Gradient boosting models for photovoltaic power estimation under partial shading conditions

The energy yield estimation of a photovoltaic (PV) system operating under partially shaded conditions is a challenging task and a very active area of research. In this paper, we attack this problem with the aid of machine learning techniques. Using data simulated by the equivalent circuit of a PV string operating under partial shading, we train and evaluate three different gradient boosted regression tree models to predict the global maximum power point (MPP). Our results show that all three approaches improve upon the state-of-the-art closed-form estimates, in terms of both average and worst-case performance. Moreover, we show that even a small number of training examples is sufficient to achieve improved global MPP estimation. The methods proposed are fast to train and deploy and allow for further improvements in performance should more computational resources be available

Computation of the lambert W function in photovoltaic modeling

Recently, the Lambert W function has emerged as a valuable mathematical tool in photovoltaic (PV) modeling and other scientific fields. This increasing interest is because it can be used to reformulate the implicit equations of the single-diode PV model into explicit form. However, the computation of the Lambert W function itself is still not clear in the literature; some studies use the iterative built-in functions in MATLAB or other computational platforms, while others adopt their own approximation formulae. This paper takes a deeper look at the ways the Lambert W function is evaluated in PV models and carries out a comparative study to assess the most commonly used methods in terms of accuracy, computational cost, and application range. These alternatives are implemented in a modern computer and a typical microcontroller to evaluate their performance in both simulations and embedded applications. The analysis concludes that some series expansions are good options for PV modeling applications, requiring less execution time than the built-in MATLAB lambertw function and exhibiting negligible approximation error

A clamping circuit based voltage measurement system for high frequency flying capacitor multilevel inverters

In an era where high-frequency flying capacitor (FC) multilevel inverters (MLI) are increasingly gaining attention in energy conversion systems that push the boundaries of power density, the need for a compact, fast, and accurate FC voltage monitoring is also increasing. In this paper we designed and developed a new FC measurement system, based on precise sampling of the inverter switching node voltage, through a bidirectional clamping circuit. The deviation of FC voltages from their nominal values are extracted by solving a set of linear equations. With a single sensor per phase and no isolation requirements, as opposed to dozens of sensors in traditional FC monitoring, our approach results in significantly lower cost, complexity, and circuit-size. Detailed device-level simulations in LTspice and system-scale simulations in Matlab, validate the accuracy and speed of the proposed measurement system and the balancing strategy in steady state, abrupt load change and imbalance conditions. Experiments carried out in a 3-phase Gallium-Nitride 5-level inverter prototype, reveal a gain in precision and bandwidth that is more than 30 times that of conventional methods, at a fraction of their cost and footprint. The recorded performance renders the developed sensor an ideal solution for fast MLIs based on wide-bandgap technolog

Grid-forming control for solar PV systems with power reserves

This paper presents a grid-forming control (GFC) scheme for two-stage photovoltaic (PV) systems that maintains power reserves by operating below the maximum power point (MPP). The PV plant in GFC mode behaves like a voltage source that supports the grid during disturbances in full or limited grid-forming mode as per the reserve availability. This is a model-free method that avoids the estimation of MPP power in real-time commonly done in the literature, which makes it simpler and more reliable. The proposed control also features an enhanced current limitation scheme that guarantees containment of the current overshoots during faults, which is not trivial in voltage-sourced GFC inverters. A thorough investigation is done, exploring various generation mixtures of synchronous machines (SM), GFC and grid-following (GFL) inverters, and all common disturbances, e.g., load change, faults and irradiance transients. The results show very favorable dynamic performance by the GFC inverters, far superior to GFL inverters and directly comparable to SMs. It is found that replacing SMs with GFC inverters may improve the frequency profile and terminal voltage during disturbances, despite losing out in the mechanical inertia and the strict inverter overcurrent limits

Noise-Scaled Euclidean Distance: A Metric for Maximum Likelihood Estimation of the PV Model Parameters

This article revisits the objective function (or metric) used in the extraction of photovoltaic (PV) model parameters. A theoretical investigation shows that the widely used current distance (CD) metric does not yield the maximum likelihood estimates (MLE) of the model parameters when there is noise in both voltage and current samples. It demonstrates that the Euclidean distance (ED) should be used instead, when the voltage and current noise powers are equal. For the general case, a new noise-scaled Euclidean distance (NSED) metric is proposed as a weighted variation of ED, which is shown to fetch the MLE of the parameters at any noise conditions. This metric requires the noise ratio (i.e., ratio of the two noise variances) as an additional input, which can be estimated by a new noise estimation (NE) method introduced in this study. One application of the new metric is to employ NSED regression as a follow-up step to existing parameter extraction methods toward fine-tuning of their outputs. Results on synthetic and experimental data show that the so-called NSED regression “add-on” improves the accurac

A Method for the Analytical Extraction of the Single-Diode PV Model Parameters

Determination of PV model parameters usually requires time consuming iterative procedures, prone to initialization and convergence difficulties. In this paper, a set of analytical expressions is introduced to determine the five parameters of the single-diode model for crystalline PV modules at any operating conditions, in a simple and straightforward manner. The derivation of these equations is based on a newly found relation between the diode ideality factor and the open circuit voltage, which is explicitly formulated using the temperature coefficients. The proposed extraction method is robust, cost-efficient, and easy-to-implement, as it relies only on datasheet information, while it is based on a solid theoretical background. Its accuracy and computational efficiency is verified and compared to other methods available in the literature through both simulation and outdoor measurements

Hybridizing Lead-Acid Batteries with Supercapacitors: A Methodology

Hybridizing a lead–acid battery energy storage system (ESS) with supercapacitors is a promising solution to cope with the increased battery degradation in standalone microgrids that suffer from irregular electricity profiles. There are many studies in the literature on such hybrid energy storage systems (HESS), usually examining the various hybridization aspects separately. This paper provides a holistic look at the design of an HESS. A new control scheme is proposed that applies power filtering to smooth out the battery profile, while strictly adhering to the supercapacitors’ voltage limits. A new lead–acid battery model is introduced, which accounts for the combined effects of a microcycle’s depth of discharge (DoD) and battery temperature, usually considered separately in the literature. Furthermore, a sensitivity analysis on the thermal parameters and an economic analysis were performed using a 90-day electricity profile from an actual DC microgrid in India to infer the hybridization benefit. The results show that the hybridization is beneficial mainly at poor thermal conditions and highlight the need for a battery degradation model that considers both the DoD effect with microcycle resolution and temperate impact to accurately assess the gain from such a hybridization

An Explicit PV String Model Based on the Lambert W Function and Simplified MPP Expressions for Operation Under Partial Shading

In this paper, a reformulation of the widely used one-diode model of the photovoltaic (PV) cell is introduced, employing the Lambert W function. This leads to an efficient PV string model, where the terminal voltage is expressed as an explicit function of the current, resulting in significantly reduced calculation times and improved robustness of simulation. The model is experimentally validated and then used for studying the operation of PV strings under partial shading conditions. Various shading patterns are investigated to outline the effect on the string I-V and P-V characteristics. Simplified formulae are then derived to calculate the maximum power points of a PV string operating under any number of irradiance levels, without resorting to detailed modeling and simulation. Both the explicit model and the simplified expressions are intended for application in shading loss and energy yield calculations

A comparison ofmethods for the calculation of all the key points of the PV single-diode model including a new algorithm for themaximum power point

A comparison ofmethods for the calculation of all the key points of the PV single-diode model including a new algorithm for themaximum power poin

Evaluation of analytical methods for parameter extraction of PV modules

© 2017 The Authors. Published by Elsevier Ltd. A review and evaluation of the main analytical techniques for parameters extraction of photovoltaic (PV) modules with due account taken of their applications in modelling photovoltaic systems is presented. Six prevalent analytical methods are investigated and assessed using software tools, which have been developed to extract the required parameters of some commercially available PV modules using these methods. The results were subsequently compared with those obtained using well-established numerical methods. It is shown that, despite the fact that analytical methods can involve a fair amount of approximations, some analytical methods can compete in terms of accuracy with their numerical counterparts with much reduced computational complexity. .Published versio