This study investigated methods to generate spatial solar PV projections at a level of 143 Swiss districts, using linear and spatial regression models by in-sample and out-of-sample accuracy testing. Although the predictor variables identified in the regression analysis allowed for computing more accurate spatial projections, these variables should not be interpreted as the drivers of solar PV diffusion because potentially important variables could have been missed due to lack of data. First, local policy incentives to promote solar PV were not included in our analysis, but such policy data could help identifying which kind of policies foster the PV diffusion in some regions more than in others. From 2016 on, only owners of small-scale PV installations could enroll for FITs, which may have encouraged further investments in 2015.
This policy change is only partially reflected in the ROI variable and could have had an influence on the low projection accuracy for 2015. Second, further financial predictor variables could be analyzed in the future. While this and previous studies showed a positive effect of electricity prices on PV diffusion [35,36,39], analysis of more complex financial variables could provide a more in-depth understanding on the role of prices. This study used the ROI metric, which enabled to account for decreasing investment costs of PV panels, spatially-explicit PV tariffs, federal FITs and spatially-spatially-explicit LCOE. However, this analysis is limited in the sense that PV adopters which received one-time subsidy instead of FIT may expect other ROI and electricity self-consumption rate should also be considered. In terms of the setup of the regression models used, future work could experiment with models that differentiate between the various sizes of solar PV installations or that focus on other spatial scales, such as municipality or even postcode levels.
In terms of testing the accuracy of spatial projections, other models, accuracy indicators, and time horizons could be added in the future. In terms of models, fixed and random effect models for classical panel regressions are straightforward [70]. A spatial panel model has been recently used to investigate predictors of PV diffusion [27], but this model was not used to generate projections and to test them for accuracy. Spatial panel models for the projections are still in their infancy, but recent studies also found no accuracy improvements [71,72] as in the case of our SEM and SAR models. Geographically-weighted regression models could also be added because they consider spatial heterogeneity in the parameter estimates, but so far have been mainly used for exploratory data analysis [73]. In terms of the accuracy indicators, the RMSLE and percentage error that were used in this study could be complemented with other indicators that compute and normalize the error differently. In this study, projections of up to 5 years have been tested for accuracy, whereas planning the grid infrastructure and addressing
demand-supply balancing challenges require thinking of at least a decade ahead. Future research could therefore produce and test spatial PV projections for the next 10 to 20 years.
5. Conclusions
This study proposed a methodology to generate spatial projections of solar PV installations at a subnational level of 143 Swiss districts, using techno-economic and socio-demographic predictor variables. Based on a comprehensive dataset covering 68’341 PV systems all over Switzerland, a linear and two spatial regression models were set up for 2010-2017. These models were used to generate 1- to 5-year-ahead spatial projections, and were then evaluated for accuracy during in-sample and out-of-sample testing. The results show that exploitable solar PV potential is a strong positive predictor for PV diffusion at a district level in Switzerland.
Household size, population density, and electricity prices are other predictors with positive effect, and the share of unproductive land area is a predictor with negative effect. Spatial regression models point to the importance of spatial autocorrelation in the data, providing evidence for spatial spillovers among proximate districts. The accuracy testing shows that spatial regression models have a slightly higher accuracy for an in-sample testing, thereby justifying the inclusion of spatial autocorrelation terms when developing spatial PV projections.
But concerning out-of-sample use, the classical multiple linear regression model performs equally well as the spatial regression models for 1- to 5-year-ahead projections, hinting to the possibility where analytical efforts can be saved. Methodology and insights obtained from this study are essential for generating reliable spatial projections of solar PV installations for the purposes of planning grid infrastructure or anticipating supply-demand balancing challenges.
Information about the socio-demographic characteristics of potential PV adopters is essential when designing adequate federal and local policies to foster the energy transition on a regional scale. The methods used in this article illustrate the case of PV diffusion in Switzerland, but can be applied to analyze other renewable energy technologies or other technology diffusion processes. If the necessary data is available, the methods can also be applied to other countries or different spatial levels such as the municipality or household level.
Competing interests
The authors declare no competing interests.
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