May 9, 2022

Photovoltaic Energy

In the last decade, solar photovoltaic has started to play a significant role in the energy mix consumption.

List of contents

Solar Photovoltaic Energy and Its Spatial Dependence


In the last decade, solar photovoltaic has started to play a significant role in the energy mix consumption. Although this growth has involved almost all the western countries, marked differences in the regional distribution of photovoltaic generation capacity have been observed. These differences appear to be weakly related to climate conditions in general, and to solar radiation specifically. The literature has started to investigate the other underlying determinants, suggesting to consider the occurrence of spatial proximity effects. Accordingly, this study aims to analyze whether and to what extent the photovoltaic energy production depends on local factors, such as climate, demand, income, innovative and responsible behavior, and so forth. Through a spatial autoregressive model, we find that the regional distribution of photovoltaic production capacity is affected by strong spatial dependence. We show that the availability of photovoltaic energy may be explained by peer effects, such as diffusion of habits and emulation of neighbors.

Introduction and background literature

The energy production and consumption models have experienced significant changes during the last decades [1]. On the supply side, although fossil fuels are still the most prominent sources, the transition to renewables is underway. Many countries have massively developed photovoltaic (PV) power generation systems. As a case in point, the share of electricity consumption met by solar energy is now more than 5% in Germany and up to 7% in Italy [2].

Worldwide, the installed capacity has grown to over ten times the level in 2007 [2]. According to IEA’s Outlook, solar energy is expected to play an increasing role in the years to come [3]. The above framework suggests investigating the PV deployment at regional and local scale and its determinants, the knowledge of which is rather limited. Balcombe et al. [4] have reviewed the motivations and barriers to the adoption of microgeneration technologies. Besides the local climate characteristics – especially the level of solar radiation [5] – several socioeconomic factors – such as age, income, investment cost, expected and actual return on investment – have been found to explain the consumers’ propensity to use renewable energy systems [6-11]. Balta-Ozkan et al. [12] show that also electricity demand, population density, pollution, and education are significant drivers.

Spatial dependence characterizes many ecological and social phenomena. It means that the behavior of a unit is affected by what happens in the surrounding areas, due to the so-called peer interaction effects, such as the diffusion of habits and the emulation of neighbors. A devoted research branch has stressed that proximity, neighborhood effects, and peer effects are important in shaping the spatial deployment of PV installations [11-17]. These effects turn out to play a prominent role, more than climate conditions [18]. A comprehensive review of the literature mentioned above can be found in Balta-Ozkan et al. [12].

Models, data, and method

We are interested in analyzing the dynamic relationship between the per capita PV production (Pp), the share of electricity consumption met by PV energy (Ps), and other explanatory covariates, in order to understand the behavior of the solar energy market. Our data are not simple cross-sectional because a spatial order characterizes the observations in the sample, which thus are not interchangeable. The spatial contiguity of the units raises a problem of serial correlation that seriously affects the statistical properties of the estimates. Analogous to the time series analysis, the issue can be solved by using spatial autoregressive (SAR) systems that include lagged terms [19,20,21]. SAR systems are useful to express the bivariate relationship between energy production and consumption.

Let us define the spatial index s=[latitude, longitude]. The first-order lagged dependent variables Pps-1 and Pss-1 are represented by the average values of Pps and Pss in the surrounding areas. Besides these lagged dependent variables, the other explanatory variables we consider are as follows: Ecs represents the per capita electricity consumption; Irs is the vector of variables assumed as proxy of innovative and responsible behavior; Efs is the vector of exogenous factors. The three following variables approximate innovative and responsible behavior: creativity index (Cis); technology index; waste recycling rate. The vector of exogenous factors include several variables: latitude; solar radiation (Srs); surface area; residential buildings; housing density (Hds); population density; households; average number of members per household (Hms); per capita gross domestic product (Gdps), manufacturing firms, share of Plc and Ltd companies.

The use of the logarithmic transformation is motivated by possible non-linear relationships between the variables. Eqs (1)-(4) are estimated using the Ordinary Least Squares method (with robust standard errors according to the White’s dispersion matrix), by performing a forward stepwise regression. The packages we use are R and Gretl. The data cover 110 provinces in Italy (according to the NUTS3 classification). The spatially lagged dependent variables are defined according to the proximity structure of the units (Fig. 1).

Results and discussion

As expected, the share of electricity consumption met by solar photovoltaic energy depends on climate factors; however, their statistical significance is rather limited. The solar radiation Srs hardly explains more than 5% of Pps variance, this raises questions about plant efficiency, network distribution and location policies of solar facilities. Instead, latitude and surface area are excluded from the models due to collinearity issues.

Other significant variables are Cis, Gdps, Hds, and Hms. The unexpected result is that they all have a negative sign. The adoption of innovative and responsible behavior does not emerge as a driver of photovoltaic production. The fact that Pps and Pss are high where income and housing density are lower, as well as where the number of household’s members is higher, confirms that photovoltaic production is strong in the less developed areas of the country. The role played by electricity consumption is controversial: Ecs positively affects Pps but negatively Pss.

The most notable outcome is that solar photovoltaic energy shows a strong spatial dependence, both at production and consumption levels. The logarithmic model enables to explain nearly the 53% of Pps variance, but more than 18% of the same variance is explained by the photovoltaic production in the surrounding areas of each province (Pps-1).

Similarly, nearly 59% of Pss variance is explained by the function based on natural logarithms, but Pss-1 explains up to 31% of the same variance.


In this study, we demonstrate that spatial dependence is a key topic in the research strand that aims to delve into the determinants of the transition to the renewables, specifically the solar photovoltaic energy. The results we achieve pose at least two issues that call for further investigations. The first concerns the nonlinearity of the relationships between dependent and independent variables, because the goodness of fit of the logarithmic functions (0.53 < Adj. R2 < 0.59) is higher than in the linear models (0.35 < Adj. R2 < 0.37). The second issue consists of the formulation of the proximity structure. The nearness between the units of observation may be measured using several indicators, such as distances, shared boundaries, and so forth. Hence, it should be analyzed whether and how much different nearness indicators lead to diverging results.