5.21 5.07 3.58 3.27 4.83 15 Chi-Hang Elementary School 2.95 4.27 4.62 4.09 3.40 4.23 4.86 16 National Science and Technology Museum 1.91 3.38 5.32 4.44 3.37 5.46 5.65 17 Dashu District Office 2.06 3.42 4.68 4.39 3.81 5.20 5.15 18 PingPei Senior High School. 1.61 2.55 3.54 2.73 3.04 3.56 3.88 19 WanLuan Junior High School 1.28 2.53 4.56 3.93 3.75 4.84 3.85 20 DungLung Elementary School 1.70 3.04 4.68 4.04 3.61 4.88 4.52 21 Yuanchang Township Office 2.93 5.01 4.76 3.82 2.95 3.91 4.90 22 Tainan Liujia Campus 3.36 4.29 4.83 3.73 3.22 3.87 4.82 Energies 2018, 11, 1374 11 of 12

Table A3. Acronym list.

Full Name Acronyms Artificial Neural Network ANN File Transfer Protocol FTP Inverse Distance Weighting IDW Mean Absolute Percentage Error MAPE Monthly Average Daily Solar Radiation MADSR Ordinary Kriging OK Particle Swarm Optimization Neural Network PSO-NN Peak Sum Hours PHS Root-Mean-Square Deviation RMSD Root-Mean-Square Error RMSE Solar Photovoltaic PV

References

1. SolarPower EuropeGlobal Market Outlook for Solar Power 2015-2019. Glob. Mark. Outlook 2014, 32. [CrossRef] 2. Renewable, I.; Agency, E. Renewable Capacity Statistics 2017; IRENA: Masdar City, United Arab Emirates, 2017; ISBN 978-92-9260-018-1. 3. Jurasz, J.; Ciapała, B. Integrating photovoltaics into energy systems by using a run-off-river power plant with pondage to smooth energy exchange with the power gird. Appl. Energy 2017, 198, 21–35. [CrossRef] 4. Ming, B.; Liu, P.; Guo, S.; Zhang, X.; Feng, M.; Wang, X. Optimizing utility-scale photovoltaic power generation for integration into a hydropower reservoir by incorporating long- and short-term operational decisions. Appl. Energy 2017, 204, 432–445. [CrossRef] 5. Oh, Y.; Park, S. Modeling and parameterization of fuel economy in Heavy Duty Vehicles (HDVs). Energies 2014, 7, 5177–5200. [CrossRef] 6. Kim, E.; Ra, I.; Rhee, K.H.; Kim, C.S. Estimation of real-time flood risk on roads based on rainfall calculated by the revised method of missing rainfall. Sustainability 2014, 6, 6418–6431. [CrossRef] 7. Alshuwaikhat, H.M.; Abubakar, I.R.; Aina, Y.A.; Adenle, Y.A.; Umair, M. The development of a GIS-based model for campus environmental sustainability assessment. Sustainability 2017, 9, 439. [CrossRef] 8. Jin, X.; Li, Y.; Zhang, J.; Zheng, J.; Liu, H. An approach to evaluating light pollution in residential zones: A case study of Beijing. Sustainability 2017, 9, 652. [CrossRef] 9. Wang, Z.; Nie, K. Measuring Spatial Distribution Characteristics of Heavy Metal Contaminations in a Network-Constrained Environment: A Case Study in River Network of Daye, China. Sustainability 2017, 9, 986. [CrossRef] 10. Madhloom, H.M.; Al-Ansari, N.; Laue, J.; Chabuk, A. Modeling spatial distribution of some contamination within the lower reaches of Diyala river using IDW interpolation. Sustainability 2017, 10.[CrossRef] 11. Hohn, M.E. An Introduction to applied geostatistics. Comput. Geosci. 1991, 17, 471–473. [CrossRef] 12. Cressie, N. The origins of kriging. Math. Geol. 1990, 22, 239–252. [CrossRef] 13. Trnka, M.; Žalud, Z.; Eitzinger, J.; Dubrovský, M. Global solar radiation in Central European lowlands estimated by various empirical formulae. Agric. For. Meteorol. 2005, 131, 54–76. [CrossRef] 14. Almorox, J.; Hontoria, C. Global solar radiation estimation using sunshine duration in Spain. Energy Convers. Manag. 2004, 45, 1529–1535. [CrossRef] 15. Li, M.F.; Fan, L.; Liu, H.B.; Wu, W.; Chen, J.L. Impact of time interval on the ångström-Prescott coefficients and their interchangeability in estimating radiation. Renew. Energy 2012, 44, 431–438. [CrossRef] 16. Behrang, M.A.; Assareh, E.; Ghanbarzadeh, A.; Noghrehabadi, A.R. The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data. Sol. Energy 2010, 84, 1468–1480. [CrossRef] 17. Rumbayan, M.; Abudureyimu, A.; Nagasaka, K. Mapping of solar energy potential in Indonesia using artificial neural network and geographical information system. Renew. Sustain. Energy Rev. 2012, 16, 1437–1449. [CrossRef] Energies 2018, 11, 1374 12 of 12

18. Mohandes, M.A. Modeling global solar radiation using Particle Swarm Optimization (PSO). Sol. Energy 2012, 86, 3137–3145. [CrossRef] 19. Janjai, S.; Pankaew, P.; Laksanaboonsong, J.; Kitichantaropas, P. Estimation of solar radiation over Cambodia from long-term satellite data. Renew. Energy 2011, 36, 1214–1220. [CrossRef] 20. Wu, W.; Liu, H.-B. Assessment of monthly solar radiation estimates using support vector machines and air temperatures. Int. J. Climatol. 2012, 32, 274–285. [CrossRef]

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