In this post I’ll discuss further developments relating to the energy transition modelling exercise covered in detail in the previous two posts (here and here). Consistent with Beyond this Brief Anomaly‘s inquiry ethos, I view the exercise as effectively open-ended. The findings at any point in time can be considered provisional and subject to refinement or revision as learning unfolds, as new ways for making sense of the modeled situation come to light, and as the ways in which the situation itself is understood change. This particular modelling effort should not be treated as the “last word” on the subject. Indeed, the best outcome from the work would be an increased public concern for the dynamics of energy transition — leading to new initiatives that explore the implications independently, going beyond what is possible with this relatively modest foray.
Nonetheless, the findings to date from this work demand close consideration from anyone seriously committed to renewable energy transition. The essential insight is this: in the rapid build-out required for a major transition in primary energy sources, effective aggregate energy return on investment (EROI) for a replacement source’s total stock of generators is lower than for an individual generator considered in isolation. The overall EROI ramps up from zero at the commencement of the transition, only reaching the nominal value for an individual generator over its full life-cycle when the transition is effectively complete i.e. when the generator stock reaches a steady state. All of the other key findings flow from this fundamental feature of any rapid transition in primary energy source. If a replacement energy source has lower nominal EROI than incumbent sources, then this becomes a critically important feasibility consideration.
The specific model developments introduced here are summarised as follows (I’ll discuss each in more detail below):
- The conversion of power outputs to energy service outputs in the form of heat and work for each supply source has been thoroughly overhauled, resulting in a far more refined implementation of this feature of the model.
- Conversion of self-power demand to emplacement and operating & maintenance (O&M) energy service demand in the form of heat and work has also been modified for each supply source.
- The maximum autonomy period that determines the amount of energy storage for wind and PV electricity can now be increased gradually as the intermittent supply penetration increases as a proportion of total electricity supply.
- For the default parameter set (now called the “reference scenario”, previously “standard run”), the maximum autonomy periods for wind and PV supply are arbitrarily reduced to 48 and 72 hours respectively, simply for the sake of heading off any knee-jerk response along the lines that “the amount of storage assumed to be necessary is unrealistic, therefore the entire model is suspect”.
- Detailed calculation is now included for levelised capital cost and O&M cost for wind and PV supply plant, and levelised capital cost for batteries (making the discussion of this in the previous post now redundant).
The updated version of the model to which this post relates is available here.
The full parameter set for the updated model’s “reference scenario” (equivalent to the “standard run” in previous posts) is available as a PDF here.
Brief comments on findings from the revised model’s “reference scenario”
The model behaviour for the default “reference scenario” in the revised model is very similar to that described in detail in the previous post, both in terms of qualitative “shape of response” characteristics and in terms of many output parameters. That’s to say, the model refinements do not change the overall story told in the previous post in any substantive way. The major refinements in conversion efficiency from power outputs to energy services outputs do result in some notable changes. The post-transition energy services ratio increase from around 4:1 to around 6:1 is especially noteworthy. There is also a modest reduction in the depth of the decline in energy services during the transition phase.
Reducing the autonomy periods (amounts of battery storage) for wind and PV electricity obviously has a significant effect in relation to self-power demand and capital cost associated with storage, but this follows from an assumption about a default input parameter, rather than from the modelling methodology or model structure. As it turns out, the overall energy availability consequence of this is more than off-set by the implications of refining the way that conversion efficiencies between energy outputs and self-demand, and energy services, is handled. It should be kept in mind also that this comes at the necessary cost of reduced confidence in supply reliability, and so the benefit provided in terms of apparently improved overall transition feasibility remains contestable.
Full details for the reference scenario can be obtained by running the model with its default parameter set (simply click on the button labelled “Simulate” at top left of screen in the Insight Maker model window) and scrolling through the simulation results charts. Readers can run their own alternative scenarios by clicking on the “Link Results to Model” icon at top right of the simulation results window (left-most of the five icons), restoring down the window and adjusting parameters via the input boxes (recommended) or sliders in the panel at right of screen, below the text on yellow background describing the model. For more details on this, see the post introducing the original version of the model here.
Financial costs of energy transition: wind and PV electricity supply
The significant new data provided by the revised model relates to the financial costs of electricity supply from onshore wind and utility-scale PV generation. Principal outputs for the reference scenario are presented in figures 1 to 6 and figures 9 and 10 below. All values are given in 2015 US dollars.
Figure 1 shows annual total capital investment in wind plant, PV plant and batteries, rising to a mean of roughly $3 trillion, around 35 years into the approximately 50 year transition period. As discussed in the previous post, this can be compared with the International Energy Agency’s forecast for investment in all global energy supply in 2035 of $2 trillion per year, presented in its World Energy Investment Outlook 2014. Note also that the “zero storage” baseline is around $1.5 trillion per year, so even storage options cheaper than lithium ion batteries (or dispatchable backup, for that matter) have little headroom available, if the IEA investment figure is taken as a rough “affordability benchmark”. This is not to suggest that this necessarily should be treated as such a benchmark, but given the status of IEA data in relation to national energy planning, actual investment requirements that exceed its forecasts will likely have significant macro-economic implications.
Figure 1 gives the “principal only” capital investment requirements. Applying the reference scenario discount rate of 7 percent per annum, the aggregate levelised cost of capital (that is, the cost of capital, including financing cost, for all plant and equipment currently being paid for in any given year) rises to around $5.8 trillion (see Figure 2).
This provides a basis for considering the overall economic scale of the modeled transition. While this is important for exploring viability and consequences at the global macro-economic scale, the implications of the dynamic view afforded by the model come into clearer view when we look at costs per unit of electricity delivered. Figures 3 (wind plus batteries) and 4 (PV plus batteries) illustrate the dramatic effect of very high investment rates associated with rapid transition. An initial spike occurs in the annual capital investment per unit of gross electricity output, with the ratio then declining during the transition period as supply capacity comes on-line. The peak value of the spike is around an order of magnitude greater, though, than the long-term steady state investment rate. A clear message can be discerned here: during a period of rapid supply transition, the capital intensity for new energy sources will initially be far greater than the long-term mean. This clearly has major implications for transition planning, if not for overall feasibility.
While the index depicted in figures 3 and 4 illustrates clearly the impact that transition dynamics has on investment for a particular source, it does not have any specific significance within conventional economic feasibility assessment frameworks. For large-scale energy planning, levelised cost of electricity (LCOE) is often used as a bench-marking basis for comparing the economic viability of competing supply sources, and so offers a more practical index for presenting the model’s simulation results. Figures 5 and 6 show LCOE (levelised cost of capital plus levelised operating and maintenance [O&M] cost) and battery levelised cost of capital per unit of gross ouput, for wind and PV respectively. For wind, LCOE converges on a steady-state value of around $0.09/kWh, and with batteries included, $0.15/kWh. For PV, the figures are around $0.14/kWh and $0.23/kWh respectively.
The specific values for each of the cost components shown are obviously dependent on the cost and discount rate assumptions used in the reference scenario. In this sense they are specific to the model, and not intended to be directly comparable to LCOE forecasts from other sources. Nonetheless, comparison with published LCOE forecast data provides a quick rule-of-thumb check on the credibility of the model outputs. Figures 7 and 8 show the estimated LCOE for new generation resources coming on-line in the USA, in 2020 and 2040 respectively. The data used to prepare the charts is from the US Energy Information Admininistration’s Annual Energy Outlook 2015. For onshore wind, LCOE is forecast to be around $0.07/kWh in 2020 and 2040. For PV, LCOE is forecast at $0.12/kWh in 2020 and $0.11/kWh in 2040.
While the difference in the relative weighting of capital and O&M costs between the EIA estimates and the model reference scenario results is more significant than the differences in absolute LCOE values, these differences all fall well within the range of plausible input parameter assumptions. In other words, the simulation results from the model can readily be made to replicate the EIA estimates simply by manipulating the user input parameters relating to LCOE, within the pre-set ranges. This suggests that the LCOE outputs from the model for wind and PV can be treated as credible, and that the model provides a useful tool for exploring how the inclusion of batteries for energy storage affects LCOE. It is of particular note that when LCOE is calculated using gross electricity output, as is the case above, dynamic effects on cost are not apparent. LCOE for both wind and PV rises rapidly and smoothly from zero at the start of the transition period, converging on the long-term steady state mean value well before the end of the transition.
To appreciate the implications of both EROI and transition dynamics on LCOE, we need to consider LCOE on a net output basis. This gives the levelised cost of electricity supply per unit of output to the economy, after the energy costs of supply are deducted. This is shown in figures 9 and 10, for wind and PV respectively. The relative increase in LCOE from gross output to net output basis, and the relative change in LCOE from start of transition to post-transition are the features of interest here.
For wind, LCOE (net output basis) converges on $0.10/kWh post-transition. It reaches a peak early in the transition phase, though, of just over $0.18/kWh. With battery cost included, the peak is just over $0.21/kWh, and the steady state post-transition LCOE is almost $0.17/kWh.
For PV, the situation is markedly different. In fact, from a macro-scale perspective, net output basis LCOE is of no meaning during the early transition phase: PV is a net energy user rather than a net supplier for roughly the first 18 years of the transition period. In figure 10, the model simulation output data is simply presented in raw form, in effect as a “negative cost”, implying that PV requires both full energy and financial subsidisation during this period. At the micro-economic scale, however, this effect is masked: each individual generator, once in operation, will provide an electricity output that is available for sale to customers and that hence can generate a revenue stream from which costs can be recovered. Provided markets are structured so that there is a sufficiently favourable price differential between the electricity output from PV, and energy inputs required by it, the consequences of this will be invisible at the micro-economic level while still being carried in full by the macro-economy.
When the PV supply stock, in aggregate, crosses over from being a net energy user to a net supplier after approximately 18 years, gross output basis LCOE does become a meaningful index. Initially though, LCOE from PV is extremely high. In figure 10, the chart range has been restricted to $1.00/kWh, but it is a further 2 years before the net output basis LCOE actually declines to this level from an initial maximum that is many times higher (and close to 4 years, when battery levelised capital cost is included). By approximately 23 years after the start of the transition, the net output basis LCOE has declined to roughly $0.50/kWh. A steady state value of approximately $0.20/kWh is finally reached post-transition, near 50 years after commencing. With batteries included, the steady state LCOE (net output basis) is around $0.34/kWh.
It is important to note that the index implemented in the model is based on net energy output rather than net electricity output, which is more directly relevant when specifically calculating cost of electricity. That is, what we would ideally like to know is how much electricity is available to the rest of the economy, after electricity used by the supply system itself is deducted. On the other hand, as the proportion of electricity in the overall energy supply increases, net energy provides an increasingly accurate proxy for net electricity. In a situation where all energy used by wind and PV is in the form of electricity, then the proxy value and actual net output would be the same. It should also be noted that the effect of the learning curve for self-power demand is omitted in calculating net energy. Applying the learning curve would result in the steady state LCOE (net output basis) converging on a slightly lower value.
Comparisons of gross and net output basis LCOE values for wind and PV, with and without batteries included, is presented in the summary tables below:
|Supply source (without batteries)
||LCOE (gross output basis)
|LCOE (net output basis) – transition peak
|LCOE (net output basis) –steady state
|Supply source (batteries included)
||LCOE (gross output basis)
|LCOE (net output basis) – transition peak
|LCOE (net output basis) –steady state
|Wind plus batteries||0.15||0.21||0.17|
|PV plus batteries||0.23||>>1.00||0.34|
Model developments in detail
The remainder of the post provides details relating to the recent model developments.
1. Converting power outputs to energy service outputs
Previously this was implemented via a rule-of-thumb estimate of average conversion efficiency from each energy source to a basket of final energy services in the form of heat and work, modified via a learning curve to give improved conversion efficiency over time.
In the revised model, this is has been thoroughly overhauled. The approach taken is to ensure that the distribution of total gross energy services delivered to the economy across four major categories (high temperature heating; low temperature heating; transport work via onboard energy storage; and all other work) matches very closely pre- and post-transition. In other words, the conversion efficiency from gross power output to gross energy service output for each energy source is set so that, overall, each energy service category accounts for the same proportion of energy services before and after the transition. A separate spreadsheet model was developed for this purpose, available for download here (Excel file). The total gross energy services out from each of the pre-transition energy sources is allocated to one or more of the four major energy service categories. This is shown in Table 1 below (based on the Excel file linked above):
The post-transition conversion efficiencies assumed for each energy service category are shown in Table 2 below. The same efficiencies are used to calculate the overall conversion efficiency for each energy source pre-transition, based on the observation that most of the scope for potential future energy efficiency improvement lies in the relationship between energy services and economic production, rather than in the relationship between final energy supply and energy services in the form of work and heat. In other words, it is assumed that improvements in conversion from specific energy forms to desired services will be relatively modest (e.g. improvement in internal combustion engine thermal efficiency), compared with improvements due to use of different energy forms to deliver a similar service (use of electrically-powered heat pumps in place of natural gas combustion for space heating), or change in the nature of service expectations (increased use of smaller, shared-ownership electric vehicles and public transport in place of larger, user-owned ICE vehicles). The latter example could be taken to imply an effective increase in energy service utility, for the same energy services delivered in the form of work and heat. In terms of what this means for the model findings, we can infer that the principal transition criterion of achieving equivalent net work and heat availability pre- and post-transition does allow scope for global increase in economic output, where this is enabled via an increase in the productivity of work and heat. The extent to which this might be achieved in practice is a question that the model is not intended to explore though.
The allocation of the post-transition gross energy services out from each source to each of the four major categories is shown in Table 3 below:
Note that the figures in Tables 1 and 3 above relate to the “standard run” of the model version discussed in the previous posts. These figures were used to derive the mean conversion efficiency values for each energy source that would provide energy service parity in each of the four major categories pre- and post-transition. The mean conversion efficiency values so derived were then fed into the revised model. This resulted in changes to the values of the gross energy service outputs relative to those that had been used as inputs in the previous step. That is, changing the conversion efficiency values, changes the calculation basis for those same conversion efficiency values — there is a feedback loop here. As such, it was necessary to check the magnitude of the resulting changes in the mean conversion efficiency values for each energy source. If the magnitude of the changes was significant, then the conversion efficiency values would need to be iterated, until convergence was reached i.e. until changes in the mean conversion efficiency values fed to the Insight Maker model as inputs resulted in no significant change when the resulting values for gross energy services were fed back into the spreadsheet from the Insight Maker model. As it turned out, an acceptable degree of convergence was reached in a single iteration. Details are provided in the Excel spreadsheet model.
2. Converting Self-Power demand to Emplacement and O&M energy service demand
In the previous model version, this was achieved via a (very rough) rule-of-thumb estimate of the relationship between required energy inputs and actual services. In the revised model, the global mean conversion efficiency from total gross power output to total gross energy services supplied to the economy is calculated dynamically. The economy-wide conversion efficiency at (approximately) the time of transition commencement is then taken as the baseline for the relationship between self-power demand and emplacement and O&M energy service demand for each source. That is, it is assumed that all parameters relating to energy investment are taken to be current at the time of transition commencement. This reference global mean conversion efficiency is set as a user-adjustable input, to allow for iteration of the value if changes in other input parameters lead to significant change in the global mean conversion efficiency at the time of transition commencement (e.g. under parameter assumptions other than those used in the reference scenario).
A time-variable adjustment factor (i.e. with an assumed learning curve built in) specific to each energy source is applied to the global mean conversion efficiency so that some multiple of the global value is applied to each source. For wind and PV plant, the adjustment factor decreases from greater than 1 pre-transition to less than 1 post-transition. For battery production, a learning curve is applied directly to the embodied energy, and so the corresponding adjustment factor reduces from greater than 1 pre-transition, to 1 post-transition.
For the purpose of calculating net output basis LCOE, the reference self power demand for wind, PV and batteries is adjusted to a current actual value using the global mean conversion efficiency from power to services out to the economy. That is, while the energy services (work and heat) required to emplace and operate and wind, PV and battery plant & equipment is assumed to be relatively stable (though reducing over time via the learning curves), the energy inputs required to provide these services varies with the global mean conversion efficiency. As this conversion efficiency increases, self power demand reduces (and vice versa).
This approach allows for simple and transparent comparison of energy use by the energy sector with energy use for economic production in the overall economy. These relationships can then be adjusted, if desired (though at this stage this is not available via direct user input and would require cloning of the model — see the first post in this series for details on how to go about this).
3. Ramping of maximum autonomy periods for Wind and PV battery storage
In the previous model version, the maximum autonomy periods for battery storage were fixed at user-adjustable constant values. This meant that as soon as wind or PV generation capacity emplacement commenced, the target for battery storage capacity was set to allow delivery of the current mean electricity supply rate for the maximum autonomy period. This does not provide an accurate representation of what we would expect to happen in practice, as storage associated with intermittent electricity sources provides far less benefit to the overall supply system at low intermittent supply penetrations. The supply reliability benefit provided by storage increases as the overall proportion of intermittent electricity supply increases. This means that at lower penetrations, we should expect to see levels of storage based on lower autonomy periods. The maximum autonomy period becomes more relevant at higher penetrations, beyond a certain intermittent electricity supply proportion threshold.
This is now accounted for in the model by allowing the autonomy periods for wind and PV electricity to ramp from zero hours at zero supply capacity, up to the user-adjustable maximum value at a user-adjustable intermittent penetration threshold, specified as the proportion of intermittent supply (i.e. wind and PV) in the overall electricity supply. In the reference scenario, the threshold proportion is set to 40 percent. This means that energy and financial investment costs associated with battery emplacement are far more modest during the early years of the transition phase. For the reference scenario, the threshold level is reached approximately 20 years after the transition commencement.
The ramping function uses an elliptical curve to interpolate the autonomy period between zero penetration and the threshold value. The form of the interpolation function is as shown below:
Where: y is the proportion of the maximum autonomy period target that is used to determine the amount of storage required at the current time (see variable [Proportion of max autonomy period for battery storage target] in the Insight Maker model), x is the maximum proportion of intermittent electricity in the overall supply realised to date (see [Intermittent electricity supply proportion max value]) and t is the threshold for the proportion of intermittent electricity in the overall supply at which the maximum autonomy period takes effect (see [Intermittent supply proportion threshold for max autonomy period]).
The elliptical function is used to avoid modelling instabilities associated with too-sudden changes (i.e. discontinuities) in the target autonomy period from one time step to the next. This means that the autonomy period initially rises relatively rapidly, with the rate of increase tapering off as the threshold proportion is approached. The effect is very modest though, and to the eye the ramping appears linear, with a transition curve at start and finish.
4. Reduced Maximum Autonomy Periods
The default parameter values for wind and PV maximum autonomy values in the previous version of the model (i.e. the “standard run”) were 72 and 148 hours respectively. For the reference scenario in the revised model, these values are reduced to 48 and 72 hours respectively. This reduction does not reflect any change to the maximum autonomy period rationale presented in detail in the previous post. It simply reflects a pragmatic decision to position the reference scenario more moderately relative to mainstream-popular renewable energy discourse. For example, an autonomy period in the order of 72 hours is often used as a rule-of-thumb starting point for considering the design of stand-alone (grid independent) PV electricity supply systems (see this article for instance). The reference scenario’s implications for feasibility assessment remain qualitatively equivalent even with these much lower autonomy periods. From this point of view, it seems prudent to assume shorter autonomy periods in order to reduce the potential that the model’s credibility will be challenged (or the simulation results dismissed outright) due to contention over storage requirements. This assumption implies, however, acceptance of a corresponding trade-off in reliability of electricity supply.
5. Financial cost calculation for Wind plant, PV plant and batteries
The financial cost calculation module in the revised Insight Maker energy transition model is highlighted in figure 11 below, at lower right of the screen shot.
Figure 12 shows a detailed view of the financial cost calculation module:
The financial cost calculation module comprises four sub-modules relating to wind generation plant, wind supply-related battery storage, PV generation plant and PV supply-related battery storage. The wind and PV generation plant sub-modules include calculations relating to capital cost and O&M cost. The battery sub-modules include calculations relating to capital cost only.
For each sub-module, the capital cost for capacity emplaced in each time step is used to calculate a capital recovery increment, based on a discount rate and plant or equipment operating life. Each capital recovery increment is added to a cumulative stock for the duration of the corresponding capacity increment’s operating life. The stock therefore represents the total annual cost of capital for all plant or equipment in operation at any time.
Primary inputs to the cost calculation module are:
- 2015 capital costs for wind plant, PV plant and batteries
- cost reduction curves for each component
- discount rate
- O&M cost per unit generation capacity for wind and PV plant
With the exception of the cost reduction curves, these inputs are all user-adjustable within fixed ranges. Other inputs are taken directly from the output of existing modules elsewhere in the model (e.g. wind and PV generation capacity; battery storage capacity). See the reference scenario parameter set pdf for the basis of each input.
Annual gross and net wind and PV energy outputs are calculated in the respective sub-modules and used to derive the related cost indices.