514 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 10, NO. 2, APRIL 2019

MPPT Perturbation Optimization of PhotovoltaicPower Systems Based on Solar Irradiance Data

ClassificationKe Yan , Yang Du , Member, IEEE, and Zixiao Ren

Abstract—The tracking accuracy and speed are two main is-sues for the fixed step perturb-and-observe maximum power pointtracking (MPPT) method. This study proposes a novel solution tobalance the tradeoff between performance and cost of the MPPTmethod. The perturbation step size is determined off-line for a spe-cific location based on the local irradiance data. The support vectormachine is employed to automatically classify the desert or coastallocations using historical irradiance data. The perturbation stepsize is optimized for better system performance without increas-ing the control complexity. Simulations and experiments have beencarried out to verify the effectiveness and superiority of the pro-posed method over existing approaches. The experimental resultsshow a 5.8% energy generation increment by selecting optimal stepsizes for different irradiance data types.

Index Terms—Maximum power point tracking (MPPT), PVpower system, irradiance, machine learning, classification, supportvector machine (SVM).

I. INTRODUCTION

A PHOTOVOLTAIC (PV) module under solar irradiancedemonstrates a non-linear current-voltage characteristicwith a specific point, called the maximum power point (MPP),where the PV module generates energy in full capacity [1]. Themain objective of the maximum power point tracker (MPPT) isto track the maximum power point under various circumstances.

Over the past years, many MPPT approaches were proposed[2]. Nevertheless, the fractional open-circuit voltage, the frac-tional short-circuit current, the hill climbing (HC) [3], the per-turb and observe (P&O) [4] and the incremental conductance(INC) [5] are still commonly used for commercial products. Forthe fractional voltage/current methods, the PV module does notoperate at the true MPP at most of the time. The HC and P&O

Manuscript received August 16, 2017; revised December 17, 2017; acceptedMarch 18, 2018. Date of publication May 8, 2018; date of current versionMarch 21, 2019. This work was supported in part by the National ScienceFoundation of China under Grant 61602431, in part by research developmentfund of Xi’an Jiaotong-Liverpool University under Grant RDF-15-01-40, and inpart by Jiangsu University S&T Programme under Grant 17KJB470012. Paperno. TSTE-00762-2017. (Corresponding author: Yang Du.)

K. Yan is with the College of Information Engineering, China Jiliang Univer-sity, Hangzhou 310018, China (e-mail:,keddiyan@gmail.com).

Y. Du and Z. Ren are with the Department of Electrical and ElectronicEngineering, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China(e-mail:,yang.du@xjtlu.edu.cn; zixiao.ren14@student.xjtlu.edu.cn).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSTE.2018.2834415

methods generate a perturbation repeatedly in the duty cycle orPV voltage to detect whether the PV module is operating at theMPP. The INC method is designed based on the fact that theslope of the PV current and voltage characteristic curve is zeroat the MPP.

The P&O method is widely adopted in real-world applicationsbecause of its simplicity in usage. Tracking accuracy and speedare recognized as two main difficulties for the P&O method.The system oscillates around the MPP because of the repetitiveperturbation. The oscillation can be minimized by reducing theperturbation step size. However, a smaller step size slows downthe MPPT. Variable step and frequency P&O MPPT methodshave been proposed to address this challenge [6], [7]. How-ever, these methods increase the computational load, resultingin overall system cost increments. Especially for distributedMPPT configurations [8], where each PV module or even eachPV cell has its own MPPT controller, the fixed step size P&Omethods are more cost effective.

PV generation can drop by 60% within seconds due to areduction in solar irradiance [9]. The solar irradiance variationis dependent upon cloud height, sun elevation and wind speed.These factors have to be considered in PV system design [10].Solar irradiance resources and meteorological data vary betweendifferent locations. Existing works investigate solar irradiancevariations at different timescales as well as their impacts to gridoperation. In [11], different types of solar irradiance variationsare investigated, a preliminary result for designing customizedMPPT methods is reported.

It is important to accurately classify irradiance data samplesinto either coastal or desert area to fully utilize the proposedmethod. It is a challenge to do this work manually. One reasonis that the data size can be tremendously large. Another reasonis that, for some data samples, it is never easy for human eyesto identify the characteristics by observation. In this study, anautomatic location identification system based on the supportvector machine (SVM) is proposed.

SVM is a supervised machine learning technique. It has beenwidely used for solar irradiance forecasting, power generationprediction, energy system fault detection and etc. [12]–[15].There are relatively less works have been reported for classifi-cation problems in the solar energy related fields. In [16], SVMhas been utilized to classify different types of cloud for moreaccurate PV power forecasting. The PV power prediction resulthas been improved by applying SVM on weather classification

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https://orcid.org/0000-0002-1611-6636https://orcid.org/0000-0003-2254-778Xhttps://orcid.org/0000-0002-9023-4665mailto:keddiyan@gmail.commailto:yang.du@xjtlu.edu.cnmailto:zixiao.ren14@student.xjtlu.edu.cn

YAN et al.: MPPT PERTURBATION OPTIMIZATION OF PHOTOVOLTAIC POWER SYSTEMS BASED ON SOLAR IRRADIANCE DATA 515

Fig. 1. Plots of solar GHI data for two locations, October 2014 [19]. (a) Humboldt State University, California (coastal area). (b) University of Nevada, Nevada(desert area).

[17]. In [18], solar irradiances on various locations has beenestimated by applying SVM on commonly measured meteo-rological variables. It was a novel approach to map the solarirradiance without using pyranometers.

In this work, the optimized selection of the perturb step sizewill be designed off-line for a specific location after this locationis identified by SVM based on historical data. The step-sizealso can be updated monthly or seasonally for better systemperformance without increasing the control complexity. Theultimate target of this study is to propose an optimized solutionto balance the trade-off between performance and cost.

In this paper, after analyzing the whole year’s data of thetwo locations, the variability of solar irradiance for differentlocations are confirmed and reported in Section II. An auto-matic location identification system based on SVM is proposedin Section III. By using a one year data as input, the systemcan automatically identify an irradiance data sample as col-lected from either coastal or desert area. In Section IV, the pro-posed method for fixed optimal perturbation size is reported. InSection V, the effectiveness of the proposed method has beenverified by case study and experiment results.

II. SOLAR IRRADIANCE VARIABILITY

The solar irradiance on the earth’s atmosphere is relativelystable and predictable. However, the radiation at the earth’ssurface can change drastically due to several reasons, e.g., thepassing clouds, water vapor and pollution. The variation patternsof the solar irradiance are different from one location to another.Fig. 1 shows the solar global horizontal irradiance (GHI) in awhole month (Oct. 2014) for two different locations at HumboldtState University (HSU) and University of Nevada, Las Vegas(UNLV). The irradiance data is collected by National RenewableEnergy Lab (NREL)’s Measurement and Instrumentation DataCenter (MIDC) [19].

The HSU is at the coastal area and the UNLV represents adesert area location. It can be seen from Fig. 1 that there is moresolar irradiance variation in the coastal area. This matches ourlife experiences. Weather in the coastal area usually changesmore frequently and dramatically than the desert area. The

Fig. 2. Geographic location of two areas with different weather condition [20].

Geographic locations of these two places are depicted in Fig.2, which is generated from Google earth [20]. It is noted thatthe two sites are not too far apart. Assumptions are made thatthe two cross continental locations have more distinguishableirradiance patterns.

Two days of the GHI data have been plotted in Fig. 3 toillustrate two typical solar irradiance patterns. They are twosolar irradiance diagrams on the same date, i.e., 20th Oct. 2014at the two different locations. It is noted that the PV system atcoastal area requires fast MPP tracking; and the system at desertarea requires accurate MPP tracking with small perturbation.

The geographical wealth of solar radiation data is availablethrough NREL’s MIDC for selected stations. The solar irradi-ance data was sampled once per minute. The characteristics oftwo different patterns have been investigated and summarized.The irradiance ramp rate (RR) is the direct indicator of irradi-ance variability. The passing cloud causes RR changes on scalesof seconds to 10 min [21]. One minute ramp rate statistics fordaytime GHI has been reported in Table I. These statistics showthat the irradiance data can be in very different patterns fordifferent locations.

516 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 10, NO. 2, APRIL 2019

Fig. 3. Daytime solar irradiance data for two locations, 20th October 2014.

TABLE IONE MINUTE RAMP RATE STATISTICS FOR DAYTIME GHI

The average and maximum of the magnitude of RRs for eachlocation on different time scales are shown in Table I. The HSUhas a large mean RR value 30.3 Wm-2 min-1 for a particu-lar day (20th Oct. 2014), while this value for the UNLV is3 Wm-2 min-1. The HSU has larger maximum RRs for all timeranges. Since the mean absolute value of the RR is already ameasure of the RR variability, the standard deviation (Std) ofthe RR (not the absolute value) is expected to give qualitativelysimilar results as described in Table I. It can be seen from allfactors in Table I that the HSU (coastal area) has higher irradi-ance variability than UNLV (desert area). This is consistent withour expectation and life experience. However, the difference be-tween the two areas becomes less obvious for the monthly andyearly data. This means that the variability is averaged out be-

Fig. 4. Flowchart of the automatic location identification system based onirradiance data.

cause of the mixed weather characteristics presented on longertime scale.

III. AN AUTOMATIC LOCATION IDENTIFICATIONSYSTEM BASED ON SVM

For the purpose of automatically identifying coastal anddesert areas, an automatic location identification method is de-signed based on SVM. The supervised location identificationsystem is established in three steps. First, the daytime solar ir-radiance data is divided into training and testing datasets. Thetraining data samples include days that can be easily labeled;and the testing dataset contains samples that cannot be easilyidentified manually. Second, a pre-processing step is performedon both training and testing datasets. Third, the SVM is mod-eled using the training dataset. The two parameters of the SVM,namely, C and γ, are tuned using a grid search algorithm basedon 10-fold cross-validation results. Last, we identify the loca-tion information of each data sample in the testing dataset usingthe trained model. The confidence levels of the automatic la-beling are obtained from SVM probability outputs. The overallflowchart of the proposed automatic location identification sys-tem is depicted in Fig. 4.

The pre-processing step consists of a normalization pro-cess and a discrete differentiation process. We denote eachtraining sample as X = {x0 , x1 , . . . , xn , y}, where y indi-cates the label; and xi denotes each time stamp data point.Each training sample X is normalized by replacing xi withxi

′ = (xi − xmin)/(xmax − xmin), where xmin and xmax are theminimal and maximal numbers in X, respectively. The discretedifferentiation process is done by replacing xi ′ with xi ′−xi+1 ′,neglecting the last data point.

SVM was first introduced by Vapnik et al. [22] and soonrecognized as one of the most popular machine learning tech-nique recently. It utilizes hyper-planes in high dimension to

YAN et al.: MPPT PERTURBATION OPTIMIZATION OF PHOTOVOLTAIC POWER SYSTEMS BASED ON SOLAR IRRADIANCE DATA 517

Fig. 5. P&O MPP tracking process with different step size.

TABLE IIPARAMETERS AND NOMINAL OPERATING CONDITIONS

FOR THE PV CONVERTER

separate the training data samples in different classes. In thetesting phase, the trained SVM model labels each testing sam-ple according to the classification probability. In this study, wereuse the classification probability as the confidence level foreach classified testing sample.

IV. PERTURBATION STEP SIZE OPTIMIZATION

Two P&O MPP tracking processes with different step sizesare shown in Fig. 5. It can be seen that the green line with largerstep size achieves MPP in less perterbation cycles. However, theMPPT with smaller step size can track the MPP more accuratelywhen the system reaches steady-state.

Simulation model has been built using Matlab/Simulink soft-ware. The specifications of the PV generator and PV converterare listed in Table II. It can be seen from Fig. 6 that the MPPTmethod with larger step size reaches MPP faster and have largeroscillation losses in the steady-state.

A common practice is to use one fixed perturbation valuefor all areas. In this paper, optimization has been performed to

Fig. 6. Simulation results of P&O MPPT with different step size.

improve the MPPT efficiency with considering of the irradiancevariation patterns for different locations.

After a data sample has been identified as collected fromeither coastal or desert area, the optimal perturbation step sizecan be designed with the following steps. The flowchart is shownin Fig. 7

1) The details of calculating the two key parameter, pertur-bation time interval Tp and step size Δx, can be foundin [23]. The perturbation time interval cannot be smallerthan the system settling time; and the power variationcaused by the perturbation has to be larger than the powervariation caused by irradiance variation. Since there areseveral parameters dependent on the irradiance level, theworst case scenario has been considered for parameterboundary analysis.

2) From the automatic location identification system, the typ-ical irradiance for each area can be found. Four differentstep sizes are used as starting points to find the optimalstep size by running the simulation.

3) The resulting data is analyzed using Matlab. The opti-mal step size for one particular location is the one yieldthe most energy. The optimal step size can be further

518 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 10, NO. 2, APRIL 2019

Fig. 7. Flowchart of optimal step size design methoed.

fine-tuned, if necessary, by repeating the steps highlightedin the red box.

V. EXPERIMENTAL RESULT

A. Automatic Location Identification Results

The SVM is implemented using LibSVM with Matlab [24].Data from two locations, HSU and UNLV, is used to train themachine learning models and test the results. The characteristicsof the locations are identified manually by observing the solarirradiance variation pattern in a whole year (2014). For datacollected from each location, data samples that can be easilyidentified as coast/desert area samples are labeled and selectedas training data samples. The selection was performed basedon user experiences and the variances of the GHI-Time curves.Each training data is labeled manually with ‘1’ for ‘coastal area’and ‘−1’ for ‘desert area’. In total, there are 219 days in HSUand 197 days in UNLV in the training dataset. The remaining146 days in HSU and 168 days in UNLV are treated as testingdata. The testing dataset contains data samples that cannot beeasily identified manually (with ambiguity).

Different machine learning techniques are compared to se-lect the most appropriate classifier for the automatic locationidentification system, which includes SVM, K-nearest-neighbor(KNN), Naı̈ve Bayes, Bayes net, J48, random tree, randomforest, decision table and multilayer perceptron. The trainingdataset is chosen as the input data. With the same input data, allclassifiers are tested on WEKA 3.8 [25]; and the classificationaccuracy rates are collected based on 10-fold cross-validation[26] (Table III). Among all available machine learning tech-niques, the SVM was selected with the highest classificationaccuracy rate at 99.76%.

The trained SVM model is firstly tested by giving HSU test-ing data set as input. The output results is very accurate for the

TABLE IIICLASSIFICATION ACCURACY FROM DIFFERENT MACHINE TECHNIQUES

(BASED ON 10-FOLD CROSS-VALIDATION)

TABLE IVHSU’S CONFIDENCE LEVEL OF SOME SPECIFIC DATE

easily labeled samples in the testing data set, for both 1 and−1 cases. However, for the other samples, the initial resultsshow that the model is too sensitive to the fluctuation. It tends toclassify a day as ‘coastal eara’ if there is only very small fluctu-ation. The very left picture in Fig. 8(a) shows the GHI in a day(May 20. 2014). The SVM model classify this day as ‘coastalarea’, which the right answer should be ‘desert area’ consider-ing that the proportion of the fluctuation is small. To improvethe accuracy of the results of the SVM model, confidence levelis used as an distingushing factor. The confidence level is posi-tively correlated to the accuracy of the estimation. A threshold isset by comparing testing results with manually labeled results.

The output of the SVM model shows that the confidencelevel for the desert area (−1) is lower than the coastal area (1).The fluctuation of the GHI increases with the increments of theconfidence levels for all samples which are classified as 1. Thelowest confidence level of the confirmed coastal area (1) data is0.9953. This confidence level is set as a threshold. All the resultswhich have been classified as 1 can be corrected as −1 if theconfidence level is lower than this threshold. All the previouslydetermined −1 will be kept unchanged, since SVM model nevermake any mistake on indentifing this category. Table IV shows

YAN et al.: MPPT PERTURBATION OPTIMIZATION OF PHOTOVOLTAIC POWER SYSTEMS BASED ON SOLAR IRRADIANCE DATA 519

Fig. 8. Correlation between the GHI variation and the SVM model output’s confidence levels. (a) HSU. (b) UNLV.

TABLE VUNLV’S CONFIDENCE LEVEL OF SOME SPECIFIC DATE

the confidence levels of the 6 days. Fig. 8(a) shows the variationof the GHI with the increments of the confidence levels.

To verify the effectiveness of the set threshold, the trainedSVM model is again tested using the testing data from UNLVdataset. The classification results of the desert area (−1) is stillaccurate. All the 1 samples with the confidence level lower thanthe threshold are corrected as −1. It can be seen from Fig. 8(b)that the fluctuation of the GHI increase with the increments ofthe confidence levels. The pre-set threshold (Oct 27) can effec-tively separate 1 and −1 cases. Table V shows the confidencelevels of the selected days in UNLV testing data set.

The proposed automatic location identification system ac-curately identifies coastal area and desert area. The testing dataof the HSU has 146 samples. The SVM model’s output resultsinclude 121 samples of coastal area (1) and 25 samples of desertarea (-1). With the addition of the training data of HSU, whichincludes 197 samples of 1 and 22 samples of -1, the proportionof coastal area samples is 87.1%, which matches with itsgeographical location information. The testing data fromUNLV dataset has 168 samples. The SVM’s results include105 samples of 1 and 63 samples of -1. With the addition of thetraining day of UNLV, which includes 113 samples of 1 and 84samples of -1, the proportion of desert area samples is 40.3%.Only in particular months, such as May, June, September andOctober, the classification results have more -1 samples than1 samples. It shows that even in the typical desert area, e.g.,UNLV, the -1 samples are still the minority. Large step size isstill preferred to maximize the whole year energy generation.However, if the small step size can be adopted in the above

Fig. 9. Experimental setup.

mentioned specific months or seasons, the energy generationcan be further improved.

The source code for the automatic solar irradiance loca-tion identification system has been provided as supplementarymaterials.

B. P&O MPP Results

An experimental test platform has been built including a boostconverter and a dSPACE control unit. A Chroma programmableDC power supply is used to simulate the PV generator. The‘Real world weather simulation’ feature allows us to importreal irradiance data from excel file to simulate the PV generator.The experimental setup has been shown as in Fig. 9.

The results are measured from experiment results. Two dif-ferent scenarios, desert and coastal areas, have been tested usingthe irradiance data shown in Fig. 3. The irradiance data was inputto the solar emulator, which emulates the current-voltage char-acteristic of the PV module. The PV emulator is connected withDC/DC converter and followed by resistive load. The PV outputvoltage and current are measured and recorded using dSPACE.The yield energy is calculated by integrating the product of cur-rent and voltage at each time point using Matlab. The originalirradiance data is at 1 min resolution. It takes 7 to 8 hours tocarry out the one experiment for one day’s data. And the mea-sured data is also too large to store or analyze. The experimenthas been speeded up by updating the irradiance data once pertwo seconds rather than one minute. The perturb time interval

520 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 10, NO. 2, APRIL 2019

Fig. 10. Experimental results.

TABLE VIENERGY GENERATION FOR DIFFERENT MPPT PERTURBATION STEP SIZE

has been set as 1s. The experimental results are depicted inFig. 10. Although it appears the MPPT is functioning in all sce-narios, there is only one optimal perturbation for each irradiancecondition.

For 1% perturbation, the step size is too small to track theMPP under rapidly changing irradiance. The slowly changingirradiance should be in favor of small step size. However, asshown in the starting stage of Fig. 10(e), the power variationcaused by the perturbation is smaller than the power variationcaused by the irradiance increase. In Fig. 10(g) and (h), thepower oscillating around the MPP caused energy losses. Thegenerated energy is calculated by integrating power shown inFig. 10 and dividing by 120. The energy generation results arelisted in Table VI.

For conventional MPPT method, which the perturbation isfixed for all areas, if the step size is 1%, in this particular day,the PV system under rapidly changing irradiance has 5.8% lessenergy generation comparing with its optimal energy genera-tion. This justifies the effectiveness of the proposed optimizationmethod.

C. Economic Consideration

The ultimate target of this study is to propose an optimizedsolution to balance the trade-off between performance and cost.

It is of interest to discuss and compare about the system costand yield energy with its counterparts.

The fixed step size perturbation method is proposed for sav-ing system cost, especially considering the trend of adoptingdistributed MPPT algorithm, which requires much more con-trol units. The fixed step size controller can be realized usinganalog circuit or very low cost 8-bit IC chips. However, themajor drawback of the conventional method is the low MPPTefficiency, since one step size is used for all products. This iswhere our step size optimization comes in to solve this problemby customized design of the step size for different locations.

In comparison, the adaptive step size methods automaticallychange perturbation size in real-time, which yield more energygeneration. However, the controller requires much more compu-tation power. The cost of the analog controller is approximatelyaround 1 dollar; and the micro-controller (such as TI28335) costmore than 20 dollars.

It is really hard to tell how much more energy the adaptivestep size MPPT can generate, since it is highly related to the irra-diance patterns and the controller parameter tuning. One paperusing low-cost analog controller reports that the MPPT track-ing efficiency is 99.92%, which is comparable with adaptiveMPPT [27].

The step-size also can be updated monthly or seasonallyfor better system performance without increasing the controlcomplexity.

VI. CONCLUSION

The characteristics of the irradiance data for two different lo-cations have been analyzed. The results show that the irradiancevariability is larger at coastal area. The idea of customized de-signing MPPT parameters for the system at a specific locationhas been raised. Simulations and experimental results confirmedthat the energy generation can be increased by selecting the op-timal perturbation size based on the local irradiance data. Anautomatic location identification framework has been proposedbased on SVM to effectively identify the specific location to beeither a coastal area or desert area. The proposed MPPT pertur-bation optimization method can achieve better energy produc-tion than the conventional fixed step size methods without usingcostly micro-controllers.

YAN et al.: MPPT PERTURBATION OPTIMIZATION OF PHOTOVOLTAIC POWER SYSTEMS BASED ON SOLAR IRRADIANCE DATA 521

ACKNOWLEDGMENT

A previous version of this paper has been published in 2015IEEE 16th Workshop on Control and Modeling for Power Elec-tronics (COMPEL) with title “Perturbation optimization of max-imum power point tracking of photovoltaic power systems basedon practical solar irradiance data.” Authors would like to thankNREL for providing the irradiance data. [19].

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Ke Yan received the bachelor’s and Ph.D. degreesin computer science from the National Universityof Singapore, Singapore, in 2006 and 2012, re-spectively. From 2013 to 2014, he was a Post-Doctoral Researcher with the Masdar Institute ofScience and Technology, Abu Dhabi, UAE. Hecurrently an Associate Professor with China Jil-iang University, Hangzhou, China. His current re-search interests include data mining, machine learn-ing, computer graphics, computational geometry, andbioinformatics.

Yang Du (S’09–M’13) received the Ph.D. degree inelectrical engineering from The University of Syd-ney, Sydney, N.S.W., Australia, in 2013. From 2013to 2014, he was with the Masdar Institute of Sci-ence and Technology, Abu Dhabi, UAE, as a Post-Doctoral Research Fellow. Since 2014, he has beena Lecturer with Xi’an Jiaotong-Liverpool University,Suzhou, China. His research interests include photo-voltaic power systems, power electronics, and smartgrid.

Zixiao Ren is currently working toward the B.Eng.degree in electrical engineering at Xi’an Jiaotong-Liverpool University, Suzhou, China. His researchinterests include photovoltaic power systems and ma-chine learning.

https://www.google.com/earth/https://www.google.com/earth/

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