Diffusion Models For Predicting Electric Vehicles Market in Morocco
Soumia Ayyadi
Mohammadia School of Engineers Mohammed V University
Rabat, Morocco [email protected]
Mohamed Maaroufi Mohammadia School of Engineers
Mohammed V University Rabat, Morocco [email protected]
Abstract—Today many countries around the world have adopted Electric Vehicles (EVs) to reduce air pollution, oil consumption and fossil fuel dependence. Morocco is one of these sustainability based committed countries, especially that its transport sector depends on oil, which is entirely imported from outside of the country. In this sense, the aim of this paper is to predict the diffusion of EVs in Moroccan market by three models Gompertz, Logistic and Bass. Then the best model that fits well our data is chosen, based on R-square and the Mean Absolute Percentage Error (MAPE). In addition, we have assessed the interaction between the cumulative sales of EVs and the battery price, using the Generalized Bass Diffusion Model. Results show that the Moroccan market reaches the maximum sales of EVs, after 14 years and the battery cost has a great effect on the market diffusion, a decreasing of the battery price could accelerate the diffusion of EVs market.
Keywords—Electric vehicles; Gompertz Model; Logistic Model;
Bass Model; Generalized Bass Diffusion Model; Battery Price.
I. INTRODUCTION
The transport sector plays an important role in the countries development. It allows the individuals to reach their destination and benefit from services that meet their individual needs. The transport system has an influence on the economic growth, population dynamics, and urbanization. However, the transport sector consumed 63.8% of world oil consumption in 2013 [1]
and emitted 25% of carbon dioxide into the atmosphere [2], which made it the main contributor to greenhouse gas emissions. Therefore, Electric vehicles (EVs) can be a possible solution to reduce the carbon dioxide, which comes from the transport sector, as they are considered 'zero tailpipe emissions' [3]. On the other hand, there are environmental controversies about the use of Electric Vehicles, since the reduction of CO2
vehicles emission might be followed by a rise in the emissions in power generation. Hence, the Electric Vehicles can be beneficial for the environment only if the electric energy used to charge their batteries comes from renewable sources; Such as Photovoltaic systems, Concentrated Solar Power (CSP), Wind and Hydraulic systems. Several African countries encourage electricity generation based on sustainable sources [4], Morocco is one of these countries; it has adopted a National Energy Strategy to increase the electricity production based on renewable energy to 52% in 2030, and also meet 15-20% of
primary energy demand through renewable sources by 2030 [5].
In this sense, many studies have developed to control Wind Farm Systems and Photovoltaic systems [6][7]. The kingdom also set a target to achieve 15% energy savings in 2030 and reduce 35% of greenhouse gas emissions caused by transport sector [5]; Electric Vehicles would be a good way to reach this aim.
Many studies have been conducted to predict the future market of EVs (include Hybrid Electric Vehicles, Plug-in Hybrid Electric Vehicles and Battery Electric Vehicles), by different models. Girish et al. [8] have assessed the future adoption of Hybrid Electric Vehicles (HEVs) in the UK based on Gompertz model; the study found that the HEVs would reach 7% of sales by 2020 and 16% by 2030. In addition, the authors conclude that oil price has an impact on HEVs market growth in the UK. Based on USA data sales of HEVs the Bass model was used by Won et al. [9] to predict the number of Plug- in Hybrid Electric Vehicles (PHEVs) in Korea, the sales of PHEVs was estimated to reach its maximum in 2032. Another study evaluates the diffusion of Battery Electric Vehicles (BEVs), the author found that the penetration rate of BEVs in the total light vehicles sales would reach 45% in 2025 and 64%
in 2030 [10]. All the previous studies have used one model to predict the Electric Vehicles market and have not taken into account the external variables that could influence the diffusion of EVs in the market such as battery price reduction. In this paper, we have forecasted the Moroccan Electric Vehicles market by three diffusion models which are Gompertz, Logistic and Bass. Then the best model that fits well the real data is chosen, based on R-square and Mean Absolute Percentage Error (MAPE). In addition, we have assessed the interaction between the cumulative sales of EVs and the battery price, using the Generalized Bass Diffusion Model.
The paper is organized as follows: Section II reviewed the methods used to predict the Electric Vehicles market. While in Section III we introduce the method used in this paper. Section IV represents the models parameters estimation. The result is shown in Section V and a conclusion is drawn in Section VI.
10th International Conference and Exposition on Electrical and Power Engineering (EPE2018)
II. REVIEWOFMARKETPREDICTINGMETHODS Several methods were applied to forecast the market penetration scenarios of Electric vehicles. We will present an overview of these prediction methods: Agent-Based Method, Consumer Choice Method and Diffusion Rate and Time Series Method.
A. Agent-Based Method
Agent-Based Method (ABM) is a simulation approach; it could simulate the interaction between various agents to evaluate their effect on the marketplace. The agents would be individuals or organizations. ABM was employed in different fields for example vehicles traffic, biomedical, epidemiology and consumer behavior. ABM was used by reference [11]; the author found that the penetration of PHEVs rate was insignificant without federal incentives it is about less than 1%
of PHEVs market share over ten years; however with federal subsidies, the rate of PHEVs can increase to reach 4% of sales in 2020. An ABM was developed by [12] to predict the future rate of HEVs, the author found that the rate of HEVs would be rise to 38% after 10 years. Another study was used a Multi- Agent-Based Simulation to forecast the zone where the rate of PHEVs would increase quickly to assess their impact on electric distribution grid [13]. PHEVs represent 4% of sales in 2020 reported by sikes et al. [14]; furthermore, the author was noted that the policy would widely affect the PHEVs market penetration.
B. Consumer Choice Method
This method is a mix of logit model and individual model, it would describe individual decision. The discrete models determine the probability of a new technology to be choosing among old technology although logit models were adopted to model the probabilistic preference of consumers. Numerous works were based on this method to evaluate the diffusion of technology. Santini et al. [15] used the logit model to assess the adoption rate of HEVs, the result show that under unconstrained the HEVs market share was estimated to be 17% in 2020 and 23% in 2050, or under a constrained (increase in fuel price) it would reach 56% in 2020 and 64% in 2050. Another author was based on the Choice Method to predict the EVs and HEVs market, the market share would range from 15% to 40% in 2035 and the PHEVs sales would range from 0 to 15% in the same year. The sales rate of HEVs would range from 13 to 17 million in 2020 and PHEVs sales would reach 3.5 million in 2020 reported by [14]. The charging infrastructure and gasoline price would be the good predictors of EVs and HEVs market according to [16] [17].
C. Diffusion Rate and Time Series Method
This method assesses the process of acceptance of a new technology or product by the market. The speed of technology or product spread into the market called rate of diffusion and the aim of this method, is to forecast the diffusion of technology on time. It was used for predicting the vehicle market; the famous models of this method are Gompertz, Bass, Generalized Bass Diffusion and Logistic.
Based on USA data sales of HEVs the Bass model was used by reference [9] to forecast the electricity future demand in Korea caused by PHEVs, the rate of PHEVs was estimated to reach its
maximum in 2032. Girish et al.[8] compared Gompertz and Logistic models to assess the future adoption of HEVs in the UK, The study found that the HEVs would reach 7% of sales in 2020 and 16% in 2030. In addition, the author concludes that oil price has an impact on HEVs market growth in the UK.
Another study was used Generalized Bass Diffusion Model to forecast the number of Electric Vehicles sales in China, and the relationship between the charging station construction and the EVs market [18]. Based only on Bass Model to evaluate the diffusion of HEVs, the author found that the penetration rate of BEVs in the total light vehicles sales would reach 45% in 2025 and 64% in 2030 [10].
III. METHODS
The most widely used method to predict the diffusion of new technologies or products in the market is "Diffusion Rate and Time Series Method" for this reason, we have chosen this method to forecast the diffusion of Electric Vehicles in the Moroccan market. To forecast the market for Electric Vehicles in Morocco we have chosen three diffusion models which are:
Gompertz, Logistic and Bass models. While to better explore the relationship between the battery price and the diffusion of EVs, we choose Generalized Bass Diffusion Model. The four models would be explained in the next subsections.
A. Gompertz Diffusion Model
The Gompertz Diffusion Model was initially developed for forecasting the growth of tumors. It has succeeded in the medical field [19] [8]. In 2007, this model was used to predict the market car in the UK [20]. Also, it was applied to forecast the uptake of cable TV’s for the same country [21]. It presented by the following equation:
ܰሺݐሻ ൌ ܯ ൈ ݁ൈష್ (1) where,
N(t): Cumulative adoption of EVs at time t.
t : Time period.
M : Maximum potential adopters.
a : Regression coefficient.
b : Growth rate.
B. Logistic Diffusion Model
This model is very useful when new technology replaces old technology because it is economically and technically better [8].
It presented by the following equation:
ܰሺݐሻ ൌ ܯ
ͳ ܽ ൈ ݁ି௧ (2) where,
N(t): Cumulative adoption of EVs at time t.
t : Time period.
M : Maximum potential adopters.
a : slope factor.
b : Growth rate.
C. Bass Diffusion Model
The Bass Diffusion Model is the most model used to predict the diffusion of new products, with meaningful parameters such as innovation factor and imitation factor. This model was applied widely to forecast the diffusion of new products. It presented by the following equation.
ܰሺݐሻ ൌ ܯ ͳ െ ݁ି௧ሺାሻ
ͳ ሺݍሻ݁ି௧ሺାሻ (3) where,
N(t) :Cumulative adoption of EVs at time t.
t : Time period.
M : Maximum potential adopters.
p : The coefficient of innovation.
q : The coefficient of imitation.
D. Generalized Bass Diffusion Model
The Bass Diffusion Model is the most widespread diffusion model, but it cannot consider the external factors that could have an effect on the diffusion of technologies. For this reason the Generalized Bass Diffusion Model (GBDM) was developed to overcome the limitation of Bass Model. Based on [22] and [18] the GBDM presented by the following equations.
݊ሺݐሻ ൌ ቆ ݍܰሺܶሻ
ܯ ቇ ൫ ܯ െ ܰሺܶሻ൯ݔሺܶሻ (4) Where,
ݔሺܶሻ ൌ ͳ ߚሺܶሻ െ ሺܶ െ ͳሻ
ሺܶ െ ͳሻ (5)
We can write the solution of the equation (4) as follows:
ܰሺݐሻ ൌ ܯ ͳ െ ݁ିሺ்ሻሺାሻ
ͳ ሺݍሻ݁ିሺ்ሻሺାሻ (6) Where,
ܺሺܶሻ ൌ ܶ ݈݊ሺܶሻ
ሺͲሻ (7)
Where,
n(T) : Number of adopters for new technology at time T.
N(T) : Cumulative number of adopters for new technology in the (0,T).
M : Maximum potential adopters.
x(T) : Mapping function.
Pr(T) : The battery price at time T.
X(T) : The cumulative mapping function.
IV. PARAMETERSESTIMATION
To get the Gompertz, Logistic and Bass models parameters, which are used to forecast the diffusion of Electric Vehicles in the Moroccan market, we should have the sales data of this type of vehicles. Nevertheless, in our case, the Electric Vehicles have not yet penetrated the market. For this reason, we have to choose an alternative product that has enough past sales data and it would have the same diffusion as Electric Vehicles, this method has called predicting by analogy, it was used in literature, Park et al. [23] have based on sales data of LPG (Liquefied Petroleum Gas) vehicles to forecast the GBDM parameters. In this study we collected the cumulative sales data of Diesel Vehicles from 1970 to 1987 according to [24], Fig.1 shows that the cumulative sales of this type of vehicles increase each year because they consume less fuel compared to Gasoline Vehicles. We predict that the Moroccan Electric Vehicles market would have the same future as Diesel Vehicles market because of its cheapness operating cost. However, the purchase cost of the Electric Vehicles is the first obstacle of diffusion of this technology in the market, we forecast that this cost decreases with reducing the price of the battery which represents between 48-50% of the price of Electric Vehicles [22]. To estimate the GBDM parameters, we have chosen the France Electric Vehicles sales from 2011 to 2017, and the price of Lithium-Ion batteries which is the most kind of batteries used for energy storage in Electric Vehicles, this data were summarized according to National Association for Development of the Electric Mobility [25] and [26] as shown in Table (I).
Fig. 1. Cumulative sales of Moroccan Diesel Vehicle
The functions of the previous diffusion models have a nonlinear form; their parameters could be estimated with a nonlinear least squares method. It was used by [18] [23] to estimate the GBDM. However, Girish et al. [8] have based on a linear least squares method to estimate the Logistic and Gompertz parameters. In this study, we have estimated the parameters of all models by a nonlinear least squares method and the results are as shown in Table (II), Table (III) and Table (IV).
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 Year
0 2 4 6 8 10 12 14
cumulative sales
104
TABLE I. THESALESVOLUME,CUMULATIVESALESAND
BATTERYPRICEFOREVS
Year The sales volume of EVs
The cumulative sales of EVs
Battery price ($/KWh) 2011 4313 4313 800
2012 9314 13627 650
2013 13954 27581 600 2014 15045 42626 540 2015 22187 64813 350 2016 27307 92120 280
2017 30921 123041 230
The first aim of this work is to compare Gompertz, Logistic and Bass models. For this reason, we have based on R-square and Mean Absolute Percentage Error (MAPE), to get the best model which fit well our data. The MAPE was presented by the equation (8). A forecast with a MAPE between 10-20% was considered a good fit and those less than 10% as an excellent fit. In our case, the MAPE of all models is less than 10%
showed by Table (II) and Table (III). To determine the best model we have compared the R-square. When the R-square is close to 1 so we get the good fit. Bass model has a MAPE = 5.3% and R-square = 0.995, this values made it the best model to our data.
ൌͳ
ȁെ ȁ
ே
ୀଵ
(8)
AT : Actual value at time T.
FT : Forecast value at time T.
N : Number of observation.
TABLE II. GOMPERTZ,LOGISTICMODELSPARAMETERS
Model M a b R2 MAPE
Gompertz 88408 6.33 0.154 0.991 6.49%
Logistic 65668 62 0.328 0.984 9.44%
TABLE III. BASSMODELPARAMETER
TABLE IV. GENERALISEDBASSDIFFUSIONMODEL PARAMETERS
V. RESULTS A. Forecasting the Moroccan EVs market
Based on Bass model we forecast the cumulative adoption of EVs from 2017 to 2050. The number of cumulative adoption of EVs could reach 5400, 11600 and 12600 respectively by 2030, 2045 and 2050, which illustrated in Fig.2. This result remains small compared to other countries. In the USA the adoption of PHEV reaches 2 million in 2050 [27]. On the other hand, 12 million of PHEV adoption was estimated in Korea in 2050 [9].
In addition, the annual Moroccan sales of EVs have shown in Fig.3 from 2017 to 2080, the maximum sales will be after 14 years of integration of the Electric Vehicles, it could be 395 in 2033; this value is modest compared to the maximum sales of PHEVs in the UK which could reach 350000 in 2030 [8]. To increase the number of adoption of Electric Vehicles, Morocco must learn from other countries experience, which has a good market share of EVs and makes policies based on incentives to promote its Electric Vehicles fleet. In literature, many researchers have focused on the importance of incentives on the EVs market, the incentives have a positive impact to promote the adoption of EVs in China according to [28], another study conducted by [29] in Europe has indicated that incentives could be a good option to increase the number of EVs in the market.
Also, the EVs market needs subsidies especially in the early stage of their integration according to [30].
Fig. 2. Prediction of cumulative EVs using Bass model
Fig. 3. Prediction of sales of EVs using Bass model Paramet
ers
M p q R2 Ajus
ted R2 Estimate
d value 5245 90
0.012 0.298 -0.408 0.999 0.99 8 Parameters M p q R2 MAPE
Estimated
value 13707.9 0.01852 0.1151 0.995 5.3%
Prediction of cumulative EV adoption by Bass model
2020 2025 2030 2035 2040 2045 2050
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000
Number of EV
Yearly sales of EVs
2020 2030 2040 2050 2060 2070 2080
Year 0
50 100 150 200 250 300 350 400 450
Number of EVs
Sales estimation
B. Sensitivity analysis
The battery price presents about 48-50% [26] of Electric Vehicles price, which makes it the most expensive component in the Electric Vehicles. This part has two objectives; firstly, it analyzes the relationship between the actual cumulative sales and the estimated cumulative sales by the GBDM. Secondly, it assesses the cost reduction of the battery on the diffusion of EVs in the market.
We have analyzed the relationship between the actual cumulative sales and the estimated cumulative sales; the Fig.4 shows the actual and estimated cumulative sales for EVs, it demonstrates that the model (GBDM) fit well the actual data.
In order to get the second aim we have forecasted the diffusion of France Electric Vehicles market for different battery prices, we have defined a rate r=(Pr(T)-Pr(T-1))/(Pr(T-1)), where Pr(T) is the battery price at time T and Pr(T-1) is the battery price at time T-1. Three cases have been evaluated:
1) r=2% which means that the battery price decreases by ʹΨ at time T compared to initial price Pr(T-1).
2) r=-20% which means that the battery price decreases by ʹͲΨ at time T compared to initial price Pr(T-1).
3) r=-50% which means that the battery price decreases by 50% at time T compared to initial price Pr(T-1).
Fig. 4. Cumulative sales of Electric vehicles
Fig. 5. Cumulative sales of Electric vehicles by battery decreasing price
If the battery price decreases, the future number of Electric Vehicles will not raise. However, it could accelerate the EVs market diffusion. The cumulative sales with r=-50% reach the saturation in 2026, but cumulative sales with r=-20% reach the saturation in 2030, while cumulative sales with r=-2% reach the saturation after 2030, as shown in Fig.5, the market of EVs reaches the saturation earlier with lower r. We can conclude that the cost reduction of batteries would have an effect on the diffusion speed of EVs market.
VI. CONCLUSION
Morocco has been engaged to decrease the energy consumption of transport by 35% in 2030 [31], the Electric Vehicles would be a good option to reach its aim. The diffusion models have been used in this work to predict adoption of Electric Vehicles. Firstly, we have compared the R- square and the Mean Absolute Percentage Error (MAPE) of Gompertz, Logistic and Bass models to get the best model which could fit well our data. Secondly, we have forecasted the EVs Moroccan market using Bass Model and we have found that the market reaches its maximum sales after 14 years; this result may be changed depending on the government subsidies. Thirdly, we have assessed the effect of battery price on EVs diffusion market using France Electric Vehicles sales and Lithium-Ion battery price based on GBDM, which could take account the external variables. In this paper the external variable was the battery price, the result shows that the battery cost reduction cannot increase the future number of EVs. Nevertheless, it would raise the diffusion speed to get rapidly the market saturation. This work is very important for the research of the development of Moroccan EVs market; it would be very useful to the policy makers to get an idea about the diffusion of EVs market, and to make a strong policy to raise the number of EVs market share.
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