Three-diode model for characterization of industrial solar generating units using Manta-rays foraging optimizer: Analysis and validations

Highlights

• This paper addresses a new attempt of the MRFO to define the uncertain model parameters of PV units.

• Two commercial PV modules are investigated with intensive simulations and necessary subsequent discussions.

• The parameters of MRFO based TDM are confirmed thru the empirical dataset points.

• Necessary performance assessments are made which signify the MRFO results compared to other recent methods.

Abstract

A new attempt of employing Manta-rays foraging optimizer (MRFO) for accurate parameters extraction of three-diode equivalent model (3DeM) of solar generating units (SGUs) is endeavored. 3DeM has nine decision variables, when they are carefully selected, it can precisely define the actual characteristics of SGUs. The optimization strategies are based on two datasets such as actual measured I/V points at specific conditions, and using only the three key points given by manufacturer’s SGU datasheets. In which, MRFO is used to generate the 3DeM nine uncertain parameters. Two test cases are investigated such as (i) Kyocera polycrystalline KC200GT solar module, which is widely used in the literature and their comparisons are obtainable, and then, (ii) an experimental set up is established for the Ultra 85-P under different changed conditions. Root mean squared errors and mean absolute errors between measured and estimated current datasets, which are widely used in the literature, are adapted to define the cost functions (CFs) for SGU’s parameters extraction. Both of these CFs are optimized sequentially using the MRFO. Comprehensive discussions regarding their performances are given along with various statistical and sensitivity metrics. Various changed conditions including sun radiations and cell temperatures are examined. It can be confirmed that performance of MRFO is indicated overall various comparisons with others and other necessary performance measures.

Introduction

Among various kinds of renewable energy sources, the solar generating panels have been proven feasible, and promising alternative [1]. Their integration with high penetrations levels to classical power systems are endowed in order to enhance their performances in terms of steady-state and dynamic actions [2]. Therefore, precise modeling of solar panels to represent their characteristics for further analysis is necessary. Roughly speaking, the solar generating units can be modelled using: (i) one-diode equivalent model (1DeM) [3], [4], [5], [6], [7], [8], (ii) two-diode equivalent model (2DeM) [9], [10], [11], and (iii) three-diode equivalent model (3DeM) [12], [13], [14], [15].

In the literature, extraction of solar panel’s parameters can be categorized into: (i) mathematical/analytical methods, and (ii) semi-empirical based on recent heuristic frameworks. Many procedures among the analytical methods [16], [17], [18] have been used to extract various uncertain parameters of solar generating units (SGUs). The quality of the results of these methods are much dependent on the initial values and in many cases, oversimplifications are employed which latterly will lead to high errors in the results of such methods. Accordingly, such methods are insufficient to characterize the models of the solar units. One of the most promising and alternative solutions is to employ techniques such as heuristic-based recent approaches.

At last years, number of researchers have paid lot of efforts of using the meta-heuristic based on algorithms to tackle such issues. These frameworks are inspired from phenomena of nature such as swarming-behaviors, evolutionary, and physics-based procedures. Among those smart heuristic-based frameworks are genetic algorithm (GA) [19], particle swarm [20], [21], [22], [23], many variants of differential evolution (DE) [24], [25], [26], [27], [28], [29], [30], sunflower optimizer (SFO) [15], salp swarm-inspired algorithm [31], modified JAYA [32], coyote optimization algorithm (COA) [33] and whale optimization algorithm (WOA) [34], [35] and many more [36], [37], [38], [39], [40], [41], [42], [43], [44], [45]. Some researchers have attempted to hybridize some of these algorithms aiming at enhancing their performances such as hybrid firefly and pattern search algorithms [28], hybrid DE with WOA algorithms [29], memetic adaptive DE [30], GA and the simulated annealing algorithm [19], trust-region reflective deterministic algorithm with the artificial bee colony algorithm [37], and hybrid algorithm based on grey wolf optimizer and cuckoo search [41]. It can be concluded that each approach has its own merits and demerits and no single algorithm can solve all engineering optimization problems. In addition to that, still no solid answer or very difficult to decide that optimization algorithm A is most suitable to optimization problem B of certain characteristics such as degree of non-linearity, convexity, separability of the control variables, modality and etc. Till getting such answer, attempts shall continue in these endeavors.

Notwithstanding numerous strategies as per the above-mentioned to define the uncertain parameters of solar units with satisfactory results, and once again, still always there are room of improvements to precisely define the models of solar units.

In line with this, manta-rays foraging optimizer (MRFO) is employed to identify the uncertain parameters of the 3DeM. MRFO is based on the behavior of manta rays in their foraging [46] with three strategies such as chain foraging, cyclone foraging, and somersaults process. Recently, MRFO has applied successfully to define the uncertain parameters of fuel cells [47]. Two test cases are demonstrated, analyzed and comprehensively discussed. Among them, the second case is organized with experimental setup with necessary validations. In addition to that, well-known cost functions (CFs) are adapted in consort with performance assessments. In the context, statistical measures are utilized to appraise the performance of the MRFO and in comparisons with other recent competitive methods. Moreover, global sensitivity analysis based on Sobol metrics is introduced to determine the sensitivity of the estimated outputs w.r.t parameters variations.

The active objectives of this current work are: (i) New effort to study the performance of the MRFO in solving solar module parameters identifications of 3DeM, (ii) The viability of the MRFO procedure is further examined using the actual I-V polarization curves of commercial SGUs namely Utlra 85-P under various operating conditions, (iii) statistical and sensitivity metrics are applied to evaluate the quality of the common CFs and the decision variables perturbations.

The rest of this manuscript body is structures as follows: Section 2 announces the mathematical formulation of 3DeM in terms of its equivalent circuit and depicted formulas. The adapted CFs complete with predefined constraints, statistical and sensitivity metrics are obvious in Section 3. The motivations and implementations of the MRFO are illustrated in Section 4. In addition, Section 5 reveals the comprehensive simulations and subsequent discussions of the obtained results along with necessary validations. At last, the concluding remarks along with prospective insights to extend this current work are drawn in Section 6.