# EROI Models

These models and simulations have been tagged “EROI”.

These models and simulations have been tagged “EROI”.

A detailed description of all model input parameters is available here. These are discussed further here and here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

23

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

34

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making a compensation to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Major update 12 December 2015 (v3.0): This new version of the model overhauls the way that incumbent energy source (fossil sources plus biomass, hydro electricity and nuclear electricity) supply capacity is implemented. This is now based on direct (exogenous) input of historical data, with the future supply curve also set directly (but using a separate input array to the historical data). For coal and natural gas fired electricity, this also requires that the simple, direct-input EROI method be used (i.e. same as for coal and NG heating, and petroleum transport fuels).

Note that this new version of the model no longer provides a historical view of the emplacement rates for energy supply sources other than wind and PV, and therefore no longer allows comparison of required emplacement rates for wind and PV with incumbent energy sources. Output data relating to this is available in model version v2.5 (see link below), for the specific transition duration built into that version of the model.

The previous version of the model (version 2.5) is available here.

The original "standard run" version of the model (v1.0) is available here.

Update 6 August 2018 (v2.8): Updated historical wind and PV deployment
data for 2016-2017, adding projected PV deployment for 2018. Data via
https://en.wikipedia.org/wiki/Growth_of_photovoltaics and
https://en.wikipedia.org/wiki/Wind_power_by_country.

Update 26 October 2017 (v2.7): Updated historical wind and PV deployment data for 2015-2016, adding projected PV deployment for 2017. Data via https://en.wikipedia.org/wiki/Growth_of_photovoltaics and https://en.wikipedia.org/wiki/Wind_power_by_country.

Update 18 December 2016 (v2.7): Added feature to calculate a global EROI index for all energy sources plus intermittency buffering (currently batteries only, but this could be diversified). The index is calculated specifically in terms of

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making an adjustment to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Note that this new version of the model no longer provides a historical view of the emplacement rates for energy supply sources other than wind and PV, and therefore no longer allows comparison of required emplacement rates for wind and PV with incumbent energy sources. Output data relating to this is available in model version v2.5 (see link below), for the specific transition duration built into that version of the model.

The previous version of the model (version 2.5) is available here.

The original "standard run" version of the model (v1.0) is available here.

Major update 12 December 2015 (v3.0): This new version of the model overhauls the way that incumbent energy source (fossil sources plus biomass, hydro electricity and nuclear electricity) supply capacity is implemented. This is now based on direct (exogenous) input of historical data, with the future supply curve also set directly (but using a separate input array to the historical data). For coal and natural gas fired electricity, this also requires that the simple, direct-input EROI method be used (i.e. same as for coal and NG heating, and petroleum transport fuels).

Note that this new version of the model no longer provides a historical view of the emplacement rates for energy supply sources other than wind and PV, and therefore no longer allows comparison of required emplacement rates for wind and PV with incumbent energy sources. Output data relating to this is available in model version v2.5 (see link below), for the specific transition duration built into that version of the model.

The previous version of the model (version 2.5) is available here.

The original "standard run" version of the model (v1.0) is available here.

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

This model aggregates energy use in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are dealt with via Li-ion battery storage. Note, however, that seasonal variation of PV is not addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

The significance of reduced energy return on energy invested (EROI) in the transition from fossil fuel to renewable primary energy sources is often disputed by both renewable energy proponents and mainstream economists. This model illustrates the impact of EROI in large-scale energy transition using a system dynamics approach. The variables of primary interest here are: 1) net energy available to "the rest of the economy" as renewable penetration increases [Total final energy services out to the economy]; and 2) the size of the energy sector as a proportion of overall economic activity, treating energy use as a very rough proxy for size [Energy services ratio].

This model aggregates energy supply in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are compensated via Li-ion battery storage. Note, however, that seasonal variation of PV is not fully addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

Update 26 October 2017 (v2.7): Updated historical wind and PV deployment data for 2015-2016, adding projected PV deployment for 2017. Data via https://en.wikipedia.org/wiki/Growth_of_photovoltaics and https://en.wikipedia.org/wiki/Wind_power_by_country.

Update 18 December 2016 (v2.7): Added feature to calculate a global EROI index for all energy sources plus intermittency buffering (currently batteries only, but this could be diversified). The index is calculated specifically in terms of

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making an adjustment to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

This model aggregates energy use in the form of fuels and electricity as a single variable, total final energy services, and treats the global economy as a single closed system.

The model includes all major incumbent energy sources, and assumes a transition to wind, PV, hydro and nuclear generated electricity, plus biomass electricity and fuels. Hydro, biomass and nuclear growth rates are built into the model from the outset, and wind and PV emplacement rates respond to the built-in retirement rates for fossil energy sources, by attempting to make up the difference between the historical maximum total energy services out to the global economy, and the current total energy services out. Intermittency of PV and wind are dealt with via Li-ion battery storage. Note, however, that seasonal variation of PV is not addressed i.e. PV is modeled using annual and global average parameters. For this to have anything close to real world validity, this would require that all PV capacity is located in highly favourable locations in terms of annual average insolation, and that energy is distributed from these regions to points of end use. The necessary distribution infrastructure is not included in the model at this stage.

It is possible to explore the effect of seasonal variation with PV assumed to be distributed more widely by de-rating capacity factor and increasing the autonomy period for storage.

This version of the model takes values for emplaced capacities of conventional sources (i.e. all energy sources except wind and PV) as exogenous inputs, based on data generated from earlier endogenously-generated emplaced capacities (for which emplacement

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making a compensation to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 6 August 2018 (v2.8): Updated historical wind and PV deployment
data for 2016-2017, adding projected PV deployment for 2018. Data via
https://en.wikipedia.org/wiki/Growth_of_photovoltaics and
https://en.wikipedia.org/wiki/Wind_power_by_country.

Update 26 October 2017 (v2.7): Updated historical wind and PV deployment data for 2015-2016, adding projected PV deployment for 2017. Data via https://en.wikipedia.org/wiki/Growth_of_photovoltaics and https://en.wikipedia.org/wiki/Wind_power_by_country.

Update 18 December 2016 (v2.7): Added feature to calculate a global EROI index for all energy sources plus intermittency buffering (currently batteries only, but this could be diversified). The index is calculated specifically in terms of

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making an adjustment to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.

11 months ago

Update 29 June 2016 (v2.6): Added historical emplacement for wind and PV capacity. The maximum historical emplacement rates are then maintained from year 114/115 until the end of the model period. This acts as a base emplacement rate that is then augmented with the contribution made via the feedback control mechanism. Note that battery buffering commences only once the additional emplacement via the feedback controller kicks in. This means that there is a base capacity for both wind and PV for which no buffering is provided, slightly reducing the energy services required for wind and PV supplies, as well as associated costs. Contributions from biomass and nuclear have also been increased slightly, in line with the earlier intention that these should approximately double during the transition period. This leads to a modest reduction in the contributions required from wind and PV.

Added calculation of global mean conversion efficiency energy to services on primary energy basis. This involves making a compensation to the gross energy outputs for all thermal electricity generation sources. The reason for this is that standard EROI analysis methodology involves inclusion of energy inputs on a primary energy equivalent basis. In order to convert correctly between energy inputs and energy

Update 14 December 2015 (v2.5): correction to net output basis LCOE calculation, to include actual self power demand for wind, PV and batteries in place of "2015 reference" values.

Update 20 November 2015 (v2.4): levelised O&M costs now added for wind & PV, so that complete (less transmission-related investments) LCOE for wind and PV is calculated, for both gross and net output.

Update 18 November 2015 (v2.3: development of capital cost estimates for wind, PV and battery buffering, adding levelised capital cost per unit net output, for comparison with levelised capital cost per unit gross output. Levelised capital cost estimate has been substantially refined, bringing this into line with standard practice for capital recovery calculation. Discount rate is user adjustable.

Default maximum autonomy periods reduced to 48 hours for wind and 72 hours for PV.

Update 22 October 2015 (v2.2): added ramped introduction of wind and PV buffering capacity. Wind and PV buffering ramps from zero to the maximum autonomy period as wind and PV generated electricity increases as a proportion of overall electricity supply. The threshold proportion for maximum autonomy period is user adjustable. Ramping uses interpolation based on an elliptical curve between zero and the threshold proportion, to avoid discontinuities that produce poor response shape in key variables.

Update 23 September 2015 (v2.1): added capital investment calculation and associated LCOE contribution for wind generation plant, PV generation plant and storage batteries.

**This version (v2.0) includes refined energy conversion efficiency estimates, increasing the global mean efficiency, but also reducing the aggressiveness of the self-demand learning curves for all sources. The basis for the conversion efficiencies, including all assumptions relating to specific types of work & heat used by the economy, is provided in this Excel spreadsheet.

Conversion of self power demand to energy services demand for each source is carried out via a reference global mean conversion efficiency, set as a user input using the global mean conversion efficiency calculated in the model at the time of transition commencement (taken to be the time for which all EROI parameter values are defined. A learning curve is applied to this value to account for future improvement in self power demand to services conversion efficiency.**

The original "standard run" version of the model is available here.