Inter national J our nal of P o wer Electr onics and Dri v e System (IJPEDS) V ol. 16, No. 1, March 2025, pp. 55 ∼ 69 ISSN: 2088-8694, DOI: 10.11591/ijpeds.v16.i1.pp55-69 ❒ 55 Adv ancing solar ener gy har v esting: Articial intelligence appr oaches to maximum po wer point tracking Meriem Boudouane 1 , Lahoussine Elmahni 1 , Rachid Zriouile 1 , Soufyane Ait El Ouahab 2 1 Materials and Rene w able Ener gy Laboratory , Ph ysics Department, Uni v ersity of Ibn Zohr , Ag adir , Morocco 2 Methodology and Information Processing Laboratory , Ph ysics Department, Uni v ersity of Ibn Zohr , Ag adir , Morocco Article Inf o Article history: Recei v ed Jun 4, 2024 Re vised Oct 27, 2024 Accepted No v 28, 2024 K eyw ords: Boost con v erter Con v entional methods Intelligent methods Modeling MPPT control PV generator ABSTRA CT This paper presents a comparati v e study of v e maximum po wer point track- ing (MPPT) control techniques in photo v oltaic (PV) systems. The algorithms e v aluated include classical methods, such as perturb and observ e (P&O) and incremental conductance (IC), as well as intelligent approaches such as fuzzy logic (FL), articial neural netw orks (ANNs), and adapti v e neuro-fuzzy infer - ence system (ANFIS). Intelligent methods pro vide f aster re sponse times and fe wer oscillations around the maximum po wer point (MPP). The structure of the PV system includes a PV generator , load, and DC/DC boost con v erter dri v en by an MPPT controller . The performanc e of these techniques is analyzed under identical climatic conditions (same irradiation and temperature) in term s of ef - cienc y , response time, response curv e, accurac y in tracking the MPP , and others considered in this w ork. Simulations were performed using MA TLAB-Simulink softw are, demonstrating that ANNs and ANFIS outperform traditional methods in dynamic en vironments, with FL being computationally i ntensi v e. P&O e x- hibited signicant oscillations, while IC a sho wed slo wer tracking speed. This is an open access article under the CC BY -SA license . Corresponding A uthor: Meriem Boudouane Materials and Rene w able Ener gy Laboratory , Ph ysics Department, F aculty of Sciences-Ag adir Uni v ersity Ibn Zohr BP 32/S, CP 80000, Ag adir , Morocco Email: meriemprof@gmail.com 1. INTR ODUCTION Global ener gy demand continues to rise, traditionally relying on fossil fuels due to their high ener gy potential. Ho we v er , the depletion of these resources and their contrib ution to greenhouse g as emissions has prompted the search for alternati v e ener gy sources. Rene w able ener gy , particularly photo v oltaic (PV), of fers a sustainable and en vironmentall y friendly solution. PV systems harness solar ener gy to generate electricity . Still, their ef cienc y highly depends on the system’ s ability t o track the maximum po wer point (MPP), which v aries with changing climatic conditions, such as solar irradiance and tem perature. Maximum po wer point tracking technology is crucial for optimizing the po wer output of PV systems. W ith its ability to adjust maximum po wer point in real time, MPPT signicantly impro v es the performance of photo v oltaic installations, boosting ef cienc y and protability . The purpose of MPP T is to track and e xtract the maximum a v ailable po wer from the PV module by adjusting its electrical operating point. T o ac complish this, a DC/DC con v erter with an MPPT controller is i nstalled between the PV generator and load to adapt its resistance by adjusting the duty c ycle con v erter . Man y MPPT approaches are utilized to operate PV systems at maximum po wer . In re vie w , v arious MPPT methodologies were suggested to e xtract the maximum po wer from the PV J ournal homepage: http://ijpeds.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
56 ❒ ISSN: 2088-8694 generators. The classical MPPT algorithms were relati v ely simple and easy to implement, such as fractional short circuit current (OSC) [1], [2], fractional open circuit v oltage (OCV) [3]-[5], perturbation and observ ation (PO) [6], [7], incremental conductance (IC) [8]-[10], and hill-climbing (HC) [11], [12]. Despite their simplicity and g ains in de v elopment, these techniques ha v e limitations, most notably a slo wer response time, notable oscillates around maximum po wer point in steady states, and lo w ef cienc y during rapid weather v ariations. No w adays, more sophisticated and intelligent techniques of fer substantial adv antages o v er clas sical methods, such as simple implementation, the capacity to follo w the MPP under whether operating conditions, and f aster con v er gence. These include metaheuristic algorithms, particle sw arm opti mization (PSO) [13], ant colon y (A C) [14], articial bee colon y (ABC) [15], herd horse optimization (HHO) [16], cuck oo search (CS) [17], and gre y w olf optimization (GW O) [18] among others. These ne w approaches ha v e impro v ed response time and systems oscillation; their main challenge is population initialization. Other intelligent approaches that ha v e pro v en rob ust in MPPT control, such as fuzzy logic (FL) [19]-[21], articial neural netw orks (ANNs) [22]-[24], and adapti v e neuro-fuzzy inference system (ANFIS) [21], [25], these techniques necessitate system learning e xpertise and a database. The goal of this paper is to conduct a comparati v e analysis of the ef cienc y of MPPT tracking us- ing con v entional perturbation and observ ation (P&O) and incremental conductance (IC) techniques, as well as articial fuzzy logic (FL), articial neural netw orks (ANNs), and adapti v e neuro-fuzzy inference system (ANFIS) techniques. The criteria for comparison implemented in this study include the con v er gence time of MPPT control, MPPT error , steady-state po wer oscillation, and ef fects on PV panel v oltage (Vpv) and current (Ipv) due to irradiat ion and temperature v ariations. DC/DC boost con v erter is used as a n interf ace between the PV generator and load. The PV system proposed is simulated using MA TLAB-Simulink softw are. Simulation results ha v e pro v en that the best technique is the adapti v e neuro-fuzzy inference system (ANFIS), outperforming other methods in MPPT controller performance, reducing the response time of PV systems, increasing ef cienc y , and eliminating oscillations. The outcomes of ANNs are v ery similar to those of ANFIS. The fuzzy logic technique (FL) produces good results, b ut its comple x calculation system mak es it tak e too long to compute. Despite their ef fecti v eness in implementing MPP tracking for climate change, con v entional methods e xhibit oscillations around the maximum po wer poi nt. The subsequent sections are or g anized as follo ws: i) Section 2 pro vides mathematical PV modeling; ii) F ollo wed by an o v ervie w of the se v eral MPPT approaches used in section 3; ii i) Section 4 describes the suggested PV system; i v) The simulation results are pro vided and analyzed in section 5; and v) The document is concluded in section 6. 2. MA THEMA TICAL PV MODELING A PV panel mathematical model describes the electrical properties of a PV generator in terms of ph ysical and en vironmental f actors, such as solar irradiation and temperature. A single-diode model [26]- [28] sho wn in Figure 1 is commonly used to simulate photo v oltaic panels, and is described by an equation that relates the current and v oltage characteristics of the panel under v arying weather conditions. The current produced by the PV cell, I pv , is deri v ed using Kirchhof f ’ s current la w , accounting for the photocurrent I ph , the diode current I d , and the shunt current I sh . This relationship is gi v en by (1). I pv = I ph − I d − I sh (1) The (2) e xpresses photocurrent, I ph , in terms of temperature and solar irradiation. I ph = [ I sc + K i ( T amb − T r ef )]( G/G r ef ) (2) Where I sc : short circuit current under standard test conditions (STC), (1000 W/m², 25 °C, AM1.5 spectrum); K i : is the temperature coef cient of the cell; T amb and T r ef : are w orking temperature and reference tem- perature in K elvin respecti v ely; G and G r ef : are w orking irradiance and reference irradiance respecti v ely G r ef = 1000 W /m 2 . The diode current is dened by (3). I d = I s exp q V d aK T − 1 = I s exp q ( V pv + R sI pv ) aK T − 1 (3) Int J Po w Elec & Dri Syst, V ol. 16, No. 1, March 2025: 55–69 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 57 Where, q : Electron char ge (1 . 6 . 10 − 19 C); K : Boltzmann constant (1 . 38 . 10 − 23 Joules/K elvin); a : Ideality f actor; and T : PV temperature in K elvin. The diode saturation current I s , can be determined using (4), where I r s is the re v erse saturation current gi v en by (5), and the relationship with temperature is go v erned by the e xponential term. I s = I r s . T amb T r ef 3 exp q E g ( 1 T r ef − 1 T amb ) aK (4) I r s = I sc exp ( q V oc N s aK T ) − 1 (5) Where E g : is the semiconductor bandg ap ener gy=1.1 eV for S i . The (6) represents the shunt resistance current I sh , which is found by the la w of node. I sh = V pv + R s .I pv R sh (6) The nal relation of cell current I pv gi v en in (7) can be obtained by substituting (3) and (6) in (1). I pv = I ph − I s exp q ( V pv + R sI pv ) aK T − 1 − V pv + R s .I pv R sh (7) In order to increase the electricity produced by photo v oltaic con v ersion, man y cells are associated in series and parallel [29] as illustrated i n Figure 2. N s and N p present the numbers of series and parallel cells. The current and v oltage deli v ered by the PV array are e xpressed as in (8) and (9). I a = N p .I pv (8) V a = N s .V pv (9) The photo v oltaic array’ s current is gi v en by (10). I a = N p I ph − N p I s exp q ( V a + N s N p R s I a ) N s aK T − 1 − V a + N s N p R s I a N s N p R sh (10) The current-v oltage characteristic of a solar panel describes the relationship between the current and v oltage it produces sho wn in Fi gure 3. Se v eral k e y electrical properties dene a solar panel’ s performance, including open circuit v oltage ( V oc ), short circuit current ( I sc ), and maximum po wer point (MPP). Solar panel output is af fected by tw o main f actors: solar irradiance and temperature. When solar irradiance decreases at a constant temperature of 25 °C, the panel output declines as sho wn in Figure 3(a). On the other hand, when the temperature rises at a constant irradiance of 1000 W/m², the v oltage decreases while the current remains steady as seen in Figure 3(b). Figure 1. Solar cell circuit diagram Figure 2. Solar PV array formation Advancing solar ener gy harvesting: Articial intellig ence appr oac hes to ... (Meriem Boudouane) Evaluation Warning : The document was created with Spire.PDF for Python.
58 ❒ ISSN: 2088-8694 (a) (b) Figure 3. I pv - V pv PV panel’ s characteristics: (a) with a steady temperature of 25 °C and (b) with a steady irradiation of 1000 W/m² 3. STRA TEGIES FOR MAXIMUM PO WER POINT TRA CKING 3.1. Maximum po wer point tracking (MPPT) Figure 4 illustrates the po wer output of a PV panel as a function of the v oltage at its terminals; this is distinguished by a peak in panel po wer output. Figures 4(a) and 4(b) indicate that MPP changes with weather conditions, so the MPPT approach is critical to k eeping systems w orking at this optimum position. This sub-section presents v e techniques de v eloped in this w ork, enabling MPPT . MPPT commands de v eloped are classical and intelligent. Classical perturbation and observ ation (P&O), incremental conductance (IC), intelligent fuzzy logic (FL), articial neural netw orks (ANNs), and adapti v e neuro-fuzzy inference system (ANFIS) methods are used rst. (a) (b) Figure 4. P pv - V pv PV panel’ s characteristics: (a) with a steady temperature of 25 °C and (b) with a steady irradiation of 1000 W/m² 3.2. Classical techniques 3.2.1. P erturb and obser v e (P&O) P&O is a commonly used approach to MPPT research, because it’ s simple and only requires v oltage and current measures of PV generator V pv , I pv [30], [31]. The o wchart of the P&O algorithm is illustrated in Figure 5. Il operates with a x ed step size. This algorithm is based on perturbation of PV panel v oltage, then calculates PV panel po wer P pv ( k ) at time k, and com pares it with pre vious time P pv ( k − 1) which determines whether the deri v ati v e of po wer is positi v e or ne g ati v e. A positi v e deri v ati v e means the operating point is approaching the MPP , the search direction is retained. When the operating point e xceeds MPP , the po wer deri v ati v e becomes ne g ati v e, and the search direction must be re v ersed to mo v e back to MPP . The direction of searching denes whether the control is increasing or decreasing duty c ycle D. At maximum po wer , the po wer deri v ati v e is null. 3.2.2. Incr emental conductance (IC) The IC algorithm is also based on the v ariation of module po wer with v oltage [10], [31]. The po wer v ariation is gi v en by (11), solving this e q ua tion equal to zero at MPP as (12) sho ws, positi v e to the left according Int J Po w Elec & Dri Syst, V ol. 16, No. 1, March 2025: 55–69 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 59 to (13) and ne g at i v e to the right of maximum according to (14). The o wchart of the IC algorithm is presented in Figure 6. dP dV = d ( V I ) dV = I + V dI dV = I + V ∆ I ∆ V (11) From the relation abo v e we nd (12)-(14). ∆ I ∆ V = − I V at MPP (12) ∆ I ∆ V > − I V on MPP’ s left (13) ∆ I ∆ V < − I V on MPP’ s right (14) Figure 5. The P&O o wchart Figure 6. The IC o wchart Advancing solar ener gy harvesting: Articial intellig ence appr oac hes to ... (Meriem Boudouane) Evaluation Warning : The document was created with Spire.PDF for Python.
60 ❒ ISSN: 2088-8694 3.3. Intelligent techniques 3.3.1. Fuzzy logic (FL) FL is an articial intelligence technique inspired by human reasoning formalism that introduces lin- guistic v ariables and rules. MPPT fuzzy controllers are implemented in three phases: fuzzication, inference, and defuzzication [21], [32]. Figure 7 sho ws the fuzzy controller structure. Fuzzication is the transformation of numerical v ariables to fuzzy v ariables (linguistic v ariables) by associating truthfulness rules with them. In fuzzy inference, rules (and results) are constructed based on lin- guistic v ariables, each rule is assigned a truthfulness v alue, and the rules are then aggre g ated to obtain a single (linguistic) result. In defuzzication, a linguistic result is con v erted to a numerical result. E is error represents the slope of the (P , V) curv e and CE is v ariation of error , as pro vided by (15) and (16), respecti v ely . E ( k ) = ∆ P ( k ) ∆ V ( k ) = P ( k ) − P ( k − 1) V ( k ) − V ( k − 1) (15) C E ( k ) = E ( k ) − E ( k − 1) (16) Input linguistic v ariables are e xpressed as ne g ati v e big (NB), ne g ati v e small (NS), zero (Z), positi v e small (PS), and positi v e big (PB). The output v ariable is e xpressed as zero (Z), small (S), medium (M), big (B), and v ery big (VB). The follo wing T able 1 presents a list of v arious rules emplo yed in fuzzy controller . Then Figure 8 sho ws the structure of membership functions E, CE, and D. T able 1. Fuzzy control rules E C E NB NS Z PS PB NB Z Z Z B M NS Z Z S M B Z Z S M B VB PS S M B VB VB PB M B VB VB VB Figure 7. Fuzzy controller structure Figure 8. E(k), CE(k), and D membership functions Int J Po w Elec & Dri Syst, V ol. 16, No. 1, March 2025: 55–69 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 61 3.3.2. Articial neural netw orks (ANNs) ANNs are one of the most po werful articial intelligence techniques. ANNs are inspired by the processing methodology of the human brain and ha v e yielded the best results in man y applications, including controlling MPPT in PV systems [33]-[35]. The basic element of the articial neural netw ork is the articial neuron sho wn in Figure 9, which is a mathematical model of biological neuron. It’ s composed of three basic elements: a set of connections to v arious inputs x i each with a weight ω i , a summator to calculate a linear combination of inputs x i weighted by coef cients ω i e xpressed by (17), and an acti v ation function f to delimit the neuron’ s output y . S = n X i =1 ω i .x i − ω 0 (17) Neuron output y equals the acti v ation function v alue gi v en by (18). The acti v ation functions commonly used are the Hea viside and Sigmo ¨ ıde function. y = f n X i =1 ω i .x i − ω 0 (18) Neural netw orks are structured by some nodes (neurons) interconnected by directional conn e ctions. Ev ery node is a processing unit, with links representing causal relationships between nodes. The nodes are or g anized as layers, illustrated in Figure 10 input, hidden, and output layers [23], [24]. The ANNs principal task is t he learning process, performed through an iterati v e process of adaptation of weights ω i to achie v e optimal function output D for each input combination (G, T). ω i v alues are randomly initialized and error - corrected between D i v alues obtained and those e xpected. Figure 9. Articial neuron structure Figure 10. ANN structure 3.3.3. Adaptati v e neur o-fuzzy infer ence system (ANFIS) ANFIS is an articial neural netw ork based on the fuzzy inference system. Combine the adv ant ages of both complementary techniques neural netw ork learning capability plus fuzzy logic e xibility and read- ability [21], [25]. ANFIS-MPPT controller is one of the strongest controllers for a PV system, featuring less uctuations around MPP optimized point, f ast tracking speed, and short computation time. ANFIS Simulink model controller is presented in Figure 11(a). ANFIS adapti v e netw ork consis ts of a multi-layer netw ork. Figure 11(b) illustrates the ANFIS controller structure used in this w ork, which is composed of v e layers. Layer 1 contains syst em inputs (irradiation G, temperature T). Layer 2 ”fuzzies” inputs G and T . Each node in this layer calculates the membership de grees of input v alues using membe rship functions. Six triangular membership functions are used, three for irradiation and three for temperature, as illus trated in Figures 11(c) and 11(d). Layer 3 is a fuzzy rules layer . Layer 4 enables normalization and computes output rules. The output (”summing”) layer contai ns a single neuron that pro vides the ANFIS output by summing the outputs of all defuzzication neurons. Advancing solar ener gy harvesting: Articial intellig ence appr oac hes to ... (Meriem Boudouane) Evaluation Warning : The document was created with Spire.PDF for Python.
62 ❒ ISSN: 2088-8694 (a) (b) (c) (d) Figure 11. ANFIS: (a) Simulink model controller , (b) controller structure, (c) membership function of irradiation, and (d) membership function of temperature 4. PR OPOSED PV SYSTEM The PV system recommended in this study is illustrated in Figure 12. It comprises a PV generator , resistor load, and DC/DC boost chopper dri v en by an MPPT controller . MPPT control is necessary to push the PV panel to run and e xtract maximum po wer under v arious weather situations. In this w ork, v e distinct MPPT approaches were de v eloped. The MPPT controller continuously recei v es v oltage and current measurements from the PV generator and adjusts duty c ycle D of the pulse width modulation (PWM) signal produced by the PWM generator . The system has been e xamined using MA TLAB-Simulink. 4.1. PV panel In this research, the simulation is performed using an API-M260 PV module. This PV module is tested under v arious irradiance and temperature conditions. T able 2 lists the major technical specications for this PV module. 4.2. DC-DC boost chopper A DC-DC chopper is an electronic po wer circuit that connects the PV generator to the load [36], [37]. The selected con v ert er is the boost, the relationship between v oltage a n d current input and output is determined by (19) and (20). Its main components are an inductor , tw o capacitors, and a transistor . A high-frequenc y switching signal (PWM) applied to the transistor g ate controls po wer transfer between the PV generator and the load. The electrical parameters for the boost con v erter are sho wn in T able 3. V out = V pv 1 − D (19) I pv = I out 1 − D (20) Where V pv and V out are PV panel and chopper output v oltages respecti v ely; I pv and I out are PV panel and chopper output currents respecti v ely; and D is the switching period’ s duty c ycle. Int J Po w Elec & Dri Syst, V ol. 16, No. 1, March 2025: 55–69 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 63 Figure 12. PV system diagram T able 2. PV panel electrical parameters under standard test conditions (STC) Electrical parameter Theoretical v alue Maximal po wer ( P max ) 260 W V oltage at maximal po wer ( V mpp ) 30.6 V Current at maximal po wer ( I mpp ) 8.5 A Open circuit v oltage ( V oc ) 37.8 V Short circuit current ( I sc ) 8.8 A T emperature coef cient of V oc − 3 . 564 . 10 − 1 % / ◦ C T emperature coef cient of I sc 5 . 3727 . 10 − 2 % / ◦ C T able 3. Boost con v erter’ s electrical parameters Electrical parameter V alue Input capacitor ( C in ) 1 mF Output capacitor ( C out ) 220 µF Inductor ( L ) 18 mH Switching frequenc y f 10 KHz 5. RESUL TS AND DISCUSSION Simulation of the PV system m odel has been performed on MA TLAB-Simulink softw are, as sho wn in Figure 13. Simulation is run for all v e MPPT control methods de v eloped in this w ork: P&O, IC, FL, ANNs, and ANFIS. The P&O, IC, and FL controllers ha v e the same inputs v oltage V pv and current I pv , whereas ANNs and ANFIS controllers ha v e i nputs are irradiation G and temperature T . T o e v aluate the performances of the v arious controllers, the model is simulated and tested under v arious weather conditions, as sho wn in Figure 14. During time interv al [0, 0.5 s] the PV generator is operated at standard weather test conditions ( G = 1000 W /m 2 , T=25 °C. The temperature remains constant during the interv al [0.5 s, 1 s], while irradiance decreases to 600 W /m 2 . The drop conti nues at 300 W /m 2 for 32 °C at interv al [1 s, 1.5 s]. At temperature 30 °C, irradiation increases to 700 W /m 2 during [1.5 s, 2 s]. In the interv al [2s, 2.5 s] the irradiance decreases to 500 W /m 2 at 27 °C. Lastly , the temperature remains constant as irradiance increases to 900 W /m 2 during [2.5 s, 3 s]. T o v erify the comparati v e performance for a more formal tone between the v e controllers, simulation results illustrated in Figure 15 are analyzed belo w . Simulation results of po wer pro vided by PV panels under dif ferent weather conditions are sho wn in Figure 15. All v e MPPT controllers demonstrated their capacity to track the maximum po wer point (MPP) under sudden changes in irradiance and temperature. The po wer outputs consistently con v er ged to w ard theo- retical maximum v alues, with v arying le v els of ef cienc y and stability across the dif ferent algorithms. High oscillations are observ ed for P&O control follo wed by the IC method, reduced by FL control, and almost zero for ANNs and ANFIS techniques. T racking time is the longest for the IC method, which is its main dra wback, whereas all other methods ha v e comparable response times. Numerical simulation v alues for maximum po wer are gi v en in T able 4. PV generator ef cienc y , po wer o v ershoot, po wer undershoot, and ripple around maximum po wer point (MPP) are also mentioned. PV generator operates under theoretical MPPT for all tested methods Advancing solar ener gy harvesting: Articial intellig ence appr oac hes to ... (Meriem Boudouane) Evaluation Warning : The document was created with Spire.PDF for Python.
64 ❒ ISSN: 2088-8694 (P&O, IC, FL, ANNs, and ANFIS) with acceptable error le v els, lo west errors are found for ANNs and AN- FIS methods. Ef cienc y is abo v e 99% for all methods studied in this w ork. No o v erruns are observ ed, and underruns are reasonable for all orders. The FL, ANNs, and ANFIS intelligent methods are the closest to the optimum. The ANNs and ANFIS techniques ha v e v ery close results, the best being ANFIS. Numerical ripple v alues of P&O control are greatest among other techniques, re aching 0.23 W . ANNs and ANFIS approaches ha v e the lo west ripple v alues, ranging between 0.0013 W and 0.005 W for ANNs and from 0.001 W to 0.007 W for ANFIS. Figure 13. PV system model simulation Figure 14. Inputs weather conditions for PV generator Figure 15. Output po wer for algorithms MPPT proposed under v arious climatic conditions Classical control methods of fer contrasting adv ant ages for a more precise description: P&O is char - acterized by high oscillations, while its response time is lo wer than IC’ s. FL combines the tw o adv antages of lo w oscillations and comparable response time to PO. In this study , ANNs and ANFIS approaches ha v e the lo west response times, and v alues are v ery close. ANFIS is the best for this criterion. Results are gi v en in T able 5. PV panel electrical v oltage and current w a v eforms at maximum po wer point (MPP) are sho wn in Figure 16. Numerical results are close to theoretical results for Impp current and Vmpp panel v oltage under dif ferent Int J Po w Elec & Dri Syst, V ol. 16, No. 1, March 2025: 55–69 Evaluation Warning : The document was created with Spire.PDF for Python.