**1. Introduction**

Owing to the significant importance of greenhouse gas emissions for climate change, in particular carbon dioxide, arising during the combustion of solid fuels in transport and the process of electricity, or, heat production, many countries have taken steps to consciously reduce harmful emissions [1]. The European Union (EU) is a particularly active entity in international relations, taking active measures to combat climate change. It aims to create a low-carbon economy in the long term.

The European Commission wants Europe to become climate neutral by 2050. Therefore, the EU has set itself targets for a gradual reduction of greenhouse gas emissions by 2050. The main climate and energy goals have been set out in two documents: the climate and energy package until 2020 [2,3] and under the 2030 climate and energy policy. The assumptions of the climate and energy package were determined by EU leaders in 2007, and in 2009, regulations were adopted in this respect. At the same time, there are the main goals of the Europe 2020 strategy for smart, sustainable, and inclusive growth. The main goals are as follows: a 20% reduction in greenhouse gas emissions (compared with 1990 levels), a 20% share of energy from renewable sources in total energy consumption in the EU, and a 20% increase in energy e fficiency [3]. In October 2014, this policy framework was adopted by the Council. The renewable energy and energy e fficiency targets were increased in 2018 [4]. Currently, under the 2030 climate and energy policy, the EU plans to reduce gas emissions by at least 40%. Greenhouse gas emissions (compared with 1990 levels) should increase to at least 32% of the share of energy from renewable sources in total energy consumption. An increase of at least 32.5% in energy e fficiency, together with a clause should enable this target to be achieved by 2023. Thus, the original target of at least 27% was corrected in 2018.

According to the managemen<sup>t</sup> system, Member States are required to adopt integrated national energy and climate plans for 2021–2030 and to develop long-term national strategies, including ensuring coherence between these strategies and their national energy and climate plans. A common approach for the period up to 2030 helps to guarantee regulatory certainty for investors and coordination of the actions of the EU countries. This framework is conducive to changes towards a low-carbon economy and the creation of an energy system.

The upcoming EU Budget and in particular the EU Regional Development Funds spending plans (Operational Programs) for 2021–2027 (to be prepared by the Member States in 2020) also o ffer a range of opportunities to increase both the climate ambition and implementation of the measures foreseen in the National Energy and Climate Plans (NECPs). Under EU legislation, the EU's current economy broad 40% emission reduction target consists of sector contributions covered by its Emissions Trading System (ETS), mainly the energy and industry sectors. It also consists of the other remaining sectors, such as agriculture, construction, waste, and transport.

Transport is currently responsible for a significant proportion of CO2 emissions. Forecasts assume that, by 2050, carbon dioxide emissions from this sector will increase from 6–7 gigatons to 16–18 gigatons. In addition, around 30% of Europeans live in cities where air pollution exceeds EU quality standards. Conventional fuels burned by buses are one of the largest sources of CO2, nitrogen oxides, and particulate emissions [5].

In this context, the development of a sustainable public transport system is of key importance. The deployment of zero-emission buses to fleets is today a priority for many urban centers around the world. Metropolises see the development of green transport as a basic instrument for combating air pollution. More than 80 cities worldwide have joined the network of C40 Cities Climate Leadership Group. "The cities use to reduce emissions from transportation include switching to e ffective modes (e.g., public transit or non-motorised transportation) and enhancing the e fficiency of fleets via shifting to zero-emission technologies" [6]. According to the Bloomberg New Energy Finance report [7], the total number of buses with electric drive (e-buses) will increase from 386,000 units in 2017 to around 1.2 million in 2025. The share of electrified buses in the global fleet will reach 47% [5]. It is also a solution decided upon by EU member states. The advantages of zero-emission vehicles are being noticed by more and more cities that decide to operate them. Thus, the share of e-buses in urban transport fleets is growing [8,9].

In the short term, the introduction of clean buses can contribute to the implementation of EU 2020 and 2030 targets, as well as national targets and local targets for CO2, air quality, and noise in several ways. On the basis of the '2030 Climate and Energy Policy Framework' [10], at least 80% of the transport work in public collective transport is to be carried out using means of transport that are not powered by conventional fuels. In addition, by 2030, CO2 emissions from the transport sector are expected to be reduced by 40% [5]. The introduction of electric buses to public transport fleets will also allow city authorities to reduce the amount of energy consumed.

In reference to the problems raised, in this article, the authors focused on the forecast of the number of zero-emission buses in individual EU countries by 2025 and 2030, respectively. As mentioned previously, the EU strategies assume two time horizons, 2020 and 2030. Owing to the fact that the most current data, which the authors used to create the simulation, refer to the period 2013–2018, from 2019 and later, a forecast is presented. In order to make it credible and focus on two time horizons that best correspond to the developed EU strategies, the years 2025 and 2030 were taken into consideration. Given the scale of energy consumption by cities in a global perspective, one of the fundamental

challenges that the city authorities face is the reduction of energy consumption [11]. The topic taken up by the authors is directly related to the energy consumption market.

It should be emphasized that the vehicles powered by alternatives to the conventional fossil-fuelled engines are a fairly diverse group of vehicles subject to di fferent definitions and classifications. The most promising technologies for use in public bus transport are battery-electric and hydrogen fuel-cells powered engines, which are more energy-e fficient and far less pollutant than the conventional diesel engines. Additionally, such vehicles have specific advantages over trolley buses and trams, such as the flexibility of use of road infrastructure without the need for powerlines or rails [12]. In this study, the authors will use the term zero-emission buses (ZEBs), which specifies a group of buses using either of these two fuel technologies, as neither type generates any pollutant emission [12–14].

Such technology applied in public transport is an innovation. Bezruchonak [6] conducted an analysis of the geographical distribution of electric buses in European countries and took into account European cities till 2018. According to him, the increase in European stock suggests that the European market is moving beyond the demonstration phase and into commercial development, and by 2030, the share of battery-electric buses will reach 50%. The United Kingdom, the Netherlands, Germany, Spain, Sweden, Poland, and Lithuania are the major European markets that order and operate fleets of electric buses. However, it is di fficult to predict how the new technology will be adopted to the market. The process of adopting an innovation by the market is particularly important from the investor's point of view. In this case, it is extremely important to predict the development of this technology owing to the enormous costs associated with constructing the essential infrastructure and the fact that financing of zero-emission, electric technology in public transport is based almost exclusively on public funds. As investigated by Brozynski and Lejbowicz, predicting the adoption of electric technology in transport is of grea<sup>t</sup> importance in investment decisions of policy makers. First of all, it is important when investing public funds. As demonstrated in their research, moving the process forward helps to avoid incurring policy costs repeatedly by lingering in stages a ffected by the policy [15].

Despite the rapid growth of the number of ZEBs, their share in the entire global bus fleet is still marginal [13]. Referring to the problems raised, this article attempts to create a simulation that shows how quickly EU members will be able to replace traditional buses with zero-emission buses and reach 95% of their share in the public transport bus fleet.

There are several models related to forecasting the development of electric transport technologies in the literature that have been extensively described and analyzed. For example, Meade and Islam present a detailed overview of mathematical (deterministic) models describing the accumulation of adoptions [16]. However, the best known and most frequently quoted model is the one proposed by Bass [17]. The Bass model was chosen, based on the existing data and on the fact that it is a deterministic model that provides precise forecasts [11]. This model is often used alongside the so-called logistic and Gompertz projections, while ordinary predictions based on the Bass model are the most pessimistic [18]. This is an additional argumen<sup>t</sup> in favor of this model. An additionally significant aspect is the duality of the model with the Rogers model [19]. The Bass model is the most common model in the literature that discusses forecasting the di ffusion of innovation in alternative fuel technology, primarily electric propulsion in transport [20]. Most of the research, however, concerns the di ffusion of this innovative technology on the individual automotive market [21], especially e-vehicles [22–24], or on the commercial market of logistics services [25]. It is noteworthy that, despite the popularity of the topic of clean buses and extensive discussions on energy reduction in the scientific literature, the simulation of saturation of ZEBs in public transport bus fleets in the EU member countries has not ye<sup>t</sup> been much presented and described.

Considering the above, the purpose of this article is to make an attempt to simulate the number of ZEBs in EU member countries in two time horizons: 2025 and 2030, and to forecast the number of clean vehicles in the precise time horizons, including before and after 2050. On the basis of the simulation, the year in which the selected countries will reach 95% saturation of their public transport fleets with ZEBs will be indicated.

The research questions posed in the article, to which the authors seek to find answers, are as follows:

Q1: What will be the number of zero-emission buses in individual EU countries over the next few years?

Q2: Which of the EU countries will reach by 2030 the level of 95% share of ZEBs in all buses, which are a fleet of public transport buses?

Q3: In which year which will EU countries reach the level of 95% share of ZEBs in all buses, which are a fleet of public transport buses?

### **2. Materials and Methods**

The use of the Bass model to predict the development of new technologies is a common approach. Especially in areas related to new technological solutions in the field of energy. The practical use of di ffusion models for prediction has nearly 40 years of history. In 1980, the U.S. Department of Energy used the Bass model to evaluate the adoption of solar batteries and delayed the technology's introduction to the market [26]. In December 2019, this method was also used to evaluate the lighting market (LED and other technology) [27]. The report [28] indicates e ffective methods of predicting the development of new technologies at various stages of innovation development (introduction, increase acceptance of new technology, mature technology). Di ffusion models are the only one e ffective method at each of these stages. In addition, other di ffusion models can be mentioned: the Fourt and Woodlock model, Mansfield model, Blackam Model, Fisher and Pry model, Kalish model, and many others (a list of di ffusion models can be found, among others, in [29]; in most cases, these are various extensions of the Bass model).

The model application in practice remains an open issue and di fferent forecasters use di fferent approaches. The Bass model parameters can be obtained on the basis of questionnaire research, historical analogies from similar technologies, and fitting the model to the data. Each of the approaches has its advantages and disadvantages [27]. The article uses the approach of fitting the model to data on the initial development of technology. There are also many approaches for the technical aspects of modeling. For example, the method of estimating parameters based on the data can be performed with one of the following methods: ordinary least squares (OLS), maximum likelihood estimation (MLE), nonlinear least squares estimation (NLS), or algebraic estimation. Mahajan et al. [30] show that the best way to estimate parameters is NLS. However, more recent research shows that the best least squares estimate for the Bass model does not necessarily exist [31]. The main inconvenience with the Bass model, encountered in this article, is a very significant change in the shape of the Bass curve along with the extension of the observations number [32].

In order to better illustrate the proceedings taken by the authors, the sequence of individual stages is presented below (Figure 1).

**Figure 1.** Subsequent stages of the proceedings [own study]. ZEB, zero-emission bus; NLS, nonlinear least square; BEV, battery electric vehicle; HEV, hybrid electric vehicle; PHEV, plug-in HEV; REEV, range-extended EV; FCEV, fuel cell EV.

To analyze the development of ZEBs, data from the Eurostat associated with type of motor energy were used. Among the available groups are the following: Petroleum products, Liquefied petroleum gases (LPG), Diesel, Electricity, Alternative Energy, Diesel (excluding hybrids), Hybrid diesel-electric, Plug-in hybrid diesel-electric, Hydrogen and fuel cells, Compressed natural gas (CNG), Liquefied natural gas (LNG), and Other. The method of data collection was established in 2013. Previous statistics only included Petroleum products and Diesel (until 2013). It should be noted that, currently, there are even more vehicle types available in various reports on Eurostat compared with those listed in the statistics. The "Electric vehicles in Europe" report highlights the following [33]:


A combination of vehicles from the electricity, hybrid diesel-electric, plug-in hybrid diesel-electric, hydrogen, and fuel cells categories was selected for analysis, which approximate BEVs, HEVs, PHEVs, REEVs, and FCEVs as best as possible, while the REEVs group is not formally indicated.

Unfortunately, Eurostat guidelines on Passenger Mobility Statistics released in 2018 [34] define groups differing from those shown above:


The categorization is inconsistent with those in the statistics and is not in line with subsequent studies on electric vehicles (for example, the statistics do not include the petrol electric group). In addition, the scope of the alternative energy group, which appears in the statistics, is unfortunately not explained in the document at all. Furthermore, in 2017, the European commission issued the document "Alternative Fuels (Expert group report)" [35], which defines this type of fuel. According to the document, alternative fuels include the following groups: Methane-based fuels (CNG, LNG, bio-methane, E-gas), LPG (propane- and butane-based fuels, BioLPG), Alcohols, Ethers and esters (ethanol, butanol, methanol, MTBE, ETBE, DME, BioDME, FAE), and Synthetic paraffinic and aromatic fuel (GTL, HVO, BTL, SIP, ATJ, CH, SAK). The aforementioned categorization raises doubts about the LPG, LNG, and CNG gas groups included in the statistics, as well as hydrogen cells, which are also sometimes recognized as alternative energy sources.

As part of the data analysis, a number of tests were performed. In most of the countries represented in Eurostat, the sums for individual groups and the total number of buses were not coherent (even after considering that Diesel is available in different variants). Apparently, the numbers distinguished by Eurostat must be included in several groups at the same time.

For the forecast, it was decided to take the number of buses in a given country, not the number of new registrations. Formally, the Bass model in the basic version does not include the replacement of technology. Regular buses (powered conventionally) have a relatively long life cycle. For example, in Poland, there are about 100,000 diesel buses and about 5000 new diesel vehicle registrations per year, which means about 20 years of their life cycle. However, the data show that the life cycle of electric vehicles is extremely short, as for buses (see Table 1). Estonia in 2013 had 91 electric buses, while that number in 2018 is only 1. Similarly, Bulgaria bought 150 buses in 2014, but only 96 came to market, which means that 54 were withdrawn; then, in 2015, 47 were newly registered and 70 were withdrawn. To maintain the number of buses from 2015, one would have to buy as many as 103 buses. This means that the life cycle of these vehicles varies somewhere between 5 and 0 years, or there are other unknown reasons for their withdrawal. Therefore, the data showing the number of buses in a given country are more suitable for estimating the parameters of the Bass model [11,17].

**Table 1.** The comparison of data on new registrations and numbers of electric buses on the example of Bulgaria and Estonia [Source: https://www.eea.europa.eu/data-and-maps/indicators/proportion-ofvehicle-fleet-meeting-4/assessment-4].


Table 2 summarizes the results for ZEBs based on the data available from Eurostat. The order of the countries with the source data from Eurostat has been preserved. Not all of the presented data are suitable for further analysis, therefore, a preliminary evaluation was carried out. The countries that do not have enough data (data not available) in most data fields (NA marked) are excluded; numbers 1,2,3,4 in Table 2 define which data are missing.

In addition, the trend of collected data was also examined. Linear regression was performed for each country. When the slope was negative, it was assumed that the trend is decreasing; the country was marked with the symbol DT and the data were excluded from further analysis. The reason for that is the assumption of growing sales, which is very important in the Bass model, especially at the beginning of innovation development. In the case of a decreasing trend, the Bass curve fit has very poor estimators. In addition, for these countries, more buses are being decommissioned than registered, which does not indicate the development of technology. Countries where data for analysis were missing or where there was a downward trend were marked in gray in Table 2. Data for 2015, 2016 for Poland and 2015 for Macedonia are gross errors (marked in red); they stand out far above the neighboring trend. It looks like the Hybrid diesel-electric fields were mistakenly copied from the Other field (both values were checked to be identical). Additionally, the values in the Other field are consistent with the others. After taking into account the amendments, the corrected data are placed in brackets; Table 2 (Poland in 2015—504 buses and in 2016—526 buses, Macedonia in 2015—1 bus).

The forecasts presented in the article were obtained using the Bass model, usually defined by the following differential equation [17]:

$$f(t) = \frac{dF(t)}{dt} = \left(p + \frac{q}{m}F(t)\right)(m - F(t)),\tag{1}$$

where

*F*(*t*)—the total number of new technology users by time *t* (numbers of ZEBs in the market),

*f*(*t*)—number of users of new technology that adopt at time *t*,

*m*—the total number of technology users (total number of buses, see Table 1),

*p*—the innovation coefficient,

*q*—the imitation coefficient (for details, see [11]).


**Table 2.** Motor coaches, buses, and trolley buses, by four types of motor energy (electricity, hybrid diesel-electric, plug-in hybrid diesel-electric, and hydrogen and fuel cells) [Source: own study based on data retrieved from Eurostat].

The analytical solution of the Bass model (1) is as follows:

$$f(t) = m \frac{\left(p+q\right)^2}{p} \frac{e^{-\left(p+q\right)t}}{\left(1 + \frac{q}{p}e^{-\left(p+q\right)t}\right)^2}.\tag{2}$$

Usually, (2) corresponds to the probability density function (PDF), which represents how many new technology users have arrived in a given time. Thus, in this study, *f*(*t*) would correspond to the changing of the number of buses/the changing number in one year to another (the number of new registrations minus the number of withdrawn buses). Because the data are represented differently, for research purposes, the cumulative number of ZEBs was used. The cumulative distribution function (CDF) for *f*(*t*) has the following form:

$$F(t) = m \frac{1 - e^{-(p+q)t}}{1 + \frac{q}{p}e^{-(p+q)t}}.\tag{3}$$

Data with gross errors identified; 1 Electricity data not available; 2 Hybrid diesel-electric data not available; 3 Plug-in hybrid diesel-electric data not available; 4 Hydrogen and fuel cells data not available; 5 Kosovo (under United Nations Security Council Resolution 1244/99); 6 North Macedonia; DT Decreasing trend; NA Insufficient data to build the model.

Nonlinear least square (NLS) method was used to estimate the parameters *p* and *q* of the Bass model for individual countries. Parameter *m* was fixed arbitrarily on the basis of the average total number of buses in 2013–2018. This is justified because this value remains almost at the same level for each country. This also rests on the assumption that, at some point in time, the entire bus market will be taken by ZEBs. In addition, it was specified that the parameter *q* should be in the range of 0.1 to 1. In the absence of this limitation, the imitation coefficient for some models was very close to zero. In this case, it would mean that there is no natural diffusion of innovation, which is a requirement of market development. On the basis of previous studies [11,26,36–39], the coefficient *q* for vehicles using clean energy was usually greater than 0.3. Therefore, setting the limit at 0.1 does not constitute a significant interference in the parameterization of the model. The estimation results of the Bass model parameters are summarized in Table 3. Table 3 includes estimates, standard errors, *t*-test statistics, and *p*-values for each parameter, as well as the coefficient of determination R<sup>2</sup> for each country model.


**Table 3.** Estimation of Bass model parameters for EU countries [Source: own study based on data retrieved from Eurostat].

Countries marked in gray have very bad parameter estimators. It has been assumed that the criterion for such countries would be the coefficient of determination R<sup>2</sup> below 0.9 (determining the quality of model fit). Bad fit of the model to the data can also be recognized. The parameter q set itself at the boundary of the range; that is, it adopted the lowest possible value of 0.1, which is accompanied by a high standard error value for this parameter. The green color indicates countries with a relatively high quality matching of *p* and *q* parameters (*p*-value less than 10%). Spain, the United Kingdom, Norway, and Turkey, are the countries for which forecasts are most likely, and detailed results are presented in the Results chapter.

The forecast for the entire EU was made on the basis of the analysis of the *p* and *q* coefficient and its arbitrary selection based on the average. This approach was dictated by the poor fit of the model to the data for the entire EU (see Table 4). Two models were presented where the market size *m* was calculated automatically. Unfortunately, the values are very low in relation to *m* = 1.6 × 10<sup>6</sup> for the entire Union. In addition, the best *p*-value for the imitation coefficient that was obtained is at the level of 63%, which practically cancels any possibility of forecast based on those models.


**Table 4.** Estimation of Bass model parameters for EU [Source: own study based on data retrieved from Eurostat].
