1. Introduction
The challenge of climate change mitigation is unprecedented. Staying within a maximum global warming of 1.5 requires accelerating the transition to a low-carbon society. A key process suggested to foster such fast, nonlinear change is social tipping (Otto et al., Reference Otto, Donges, Cremades, Bhowmik, Hewitt, Lucht, Rockstro¨m, Allerberger, McCaffrey, Doe, Lenferna, Mor´an, van Vuuren and Schellnhuber2020). Social tipping dynamics, also known as positive tipping, occur in low-carbon transitions when a small change or intervention in the socioeconomic system has a disproportionately large effect on emission reductions. With positive tipping, the reinforcing feedback in a system overwhelms balancing feedback, triggering self-propelling change, which leads to acceleration toward a more sustainable state (Lenton et al., Reference Lenton, Milkoreit, Willcock, Abrams, Armstrong McKay, Buxton, Donges, Loriani, Wunderling and Alkemade2025). When tipping in one system or sector spills over to another system or sector, this may lead to tipping cascades, further accelerating the overall transition to sustainability.
The rapidly growing literature on social tipping suggests various processes that can contribute to tipping dynamics, including education and information provision, norm changes, coordinated policy efforts, and technological learning (Otto et al., Reference Otto, Donges, Cremades, Bhowmik, Hewitt, Lucht, Rockstro¨m, Allerberger, McCaffrey, Doe, Lenferna, Mor´an, van Vuuren and Schellnhuber2020; Stadelmann-Steffen et al., Reference Stadelmann-Steffen, Eder, Harring, Spilker and Katsanidou2021). The empirical support for the accelerating effect of technological learning in key technologies like wind and solar is quite strong, but the evidence base for other potential social tipping dynamics and the tipping criteria is less clear (Milkoreit, Reference Milkoreit2023). For example, while the potential impact of behavioral and norm changes is widely recognized, such changes typically involve affecting the routines or social practices of people, which is often difficult (Kollmuss & Agyeman, Reference Kollmuss and Agyeman2002; Steg et al., Reference Steg, Perlaviciute and van der Werff2015).
The sustainability transitions literature has long recognized these difficulties and offers a systems perspective on how transformations in socio-technical systems occur. It analyzes how promising new system configurations that emerge in niches can scale up to the system level, analyzing factors that support and hinder the change. Geels (Reference Geels2018), for example, illustrates how changes that involve a radical technical innovation and require a substantial change in social and user practices are the most difficult. Sovacool et al. (Reference Sovacool, Geels, Andersen, Grubb, Jordan, Kern, Kivimaa, Lockwood, Markard, Meadowcroft and Meckling2025) identify five dimensions of acceleration: economics and innovation, technology, business, policy, and culture. Rooted in the multilevel perspective on transitions, Geels and Ayoub (Reference Geels and Ayoub2023) offer a broader systems view on tipping dynamics and identify seven feedback loops between users, technology, firms, policymakers, and the wider public. In this view, tipping occurs when there is alignment between system elements. Such alignment, for example, occurs when technologies contribute to multiple policy goals or when the diffusion of one technology increases the attractiveness of other (complementary) technologies.
Policy can create incentives that stimulate this alignment and thereby social tipping. Purchase price subsidies and feed-in tariffs are key instruments to realize cost reductions through technical learning. The Global Tipping Points Report 2025 identifies mandates as one of the most effective interventions (Lenton et al., Reference Lenton, Milkoreit, Willcock, Abrams, Armstrong McKay, Buxton, Donges, Loriani, Wunderling and Alkemade2025). However, mandates only become politically feasible when there is a suitable alternative available, and instruments like feed-in tariffs and purchase price subsidies accelerate the diffusion of zero-emission technologies. But such instruments are also costly and are now being phased out in some countries due to net congestion. As the policy mix and the socio-technical system interact through different feedbacks, the timing and sequencing of policy interventions thus require attention (Edmondson et al., Reference Edmondson, Kern and Rogge2019; Meckling, Reference Meckling2019; Meckling et al., Reference Meckling, Sterner and Wagner2017). There may, for example, be delays in the change observed in one system and in the cascading effect on another system. This can be due to threshold effects (Pizziol & Tavoni, Reference Pizziol and Tavoni2024), as well as due to different mechanisms operating on different timescales. Behavior change can be quite immediate, whereas the adoption of new technologies also depends on lifecycles and replacement rates.
These general conceptualizations highlight the role of system couplings in accelerating system transformation, providing a good starting point for analyzing tipping dynamics. However, when translating these insights into interventions, we seek to identify specific leverage points that can trigger such cascades (Allen & Malekpour, Reference Allen and Malekpour2023). Supporting tipping cascades thus requires a model of how social processes and interventions scale up (upward scaling cascades) through socio-technical systems (Franzke et al., Reference Franzke, Ciullo, Gilmore, Matias, Nagabhatla, Orlov, Paterson, Scheffran and Sillmann2022), identifying the potential policy leverage points. This paper, therefore, develops a stylized modeling exercise to explore the potential emergence of cascades from the existing evidence about interactions within and between the energy, mobility, and housing sectors. Specifically, we focus on four household technologies that experience fast cost reductions through learning, and where tipping dynamics may occur (Alkemade et al. Reference Alkemade, de Bruin, El-feiaz, Pasimeni, Niamir and Wade2024; Lenton et al., Reference Lenton, Milkoreit, Willcock, Abrams, Armstrong McKay, Buxton, Donges, Loriani, Wunderling and Alkemade2025): electric vehicles (EV), heat pumps (HPs), rooftop solar photovoltaic (PV), and HBs. These technologies serve different basic household needs such as heat and mobility. Individually, the adoption of these technologies does not necessarily require large changes in social practices, but when taken together as a system, they might. When self-sufficiency at the household level becomes the norm, this leads to a radically different, more decentralized, and highly integrated system. The transition to such a new energy system is supported by reinforcing feedback loops from technology learning, but also faces balancing feedback due to, for example, net congestion.
The model presents insights into the interactions between reinforcing and balancing feedback loops, and potential leverage points, within and across subsystems. To model and analyze the potential feedbacks between the different technologies requires a deeper understanding of what classifies as a cascade, how likely different feedbacks are to occur, and which feedbacks initialize the cascade. In this study, cascade dynamics is conceptualized as the sequential and interdependent diffusion of technologies across the energy, mobility and housing domains, where adoption in one subsystem modifies the conditions for adoption in others, leading to system transformation. We conceptualize such transformation as the level of householders’ self-consumption (SC) that is enabled by the diffusion of modular and decentralized energy technologies. A norm shift in self-sufficiency signals a transformation in how key societal functions for household energy and mobility provision are delivered.
The main contribution of the paper is therefore the development of a stylized agent-based model that integrates multiple interconnected and interacting household technologies within a single framework. This allows us to explore how adoption dynamics emerge from the bottom up and how interactions across the energy, mobility, and housing sectors can facilitate or constrain cascade processes. A further contribution is the explicit representation of reinforcing and balancing feedbacks between technologies, including the role of behavioral preferences for SC as a driver of the transformation to a more decentralized energy system. Finally, the paper proposes a simple operational approach to analyzing cascade dynamics through the sequencing of technology diffusion across interconnected subsystems, thereby providing a complementary perspective to existing tipping-point and system-dynamics approaches.
To this end, the paper proceeds as follows. First, in Section 2, we provide a brief overview of the literature on social tipping and tipping cascades in sustainability transitions. We present the technology domains considered in this study and the adoption feedback occurring within and between such domains. We also present the contribution of our model in relation to the modeling literature in the social tipping literature. In Section 3, we explain the model, and in Section 4 we present the results. In Section 5, we discuss the findings, provide conclusions, and acknowledge the limitations, assumptions, and avenues for future research.
2. Understanding tipping cascades
2.1. Conceptualizing tipping cascades in sustainability transitions
The literature on social tipping and tipping cascades originated from an analogy with tipping in ecological systems, where tipping cascades involve clearly defined ecosystem levels. When positive tipping in one domain or sector spills over into another domain, positive tipping cascades may occur, leading to an acceleration of sustainability transitions. Specifically, upward-scaling tipping cascades occur in interconnected complex systems when the ‘activation of one tipping point increases the likelihood of triggering another at a larger scale, and then another at a still larger scale’ (Lenton, Reference Lenton2020; Sharpe & Lenton, Reference Sharpe and Lenton2021; Ta`bara et al., Reference Ta`bara, Frantzeskaki, Ho¨lscher, Pedde, Kok, Lamperti, Christensen, Ja¨ger and Berry2018). As the definition of social tipping concerns tipping to a different, more sustainable system state, tipping cascades, in this context, also have this same normative connotation.
This upscaling in socio-technical systems can take different forms (Miörner & Binz, Reference Miörner and Binz2021) and tipping cascades can involve both upscaling and transformation. Scaling and transformation may go hand in hand, but this is not always the case. Specifically, while some technologies scale up globally (Binz & Truffer, Reference Binz and Truffer2017) and change global systems, other forms of scaling can also be transformative. This can occur, for example, through spillovers when actors seek to incorporate additional sustainable technologies into their practices, or when cost reduction in one technology increases the attractiveness of complementary technologies (Ate¸s et al., Reference Ate¸s, Rogge and Lovell2024). The literature on deep transitions addresses this difference between diffusion and transformation in the context of social tipping (Yang & Schot, Reference Yang and Schot2025).
The interconnections between systems are the enablers of acceleration in this context. At the same time, these interconnections are typically also a source of lock-in in the old system (Seto et al., Reference Seto, Davis, Mitchell, Stokes, Unruh and Urge-vorsatz2016). Tipping one system element can thus provide momentum to escape this lock-in and set in motion further change and system reconfiguration. A key source of tipping dynamics in sustainable energy and mobility transitions is the learning curve. Especially, small and modular, or so-called granular, technologies such as solar PV and batteries exhibit rapid cost reductions through learning (Way et al., Reference Way, Ives, Mealy and Farmer2022). The sustainability transitions literature also acknowledges the importance of the interconnections between systems. Multisystem interactions can lead to competition, symbiosis, integration, and spill-over, and can be important determinants of transformative change (Raven & Verbong, Reference Raven and Verbong2007). More recently, Andersen and Geels (Reference Andersen and Geels2023) conceptualize multisystem interactions between different regimes and niches. Regimes are coupled both structurally, through elements that exist between systems in three structural dimensions – technology, actors, and institutions – and functionally through flows of resources across systems.
Against this background, this study examines feedback mechanisms within and between technology domains. Increased adoption of one technology may enhance the attractiveness of complementary technologies through reinforcing feedbacks, but it can also generate balancing feedbacks that drive further change and system reconfiguration. We therefore conceptualize cascade dynamics as the sequential and interdependent diffusion of technologies, whereby adoption in one subsystem modifies the conditions for adoption in others through both reinforcing and balancing feedback mechanisms.
2.2. Technology domains and adoption feedback
In various domains, including energy, mobility, and housing, small-scale decentralized and modular energy technologies are a key determinant of system transformation (Bouffard & Kirschen, Reference Bouffard and Kirschen2008). Not only can these technologies enable more efficient use of (renewable) energy resources, but they also empower households to adopt and use them (almost) independently of the central planner (Raven et al., Reference Raven, Lane, Lindsay, Reynolds and Kronsell2025, Reference Raven, Reynolds, Lane, Lindsay, Kronsell and Arunachalam2021).
In this paper, we focus on four specific small-scale decentralized and modular energy technologies: rooftop solar PV (PV), HBs, EV, and HPs. PV and HP systems are often adopted as stand-alone technologies first (Lagomarsino et al., Reference Lagomarsino, van der Kam, Azad, Parra and Hahnel2023). However, the adoption of a technology may hinder or stimulate the co-adoption with another technology (Fleiß et al., Reference Fleiß, Hatzl and Rauscher2024). For example, EVs still align with the paradigm of individual car-based mobility as the dominant mode of transport for many households. However, their use as part of a decentralized and integrated system may require and enable new energy and mobility practices. HPs can provide a more efficient and low-cost heating system to householders, but they can also be a source of flexibility and SC in the housing sector (Gaur et al., Reference Gaur, Fitiwi and Curtis2021). HBs are emerging as a key technology for enhancing SC, providing flexibility, and supporting household electrification (van der Kam, Pena-Bello, et al., Reference van der Kam, Pena-Bello and Parra2025).
Evidence of technology-to-technology feedback and synergies between technologies that lead to co-adoption and adoption sequencing was, for example, observed for the co-development of power and heat in the Netherlands (Raven & Verbong, Reference Raven and Verbong2007). The co-adoption of solar PV and EVs usually takes place in a sequential order, suggesting that the adoption of one technology may be influenced by the adoption of the other. Based on interviews in the United States, Bull et al. (Reference Bull, Buch, Freling, Hardman and Firestone2025) propose the concept of conditional value as a driver of PV–EV co-adoption, in which EV adopters consider PV to reduce electricity costs and PV adopters consider EVs to utilize excess PV generation. Other simulation exercises have shown that the diffusion of EVs and HPs increases the market potential of stationary HBs by enhancing the local utilization of self-generated PV electricity (Klingler, Reference Klingler2018; Parra et al., Reference Parra, Walker and Gillott2014). Furthermore, a cross-national survey in Germany, the Netherlands, and the UK shows that 41% of the respondents have adopted at least one of the following technologies: PV, HB, EV, and HP with a very high degree of co-adoption among them (Hedde-von Westernhagen et al., Reference Hedde-von Westernhagen, Pasimeni, Van Den Broek and Alkemade2026).
While there is thus some evidence for technology-to-technology feedbacks and strong empirical evidence for the feedback between technology diffusion, cost reduction, and further diffusion through the learning curve, the evidence for other feedbacks between household energy-relevant behaviors is less clear. For instance, the evidence about the effects of household renewable energy (technology) adoption on household energy consumption is mixed, as both positive spillovers and rebound effects have been observed (Du¨tschke et al., Reference Du¨tschke, Galvin and Brunzema2021; Sorrell et al., Reference Sorrell, Gatersleben and Druckman2020). Positive spillovers occur when, for example, households that adopt rooftop solar PV also want to become more environmentally friendly in their other energy behaviors, leading to a reduction in energy consumption (Steg et al., Reference Steg, Perlaviciute and van der Werff2015).
Rebound effects occur when the ‘free electricity’ from PV leads to the adoption of new energy-intensive practices (Qiu et al., Reference Qiu, Kahn and Xing2019). Furthermore, demographic and psychological characteristics, technology attitudes, and living arrangements remain key determinants of co-adoption (Hajhashemi et al., Reference Hajhashemi, Sauri Lavieri and Nassir2024; Lagomarsino et al., Reference Lagomarsino, van der Kam, Azad, Parra and Hahnel2023), and therefore influence the feedback mechanisms between domains.
The four technologies considered in this study together cover various forms of SC enhancement, from increasing the household electricity demand to adding flexibility to household consumption. Our choice of technologies aims to balance the realism of complex cross-domain interactions and the tractability of the resulting dynamics. While a more comprehensive model could include additional technologies and flexibility solutions (e.g., vehicle-to-grid [V2G] or smart meters), EVs, PV, HPs, and HBs represent a set of technologically mature and increasingly widespread household technologies that cover the central functional domains of a future integrated energy system: energy generation, energy storage, heating, and mobility (Cambini et al., Reference Cambini, Congiu, Jamasb, Llorca and Soroush2020; European Commission, 2020). Existing research on integrated residential energy systems and sector coupling highlights the strong operational interdependencies among these domains and the cascading effects that may emerge from household-level investment and operational decisions under current market and regulatory conditions (Angenendt et al., Reference Angenendt, Zurmu¨hlen, Ru Cker, Axelsen and Sauer2019; Aniello & Bertsch, Reference Aniello and Bertsch2023).
Furthermore, apart from a few exceptions (Lagomarsino et al., Reference Lagomarsino, van der Kam, Azad, Parra and Hahnel2023; van der Kam, Lagomarsino, et al., Reference van der Kam, Lagomarsino, Parra and Hahnel2025), studies on household-level technology adoption across domains have mostly treated the synergies between pairs of technologies (Brown & Chapman, Reference Brown and Chapman2023). By investigating the interdependencies among four technologies (PV, HBs, EVs, and HPs), our study extends this literature by advancing the understanding of higher-dimensional adoption and diffusion dynamics and the feedback mechanisms that drive cross-domain cascade dynamics.
2.3. Modeling tipping cascade
Modeling tipping and cascade dynamics within the socio-technical context is becoming highly relevant to provide insights for informing interventions (Niamir & Creutzig, Reference Niamir and Creutzig2025). The model presented in this study is conceptually grounded in the social tipping literature (Otto et al., Reference Otto, Donges, Cremades, Bhowmik, Hewitt, Lucht, Rockstro¨m, Allerberger, McCaffrey, Doe, Lenferna, Mor´an, van Vuuren and Schellnhuber2020). In particular, it aligns with the energy production and storage social tipping element, where decentralized energy production, storage, and flexible demand play a central role in accelerating system transformation. The aim is to provide insights into how the adoption of one household technology unlocks or prevents the adoption of others, and therefore when reinforcing and balancing feedbacks combine to produce a cross-domain cascade.
The literature on social tipping in the energy transition mostly take two different modeling perspectives: a macro/system-level perspective and a micro/individual-level perspective. The macro perspective asks how the feedback mechanisms within the system as a whole give rise to system tipping (Eker et al., Reference Eker, Wilson, Ho¨hne, McCaffrey, Monasterolo, Niamir and Zimm2024; Geels & Ayoub, Reference Geels and Ayoub2023), but these approaches remain largely qualitative. The micro perspective applies this feedback logic at the level of heterogeneous individuals who influence one another and adopt under peer effects. However, in this approach, tipping typically arises once a critical mass is reached (Pizziol & Tavoni, Reference Pizziol and Tavoni2024; Smith et al., Reference Smith, Wiedermann, Donges, Heitzig and Winkelmann2025; Wiedermann et al., Reference Wiedermann, Smith, Heitzig and Donges2020).
On the one hand, we combine both perspectives. We take the macro perspective because a cascade is a property of the system-level feedbacks between technologies, and the micro perspective because whether those feedbacks engage depends on the discrete adoption decisions of individual households operating under their own budgets and heterogeneous preferences. In fact, individual households interact with aggregated system-level parameters (e.g., the diffusion of each technology and grid constraints) and act based on individual attributes (e.g., household budgets and preferences). The dynamics of the model thus arise from the interplay between the two levels, as system-level feedbacks shape household adoption decisions, and these decisions in turn update the system-level conditions to which other households respond.
On the other hand, we also differentiate from both perspectives. Previous works primarily analyze system dynamics at an aggregate level, while our model represents household-level adoption decisions and interactions between decentralized technologies across the specific energy, mobility, and housing domains. Our approach also differs from microlevel, threshold-based tipping models. The objective of our model is not to identify a precise tipping threshold at which a system shifts to a new equilibrium. Rather, we examine how interacting technology diffusion processes can generate cascade dynamics through reinforcing and balancing feedback mechanisms. Although we use a diffusion threshold as a reference point (more on this in the next sections), this serves only as an operational indicator to compare the sequencing and magnitude of technology diffusion across scenarios, rather than as a theoretical tipping point.
The contribution of the model is therefore not to predict a specific transition pathway but to explore how different system conditions shape the sequencing of adoption processes and the resulting levels of SC. Although adoption decisions are modeled at the household level, our interest lies in how these individual choices aggregate into diffusion patterns and broader system outcomes. The analysis therefore focuses not only on final adoption levels but also on the interactions and sequencing of diffusion processes across subsystems. In this way, the model provides insight into how interconnected diffusion processes can facilitate or constrain cascade mechanisms.
3. The model
We model how households adopt and operate a set of decentralized energy technologies over time, and how these household decisions interact with broader system conditions.Footnote 1 The adoption decisions modeled are PV panels, HBs, EVs, HPs, and energy efficiency (EE) behavioral measures. The model assumes a population of households making decisions sequentially and adaptively based on economic conditions, technology visibility, available energy resources, and social and behavioral preferences. The simulation progresses in discrete time steps, in which at each time step one household is selected to consider the adoption of one of these options.
Technologies differ in their role within the energy system. PV systems generate renewable electricity; HBs store this electricity for later use; and EVs and HPs can be powered either via the national electricity grid or via SC of PV-generated electricity, depending on household choice and the availability of (stored) electricity. EE measures, by contrast, reduce energy expenditure and increase the household budget over time, but do not require upfront investment. Instead, PV adoption does not generate direct household income through electricity exports to the grid, reflecting the increasingly common situations in which feed-in tariffs are phased out and excess residential PV generation receives limited, zero, or even negative compensation due to grid congestion (Brown et al., Reference Brown, Hall and Davis2019).
When households switch from using mostly grid electricity to high levels of SC, we consider this to be a transformative change. In our model, SC describes the share of household electricity demand that is met through locally generated or stored PV energy rather than through the national grid (NG). SC is desirable for households to varying degrees, depending on their behavioral preferences for self-sufficiency and technology co-adoption (Alipour et al., Reference Alipour, Taghikhah, Irannezhad, Stewart and Sahin2022; van der Kam, Lagomarsino, et al., Reference van der Kam, Lagomarsino, Parra and Hahnel2025). Households with a high preference for SC will be more inclined to operate EVs and HPs using self-generated electricity rather than the NG, provided that the necessary PV and storage capacity are in place.
The system includes a PV buffer, representing the shared constraint on how much PV electricity can be stored for later SC. If the system is highly saturated with PV generation, the buffer becomes constrained, which reduces the incentive to adopt new PV units unless households have ways of using this electricity internally via HB storage or through EV and HP charging. Thus, PV adoption becomes more attractive when grid congestion is low and less attractive when congestion increases, a situation currently faced by several European countries.
In line with the literature described above, each household is characterized by its current level of technology adoption, available budget, and a behavioral preference parameter that describes how strongly it values SC of locally generated electricity. Households evaluate adoption through a sequence of feasibility checks that reflect economic and infrastructural constraints. For example, households may only adopt a new technology if they have sufficient budget, if they have not yet reached the maximum number of units they can own, and if the technology is visible to them. Visibility represents household awareness of the technology and can evolve through diffusion, mimicking, imitation, and social influence.
When considering EV and HP adoption, households additionally evaluate whether to operate these technologies using the NG or via SC. If PV capacity is available and the household has a strong SC preference, an adopted EV or HP can immediately operate on locally generated electricity. Otherwise, it is adopted as grid-dependent, with the potential to switch to SC later if conditions improve (e.g., if PV capacity increases).
Adoption is probabilistic rather than deterministic. Each technology has an adoption probability that depends on its current market share, household preferences, and systemwide conditions. For example, the probability of adopting PV declines as the PV buffer saturates but increases when many EVs and HPs are still operated via the grid, since PV would help shift these uses toward SC. The probability of adopting HBs, conversely, increases when the PV buffer becomes tight, since storage helps relieve this constraint. EV and HP adoption probabilities are influenced by the availability of PV and HB capacity to support SC, as well as by whether other EV or HP units are already being operated via the grid. This creates a dynamic interdependence among technologies: the adoption of one technology may enable or discourage adoption of another, as has also been described in the literature reviewed earlier.
Such interdependencies are presented in Figure 1. In short, the model simulates mechanisms that generate a combination of complementary and competitive adoption dynamics that shape technology diffusion and the emergence of cascade effects across subsystems. First, PV, HB, EV and HP technologies compete for limited household financial resources, creating crowding-out dynamics through budget reduction, while EE measures instead generate savings that can enable later adoption decisions.Footnote 2 Second, some technologies generate complementary effects that increase the attractiveness or feasibility of adopting other technologies (e.g., PV increases the attractiveness of SC operation of EV and HP, and HB adoption). Third, some technologies interact through both reinforcing and balancing mechanisms depending on system conditions (e.g., increasing buffer capacity acts as a balancing feedback on self-consuming EVs/HPs via reducing the incentive for HB adoption). Over time, these feedbacks shape technology diffusion patterns, household electricity SC, and the overall balance between local renewable use and grid dependence.
Feedback loops.
Figure 1 Long description
This causal loop diagram represents the reinforcing and balancing mechanisms of the energy system in the model. There are seven components: PV, Buffer, HB, HP (operating using electricity from the national grid (NG) or through self-consumption (SC), and EV (operating using electricity from the national grid (NG) or through self-consumption (SC). Each component is represented by a labeled rectangle and arrow are marked with a plus or minus sign, indicating reinforcing and balancing feedback, respectively. The diagram illustrates the complex interdependencies and feedback loops within the system, highlighting how each component influences others.
The key outcome of interest in this model is the evolution of household SC. As modeled here, increasing SC does not simply change how households adopt and use energy technologies; it actively reshapes the structure of the energy system itself. Households move from passive consumers to active participants in local energy production, storage, and demand management, thus influencing the operation of the system and sectoral dynamics. This transformation unfolds gradually and across technologies, meaning that the timing and sequence of adoption matter. For this reason, we also analyze the adoption shares of each technology and the order in which they diffuse over time.
Model initialization
Table 1 Long description
Columns list Symbol, Description, and Initial value for householders and five technologies plus simulation settings. Householders include M, total number of households, 200; Bi, budget, normally distributed with mean 10 and standard deviation 1.5; and Ri, preference for self consumption, normally distributed with mean 0.5 and standard deviation 0.05. We index the five alternatives by j = 1, …, 5, where j = 1 corresponds to PV, j = 2 to HBs, j = 3 to EVs, j = 4 to HPs, and j = 5 to EE. Initialised values for thechnologies include adoption cost (Cj) 1, subsidy rate (Lj), max units per household (Maxj), market share at time t=1 (Sj,t=0) , and electricity potential enabled (ηj). Simulation steps are 150,000 and simulation runs are 20.
4. Results
4.1. The system transformation
4.1.1. Model initialization
The model is initialized as in Table 1.Footnote 3 We simulate the adoption decisions of a population of M = 200 heterogeneous householders. Each householder has an initial preference for SC (Ri) that is randomly drawn from a normal distribution with mean 0.5 and standard deviation 0.05, meaning that at each decision step, there is, on average, a 50% probability of preferring to operate an EV or HP in SC mode rather than via the NG.
All households have an initial budget (Bi) randomly drawn from a normal distribution with a mean of 10 and a standard deviation of 1.5. This allows the simulation of a heterogeneous population with varying economic capacities but that, on average, has sufficient budget to allow the adoption of any technology over time, including through savings generated by EE measures. The budget is expressed in stylized units of credits, with technology adoption costs defined in corresponding units. With this abstraction, we aim to capture the budget/investment trade-off to remain proportional to real-world cost ratios, without requiring direct monetary calibration.Footnote 4
The buffer’s maximum capacity is set to F max = 80, implying that the electricity system (i.e., the grid) can accommodate up to approximately 40% of households adopting PV without requiring SC. Beyond this level, additional PV generation would exceed the grid’s capacity to absorb surplus electricity exported back to the grid.
One credit (C HB) is the cost of adopting one unit of HB, and each householder can adopt a maximum of two HB units (MaxHB). The fraction of PV electricity that can be made usable per unit of HB adopted is set at 25% (η HB), meaning that two HB units are required for a household to fully utilize the electricity potential generated by its adopted PV units.
EVs are the most expensive household technology, with a cost equal to twice that of one PV unit (CEV = 2). Based on household vehicle ownership statistics, we allow each householder to adopt up to three EV units (MaxEV). When operated in SC mode, one EV unit uses 50% of the available electricity potential (η EV = 0.5).
Householders may also adopt up to two HP units (MaxHP). Each HP unit costs one credit (C HP = 1), and when operated in SC mode, one HP unit uses 50% of the available electricity potential (η HP = 0.5).
In this initial configuration, no subsidies are provided for the four household energy technologies. However, adopting one EE measure yields a saving of 0.1 (L EE), which increases the householder's budget accordingly. Householders may adopt up to 10 EE measures (MaxEE), meaning that full adoption may generate an additional credit unit in total.
All alternatives start with an initial market share of 10% (Sj,t =0), which corresponds to their initial probability of adoption at the beginning of the simulation.
The model is run for 150,000 time steps. Since only one householder evaluates one alternative at each step, this corresponds to each householder, on average, evaluating each alternative approximately 150 times over the simulation. For each parameter configuration, the model is run 20 times with different random seeds to account for stochastic variability, and results are reported as the average across these runs.Footnote 5
4.1.2. Transformation dynamics
Based on this initial, favorable scenario, which represents a relatively wealthy population with a medium level of preference for SC and grid capacity, Figure 2 illustrates the main dynamics we observed in the different simulations.
The model dynamics.
Figure 2 Long description
The charts in this figure show (a) the diffusion rate over time for the five alternatives; (b) the adoption probabilities for these alternatives and the status of the PV buffer over time; (c) the level of self-consumption (SC), the usable electricity potential (left vertical axis), and the average household budget over time (right vertical axis); and (d) the share of both EVs and HPs operating via the national grid (NG) and in SC mode.
Four of the five alternatives, namely HP, EV, PV, and EE, reach almost full diffusion following an S-shaped curve (plot (a)), although at different times and in a specific order. In contrast, HB reaches about 70%. HP is the first to fully diffuse with a diffusion speed similar to that of EV. However, as shown in plot (d), the majority of EVs and HPs initially operate via the NG. Only after roughly half of the simulation run, around 25% of the already-adopted EVs and HPs switch to SC mode.
This switch occurs because the usable electricity potential increases, mainly due to the adoption of HB, which enables a greater share of PV-generated electricity to be used in SC. PV is the third technology to diffuse, but its adoption initially slows because it is constrained by the buffer (plot (b)). When PV-generated electricity cannot be used in SC, it flows into the buffer, gradually filling it. As the buffer approaches full capacity, the probability of further PV adoption decreases.
Meanwhile, since most EVs and HPs still operate via the NG and the buffer space is not fully available, the probability of adopting HBs increases. HB adoption releases more usable electricity potential (plot (c)), which in turn enables EVs and HPs to switch into SC mode. This switch then reduces pressure on the buffer (plot (b)), allowing PV adoption to accelerate again. In this way, a sequence of reinforcing and balancing feedback loops drives the co-evolution of the system.
EE measures play a crucial role in these dynamics. As seen in plot (c), the average household budget initially decreases rapidly due to the early adoption of EVs, HPs, and PV. Once EE measures begin to diffuse, they generate savings that replenish household budgets. These savings are frequently invested in HB adoption, which is key to unlocking usable electricity potential and sustaining the growth of SC.
The overall degree of SC is shown in plot (c). During the first part of the simulation, the SC rate rises rapidly due to the simultaneous adoption of HPs and EVs, with a portion already operating in SC mode. At this stage, SC reaches approximately 75%. The rate then decreases slightly as the usable electricity potential increases due to HB adoption, which is not yet fully utilized. As more HB units are adopted, buffer space expands, additional PV units are installed, and electricity potential is largely used as EVs and HPs switch to SC.
This scenario shows how a transformation of the system can occur, in which household energy technologies are not only adopted but also operated using locally generated electricity. The trend in buffer space (plot (b)) deserves particular attention: the grid initially acts as an enabler of the transformation, constraining and incentivizing the adoption of SC technologies and behaviors. Once the transformation is established, however, much of the grid capacity remains unused.
4.2. The cascade effect
In this section, we simulate four different scenarios to study the cascade effect and how it leads to different system transformations. We do so by examining the diffusion shares of the five alternatives and ranking them according to the time at which the first one reaches a 50% diffusion rate. At the time step (when the first alternative reaches this threshold), we then observe the diffusion levels of the remaining four alternatives. Rather than representing a definitive tipping point in a strict theoretical sense, we use the 50% threshold as a simple indicator of majority diffusion within a technology subsystem, which may contribute to accelerating diffusion in other domains through cascade mechanisms.Footnote 6
The first scenario assumes a population with a very high preference for SC. The second scenario assumes a medium-level preference for SC but introduces subsidies for three of the four household energy technologies: HBs and HPs receive a 25% reduction in adoption cost, while EVs receive a 5% reduction. PV does not receive subsidies, reflecting its current trend toward affordability due to technological learning curves and congestion concerns. The third scenario tests the effect of a low PV buffer capacity (i.e., a rapidly congested grid) without subsidies. Finally, the fourth scenario considers a population with strong budget constraints, where households have limited resources available for adoption. Table 2 summarizes the initialization settings for these four scenarios.
Scenario initialization
Table 2 Long description
Table shows the four scenarios simlulated, each with a specific initialisation of key model parameters: budget (Bi), preference for self-consumption (Ri), the PV buffer max space (Fmax) and subsidy (Lj). The four scenarios simulated are: High self-consumption, Subsidy, Low buffer, and Low budget. Scenarios High self-consumption, Subsidy, and Low buffer have Bi initialised with a normal distribution with mean 5 and standard deviation 1.5, while Low budget shows Bi=1. For Ri, High self-consumption scenario shows 1, while Subsidy, Low buffer, and Low budget scenarios each show a normal distribution with mean 0.5 and standard deviation 0.05. For Fmax, High self-consumption, Subsidy, and Low budget each have 80 as initialised value, while Low buffer has 40. The Subsidy scenario shows values for LHB=0.25, LEV=0.05, and LHP=0.25.
Notes: The five alternatives in these scenarios have the following initial market shares: S PV,t=0 = 0.4, S HB,t=0 = 0.1, S EV,t=0 = 0.2, S HP,t=0 = 0.1, and S EE,t=0 = 0.1. All remaining model parameters are initialized as in Table 1.
Figure 3 summarizes the main outcome of the scenario analysis. In the first scenario, where householders have a strong preference for SC (i.e., they always prefer to operate EVs and HPs in SC mode and switch to SC), PV becomes the leading technology driving system transformation. Since PV supplies the electricity needed for SC operation, high PV adoption is a precondition for widespread SC. This highlights that behavioral preferences can significantly reshape cascade dynamics by altering the ordering of technologies. In particular, a high SC preference strengthens the coupling between PV and end-use electrification, where PV becomes an enabling technology in the sequencing of subsystem transitions.
The cascade effect: scenario analysis.
In the second scenario, subsidies accelerate adoption dynamics but do not fundamentally alter the order in which technologies diffuse compared to the previous scenario, although EVs and HPs are adopted slightly faster due to reduced costs. This suggests that while subsidies reduce economic barriers and accelerate diffusion, they do not generate new dominant feedback loops capable of reordering the cascade structure. Therefore, cost reductions alone have limited capacity to reshape cascade dynamics, and instead tend to reinforce an already existing diffusion sequence.
In contrast, low buffer capacity (the third scenario), which represents a congested grid, drastically reduces PV adoption. As a result, HPs become the first technology to reach 50%, followed by EVs. However, both mainly operate via the NG, leading to the lowest final SC level among all scenarios (around 36%), compared to approximately 73% in the previous cases. This suggests that limited buffering capacity not only affects individual technology uptake but also weakens the reinforcing feedbacks between PV generation and electrified end uses. As a result, cascade dynamics are dampened, indicating that grid congestion can act as a structural constraint that prevents the emergence of self-reinforcing adoption loops across subsystems.
Finally, the low-budget scenario (the fourth scenario) leads householders to adopt EE measures first, making EE the first alternative to reach 50%, followed by PV and HPs. EVs and HBs are not adopted at all. Interestingly, despite strong financial constraints, this scenario still achieves a relatively high SC level (around 56%), suggesting that limited resources incentivize householders to prioritize efficiency and maximize the use of available local electricity. This indicates that financial constraints do not necessarily undermine cascade dynamics, but instead reconfigure them by shifting adoption priorities toward low-cost, high-impact measures. As a result, cascade effects become more selective and efficiency-driven, suggesting that budget constraints can reshape cascade dynamics while still enabling relatively high levels of SC.
Overall, these scenarios highlight how different structural and behavioral factors shape the diffusion of technology and the dynamics of the cascade. For example, when the PV buffer has low maximum space (i.e., low F max), excess solar energy cannot be efficiently stored, so households can adopt EVs and HPs without prior PV investment, leading to continued use of grid electricity and a low SC rate. In contrast, when households have a strong preference for SC (Ri = 1), PV adoption increases first and enables further electrification across sectors. Subsidies mainly accelerate adoption by reducing costs but do not change the sequencing of technology adoption; hence, they do not alter the cascade. When householders face low-budget conditions, adoption is constrained, but EE measures still allow for relatively high SC. Therefore, technology adoption and cascade dynamics depend on whether interdependencies reinforce feedbacks or instead weaken or reconfigure them.
4.3. The effect of householders’ budget and PV buffer
In this section, we analyze the combined impact of householders’ budget and the PV buffer on the overall rate of SC in the system, considering it as an indicator of system transformation. Higher SC rates may indicate a reshaping of the energy system structure, which in turn influences system operation and sectoral dynamics.
We vary the mean value of the householders’ budget (µB) between 2 and 10, and the PV buffer’s maximum capacity (F max) from 20 to 180 at regular intervals of 20. This setup allows us to explore scenarios ranging from very low to very high grid capacity, and from highly budget-constrained to wealthy populations.
The results, reported in the heat map in Figure 4, show that unless the population is extremely budget-constrained (µB < 2) or has enough resources to adopt all alternatives (µB > 10, in which case almost full SC is reached), the level of SC strongly depends on the buffer size. For very high buffer capacity, the SC rate can reach around 76% or more, while it drops significantly for lower buffer levels.
The combined effect of budget and buffer.
Interestingly, this analysis shows that while the system (i.e., the buffer) can support at least 50% of the population adopting PV without SC, increasing buffer capacity beyond this threshold does not substantially increase SC. This implies that, for grid management purposes, the buffer can be designed to achieve a target SC level without over dimensioning the system. Conversely, a PV buffer designed to accommodate less than 50% of PV adopters without SC may reduce performance, and decreasing the buffer from 50% to 20% could lower SC from approximately 75% to 35%.
4.4. The effect of subsidies
In this section, we analyze the effect of subsidies on the rate of SC. We define scenarios in which the subsidies for EVs, HBs, and HPs vary from a 5% to a 25% reduction in adoption cost, in increments of 5%. These subsidy combinations are tested in a context where householders face strong budget constraints (Bi = 1). The rationale is that under such financial limitations, households would benefit more from subsidies than in situations where a moderate budget already allows for technology adoption. Results are reported in the heat map in Figure 5.
The effect of different levels of subsidies on an EV, HB, and HP.
Figure 5 Long description
Three heatmaps display self-consumption rates under varying subsidy levels for electric vehicles, home batteries and heat pumps. Each heatmap corresponds to a specific subsidy level for electric vehicles: 0.05, 0.15 and 0.25. The vertical axis is labeled with subsidy level for home battery values from 0.05 to 0.25 and the horizontal axis with subsidy level for heat pump values from 0.05 to 0.25. Numerical values within the cells range from 0.17 to 0.22, with darker shades indicating higher self-consumption rates.
The results indicate that, as expected, the limited budget scenario constrains the overall potential for SC. Once one of the major technologies (EV or HP) is adopted due to the subsidy, the household faces even stronger budget constraints, preventing further purchases. In this case, subsidies that strongly promote EV or HP adoption may actually reduce the transformative effect of the system, because they accelerate the diffusion of technologies that do not directly increase usable electricity potential. As seen in previous scenarios, EVs and HPs typically diffuse faster than HBs or PV, but without HBs or additional PV, the SC potential cannot be expanded.
This highlights the importance of balanced policy design. Supporting a single technology in isolation does not necessarily generate positive cascading effects across the system. In fact, poorly targeted subsidies may lock the system into a less transformative state, where households adopt EVs or HPs but lack the means to adopt PV or HB units that would enable SC. Effective subsidy schemes should therefore consider the interdependencies among technologies, aiming to support a coordinated transformation rather than isolated increases in adoption.
5. Discussion and conclusion
Cascades occur when social tipping in one system enables tipping in another system. When this leads to an overall system transformation, this can be considered a tipping cascade. Tipping cascades hold a promise to accelerate the transformation of the energy system, but empirical evidence that can form the basis for actionable policy advice is lacking. This paper provides a stylized model that explores tipping dynamics in the context of household-level energy, housing, and mobility technologies. Based on the literature, we modeled both reinforcing and balancing feedbacks between household adoption of EV, HPs, solar PV, and HBs. We labeled model outcomes as tipping cascades when households switched from grid electricity to the SC of renewable electricity to meet their energy needs. When this new way of organizing household-level energy and mobility becomes the norm, this signals a transformation to a fundamentally different, more decentralized and integrated sustainable energy system.
In our stylized model, we find that such a transformation can occur in a wide variety of settings and can take different forms. Of particular interest is the role of balancing feedbacks or system constraints. Below, we summarize the simulation results:
1. The model shows that transformative change in the energy system emerges when households adopt multiple technologies. Adoption of a single technology, such as PV alone or EV alone, is insufficient to shift the system dynamics. Co-adoption (e.g., PV with HBs and EVs or HPs) unlocks SC, increases local electricity use, and triggers feedback loops that cascade across the system.
2. Households with constrained budgets achieve high levels of SC. Limited resources force households to prioritize technologies that maximize electricity efficiency. They adopt EE measures first, then strategically adopt other technologies to exploit the available electricity potential. This approach results in more local consumption of generated electricity, demonstrating that scarcity can incentivize efficiency and effective resource management. Supporting energy-poor households in a just energy transition thus requires careful policy design.
3. The model shows that simply expanding buffer capacity does not necessarily improve system SC. Excess capacity can reduce incentives for households to co-adopt, leaving electricity potential underused. Effective grid management should therefore balance capacity constraints with incentives for local electricity use.
4. Subsidies can fail if households redirect benefits to non-energy expenses (the rebound effect). The model constrains households to reinvest savings from EE measures into energy-related technologies, such as PV, HB, EV, or HP. With this approach, the model shows that households make decisions that can increase the transformative potential of the system.
5. Subsidies can help households with limited budgets to adopt technologies. However, the model shows that they can reduce systemic transformation. Subsidies that accelerate adoption of EVs or HPs do not increase usable electricity potential. If such technologies are adopted thanks to subsidies, households re-experience budget-constraints and cannot adopt complementary PV or HB units necessary for SC. This implies that, under certain conditions, the diffusion of certain technologies can block the positive cascade effect.
These model outcomes allow us to put forward some insights in relation to policy coordination and sequencing in enabling system transformation (Lawrence et al., Reference Lawrence, Blackett and Cradock-henry2020; Voulvoulis et al., Reference Voulvoulis, Giakoumis, Hunt, Kioupi, Petrou, Souliotis, Vaghela and Binti Wan Rosely2022). The findings support emerging perspectives in the social tipping and transition literature that emphasize the importance of reinforcing feedbacks and cross-sector interactions in accelerating decarbonization. Rather than viewing technology adoption as a set of independent diffusion processes, the results illustrate how changes in one domain can create enabling or constraining conditions for change in others.
Subsidies can accelerate the adoption of individual technologies by reducing economic barriers; however, our findings suggest that support for a single technology alone may be insufficient to trigger broader cascade dynamics and more transformative change. For example, accelerating the uptake of EVs or HPs without simultaneously enabling local renewable generation and flexibility can increase reliance on the electricity grid rather than stimulate SC. In contrast, policies that support complementary technologies can strengthen reinforcing feedbacks across sectors and create conditions to accelerate system transformation. This finding is consistent with the literature on policy mixes and transition governance, which indicates that successful decarbonization often depends on individual policy instruments and their alignment, interaction, and sequencing over time (Edmondson et al., Reference Edmondson, Kern and Rogge2019; Meckling, Reference Meckling2019; Meckling et al., Reference Meckling, Sterner and Wagner2017). From this perspective, policy design should focus on fostering synergies between technologies and sectors rather than maximizing the deployment of individual technologies in isolation.
However, such interactions are likely to be context and country dependent, as national policies and cultural specificities may shape cascade dynamics in different ways. In this respect, the results also align with growing evidence that interventions are most effective when they strengthen not only technological complementarities but also social norms (Hansson et al., Reference Hansson, Anshelm and Haikola2025; Nyborg et al., Reference Nyborg, Anderies, Dannenberg, Lindahl, Schill, Schlüter, Adger, Arrow, Barrett, Carpenter, Chapin, Crépin, Daily, Ehrlich, Folke, Jager, Kautsky, Levin, Madsen and de Zeeuw2016). Therefore, understanding how behavioral preferences (in our case, linked to SC attitudes) and policy interventions interact may be as important as understanding the diffusion of individual technologies themselves.
While adoption decisions are modeled at the household level in this research, the findings may also hold relevance for the community scale of analysis. Energy communities (ECs) are new market actors and are increasingly involved in collectively producing, sharing, storing and consuming electricity and heat (Lub et al., Reference Lub, Wade, van Summeren and Devenish2026; Wade et al., Reference Wade, Pasimeni, Loomans and Alkemade2025). ECs can combine individually owned rooftop solar or co-invest. Similarly, the adoption of household- or community-scale storage technologies can also support SC by ECs. Many of the causal dynamics discussed here could therefore equally apply to the investment decisions of ECs.
5.1. Limitations, assumptions, and future research
The results of this study should be interpreted in light of some assumptions and limitations of the model. First, the model is highly stylized and designed to explore the behavioral and systemic interactions underlying adoption and cascade dynamics rather than to provide quantitative forecasts. Several parameter values and interaction mechanisms are informed by empirical literature, but other elements are simplified to facilitate the exploration of such dynamics.
The first limitation is that technology adoption is cumulative, which means that technologies do not depreciate or become obsolete over time. Once adopted, a technology remains available throughout the simulation. In addition, the model represents household financial resources with a budget that only captures the resources available for technology adoption. In reality, households allocate income to many needs and expenditures.
The model also abstracts from several important sources of complexity. Although households differ in their initial budgets and preferences, the model does not include other forms of heterogeneity, explicit network effects (beyond a generic visibility mechanism), or external shocks such as price or policy changes. These simplifications imply that quantitative results should not be interpreted as predictions but rather as exploratory insights into possible cascade mechanisms.
The model further assumes that PV adoption does not generate direct household income through electricity exports to the grid. This reflects increasingly common situations in which excess residential PV generation receives limited, zero, or even negative compensation due to grid congestion. In addition, the model does not incorporate endogenous technology learning curves or cost-reduction trajectories. This assumption is intentional, as the focus is on how technological complementarities, behavioral preferences, and budget constraints shape the adoption dynamics rather than on the diffusion of technology driven by declining costs.
Several avenues for future research emerge from these limitations. Extending the model to include V2G interactions could provide additional insights into the role of flexibility in SC cascades. V2G interactions may further amplify these dynamics, as they introduce additional flexibility and storage interactions that could integrate with the core functions already represented in our model, particularly those involving EVs and HBs.
Similarly, incorporating other forms of household heterogeneity, network effects, technology depreciation or learning, and external shocks could improve the representation of real-world transition dynamics. Future work could also explore alternative policy interventions beyond subsidies, including market redesign, peer-to-peer energy trading schemes, and regulatory changes that affect incentive structures. Finally, some of the qualitative insights generated by the model (such as the finding that scarce resources can promote efficient co-adoption pathways through prioritization of EE and PV) should be viewed as hypotheses that deserve further investigation using empirical data and more detailed modeling approaches.
Author contributions
F.A. and F.P. are responsible for writing, conceptualization, and analysis. F.P. implemented the model. C.H.-v.W. collected and processed the data on co-adoption. B.B., O.-Y.D., T.W., I.W., C.H.W., and R.W. contributed to conceptualization, writing, reviewing, and editing.
Funding statement
F.A., F.P., B.B., C.H.-v.W., and T.W. acknowledge the support of the European Union (ERC, FAST, 101044076).
Competing interests
The authors declare no conflicts of interest.
Appendix
A.1. Model description
In this section, the full model is described, including its detailed mathematical formulation. Figure A1 presents a flowchart illustrating the model dynamics, including both within-domain interactions and cross-domain feedback mechanisms.
Model’s key components
The five alternatives
The model simulates the adoption decisions of householders concerning five available alternatives. These alternatives span multiple technological domains and sectors, including energy, mobility, and housing. Four of the alternatives correspond to specific household energy technologies: rooftop solar photovoltaic (PV), home batteries (HBs), electric vehicles (EVs), and heat pumps (HPs). The fifth alternative represents nonfinancial energy efficiency (EE) measures. We index alternatives by j = 1, …, 5, where j = 1 corresponds to PV, j = 2 to HBs, j = 3 to EVs, j = 4 to HPs, and j = 5 to EE.
PVs, EVs, HPs, and EE can be adopted independently, as they do not require the prior adoption of other alternatives. In contrast, HB can only be adopted if at least one unit of PV has already been adopted, since storage requires available generation.
Adoption is modeled in terms of units, where each unit represents a single instance of adoption. The model does not distinguish between different sizes, capacities, or usage levels of the adopted technologies. This abstraction is intentional: it allows the model to focus on macro-level patterns of systemic change rather than household-level optimization or detailed technical characteristics.
Maximum adoption and adoption costs
Each householder may adopt up to a maximum number of units for each of the five alternatives, denoted by Maxj for j = 1, …, 5. Each alternative is also associated with an adoption cost, denoted by Cj for j = 1, …, 5.
The EE alternative (j = 5) is considered nonfinancial, meaning that it does not require direct monetary expenditure. We therefore set C EE = 0. As a result, householders may always choose to adopt EE measures regardless of their financial situation. This reflects the interpretation of EE as behavioral changes rather than investment-based decisions.
Subsidies and savings, Lj
Each of the four household energy technologies may benefit from subsidies (Lj for j = 1, …, 4), which are introduced to stimulate the adoption of these technologies by reducing their effective adoption cost. Subsidies are expressed as a percentage of the full cost, such that the cost of adopting technology j is adjusted accordingly: (Cj · (1 − Lj)).
In contrast, the fifth alternative, EE measures, does not involve an upfront cost reduction but instead generates savings for the household over time. These savings are modeled as an increase in the household's available budget at the next time step, such that Bi,t +1 = Bi,t+ LEE.
Overview of the model dynamics.
Figure A1 Long description
The flow chart illustrates the model dynamics at time step t. A randomly activated agent i selects one of five alternatives at random (PV, HB, EV, HP, or EE), after which the corresponding decision process is followed (solid lines). Dotted lines represent technology and system feedback that influence the model dynamics in the subsequent time step.
Householders
The model considers a population of M householders, indexed by i = 1, …, M. Each householder has a budget Bi that can be used to purchase the four investment-based technologies (PV, HB, EV, and HP). In addition, each householder has a preference for self-consumption (SC), denoted by Ri, reflecting the household’s inclination to use electricity generated by PV and stored in HBs to operate EVs and HPs (details are provided in a later section).
At each time step, a single householder is randomly selected (activated). During this activation, one of the five alternatives is chosen uniformly at random with probability 1/5. The activated householder then evaluates whether to adopt one unit of the selected alternative, subject to their individual constraints (e.g., budget Bi and SC preference Ri) as well as global or alternative-specific conditions. These include the maximum number of units allowed (Maxj), the adoption probability (ϕj), the total market share of the technology (Sj,t), and its visibility (Vi,j,t), all of which are introduced below.
Householders are assumed to have bounded rationality. That is, when making adoption decisions, they behave myopically and do not fully evaluate the long-term consequences of their choices. As a result, adoption decisions may not be strictly utility-maximising. For example, a householder facing budget constraints may choose to adopt a single high-cost technology even when adopting two lower-cost technologies would yield greater overall benefits in terms of SC. This behavioral assumption reflects the fact that real-world decision-making is often shaped by limited information, cognitive constraints, and satisficing rather than optimization.
Adoption probability ϕj
The adoption of alternative j occurs with probability ϕj,t ∈ [0,1] for j = 1, …, 5. These probabilities are not fixed but evolve dynamically over time (see the dedicated section below). Interactions across technologies and sectors can influence these probabilities. In particular, adoption decisions may exhibit complementarity, where adopting one alternative increases the likelihood of adopting another, or substitution, where adopting one alternative reduces the likelihood of adopting another.
Total market share and adoption share Sj,t
For each alternative j, the model computes its total market share, Sj,t, as shown in Eq. 1. Here, Aj,t denotes the total number of adopted units of alternative j in the population at time t, Maxj is the maximum number of units that each household may adopt, and M is the total number of households. By construction, Sj,t ∈ [0,1]. Thus, Sj,t represents the diffusion level (or adoption share) of alternative j within the population.
\begin{equation}{S_{j,t}} = \frac{{{A_{j,t}}}}{{{\text{Ma}}{{\text{x}}_j} \cdot M}}\end{equation}Visibility and individual visibility adjustment Vi,j,t
The total market share Sj,t of alternative j at time t (Eq. 1) is interpreted as its population-level visibility. A higher value of Sj,t implies that the alternative is more commonly observed or recognized among householders.
However, visibility is adjusted at the individual level to reflect diminishing informational relevance once a householder has already adopted units of that alternative. Let ai,j,t denote the number of units of alternative j that householder i has adopted at time t, with 0 ≤ ai,j,t ≤ Maxj.Footnote 7 The individual visibility of alternative j for householder i is given by
\begin{equation}{V_{i,j,t}} = {S_{j,t}}\left( {1 - \frac{{{a_{i,j,t}}}}{{{\text{Ma}}{{\text{x}}_j}}}} \right)\end{equation}Individual visibility therefore decreases linearly with the share of the maximum number of units already adopted.Footnote 8 When ai,j,t = 0, individual visibility equals full population-level visibility (Vi,j,t = Sj,t). When ai,j,t = Maxj, visibility becomes zero (Vi,j,t = 0).
The stylized electricity system
Household electricity potential, Pi,t U
Each unit of PV adopted by householder i (denoted ai,PV,t) generates an amount of renewable electricity, EPV. A fraction η PV ∈ [0,1] of this electricity can be directly selfconsumed by the householder. This contributes to the householder's usable PV electricity potential, denoted Pi,t UPV in Eq. 3. The remaining fraction 1 − η PV represents non-usable PV electricity, denoted Pi,t NUPV in Eq. 4.
\begin{equation}P_{i,t}^{{{\text{U}}_{{\text{PV}}}}} = {E_{{\text{PV}}}} \cdot {a_{i,{\text{PV}},t}} \cdot {\eta _{{\text{PV}}}}\end{equation}
\begin{equation}P_{i,t}^{{\text{N}}{{\text{U}}_{{\text{PV}}}}} = {E_{{\text{PV}}}} \cdot {a_{i,{\text{PV}},t}} \cdot \left( {1 - {\eta _{{\text{PV}}}}} \right)\end{equation}The non-usable PV electricity potential becomes usable only when storage capacity (HB) is available. Let η HB ∈ [0,1] denote the fraction of PV electricity that can be made usable per unit of HBs adopted, and let ai, HB,t denote the number of HB units adopted by householder i at time t. The usable PV electricity enabled by HB adoption, denoted Pi,t UHB, is given by
\begin{equation}P_{i,t}^{{{\text{U}}_{{\text{HB}}}}} = {E_{{\text{PV}}}} \cdot {a_{i,{\text{PV}},t}} \cdot {a_{i,{\text{HB}},t}} \cdot {\eta _{{\text{HB}}}}{\text{ }}\end{equation}Thus, once at least one unit of HB is adopted, the total usable PV electricity potential increases by Pi,t UHB, while the non-usable potential decreases by the same amount:
\begin{equation}P_{i,t}^{\text{U}} = P_{i,t}^{{{\text{U}}_{{\text{PV}}}}} + P_{i,t}^{{{\text{U}}_{{\text{HB}}}}}\end{equation}
\begin{equation}P_{i,t}^{{\text{NU}}} = P_{i,t}^{{\text{N}}{{\text{U}}_{{\text{PV}}}}} - P_{i,t}^{{{\text{U}}_{{\text{HB}}}}}\end{equation}Usage of household electricity potential Ui,t SC
While PV and HBs increase the electricity potential available to a household, EVs and HPs enable the use of this electricity in SC mode. SC refers to operating these devices using electricity generated and stored locally, rather than drawing electricity from the national grid (NG). Both EVs and HPs can therefore be adopted and operated either via the NG or via SC.
Let ai, EVNG,t and ai, EVSC,t denote, respectively, the number of EV units adopted by householder i at time t operating via the NG and via SC. Similarly, let ai, HPNG,t and ai, HPSC,t denote the number of HP units operating via the NG and SC. Let η EVSC ∈ [0,1] and η HPSC ∈ [0,1] represent the amount of electricity required to operate one unit of EV or HP, respectively, in SC mode.
The electricity used in SC by EVs and HPs is then given by
\begin{equation}U_{i,t}^{{\text{E}}{{\text{V}}_{{\text{SC}}}}} = {a_{i,{\text{E}}{{\text{V}}_{{\text{SC}}}},t}} \cdot {\eta _{{\text{E}}{{\text{V}}_{{\text{SC}}}}}}\end{equation}
\begin{equation}U_{i,t}^{{\text{H}}{{\text{P}}_{{\text{SC}}}}} = {a_{i,{\text{H}}{{\text{P}}_{{\text{SC}}}},t}} \cdot {\eta _{{\text{H}}{{\text{P}}_{{\text{SC}}}}}}\end{equation}The total electricity used in SC mode by householder i is therefore
\begin{equation}U_{i,t}^{{\text{SC}}} = U_{i,t}^{{\text{E}}{{\text{V}}_{{\text{SC}}}}} + U_{i,t}^{{\text{H}}{{\text{P}}_{{\text{SC}}}}}\end{equation}Household SC SCi,t
Depending on their adoption decisions, each householder exhibits an individual level of electricity usage in SC mode. This level depends on both the available usable PV electricity (determined by the number of PV and HB units adopted) and the number of EV and HP units operated in SC mode. Each EV or HP unit operated in SC mode increases the electricity used in SC Ui,t SC while contributing to the reduction of the total usable electricity potential Pi,t U.
The individual SC share of householder i at time t is defined as the ratio of electricity used in SC to the sum of the total usable PV electricity potential and the electricity used in SC. This is given by Eq. 11:
\begin{equation}S{C_{i,t}} = \frac{{U_{i,t}^{{\text{SC}}}}}{{P_{i,t}^{\text{U}} + U_{i,t}^{{\text{SC}}}}}\end{equation}PV buffer Ft
When there is no immediate demand for SC, household PV electricity is assumed to be stored in a shared system-level buffer. This buffer has an upper bound, F max, representing the maximum amount of PV electricity the system can accommodate.
For example, when no PV units have been adopted (Σiai,PV,t = APV,t = 0), the total usable and non-usable PV electricity is zero (Σi(Pi,t U + Pi,t NU) = 0), and the buffer is fully available. As one or more PV units are adopted (Σi(Pi,t U + Pi,t NU) > 0), the available buffer space decreases. The PV buffer Ft ∈ [0,1] is defined as
\begin{equation}{F_t} = 1 - \frac{{\mathop \sum \nolimits_i \left( {P_{i,t}^{\text{U}} + P_{i,t}^{{\text{NU}}}} \right)}}{{{F_{{\text{max}}}}}}\end{equation}Here, Ft = 1 indicates that the buffer is fully available, while Ft = 0 indicates that the buffer is full and no additional PV units can be adopted. This buffer represents system-level constraints, such as grid capacity limits, that cap the total PV electricity the system can support.
Importantly, if existing PV electricity (potentially stored via HB) is subsequently consumed by EVs or HPs operating in SC mode, the total usable PV electricity Pi,t U decreases, thereby freeing buffer space. This allows additional PV units to be adopted without exceeding the system limit.
Evaluating adoption alternatives
Evaluate PV adoption
When a householder i is randomly selected at time t to evaluate the option of adopting a PV unit, the adoption decision is subject to several conditions.
The householder must have sufficient budget to cover the PV adoption cost (Bi,t ≥ C PV · (1 − L PV)). The number of PV units already adopted must not exceed the maximum allowed (ai, PV,t ≤ MaxPV). The PV alternative must be visible to the householder. This is evaluated by drawing a random variable RND ∈ [0,1] and checking whether RND ≤ Vi, PV,t. The PV buffer must be able to accommodate at least one unit of PV based on its corresponding renewable electricity potential (Ft ≥ E PV). Finally, the householder adopts PV with probability ϕ PV. This is evaluated by drawing a random variable RND ∈ [0,1] and checking whether RND ≤ ϕ PV. This adoption probability ϕ PV evolves over time, taking into account buffer saturation and the operation of EVs and HPs using the NG. This specific mechanism for changes in probabilities is described in a dedicated section below.
If any of these conditions are not satisfied, adoption does not occur, and the model proceeds to the next time step. If all conditions are satisfied, householder i adopts one PV unit. This updates both household-level and system-level states for the next time step. For example, ai,PV,t +1 = ai,PV,t +1 and Bi,t +1 = Bi,t − C PV · (1 − L PV). Similarly, the householder's SC level SCi,t +1, the PV buffer Ft +1, and individual visibility Vi, PV,t+1 are updated accordingly.
Evaluate HB adoption
When householder i is randomly selected at time t to evaluate the option of adopting an HB unit, the adoption decision is subject to the following conditions. At least one PV unit must already be installed (ai,PV,t ≥ 1). Since HBs store electricity generated from PV, adopting an HB without PV capacity would not be meaningful. The amount of non-usable PV electricity must be greater than or equal to the usable electricity that the HBs would enable (Pi,t NUPV ≥ Pi,t UHB). The householder must have sufficient budget to cover the HB adoption cost (Bi,t ≥ CHB ·(1 − LHB)). The number of HB units already adopted must not exceed the maximum allowed (ai,HB,t ≤ MaxHB). The HB alternative must be visible to the householder. This is evaluated by drawing a random variable RND ∈ [0,1] and checking whether RND ≤ Vi, HB,t. Finally, adoption occurs with probability ϕHB.
If any of these conditions are not satisfied, adoption does not occur and the model moves to the next time step. If all conditions are satisfied, householder i adopts one HB unit, updating both household-level and system-level states for the next period. For example, ai,HB,t +1 = ai,HB,t +1 and Bi,t +1 = Bi,t − C HB · (1 − L HB). Similarly, the householder's SC level SCi,t +1 and visibility Vi, HB,t + 1 are updated accordingly.
HBs extend the use of PV-generated electricity by enabling storage and later consumption, particularly when operating EVs and HPs in SC mode. Unlike PV adoption, however, HB adoption does not directly affect the PV buffer Ft. Nevertheless, by increasing SC and reducing unused PV electricity over time, HBs can indirectly contribute to freeing buffer capacity at later stages, thereby enabling further PV adoption.
Evaluate EV and HP adoption
EVs and HPs are modeled analogously, as they are independent technologies. Both can be adopted regardless of whether PV or HB units are present, since they can also operate using electricity supplied by the NG.
When EV or HP is selected for evaluation at time t, the householder first considers whether to switch an already adopted unit from NG operation to SC mode. If the householder currently owns at least one unit operating via the NG (i.e., ai, EVNG,t > 0 or ai, HPNG,t > 0), the switch is made if the following conditions are simultaneously satisfied. First, the householder expresses a preference for SC (evaluated as RND ≤ Ri). Second, sufficient usable PV electricity is available to support the operation in SC mode (Pi,t U ≥ Ui,t EVSC or Pi,t U ≥ Ui,t HPSC).
If a switch occurs, one EV or HP unit is reallocated from NGd operation to selfconsumption mode (ai, EVSC,t +1 = ai, EVSC,t +1 and ai, EVNG,t +1 = ai, EVNG,t –1). Analogous updates occur for HPs. The householder’s SC level SCi,t +1 is updated accordingly. Because SC reduces unused PV production, the PV buffer Ft +1 may expand.
If no switch is made, the householder proceeds to evaluate the adoption of a new EV or HP unit. Adoption occurs under the following conditions: the householder has sufficient budget (e.g., Bi,t ≥ C EV · (1 − L EV) or Bi,t ≥ C HP · (1 − L HP)), and the number of existing units does not exceed the maximum allowable (ai, EV,t ≤ MaxEV or ai, HP,t ≤ MaxHP).
The technology is visible to the householder (RND ≤ Vi, EV,t or RND ≤ Vi, HP,t).
If these conditions hold, the householder adopts one new unit. The mode of operation (SC or NG) is then determined as follows. If the householder prefers SC (RND ≤ Ri), sufficient usable PV electricity is available, and the adoption probability threshold is met (RND ≤ ϕ EV or RND ≤ ϕ HP), the new unit is adopted in SC mode. Otherwise, the new unit is adopted and operated using electricity from the NG. After adoption, the householder’s budget, SC level, and relevant system-level variables are updated.
Evaluate EE adoption
When householder i is randomly selected at time t to evaluate the option of adopting an EE measure, the adoption decision is subject to only two conditions. First, the number of EE measures already adopted must not exceed the maximum allowed (ai,EE,t ≤ MaxEE). Second, adoption occurs with probability ϕ EE, evaluated by drawing a random variable RND ∈ [0,1] and checking whether RND ≤ ϕ EE.
If both conditions are satisfied, one EE measure is adopted. This updates the householder’s state as follows: ai, EE,t +1 = ai ,EE,t +1 and Bi,t +1 = Bi,t + L EE, where LEE is the monetary savings generated by the EE measure.
EE measures are nonfinancial behavioral changes (e.g., reducing appliance use or taking shorter showers) and therefore do not require an upfront expenditure. They do not affect electricity generation or consumption potential, but they do increase the householder's budget by lowering ongoing energy costs. As a result, EE measures can be adopted even when no budget is available. Over time, accumulated savings may enable the adoption of other technologies, contributing to a rebound effect in which behavioral savings facilitate subsequent investment-based adoption.
Changes in adoption probabilities, ϕj,t
The adoption probabilities of the household energy technologies ϕj,t ∈ [0,1] for j = 1, …, 4 are influenced primarily by the total market share of each technology, Sj,t, but also evolve endogenously over time through interactions among technologies and system-level constraints. Thus, when a householder evaluates whether to adopt a technology, the decision is influenced not only by Sj,t but also by system-level variables that reflect the current state of the energy system.
PV probability, ϕ PV,t
The probability of adopting a PV unit at time t, denoted ϕ PV,t, is given in Eq. 13. The probability increases when there is available system capacity (i.e., buffer space) and when a larger share of EVs and HPs currently operate using electricity from the NG rather than SC.
\begin{equation}{\phi _{{\text{PV}},t}} = {S_{{\text{PV}},t}} \cdot \left( {1 - {{\left( {1 - {F_t}} \right)}^3}} \right) \cdot \left( {1 + {{\left( {\frac{{{A_{{\text{E}}{{\text{V}}_{{\text{NG}}}},t}} + {A_{{\text{H}}{{\text{P}}_{{\text{NG}}}},t}}}}{{{A_{{\text{E}}{{\text{V}}_{{\text{NG + SC}}}},t}} + {A_{{\text{H}}{{\text{P}}_{{\text{NG + SC}}}},t}}}}} \right)}^3}} \right)\end{equation}The first adjustment term captures the effect of system-level constraints: as the PV buffer Ft decreases, the probability of PV adoption decreases sharply. When the buffer is fully available (Ft = 1), the adoption probability equals the market share SPV,t. As the buffer fills (Ft → 0), the term (1 − (1 − Ft)3) approaches zero, meaning that PV adoption becomes increasingly unlikely.
The second adjustment term reflects technological interdependence: if many EV and HP units currently operate using the NG, PV becomes more attractive because it enables future SC, thereby reducing electricity costs and grid dependence. The term increases ϕ PV,t when the ratio of EV and HP units operating via the grid to the total number of such units increases.
Overall, the formulation captures two systemic effects. The first is the grid saturation effect that is lower buffer availability discourages PV adoption. The second regards selfconsumption incentive, meaning that EVs’ and HPs’ usage via the grid increases the incentive to adopt PV. This reflects the interdependence among technologies, where PV adoption supports the shift of EVs and HPs from grid-dependent to SC-based operation, and system constraints feed back into adoption decisions.
HB probability, ϕ HB,t
The probability of adopting an HB unit at time t, denoted ϕ HB,t, is given by Eq. 14. Similar to PV adoption, the probability depends on the technology’s market share, S HB,t, and on the number of EV and HP units currently operating via the NG. However, in contrast to PV adoption, HB adoption is encouraged when the PV buffer is reduced. When the system is close to reaching its PV capacity limit, HBs provide an alternative means to utilize excess PV electricity, thereby increasing the incentive to adopt them.
\begin{equation}{\phi _{{\text{HB}},t}} = {S_{{\text{HB}},t}} \cdot \left( {1 - F_t^3} \right) \cdot \left( {1 + {{\left( {\frac{{{A_{{\text{E}}{{\text{V}}_{{\text{NG}}}},t}} + {A_{{\text{H}}{{\text{P}}_{{\text{NG}}}},t}}}}{{{A_{{\text{E}}{{\text{V}}_{{\text{NG + SC}}}},t}} + {A_{{\text{H}}{{\text{P}}_{{\text{NG + SC}}}},t}}}}} \right)}^3}} \right)\end{equation}The term (1 − Ft 3) increases as the PV buffer Ft decreases, meaning that the probability of HB adoption is highest when the system is saturated with PV and additional storage is needed to make use of the generated electricity. Conversely, when buffer space is widely available (Ft ≈ 1), HB adoption is less likely.
The second adjustment term captures the incentive created by EVs and HPs operating via the NG. A larger number of such units increases ϕ HB,t, because adopting an HB can enable these technologies to shift from grid-powered to SC operation using stored PV electricity.
Overall, ϕ HB,t increases when the PV buffer is nearing saturation (i.e., Ft is small) and when a higher share of EV and HP units currently rely on the NG. This reflects the role of HBs as a bridging technology that supports the transition from grid-dependent operation toward greater SC.
EV and HP probability, ϕ EV,t and ϕ HP,t
EVs and HPs can be adopted regardless of whether PV or HB units are present, since they can always operate using electricity from the NG. However, the probability of adopting an EV or HP in SC mode depends on the available usable PV electricity potential and on how many units are currently operating via the NG.
Cascade effect – Scenario 1: High self-consumption.
Figure A2 Long description
The charts in this figure show (a) the diffusion rate over time for the five alternatives, (b) the adoption probabilities for these alternatives and the status of the PV buffer over time, (c) the level of self-consumption (SC), the usable electricity potential (left vertical axis), and the average household budget over time (right vertical axis), and (d) the shares of both EVs and HPs operating via the national grid (NG) and in SC mode.
The probability of adopting an EV in SC mode at time t, ϕ EV,t, and the probability of adopting an HP in SC mode, ϕ HP,t, are given in Eqs. 15 and 16.
\begin{equation}{\phi _{{\text{EV}},t}} = {S_{{\text{EV}},t}} \cdot \left( {1 - {{\left( {1 - {F_t}} \right)}^3}} \right) \cdot \left( {1 + {{\left( {\frac{{{A_{{\text{E}}{{\text{V}}_{{\text{NG}}}},t}}}}{{{A_{{\text{E}}{{\text{V}}_{{\text{NG + SC}}}},t}}}}} \right)}^3}} \right)\end{equation}
\begin{equation}{\phi _{{\text{HP}},t}} = {S_{{\text{HP}},t}} \cdot \left( {1 - {{\left( {1 - {F_t}} \right)}^3}} \right) \cdot \left( {1 + {{\left( {\frac{{{A_{{\text{H}}{{\text{P}}_{{\text{NG}}}},t}}}}{{{A_{{\text{H}}{{\text{P}}_{{\text{NG + SC}}}},t}}}}} \right)}^3}} \right)\end{equation}The term (1 − (1 − Ft)3) increases with available buffer space, implying that the probability of EV and HP adoption in SC mode rises when the system has unused electricity potential. In other words, when more PV electricity is available to be consumed locally, EVs and HPs become more attractive as complementary technologies.
The second adjustment term reflects technological substitution for grid electricity. If many EV or HP units currently operate using the NG (i.e., A EVNG,t or A HPNG,t is high), then ϕ EV,t or ϕ HP,t increases. This represents the incentive to shift these technologies toward SC by adopting PV-supported operation.
Overall, the probability of EV or HP adoption in SC mode increases when there is substantial usable electricity potential, and when many EV or HP units are currently grid-dependent.
However, EV and HP adoption may also interact competitively: since both technologies draw on the same usable electricity potential, adopting one in SC mode reduces the potential available for the other. Consequently, when an EV is adopted in SC mode, ϕ HP,t is reduced, and vice versa.
All adoption probabilities ϕj,t are bounded within [0,1] at each time step. To ensure consistency with their probabilistic interpretation, they are capped after calculation as follows: ϕj,t = min(1,max(0,ϕj,t))for j = 1, …, 4.
A.2 Cascade effect – full scenario analysis
In this section, we report the full scenario analysis related to Section 4.2, in which four different scenarios are presented to study the cascade effect and its impact on system transformations. For completeness, we show the full dynamic trajectories for all four scenarios here, using the same format as Figure 2.
Cascade effect – Scenario 2: Subsidy.
Figure A3 Long description
The charts in this figure show (a) the diffusion rate over time for the five alternatives, (b) the adoption probabilities for these alternatives and the status of the PV buffer over time, (c) the level of self-consumption (SC), the usable electricity potential (left vertical axis), and the average household budget over time (right vertical axis), and (d) the share of both EVs and HPs operating via the national grid (NG) and in SC mode.
Cascade effect – Scenario 3: Low buffer.
Figure A4 Long description
The charts in this figure show (a) the diffusion rate over time for the five alternatives, (b) the adoption probabilities for these alternatives and the status of the PV buffer over time, (c) the level of self-consumption (SC), the usable electricity potential (left vertical axis), and the average household budget over time (right vertical axis), and (d) the share of both EVs and HPs operating via the national grid (NG) and in SC mode.
Cascade effect – Scenario 4: Low budget.
Figure A5 Long description
The charts in this figure show (a) the diffusion rate over time for the five alternatives, (b) the adoption probabilities for these alternatives and the status of the PV buffer over time, (c) the level of SC, the usable electricity potential (left vertical axis), and the average household budget over time (right vertical axis), and (d) the share of both EVs and HPs operating via the national grid (NG) and in SC mode.
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