Alternative energy sources are of great importance in the world in order to reduce hydrocarbon dependency in electricity generation. Being a sustainable, emission-free and cost effective source, the share of solar energy inside the overall electricity generation is rapidly increasing. PV systems have become widespread in recent years [
1]. In order to use the solar energy sources reliably in grid operations, it is important to forecast accurately the total electricity generated from the PV system in order to realize planning of a PV system under different environmental conditions. With an accurate estimation of the total power generated from the solar system, it is possible to perform efficient energy analysis in order to meet the required energy demand. Consequently, it becomes possible to help grid operators manage the power balance between electricity demand and supply. Especially in applications such as optimum bidding [
2] and sizing of energy storage [
3] for microgrids, the accurate maximum power output of solar PV panels are required. In the literature, different studies have been carried out regarding the estimation methods for solar electricity generation. In general, these methods are divided into three basic groups as (i) physical; (ii) statistical and (iii) hybrid methods [
4]. Physical models use global solar radiation, ambient temperature, relative humidity and some other outdoor weather parameters [
5,
6]; statistical techniques use past recorded data to model linear time series via related characteristics of the past days [
7,
8,
9]. Hybrid models were developed to combine two or more models in order to avoid the disadvantages of a single model [
10,
11,
12]. Some heuristic approaches based on artificial intelligence were also applied to forecast energy generation successfully [
13,
14,
15,
16,
17,
18]. The most commonly used (and accepted as state of the art in several applications) maximum power output model uses global solar radiation and ambient temperature values as input parameters to the forecasting function [
2,
3,
19,
20]. The expected global solar radiation value on PV panels at a certain time can be calculated/estimated by the locations and orientations of the panels [
5]. However, due to the high uncertainty on the variation of climatic conditions in any specified region, it is quite difficult to predict the solar radiation on PV panels. Several attempts exist for forecasting global solar radiation [
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31].
The efficiency of PV panels and the unavoidable system losses directly affect the power output. Unfortunately, losses and efficiency of the overall system are not static. Unavoidably, they deteriorate in the long run by aging. More importantly, they show shorter performance variations due to changing ambient temperatures. PV panels’ current-voltage (I-V) curves depend on both solar radiation and temperature [
32]. It is also reported that panel electricity generation depends on whether parameters such as humidity, wind speed/direction, etc. [
33]. These parameters are naturally time varying and have nonlinear relations to output power values. Even if global solar radiation and temperature values are known, the used output power model in [
3] for PV panels is insufficient when compared with real measurements. In our previous study [
34], we observed that a certain solar radiation value causes the generation of different electric power values depending on whether the same radiation value appears in the morning or in the afternoon. In [
34] we propose that this difference in the morning and afternoon radiation-to-power generation efficiencies can be modeled as a piece-wise time-dependent function with three parts (corresponding to morning, noon and afternoon times). In that work, each piece-wise part was modeled a 2nd order function of the solar radiation. According to that model, it was concluded that the global solar radiation-to-energy conversion phenomenon is not only non-linear, but it also has a strong time-varying characteristic. In
Section 3, it is illustrated that the solar radiation-to-power conversion function requires a time varying model that exhibits a hysteresis behavior on the conversion curve. In general, the term hysteresis is used for describing systems that exhibit a history-dependent behavior causing a change (usually a lag) in the output of a function to input values. More precisely, hysteresis is defined as “the phenomenon in which the value of a physical property lags behind changes in the effect causing it” [
35]. This phenomenon is encountered in a rich class of disciplines, ranging from chemistry to engineering, from biology to even economics [
35]. A related hysteresis phenomenon was encountered in solar cells, where an anomalous hysteresis phenomena was observed in the current-voltage curves due to their temperature dependency [
36,
37]. In this study, the characteristics of the solar radiation-to-power conversion of PV panels are considered. According to the above hysteresis definition [
35], the physical property of the system is taken as electric energy (voltaic output) and the “effect causing it” is taken as solar radiation (photons), hence the name of the device: photo-voltaic panel. In our recent studes, it was observed that, when the input is considered as solar radiation, the output (electricity) shows a lag, indicating a hysteresis behavior [
34]. An example of this lag phenomenon is illustrated in Figure 6a. Since the lag occurs in the morning times (where the weather is usually colder) and is compensated in the afternoon (where the weather gets warmer), the hysteresis is mostly attributed to the temperature dependency of the solar cells. Nonetheless, as long as the input is considered as the solar radiation and the output is taken as the electrical energy, the conversion corresponds to a hysteresis curve. Furthermore, although classical models already incorporate temperature together with solar radiation values, those models are unable to exhibit the lag shape in the solar radiation to electricity curves, as will be presented in
Section 3.
Extending the idea in [
34], this study proposes a new PV panel output power modeling strategy, which is based on real measurements. The model is constructed for both fixed and sun tracking PV systems. It is argued that the hysteresis shape is due to the ambient temperature variation difference in the morning (when the weather and the PV panel are cold) and afternoon (when the PV panel is already warm). In order to construct an accurate model, pyranometer and temperature measurements are recorded (in one-second intervals) with the corresponding inverter power outputs of both the fixed and sun tracking PV panels throughout the whole winter season from our Renewable Energy Research Home (RERH) system. We have deliberately chosen to handle the winter season, since it is expected to be more difficult to follow the weather changes in this season due to abrupt changes in cloudiness and precipitation values as compared to other seasons. We observed that the time varying hysteresis effect of the conversion curve shows a higher fluctuation than in summer days. It was also observed that the conversion curves are significantly different for cases of sun tracking and fixed PV systems. After conducting a numerous set of experiments, we proposed eight new models consisting of addition and multiplication of 1st and 2nd order functions of both the global solar radiation and ambient temperature values. For the model used in our previous study, a piecewise model was introduced because a single mathematical function could not be obtained using only the solar radiation, whereas in this study, it was possible to obtain a unified mathematical function. The results are compared with the state-of-the-art models. It is observed that all of the eight proposed models show more accurate results than the best model available in the literature. It is concluded that since the previous models in the literature do not consider modeling the hysteresis relation between solar radiation and output power, the proposed models retain a clear advantage. Since other state-of-the-art methods also require a period for data collection for modeling, the proposed method is claimed to be a successful alternative for radiation-to-power conversion modeling.
In the remaining parts of the paper, we start by describing our RERH system, where our data collection takes place. Then we explain the PV power generation observations to continue with our proposed hysteresis model. Eight different models are explained as an attempt to describe the hysteresis effect and their accuracies are presented. The paper ends by concluding that the mean absolute error (MAE) of our models (in conversion value) goes down to 1.28 as opposed to the minimum value of 4.87 that can be achieved by the current state-of-the-art model in the literature.