Data-driven PV modules modelling: Comparison between equivalent electric circuit and artificial intelligence based models

https://doi.org/10.1016/j.seta.2018.10.011Get rights and content

Abstract

This paper aims to contribute to the answering of the research question: “Are the modern models of DC power output forecast of PV modules, which are based on artificial intelligence, able to beneficially replace the classical equivalent electric circuits models?” This is a pertinent question as it is nowadays commonly accepted that the next phase of RES integration in the power system will be based on PV power. The success of this integration will depend crucially on the accuracy of PV power forecasts. The classical PV performance models – simplified fast estimate (FE), 1 diode and 3 parameters (1D + 3P), 1 diode and 5 parameters (1D + 5P), and modern ANN based models are reviewed. Both the classical and modern models are validated against datasheet information and experimental data of PV modules. The conclusion of this study points to the fact that the modern model performs competitively. In the validation against experimental results, the errors associated with the modern model are lower than the ones achieved by the classical models. The computation time is nevertheless higher, but still acceptable. The drawback of the modern model is that it is unable to explain the physical nature of the phenomena associated with PV electricity generation.

Introduction

Portugal has valuable experience with regards to the integration of Renewable Energy Sources (RES) in the existing power system. The operating experience with the installation of large hydro plants was already significant when, in the period between the1980’s and 1990’s Portugal started deploying its first small hydro power plants. The installed capacity was relatively small due to several reasons including the difficulty of finding adequate locations. The main reason for the low amount of installed capacity can be attributed to the generous feed-in tariffs that were offered to the newly arriving wind power producers. This wind power phase started in the beginning of the 21st century and was characterized by the massive installation of wind turbine generators. This resulted in Portugal currently having a total installed capacity of 5 GW of wind power which is about one third of the total power generation capacity.

The integration of RES in the existing Portuguese power system has been successfully carried out with the necessity of RES curtailment being extremely rare. Nowadays, wind power accounts for about 25% of the Portuguese load supply.

One of the main reasons for this success was the use of advanced wind forecasting techniques. These forecasts are crucial to ensure power system operates in a secure manner. When the wind fluctuations are not adequately predicted, it is necessary to activate extra reserves, which are usually expensive generators, to compensate for the imbalance between generation and load.

Today, it is commonly accepted that the next stage of RES development will rely on Photovoltaic (PV) generators. This will take advantage of the impressive cost decrease that have been witnessed in recent years. The current installed PV capacity in Portugal is still modest (about 0.5 GW), but the expectation is that it will steadily increase in the coming years. As in the case of wind power, the success of the integration of massive quantities of PV power in the existing power system will be crucially dependent on the reliability of PV power output forecasts.

In order to make good forecasts it is essential to have good models. PV forecasting can be performed in various ways. This paper will concentrate on the techniques that make these predictions based on the measuring (or forecasting) of the quantities that directly affect PV power namely; global irradiance and module temperature. Assuming that these quantities are available, there are two ways of performing a PV power forecast:

  • 1.

    To use a mathematical model that relates the input parameters (irradiance and temperature) with the output quantity (PV power) through an equivalent ELECTRIC circuit. These models are based on defining adequate relationships between the electric output and its dependency on the input variables. The models that use this technique are called classical models, in this paper.

  • 2.

    To use machine learning techniques, which are characterised by training a learning processing system to make it capable of setting purely mathematical relationships between past inputs and outputs. In this paper, this method is called the modern method.

A great number of models belonging to the classical solution are available. The most commonly used classical models are: the fast estimate (FE) simplified model, the intermediate 1 diode and 3 parameters (1D + 3P) model, and the detailed 1 diode and 5 parameters (1D + 5P) model. The literature reports a large number of variants for each of these models. This paper will only focus on the most known variants.

There are also a great number of tools which may be used to apply the modern method. Artificial Neural Networks (ANN) is one of the most used techniques, because through learning by experience, they allow the definition of proper functions that relate the inputs with the output with a good degree of accuracy.

The planning and operation of electrical grids is currently facing a paradigm shift. In the power grids of the past, the power flowed unidirectionally from the large power plants to the consumers, with no intermediate power injections. In the power grids of the future (the so-called Smart-Grids) more and more dispersed production, mainly RES based, will be connected in the distribution grids, giving rise to bidirectional power flows. The abundance of distributed production located at various points of the grids, together with the consumers that want to be producers (the prosumers), is demanding new ways of planning and operating the grids which need to ensure security and reliability in this novel environment.

The support tools, namely the ones that allow the prediction of the system status, are following this paradigm shift. Classic mathematical models are based on complex equations that relate the different electrical parameters, but the solution to this model may be hard to obtain. These algorithms are being challenged by new artificial intelligence techniques which learn from experience, and this helps to ease the complicated relationships between the variables of interest.

This paper focus on the last aspect and seeks to answer the following research question ‘To what extent can artificial intelligence based advanced techniques replace the classical models which are grounded in explicit relationships between the electrical quantities?’

The question will be answered by forecasting the PV module DC power output using the classical models and the modern one. The objective is to find out if the later can replace the former method. The assessment metrics used to evaluate the results is the error between forecasted values and experimental ones and also monitoring the computational burden involved in the forecasting process.

To predict the DC power output of a PV module, one can use classical equivalent electric circuit models that relate the output quantity with the input variables (irradiance and temperature) through mathematical relationships. A recent alternative is to use a machine learning based model, which is able to predict future power values from past historical ones, after a properly trained neural network is applied. In this paper, a comparison between the performance of these prediction alternatives is carried out. The main contribution of the paper is to quantify the errors made using the two aforementioned approaches by comparing the predictions with experimental measurements of the DC power output of PV modules. To the best knowledge of the authors this contribution is innovative, since a combined assessment of the two prediction approaches is not available in the literature.

The objective of this paper is not performance optimization, i.e., the paper does not aim to finding the best model, classical or modern, to forecast the PV module DC power output. Instead, a concept demonstration is presented that, by using default parameters, assesses if the modern model is able to compete with the classical models, with regard to reliability, results accuracy and computation time.

The paper is organized as follows. After this introductory section, Section 2 is concerned with a brief state-of-the-art review. The theoretical formulation of the models used in this work – classical (FE, 1D + 3P and 1D + 5P) and modern (ANN based) is presented in Section 3. In Section 4, both the classical and modern models are validated against datasheet information and experimental data of PV modules and their performance is assessed. Finally, in Section 5, the main conclusions drawn from this work are presented.

Section snippets

State-of-the-art review

The FE and 1D + 3P are very simple models and there is plenty of available information regarding the modelling details. As far as the 1D + 5P model is concerned, the question is quite different, because the set of non-linear equations that is obtained requires numerical methods to be solved and the solution convergence is not easy to achieve. The literature reports some techniques that are used to overcome this difficulty, ranging from the analytical ones to using optimization methods.

For

PV systems performance models

In this chapter, the theoretical backgrounds of the models used in this current investigation are presented. The classical (simplified FE, intermediate 1D + 3P and detailed 1D + 5P) models are reviewed, as well as the modern ANN-based model.

Models validation

In this chapter, the validation of both the classical and modern models will be made. For this purpose, two datasets are used.

  • Dataset #A – Datasheets of 27 PV modules, with the following distribution per technology: single-crystalline silicon – 8; multi-crystalline silicon – 15; thin films – 4. The average STC efficiencies were 15.5%, 14.8% and 13.4%, respectively.

  • Dataset #B – Set of experimental measurements for three horizontally mounted PV modules (one of single-crystalline silicon (M#1) and

Conclusions

The main objective motivating this work was to assess if modern models, based on artificial intelligence techniques, are able to compete with classical models, based on equivalent electric circuits, in the task of predicting the DC power output of a PV module.

Based on the obtained results, the answer to this question is yes, modern models are capable of replacing the classical ones with some extra benefits. This conclusion is in accordance with the ongoing paradigm shift in the planning and

Acknowledgments

This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013. EDP Group is deeply acknowledged for supporting the execution of this work. We thank Mr. Matthew Gough for his thoroughly revision of the paper.

References (23)

  • Y. Kashyap et al.

    Solar radiation forecasting with multiple parameters neural networks

    Renewable Sustainable Energy Rev

    (2015)
  • Cited by (0)

    View full text