Temporal Complementarity Analysis of Wind and Solar Power Potential for Distributed Hybrid Electric Generation in Chile

The study addresses the need to support Chile’s transition to a 100% renewable electricity generation matrix by 2030, driven by global climate goals and domestic policy commitments. Variable renewable energy (VRE) sources, primarily solar PV and wind, already contribute significantly to Chile’s Sistema Eléctrico Nacional (SEN) and are projected to reach 55% of installed capacity by 2030. However, their variability introduces operational challenges, including non-dispatchability, transmission congestion, energy curtailment, and price distortions that hinder investment. The paper frames solutions from demand-side efficiency and smart grids to supply-side strategies, including increased VRE capacity, expanded storage, efficiency improvements, and distributed hybrid renewable energy systems (HRES). The central research question is whether wind and solar resources in Chile exhibit statistically significant temporal complementarity that can guide optimal siting and design of hybrid generation to mitigate VRE variability and reduce storage needs.

The paper reviews complementarity concepts and metrics (Pearson, Spearman, Kendall, autocorrelation, cross-correlation, wavelet-based indices, temporal complementarity indices) noting no standard methodology. International studies show diverse wind–solar complementarity patterns: Mexico (north-central zones favorable), North America (Gulf of Mexico and parts of Caribbean and Pacific coastal regions), China (strong complementarity in the north; maritime regions complementary across temporal scales), Portugal (local complementarity supports hybridizing existing wind parks), Brazil (offshore wind complements hydro; spatial complementarity often stronger than temporal), and Colombia (alternative variation-based complementarity metrics; wind/solar complement hydro during droughts). Regional Latin American work indicates that strategically adding wind/solar can mitigate ENSO impacts, and climate change may degrade complementarity toward century’s end. For Chile, prior work focused on spatial diversification impacts on market value, technical-economic assessments of wind–solar-to-hydrogen projects, sizing hybrid resources with storage, and long-term planning frameworks, but no national-scale temporal complementarity study existed.

The study evaluates daily wind–solar temporal complementarity across continental Chile using hourly data from 2004–2016 for 176 geographically distributed points. Data sources: the public “Explorador Solar” database provides hourly solar irradiance and wind speed at 5.5 m; missing point data are interpolated from neighbors. Steps: 1) Select points on a 25 km × 25 km grid across Chile (approximately 50 km longitude and 100 km latitude spacing), yielding 176 points with coordinates and IDs; 2) Extract hourly solar radiation (W/m²) and wind speed (m/s) at 5.5 m for 2004–2016; 3) Pre-process ~40 million values and interpolate gaps; 4) Build an hourly time series database; 5) Compute daily averages of solar radiation and wind speed at 5.5 m using Python; 6) Estimate daily average wind speed at 100 m via Hellman’s exponential law: V_h = V_i × (h/i)^a, with i = 5.5 m, h = 100 m, and terrain-dependent exponent a (values assigned per point: 0.005, 0.03, 0.1, 0.5 based on terrain roughness); 7) Compute daily wind power potential (W/m²) as P/A = ρ × V^3 with air density ρ = 1.12 kg/m³, to compare wind with solar power potential; 8) Calculate Spearman’s rank correlation coefficient (ρ_s) between daily wind and solar power potential time series for the entire period and for each year, classifying correlation strength using established thresholds; 9) Compile databases of total (2004–2016) and annual complementarity; 10) Generate heat maps in ArcGIS Pro to visualize spatial patterns of complementarity. Statistical analyses include pointwise significance testing (α = 0.05; critical |ρ| ≈ 0.028 for N ≈ 4745 daily observations) and zone-level mean tests with confidence intervals and p-values.

- Four zones of wind–solar temporal complementarity were identified across Chile using Spearman’s correlation of daily power potentials (2004–2016): - Zone A1 (coast and valleys, 18° S–36° S; n = 45): Moderate positive correlation; median ρ ≈ +0.44; interquartile range (IQR) ≈ +0.23 to +0.60. - Zone A2 (north Andes, 25° S–33° S; n = 27): Weak negative correlation; median ρ ≈ −0.18; IQR ≈ −0.37 to −0.01. - Zone B (center-south, 36° S–51° S; n = 77): Weak to moderate negative correlation; median ρ ≈ −0.18; IQR ≈ −0.33 to −0.07. - Zone C (far south, 51° S–55° S; n = 27): Weak positive to no correlation; median ρ ≈ +0.05; IQR ≈ −0.04 to +0.12. - Interannual behavior (2004–2016): - Zone A1: Median stable around +0.5; notable dips in 2010 and 2015 (~+0.25); negative kurtosis; uniform IQR and extremes. - Zone A2: Median around −0.25, rising to ~0 in 2015; positive kurtosis; stable extremes; varying IQRs. - Zone B: Median oscillates without clear trend; uniform extremes; weakly varying IQR; more outliers. - Zone C: Median oscillates between ~−0.08 and +0.17; no clear trends in IQR or extremes. - Illustrative points (2014): A1 point 12 (ρ = +0.79, strong positive); A2 point 45 (ρ = −0.58, moderate negative); B point 104 (ρ = −0.48, moderate negative); C point 147 (ρ = −0.06, near zero). - Statistical significance: Pointwise testing finds 9 of 176 points not significant (|ρ| ≤ 0.028); thus 167/176 are significant at α = 0.05. Zone-level mean tests show significant correlations in A1, A2, and B (p-values: A1 ≈ 4.0×10⁻¹³; A2 ≈ 5.47×10⁻⁵; B ≈ 1.47×10⁻¹²), with Zone C marginally significant (p ≈ 0.0204). Zone means (±95% CI): A1 mean 0.4227 (0.3389; 0.5066); A2 mean −0.1948 (−0.2779; −0.1116); B mean −0.1793 (−0.2215; −0.1371); C mean 0.0502 (0.0084; 0.0921).

The identification of spatially coherent zones of wind–solar temporal complementarity across Chile provides actionable guidance for the siting and design of distributed hybrid renewable energy systems. Negative correlations in Zones A2 and B imply that wind output tends to peak when solar output is low (e.g., winter), reducing simultaneous deficits and thus potentially lowering storage requirements and curtailment. Zone A2’s weak-to-moderate negative complementarity aligns with the location of major mining loads, suggesting that wind–solar hybridization near these sites could improve supply reliability and reduce dependence on large-scale storage. In contrast, Zone A1’s moderate positive correlation indicates co-varying resources (both peak in summer), which may help meet seasonal demand peaks but offers less intra-day or inter-season balancing; hybridization here should be paired with storage or flexible demand to manage simultaneous lows. The near-zero correlation in Zone C implies limited temporal balancing benefits; other strategies (e.g., storage, transmission reinforcement, or inclusion of additional resources) may be more effective. The high rate of statistically significant correlations supports the robustness of these patterns, and the interannual analysis shows stability in A1, persistent complementarity in A2 and B, and higher dispersion in C. Overall, leveraging these complementarity maps can help optimize investments, reduce curtailment and congestion, and support Chile’s pathway to a high-VRE, 100% renewable grid.

This national-scale assessment of daily wind–solar temporal complementarity in Chile (2004–2016) using Spearman’s coefficient reveals four distinct zones with differing correlation patterns: A1 (moderate positive), A2 (weak negative), B (weak to moderate negative), and C (weak positive to null). Interannual analyses show stable behavior in A1, consistent negative complementarity in A2 and B with varying medians, and higher dispersion in C. Statistical testing confirms significance for most points and for zones A1, A2, and B, with C marginally significant. These findings provide a practical basis for planning distributed hybrid generation, indicating where wind–solar combinations can intrinsically balance variability and reduce storage needs. The authors recommend incentivizing hybrid wind–solar deployments, especially in A2 (mining regions), to reduce investment and operational costs and carbon footprints. Future work will address: (1) spatial complementarity, (2) optimal sizing of distributed hybrid generation considering complementarity levels, and (3) impacts of climate change on wind–solar complementarity.

- Spatial aggregation to discrete grid points may introduce modeling errors relative to continuous fields. - The approach is static and retrospective, not projecting future complementarity under changing climate or system conditions. - Zone delineations may vary with different datasets, resolutions, or updated measurements; repeat applications may not yield identical zones. - Interpolation for missing data can introduce uncertainty. - Terrain roughness (Hellman exponent) is simplified by categorical assignments, potentially affecting wind extrapolation accuracy.