The market competition in FTT:Power is represented by coupled logistic differential equa- tions. This framework is the same as that used to model evolutionary dynamics and compe- tition in biological systems (Kucharavy and De Guio, 2011; Lotka, 1910; Volterra, 1927). Electricity generation technologies compete for market share at a regional level.3 Technolo- gies in FTT:Power are compared on a pairwise basis. Switches between the two technologies within each pair is measured based on the flow of market share in electricity generation capacity (Mercure et al., 2014).
The rate at which shares of one type of technology (j) can be replaced by shares of another type (i) is proportional to:
1. The rate at which units of technology j come to the end of their lifetime and how many old units require replacement.
2. The rate at which the construction capacity for technology i can be expanded.
3. The market position of technologies i and j (in terms of shares of installed capacity).
4. Investors’ preferences (see figure 4.4).
5. Other technical constraints.
Items 1 and 2 are constraints that define the growth rate limits for the market shares, based on the life cycle specifications of the underlying technologies. So, for instance, the long construction time required for nuclear power stations, as well as the long lifetime of hydro- electric dams, create natural limits for the maximum rate of installation and replacement of these technologies.
3The regions in FTT consist either of countries (such as UK, Germany, USA or Brazil) or groups of countries
4.6 Market Competition 57
The size of an industry also constrains the speed at which new power stations of that technology can be built. Very small industries face growth limitations, connected to the size of the underlying manufacturing capacity. As the industry grows, the manufacturing capacity to support that industry expands. This phenomenon is addressed by the third constraint in the list.
The main driver for the installation of new power stations is, of course, investment. This is captured by the four constraint in the list. If investors allocate more resources in a particular technology, the market size of that technology expands. The investment decision model inside FTT:Power is analysed in detail in chapter 10, and expanded in chapter 11.
Finally, the last item in the list, corresponds to technical constraints. The maximum amount of energy that can be produced from a specific source in FTT:Power, is limited by stability constraints. The stability constraints of FTT:Power are analysed in section 4.6.2.
Equation 4.3 describes, in a simplified case with only two alternatives, how the market share Siof technology i evolves over time, when faced with competition from technology j. This is a logistic differential equation from the Lotka-Volterra family, with the analytical solution shown in equation 4.4. dSi dt = α · Si· Sj= α · Si· (1 − Si) (4.3) Si(t) = 1 1 + e−α(t−t0) (4.4)
In equations 4.3 and 4.4, α is a measure of the speed at which technology Sican take market
share from technology Sj.4 If only two technologies were available, as in the case presented
in equation 4.3, then the evolution of market share follows a perfect logistic pattern, described by the functional form of equation 4.4 and the left-hand chart of figure 4.3. In a more general case, when there are more than two options, the pattern of technology diffusion is more complex, but follows the same principles. The right-hand chart of figure 4.3 shows a simple example with three technologies.
The dynamics associated with the evolution of shares in FTT:Power is presented in equation 4.5. It is called the “shares equation”.5
4In mathematical ecology, the equation 4.3 represents the population dynamic for a species with an ‘intrinsic
rate of growth’ α (Kot, 2001).
Figure 4.3 Example of technology diffusion patterns, modelled using logistic differential equations from the Lotka-Volterra family. On the left, a perfectly logistic transition from the blue technology to the green technology. On the right, a more complex (not perfectly logistic) transition involving three technologies. Early on in that simulation, the red technology (incumbent) is replaced by the blue technology, on a fast transition. The green technology, which enters the market later on, replaces the blue technology, with a more gradual transition. The slopes of the transitions are governed by the equivalent of the parameter αi j in equation
4.5. ∆Si=
∑
j SiSj Ai jGi jFi j ∆Ci j − AjiGjiFji ∆Cji ∆t ¯ τ =∑
j SiSjαi j (4.5)The speed at which technology i can capture market share from technology j (measured by the parameter αi j, the equivalent to the parameter α in equations 4.3 and 4.4) in FTT:Power
depends on several factors, including:
Ai j Technology diffusion rates, that define the speed at which technology i can be deployed, and technology j can be replaced. They depend on the construction time and lifetime of the different alternatives. For instance, technologies such as hydroelectricity and nuclear energy have a small diffusion rate (given by their long construction time and lifetime), while technologies such as thermoelectric power plants and wind farms have faster diffusion rates.
Gi j Technical constraints, to ensure grid stability and balance of baseload with flexible
and variable generation technologies. These technical constraints are particularly important in scenarios with large amount of variable renewable energy (such as solar or wind), because the system is required to balance the growth of variable generation with flexible alternatives. This phenomenon is analysed in detail in chapter 9.
∆Ci j Cost difference between technologies i and j, measured as the difference in the LCOE
4.6 Market Competition 59
Fi j Investors’ preferences, based on the cost structure of technologies i and j. This term
provides the likelihood of a switch from technology j to i, given the difference in the relative cost of both technologies (∆Ci j). In chapter 10, investor’s preferences
are analysed in detail, to see how the inclusion of other criteria (beyond the cost of producing electricity) might influence investment allocation.
∆t is the time interval in which the change in market shares takes place, and ¯τ is the average sectoral rate of technology turnover. To calculate the aggregated changes in market share of technology i (∆Siin equation 4.5), the technology has to be compared with all the other
technologies, using pairwise comparisons. In a simple system with only two options, equation 4.5 leads to a logistic pattern of diffusion, with α = Ai jGi jFi j ∆Ci j − AjiGjiFji ∆Cji. In
the case of FTT:Power, the interaction of the 24 different technologies generates a complex pattern of diffusion. The equation cannot be solved analytically, but is straightforward to solve numerically.6
As mentioned at the beginning of section 4.6, the size of an industry constrains the speed at which new power stations of that technology can be built. In mathematical terms, this is defined by the proportionality of ∆Si(change in shares of technology i) and Si (size of
industry associated to technology i) in the shares equation. This constraint reflects the fact that the manufacturing capacity of the supply chain of technology i is limited, and grows in parallel with the market expansion of the technology itself. While this approach provides a good representation of a market driven technology diffusion process, it has some caveats:
• This approach does not account for drivers beyond market considerations, such as technology diffusion driven by geopolitical change. As analysed in section 2.3, drivers such as direct state intervention have had a strong influence in energy transitions in the past (e.g. adoption of coal during the Industrial Revolution and oil after the Second World War).
• Incumbent technologies (those with large Si) tend to perpetuate their dominance,
while at the same time new entrants have limited growth rate. The dominance of the incumbents could be considered as a constraint for studying rapid technology diffusion scenarios. However, it can also be argued that this modelling approach is a realistic representation of the current limitations in the development of innovation systems around renewable energy technologies (Negro et al., 2012).
6In FTT:Power, the scenarios are simulated on a discrete time step, not solved using a differential equation
In the context of the stylised modelling framework provided by FTT:Power, in which technology diffusion is driven by market interactions, there is room for exogenous definition of technology uptake. Non market driven scenarios, such as those driven by geopolitical forces, which are beyond the scope of the model, can be analysed in this way. In every region it is possible to specify the capacity installed for each technology at every time step. This capability of the model is the basis to define policies that regulate the use of specific technologies, something that is addressed in detail in section 5.2.3.
In FTT:Power, technologies are divided in three main groups, based on their electricity generation characteristics:
Baseload : technologies that are expected to produce a steady flow of electricity.
Flexible : technologies that rapidly increase or decrease the amount of electricity they produce.
Variable : technologies that cannot precisely manage the production of electricity, due to the intermittent availability of the underlying primary energy resource, such as wind blowing or sun shining.
Due to the unpredictable nature of some renewable energy sources, it is necessary to comple- ment the installed capacity of variable technologies with some flexible capacity, that can be made rapidly available on demand. The composition of the electricity matrix is, therefore, constrained by lower and upper limits of baseload, flexible and variable technologies. The specific requirements in terms of baseload, flexible and variable generation and installed capacity in FTT:Power, are analysed in section 4.6.2. Table 4.1 lists the technologies with their respective classification.
4.6.1
Levelised Cost of Electricity - LCOE
The term Fi j in equation 4.5 corresponds to the preference of investors when comparing
technologies i and j. In order to make such a comparison, investors in FTT:Power require a metric to compare the 24 available electricity generation technologies. This metric has to incorporate as much information as possible, including lifetime of the power stations, energy produced, investment cost, operation costs, fuel use and environmental impact. The metric chosen for FTT:Power was the Levelised Cost of Electricity or LCOE, a standard methodology used extensively for the comparison of power sector investment projects (IEA et al., 2010, 2015).
4.6 Market Competition 61
Index Technologies Group Index Technologies Group
1 Nuclear Baseload 13 Biogas Flexible
2 Oil Flexible 14 Biogas + CCS Flexible
3 Coal Baseload 15 Tidal Baseload
4 Coal + CCS Baseload 16 Hydroelectricity Flexible 5 IGCC Baseload 17 Onshore Wind Variable 6 IGCC + CCS Baseload 18 Offshore Wind Variable
7 CCGT Flexible 19 Solar PV Variable
8 CCGT + CCS Flexible 20 CSP Variable
9 Solid Biomass Baseload 21 Geothermal Baseload 10 Solid Biomass + CCS Baseload 22 Wave Variable 11 BIGCC Baseload 23 Fuel Cells Baseload 12 BIGCC + CCS Baseload 24 CHP Baseload Table 4.1 Technologies in FTT:Power. Baseload technologies are those typically used as base load supply. Flexible technologies are those able to respond to changes in peak demand, and Variable technologies are wind, solar and wave, technologies under variable conditions of electricity production during the day. +CCS indicates the use of Carbon Capture and Storage
Some electricity generation technologies, such as hydroelectric dams and nuclear power stations, are characterised by capital intensive investment and long installation periods, but low fuel and maintenance costs. Others, such as gas or coal power stations, require less investment capital and have shorter installation periods, but have higher fuel and maintenance costs. In order to be able to compare these technologies, it is necessary to normalise the values in time and per energy produced. The most common way of doing this is using net present values per unit of energy, which is the approach on which the LCOE is based.
Inequality 4.6 is a very basic criterion on which investors might base a decision to allocate resources in a new power plant: the net present value of revenues have to be higher or equal to the net present value of the costs of producing electricity.
T
∑
t=0 Pi(t) · EPi(t) (1 + r)t ≤ T∑
t=0 TIi(t) + OMi(t) + FCi(t) + CCi(t) (1 + r)t (4.6)Pdenotes the price of electricity, EP is the energy expected to be produced, TI corresponds to the specific technology investment cost, OM the operation and maintenance costs, FC the fuel costs, CC the carbon cost component associated with emissions allowances or taxes where applicable, r the technology or region specific discount rate, t is time and T is the lifetime of the project. The subscript i represents either technology or region, depending
on the context (Mercure, 2012).7 The LCOE is the price of electricity that balances the net present value of revenues and costs. In other words, it corresponds to the minimum long term price of electricity such that investors do not face losses, assuming perfect foresight of costs and energy production. From inequality 4.6, LCOE is calculated as the constant price of electricity that makes both sides equal:
LCOE = Pi= ∑Tt=0 TIi(t)+OMi(t)+FCi(t)+CCi(t) (1+r)t ∑Tt=0 EPi(t) (1+r)t (4.7)
In FTT:Power, the LCOE terms are normalised by unit of energy. So, the equation 4.7 can be expressed as:
LCOE = LCOET I/EP+ LCOEOM/EP+ LCOEFC/EP+ LCOECC/EP (4.8)
Each of these terms (except LCOEC/E which is based on specific carbon price policies) are based on the International Energy Agency values published in IEA et al. (2010).
The LCOE framework is typically used for comparing specific projects (for instance, one power plant versus another). In the case of FTT:Power, however, investment allocation represents aggregated investment decisions at the regional level. In this context, the LCOE framework is used in FTT:Power to compare aggregated regional investment. The aggregation process conceals large variations related to aspects of local nature, such as the cost of land and labour, and decisional issues which may or may not lead to the rational choice of the option with the lowest LCOE. From a behavioural economics perspective, these variations are a representation of the heterogeneity of the system. Investment decisions are taken at the firm level, with no expected coordination among agents, access to limited information and bounded rationality (Simon, 1984), as opposed to system level optimisation, where full coordination and foresight is assumed. In this context, is appropriate to use a probabilistic representation of costs. Figure 4.4 shows a representation of two technologies, with different LCOE distributions. The use of distributions instead of single values captures the uncertain nature of the LCOE estimation.8 The variance of the distributions partly determines the time of diffusion given the price differential, i.e. for an average cost difference, the narrower the
7Due to the discounting, the net present value of decommissioning costs are assumed to be negligible in this
context.
8Details about the data used for the estimation of the LCOE distributions are presented in the Supplementary
4.6 Market Competition 63
distributions (the more identical agent perceptions are), the faster diffusion takes place, given the specific technology diffusion rates (Mercure et al., 2014).
Figure 4.4 Distribution of LCOE values for two technologies i and j. At the firm level, technologies are compared through single values, corresponding to the LCOE calculations from the perspective of the single investor. Due to the variability among conditions and preferences that different investors face, the comparison of technologies at the aggregate level is represented by the comparison of distributions. The probability of technology i being chosen over technology j in the aggregate, is proportional to the frequency in which technology i is less costly than technology j. This comparison is represented by the shaded areas in the chart: the number of units of technology j that emerge as less costly than the median value of the distribution of technology i corresponds to the red shaded area, a value much smaller than the reverse, which is the blue area. Therefore, technology i is preferred over j in aggregate terms. Based on Mercure (2012).
.
Figure 4.4 shows an example of LCOE median values Ciand Cj for technologies i and j
respectively. Under the scenario depicted by figure 4.4, technology i is less costly, and is therefore preferred over j by the investors in aggregate terms. However, that is not always the case, because there is a probability larger than zero that technology j might be less costly than technology i in some particular cases. If the distributions of figure 4.4 are interpreted using a frequentist approach, then the blue area represents the fraction of the total amount of cases in which technology i is less costly than the median value of technology j. Equivalently, the red area represents the fraction of the total cases in which technology j is less costly
than the median value of technology i. While, in aggregate, i is less costly than j (the blue area is larger than the red area), there is a fraction of investors that will prefer technology j over i. Following this approach, given that the median value of technology i is less costly than the median value of technology j, over time the system moves towards the technology with the lowest cost. This probabilistic framework of incomplete overlapping of investor’s preferences is the starting point for the development of a more complex model of investment decisions, which is explained in detail in chapter 10.
4.6.2
Stability constraints and storage in FTT:Power
In the past, electricity was produced mainly by two types of power plants: baseload gen- erators, which run at nearly constant output, and load-following (or flexible) units, which meet the variation in demand as well as provide operating reserves. With the adoption of wind and solar energy, variable electricity was incorporated into the system. The limited control of the output coming from variable generators has brought new challenges to national energy grids, particularly in Europe, where several countries are deploying large amount of wind and solar energy (Weitemeyer et al., 2015). In places like Germany, where the share of non-hydropower renewable generation reached 24% in 2014, the maximum share of variable generation that the system can handle is subject of debate (REN21, 2015; Weitemeyer et al., 2015).
The constraints of the current power sector to balance the amount of baseload, flexible and variable technologies are modelled in FTT:Power as stability constraints. These stability constraints depend on the peak demand pattern of electricity consumption, on the amount of energy storage available on the system, and the current energy mix. So, based on these technical considerations, there are some limits associated with the amount of renewable