An Enhanced MPPT Method based on ANN-assisted Sequential Monte Carlo and Quickest Change Detection

1 An Enhanced MPPT Method based on ANN-assisted Sequential Monte Carlo and Quickest Change Detection Leian Chen and Xiaodong W ang*, F ellow , IEEE Abstract The performance of a photo voltaic system is subject to varying en vironmental conditions, and it becomes more challenging to track the maximum power point (MPP) and maintain the optimal performance when partial shading occurs. In this paper , we propose an enhanced maximum po wer point tracking (MPPT) method utilizing the state estimation by the sequential Monte Carlo (SMC) filtering which is assisted by the prediction of MPP via an artificial neural network (ANN). A state-space model for the sequential estimation of MPP is proposed in the framework of incremental conductance (I-C) MPPT approach, and the ANN model based on the observ ed voltage and current or irradiance data predicts the global MPP (GMPP) to refine the estimation by SMC. Moreover , a quick irrandiance change detection method is applied, such that the SMC-based MPPT method resorts to the assistance from ANN only when partial shading is detected. Simulation results sho w that the proposed enhanced MPPT method achiev es high efficiency and is robust to rapid irradiance change under different noise lev els. Index T erms Photov oltaic (PV) systems, partial shading, maximum po wer point tracking (MPPT), sequential Monte Carlo, artificial neural network, quickest change detection. I . I N T RO D U C T I O N The photo voltaic (PV) technology that harnesses the solar energy to generate electricity has experienced a rapid growth in deployment ov er the past years. Since the ef ficiency of power * Corresponding author . L. Chen and X. W ang are with the Department of Electrical Engineering, Columbia Univ ersity , New Y ork, NY , 10027 USA (e-mail: chen.leian@columbia.edu, wangx@ee.columbia.edu). March 16, 2018 DRAFT transfer from the PV cell depends on both the amount of solar irraidance receiv ed by PV panels and the electrical characteristics of the load, it is important to maximize po wer e xtraction under all conditions. As the amount of solar irradiance varies o ver time, and so doest the load characteristic that gives the highest power transfer efficienc y . The maximum po wer point tracking (MPPT) technique tracks the load characteristic (called maximum power point (MPP)) that maximizes the power . A. Related W orks MPPT methods can be generally classified into two categories: con ventional methods (e.g., the Perturbation and Observation (P&O) method, the Incremental Conductance (I-C) method), and adv anced methods (e.g., methods based on fuzzy logic (FL) based, artificial neural network (ANN) based and particle swarm optimization (PSO)). The con v entional MPPT methods are widely used since they are generally simple and cheap. Both P&O [1]–[3] and I-C [4]–[6] methods control the reference signal of a DC-DC con verter that matches the PV module voltage with that of the DC b us or works as a battery char ge. In the P&O method, the controller adjusts the voltage by a small amount from the array and observes the po wer change; if the po wer increases, it adjusts the operating voltage in that direction until the output po wer no longer increases. The I-C method is based on the fact that the slope of the po wer -voltage curve characterizing the PV array is zero at the MPP , positive on the left, and negati ve on the right of the MPP . The controller measures the incremental changes in PV array current and voltage to predict the effect of a voltage change. Ho we ver , the con ventional methods are not efficient and can e ven fail under some special conditions, such as an abrupt irradiance change due to shadings. Therefore, more intelligent MPPT techniques have been proposed for better transient and steady-state performance. FL MPPT controllers [7] [8] does not need an accurate mathematical model and can work with imprecise measurement inputs. V ariations of the PSO based methods are proposed in [9]– [13], where the controller searches the optima in a population of potential solutions (particles). ANN-based methods [14] [15] hav e sho wn good performance under rapidly varying irradiance, especially in terms of efficienc y and quick response. [16] presents a reinforcement learning based MPPT method that observ es the en vironment state of the PV array in the training process and autonomously adjusts the perturbation to the online operating voltage. Note that despite of the higher efficienc y , these advanced approaches are much more complex compared to the con ventional techniques. Moreover , the performance of the machine learning approaches is heavily dependent on the accuracy of the trained model that is determined by the quality of training data. B. Our Contributions W e aim to find a cost-effecti ve MPPT method by exploiting the advantages of both the con ventional and adv anced approaches. The contribution of our proposed MPPT method is three fold. 1) T o the best of our kno wledge, it is the first time that an sequential Monte Carlo (SMC) method is applied under the framew ork of I-C approach to tackle the nonlinearity when the step-size of voltage adjustment is time-varying. 2) Considering the challenge of partial shading which leads to multiple local optimal operation points, we further adopt the ANN method based on multiple measurement inputs for refinement in the SMC-based I-C method to find the global optimal operation point more efficiently . 3) Moreov er , to spare the redundant ANN predictions when the receiv ed irradiance is steady , the ANN prediction is triggered only when the proposed GLLR detector declares an irradiance change. The intelligent integration of our SMC-based I- C approach and the refinement by ANN provides an efficient and economical MPPT solution. Extensi ve simulation results demonstrate that our method is robust to the various shading patterns and process noises. The remainder of the paper is organized as follo ws. Section II introduces the mathematical model for PV systems, and the state-of-the-art three-component MPPT framework. In Section III, we present our proposed enhancements to the three-component MPPT approach. In Section IV , the proposed method is applied to a simulated partially shaded PV system and its performance is compared with the existing ANN-based MPPT methods exploiting the observations of the irradiance in [14] or the voltage and current in [15]. Section V concludes the paper . I I . B A C K G RO U N D O N M P P T F O R P V S Y S T E M S In this section we first gi ve an overvie w of the structure of an PV system and present the analytical model characterizing the circuits that generate the electricity . W e then briefly summarize the three-component framework of MPPT under partial shading adopted in [15] [14] that mak es use of ANN to assist the con ventional approaches (e.g., I-C and P&O). Finally we highlight our proposed enhancement to each one of the three components of the frame work. A. Overview of PV Systems and the Analytical Model PV systems harvest the energy from sunlight to generate electricity via an electronic process in semiconductors. As sho wn in Fig. 1, a typical PV system for residential or industrial electricity supply usually consists of the PV array which generates electricity directly from sun irradiance, and other follo w-up components which are often referred to as “balance of components” (BOC). An M × N PV array is composed of numerous PV cells which are encapsulated into PV modules. N modules are first serially connected as a string to accumulate the desired output voltage and then M strings are connected in parallel to increase the output current. T o utilize the electricity generated by PV arrays, the BOC transforms and stores the energy into the form that can be directly delivered for daily applications. The BOC basically includes the mounting structures to fix and direct PV modules towards the sun, the DC-AC con verters (also known as in verters) for applications requiring A C, the MPPT components for adjusting the operating voltage and current, the batteries for energy storage, and a charger regulator for smooth operation of the PV system. Since the PV array determines the efficienc y of transforming the solar energy into electricity , it is of fundamental interest to characterize the relationship between the receiv ed irradiance at a gi ven PV cell and the corresponding output power . V arious analytical models have been proposed to characterize the circuits in a PV cell. In this paper, we utilize a typical equiv alent single diode circuit model shown in Fig. 2, where V P V and I P V denote the output voltage and current respectiv ely , R s is the series parasitic resistance, and R p is the parallel parasitic resistance. Since typically R s is very small and R p is very large, they are ne gligible. The simplified model is gi ven as [17] I P V = I ph − I sc,S T C exp ( q kT B ) h exp  q kT B V P V V oc,S T C  − 1 i , (1) I ph = I ph,S T C + K I ( T − T S T C ) λ λ S T C , (2) where the definitions of parameters are giv en in T able I. In this paper , we set B = 0 . 2464 as suggested in [6]. Note that, in (1) and (2), the only v ariables are the instantaneous irradiance λ and temperature T , and the corresponding output voltage V P V and current I P V ; the other parameters are constants determined by the hardw are attributes. M o d u l e 1 M o d u l e N M o d u l e 2 M o d u l e N - 1 M o d u l e 1 M o d u l e N M o d u l e 2 M o d u l e N - 1 M o d u l e 1 M o d u l e N M o d u l e 2 M o d u l e N - 1 S t r i n g 1 S t r i n g 2 S t r i n g M + - M P P T M e a s u r e m e n t s   ˆ ˆ , PV PV VI D C - A C C o n v e r t e r L o a d R e f e r e n c e v o l t a g e V Fig. 1. Illustration of a PV system. The shaded blocks denote the PV module under partial shading. Fig. 2. Equi v alent circuit of a PV array . B. Thr ee-component MPPT F r ame work The task of the MPPT block in a PV system sho wn in Fig. 1 is to obtain the maximum po wer output by finding the optimal operating v oltage and the corresponding operating current re gulated by (1). Specifically , gi v en a certain sampling frequenc y f s , the MPPT block monitors the output po wer of a gi v en PV system (including the measured noisy v oltage b V P V ( t ) and the current b I P V ( t ) ) for each time instant t , estimates the optimal operat ing v oltage V ( t + 1) leading to the MPP , and then adjusts the system accordingly to closely follo w the MPP under dynamic en vironmental conditions. T ABLE I P A R A M E T E R S I N T H E S I M P L I FI E D P V C I R C U I T M O D E L Parameter Definition V P V , I P V Output voltage and current of the PV array I ph , I ph,S T C Photo-generated current under operation and standard test conditions (STC), i.e., at 1kW/m 2 and 25 ◦ C I sc,S T C Short circuit current measured at STC T T emperature under operation V oc , V oc,S T C Open circuit voltage under operation and STC λ , λ S T C Irradiance under operation and STC in kW/m 2 K I T emperature coefficient of short-circuit current q Electron charge k Boltzmanns constant Fig. 3. Flowchart of the three-component MPPT method. Con ventional methods (P&O, I-C, etc.) only relies on the analytical model in (1)-(2) and the observation data to determine the next adjustment, and they tend to fail when the PV system is subject to rapid en vironmental change. Recent works hav e proposed a three-component MPPT framew ork illustrated in Fig.3 to ov ercome the drawbacks of con ventional approaches by making use of machine learning tools [14] [15] [16]. Generally , the three components tackle the problems of the detection of partial shading, (local) optimal operating voltage estimation based on conv entional methods and the prediction of the global MPP (GMPP) using machine learning methods, respectiv ely . In particular , in [14] [15], given an online measurement at time t , the controller decides whether the ANN prediction needs to be triggered due to an abrupt irradiance change. If so, the prediction from ANN will refine the estimation of the operating voltage at t + 1 via con ventional methods; otherwise, only the conv entional I-C or P&O methods is implemented under the assumption of steady en vironmental conditions. Finally , the controller directs the system to operate at the estimated voltage and observes the output power at t + 1 . C. Pr oposed Enhancements In this paper , we also adopt the three-component frame work but we propose ne w method for each component to enhance the overall MPPT performance. 1) For irradiance change detection, the simple threshold-based detection rule in [14] only relies on the difference between two consecutiv e power measurements and tends to have lar ge detection delay when a long false alarm period is desired. Since the power readings are not constant due to measurement noise, we need to distinguish the abnormal fluctuation due to partial shading or other faulty conditions from the noisy measurements, and quickly detect any small faulty signal gi ven a certain false alarm period. In this work, we propose to employ the sequential change detection technique for this purpose. 2) For the optimal operating voltage estimation, [14] [15] simply use an I-C method with the kernel of v oltage transition model giv en by V ( t + 1) = V ( t ) + m 0 dP ( t ) dV ( t ) , (3) where m 0 is a step-size constant, and dP ( t ) dV ( t ) is the slope of the po wer -vs-voltage (P-V) curve illustrated in Fig. 4. On one hand, the controller does not adjust the operating voltage when dP ( t ) dV ( t ) = 0 indicating the peak in the P-V curve. Ho we ver , the efficienc y can be further improv ed by using a v ariable step-size. Intuiti vely , giv en the prediction of the GMPP , we can use a relati vely large step-size when the current operating voltage is f ar from the GMPP and a small step-size otherwise. On the other hand, note that the output current I P V and the v oltage V P V in (1) are 0 5 10 15 20 25 30 35 40 0 5 10 Current (A) 0 5 10 15 20 25 30 35 40 Voltage (V) 0 100 200 300 Power (W) (a) I-V and P-V characteristics under uniform irradiance. 0 5 10 15 20 25 30 35 40 0 5 10 Current (A) 0 5 10 15 20 25 30 35 40 Voltage (V) 0 50 100 Power (W) V max V min (b) I-V and P-V characteristics under partial shading. Fig. 4. I-V and P-V characteristics of a 3-panel PV system under different irradiance conditions. The red dot denotes the global MPP point assumed to be noise-free while only noisy measurements can be obtained in real PV systems and the predicted V ( t + 1) in (3) is not the true (noise-free) optimal operating voltage. Since we can nev er tell if the MPP is achie ved gi ven a single noisy measurement, we need to sequentially estimate the reference voltage V ( t ) (a noise-free state v ariable) which leads to MPP at each sampling instant t . The controller iterati vely tunes the operating voltage gi ven the current estimate of V ( t ) , and updates the estimate with ne w measurements at t + 1 . When the voltage transition model becomes nonlinear as we adopt a v ariable step size, the v oltage estimation based on the basic I-C method is no longer effecti ve, which necessitates the adoption of nonlinear estimation approach. 3) T o tackle the MPPT under partial shading when multiple peaks occur in the P-V curve as in Fig. 4(b), the ANN is used in [14] [15] to predict the GMPP and forces the I-C estimation within in the region of GMPP , ( V min , V max ) . In this paper , we adopt an ANN model with the input data from a short sequence of voltage and current measurements or se veral irradiance measurements from different PV panels. In comparison with [14] and [15] where only the instantaneous total voltage and current or irradiance measurements are used, the prediction of our ANN model is more robust especially when the measurements are noisy . I I I . P RO P O S E D E N H A N C E D M P P T Based on the above analytical system model, an improved MPPT method under partial shading is de veloped. W e first giv e an ov ervie w of the proposed method and then specify the detailed steps. Follo wing the three-component framework in Fig. 3, we propose to replace each component by some more advanced module. In particular , for the irradiance change detection component, we propose to employ the sequential GLLR change detection; for the nonlinear local MPP estimation, we adopt the sequential Monte Carlo method; for the GMPP prediction, a trained ANN model based on multiple local measurements is triggered when an irradiance change occurs. The overall MPPT block works as follo ws. First, the measurements (e.g., power , v oltage, current, irradiance) are acquired by the MPPT controller . Whene ver the proposed GLLR change detector does not declare an abrupt power variation, we assume that the P-V curve maintains the same shape as in the previous sampling cycle, and the MPP is tracked by the SMC-based method. If the change detector declares an abrupt po wer fluctuation due to partial shading, the ANN-assisted MPPT algorithm is triggered. The trained ANN model utilizes a small group of se veral local measurements as the input and predicts the GMPP under the current shading condition. Then, refined by the prediction of ANN, the SMC-based I-C algorithm updates the voltage estimation. Finally , the controller steers the operating point to the estimated optimal voltage b V ( t ) and waits for the next MPPT cycle. In the follo wing subsections, we first present the GLLR-based quickest change detection method, then describe the voltage state estimation by SMC gi ven the input from the ANN, and finally specify the GMPP prediction method by ANN. A. GLLR Change Detector Con ventionally , the MPPT is continuously run whenev er the PV system is under operation, which is not economical since normally the output po wer does not exhibit dramatic changes with steady irradiance input during which the MPPT is redundant. Existing works have proposed some simple rules to trigger the ANN prediction in MPPT . For example, in [14], the ANN is implemented to assist the con ventional P&O and I-C methods when the dif ference between adjacent power measurements | P ( t ) − P ( t − 1) | exceeds a predetermined threshold. Such a method is quite ad hoc and is not ef fecti ve in fast detection of partial shading. Here we propose a principled approach to detecting the abnormal fluctuation in the framew ork of sequential quickest change detection [18]. In what follo ws, we first formulate the problem of sequential irradiance change detection based on the vector autore gressi ve (AR) model. Then a quickest f ault detection method based on the GLLR test is presented. W e assume that the statistical properties of the measurement signal (voltage, current or power) under normal conditions, i.e., before the irradiance change, are known (or av ailable from historical data) while properties of the signal after the change are totally unknown. 1) P ower Measurement Models: Our goal is to detect an unknown power shift between dif ferent irradiance conditions. W e assume that the output power of a PV system before an abrupt irradiance change is known. Specifically , when the system is under uniform irradiance with a certain set of en vironmental inputs (irradiance, temperature, etc.), the DC output power should be a constant kno wn by design; when the system is under a relativ ely steady shading condition, the corresponding nominal output power can be approximated by the average meter readings. Then we can subtract the constant from the measured voltage signal to obtain the post-processing signal e P ( t ) that comprises the measurement noise only or possibly a “faulty” signal due to irradiance change. In particular , before the po wer shift occurs at t = t 0 , the post- processing signal consists of the measurement noise ν ( t ) only , which is modeled as a white Gaussian process, i.e., e P ( t ) = ν ( t ) ∼ N (0 , σ 2 ν ) , t < t 0 , (4) where σ 2 ν is the variance. After t 0 , the DC power output is corrupted by both the faulty signal and noise, i.e., e P ( t ) = s ( t ) + ν ( t ) , t ≥ t 0 , (5) where s ( t ) is the disturbance signal caused by the irradiance change. Dif ferent from the mea- surement noise ν ( t ) that is uncorrelated in time, the faulty signal s ( t ) is correlated in time, which is the basis for the GLLR detection scheme in this paper . In particular , we use an autoregressi ve (AR) model to characterize the statistical property of the f aulty signal s ( t ) . The AR model has been employed to characterize the disturbance [19] [20] and inter-area oscillations [21] in power grid systems, the gear tooth fault signals in mechanical systems [22], speech signals [23], etc. Specifically , the faulty signal in the PV system is modeled as s ( t ) = ˜ µ + X p j =1 a ( j ) [ s ( t − j ) − ˜ µ ] + ω ( t ) (6) where p denotes the order of the AR model, ˜ µ is the mean, ω ( t ) is the innov ation noise and a ( j ) , j = 1 , ...p , are the AR coef ficients. Substituting (6) into (5), we have e P ( t ) = µ + X p j =1 a ( j ) e P ( t − j ) + ε ( t ) , t ≥ t 0 (7) where µ , µ [1 − p P j =1 a ( j )] and ε ( t ) = [ ν ( t ) − p P j =1 a ( j ) ν ( t − j ) + ω ( t )] ∼ N (0 , σ 2 ε ) with σ 2 ε = [1 + p P j =1 a 2 ( j )] σ 2 ν + σ 2 ω reflecting the impacts of both the disturbance signal and the measurement noise. 2) GLLR Change Detector: The occurrence of an po wer change of interest is declared at time T via the following sequential change detection procedure, called the generalized local likelihood ratio (GLLR) test [18], g t = ( g t − 1 + l t ) + , (8) T = inf { t : g t ≥ h } , (9) where ( x ) + , max { x, 0 } , g 0 = 0 , h is a threshold determined by the desired false alarm period γ , and l t is the generalized log lik elihood ratio (GLLR) giv en all pre vious measurements by t . As in [24], we aim to detect a small change corresponding to the most challenging scenario, and thus assume that θ 0 ≈ θ 1 where θ 0 and θ 1 denotes the model parameters before and after change. T o that end, l t is approximated by the local second-order expansion of the GLLR by assuming θ 1 → θ 0 , giv en by l t ≈ b k ˜ z t k − 1 2 b 2 , (10) where k·k denotes the vector l 2 -norm, b > 0 is a predetermined parameter reflecting the deviation of the output power , and ˜ z t =      1 σ 2 ν e P ( t ) e P t − 1 t − p 1 √ 2  e P ( t ) 2 σ 2 ν − 1  e P ( t ) σ ν      , (11) where e P j i , h e P ( i ) , e P ( i + 1) , ..., e P ( j ) i . Note that whenev er g t exceeds the threshold h at time T , the detector declares an abnormal po wer change and the ANN-assisted MPPT algorithm is implemented. Otherwise, we implement the SMC-based MPPT without the GMPP estimation by ANN, assuming the P-V curve does not change when no irradiance change occurs. The GLLR detector is restarted immediately after the pre vious alarm and the post-processing signals during this detection cycle are obtained by subtracting the new power measurements at time T + 1 . Generally , smaller values of b and h leads to a more “sensitiv e” detector but a false alarm could occur when the irradiance condition actually does not change and the ANN is triggered unnecessarily . The v alue of b is generally set to be proportional to the average drifts of empirical voltage readings (i.e., noise le vel ) when the PV system is under normal operation. Since a large false alarm period is usually preferred, the threshold h is tuned accordingly . B. V oltage State Estimation via SMC W e first present a nonlinear state-space model characterizing the voltage estimation process, and then specify the SMC algorithm based on the defined model. 1) State-space Model: T o adopt the frame work of SMC, we define the voltage state transition model and the measurement model as follo ws. A discrete-time state-space model is considered for a PV system, i.e. the sampling frequency f s is a fix ed constant. Based on the I-C structure in (3), we define the reference voltage V ( t ) as the state variable updated over time and the noisy voltage readings b V P V ( t ) as the measurement variable. Note that V ( t ) is the hypothesized quantity reflecting the estimated GMPP and the operating voltage of the PV system is adjusted to get close to V ( t ) . • State T ransition Model The P-V curv e illustrates that the power increases with a gradual positi ve slope until it reaches a global/local optimal point, and then decreases sharply after that, which inspires the so called incremental conductance (I-C) MPPT method. The I-C method is based on the observation that at the maximum power point, the slope dP /dV P V = 0 and P = I P V V P V . Accordingly , a general form of the voltage estimation model in the I-C approach is giv en as V ( t + 1) = f ( V ( t )) + u ( t ) + w ( t ) =  V ( t ) + m ( t ) dP ( t ) dV P V ( t )  + u ( t ) + w ( t ) , (12) where P ( t ) and V P V ( t ) are the true noise-free power and voltage observ ations; m ( t ) determines the step size of the voltage adjustment, u ( t ) is an external input for refinement (e.g., ANN prediction result), and w ( t ) ∼ N (0 , σ 2 w ) . Given (1), the true instantaneous slope dP ( t ) dV P V ( t ) is expressed by dP ( t ) dV P V ( t ) = dV P V I P V ( t ) dV P V ( t ) = I P V ( t ) + V P V dI P V ( t ) dV P V ( t ) = I P V ( t ) − V P V ( t ) I sc, S T C exp( qB K T ) h q B K T V oc, S T C exp  q B V P V ( t ) K T V oc, S T C  i . (13) Note that, in practice, the value of dP ( t ) dV P V ( t ) can be either directly reported by meters or computed gi ven the observed voltage and current (and thus are noisy). For the latter case, we can use the approximate value d b P ( t ) d b V P V ( t ) . In particular , we propose to employ an adaptiv e step size m ( t ) giv en as m ( t ) , m 0 [ V ( t ) − V E GM P P ( t )] 2 , (14) in contrast with the con ventional methods where the step size is a constant m 0 . The proposed m ( t ) ensures that the step size is relati vely small when the current reference voltage is close to the estimated GMPP V E GM P P , and thus increases the “resolution” of the I-C method. The constant parameter m 0 can be chosen by fitting a sequence of voltage measurements during the MPPT under uniform irradiance to the model in (12) based on the chosen criterion, e.g., the least squares method. The refinement function u ( t ) compensates the gap between the current noisy voltage mea- surement b V P V ( t ) and the latest estimated GMPP V E GM P P ( t ) by ANN, giv en as u ( t ) , h V E GM P P ( t ) − b V P V ( t ) i 1 g t >h . (15) (15) implies the refinement term is nonzero only when an irradiance change is declared. Note that the refinement term u ( t ) effecti vely drives the system to operate at the global optimum in case that the system gets stuck at a local optimum. Algorithm 1 SMC-based State Estimator 1: Initialization: t = 0 , draw N samples,  V ( j ) (0)  N j =1 , according to the prior distribution N ( V 0 , σ 2 0 ) . Set the weight w ( j ) (0) = 1 / N for all j . 2: f or t = 1 , 2 , ... do 3: Generate the current samples V ( j ) ( k ) according to (19). 4: Update the weight w ( j ) ( k ) according to (20) 5: Compute the state estimates, b V ( t ) , according to (22). 6: Perform resampling if b N eff is below a giv en threshold. 7: end for • Measurement Model Since the measured voltage includes the true reference voltage and the noise, the measurement equation is giv en by b V P V ( t ) = V ( t ) + v ( t ) , (16) where v ( t ) ∼ N (0 , σ 2 v ) is a Gaussian measurement noise. Gi ven the input values, b V P V ( t ) , dP ( t ) dV P V ( t ) and u ( t ) , an SMC filtering can be implemented to estimate V ( t ) based on the nonlinear state transition model (12) and the measurement model (16). 2) Online Estimation by SMC: Our proposed MPPT approach is based on the voltage estima- tion by the SMC method. In SMC [25], a set of weighted samples are used to approximate an underlying distribution that is to be estimated. And the samples and their associated weights are sequentially updated based on the new measurements. The proposed SMC-based state estimator is summarized in Algorithm 1. The algorithmic details are presented as follows. • Initialization For t = 0 , dra w N initial samples,  V ( j ) (0)  N j =1 , from the prior probability density function characterized by V 0 and σ 2 0 , i.e., V ( j ) (0) ∼ N ( V 0 , σ 2 0 ) , j = 1 , 2 , ..., N . (17) Set initial weights w ( j ) (0) = 1 / N for all j . Note that the prior distribution N ( V 0 , σ 2 0 ) for drawing the initial samples can be estimated during the offline training process. Specifically , gi ven a set of voltage measurements under normal operation with uniform irradiance, V 0 and σ 2 0 are approximated by the sample mean and variance respecti vely . The number of samples N should be sufficiently large to characterize the distribution of V ( t ) . Numerical studies rev eals that 300 < N < 800 can provide decent estimation accuracy gi ven the computational budget. • Online State Estimation During the online phase, the MPPT controller sequentially updates the state estimate and adjusts the operating voltage accordingly . An SMC update step consists of sample g eneration , weight update , and r esampling , as highlighted in Algorithm 1. Sample generation : The basic idea of SMC is to perform the sequential importance sam- pling (SIS). At each time, N samples  V ( j ) ( t )  N j =1 are drawn from some trial distrib ution π  V ( j ) ( t ) | V ( j ) ( t − 1) , b V P V ( t )  with V ( j ) ( t − 1) ,  V ( j ) (1) , V ( j ) (2) , ..., V ( j ) ( t − 1)  and b V P V ( t ) , n b V P V (1) , b V P V (2) , ..., b V P V ( t ) o . Here we choose the state transition density as the trial distribu- tion, i.e., π  V ( j ) ( t ) | V ( j ) ( t − 1) , b V P V ( t )  , p  V ( j ) ( t ) | V ( j ) ( t − 1)  . (18) Hence according to (13), V ( j ) ( k ) ∼ N  f  V ( j ) ( t − 1)  + u ( t ) , σ 2 w  . (19) W eight update : The corresponding weight w ( j ) ( t ) for sample V ( j ) ( t ) is calculated by w ( j ) ( t ) ∝ w ( j ) ( t − 1) p ( b V P V ( t ) | V ( j ) ( t )) p ( V ( j ) ( t ) | V ( j ) ( t − 1)) π  V ( j ) ( t ) | V ( j ) ( t − 1) , b V P V ( t )  ∝ w ( j ) ( t − 1) p  b V P V ( t ) | V ( j ) ( t )  ∝ w ( j ) ( t − 1) · exp  − 1 2 σ 2 v  b V P V ( t ) − V ( j ) ( t )  2  , (20) where the normalized weight w ( j ) ( t ) is giv en as w ( j ) ( t ) = w ( j ) ( t ) P N j =1 w ( j ) ( t ) . (21) Gi ven the current weighted samples { V ( j ) ( t ) , w ( j ) ( t ) } N j =1 , we can estimate the state variable as b V ( t ) = N X j =1 w ( j ) ( t ) V ( j ) ( t ) . (22) Then the controller sets the operating v oltage to b V ( t ) . Resampling : The resampling step aims to av oid the problem of degenerac y of the SMC algorithm, that is, the situation that all but one of the importance weights are close to zero [26] [27]. The basic solution is to retain the samples with high weights and discard the samples with low weights. The resampling is implemented only when the effecti ve number of samples N eff is below a predetermined threshold N thr . An estimate of N eff is giv en by b N eff = 1 P N i =1  w ( j ) ( t )  2 , (23) which reflects the variation of the weights [26]. If b N eff is less than a gi ven threshold, N thr , we perform resampling to obtain N ne w samples, n e V ( j ) ( t ) o N j =1 , that is, to draw N samples from the current sample set with probabilities proportional to the corresponding weights.. The corresponding weights for the new samples are set as e w ( j ) ( t ) = 1 / N . C. ANN-assisted Maximum P ower P oint Pr ediction As illustrated in Fig. 4, when partial shading occurs, the P-V curve has multiple peaks, and the basic I-C approach without the refinement term u ( t ) can mislead the system to ope rate at the local optimal points when the initial estimation falls out of the global optimal region ( V min , V max ) . T o tackle the disadvantage of the I-C approach, a trained artificial neural network is applied to estimate the global optimum when an irradiance change is detected and thus forces the I-C estimation to fall into the region of GMPP . In particular , we propose to adopt the architecture and inputs specified as follows. 1) ANN Ar chitectur e for MPPT : In this paper , we apply the most popular ANN structure, a multilayered feed-forward neural network (FNN) [28], which consists of an input layer , one or more hidden layers, and an output layer . A neuron is a processing unit that first linearly weights the inputs, then feeds the sum to a nonlinear acti v ation function g ( . ) , and propagates the results to the following neurons [29]. Explicitly , denoting the K incoming signals at a giv en node j as { x 1 ,j , x 2 ,j , ..., x K,j } with the corresponding weights { ω 1 ,j , ω 2 ,j , ..., ω K,j } , the output y j of node j is gi ven as y j = g K X i =1 ω i,j x i,j + α ! , (24) where α is a bias v alue, and the weights associated with the input v alues are adjusted by the learning rule in the training process. V arious acti v ation functions ha ve been proposed, and we utilize the sigmoid functions [29] given as g ( z ) = 1 1 + exp( − z ) , (25) where z , P K i =1 ω i,j x i + α . 2) Input V ariables of ANN: In particular , we consider a multilayer FNN where the neurons of the input layer simply act as buf fers for distributing the input signal and the number of hidden layers is determined in the training phase. For MPPT , the input signals can be PV array parameters (e.g, PV voltages and currents), environmental data (e.g., irradiance and temperature), or any combination of these. The output is usually one or sev eral reference signal(s), such as the estimated GMPP which is used to driv e the electronic con verter to operate at or close to the MPP . T o establish an ANN model for online MPPT , we need to train the model utilizing the input and output data from empirical measurements or model-based simulation results. Here we present two ANN methods for predicting the global optimum using different input data i.e., voltage and current, and irradiance measurements. • ANN based on V oltage and Current Measur ements When the ANN-assisted MPPT is triggered at t , the PV panels are forced to operate M dif ferent voltages by tuning the resistance observed by the PV system at the ne xt M sampling time instants. Essentially , the choice of M online inputs can be randomly generated as along as these v alues fall into the range of possible operating v oltages since the training data for the ANN model should cover the whole scope. T o utilize the current online observ ation, we propose to independently generate M inputs in the interval h b V P V ( t ) − 10 , b V P V ( t ) + 10 i . Then the ANN acquires the output voltage measurements along with the corresponding currents as the input of ANN. In a word, the M online samples { ( V P V ,i , I P V ,i ) } M i =1 are fed to ANN, and the estimated voltage V E GM P P corresponding to the global MPP giv en the current operating condition is the output of the ANN, which is used to refine the estimation by SMC in (15). • ANN based on Irradiance Measurements Owing to the hardw are that supports online irradiance measurements, we can directly model the relationship between the receiv ed solar energy and the output power . The measured irradiance data at dif ferent locations among PV panels serves as the inputs of ANN, i.e., the number of input neurons M equals the number of av ailable local irradiance measurements in a giv en system. Again, the output of the ANN is the estimated optimal voltage V E GM P P . 3) T raining and Selection of ANN models: After setting the number of inputs M , the number of hidden layers, and the number of neuron in the each hidden layer, we can train the giv en ANN model during the of fline phase. First, we need to obtain a set of training patterns (including the measured voltage and current or irradiance and the GMPP obtained via the P-V curve) that cov ers the possible operating conditions. For instance, in a x × y PV array , we manually adjust the operating voltage and current or the input irradiance of each panel by choosing from z possible values, and record the corresponding output GMPPs. Then we ha ve totally z x × y pieces of training data. Then { ω i,j } and α can be obtained based on the training samples, e.g., by using the back-propagation (BP) algorithm with the Le venberg-Marquardt optimization method [14]. In general, the training algorithm is used to find the weights that minimize some o verall error measure such as the mean squared error (MSE). Since e ven with the same training data, the performance varies when we choose dif ference ANN models, we need to find an “optimal” one before the online implementation. T o ev aluate the performances of different ANN models, we first define a key index quantifying the prediction accuracy . • Prediction Quality Index (PQI) Generally , the accuracy of the ANN model can be improv ed when the number of hidden layers and the number of neurons increase, at the cost of computational comple xity . T o assess the prediction accurac y of a giv en ANN model, we define the average prediction quality index (PQI) as [14] P QI = 1 G G X i =1  V E GM P P ,i V GM P P ,i  × 100% , (26) where G is the number of ANN prediction tests, V E GM P P ,i is the estimated GMPP in the i th test, and V GM P P ,i is the true GMPP under the corresponding irradiance condition. • Perf ormance Evaluation based on PQI Here we present the training results of an irradiance-based ANN as an illustrati ve example. In our simulated PV system with 3 × 3 modules specified in T able II, 6 3 × 3 training samples are av ailable when the irradiance of each cell is chosen from 6 possible v alues. In order to ev aluate the accurac y performances of the ANN prediction, different ANN struc- tures hav e been in vestigated. In particular , T able III reports the v ariation ranges related to the number of input PV couples, the number of hidden layers and neurons in the first hidden layer (HL1). The number of neurons in the hidden layers following the first one is set as half of T ABLE II S P E C I FI C A T I O N O F P V M O D U L E S Parameter V alue V oc,S T C 21.06 V I sc,S T C 3.80 A Current at P max ( I M P P ) 3.50 A V oltage at P max ( V M P P ) 17.10 V Maximum power ( P M P P ) 59.90W V oc coef. of temperature ( K V ) 0.084 V/C I sc coef. of temperature ( K I ) 3.3 × 10 − 4 A/C T ABLE III P A R A M E T E R R A N G E S O F A N N M O D E L S Parameter Min. Max. Number of inputs ( ( V P V , I P V ) or irradiance) 3 10 Number of hidden layers 1 4 Size of the first hidden layer 4 20 neuron number in the previous layer . During the training process, each ANN model was trained by using 6 3 × 3 data points. In particular , to apply the BP , the input (i.e., v alues of ( V P V , I P V ) or the irradiance) and the output (i.e., estimated voltage leading to GMPP) obtained from the P-V characteristic curve have been provided to each ANN model 500 times. W ith the trained ANN models, the PQIs were e valuated by simulating 1000 randomly-generated irradiance inputs for each ANN model. For each random experiment, the PQI was calculated based on the reported V E GM P P . Fig. 5(a)-(c) are the plots of the Pareto frontier as a scatter plot matrix which represents a 3-D P areto frontier by showing the v alue of a pair of objecti ve functions in each figure for each solution. Particularly , Fig. 5(a) and 5(b) demonstrate the tradeoff between the number of input pairs and synapsesa gainst the values of PQI, respectiv ely . That is, larger numbers of input pairs and synapses lead to higher prediction accuracy . I V . S I M U L A T I O N R E S U LT S In this section, we present the performance of the proposed method in both small and lar ge simulated PV systems. For each system with different shading patterns (SP), we first show the performance improv ement in each of the three components by comparing with the counterparts in [15] [14], and then ev aluate the overall enhancement by presenting the po wer tracking dynamics of our proposed method in comparison with the methods in [15] and [14]. T o quantify the o verall 2 3 4 5 6 7 8 9 10 11 60 65 70 75 80 85 90 95 100 Number of inputs PQI(%) (a) Number of inputs versus PQI. 0 100 200 300 400 500 600 700 60 65 70 75 80 85 90 95 100 Number of synapses PQI(%) (b) Number of synapses versus PQI. 2 3 4 5 6 7 8 9 10 11 0 100 200 300 400 500 600 700 Number of inputs Number of synapses (c) Number of inputs versus number of synapses. Fig. 5. Scatter plot matrix of the Pareto frontier . ef ficiency of the proposed MPPT algorithm, we run the proposed MPPT method 500 times with the identical setup, and present the ratio V P V ( t ) V GM P P for T shading ≤ t ≤ T GM P P , where V P V ( t ) is the av erage observ ed output v oltage at t , T shading is the time instant when the shading occurs, and T GM P P is the instant when the system arri ves at the new GMPP . A. System Setup In our e xperiments, we simulate different shading conditions in a PV system using the toolbox Simscape Power Systems in Matlab . As illustrated in Fig. 6, the number of PV cells and the input irradiances in each PV array can be tuned to simulate different shading conditions. The input irradiance, and the output power , voltage and current fed into the MPPT algorithm are obtained from the simulated system. The detailed setups to implement the proposed method and other methods for comparison are described belo w . 1) Pr oposed Method: The MPPT controller adjusts the operating voltage ev ery 0.05s, i.e., the sampling frequency f s = 20 Hz. The variance of the process noise σ 2 v is set to 10 − 5 (small PV system) or 10 − 3 (large PV system). The measurement noise variance σ 2 w = 10 − 3 for both systems. For the GLLR change detector , the threshold h is tuned based on the desired false alarm Fig. 6. A simulated PV system under partial shading (four PV panels). period λ . The order of the AR model is set as p = 5 . In particular , to ev aluate the performance of the AR model in characterizing faulty signals, we employed the cross-validation method [30] [24] and compared the model predicted output with the actual output. The numerical results show that the normalized root-mean-squared error (NRMSE) of the AR prediction varies from 12% to 2% for when the order p increases from 1 to 5, which demonstrates the high ef fecti veness of the AR model in characterizing the f aulty signals in PV systems. For the SMC algorithm, the step-size coefficient m 0 = 10 − 2 , the number of samples before and after resampling are set as N = 500 . The initial samples { V ( j ) (0) } N j =1 are drawn from the prior probability density function N ( V 0 , σ 2 0 ) where V 0 is the nominal voltage output under normal operation, and σ 2 0 is approximated by the sample voltage v ariance obtained during the of fline phase. For the ANN models, the number of inputs is 8 for both the voltage-and-current-based and the irradiance-based model, and the number of hidden layer is 2 each with size 20 and 10. 2) Methods for Comparison: Here we briefly describe the methods in [15] and [14] where dif ferent ANN models are integrated with the basic I-C approach. The step size of tuning the reference voltage V ( t ) is ∆ = 0 . 2 × dP ( t ) dV P V ( t ) . • I-C method assisted by voltage-and-curr ent-based ANN [14] In this approach, the PV system only implements the I-C method when two neighboring po wer measurements does not exceed a gi ven threshold, i.e., | P ( t ) − P ( t − 1) | < h 1 . h 1 is tuned such that the false alarm period is also 100s. When the voltage-and-current-based ANN is triggered, the prediction of GMPP by ANN is giv en as a starting point of the I-C method. • I-C method assisted by irradiance-based ANN [15] Here the ANN model utilizes the irradiance measurements from each PV panel. For a fair comparison, the irradiance-based ANN is triggered based the same threshold-based rule in [14]. The outputs of ANN are the minimum and maximum v oltages ( V min , V max ) which form the boundaries of the global peak on the P-V curve (Fig. 4(b)). Whene ver the ANN is triggered, the I-C method is forced to start with the predicted V min . B. MPPT P erformance in a Small PV System In the simulated small PV system, there are 12 PV panels each with size 5 × 1 . The I-V and P- V characteristics under uniform irradiance (1000 W/m 2 ) are shown in Fig. 7(a) where the red dot indicates the maximum power P M P P , 0 = 5 KW with the corresponding voltage V M P P , 0 = 125 V . According to the input irradiance, the PV cells are grouped into three sets with size 5 × 5 , 5 × 5 and 5 × 2 respecti vely . T wo shading patterns (“SP 1” and “SP 2”) are simulated by setting the recei ved irradiance of three PV cell groups as { 1000 W/m 2 , 800 W/m 2 , 500 W/m 2 } or { 1000 W/m 2 , 300 W/m 2 , 200 W/m 2 } , and the corresponding I-V and P-V curves are giv en in Fig.7(b)- (c). The red dots denoting the location of the GMPPs rev eals the optimal operating voltages leading to GMPP , i.e., V GM P P , 1 ≈ 107 V and V GM P P , 2 ≈ 50 V . 1) Component-wise Impr ovements: T ables. IV-VI demonstrate the advantages of three en- hanced components where the results are all based on 500 independent experiments. For the change detection component, as sho wn in T able IV, we ev aluate the resource saving by the GLLR change detection that reduces the number of redundant triggers of the ANN. The sav ed resource is ev aluated by the redundant ANN triggers within the time interval during which the system catches up with the new GMPP after the irradiance change. Specifically , we compared the average number of shading alarms per second N GLLR with that of the threshold- based approach N th gi ven the same detection delay . The rate of resource saving is gi ven by  1 − N GLLR /N th  × 100% . In particular , the rates of resource saving by our GLLR detector are 0 20 40 60 80 100 120 140 160 0 20 40 60 Current (A) 0 20 40 60 80 100 120 140 160 Voltage (V) 0 2000 4000 6000 Power (W) (a) I-V and P-V characteristics under uniform irradiance. 0 20 40 60 80 100 120 140 160 0 20 40 60 Current (A) 0 20 40 60 80 100 120 140 160 Voltage (V) 0 1000 2000 3000 4000 Power (W) (b) I-V and P-V characteristics with SP 1. 0 50 100 150 0 20 40 60 Current (A) 0 50 100 150 Voltage (V) 0 1000 2000 3000 Power (W) (c) I-V and P-V characteristics with SP 2. Fig. 7. I-V and P-V characteristics of a small PV system under different irradiance conditions. The red dot denotes the global MPP point all abov e 36.6% under different detection delays, which demonstrates the high efficienc y of our sequential approach. For the local MPP estimation component, we e v aluate the average delay during which the estimated optimal operating voltage gradually approaches the new MPP , P GM P P , 2 , after the shading pattern changes from “SP 1” to “SP 2”. As shown in T able V, the delays of our proposed SMC are smaller than that of the I-C method in [15] [14]. For the ANN prediction component, T able VI shows the PQIs of our ANN models with multiple ( V P V , I P V ) or irradiance inputs, in comparison with the ANN model based on a single measurement. In general, the PQI v alues of our ANN models is 5% greater than that of the single-measurement based ANN models at least. T ABLE IV I R R A D I A N C E C H A N G E D E T E C T O R P E R F O R M A N C E . Detection delay Rate of resource saving “normal” → “SP 1” “SP 1” → “SP 2” 10 s 36.6% 42.6% 15 s 38.3% 45.4% 20 s 38.1% 46.3% T ABLE V M P P E S T I M ATI O N P E R F O R M A N C E ( F R O M “ S P 1 ” T O “ S P 2 ” ) Po wer Delay SMC I-C 70% × P GM P P , 2 0.06s 0.08s 80% × P GM P P , 2 0.09s 0.13s 95% × P GM P P , 2 0.22s 0.35s T ABLE VI A C C U R AC Y O F A N N P R E D I C T I O N ( F R O M “ S P 1 ” T O “ S P 2 ” ) Input type PQI voltage and current based Irradiance based Multiple inputs 96.2% 94.5% Single input 91.1% 87.7% 2) Overall P erformance: T o present the ef ficiency of the proposed MPPT method, the input irradiances of three PV cell groups were tuned to switch the system mode (“normal” and various “shaded” modes). Fig. 8 shows the tracking dynamics of our method where the system receiv es uniform irradiance until t = 5 . 75 s when the SP 1 occurs, and the SP 2 takes effect at t = 7 . 75 s. In response to the abrupt irradiance change, the output power significantly decreases since the pre vious operating voltage no longer leads to the maximum power under different shading conditions. Then the system using our enhanced MPPT method quickly catches up with the new GMPPs within 0.7s while the delays of the methods in [14] [15] exceed 1s. In this small PV system, the performance difference between the voltage and current-based ANN and the irradiance-based ANN is not obvious. W e obtained the v oltage tracking data in 500 identical experiments where the PV system mode switched from “SP 1” to “SP 2”. Fig. 9 gi ves an a verage efficienc y ev aluation of the proposed 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Time (s) 1000 1500 2000 2500 3000 3500 4000 4500 Power (W) Proposed enhanced MPPT method MPPT method in [14] GMPP (a) Power dynamics with the ANN using voltage measurement. 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Time (s) 1000 1500 2000 2500 3000 3500 4000 4500 Power (W) Proposed enhanced MPPT method MPPT method in [15] GMPP (b) Power dynamics with the ANN using irradiance measurement. Fig. 8. Power dynamics under different irradiance conditions in a small PV system. ( γ = 20 s, σ v = 10 − 5 ). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Delay (s) 0.7 0.75 0.8 0.85 0.9 0.95 1 Proposed enhanced MPPT method MPPT method in [14] (a) A verage ef ficiency performance with the voltage-and-current- based ANN. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Delay (s) 0.7 0.75 0.8 0.85 0.9 0.95 1 Proposed enhanced MPPT method MPPT method in [15] (b) A verage efficiency performance with the irradiance-based ANN. Fig. 9. A verage efficienc y performance in a small PV system ( γ = 20 s, σ v = 10 − 5 ). method. The horizontal axis denoted as “delay” refers to the time interval ( t − T shading ) of 500 voltage measurements { P i ( t ) } 500 i =1 taken at t after the irradiance change at T shading , and the vertical axis presents the corresponding value P ( t ) P GM P P , 2 , P 500 i =1 P ( t ) 500 V GM P P , 2 . It is seen that the delay of the competing methods in [15] [14] is greater than 0.6s. In contrast, our proposed method can achie ve 0 . 95 P GM P P , 2 within 0.28s after the irradiance change and gain the ne w GMPP within 0.5s, and hence exhibits a higher efficienc y . 0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 Current (A) 0 200 400 600 800 1000 1200 1400 1600 1800 Voltage (V) 0 2 4 6 Power (W) 10 5 (a) I-V and P-V characteristics under uniform irradiance. 0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 Current (A) 0 200 400 600 800 1000 1200 1400 1600 1800 Voltage (V) 0 1 2 3 4 Power (W) 10 5 (b) I-V and P-V characteristics with partial shading pattern 1. 0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 Current (A) 0 200 400 600 800 1000 1200 1400 1600 1800 Voltage (V) 0 1 2 3 Power (W) 10 5 (c) I-V and P-V characteristics with partial shading pattern 2. Fig. 10. I-V and P-V characteristics of a large PV system under different irradiance conditions. The red dot denotes the global MPP point C. MPPT P erformance in a Lar ge PV System The large PV system consists of 120 PV panels each with size 50 × 1 , and they are cate gorized into three groups of size 50 × 50 , 50 × 50 and 50 × 20 respecti vely . As shown in Fig. 10(a), under uniform irradiance (1000 W/m 2 ), the maximum power is around 590KW and V M P P , 0 = 1400 V . Fig.10(b)-(c) presents the I-V and P-V characteristics under two shading patterns when the recei ved irradiance of three PV cell groups are set as { 1000 W/m 2 , 600 W/m 2 , 500 W/m 2 } or { 1000 W/m 2 , 500 W/m 2 , 200 W/m 2 } . 1) Component-wise Impr ovements: The performances of each component are giv en in T a- bles.VII-IX. T able VII presents the resource savings by the GLLR change detector with different T ABLE VII I R R A D I A N C E C H A N G E D E T E C T O R P E R F O R M A N C E . Detection delay Resource saving “normal” → “SP 1” “SP 1” → “SP2” 10 s 34.6% 41.6% 15 s 37.3% 42.4% 20 s 37.6% 43.3% T ABLE VIII M P P E S T I M ATI O N P E R F O R M A N C E ( F R O M “ S P 1 ” T O “ S P 2 ” ) Po wer Delay SMC I-C 70% × P GM P P , 2 0.08s 0.11s 80% × P GM P P , 2 0.14s 0.16s 95% × P GM P P , 2 0.28s 0.41s T ABLE IX A C C U R AC Y O F A N N P R E D I C T I O N ( F R O M “ S P 1 ” T O “ S P 2 ” ) Input type PQI voltage and current based Irradiance based Multiple inputs 94.2% 92.3% Single input 85.4% 83.2% detection delays. In comparison with T able IV, as the noise variance increases in the lar ge PV system, the ANN is triggered more frequently and thus the amount of the saved resource slightly decreases. Our GLLR detector leads to less redundant alarms (smaller false alarms period) gi ven the same detection delay . T able VIII sho ws that the SMC-based estimation achie ves 95% of the ne w MPP within 0.28s, while the delay of the I-C method is 0.41s. The accurac y performance of ANN predictions is giv en in T able IX where our ANN model with multiple inputs has higher PQIs demonstrating the robustness of our method when the measurements are noisy . In general, the performance gaps between the enhanced components and their counterparts are more obvious than those in a less-noisy small PV system, which demonstrates the superiority of our proposed method. 2) Overall P erformance: The po wer dynamics are sho wn in Fig. 11, where the irradiance condition first switches from “normal” to “SP 1” at t = 5 . 8 s and then to “SP 2” at t = 7 . 8 s. 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Time (s) 1.5 2 2.5 3 3.5 4 Power (W) 10 5 Proposed enhanced MPPT method MPPT method in [14] GMPP (a) Power dynamics with the ANN using voltage measurement. 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Time (s) 1.5 2 2.5 3 3.5 4 Power (W) 10 5 Proposed enhanced MPPT method MPPT method in [15] GMPP (b) Power dynamics with the ANN using irradiance measurement. Fig. 11. Power dynamics under different irradiance conditions in a large PV system ( γ = 20 s, σ v = 10 − 3 ). 0 0.2 0.4 0.6 0.8 1 Delay (s) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Proposed enhanced MPPT method MPPT method in [14] (a) A verage ef ficiency performance with the voltage-and-current- based ANN. 0 0.2 0.4 0.6 0.8 1 Delay (s) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Proposed enhanced MPPT method MPPT method in [15] (b) A verage efficiency performance with the irradiance-based ANN. Fig. 12. A verage efficienc y performance in a large PV system ( γ = 20 s, σ v = 10 − 3 ). The corresponding GMPP first decreases from 590KW to 340KV and then to 230KV . Similar to Fig. 8, the proposed MPPT method exhibits less delays ( ≈ 0 . 4 s) before the the system arrives at the new GMPP . Fig. 12 quantifies the av erage tracking efficienc y . On one hand, compared with Fig. 9, the delay of our methods almost maintains the same as that in the small system, while the delays of the methods in [15] [14] increase from 0.6s to 0.85s. The obvious gap between the two implies the robustness of our method. V . C O N C L U S I O N In this paper , we proposed an improv ed MPPT method for PV systems under partial shading, by utilizing the prediction of the GMPP via ANN to refine the SMC-based I-C tracking algorithm. The SMC algorithm tackles the nonlinear voltage transition model when the step size is v ariable. The ANN model is based on the input of the voltage and current or the irradiance measurements, and predicts the GMPP gi ven the knowledge learned from training data. Furthermore, the ANN-based refinement is triggered only when the proposed GLLR change detector declares the irradiance change, which decreases the number of redundant ANN predictions when the irradiance is steady . 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