Community-Based Adoption and Diffusion of Micro-Grids: Analysis of the Italian Case with Agent-Based Model

The electricity generation and distribution system in many developed economies is based primarily on the centralised grid. However, there is a need to shi from this traditional system to a newly more decentralisedelectricity system. Thispaperexplorespossible scenariosof adoptionanddi usionofMicro-Grids (MGs) in Italy. An agent-based model is formulated to simulate the di usion process as function of regional factors, subsidies and people’s attitude. It assumes that MGs are purchased directly by communities of neighbours, which benefit from cost sharing. Results show high dependence of the di usion process on regional factors: electricity demand, renewable potential and population. The model confirms that subsidies boost di usion, mainly when they are regional-based rather than national-based. Higher green attitude accelerates di usion and reduces environmental impact of the electricity system.


Introduction
. Generation of electricity and heat represents the main cause of CO emissions; in , they accounted for % of world greenhouses gas (GHG) emissions (IEA/OECD, ). Countries are challenging global warming and climate change by addressing household energy use in a number of ways: improving e iciency, adopting zeroemission technologies and fostering di usion of decentralised generation systems (DGs). DGs aim at a more sustainable production and distribution of electricity and, consequently, they have attracted interest from the technical and scientific community (Ackermann et al. ; Asmus ; IEA ; Hatziargyriou & Meliopoulos ; Lasseter ). DGs are defined as "any source of electric power of limited capacity, directly connected to the power system distribution network where it is consumed by the end users" (Akorede et al. , p. ). Moreover, since DGs combine "cluster of loads and micro-sources operating as a single controllable system", these are also defined Micro-Grids (MGs) (Lasseter , p. ). .

The interest on DGs and
MGs is driven by three main factors that might positively impact the transition to a more sustainable production and use of energy. These are: (i) minimise transmission losses by reducing the distance between electricity generation and final users (Ackermann et al.
; Pepermans et al. ); (ii) deploy higher share of renewable technologies and, consequently, reduce CO emissions (Hadley & Van Dyke ; Chiradeja & Ramakumar ); and (iii) improve energy security (Asmus ). Along with these studies, stressing the importance of DGs and MGs in the transition towards a more e icient, sustainable and inclusive electricity production system, there are others that indicate the parallel need of public and private investments (Block et al. ; Lopes et al. ; Driesen & Katiraei ; Marnay et al. ; Battaglini et al. ; Agrell et al. ). In fact, the ownership structure and the relative market dynamics are important in the di usion process of MGs. The growing market liberalisations in the energy sector have facilitated adoption of decentralised systems (Madlener & Schmid ; Markard & Tru er ), where energy utilities have been the major beneficiaries of this deregulation (Siddiqui & Maribu ). .
Over the next decades, demand for electricity is estimated to increase along with population growth and consumer budgetary constraints. For these reasons, citizens are requested to be engaged in the challenge against the threats of global warming and climate change (European Commission ; Hyysalo et al. ; Schot et al. ; Vasiljevska et al. ). Micro-Grids can facilitate this process since consumers become the central node in this new energy infrastructure (Watson ): they are not only the final users but also, simultaneously, generators of electricity (so-called prosumers). Hence, adoption and di usion of MGs necessitate users' direct involvement: they are requested to commit individual e ort into the capital investment and to be willing to install MGs in their neighbourhood (Sauter & Watson ). Nonetheless, such types of initiatives become profitable primarily when they generate savings to users compared to the current status (i.e. purchasing electricity from the centralised system). In conclusion, building a decentralised electricity system is an emerging bottom-up process requiring a comprehensive understanding of consumers' behaviour and perspective (Groh ). .
The assumption that MGs may speed up the transition towards a decentralised electricity system, which is expected to be more inclusive, sustainable and secure compared to the current centralised system, raises the following question: what are the drivers that could favour di usion of Micro-Grids? This paper addresses this question and develops an agent-based model (ABM) for this scope. It models an economy in which agents are users that evaluate the option to shi from the current centralised electricity system towards Micro-Grids. The shi is modelled as a common decision which requires a collective action. Agents are clustered in neighbours and individual electricity demand depend on their geographical location. Electricity production is heterogeneous since renewable potential di ers among locations. Regional variations in demand and production lead to a distribution of take-up in new energy systems. .
The model is calibrated to the Italian electricity system which is representative of many other developed countries that have a well-established centralised electricity infrastructure. Italy presents ine iciencies in the transmission system, it is highly dependent on imports, but, at the same time, it has a high renewable potential. In these contexts, the transition towards a decentralised system is more di icult since new technologies face the incumbent technologies, which prevent the (desired) smooth process of substitution or co-existence and integration. Results show that the di usion process of MGs is influenced by regional heterogeneity (demand, renewable potential and population). Subsidy boosts di usion, mainly when they are regional-based rather than national-based, and higher green users' attitude accelerates di usion and generates reduction of CO emissions. Therefore, policy instruments tailored to consumers' attitudes and regional characteristics can encourage the shi from the traditional centralised grid to a new decentralised electricity system. Beyond the Italian case, this paper provides policy implications that can be generalised and applied to other national contexts.
. The paper is structured as follows. Section reviews the classic literature on di usion and it shows how ABM have contributed to this discussion, particularly on the topic of di usion of eco-innovations. The model is presented in Section and results are discussed in Section . Section concludes.

Literature Background
. A Micro-Grid (MG) is an indivisible and capital-intensive good and, when purchased by users only, it requires a common action (Olson ) in order to cover the high fixed costs. In this way, MG can be considered a common pool resources (Wolsink ) for which the theory of governing common properties has suggested that local interactions are preferred over other approaches, namely privatisation and external regulation (Ouchi ; Ostrom ; Ostrom et al. ). Users organise themselves into communities and cooperate in order to reach the maximum benefit from the common property. Consequently, adoption of MGs is a case of technology di usion that takes place collectively. Rogers defines this action as a "collective innovation decision where there is consensus among the members of a systems" and they "must conform to the system's decision once it is made" (Rogers , p. ). Accordingly, this paper studies di usion of MGs driven by the adoption decision that is taken commonly by a group of neighbours (Bollinger et al. ).
. However, di usion of eco-innovations o en focuses on individual adoption. This is the case, for example, of the adoption of electric vehicles (Diamond ), more e icient boilers (Weiss et al. ) or solar photovoltaic panels (Bollinger & Gillingham ). This literature considers adoption as a decision conditioned by continuous and complex interactions between di erent actors (Antonelli & Ferraris ). Agent-based models (ABM) are used in order to study these phenomena that emerge from cooperation among people (Gilbert ; Tesfatsion ; Borrill & Tesfatsion ; Garcia & Jager ). Furthermore, by means of ABM it is possible to model policy interventions (Safarzyńska et al. ) and to study their implications on technological transitions and consumer demand (Faber & Frenken ). Given these relevant peculiarities, ABM have contributed to the literature of di usion of eco-innovation in a number of ways.

Schwarz & Ernst (
) examine the di usion of three water-saving innovations in Germany, considering real geographical data. An ABM simulates the householders' decision which reflects sociological and psychological theories rather than only economic perspectives. Faber et al. ( ) explore the di usion of micro-cogeneration technology in the Netherlands driven by cost-related decision. Their agent-based model simulates the market competition between two technologies, traditional boiler and micro-CHP, in which gas and electricity prices varies and subsidy schemes shape di erent adoption scenarios. Hamilton et al. ( ) develop an ABM to assess the possibility to shi from a centralised gird to a decentralised electricity supply. The authors consider spatial externalities in the decisional process and the fashion e ect. Zhang et al. ( ) evaluate the adoption trend of alternative fuel vehicles (AFVs) in the United States. In their model, interaction among consumers, manufacturers and policy makers determines di erent di usion scenarios for AFVs. Zhang & Nuttall ( ) examine with ABM di usion of smart electricity meters in the UK and evaluate the e ectiveness of policy options. Their goal is to provide stakeholders (namely suppliers and government agencies) with a ABM-related tool able to analyse di usion policies. .
In all these contributions, ABMs have been applied to study di usion of eco-innovations for which the adoption decision is made individually. However, as pointed out earlier in this section, capital-intensive goods, such as MG, can be also purchased by a group of people in order to mitigate the high investment costs. There exists, therefore, a gap in literature concerning the analysis of di usion processes that depend on the adoption decision which is taken by a group of consumers rather than individual users. This paper aims at contributing to this area and it develops an agent-based model in which aspects of di usion theories (i.e. bandwagon e ect, fashion e ect, technology progress, people attitudes, etc.) are combined to the condition that the adoption decision is taken commonly by a group of people. This paper is distinguished from other works since it expands the notion of individual technology adoption to common adoption, which is driven by the high fixed costs of MG. Moreover, the model simulates policy interventions and evaluates their impact on the di usion process.

The Model
. The model simulates a market economy, which consists of a demand side and a supply side ( Figure ). The demand side contains several regions in which consumers are split into groups. Groups represent neighbourhoods where people live in proximity, which is important since MGs are small-scaled energy infrastructure and require to be installed and used by consumers living in the same geographical area. Regions define specific characteristics, both in the demand side (i.e. consumers' electricity demand, share of adoption) and in the supply side (i.e. functioning hours of renewable technologies). .
In the model, groups of citizens make the choice to invest into a micro-grid solution on the basis of cost considerations. At the beginning of the simulation all consumers are connected to the national grid, which is one of the two options in the supply side. The alternative is the Micro-Grid which requires a common investment. Three technologies form the Micro-Grid: solar photovoltaic panels (PV), micro wind turbines (< kW) and micro combined heat and power systems (micro-CHP, < kW).

.
There are two options available to agents: (i) maintain the current energy supply system, which is the national grid, and pay only the cost of energy consumed; or (ii) shi to a quasi-independent MG energy system, where costs are shared with others. Costs of the two alternatives change over time, and consumers adapt their decision accordingly. The two options are compared based on the same investment horizon: it is assumed that components of the MG become obsolete and they have to be removed and substituted a er a certain period. Substitution implies that agents evaluate the two alternatives based on cost conditions that have changed compared to previous judgments. Evaluation consists on the comparison between the total cost of the two options: the option with the lowest cost is chosen. Importantly, consumers evaluate the MG option only if they are aware of this opportunity and if they demonstrate positive attitude towards the common investment. The components of the adoption decision are summarised in the schema in Figure in Appendix A.
The supply side .
The market gives consumers two alternatives to satisfy their electricity needs: national grid (NG) and microgrid (MG). In option , the electricity price (E t in e/kWh) is the only cost component for consumers. The price is not constant over time, but it varies continuously, and its value is defined endogenously every time step in the simulation as in Equation : is a random number generated in order to keep the raising trend in the price of electricity similar to that one observed in Italy in recent years. Values v min and v max are respectively computed as the average of negative and positive changes in percentage between two consecutive observations of electricity price in Italy, from January to June . Consumers connected to NG pay a total cost (T otN G t,r ) which depends on their demand (D r , function of regional characteristics) and on the time horizon T , as in Equation : Electricity generated and distributed by the national grid serves as a back-up to MGs. Therefore, E t enters in the computation of the cost in option (as in Equation ). The overall cost of MG depends on technologies that form the MG itself. The cost for every technology k is defined through a variable and a fixed component. The variable cost (V C k,t in Equation and measured in e/kWh) is dependent on fuel cost (F k,t ), operation cost (O k,t ) and incentive granted to each technology (S k,t ).
. The fixed technology cost is I k , measured in e. The fixed cost of the entire MG (calculated as in Equation ), consisting of three technologies (k= ), includes the cost of batteries (B), which are needed to store the electricity produced by the intermittent renewable sources, and the possible subsidy (SP t ), that can be provided to stimulate adoption of MG.
B is the cost of battery [e]; SP t is the subsidy received by the group of consumers to adopt a MG [e]; N C t−1,r is the number of MGs adopted in a region r; α is a parameter exogenously set which reflects the rate of cost decrease and determines the progress rate (P R = 2 α ) (Faber et al. ). In Equation , α reduces also the value of subsidies provided to MG adoption since it is assumed that these decrease together with the technological progress. .
The total investment cost relative to MG is regional-dependent. Regional di erences depend on how many hours the three technologies can work and satisfy consumers' electricity needs. It is assumed that MG can work continuously for hours per year and that Micro-CHP has a constant utilisation share (x CHP,r ), regardless its regional location. Time covered by PV (x P V,r ) and wind (x W ind,r ) varies among regions and it depends on weather and climate conditions. If needed, national grid will work as back-up for the remaining hours (x N G,r ).
In this way, the model takes into account the regional utilisation factor in order to capture regional characteristics. At regional level, wind and PV cover a di erent percentage of the yearly production while the cogeneration system is stable in its utilisation. The national grid satisfies the remaining demand. MG can supply electricity to a maximum number of users only (N t,r ), which defines the size of regional communities. The fixed cost (F C t,r ) is equally split among consumers that adopt commonly a MG. Users' demand (D r ) defines the contribution of the variable cost (V C r,t and E t ) which, in turn, depends on the technology utilisation share (x k,r ). Therefore, the individual cost at time t, in region r and for the time horizon T is computed as in Equation . T The following hypotheses are therefore proposed regarding the relationship between di usion of MG and characteristics of the supply side: H : Large regional communities improve cost sharing H : Demand increases the total cost of MG, but this e ect is balanced by regional renewable potential, which decreases the share of electricity supplied by the national grid H : Di usion is boosted when the fixed of MG decreases, hence with low cost of battery and high subsidy The demand side .
The demand side of the market economy concerns consumers and their characteristics. MG supplies electricity to a restricted local area where communities are formed among people living in the same neighbourhood. In order to represent geographical proximity, the model defines exogenously a number of groups of consumers in each region with similar characteristics. In order to be able to evaluate option , every consumer has to be (i) aware if this opportunity and then (ii) willing to invest commonly into a MG. .
The model endogenously defines people awareness by means of a variable, visibility (V t,r ), which is function of regional characteristics. It is computed every time-step as in Equation , and it represents the extent to which the MG alternative is known in the region (Faber et al. ). The higher the regional di usion share, the higher consumer's probability to know the option to invest in MG.
where: M Gus t−1,r ∈ [0; 1] represents the share of the total users in a region that have already adopted MG; δ is a parameter exogenously set and reflects the bandwagon e ect (Abrahamson & Rosenkopf , ). This parameter considers societal trends that influence the decision of later adopters (Tarde ; Arthur ; Smallwood & Conlisk ). .
Willingness to invest jointly with neighbours in MG is defined through consumers' attitude towards green investments (Balram & Dragićević ; Hansla et al. ). The model uses a parameter (Ψ) exogenously set, to establish the probability that a consumer is inclined to invest in a decentralised electricity system. This is user's green attitude and, the higher its value, the higher the opportunity to evaluate the common investment. .
In conclusion, in each regional group, all consumers check their awareness and willingness towards MG. Those that satisfy these preliminary conditions are involved in the evaluation process. Each agent declares as optimal the option that generates the lowest individual cost; when it concerns MG, agent becomes a potential adopter. MG produces electricity that permits to satisfy a limited demand, although its capacity varies among regions. This implies that regional communities have a fixed number of participants. If the number of potential adopters reaches the fixed size of regional communities (or a multiple of its value), these agents adopt the MG. .
The following hypothesis is therefore proposed regarding the relationship between di usion of MG and characteristics of the demand side:  Consumers' demand (D r ) is heterogeneous across regions but it is homogenous within regions. Its value is initialised based on the regional average of consumption per capita In Italy (Table in Appendix B). Consumers' attitude towards green investments, Ψ, is exogenously set. They have . % probability to be green. Assessing or quantifying the attitude needed to adopt eco-innovations is not straightforward. Di iculties are more acute when the focus is on the specific case of MG, which implies self-generation and self-consumption of electricity. While many studies propose surveys to assess consumers' attitude regarding environmental friendly products, no contribution related to autonomous electricity generation has been found. To work around these di iculties, the share of electricity produced in Italy for self-consumption over the total production is used as proxy of green attitude. However, acknowledging the high relevance of this parameter, a sensitivity analysis is presented and discussed later in the paper.
. Consumers belong to regional groups of people each. This size represents the proximity constraint among people. In order to simulate the Italian case, the model defines regions. The total number of groups per region is set proportional to the number of residents in each region. Moreover, in order to maintain some speed in the simulation, the number of people considered in the analysis is only % of the total Italian citizens; this proportion has been maintained in regions as well. Table in Appendix B shows the number of groups of thousand people per region.
.  . /jasss. . The regional utilisation factor (x k,r ) for each technology included in the MG infrastructure is calculated in relation to the functioning hours. The two renewables technologies, wind and photovoltaic, supply electricity for a number of hours which depends on regional weather and climate conditions. In order to estimate their potential, online databases and so ware are consulted. For wind technology, the average wind speed in each region is used and then the potential for wind plants computed. A similar procedure is used to obtain the values for PV plant, for which the main parameter is the solar irradiation. The micro-CHP system, is assumed to work for hours per year in all regions. The number of hours in which the micro grid uses electricity from the national grid is the remaining time. Assuming that option supplies electricity during the whole year ( hours), Table in Appendix B summarises the share of hours during which each technology supplies electricity power and the share of time the MG necessitates back-up from nation grid. As an example, consumers in the region of Abruzzi compute the variable cost of MG as follows: . % is due to the Wind cost, . % to PV, . % to CHP and the remaining part, . %, is due to the electricity cost purchased from the national grid. .
In order to calculate the maximum number of users that can receive electricity from a MG in each region (N t,r ) it is necessary to estimate how much can be produced and supplied by a MG. To do so, the power installed for each technology (Table ) is multiplied with the respective number of functioning hours (Table ). Then, since the regional demand per capita is known (Table ), it is also possible to measure the maximum number of users that can join a community in a specific region (Table in Appendix B). .
Adoption and di usion of Micro-Grids in Italy is analysed for years. The time horizon T is years. Each time step represents one year. The model runs simulations for each configuration, with di erent random seeds, in order to control the random e ect of the stochastic variables of the model. Therefore, the result of a configuration is presented as an average between those ten simulations.

Results and Discussion
. This section presents and discusses the results of the model simulation. A first overview of the outcomes is given in relation to the classic literature on di usion of innovations. Three sub-sections analyse di erent topic areas: (i) regional factors that influence di usion of MGs; (ii) policy scenarios to assess the e ectiveness of subsidy schema; (iii) sensitivity analysis on user's green attitude and on the cost of the battery.

National di usion .
The di usion process of MGs in Italy follows an S-shaped curve ( Figure ) and the adoption curve follows a bellshape trend, as theorised by Rogers ( ). It is the result of the cost function and increasing returns to scale in adoption in each region (without subsidies, SP t = ). .
The di usion curve shows a slow trend during the first third of the time horizon analysed. In this phase, early adopters opt for MG and decide to move to the decentralised electricity system. Early adoption increases the visibility of MG across the population, which becomes more attractive. The subsequent take-o period determines a rapid surge of MG di usion: in a very short time, it reaches (almost) its maximum value. The steady level is about %, meaning that only half of the population embraces MG, as in hypothesis H . The low di usion share is not surprising but is common in di usion of eco-innovations (Faber et al. ; Higgins et al. ; Shafiei et al. ). Consumers do not shi to MG because of two main reasons. The first one regards the fact that communities in regional groups have a limited size (N t,r ). Not all consumers have the opportunity to join a community if it reaches its maximum capacity. The second reason is related to the previous one and to the social system. People's awareness regarding option increases with di usion (see Equation ), hence with the fashion e ect determined by what other citizens have done in previous steps. Since di usion does not reach an elevate share of the population, the individual chance to know the option to invest in MG is less probable. Moreover, the degree of adoption is also influenced by the individual green attitude and by the initial cost of the battery (B). These two factors will be analysed later in the paper. .
The model permit to study adoption and di usion of MGs as a collective innovation decision. This means that people have to take a decision together. According to di usion theory involving network externalities, large communities have a double and opposite e ect: on the one hand, they reduce the individual cost, and, on the other hand, they slow down di usion (Olson ). A correlation analysis helps to verify whether or not this prerogative is confirmed. It evaluates correlation between the maximum number of people in a regional community with the regional per capita investment cost and the number of years necessary to reach % of di usion at a regional level. The per capita investment cost is the total amount requested to buy a MG when a consumer joins a regional community, computed as the average cost during the full duration of the analysis. The rate of % di usion has been chosen because it is a value reached by all the regions and it represents % of the steady di usion level.  Table : Variables considered in the correlation analysis Figure : Relation between the maximum number of people in a regional community, the cost per capita and the years at % di usion.
. The correlation analysis is significant (Table ) and confirms what is shown in Figure . The correlation between the maximum number of people in a regional community and the per capita investment cost are negatively correlated. Therefore, the cost of MG decreases when the number of people in a community is high (hypothesis H ). Conversely, the correlation between N t,r and the time horizon necessary to reach % of regional di usion is positive and strong. This means that the more the people in a community, the longer the time to reach a certain degree of di usion. This result conforms with classical di usion theories (Rogers ) saying that di usion process dependent on collective decisions requires more time to be accomplished than if it occurs by means of individual adoption decisions. These two results further validate the model, since they conform to theoretical assumption of the phenomenon studied.

Regional di usion .
The analysis presented in this section studies the duration of the di usion process at regional level. It additionally identifies what are the factors influencing di usion at regional level. These analyses concerns the baseline scenario without subsidies. . Figure shows regional di usion curves that follow the S-shaped trend. A er the take-o period, they present a peak of di usion, which is higher than the steady level of the maturity period. This trend depends on fact that the investment duration is years long and that, a er this time, agents dismiss the installed MG and look for substitution. It happens that a large number of adopters simultaneously abandon the MG installed during the take-o period. These consumers may decide to substitute the MG and start a new decisional process by finding a new group of people willing to adopt once again the decentralised system. Hence, the combined desertion causes the short decrease in the di usion curve, a er the peak point. The second decisional phase, however, is faster than before since MG has already achieved a certain degree of visibility. A er a transitory moment, the steady state is reached in every region.
. Figure di erentiate for speed of di usion. Therefore, it is important to analyse regional factors that may have an impact on this process. A linear regression model is applied for this scope. The dependent variable is the number of years needed to reach a % level of di usion at regional level, and the independent variables are the regional electricity demand, the sum of wind and PV regional potential (expressed in hours) and the number of regional residents (expressed in thousands, see Table ). These are normally distributed, and

.
The regression model (Table ) is significant and explains % of the total variation in the dependent variable. The three independent variables have a positive e ect on the speed of di usion since they, ceteris paribus, decrease the time needed to reach % di usion of MG at regional level. An increase by kWh in the regional demand reduces the dependent variable by . , holding constant all the other independent variables. It means that each additional kWh demanded by the consumer increases the speed of di usion by about days. In other words, the speed of MG di usion is faster when the regional electricity demand is high. Why? People living in regions where the electricity demand is elevated, at the starting point of the simulation, pay a higher price for electricity than in regions where demand is lower, since the electricity price (E t ) is equal in all national territory. Furthermore, the price of the electricity provided by the national grid increased every time step (as explained in Equation , and supposed in H ). For these reasons, over time, the option to invest in Micro-Grids is more profitable for people living in regions where electricity demand is high. Similarly, the combined wind and PV regional potential variable positively a ects the speed of regional di usion. An increase by one hour in the regional potential a ects the dependent variable by decreasing its value of . (four days). Micro-Grid di usion, therefore, is strictly related to the renewable potential because it reduces the variable cost of Micro-Grids. Lastly, population also increases the speed of di usion. An increment by people at a regional level, ceteris paribus, decreases the number of years necessary to reach % di usion by .
, which means about one month in time. This result is explained by the fact that, since early adoption causes more visibility, it increases fashion e ect.

.
In conclusion, regional adoption and di usion of Micro-Grids in Italy is a process susceptible to many variables. Since the adoption decision involves a community of final users, the speed of di usion decreases along with the increase of the maximum number of people that can enter in that community. Moreover, electricity demand, JASSS, ( ) , http://jasss.soc.surrey.ac.uk/ / / .html Doi: . /jasss. wind and PV potential and the number of residents influence positively the speed of regional MG di usion.

The role of subsidy .
This section analyses the role of subsidies and how they influence di usion of MG. The baseline scenario, which does not include subsidy, reaches % of di usion share a er years. In order to see whether subsidies stimulate adoption and accelerate di usion, four di erent policy scenarios are simulated. A the begin of the simulation, communities receive subsidy that reduces the cost of the total investment by a fixed amount: e k, e k, e k and e k. However, the amount granted decreases along with adoption (see Equation ). Figure shows the di usion curves under the four policy scenarios. Not surprisingly, the higher the amount subsidised the faster the di usion (as in hypothesis H ). The most e ective scenario, Subs200k, permits to reach % di usion, that is half of the maximum share, in only years. However, it is also the most expensive policy intervention: based on the cumulative expenses, it amounts to e . Bn. .
According to di usion theory, e icient policy interventions should stimulate rapidly the formation of a critical mass which are necessary to the take-o of the adoption process (Gersho & Mitra ). Therefore, to increase the probability of a faster di usion it is important to incentivise early adopters. Rogers a irms that "once a level of, say, percent adoption is reached in a social system, the economic incentive is discontinued" (Rogers , p. ). In order to verify whether these theoretical assumptions are met by the model, di erent policy scenarios are simulated. These grant subsidy (e k) only until a certain rate of di usion is reached at national level. . Figure have the same trend until % of share. A er this value, and depending on the limit set to subsidy, curves change their trend: those with higher limitations proceed faster than others. Although subsidy accelerates di usion processes, some regions do not benefit from this policy intervention because their di usion process takes-o a er the limit is reached at national level. Therefore, this policy intervention, which is based on national threshold, does not have an equal impact on all regions. Moreover, although these scenarios reduce the overall expenditure (see Figure ), the small acceleration of the di usion does not justify entirely the cost of these policy interventions.

Di usion curves in
.
In order to analyses di usion of MG when policy interventions are bounded at regional level, two additional scenarios are simulated. Here the threshold for subsidy is set based on regional di usion shares rather than at the national level. Figure  curves that are very similar to the Subs200k scenario. Subsidy ends when regions reach % or % of di usion. This strategy permits to allocate subsidy fairly among regions, maintaining e iciency and e ectiveness of the policy intervention. In fact, the cumulative expenditure is much lower than the case with limits are based on national di usion share: in the Subs200k 1%reg it amounts to e . Bn while in the Subs200k 5%reg to e . Bn. Figure : Di usion curves with k subsidy and regional limitations. .
In conclusion, this analysis suggests that, in order to accelerate di usion and adoption of decentralised electricity systems, policy interventions are more e ective when they are based on regional characteristics rather than when these are national-based. This depends on the fact that regional areas, such as those in the Italian territory, are heterogeneous, particularly in terms of demographic, climatic and demand characteristics. Therefore, policy-makers have to take into account these factors during the process of policy design.

Sensitivity analysis .
This last section focuses on the impact that two factors have on the di usion of MG. The first regards the green attitude of users and how this influences the potential environmental benefits of MG system, while the second regards the initial cost of the battery (B). Micro-grids have the very likely potential to improve environmental performances since they incorporate renewable technologies bringing to cleaner electricity production and to higher share of self-consumption. Therefore, the bottom-up process driving di usion of MG is a key strategy to achieve countries' environmental goals. The energy mix resulting from the baseline scenario simulated in this paper allows a constant increment of the renewable power installed every year (+ . MW). MG adoption, hence, reduces by , tonnes the production CO emissions every year in Italy.
. Users' green attitude is a key aspect of the di usion process, since it defines agents' probability to be willing to invest in a MG. It would be expected that the higher the green attitude the higher the di usion of MG (hypothesis H ) and, consequently, the higher the environmental benefit. In order to test this hypothesis, a sensitivity analysis is conducted on this parameter. The baseline scenario, where the green attitude is set at . %, is compared with other scenarios where users have di erent attitude. Figure summarises the outcome of the sensitivity analysis. As expected, higher green attitude generates higher di usion and better environmental performances. However, this is not a linear relation, but it follows a logarithmic growth: di usion of MG and its environmental benefit increases with a growth rate which decreases along with the increase of users' green attitude. From a policy point of view, this result implies that, although it is necessary to nudge people's attitude toward decentralised electricity systems in order to generate positive environmental outcomes, it is equally important to .
The cost of battery (B) is another important factor that impact on the fixed cost of the entire MG, and on its di usion. Its value is also di icult to estimate with high degree of certainty due to the recent and continuos progress in terms of technological e iciency and capacity. The baseline scenario simulates adoption and di usion of MG with a cost of battery set to e . Figure shows the result of the sensitivity analysis conducted on this parameter, where the impact of di erent costs are tested. Low cost of battery generates faster di usion of MG, which, however, remains constant in terms of overall di usion share (as in hypothesis H ). Batteries are important components for decentralised electricity systems, particularly for those that combine together renewable technologies, which require storage systems to fully take advantage of their intermittent production. Therefore, this result is important since the learning curve related to batteries will certainly produce a reduction of initial cost that positively impacts the speed of di usion of MG.

Conclusion
. This paper analyses the adoption and di usion of Micro-Grids (MG). These are decentralised electricity systems working quasi-independently from the national centralised grid. MG involves a cluster of technologies that supply electricity to a limited number of users living in proximity of the system and that are directly connected to it. Renewable energy sources (RES), such as micro wind turbines and photovoltaic panels, and biomassbased micro-cogenerators are components of this infrastructure. Decentralised systems are expected to bring environmental benefits, energy security and reduction of transmission losses. However, although all technical elements surrounding MGs seem to be ready for implementation, a wide di usion is not visible yet.
. The paper develops an agent-based model that is used to analyse adoption and di usion of MG in Italy. The Italian electricity supply infrastructure is strongly based on the centralised grid, it presents high ine iciencies (in , losses in the transmission system amount for . % of net electricity production) and it is highly importdependent ( . % of fuel was imported in and % of electricity was imported in ). However, the renewable potential is very high in Italy. The model simulates di erent scenarios in which several factors are studied. .
Di usion of MG in Italy depends on three main aspects: regional specificities, subsidies and people's attitude. Given the high heterogeneity of Italian regions in terms of electricity demand (mean: µ= and standard deviation: σ= kWh/y per capita), renewable potential (µ= and σ= functioning hours per year) and population (µ= and σ= . millions of residents per region), MG di usion di ers substantially from one place to another (µ= and σ= years to reach % of di usion rate). On average, Italy shows a slow di usion process, that reaches only % of the population. Subsidy accelerates di usion ( years less to reach a level of di usion of % compared to a scenario without subsidies). However, total expenditure is elevated: the amount decreases when policies are designed and implemented based on regional criteria rather than national. Lastly, users' attitude has a big impact on di usion of MG: the higher people green attitude, the faster the di usion and, consequently, the higher the reduction of CO emissions. .
In conclusion, the agent-based model presented in this paper proposes a replicable tool to design policy interventions aiming at the promotion of di usion of community-based eco-innovations. Transition towards a new decentralised electricity system implies that new technologies can substitute or integrate the existing centralised infrastructure. In order to achieve this goal, policy-makers should consider di erent aspects. The shi towards a sustainable and environmental friendly system is more rapid in areas where the renewable potential is higher and where there is an elevate electricity demand. This is because new technologies guarantee a more e icient electricity production, and a cheaper supply. Depending on country heterogeneity, policies would be more e ective if tailored to regional areas rather than being national-based. Importantly, transition highly depends on people attitude since their decision shapes adoption. Therefore, it is important to implement policy strategies that can increase people awareness and willingness to invest in more sustainable and environmental friendly energy infrastructures.
. This last point poses important basis for future development of this research. First, energy transition is characterised by uncertainties that can be assessed also by additional methods, such as exploratory modelling (Kwakkel & Pruyt ; Eker & van Daalen ; Moallemi et al. ). Second, the model assumes an exogenous inclination of consumers to invest in decentralised systems, defined as green attitude. Consequently, people do not change or adapt their attitude in relation to the evolving dynamics of the di usion process. This aspect of the model can be questioned and certainly improved in future research. Furthermore, the current structure of the agent-based model presents groups of consumers that are established in advance. Instead, it would be interesting to make endogenous the preliminary phase of group formation based on people interaction. In other words, the continuation of this research consists of modelling the decisional process as an endogenous dynamic phenomenon which evolves with the di usion of decentralised energy system. This will provide more meaningful insights to design e ective and adequate policy interventions.     The model is implemented in C++ by using the LSD so ware (Laboratory for Simulation Development) specifically geared for evolutionary modelling (Valente ). Code and data input are available here: https: //www.comses.net/codebase-release/b6e7c975-2547-403d-bc7f-b2d2e4d5adc0/.
The value has been computed by multiplying the parameter of the CO avoided by renewable electricity production (Bechis & Marangon ) with the renewable electricity produced in MGs. This last value, on yearly average, is the net amount of new wind and PV installed capacity in new communities multiplied by the Italian average of functioning hours for both sources.