Developing a diffusion model of competing
alternative drive-train technologies (cadt-model)
M. Bosshardt’, S. Ulli-Beer*’, F. Gassmann*, A. Wokaun*
“Paul Scherrer Institute, Switzerland
*TKAO, University of Berne, Switzerland
Dynamics of Innovative Systems (DIS), 5232 Villigen PSI, Switzerland
Tel. +41 (0)56 310 24 41, Fax +41 (0)56 310 26 24
mathias. bosshardt@psi.ch
Strategic measures for global ecology and security of energy supply particularly affect road
traffic, as a main originator of greenhouse gas emissions by use of fossil energy. The
introduction of several alternative, eco-friendly drive-train technologies in the automotive
fleet leads to a competition with the existing petrol and diesel engines as well as with each
other. A system dynamics model is developed to understand the fundamental competing
forces driving the market penetration of the new technologies, and to derive policy implica-
tions and strategies potentially contributing to their successful introduction. A conceptual
model is presented to examine different diffusion patterns between competing technolo-
gies. First results show, that reaching a critical market share in time is a decisive factor.
This is demonstrated for the case of Switzerland, that represents a demand driven market
without an autonomous automotive industry.
Keywords: technology diffusion, market share, alternative drive-train, system dynamics,
competition, social norm, critical mass, potential
1 Introduction
These days the worldwide per-capita energy consumption averages 18000 avn which cor-
responds to an average power of 2100 W. In Switzerland about 5000 Watt per capita is
spent, i.e. 2.5 times more than the global average (novatlantis — Nachhaltigkeit im ETH
Bereich, 2005). The vision of “novatlantis — Sustainability in the ETH-Domain“ (no-
vatlantis — Nachhaltigkeit im ETH Bereich, 2005) is the so-called “2000-Watt-Society “
(Energie-Spiegel, 2007), aiming at a reduction of the per-capita consumption to the
current global average of some 2000 W, which is considered as a contribution to the
establishment of a balance between the industrial countries and the developing world.
Facing global climate change — boosted by accumulated greenhouse gas emissions, es-
pecially COz — and the oncoming shortage of fossil resources, it is necessary to reduce
overall primary energy consumption and to advance a sustainable development towards
more eco-friendly, renewable energy sources and energy efficient technologies. Emanating
from a consistent progression in all sectors, the energy consumption in the Swiss light
duty vehicle sector in particular has to be reduced from about 6.8 GW in 2005 towards
a 2.7 GW landmark (Bericht des BFE, 2004). For the biggest effect possible of this envi-
sioned reduction path, alternative fuel technologies need to be promoted, since they are
still sparsely represented in today‘s carfleet. This spread of one or more new drive-train
technologies throughout society represents an innovation diffusion process (Rogers, 1969),
which is needed to achieve long-term climate and energy policy goals.
To answer the overarching research question of how to reach a successful introduction
of new drive-train technologies resulting in an required fuel split in the car fleet, several
steps have to be performed. The purpose of this paper is to develop and analyse a cadt-
model (competing alternative drive-train technologies model) that illustrates the effect
of a critical mass. This has big relevance for those who are interested in the potential or
the spread of new drive-train technologies, as for instance fuel suppliers or governmental
authorities at different levels. Learning about the critical quantities or significant leverage
points in the system is fundamentally important to exert influence on the development of
the system. System understanding gives insights that form the basis for the development
of implementation strategies and a long-term policy.
The aim of this paper is to point out an adapted methodology of describing and explaining
the diffusion rates of new drive-train technologies with a simulation model. To realise
an adequate technology path leading to the adoption of the new technologies, the most
important factors and processes favouring or retarding this path must be identified. The
basic relations applied in our model show the important role of a critical market share,
which determines success or failure of the diffusion process. Because of the competition
between different alternatives the single developments will be the result of interdependent
dynamic processes.
2 System analysis
First of all it is necessary to describe the system represented by the model. Building
on our case study in Switzerland we are illustrating the case of a small industrialised
country without any autonomous automotive industry. Several aspects can be adopted
from Janssen (2004), whose work is to be continued and expanded by the current study.
According to the system analysis of Janssen (2004) three main groups of stakeholders
interact in the market of our system: The customer sector, the car import and retail
sector and the fuelling station sector. Fig. 1 shows a sector model of the system with the
three groups mentioned in the centre.
Stakeholders of these groups experience basic conditions like technology availability, per-
formance, fuel price, car purchase price, taxes etc. Their options basically consist in
adopting or not adopting new drive-train technologies, and their actions have an influ-
ence on the decisions of other stakeholders within their own as well as in other sectors.
The distinction of all customers into private ones and flect carriers has not yet been in-
corporated into the model, but seems to be important in an early market implementation
phase (Nesbitt und Sperling, 1998).
A second point concerns the distinction between endogenous (‘customers’, ‘fueling sta-
tions‘, ‘car import, retail and service‘) and exogenous stakeholders, defining the model
boundaries of the system dynamic (SD) model. In contrast to the first group mapped with
an SD model, the latter have to be treated with a different approach. In order to simulate
realistic behaviour it would be preferable to have a framework making different scenarios
reasonable and putting the model parameter values in a major context. They should be
deduced from strategies of policy-making stakeholders, acting rather like players than as
a homogeneous mass. The initial position with different individuals or parties pursuing
different interests forms a conflict situation, characterised by interaction of all parties
involved in terms of rational statements about the participants, their possible options,
2
Exogenous stakeholders
- constitute general conditions
- operate €s ind viduals
- interact with each other as well as with the system of collective stakeholders
- description with game theoretical approach Consumption
- scenarios bacome reasonable
Municipal
authority Y
Endogenous stakeholders
- operate as collective ‘Adeption, paradign,
“respond Lo general conditions caning felng stations
give feedback to exogenous stakeholders ES
= description with system dynamics Customers Sector
Fueling Station
Sector
Encourscina
— Drive ta
Drive train Axcess technologies ated
technologies 9 ee
Paradigm facturer B
Government. Purchase
| = \ ae
Subsitios
anok
Ofer Fleet cartiets:
Car Import, Retail,
Service Sector
Drive wain
Purchase sethijolagics:
eal Dive wan Competition
ex eduction feclivologies ee Reproduction
Addional
YA Pit Faden a Beepelacion *ypas uJ
Consumption Coneupion 4 Purchase
Colaboration
adele Adjustment
CNG Supplier — H, Supplier Car manu-
U “Vv — facturer A
Figure 1: Box diagram, showing the model boundaries and the different subsystems.
their strategies and mutual information exchange. The analysis of such situations is the
quintessence of game theory (cf. Manteuffel und Stumpe, 1977; Krabs, 2005). The model
structure is therefore extended by an outer framework for policy making stakeholders.
The coupling would lead to a combined model comprising a system dynamical as well as
an explaining game theoretical part. However, this step still needs further research.
So far there are three different sorts of policy making stakeholders in the system: Fuel
suppliers, car manufacturers and municipal and governmental authorities. It is them who
determine the the basic conditions of the market. The options they can use to influence
the market are described as follows:
Subsidies on alternative vehicles are a one-time financial support given directly to
the customer and reducing the purchase price of such vehicles. This instrument
makes the investments smaller and therefore increases the attractiveness of new
technologies. Subsidies can be granted by the government or the fuel indus-
try, for example in the context of a bonus malus system as discussed in Switzerland.
Fueling station subsidies work in an analogue way as the subsidies on alternative
vehicles, but relating to the installation or construction of filling facilities for corre-
sponding fuels. Like for vehicles we are dealing with a one-time subsidy, lowering the
fueling station managers invested capital and therefore raising profitability. This
sort of financial support can be granted by the government, the fuel industry
3
or together with car manufacturers!.
Fuel tax advantages can be given to fueling station managers, who can shift a certain
amount to the customers by a reduction of the end user fuel prices. The tax
reductions are to be seen in comparison to non-leaded petrol”. Tax advantages are
granted by the government.
Information spread has an influence on the fraction of possible adopters that effec-
tively adopt a new technology. The estimation of the effect of information is very
difficult and needs a measure for its effectiveness, which depends on the total amount
invested in information spread. This measure is taken by the government, car
manufacturers and the fuel industry.
Technology improvement as a result of research and development is supported by the
state. Its time dependent behaviour is difficult to estimate over the models time
horizon of up to 100 years. Technology improvement is based on investments
made by the government, car manufacturers or the fuel industry.
Fuel marketing measures comprise cost-free or price-reduced fuel. The offer can hold
for the initial purchase of a promoted car, and can be extended, if the customer
agrees on using his car as an advertising medium. An example is the natural gas
campaign “Aktion Naturgas“ (Erdgas Ziirich, 2006) of the regional gas supplier
Erdgas Ziirich in Switzerland. This sort of support is granted by the fuel in-
dustry.
Car marketing measures comprise publicity, price reductions on cars or an increase in
product diversity, improving customer-friendliness. This sort of support is granted
by car manufacturers.
Today‘s almost exclusively used fuels in the Swiss passenger car sector are petrol and
diesel for internal combustion engines (ICEs). Following the manufacturers of the ten
best sold car makes in Switzerland, bifuelled natural gas vehicles (NGVs) driven by
an ICE operating with petrol/diesel and natural gas, and ICE/electric hybrids (HEVs
— hybrid electric vehicles) are the most promising alternatives. The hydrogen fuel cell
vehicle (FCV) is commonly seen as an optimal long term option. An important issue is the
competition between all four alternatives and its consequences on fueling infrastructure
built up. Some developments may hinder or delay the emergence of hydrogen technology,
while others could support it due to technical and social spill-overs.
The Swiss federal statistical office calculated the average age of passenger cars to be 7.4
years in 2004 (Bundesamt fiir Statistik, 2004), with increasing tendency. Some future
technologies such as hydrogen powered fuel cell vehicles will enter the mass market only
in some 20 years. Therefore the time horizon to perceive relevant changes in the passenger
car fleet should at least be 40 to 50 years. If we want to analyse behaviours with delayed
technology diffusion we have to extend the time horizon up to 100 years. It is clear that
the reliability of the model forecasts will decrease towards the time horizon.
Although we are primarily interested in the development of the light duty vehicle fleet
referring to Switzerland, our basic characterisation of the system should also apply to
most industrial countries. The Central questions to be answered are:
1See for instance Clean Energy Partnership (CEP) (2006).
2Diesel has therefore a negative tax advantage in Switzerland (Eidgendssische Zollverwaltung (EZV),
2006).
e Which processes can influence the share of alternative technologies, and under which
conditions?
e When does a critical mass occur and what is its effect?
e What influence does the competition between different alternatives have?
3 Diffusion of drive-train technologies
A simplified, idealised innovation diffusion (Rogers, 1969) in general follows — at least
until a certain point in time — a sigmoid form, as it is shown in figure 2.a. The graph
shows the number of units for a certain technology plotted against time (x-axis). We
will refer to a successful development, if the curve follows a sigmoid form that reaches
a desired level within an acceptable time span depending on the goals being set for the
development of the system. Possible failures in this sense would be “extended diffusion
time“ (diffusion takes more time than acceptable, fig. 2.b), “limited growth“ (diffusion
does not reach an acceptable level, fig. 2.c) or “unstable development and decline“ (strong
fluctuations with subsequent disappearance, fig. 2.d).
2 2
. ie . Tine
a) Successful development b) Extended diffusion time
g 3
Bos Bes
5] a
: . © time . ° . “me” *
c) Undersized growth d) Instable development-path
Figure 2: Comparison of four different fundamental behaviours of the sigmoidal diffusion
curve. These curves should be considered as qualitative. In theses graphs adoption is
normalised to 1, and the time axis has arbitrary units.
Curves with a completely different outcome show a similar behaviour at the beginning.
Success or failure can possibly not be distinguished in the starting phase of the diffusion
process, and the difference in early observable numbers may lie below precision of mea-
surements. Once collapsed, a diffusion process can hardly be re-initiated. This shows
why a better understanding of the early implementation phase is needed to anticipate
unwanted development in an early stage.
Following the definition of Rogers (1969) the introduction of alternative drive-trains and
their corresponding fuelling infrastructure in a car flect is a process of technology diffusion.
The way for the diffusion of the innovation‘s hardware is paved by communication. For
a successful introduction of alternative technologies in the Swiss car fleet corresponding
with a 2000-Watt-vision, stimulation and support of an optimal technology development
path is of fundamental importance. The timing and the sequence in which different
technologies appear can be very crucial for a further development. Technical spill overs
for example can foster the diffusion by saving expenses, or customised features of certain
systems can eliminate handicaps and lead to the emergence and the approvement of new
technologies. However, lock-in effects for certain technologies (cf. e.g. Arthur, 1989) have
always the consequence of locking out competing technologies, what might especially not
be preferable in the case of alternative drive trains and fuels.
Likewise Leydesdorff (2001) is speaking about a “point of no return“, meaning a stage
in the diffusion process, where established standards lead to an exclusion of alternatives.
According to Leydesdorff a break-out of a lock-in situation and a return to equilibrium
remain possible, but changes in parameters in the order of magnitude are possibly needed.
Considering the lock-in as a grown state, the result of a “selection over time by an
emerging system“ as Leydesdorff says, we can look at today‘s passenger cars‘ drive-train
technology as a lock-in of the internal combustion engine (ICE) and all its corresponding
systems, such as fueling infrastructure for example. In this sense the challenge with
introducing new drive-train systems is not the diffusion of a new technology, but replacing
an existing one with the same purpose and of excellent performance, at least from a
customer‘s point of view. This means that a break-out must happen first to reestablish
the possibility of a shift in direction. Furthermore, where we are facing the problem of
substitution as in our case, the “point of no return“ denotes the time when the decision
in favour of one of the competing technologies is being taken. This is not directly related
to the overall success of the chosen technology’s diffusion, which can also have sort of a
“point of no return“. It is still able to fail, even if it has prevailed in the market against
other alternatives, but not against the predominant system.
Similarly Rogers identifies a “point of no return“ in a diffusion process. It becomes man-
ifest in the number of adopters of the concerning technology, the critical mass (Rogers,
1969, p. 343ff.), that is needed for the further rate of adoption to become self-sustaining.
This means that we get a process where stimulating measures become redundant. Fol-
lowing Rogers (1969) the critical ma: a fundamental concept that expresses the social
nature of the diffusion process. Assuming the critical mass exists, two questions — from
our point of view not yet answered in literature — immediately arise: How large is the
critical mass? And what are the conditions to reach it in the diffusion process?
As we will see below the critical mass is not always accessible by means of a model,
although being a very important quantity regarding policy considerations. However,
using a system dynamics model together with Rogers‘ characterisation of “reaching the
critical mass“ as the “moment when the adoption rate experiences an acceleration“, the
amount of the critical mass can be estimated. Gassmann und Ulli-Beer (2006) show a
criterion to determine whether a critical mass exists for a given model, and they show
that the widely used Bass model does not map this important concept. The critical
mass coming of our cadt-model depends on the norm building process, actually on its
nonlinearity.
4 Model description and setup
The purpose of the cadt-model is to explain the chronological sequence of the diffusion
rates of alternative drive-train technologies. Its main function is therefore to link the
single technology layers and describe the transfer between them. The effect of certain
policy measures and strategies is to be analysed in different scenarios, which are not
described in this paper.
4.1 Modelling approach
The dynamics underlying the system and the treatment of several quantities like e.g.
customers, number of fueling stations or vehicles as aggregated clusters, indicate a differ-
ential equation based modelling approach. System dynamics (cf. Sterman, 2000) provides
a method and a language to build and communicate such differential equation models.
Graphical interfaces assist in dealing with causal structures, while the normally complex
em of coupled equations is being solved with numeric integration by means of Euler
or Runge-Kutta methods.
In system dynamics, variables representing quantities of our system are subdivided into
three groups (Sterman, 2000): endogenous, exogenous and excluded, i.e. dynamically
tied up variables, given variables from outside the model and variables not being consid-
ered. In the following we will further talk about stocks of different technologies, meaning
cumulative quantities in the system belonging to a certain drive-train technology, and
flows, which are the rates defining the transfers between the stocks. The flows are de-
termined by a number of factors discussed below. Other variables than stocks and flows
exist and influence the rates, possibly being time dependent. The entirety of variables
associated with the same drive-train technology are designated as a technology platform.
The idea of different technology platforms was developed and implemented into a model
by Struben (2004a), and is used in our case in a similar, slightly modified manner. To-
gether with the stakeholders interacting in the market — referred to as the endogenous
stakeholders — we get the following subsystem shown in figure 3.
4.2 Model structure
The basic model structure is generic and could be applied to other single or regions of
multiple countries (e.g. Europe) and different drive-train technologies after few modifi-
cations. While Janssen (2004) developed a model with only one alternative drive-train
technology and worked out the relationships between car stocks, import and infrastruc-
ture within a technology platform, our model is primarily aiming at the interactions
between different platforms.
The following table on page 7 gives an overview of the variables so far considered in the
model, where market forecasting, filling facility cost, fleet aging and mileage have been
omitted for the time being:
Endogenous stakeholders
- operate as collective
- description with system dynamics
Fueling Station
Sector
Fuel alternatives
Car Import, Retail,
Service Sector
Drive train
technologies
Customer Sector
Conventional &
alternative cars
Figure 3: Box diagram showing the model structure: The simultanous handling of more
than one alternative fuel technology with the resulting competition can be realised by the
introduction of different coupled platforms, similarly structured within the same sector.
Classification Variable
Description
Endogenous Car stocks
Social norm
Comparative attractiveness
Perceived attractiveness
Customer satisfaction
Adopter potential
Median lifetime
Fleet growth
Availability
Exogenous
Fueling stations
Type spectrum
Fuel price
Purchase price
Inherent attractiveness
Numbers of petrol or diesel cars etc.
The strength of the social norm (accep-
tance of a drive-train technology)
Based on financial incentives for adopt-
ing a certain drive-train technology
Product of social norm and compara-
tive attractiveness
Degree to which customers are satisfied
with a technology (€ [0, 1})
Product of customer satisfaction and
perceived attractiveness
The time a car is registered
Annual fleet growth rate
Degree to which a technology is avail-
able for customers (€ [0, 1])
Numbers of fueling stations providing
dedicated fuels
Diversity of car types offered
Fuel price per litre petrol equivalent
Purchase price of a typical car for each
technology
Basic attractiveness during start-up
phase
In our present model stocks are defined as number of cars. Technology substitution occurs
when a car is scrapped and replaced by a new one of the same or another drive-train type,
while the total size of the fleet remains constant. All stocks are linked to each other by
flows in a symmetrical way. This allows a customer to replace his car after scrapping
by one of any of the four chosen drive-train technologies. There we assume that a car is
scrapped and replaced after an average lifetime of 12 years. The time horizon is set to
100 years (see above).
The options for the policy making stakeholders — like e.g. subsidies and tax reductions —
are not explicitly included in the model yet. They are implicitly manifest in the variables
“comparative attractiveness“, “customer satisfaction“ and “availability. These are in-
fluencing the purchase decision of the customers and determine the flow rates between the
stocks and therefore the technology substitution. The variable “comparative attractive-
ness“ consists of a constant basic and a time dependent part. The first one corresponds
to an attractiveness a technology always has, for example on innovative persons. The
second one is accessible by means of the policy measures discussed in section 2.
The dynamic hypothesis of the model is illustrated in figure 4. The causal loop diagram
shows the whole decision-taking structure, which counts for all technology platforms, but
with different stock values and input parameters.
Fuel Price Purchase Price
Fuel Availability Spectrum . J
Satisfaction Satisfaction Comparative
Attractiveness
+
+ +,
Customer ;
Satisfaction Perceived Inherent
Attractiveness Attractiveness
+ + + +
Adopter Societal Norm
Potential
+ Median Lifetime
+
Light Duty! :
Vehicles
Sales Discards
ra a
New Sales
Figure 4: Causal loop diagram of the current model, showing the decision-taking process.
In this work the new sales are set to zero in order to point out the effect of the decision
process more clearly, and particularly the effect of the social norm. The interpretation of
the normalised adopter potential as the probability of purchase allows the multiplication
of all flow rates with this number, considered as the percentage of adopters.
An alternative way to look at the model is exemplified in figure 5, taking three different
drive-train technologies into account. This illustration shows the competition much more
clearly, and the way the different drive-train platforms interact with each other. There
is theoretically no limitation on the number of technologies considered, although there is
9
certainly a limitation by the market itself.
P&D vs. NGV
Substitution
Natural Gas
Vehicles New Sales NGV
rol & Diesel
Petrol Ty “yy
Oo - = P| Vehicles EV vs. NGV
New Sales P&D i Substitution
Hybrid Electric
; a
P&D vs. HEV New Sales HEV
Substitution
Figure 5: Stock and flow diagram, showing the basic model structure for three different
car stocks. The structure can be extended to more than three technology layers.
Figure 6 shows the general formation of the substitution rates. The rates back to the
stock of conventional ICEs are treated later.
Figure 6: General structure of a flow rate. All rates in the model, excepted the flows
back to conventional ICE vehicles, are built with this structure.
The calculation performed for the flowrate of stock N; to stock Nj reads as follows:
r(t) = 2 past) A a)
with
p(t) = 6,(2O)*. 55) + eas(t (2)
where Cj is a constant factor and weight of the normbuilding process, and
10
rj(t) : substitution rate Not + number of vehicles on road
N;,(t) + car stock i N;j(t) : car stock j
to : median lifetime t : time
pa;(t) : perceived attractiveness ca;(t) : comparative attractiveness
s;(t) : customer satisfaction Aj : availability
Ni(t)
Let us first consider equation (1). The fraction 7, on the right hand is the average
number of cars with technology i that are replaced per time unit, because they reach the
end of their lifetime, to. This fraction is multiplied with a technology-specific “perceived
attractiveness“ pa; (c.f. equation (2)) which is explained below. This attractiveness
of technology j is interpreted as the percentage of cars that are substituted by this
technology. Since the sum of all cars that are replaced in N; is limited to oe the sum
over j with j ¥ i of all perceived attractivenesses pa; must have a maximum of 1. The
final factor A; is a potentially limiting factor with the range of 0 to 1. It represents
the fact that a substitution will not take place instantly, because there may be a delay
for several reasons, like delivery problems or a lack of infrastructure for instance. It is
standardised to today‘s ICE standard, being considered relatively to this technology and
its infrastructure. It is not likely that alternative technologies would have better retail
and service attributes etc. than ICEs.
In equation (2) it can be seen that the perceived attractiveness is determined by two
additive terms: The first term in brackets is a product of the “customer satisfaction “
s; with the square of the fraction of cars belonging to technology j. s; is a perceived
satisfaction in relation to today‘s standard technology’s supply of needs — of ICEs in our
case — which is assumed to be the maximum. The norm factor (BO) describes the
measure of perception (cf. Rogers, 1969, p. 352f.) of technology j. The second power has
been chosen to fulfil three simple conditions to the effect of the social norm: The norm
must disappear if Nj is zero, and it should grow slowly with Nj; in the beginning but
faster with increasing Nj (cf. Gassmann und Ulli-Beer, 2006). Cj is a weighting factor
for the norm, describing the societal desirability of technology j. It is standardised in the
same way as A;. The second summand ca,(t) represents a given basic attractiveness of
technology j, but has also a time dependent part which is added. This value is associated
with the potential to launch the technology substitution process. In the current model
it has to be ensured during runtime that the sum of the attractivenesses mentioned
above does not exceed 1, which still has to be improved, for instance by introducing a
normalisation.
Flow rates from any car stock back to ICEs are formulated slightly different. All the flows
back to conventional ICEs could shrink independently on their comparative attractiveness
or norm over time due to the assumption, that petrol and diesel will decline with the
future lack of crude oil resources. Furthermore Ajcg as well as C)cg equals 1 because of
the standardisation and can therefore be omitted. Figure 7 shows the formation of such
a rate.
The appropriate calculation for the flow rate N; to stock Nicg reads as follows:
rscett) = SO. parcel 3)
with
parop(t) = ((“EP)”. sroplt) +emrce(t)) Steel) “)
11
CaicE
Aq
Sick
Ni we Nick
TICE
Figure 7: Structure for a flow rate back to conventional ICE vehicles. The availability
factor A; is set to 1, according to its definition (see below). However, there is an additional
factor S;cm appearing in the definition of the perceived attractiveness, describing the
decreasing availability of crude oil.
where
Sicr(t) : shortage of resources
The other variables and parameters are equally defined as in equations (1) and (2).
The additional factor S;cp(t) in equation (4) represents the mentioned possible disap-
pearence of fossil fuelled drive-train technologies due to decreasing resources. This would
cause a general loss of attractiveness, although the corresponding drive-trains could still
be technologically attractive.
It is important to remark that the exogenous variables caj,Aj,8; and Sjcg can be time
dependent. This has a great influence on the model behaviour. To keep it simple these
variables are chosen to be functions like gaussian or sigmoid curves. Of course these
simple functions are incapable of reproducing complicated and detailed look-up curves as
model input, but on the model’s level of aggregation they are adequate to investigate the
most important and characteristic behaviours. The great advantage is the controlling of
the functions‘ behaviour by only few parameters. The following example illustrates the
simplicity of this approach:
The time dependent part of the comparative attractiveness of hybrid vehicles caypy
might grow in the near future, because they become more economic and ecologic than
conventional ICEs. However, since they still need liquid or gaseous fuels for their com-
bustion engine in addition to the electric power train, their consumer satisfaction might
peak after a certain time and eventually decrease again due to certain taxes or perhaps
a complicated handling compared to future standards. This behaviour can qualitatively
be reproduced by the following gaussian function:
_o
cangv(t) = Cmax 2? (5)
where
Cmax : determines the maximum value achieved
Le : denotes the point in time where ¢,,q, is taken (mean value)
o : is the standard deviation
The shape of the curve can easily be determined by adjusting these three parameters.
Figure 8 shows a numerical sample.
‘Comparative attractiveness HEV
1
0.85
a a with parameter setting:
or Lai Pp 8
Cmax: 0.8
os Lu : 30a
oA oO : 30a
0 5 WwW i 2 2 8 3 4 45 50
‘Tine (year)
Figure 8: Numeric example of a gaussian function (5) used for the qualitative behaviour
of the time dependent part of cay py.
5 First results
In this section we will discuss some preliminary, qualitative comparative scenario results,
achieved with the rather simple model structure described in the last section. As an
example we will focus on two interrelated model runs. We choose initial values for the
stocks comparable to the present situation in Switzerland: Some 3.8 million conventional
ICEs, about 2000 NGVs and 200 HEVs respectively. To keep it clear, only the three
technologies chosen above were kept and taken into account for these exemplary model
runs. Both runs have been performed with a time horizon of 100 years. Our interest
lies on the resulting characteristics of the development of the NGV and HEV stocks,
which is shown in the following graphs. The curves for the ICE stock have been omitted,
but can be reconstructed from the difference to the total amount of cars in the model.
All parameters have been set to constant values: Customer satisfaction is highest for
HEVs, and the comparative attractivenesses are at 2% for HEVs and NGVs, and 5%
for ICEs. Only the comparative attractiveness of HEVs caypy shows a slightly varying
characteristic: It grows to a maximum of 0.03, decreases over a period of about 20
years, and eventually levels off on 0.02. The coupling constants are chosen to increase
the visibility of the effects by the critical mass, hence the model is not yet calibrated.
Finally, the availabilities, customer satisfactions as well as the ICE‘s shortage of resources
are all set to 1 for simplicity.
Figure 9 shows a behaviour where both, HEVs and NGVs end up at the same level,
which is a stable state of the model. Although HEVs have a quite strong rise at first,
they eventually decline again after not having reached their critical mass. Their market
share was too small to establish a norm. This means that most cars discarded are replaced
by conventional ICEs in this scenario, and both alternatives just go into a niche market.
We now change the situation for HEVs. Their comparative attractiveness will now peak
to a higher value of 0.195 and decrease again to 0.02, but in a slower manner. The
13
Fleetshare
Year
[Natural Gas —Hybrid ——Petrol & Diesel |
Figure 9: Development of the three stocks of ICEs, NGVs and HEVs reaching an
equilibrium.
consequence is that HEVs reach a critical number of cars, before their attractiveness
shrinks again. The norm building effect is already strong enough and leads to a self-
sustaining growth behaviour as shown in figure 10. We see that the HEVs move beyond
the tipping point. The NGVs end up with a small number comparable to that in figure
9.
Fleetshare
2000 2020 2040 2060 2080, 210g
Year
[Natural Gas —Hybrid —Petrol & Diesel]
Figure 10: Same situation as with figure 9, but now with a higher peak and a slower
decline of caypy.
The final states achieved in both cases become apparent as the only possible solutions
for the development with the parameters given, which can be predicted. Reaching the
critical mass implies a self-sustaining process, that cannot be stopped offhand in this
model. The reason for the existence of a critical mass in this model is the nonlinearity of
14
the normbuilding term in equation (2).
6 Discussion
Equation (2) shows, that for small stocks, as it is the case in our example for HEVs as
well as NGVs for small t, the perceived attractiveness is almost fully determined by the
comparative attractiveness. The term Aue in payry is too small during the whole run
to have a substantial influence. Therefore, “the stock of HEVs in our first case increases
with caypy, the comparative attractiveness, and eventually reaches equilibrium. In the
second situation, the peak in caypy is high and broad enough to let the stock grow to a
certain extent which enables Sat to contribute essentially. Beyond that it compensates
the subsequent decrease of cayey and leads to a strong rise of the stock. The normative
effect becomes strong enough after reaching a critical mass and make the diffusion of
HEVs become self-sustaining.
Even if now the influence of the critical mass on the development becomes tangible in this
model, corresponding to the description of Rogers (1969, pp. 343ff.), it would be difficult
or almost impossible to determine its size by trial and error. In the following paragraphs
an analytical method is used to access the critical mass of the model. It will further allow
to determine the stable equilibriua and finally help us to answer the questions at the end
of section 2 (page 5).
The diffusion process in our model can reach stable states of equilibrium which can be
calculated and predicted. This is shown using the method developed by Gassmann und
Ulli-Beer (2006). They use the dynamics of a light ball moving downhill and compare
it to a system dynamics model. A model with two stocks and a constant sum of their
elements can be reduced to one rate-equation oa with only one variable x representing one
stock. This equation can be written in the same form as the dynamics of the mechanical
analogon, with x corresponding to the ball‘s position on a coordinate axis. Then a
potential V can in some cases be found, determining the system‘s behaviour by means of
the equation ae = aa of the approximated mechanical dynamics. The potential gives
information about the states of equilibrium, the critical mass etc. Each minimum in the
potential is a stable state, while in one dimension (two stocks) the maxima point out the
critical masses. This method of analysis is very useful to answer two of the main questions
of this work. It allows to calculate the critical masses, and further the potential shows
the maximum forces needed to push the system in a desired direction.
In our situation with 4 stocks, we have 3 coordinate axes, and also 3 independent rate-
equations. As in the results shown we omit the FCV stock, which plays only an ancillary
role in many scenarios, and normalise the stocks with the total number of vehicles “a
We identify « with ICEs, y with NGVs and z with HEVs, and note that z = 1—2—y.
This leads to two independent rate-equations:
dx
Be te tle ae + Pee (6)
dy
rs ee tte — (7)
By applying equations (1) to (4) (with again the availabilities as well as the ICE‘s shortage
of resources all set to 1), we get
a y — (sy + 8,)zy? + (8, + 28,)0?+
2s.ry — (Sz + Caz + Cay + caz)0 + ca)
di 1 j :
- = =( — (sy + s,)y? — 2s,cy? — (8; + sz)yax? + (sy + 282)y?+
lt 0
2s,cy — (8, + Caz + Cay + ca,z)y + ca)
Because of some terms proportional to mixed powers of x and y it is impossible to define
a potential V(x, y) satisfying
dx dW | dy dV 2
ae ae and aT V(a,y) ER
However, an approximated potential V(x,y) would have leading terms of fourth degree in
x and y, showing up to two stable states (minima). Though, it is not necessary to know
the potential. The sought minima result from the roots of the vector field
given by equations 6 and 7. The shape of the vector field F in A = {(x,y) € R?|z >
0O,y > 0,2 +y < 1} — the permitted region for x and y — depends on the parameter
set. To have a critical mass in the model, at least a potential-wall or a maximum must
lie within A. Stable states only exist in the model, when minima lie in A. In case the
parameters are functions of time, this can change during the run, but with knowledge
of these shapes we can calculate the resulting technology share at the end of the model
run. This explains why the model is strongly determined by the time development of
the parameter curves, and also why it is difficult to characterise its behaviour by trial
and error. Figure 11 shows a vector plot of F for the allowed region A of x and y, with
additionally all s; set to 1. The state of the system in this graph is given by the two
technology shares x and y as coordinates. Scales go from 0 to 1, according to the degree
(or percentage) of adoption of the alternative technologies (HEV and NGV), where the
conventional technology share (ICE) is given by the difference 1— a —y. All three shares
added cannot exceed 1. The direction and the strength of the system’s development at
its particular position is shown by the direction and the length of the vectors. The longer
the vector, the stronger the “force“ driving the system. The occurring maximum is green,
minima red and saddle points are blue encircled. The have been calculated numerically.
The system development will always end in one of the attracting minima, which denote
stable states.
Figure 11 points out, that the critical mass corresponds to certain shares x and y, where
a fundamental change of the vector’s direction occurs when moving slightly. This is the
case along the connecting lines from the maximum to each of the three saddle points,
which can be imagined like water sheds, that divide A into three areas. In each area the
system will finally end in its related minimum.
16
oe
ee
Figure 11: Mathematica-plot of the vector field F. The longer a vector appears in the
picture, the stronger the “force“ at this point. The encircled areas contain critical points:
maxima (green), minima(red) and saddle points (blue), which do not coincide with the
coordinates.
This brings us back to the questions on page 5. We conclude that the critical mass acts
like a water shed, which would not exist, if the norm building fraction ne was considered
as linear in equation (1), as shown by Gassmann und Ulli-Beer (2006). Further we can
see that the critical mass depends on the state of the system, by no means it is constant
for one type of technology. As we can sce in the picture of the vector field, a certain
amount of NGVs diminishes the critical mass of HEVs, but after a certain point it will
be increased tremendously. This is an effect of the competition between two alternative
technologies.
The processes involved — the norm building effect and the perception of the comparative
attractiveness — shape the vector field, and a stand-alone system would follow this shape.
Reaching a critical share (“crossing the water shed“) could be achieved by forcing the
system into one direction by an external force. In our case the time dependent part of
the comparative attractiveness can play this role, as we used it to succeed with the HEVs
(cf. figure 10). However, this break out of a sort of lock-in situation does not guarantee
that the minimum aimed at will lie at 100% adoption of a certain technology, but without
exceeding the critical mass it will only reach a niche market.
With this model we can finally conclude, that all this gives no evidence about the time
needed for the system to get to a stable equilibrium. It is strongly dependent on the path
that is chosen and the measures leading to an increase of the comparative attractiveness
17
of certain technologies and a deformation of the vector field. Finally, the norm building
processes is only one among others and contributes to a superposition determining the
final model behaviour.
A remark is to be added on the average age of a car. In the style of the word “demog-
raphy“ we could summarise the analysis of development and changes of a car fleet with
“stolography“ (from Greek o76Aog¢ - fleet), especially when we are talking of quantity
and ageing structure. A very important statement of stolography is the average lifetime
of a car, which is used in our model to determine the rate of discard. The application of
the median lifetime instead of the average is required in situations, where data on vehicle
age is given in categories with varying intervals. The median has the two advantages of
being more robust against outliers and of being applicable to data in an ordinal scale.
Regardless on which value is used, an improvement can be achieved by using a time
dependent lifetime, reflecting the expected trend (Janssen, 2004).
Still an open question at the moment is the potential of replacements for liquid fossil fuels,
like for example biodiesel as a replacement for diesel, but this could be incorporated into
the model in a similar way as the reduction of fossil resources availability. Therefore, and
since the environmental impact of such substitutions is not yet accessed, no additional
stock for liquid bio-fuels in internal combustion engines is needed at this time.
7 Outlook
The model can be used to simulate the emerging technology diffusion in different scenarios
with competition of several alternatives. However, it has not yet been calibrated or
empirically approved. This, and also the refinement of the model will be done within
an oncoming study about the potential of different alternative drive-train technologies in
Europe and their effect on greenhouse gas emissions, mainly CO2. The study will use
a combined model with a part developed by Anup Bandivadekar at MIT (Bandivadekar
und et al., 2007). With the new model, impacts on CO -emissions for example will base
on simulated diffusion rates and not on estimated developments. The European results
will be compared to a similar study by Anup Bandivadekar for the USA.
The estimation of the potential of different drive train technologies and the corresponding
model specifications could be done with indicators (cf. table 1).
For the time being we defined 12 such indicators being assigned to three categories:
attractiveness, potential and system development. Particularly the final two have also
diagnostic character. Table 2 finally shows their impact on the model.
18
Table 1: Indicators by categories. Particularly potential and system development indica-
tors have also diagnostic character.
Category Indicator Comment
Attractiveness I APurchase price Price difference to reference technol-
ogy, e.g. “Petrol-ICE“
II AVariable costs Operational and fuel costs
III Stimulating measures Fiscal impact of fuels, subsidies,
CO>-charge, etc.
Potential IV #Private early adopters | Determines early diffusion rates
V #LDV Vehicles with a weight of < 3.5 t,
broken down by fuel
VI Makes 10 best-selling car makes
VII Income Per capita national income
VIL Resources Access to fuel resources (e.g. fossil
resources)
IX R&D Investments in research and develop-
ment
X Coverage Share of inhabitants with natural
gas connection
System XI Fuel share Share of energy
development XII CO, Tons of CO, emitted, broken down
by fuel
Table 2: Indicators and their integration into the model.
Indicators | Influence on...
I, Hf, IV, VI | Comparative attractiveness
Ill Indicators I&II
Vv Initial stock values
VII Importance of prices
VIII, IX, X | Stimulating measures, scenarios
V, XI, XII | system evaluation
19
8 Acknowledgments
Je thank Alexander Wokaun for supporting our work with interest and giving helpful
input. Financial support to the project is given from novatlantis, a sustainability initiative
of the Board of ETH Ziirich.
References
[Arthur 1989] ArrHuR, W. B.: Competing Technologies, Increasing Returns, and
Lock-In by Historical Events. In: The Economic Journal 99 (1989), March, Nr. 394,
S. 116-131
[Bandivadekar und et al. 2007} BANDIVADEKAR, Anup ; ET AL.: Reducing the Fuel
Use and Greenhouse Gas Emissions of the U.S. Vehicle Fleet. Draft Paper. 2007. —
MIT Laboratory for Energy and the Enviornment
[Bericht des BFE 2004] BERICHT DES BFE: Schweizerische Gesamtenergiestatistik
2004 / Bundesamt fiir Energie (BFE), Bern. 2004. — Energiestatistik
[Bundesamt fiir Statistik 2004] _BUNDESAMT FUR STATISTIK: Motorfahrzeuge in der
Schweiz. 2004. — Neuchatel, Verlag BFS
[Clean Energy Partnership (CEP) 2006] | CLEAN ENERGY PARTNERSHIP (CEP): Mo-
bil mit Wasserstoff — Staying mobile with hydrogen. 2006. — URL http://www.
cep-berlin.de/cep.html
idgenossische Zollverwaltung IDGENOSSISCHE OLLVERWALTUNG
Eidgenéssische Zoll a EZV) 2006 E 6 Zi
(EZV): Mineralélsteuer. 2006.- URL http://www.ezv.admin.ch/zollinfo_firmen/
steuern_abgaben/
[Energie-Spiegel 2007] ENERGIE-SPIEGEL: Die 2000-Gesellschaft: Norm oder Weg-
weiser? / Paul Scherrer Institut (PSI). URL http://www.psi.ch/index_bilder/
Energiespiegel_18d.pdf, April 2007 (18). — Forschungsbericht
[Erdgas Ziirich 2006] ERDGAs ZiRicu: Aktion Naturgas. 2006.— URL http://www.
erdgaszuerich.ch/automobil.html
[Gassmann und Ulli-Beer 2006] GASSMANN, F. ; ULLI-BEER, S.: Acceptance Dy-
namics. In: System Dynamics Society Conference Nijmegen 2006, System Dynamics
Society, July 2006
[Janssen 2004] JANSSEN, A.: Modeling the Market Penetration of Passenger Cars with
new Drive-Train Techchnologies, ETH Nr. 15855, Dissertation, 2004
[Krabs 2005] Krass, W.: Spieltheorie — Dynamische Behandlung von Spielen.
Stuttgart, Leipzig, Wiesbaden : Teubner, 2005
[Leydesdorff 2001] | LEYDESDoRFF, Loet: Technology and Culture: The Dissemination
and the Potential ‘Lock-in‘ of New Technologies. In: Journal of Artificial Societies and
Social Simulation 4 (2001), June, Nr. 3, S. 1-27.— URL http://jasss.soc.surrey.
ac.uk/4/3/5. html
[Manteuffel und Stumpe 1977] MANTEUFFEL, K. ; STUMPE, D.: — Spieltheorie.
Stuttgart, Leipzig, Wiesbaden : Teubner, 1977
[Nesbitt und Sperling 1998] NesBirt, K. ; SPERLING, D.: Myths regarding alternative
fuel vehicle demand by light-duty vehicle fleets. In: Transportation Research — D 3
(1998), Nr. 4, S. 259-269
{novatlantis — Nachhaltigkeit im ETH Bereich 2005] NOVATLANTIS — NACHHALTIGKEIT
IM ETH BerEIcH: 2000 Watt Gesellschaft. Dezember 2005. —- URL http://www.
novatlantis.ch/frames_d.html
[Rogers 1969] Rocers, E. M. ; Press, New York: F.: Diffusion of Innovations. 5.
New York: Free Press, 1969
[Sterman 2000] | STERMAN, J.D.: Business Dynamics. McGraw-Hill, 2000
[Struben 2004a] STRUBEN, J.: Technology transitions: identifying challenges for hydro-
gen vehicles, Proceedings of the 22"4 International Conference of the System Dynamics
Society, Oxford, England, Jul 25 — 29, 2004a
