Impacts of solar intermittency on future photovoltaic reliability

The study addresses how future climate-driven changes in solar radiation, particularly its day-to-day intermittency, affect the reliability of photovoltaic (PV) power. While solar energy is critical for decarbonization, its short-term variability limits reliability, imposing costs on grid integration and leading to penalties or reliance on dispatchable backup (e.g., fines to PV plants in Northwestern China; diesel backup on overcast days in Kauai, Hawaii). Traditional analyses emphasize mean solar radiation changes, but reliability metrics like the loss-of-load probability (LOLP)—the fraction of days when PV output fails to meet demand—depend on the full distribution of solar input, not only the mean. The research aims to quantify how changes in mean and variability of daily solar irradiance under climate change influence PV reliability, and to derive a general framework linking mean-radiation projections to reliability outcomes across regions and seasons.

Prior work has largely projected long-term changes in mean solar radiation and PV yields using climate models and observational datasets, with regional studies in Europe, Africa, the Western US, and globally noting modest but spatially variable impacts on PV energy output. However, the intermittency dimension has been underexplored in climate impact studies, despite its centrality for planning storage, backup, and grid operation. Reliability concepts such as LOLP have long been used in off-grid PV sizing and power system adequacy assessment, yet translating mean-radiation projections into reliability changes has lacked a systematic, distribution-based framework. Additionally, climate-driven shifts in clouds and aerosols, diurnal cloud-cycle biases in models, and aerosol-cloud interactions can modulate solar resource variability, indicating the need to move beyond mean-only metrics.

• Data sources: Daily global horizontal irradiance (GHI) from CERES SYN1deg (2001–2018) and from 11 CMIP5 climate models (ACCESS1.3, BCC-CSM1.1m, CanESM2, CCSM4, CMCC-CMS, CSIRO-Mk3.6.0, EC-EARTH, GFDL-CM3, INM-CM4, IPSL-CM5A, MPI-ESM) under RCP4.5 for 2006–2015 and 2041–2050.
• Clearness index: Daily clearness index K is defined as the ratio of daily GHI to extraterrestrial horizontal irradiance (EHI), capturing atmospheric effects (clouds, aerosols). Empirical distributions of daily K are constructed for regions and months.
• Reliability metric: LOLP is defined as the fraction of days when PV energy supply is below a fixed daily demand, which can be expressed as the cumulative distribution function of K evaluated at a threshold K_D corresponding to the demand. Design LOLP (LOLP_D) is computed from historical-period K distributions (e.g., 2006–2015) for assumed demand; the study commonly uses LOLP_D = 0.3 and explores others.
• Statistical modeling: The distribution of daily K is modeled with a beta distribution (bounded [0,1]) parameterized by its mean μ and standard deviation σ. Observations show σ depends on μ approximately quadratically (σ ≈ −0.83 μ^2 + 0.65 μ + 0.03), a relationship that remains stable across periods and models.
• Sensitivity framework: A first-order Taylor expansion links changes in LOLP to relative changes in μ via a sensitivity L_s that depends nonlinearly on μ and the design K_D (or design LOLP). Analytical expressions for L_s are derived under the beta distribution assumption and validated against numerical estimates from climate models (ΔLOLP divided by Δμ/μ between periods).
• Future scenarios: Changes in μ and LOLP are computed between 2006–2015 and 2041–2050, matching typical PV module lifetimes. Ensemble means and significance (t-tests at 5%) across the 11 models are mapped for January and July.
• Case studies: CERES-based examples in Southern Romania and Dubai evaluate historical shifts (2001–2009 vs 2010–2018) in μ and corresponding LOLP changes.
• Extensions: The framework incorporates (a) temperature impacts by adjusting the demand threshold K_D with a temperature coefficient (~0.45% power decrease per K), yielding an additional positive sensitivity term; and (b) storage impacts via variance reduction of K (smoothing with factors b=0.75 and 0.5 to represent 25% and 50% variability mitigation) to reassess LOLP under future climates.
• Validation and accuracy: Satellite and model K are compared with NSRDB products (SUNY, METSTAT) over the U.S., with RMSE around 0.05 between NSRDB products and similar magnitudes relative to CERES and several models. Model differences and aerosol treatment are documented.

• Nonlinear linkage: Increases in mean clearness index (μ) generally reduce LOLP, but the relationship is strongly nonlinear and regionally heterogeneous. Reliability is more sensitive to μ changes in sunny regions (higher μ), particularly hot arid zones.
• Historical cases: In Southern Romania, μ increased by 0.015 (January) and 0.03 (July) from 2001–2009 to 2010–2018, decreasing LOLP from 0.3 to 0.27 (ΔLOLP −0.03) in winter and to 0.21 (ΔLOLP −0.09) in summer. In Dubai, winter μ increased (likely tied to aerosol trends), reducing LOLP, while summer μ stayed relatively constant, with little change in LOLP.
• Future projections (2006–2015 to 2041–2050, RCP4.5): Europe shows projected μ decreases in January and increases in July; the Middle East exhibits μ decreases, consistent with circulation, cloudiness, and aerosol trends. Corresponding ΔLOLP maps reveal substantial regional-seasonal variability, with some areas experiencing large reliability deterioration from small μ declines (e.g., Middle East and North Africa), and others showing pronounced reliability gains where μ increases (e.g., west of the Amazon in July).
• Sensitivity L_s: Analytical and model-based estimates agree that |L_s| is larger at higher μ and depends on design LOLP. Example: For Southern Romania with design LOLP 0.3, L_s ≈ −0.8 (January) and ≈ −1.6 (July). Model-based regressions in selected μ bins yield slopes consistent with these values.
• Storage effects: Reducing day-to-day variability (25–50% σ mitigation) lowers LOLP broadly, enhancing reliability; however, in regions with substantial μ declines (e.g., parts of the Middle East), storage alone may not offset reliability losses, implying simultaneous needs for increased storage and PV capacity.
• Temperature effect: Added sensitivity term is always positive; warming increases LOLP by effectively increasing the demand relative to temperature-sensitive PV efficiency, though this impact is secondary to irradiance changes over PV lifetimes in many regions.
• Practical output: Global maps of L_s provide a lookup to translate projected μ changes into reliability impacts, enabling planning that accounts for both mean and intermittency.

The findings demonstrate that PV reliability under climate change cannot be inferred from mean solar radiation changes alone. Because the K distribution’s shape and the σ–μ relationship remain relatively invariant, small shifts in μ in already sunny regions can cause disproportionately large changes in LOLP. This explains the observed heterogeneity: humid subtropics with lower μ and flatter σ–μ slopes exhibit lower sensitivity (smaller |L_s|), while hot arid regions display high sensitivity, making them vulnerable to even modest μ decreases. The framework bridges conventional mean-resource projections and operational reliability metrics pertinent to grid planning, peaking plant costs, and storage sizing. It underscores a tradeoff between availability (mean energy yield) and reliability (intermittency-driven risk of unmet demand), advocating integrated assessments that simultaneously consider both dimensions.

This work introduces and validates a general, distribution-based sensitivity framework that links projected changes in mean solar irradiance to PV reliability via the loss-of-load probability. By characterizing daily clearness index distributions and deriving analytical sensitivities, the study provides global maps and simple tools to infer reliability impacts from mean-radiation projections. Key contributions include revealing strong, spatially variable, and nonlinear sensitivities—highest in sunny, arid regions—and quantifying how storage and temperature influence reliability. The results call for reliability-aware PV planning that integrates mean resource changes and intermittency. Future research should downscale from daily to sub-daily timescales, couple across multiple power sectors (generation, storage, transmission, markets), refine aerosol-cloud representations in climate projections, and extend the framework to other distributions and regional peculiarities to enhance robustness.

• Assumes daily timescale; intra-day variability and operational constraints are not explicitly modeled and would require downscaling.
• Uses beta distributions for K; while broadly validated, some regions may be better represented by other distributions.
• Relies on CMIP5 RCP4.5 projections; aerosol emissions and indirect aerosol-cloud effects vary by model and may influence irradiance projections.
• Treats PV output as a monotonic function of K, abstracting away technology-specific factors (soiling, shading, spectral effects) and assumes these are managed operationally.
• Storage impacts are approximated via variance reduction rather than detailed storage-operation models.
• Temperature effects are included via a linear efficiency penalty; real-world responses may vary by technology and system design.
• Design LOLP and demand threshold are fixed for analysis; real systems may adapt demand, capacity, or storage over time.