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Nature Energy (2026)Cite this article
The solar rebound effect (SRE) occurs when rooftop photovoltaic adoption increases household electricity consumption, driven by the perception of solar energy as a free resource. Although empirically observed, the SRE has not yet been accounted for in energy system modelling or abatement scenarios. This study integrates empirically derived SRE intensities into an open-source optimization model of the European energy system, translating behavioural effects into temporally distinct demand profiles. The results show that not only the magnitude but also the timing of the rebound determines its system impact. Additional demand leads to increases in renewable investment needs, flexibility requirements and overall system costs while inducing regressive effects, as households driving the rebound do not bear its full costs. The findings call for explicit inclusion of SRE in abatement scenarios and grid planning and highlight load-shifting incentives and energy efficiency policies as key tools to mitigate rebound effects and align demand with renewable generation.
Imagine a single-family house with a rooftop photovoltaic (PV) system that, on sunny days, generates electricity perceived as free. This lowers the household’s effective electricity costs, leveraging the price elasticity of demand and incentivizing higher consumption, an outcome called the solar rebound effect (SRE)¹. The SRE may also stem from income effects (as compensation through net metering or feed-in tariffs increases disposable income) and moral licensing, whereby households feel entitled to consume more after investing in green technology^2,3. Although it is beneficial to individual households, this behaviour can undermine overall energy and emissions savings. Its potential scale becomes clearer when global energy forecasts are considered. According to the World Energy Outlook (Net Zero Emissions scenario), global electricity demand will reach 66,000 TWh in 2050, with more than 34,000 TWh supplied by solar power⁴. Following the 2050 supply trajectories of the Ten-Year Network Development Plan (TYNDP), approximately 30% of total solar electricity will be generated on rooftops⁵. Applying empirically observed SRE intensities from existing studies (7.7–33.0%, with an average of 17.2%), the resulting additional electricity demand in 2050 will range between around 800 and 3,400 TWh, equivalent to up to 5% of the global projected electricity demand. Although this figure might appear small in relative terms, the lower bound of this range corresponds to roughly one-third of the entire current electricity consumption of the 27 member states of the European Union in 2024 (2,729 TWh), and the higher bound is greater than this value⁶, underscoring the economic meaning of the SRE.Whereas the World Energy Outlook partially accounts for rebound effects in the transport sector, the SRE is ignored in the electricity and heat scenarios⁴. This applies equally to other global and European scenarios^5,7,8.
The scale of these potential effects underscores the need to examine their implications for regional energy systems. Especially given the rapid growth of rooftop PV across the European Union (EU)⁹, the SRE is particularly relevant due to its impact on electricity demand patterns. Although the behavioural dimensions of the SRE have been empirically studied (for example, refs. ^10,11,12), its role within the energy system and in abatement scenarios remains unexplored (for example, refs. ^13,14,15), leaving a notable research gap. Given these dynamics, the European power system provides a particularly suitable context for analysis, combining high PV adoption rates⁹ within the world’s most extensive interconnected power system¹⁶ and its ambitious climate targets^14,17. To address this research gap, we integrate empirically derived SRE strengths into the open-source Stochastic European Energy Market Model (E2M2s)^{18,19,20,21,22,23}. This analysis examines how varying temporal distributions of additional demand impact operations and investments within a sector-coupled framework. Unlike substitution-driven demand from electrification, the SRE reflects a behavioural response that adds consumption beyond service needs; our study, therefore, explicitly positions rebound-related demand within the broader context of sectoral and overall demand uncertainties. Specifically, we examine how the SRE influences technology deployment and system planning, total and CO₂ abatement costs and consumer impacts through changes in electricity and CO₂ prices.
Existing studies distinguish between two main interpretations of the SRE^24,25. The discrete solar rebound refers to the change in electricity consumption that occurs due to the adoption of PV systems, irrespective of the actual amount of electricity generated by these systems^{2,12,25,26,27,28}. This interpretation treats the SRE as a relative increase in electricity consumption compared with the pre-adoption baseline. In contrast, the marginal solar rebound quantifies the additional electricity demand per unit of solar electricity generated in a specific time step after PV installation^{2,10,11,24,25,29,30,31,32}. This is formally expressed as the ratio between the change in electricity consumption and solar PV generation before and after adoption³³. The following analysis focuses on the marginal definition of the SRE, which guides model implementation. Figure 1 summarizes the marginal and discrete estimates reported in empirical studies published between 2015 and 2025.
Shown are the reported SRE sizes by study, placed at the final year covered by the underlying data to convey how recent the evidence is relative to the publication date. The black circles and grey squares denote marginal and discrete estimates, respectively. The horizontal dashed lines indicate the simple means for each group (marginal = ~17.2%; discrete = ~14.1%). The lowest and highest reported values for marginal estimates are 7.7% (Aydın et al.²⁹; the Netherlands) and 33.0% (Galvin et al.¹¹; Germany). The lowest and highest reported values for estimates are 2.9% (Toroghi and Oliver²⁶; USA) and 35.0% (Boccard and Gautier²⁷ (Belgium) and Frondel et al.²⁵ (Germany)). Studies reporting multiple estimates appear more than once. Only observational or data-driven studies using real-world evidence are included.
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Most studies examine changes in consumption over several years and show persistent post-adoption increases in electricity use^2,10,24,27. In particular, Beppler et al.²⁴ and Havas et al.³⁰ confirm long-term rebound effects over 6 months to 3 years after adoption. Aydın et al.²⁹, Qiu et al.³¹ and Kim and Trevena²⁸ likewise observe seasonal or regional fluctuations around a stable mean. Galvin et al.¹¹ emphasize enduring behavioural drivers, such as perceived free energy, income effects and moral licensing. The decline found by Nguyen et al.¹² probably reflects a methodological artefact in a setting with small-scale PV and without grid feed-in. Overall, the SRE can be regarded as a temporally persistent behavioural phenomenon in long-term modelling.
Capturing the temporal resolution of the SRE is essential, yet most studies assess it only at an aggregate level, with fixed effect sizes. So far, only Kim and Trevena²⁸, Qiu et al.³¹ and Aydın et al.²⁹ provide a seasonal and temporal perspective, highlighting critical variations in the manifestation of SRE. Aydın et al.²⁹ estimate an average intensity of 7.7%, with marked seasonal fluctuations ranging from 16% in summer to 3% in winter. Kim and Trevena²⁸ identify an average SRE of 6.6%, with variations ranging from 4.9–8.3% across different climate zones, and a notable shift in additional demand towards evening and nighttime hours. The study by Qiu et al.³¹ comes to similar conclusions.
A key challenge for assessing the SRE is the lack of high-resolution load profiles that capture sub-daily household usage before and after PV adoption. For this reason, we have opted for a scenario-based analysis that accounts for uncertainty in both the temporal distribution and the magnitude of the SRE, as shown in Table 1. The temporal distribution includes three profiles: (1) sweeping (the simplest interpretation); (2) simultaneous (rebound aligned with solar PV generation); and (3) dynamic (a time-resolved distribution of additional demand). In the sweeping profile, the effect relies on aggregated SRE estimates and is evenly distributed over time. Under this profile, the SRE is independent of direct solar power generation, representing a naive scenario. Yet, it allows the error to be assessed from an energy system modelling perspective with simplified mapping and no temporal resolution of the SRE. In the simultaneous profile, the SRE fully aligns with solar PV generation. This profile leads to a higher SRE during daytime and summer, as shown by Aydın et al.²⁹. The dynamic profile represents the most realistic data-driven temporal distribution of the SRE. It combines predominantly simultaneous daytime rebound with an off-peak component to capture discrete elevated baseload and additional demand peaks during periods of low or no PV generation. The parameterization draws on hourly consumption patterns reported by Kim and Trevena²⁸, which are used to calibrate the dynamics of the effect.
Each rebound demand profile is examined with three empirical rebound intensities for residential households (rooftop PV owners only) to incorporate uncertainties in behavioural adaptation: 7.7% (low)²⁹, 17.2% (average), derived from the reviewed studies, and 33.0% (high)¹¹. The high scenario represents the upper empirical boundary of observed rebound magnitudes. Galvin et al.¹¹ report an SRE of around 33% for German prosumers after 2011, driven by reduced feed-in tariffs and rising electricity prices that strengthened incentives for self-consumption. Comparable regulatory and market conditions still apply in most parts of Europe. More generally, post-adoption electricity demand may also reflect concurrent electrification trends that confound rebound attribution. Galvin et al.¹¹ note this explicitly for heat pumps: electrified winter space heating is unlikely to be PV associated (given low winter PV output) and would therefore not be meaningfully attributable to solar rebound. Similarly, adopting an electric vehicle represents a substitution-driven increase in load and, by itself, does not constitute rebound. Accordingly, Galvin et al.’s 33% estimate reflects the behaviour-induced post-adoption increase in electricity use, which represents a rebound rather than a substitution-driven demand effect. A similarly high effect (28.5%) is found by Beppler et al.²⁴ for US households. Together, these findings justify 33% as a realistic upper-bound scenario under strong economic incentives. All scenarios are applied to the European energy system (the current 27 member states of the European Union plus Norway, Switzerland, the UK and the Balkans) for 2030–2050.
The European-wide impact of the SRE depends on both its magnitude and the timing of additional electricity use. In modelling terms, higher self-consumption reduces projected grid feed-in, which must be offset by additional generation to meet total demand. Even small rebound intensities can accumulate gradually, yet the timing of demand becomes system relevant only under higher PV penetration and stronger effect levels (Fig. 2). Although all three temporal profiles assume the same relative effect size, their total additional electricity demand (in TWh yr⁻¹) differs slightly. This reflects the marginal definition of the SRE, where identical percentage effects translate into different absolute demand increases as solar capacity and temporal rebound patterns (midday versus evening) interact.
a, Total electricity demand (including electrolysis) under the reference scenario and for the maximum SRE case. The annotations indicate the additional demand relative to the reference. b–d, SRE-induced additional electricity demand for low (7.7%;b), average (17.2%; c) and high (33%; d) effect strengths, shown for dynamic, simultaneous and sweeping profiles. In 2050, additional demand reaches 80.8 TWh (low), 160.7 TWh (average) and 314.9 TWh (high) for the dynamic profile; corresponding values are 63.1, 145.5 and 301.9 TWh for the simultaneous profile and 62.1, 140.8 and 276.3 TWh for the sweeping profile. Europe comprises the 27 member states of the European Union, plus the UK, Norway, Switzerland and the Balkans.
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Accordingly, in 2050, the SRE will generate additional electricity demand of between 63 and 314 TWh yr⁻¹, depending on the scenario. In relation to total electricity demand (including electrolysis) in Europe, this represents an additional increase of up to 5.1%. Although this may appear marginal at first glance, its relevance becomes evident in the context of sector-specific uncertainties. In the residential sector, electricity demand in 2019 amounted to 1,335 TWh yr⁻¹, and long-term projections from existing studies, such as the TYNDP and EU reference scenarios, vary by around 300 TWh yr⁻¹ (1,262–1,565 TWh yr⁻¹), implying an uncertainty of roughly the same order as the SRE itself^5,34. Similar variation exists in other sectors, such as transport (780–850 TWh yr⁻¹) and industry (1,378–1,716 TWh yr⁻¹). For total electricity demand including electrolysis, the expected range of 5,800–6,800 TWh yr⁻¹ in these studies further illustrates the uncertainty shaping Europe’s future energy system. Against this backdrop, the additional SRE-induced demand of up to 314 TWh yr⁻¹ constitutes a non-negligible source of uncertainty, particularly for residential electricity consumption and its contribution to system-level demand growth.
To meet the additional demand, the energy system must rely on various flexibility options. These include battery storage for short-term balancing, hydrogen technologies for seasonal flexibility, and dispatchable generation to cover high residual load. Figure 3 illustrates the capacity expansion pathways up to 2050 for the average scenario (Extended Data Figs. 1 and 2 provide the results of other scenarios). PV capacity rises most under the dynamic and simultaneous profiles, since midday rebound demand can be met by solar generation. Moreover, both profiles efficiently utilize otherwise curtailed energy during peak generation hours. Higher intraday price spreads, particularly during the summer, enable higher revenues for battery storage, which leads to greater expansion of storage facilities. In the dynamic profile, this effect is further amplified by additional demand peaks during evening hours. At the same time, increased peak loads require additional backup capacity through hydrogen power stations to maintain generation adequacy in the event of a power outage. Under the sweeping profile, demand shifts to later hours, driving battery storage and wind capacity, as the rebound demand profile decouples, partly from solar generation. This highlights that the SRE’s temporal structure—not just its intensity—critically determines the needed technology mix.
a, Installed capacity by energy source under the reference scenario (without SRE) and for the average SRE scenario, shown for the dynamic, simultaneous and sweeping temporal profiles (2030–2050). b, Difference in installed capacity relative to the reference, highlighting that the dynamic profile leads to the largest expansion of solar PV capacity, whereas the sweeping profile yields larger additions of wind power, battery storage and electrolysers due to the shifted timing of additional demand. The simultaneous profile enables efficient solar integration, but requires complementary hydrogen backup capacity to satisfy the peak adequacy constraint (equation (7)). Note that from 2045 onwards, the energy source described as conventional only includes nuclear power plants.
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The generation mix in Fig. 4 reveals critical operational shifts beyond capacity expansion (Extended Data Figs. 3 and 4 present the results of other scenarios). Although the dynamic profile drives the highest solar PV generation (2,006 TWh in 2050), its key distinction lies in its use of flexibility: it stimulates a higher combined output from battery storage and hydrogen while causing the largest reduction in electrolyser operation compared with the reference (−37 TWh yr⁻¹). This indicates that the additional storage facilities are effectively exploiting the wider intraday price spreads, driven by rebound demand and additional solar PV generation. The substantially higher generation from renewable energies is absorbed by the SRE and the changed flexibility mix, thereby reducing curtailment of renewables by up to 13.8%. As a result, hydrogen production in Europe becomes less attractive, offset by increased hydrogen imports. The simultaneous profile shows similar solar generation levels and system interactions. Still, it requires less flexibility because it eliminates rebound demand during off-peak periods. In contrast, the sweeping profile’s uniform demand maximizes absolute battery storage (304 TWh yr⁻¹) and hydrogen output (526 TWh in 2050), highlighting its greater reliance on short- and long-term flexibility options. Moreover, electrolysis scales with the availability of renewable energy, particularly wind energy.
a, Annual electricity production and electricity use for charging, pumping and conversion across the reference scenario (without SRE) and average SRE scenario (for the dynamic, simultaneous and sweeping profiles), shown for 2030–2050. Negative values indicate electricity use for electric vehicle charging, electrolysis, battery charging and pumped hydro pumping. b, Difference in electricity production relative to the reference scenario. Biomass and other renewable sources contribute marginally compared with the expansion in wind and solar power. Conventional electricity generation (including nuclear power, coal and gas) decreases sharply towards 2045 as the system approaches climate neutrality. c, Difference in electricity use for charging and pumping relative to the reference scenario. Only unidirectional charging is represented for electric vehicles.
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Changes in the generation mix directly affect CO₂ abatement costs. Total emissions follow a fixed path aligned with the Paris Agreement¹⁷, but the cost of avoiding them depends on how rebound demand is supplied. Because the SRE shifts demand volume and timing, it creates path dependencies and lock-in effects in capacity expansion, altering abatement costs. In the model, CO₂ costs are calculated by multiplying the fuel-specific emission factors by the CO₂ shadow price and dividing by plant efficiency, yielding technology- and time-specific CO₂ cost coefficients applied to electricity and heat generation. These, alongside investment and operating costs, form part of the total system costs evaluated below. Given the model’s 2045 net zero target, efficient allocation of abatement becomes increasingly essential, especially regarding gas-based power, which fills gaps when storage falls short (Extended Data Fig. 5). In the dynamic and simultaneous profiles, extra demand aligns with midday PV output, keeping cost impacts low or even negative in 2040 (−€349 million for the high–simultaneous scenario). In 2035, the SRE raises the CO₂ price, temporarily increasing CO₂ costs. These elevated CO₂ prices accelerate investment in renewable capacity, resulting in a cleaner generation mix and lower CO₂ prices and abatement costs in 2040. Conversely, sweeping pushes demand into evenings and winters, maximizing gas use and costs (+€1.5 billion). Coal and lignite change little due to exogenous phase-outs. All monetary values are in constant 2023 euros. Overall, both the scale and timing of the SRE materially influence the cost of meeting climate targets.
Over the long term, grid expansion is a key flexibility option. Using transmission shadow prices, we assess how the SRE alters the benefits of grid expansion in terms of potential system cost savings. Figure 5 compares the annual benefit of an additional megawatt of transfer capacity, computed as the sum of the hourly shadow prices of the transmission restrictions (equations (2) and (3)) relative to the reference, for 2040, a typical planning horizon. A value of 0.7, for example, corresponds to system cost savings of €0.7 million per megawatt and year. When considering the SRE, there is a marked change in the spatial pattern of grid expansion needs. Under the simultaneous and dynamic profiles, increased rebound demand coincides with solar generation and requires additional renewable deployment. Whereas Southern Europe can still expand PV capacity, most of the PV potential in Northwestern Europe is already exhausted by 2040, prompting further wind expansion in the UK. As a result, interconnection reinforcement between the UK and the Benelux region becomes economically viable. Under the sweeping profile, in contrast, rebound demand during off-peak periods is primarily met by additional wind generation and higher nuclear output in France, whereas hydropower reservoirs partly supply seasonal flexibility. Together, these developments create economic signals for stronger integration of Scandinavia, the North Sea region and France within the European grid. Overall, this finding suggests that omitting the SRE from current grid planning may yield divergent results in the cost–benefit assessment of individual interconnectors.
a–c, Spatial distribution of changes in grid expansion benefits relative to the reference scenario without rebound (that is, the sum of the hourly shadow prices of the transmission constraints from equations (2) and (3) in million euros (m€) per megawatt per year), shown for the average scenario under the dynamic (a), simultaneous (b) and sweeping (c) rebound profiles.The line thickness encodes the congestion severity: thicker links indicate larger (more negative) shadow prices and thus greater potential system cost savings from additional cross-border transfer capacity. Near-zero values appear very thin. All monetary values are expressed in constant 2023 euros. Basemap administrative boundaries from the World Food Programme under an Open Government Licence v3.0.
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From an economic perspective, the SRE leads to higher total system costs, especially as its intensity increases (Fig. 6). Cumulative additional costs rise from €12.7–18.6 billion under the low scenario to €72.3–82.9 billion under the high scenario by 2050. With low rebound intensity, only small differences between the profiles can be observed, with dynamic and sweeping patterns yielding nearly identical results (€18.6 billion versus €18.3 billion). This similarity results from two counteracting effects: under the dynamic profile rebound demand is higher as it extends into off-peak hours, whereas under the sweeping profile additional demand is lower, but the simplified mapping of the SRE introduces additional inefficiencies. As intensity increases, the role of temporal patterns becomes clear: the simultaneous profile is cheapest through optimized solar utilization, whereas the sweeping profile incurs the highest costs due to reliance on wind and costly flexibility options. The more realistic dynamic profile falls somewhere between the two.
a, Total system costs (reference scenario and rebound cases) and the corresponding cumulative increase relative to the reference scenario. The cost impacts are small at low rebound levels, but become pronounced at higher intensities, reaching a maximum increase of 4.2% in 2050. b–d, Cumulative additional system costs relative to the reference scenario for the low (7.7%; b), average (17.2%; c) and high (33%; d) rebound effect strengths, shown for the dynamic, simultaneous and sweeping rebound profiles. System costs include investment, fixed and variable operating costs, start-up costs, curtailment, transport and hydrogen supply costs (as defined in the model objective function). All monetary values are expressed in constant 2023 euros.
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Rebound demand increases CO₂ prices under the decarbonization target by 2045¹⁷ (Extended Data Fig. 5) and raises electricity market prices, as shown in Fig. 7 (see also Extended Data Figs. 6 and 7), with the effects shaped by national generation mixes and the timing of rebound demand. The dynamic profile produces moderate price increases (+€0.06 MWh⁻¹ in France to +€0.76 MWh⁻¹ in Belgium) due to its combined demand pattern, which requires additional flexibility, particularly in Central Europe, where gas-fired generation compensates for low solar periods. The simultaneous profile shows lower impacts or, in the case of high SRE intensity, even slightly falling prices in southern and south-eastern Europe, as it balances the increase in demand with solar peaks. Although total system costs rise due to additional investments in backup capacity, the short-term marginal costs of electricity production (that is, electricity prices) may fall in some cases—a positive side effect of the SRE. In contrast, the sweeping profile drives the largest price surges (+€1.55 MWh⁻¹ in Germany and +€1.64 MWh⁻¹ in Slovakia), as its uniform demand creates persistent reliance on gas-fired plants during winter, particularly in regions with limited flexibility and grid constraints. These patterns, consistent with earlier grid expansion analysis, highlight Central Europe’s particular vulnerability and underscore that rebound timing, not just its magnitude, determines both infrastructure needs and consumer prices.
a, Load-weighted wholesale electricity price levels for the reference scenario without rebound (0% SRE). b–d, Price differences relative to the reference scenario for the dynamic (b), simultaneous (c) and sweeping (d) rebound profiles. Prices are defined as the load-weighted wholesale electricity price based on the hourly shadow price of the electricity demand-balance constraint in equation (1). Price impacts are spatially heterogeneous, with the largest increases concentrated in central Europe for the dynamic and sweeping profiles. All monetary values are expressed in constant 2023 euros. Basemap administrative boundaries from the World Food Programme under an Open Government Licence v3.0.
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The SRE raises serious equity concerns due to its asymmetric cost distribution. Several interlinked factors contribute to its regressive impacts. First, the capital-intensive nature of PV systems, despite lower module prices, means that adoption remains rather correlated with higher income levels, a relationship further confined to households with a roof, creating an imbalance in access to the technology’s benefits. Second, Europe’s regulatory framework maintains tariff structures that tax grid electricity more heavily than self-consumed PV power³⁵, effectively subsidizing rebound behaviour while passing the system costs on to all consumers. However, the current uniform cost distribution, rooted in an era of stable marginal generation costs, is increasingly challenged by variable renewables and rising capacity needs, making future cost allocation a policy choice rather than a historical convention. The temporal dimension of the SRE further complicates this picture. When households shift increased electricity consumption to periods with low solar generation, the system must deploy expensive backup capacity to meet this demand. These costs manifest as higher wholesale electricity prices that affect all consumers equally (Extended Data Fig. 8). As with CO₂ costs, the burden of maintaining this capacity is borne by all consumers, creating an implicit cross-subsidy from non-adopters to adopters that widens energy inequalities, especially for lower-income households who spend a larger share of income on energy and lack self-generation^36,37,38,39.
This study provides a comprehensive model-based analysis of the SRE and its system interactions, using Europe as an example. Previous research has focused on empirical description and largely overlooked its technological and economic implications. Our findings reveal that the SRE cannot be analysed in isolation; it is embedded in complex interactions with other energy system elements. Overall, the SRE entails both adverse and beneficial effects that differ across spatial and temporal dimensions. The increased electricity demand requires additional renewable investments to achieve climate neutrality, while also creating challenges for integrating renewables and necessitating greater reliance on flexibility options. This raises total system and end-consumer costs. However, potential positive effects arise from the specific temporal distribution of additional consumption: under the simultaneous profile, the SRE may reduce renewables curtailment, binding grid constraints and expansion needs. Moreover, the SRE can also reflect welfare gains, as prosumers benefit from low-cost self-consumption, enhancing comfort or energy services.
The results should be interpreted in light of the model’s limitations. Private households are aggregated to capture the system-level focus. One potential enhancement is a better differentiation of PV and storage types. The model also overlooks price elasticity, potentially overstating the SRE’s regressive effects, yet low-income, price-sensitive households remain disadvantaged. Additionally, high-resolution, hourly data on household demand and generation would improve the model’s accuracy. Future model-based research should extend our approach to include interactions with additional rebound effects across coupled sectors. Moreover, the SRE’s magnitude may not be static but endogenous to technology co-adoption. Empirical studies indicate that battery storage can mitigate rebound behaviour by shifting consumption patterns, whereas electric vehicles and heat pumps may amplify it². Capturing such interactions would improve forecasts of future rebound trajectories and better reflect the dynamic nature of household energy systems.
The results of this study provide a foundation for developing policy strategies that enhance the positive effects of the SRE while mitigating its negative impacts. The first practical takeaway is that the SRE should be explicitly integrated into abatement scenarios and simulation studies, because our findings show that excluding it leads to different system outcomes. Building on this insight, supporting households in shifting flexible demand to solar-rich hours (through demand-side response instruments such as time-varying tariffs) can amplify the system benefits observed for the simultaneous profile³⁶. Our findings call for greater attention to load-shifting policies that promote closer alignment between consumption and renewable generation³⁷. Making solar PV subsidies conditional on energy efficiency measures can also be a relevant tool for reducing the SRE, as energy-efficient households tend to exhibit lower rebound effects³⁸. At the European level, these findings underscore the importance of integrated policy frameworks that address both behavioural incentives and infrastructure gaps. Finally, this study suggests that omitting the SRE from current grid planning may yield divergent results in the cost–benefit assessment of individual interconnectors, underscoring the importance of EU-wide coordination on grid expansion.
The modelling of the SRE captures a broad range of systemic interactions, from initial investment decisions in PV systems to dynamics in the wholesale electricity market. A central challenge lies in the temporal alignment between solar power generation and the additional demand it triggers, as this coincidence critically shapes system-level impacts. The following text outlines how relevant behavioural assumptions can be incorporated into energy system modelling, with particular attention to the structural decisions and temporal patterns required to accurately represent the SRE.
The occurrence of the SRE involves a series of decisions, from planning and investment to long-term use of the solar PV system, as detailed in Extended Data Fig. 9 and the description below.
Information and planning form the initial phase, during which the person collects detailed information about PV systems, compares offers and examines various options. In this period, essential considerations are made, ranging from financial conditions (for example, credit financing or leasing) to technical details³⁹. This also includes assumptions about the anticipated electricity consumption, usually based on the most recent electricity bill. This is followed by the investment phase, in which the person decides to install a solar PV system. At this stage, risk and time preferences may play an important role, for example, due to uncertainties about investment costs and the future economic benefits of the investment^40,41,42. After ordering, there is usually a time lag before the installation is completed. Once the PV system has been installed, the first-use phase begins, during which the electricity produced is consumed for the first time. Subsequent adaptation and optimization reflect that the widespread availability of inexpensive renewable electricity, produced at nearly zero marginal cost, is driving a change in consumption patterns by making electricity more accessible¹⁰. In this phase, households optimize their electricity consumption behaviour to maximize their consumption or utilization of the energy generated. This is done, for example, by shifting the use of electrical devices to the hours of high PV generation²⁹. The following rebound phase shows that awareness of the cheaper or perceived free solar power leads to increased electricity consumption. As the study by Beppler et al.²⁴ shows, prosumers generally only adjust their consumption when they recognize the reduced electricity costs from the PV system. Moreover, households can be expected to increase their use of energy-intensive appliances with the installation of PV systems⁴³. Examples are the longer operation of air conditioning systems or the selection of more energy-intensive programmes for dishwashers and washing machines. Finally, interaction effects cover the exchange between rebound demand and wholesale market dynamics. The higher-level system perspective is considered, particularly regarding the impact of the rebound effect. Surplus solar power fed into the grid in the past is no longer available to other households due to prosumers’ private consumption. This can limit the availability of cheap electricity for other consumers and can have a lasting impact on the electricity markets and capacity planning⁴⁴.
The first assumption for SRE modelling is derived from the outlined decision-making process. A household first decides to invest in a solar PV system, installs it and subsequently begins using the generated electricity. The rebound effect only arises during the usage phase. Crucially, the investment decision is based on current conditions—particularly existing electricity consumption—at a time when rebound effects have not yet manifested and therefore do not influence the initial choice. Note that the anticipation of additional electricity consumption (as would occur due to the purchase of an electric car, for example) is not a rebound effect but a substitution effect⁴⁵. The time lag between the investment decision and the occurrence of the SRE necessitates a dynamic–recursive model structure to capture the time sequence correctly. Furthermore, it is assumed that actors base their decisions on myopic expectations. This means that current conditions are extrapolated into the future and the SRE is thus not anticipated.
Another essential modelling requirement is the representation of electricity consumption during the usage phase of the solar PV system. Energy system models generally consider an hourly resolution, which poses challenges for integrating aggregated annual SRE values derived from empirical studies. As outlined in the empirical foundation, the absence of high-resolution load data prevents the rebound structure from being modelled accurately at an hourly level. Due to this data gap, we opted for a scenario-based approach, which addresses the simultaneity or non-simultaneity of PV generation and the SRE at a conceptual level. This is particularly relevant because the temporal distribution of the rebound remains empirically unresolved (that is, the additional consumption may occur at different times of day). Extended Data Fig. 10 illustrates this by juxtaposing a scaled PV generation profile based on ENTSO-E Transparency Platform data for actual generation per production type (solar)⁴⁶ on the left with a representative load profile for a prosumer household with a PV system based on the BDEW P25-profile⁴⁷ on the right.
Under the simultaneous profile, according to microeconomic theory, a fall in the price of electricity, especially down to a price of zero, leads to an increase in demand. This is due to the price elasticity of demand, which measures how much the quantity demanded responds to price changes, following the law of demand⁴⁸. In private households with a PV system, the perception of free solar power creates an incentive to increase the use of electrical devices, both in frequency and duration. Accordingly, the SRE should be temporarily linked to solar power generation. This hypothesis is supported by the results of Aydın et al.²⁹, which show that electricity consumption increases markedly during periods of high PV generation. From this, the simultaneous profile can be derived (see also equation (4)). The green curves in Extended Data Fig. 10 proportionally follow the solar feed-in represented by the orange reference curve. In the model, this behaviour is implemented using a proportional factor based on PV generation and the strength of the considered SRE.
In the sweeping profile, the additional electricity demand from the SRE is evenly distributed over time. This pattern is based on the findings of Kim and Trevena²⁸, who observed increased electricity consumption even outside solar power generation times. In contrast with the simultaneous profile, the blue dotted line in Extended Data Fig. 10 shows a smoothed, constant distribution of additional consumption to represent the shift into the off-peak periods. It symbolizes a uniform increase in consumption throughout the day, without marked peaks (see also equation (5)).
The sweeping and simultaneous profiles can be considered extreme scenarios that make specific assumptions about consumption behaviour. Both approaches can lead to overestimates: the simultaneous profile ignores potential shifts into the evening hours, whereas the sweeping profile underestimates actual consumption during solar production. A third profile addresses these weaknesses and offers a more pragmatic, data-driven approach to SRE allocation. In Extended Data Fig. 10, the dynamic profile is represented by the slightly spread purple curve, which combines simultaneous rebound during daytime hours with a discrete off-peak demand component, reflecting both immediate consumption during PV generation and elevated baseline demand during periods of low or no solar output (see also equation (6)). This approach is calibrated using empirically observed consumption patterns reported by Kim and Trevena²⁸, ensuring the profile captures the full temporal complexity of rebound behaviour.
The open-source E2M2s model is a long-term planning and dispatch model for the European power, heating and mobility sectors¹⁸. It is formulated as a linear problem and based on a dynamic, recursive optimization approach that simulates selected years (2030–2050, in five-yearly stages) under myopic expectations. The model endogenously expands generation and storage capacity within 34 European market areas (countries). At the same time, cross-border electricity trade is represented by a net transfer capacity-based approach (paired with an exogenously given grid expansion path). The objective is to minimize total system costs, including investment and fixed and operating costs, thereby replicating a competitive market outcome. To reduce computational complexity, the modelling period is divided into eight representative days, each with seven time segments, capturing different weekdays, months and load patterns. A set of recombining trees is applied to reflect the volatility of renewable generation. Beyond power and heat, the open-source model also covers aspects of the mobility and hydrogen sectors. Numerous applications of E2M2s are reported by Swider and Weber¹⁹, Spiecker et al.²⁰, Spiecker and Weber²¹, Bucksteeg et al.²² and Blumberg et al.²³.
The following describes the relevant equations and adjustments to the model. The demand balance equation ensures that total electricity generation meets the electric load in each region at every time step. In simplified form, it states that the sum of the terms of the regional load ({l}_{r,t}), summarized electricity consumption of storage and electrolyser ({P}_{r,u,t,n}^{mathrm{cons}}) and solar PV-induced rebound ({mathrm{SRE}}_{r,u,t}) must equal the summarized power production ({P}_{r,u,t,n}) and net exports ({E}_{{r}^{{prime} }to r,t,n}-{E}_{rto {r}^{{prime} },t,n}). Parameters are denoted by lowercase letters, while decision variables appear in uppercase (see also the nomenclature in the Supplementary Information).
The demand balance plays a central role in understanding the impact of the SRE on electricity supply and the utilization of flexibilities, such as storage and electrolysis. This is because increased solar energy production stimulates electricity consumption via the SRE, influencing power plant dispatch and the use of flexibility options, thereby altering electricity market dynamics. These effects also extend to cross-border electricity exchange and the associated grid infrastructure.
Although meeting demand is essential, the power system must also operate within the physical constraints of its infrastructure. This limitation is mathematically expressed by ensuring that the power flow ({E}_{rto {r}^{{prime} },t,n}) from region (rto r{prime}) to region ({r}^{{prime} }to r) at a given node and time segment does not exceed the available cross-border capacities for ({C}_{f}(rto {r}^{{prime} })) and ({C}_{f}({r}^{{prime} }to r)). Analysing the shadow prices associated with this restriction allows us to assess the impact of the additional electricity demand due to the SRE on the benefits of network upgrades.
In the context of the demand balance equation presented above, the simultaneous solar rebound ({mathrm{SRE}}_{r,t,n}^{mathrm{sim}}) is modelled so that the additional electricity consumption increases proportionately to the produced solar energy. To this end, a rebound term is included in the balance equation in addition to the basic load, which is based on the capacity of the previous year c_r,u, the capacity factor (that is, the generation profile) ({phi }_{r,u,t,n}), a selected effect size sre and the household share α. This formulation uses the marginal SRE definition, in which additional consumption is expressed per unit of solar generation. This allows for consistent integration of the rebound effect into the temporal generation structure, directly linking additional demand to the hourly PV output profile.
For the sweeping profile, the rebound is evenly distributed throughout the day, depending on the selected intensity. This is modelled by a time-averaged PV profile based on the capacity factor ({phi }_{r,u,t,n}). As a result, the SRE occurs not only during PV production times but also during off-peak periods, as it is spread evenly over time.
The dynamic solar rebound ({mathrm{SRE}}_{r,t,n}^{mathrm{dyn}}) is a combination of a PV-coincident marginal component and an off-peak discrete baseline uplift. Based on the simultaneous profile, the first term links additional consumption proportionally to contemporaneous PV generation, whereas the second captures consumption increases that also occur when PV output is low or zero. The time-varying weights ({beta }_{r,t}^{mathrm{sim}}) and ({beta }_{r,t}^{mathrm{off}}) govern the share of both components, enabling both profiles to overlap, especially at the beginning and end of the day.
where
and
Furthermore, the model includes a capacity constraint to ensure sufficient generation resources are available to cover peak demand, as the representative-day approach might not perfectly capture actual annual load peaks. The maximum total electricity demand by country is given on the right-hand side of this constraint, whereas the left-hand side aggregates all secure capacity. This includes conventional units and storage (weighted by an availability factor), minimum guaranteed hydro inflows and the lowest feasible production from variable renewables in a worst-case scenario (for example, a dark doldrum (dunkelflaute) situation).
Here, avail_t,u and ({phi }_{t,r,u}) capture technology- and region-specific availability factors, ({c}_{r,u}) denotes installed capacities, ({w}_{t,r,u}) represents the minimal usable water inflows and ({L}_{r}^{max }) is the maximum total electricity demand.
Depending on the SRE case, the maximum total electricity demand varies. Part of the electricity demand is endogenous, caused by the electricity consumption of electric cars, electrolysers and heat pumps. The following formula defines the peak electricity demand and illustrates, through the rebound term, how higher electricity demand can arise as PV generation on private house roofs increases. Accordingly, the maximum electricity demand ({L}_{r}^{max }) is given by the maximum of the summarized exogenous electricity demand ({l}_{r,t}), additional demand from electromobility ({L}_{r,t,n}^{mathrm{emob}}) (only charging electricity), electricity demand from electrolysis ({L}_{r,t,n}^{{{rm{H}}}_{2}}), the heat pump demand ({L}_{r,t,n}^{mathrm{heatpump}}) and the solar rebound term ({mathrm{SRE}}_{r,t,n}) (sweeping, simultaneous or dynamic).
The modelling framework integrates diverse data sources to provide a comprehensive representation of the European energy system. Key inputs include renewable energy availability, demand forecasts, the existing power plant fleet (utilizing a brownfield approach) and techno-economic parameters such as investment costs and fuel prices. These parameters are primarily sourced from established references, including the TYNDP⁵ and World Energy Outlook⁴.
Electricity, hydrogen, mobility and district heating demands are exogenously modelled based on the Distributed Energy scenario of the 2024 TYNDP⁵. Based on bottom-up national input data, this scenario accounts for reduced energy demand through behavioural and technological shifts. These include higher renovation rates, lower surface per person and higher levels of energy-efficient consumer behaviour. At the same time, the scenario also highlights how new consumption patterns can partially counteract such efficiency gains; for instance, through the use of reversible heat pumps for cooling in summer, which may increase electricity demand despite their heating efficiency. The scenario data include the uptake of new electricity consumers (electric vehicles, heat pumps and air conditioning systems). Electricity demand (excluding electrolysis) in Europe exhibits a substantial upward trend, increasing from approximately 4,000 TWh in 2030 to over 5,000 TWh by 2050, driven by higher electrification. Hydrogen demand is projected to grow substantially, from 524 TWh in 2030 to 1,400 TWh by 2050. In comparison, district heating demand growth remains relatively modest over the same period, reflecting its stable role within the energy system. In contrast, the SRE is not captured within the TYNDP demand pathways. Our framework introduces the SRE as an endogenous electricity demand that depends on solar PV adoption and generation. Furthermore, an aggregated SRE is considered, meaning that empirically identified positive and negative rebounds are implicitly included²⁹.
The model includes Europe’s interconnector infrastructure for electricity and planned hydrogen networks. Net transfer capacities for electricity and hydrogen transfer capacities enable energy exchange between regions, which is essential for balancing supply and demand under high renewable energy penetration. Both net transfer capacities and hydrogen transfer capacities are treated as exogenous parameters that follow predefined expansion trajectories rather than being endogenously optimized within the model. The data for infrastructure development are based on the 2024 TYNDP⁵ and the European Hydrogen Backbone^49,50.
The decarbonization pathway is represented through a CO₂ cap that limits emissions across the electricity and heat sectors. This constraint enforces a gradual reduction in allowable emissions, starting in 2030 and reaching CO₂ neutrality by 2045, following a trajectory based on the European climate objectives¹⁷. The CO₂ price, determined endogenously through the dual variable of the constraint, reflects the marginal cost of emission reductions. Investment costs and technology lifetimes for capacity expansion are sourced from the Net Zero Emissions by 2050 scenario in the World Energy Outlook 2024⁴, ensuring alignment with internationally recognized decarbonization pathways.
The model distinguishes between residential (rooftop) PV and utility-scale PV. The SRE is exclusively linked to the residential rooftop segment¹, parameterized by ({alpha }_{r,t}), which specifies the share of total PV capacity installed at the household level. Respective solar generation shares are primarily derived from TYNDP projections⁵.
All input, processed and output data used in this study are available for access or reproduction via the GitHub repository branch at https://github.com/ude-ewl/osE2M2s/tree/Paper-SRE. Scenario-specific output and processed results are available there. All figures were created using Python, specifically the package Matplotlib. QGIS was used to create geographical maps, including the electricity price maps and the visualization of the benefits of additional transmission grid capacity. The corresponding QGIS project file and shapefiles for the figures that show geographical maps are included in the repository. Source data are provided with this paper.
The full model code and all scripts used for the visualizations are available at https://github.com/ude-ewl/osE2M2s/tree/Paper-SRE. The version of the underlying open-source E2M2s workflow referenced therein is available at https://github.com/ude-ewl/osE2M2s.
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We thank all of the colleagues who shared their insights and suggestions for this study at various conferences and workshops. Special thanks go to S. Poier, O. Ruhnau and J. Thomsen for valuable feedback throughout the development of this work. We also thank J. Radek and M. Breder for help with preparing the dataset used in this study. Open access funding was enabled and organized by Projekt DEAL.
Open access funding provided by FernUniversität in Hagen.
FernUniversität in Hagen, Hagen, Germany
Mensur Delic & Michael Bucksteeg
Institute of Energy Economics, University of Cologne, Cologne, Germany
Michael Bucksteeg
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Search author on:PubMed Google Scholar
M.D. and M.B. were responsible for software development, validation, formal analysis, investigation and writing (original draft and reviewing and editing). M.D. was responsible for data curation and visualization. M.B. was responsible for conceptualization, methodology and supervision.
Correspondence to Mensur Delic.
The authors declare no competing interests.
Nature Energy thanks Dogan Keles and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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a, Installed capacity (GW) by energy source in the reference scenario (without SRE) and in the low SRE scenario, shown for the dynamic, simultaneous and sweeping rebound profiles (2030–2050). b, Difference in installed capacity relative to the reference (GW). From 2045 onwards, Conventional only includes nuclear power plants.
Source data
a, Installed capacity (GW) by energy source in the reference scenario (without SRE) and in the high SRE scenario, shown for the dynamic, simultaneous and sweeping rebound profiles (2030–2050). b, Difference in installed capacity relative to the reference (GW). From 2045 onwards, Conventional only includes nuclear power plants.
Source data
a, Annual electricity production and electricity use for charging/pumping and conversion across the reference scenario (without SRE) and the low SRE scenario (dynamic, simultaneous and sweeping profiles), shown for 2030–2050 (TWh/yr). Negative values indicate electricity use for electric-vehicle charging, electrolysis, battery charging and pumped-hydro pumping. b, Difference in electricity production relative to the reference scenario (TWh/yr). c, Difference in electricity use for charging/pumping relative to the reference scenario (TWh/yr). Only unidirectional charging is represented for electric vehicles.
Source data
a, Annual electricity production and electricity use for charging/pumping and conversion across the reference scenario (without SRE) and the high SRE scenario (dynamic, simultaneous and sweeping profiles), shown for 2030–2050 (TWh/yr). Negative values indicate electricity use for electric-vehicle charging, electrolysis, battery charging and pumped-hydro pumping. b, Difference in electricity production relative to the reference scenario (TWh/yr). c, Difference in electricity use for charging/pumping relative to the reference scenario (TWh/yr). Only unidirectional charging is represented for electric vehicles.
Source data
a, Low scenario (7.7% SRE): CO₂ prices (green labels, €/t) and the associated abatement cost components (stacked bars; see legend) across model years for the dynamic, simultaneous and sweeping demand profiles. b, Average scenario (17.2% SRE; same as in a). c, High scenario (33% SRE; same as in a). Abatement costs represent CO₂-related cost components implied by the CO₂ shadow price. All monetary values are expressed in constant 2023 euros.
Source data
a, Reference scenario without rebound (0% SRE): load-weighted wholesale electricity price level (€/MWh). b, Price differences relative to the reference scenario (€/MWh) for the dynamic rebound profile. c, Same as in b, but for the simultaneous profile. d, Same as in b, but for the sweeping profile. Prices for households are defined as load-weighted wholesale electricity prices based on the hourly shadow price of the electricity demand-balance constraint in Eq. 1. Price impacts are spatially heterogeneous. All monetary values are expressed in constant 2023 euros. Basemap administrative boundaries from the World Food Programme under an Open Government Licence v3.0.
Source data
a, Reference scenario without rebound (0% SRE): load-weighted wholesale electricity price level (€/MWh). b, Price differences relative to the reference scenario (€/MWh) for the dynamic rebound profile. c, Same as in b, but for the simultaneous profile. d, Same as in b, but for the sweeping profile. Prices for households are defined as the load-weighted wholesale electricity price based on the hourly shadow price of the electricity demand-balance constraint in Eq. 1. Price impacts are spatially heterogeneous. All monetary values are expressed in constant 2023 euros. Basemap administrative boundaries from the World Food Programme under an Open Government Licence v3.0.
Source data
Each box-and-whisker plot summarizes the distribution of annual average wholesale electricity prices across market zones for a single scenario (n = 34 market zones; one value per zone). The thick horizontal line is the median; the multiplication symbol marks the arithmetic mean; the box encloses the interquartile range (25th–75th percentile); and whiskers extend to the most extreme values within 1.5 times the interquartile range. The reference scenario (0% SRE) serves as the control case. The boxplots illustrate how SRE-induced demand shifts affect the distribution of procurement-relevant wholesale prices across zones in 2040.
Source data
a, Information and planning involve collecting details, comparing offers, and considering finances and technical aspects. b, The investment decision reflects deciding to adopt PV under risk preferences. c, Installation covers the commissioning of the PV system, typically with a time lag. d, At first use, the household becomes a prosumer and starts self-consuming PV electricity. e, Adaptation and optimization describe adjusting consumption patterns to maximize PV electricity use. f, In the rebound phase, electricity use increases as solar power is perceived as ‘free’. g, Interaction effects capture system-level impacts on markets and other consumers.
a, Normalized PV generation profile and the corresponding incremental rebound demand under the sweeping, simultaneous and dynamic profiles. b, Synthesized household load profile (without rebound) and the resulting total load when adding the profile-specific incremental rebound demand. Dashed lines indicate incremental demand attributable to the SRE.
Source data
Nomenclature (definitions of indices, sets, parameters, variables and equations).
E2M2s SRE source code and accompanying input files for reproducing the optimization runs, including a README mirror of the GitHub repository at https://github.com/ude-ewl/osE2M2s/tree/Paper-SRE.
Empirical data.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Processed model output data as plotted.
Generation profiles for panel a and standard load profile for panel b.
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Delic, M., Bucksteeg, M. Implications of the solar rebound effect for the European energy transition. Nat Energy (2026). https://doi.org/10.1038/s41560-026-02031-8
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Received: 25 July 2025
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Published: 14 April 2026
Version of record: 14 April 2026
DOI: https://doi.org/10.1038/s41560-026-02031-8
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