2.1 Public policy and the EV market

Several studies have been conducted to understand how public policy affects consumer choices, manufacturer decisions, and EV market growth. Gallagher et al. studied US vehicle market trends from 2000 to 2006 and associated them with state and federal public policies implemented during the same period (Gallagher & Muehlegger Reference Gallagher and Muehlegger2011). Their findings suggest that growth in EV adoption is mostly caused by rising gasoline prices and social preferences rather than by implementing public policies; among all policy measures, sales tax incentives have the greatest effect, being perceived as an instant monetary return. A more recent study by Morrow et al. showed that sales tax incentives would be too expensive to implement, with an unintended effect of decreasing new conventional vehicle fuel economy (Morrow et al. Reference Morrow, Gallagher, Collantes and Lee2010). Consistent with Gallagher & Muehlegger (Reference Gallagher and Muehlegger2011), Morrow et al. favor a fuel tax increase ahead of EV sales tax incentives as the most effective measure for GHG emission reduction. Egbue and Long’s survey suggested that investments in non-tax-related measures such as education on EV technologies, battery swap programs, and strong warranties on batteries are necessary for improving EV adoption (Egbue & Long Reference Egbue and Long2012). Scant knowledge regarding fuel economy by US consumers was also pointed out in (Greene & Plotkin Reference Greene and Plotkin2011). Skerlos and Winebrake suggested tax credits be targeted at regions where PHEV technology has high social benefits (e.g., with high vehicle miles traveled (VMT) and availability of charging infrastructure), and be dependent on consumer income (Skerlos & Winebrake Reference Skerlos and Winebrake2010).

Beyond the US market, Brand et al. investigated the role of a variety of consumer-related incentives in the UK (Brand, Anable & Tran Reference Brand, Anable and Tran2013). Their study also showed that car purchase taxes and ‘feebates’ are more effective in accelerating EV adoption than road taxes and scrappage incentives (scrappage schemes co-funded with the manufacturers aim at increasing automobile demand). Hao et al. analyzed a set of policy instruments for the Chinese market, with constrained vehicle license and vehicle downsizing being the most effective measures, followed by EV promotion and strengthened fuel economy standard (Hao et al. Reference Hao, Wang and Ouyang2011). The study, however, assumed full compliance to the policies by all stakeholders in the market.

Yabe et al. proposed an optimization framework for passenger EVs and the power grid. Their analysis predicted trends of EV adoption rate along with battery unit change and EV life cycle costs from 2010 to 2050, assuming that consumers switch to EVs once their life cycle costs become more economical than conventional vehicles. Their results also suggested the necessity of government intervention for EV penetration (Yabe et al. Reference Yabe, Shinoda, Seki, Tanaka and Akisawa2012). The study by Helveston et al. (Reference Helveston, Liu, Feit, Fuchs, Klampfl and Michalek2015) modeled consumer preferences for conventional, hybrid electric, plug-in hybrid electric, and battery EVs in China and USA using 2012–13 data from choice-based conjoint surveys. They found gasoline vehicles to be most attractive in both countries and a much lower relative willingness to pay for BEVs in USA. They also found that with or without each country’s 2012–13 subsidies, Chinese consumers were willing to adopt current BEVs and mid-range PHEVs at similar rates as the respective gasoline vehicles, whereas US consumers preferred low-range PHEVs despite subsidies.

Besides consumer choices, manufacturers’ decisions are affected by public policies, occasionally in unintended ways. Michalek et al. proposed to analyze the influence of government policies by combining decision models of consumers and manufacturers. Within a game-theoretic framework, they showed that policies trigger manufacturers to produce more efficient vehicles of higher costs (Michalek et al. Reference Michalek, Papalambros and Skerlos2004). Nonetheless, in investigating the automakers’ reactions to revised US Corporate Average Fuel Economy (CAFE) standards, Whitefoot et al. predicted an increase in market share of companies that choose to violate the 2011 US CAFE standard by offering heavier pickup trucks, thus offsetting potential fuel efficiency improvements by the standard (Whitefoot & Skerlos Reference Whitefoot and Skerlos2012). Frischknecht and Papalambros investigated quantitatively the trade-off between the public goal of GHG emission reduction and the private pursuits of profit under degrees of alignment of the two (Frischknecht & Papalambros Reference Frischknecht and Papalambros2008). Concerning the charging station operators’ role, Schroeder and Traber predicted that low EV adoption rate and competition between public and private charging facilities will cause low profitability for public fast-charging services in Germany. They also suggested temporally variable grid tariff exemption be the treatment to incentivize charging operators and investors (Schroeder & Traber Reference Schroeder and Traber2012).

These reports suggest that a more elaborate, holistic assessment of a policy’s impact may be gained with comprehensive quantitative models that connect all stakeholders in the EV market.

2.2 EV engineering design

The powertrain design of an EV directly governs its fuel economy. A typical BEV powertrain consists of a battery pack and one or more motors connecting to wheels through a final (reduction) drive. In addition to these, a PHEV has an internal combustion engine and a transmission that combines and distributes the power from the engine and motors to the final drive. Figure 1 shows the BEV and PHEV powertrain systems for the Nissan Leaf and Toyota Prius models, respectively, along with powertrain components. A battery pack consists of battery cells connected in series to form a branch, and multiple branches connected in parallel. The battery voltage and current limits are dependent on the number of series and parallel connections, respectively, and these further limit the power output from the motors. In addition, the size of the battery pack influences the weight of the vehicle and thus its MPG, acceleration performance, and emissions.

Figure 1. Typical EV powertrain systems and components: Nissan Leaf and Toyota Prius powertrain diagrams.

The final drive transforms high speed and low torque input from the transmission (or directly from the motor in BEVs) to low speed and high torque output to the wheels. The ratio between the input and output speed is the final drive ratio: a higher ratio leads to larger torque for launching the vehicle from a lower to a higher speed and thus better acceleration performance, while a lower ratio allows higher maximum vehicle speed. The final drive ratio significantly affects vehicle fuel economy and emissions, and must be fine-tuned for given vehicle specifications and driving conditions. Some HEVs and PHEVs use planetary (epicyclic) gear sets to decouple the engine from external power requirements in order to run in higher efficiency speed–torque regions.

Fuel economy and emissions can be improved at three levels: component, Architecture, and control. At the component level, the battery, motor(s), and engine are sized to meet target driving requirements, e.g., short-range city drive or long-range highway drive. A detailed review of battery technology choices for PHEV applications can be found in Axsen, Burke & Kurani (Reference Axsen, Burke and Kurani2008). The components are connected through a transmission to form a driving mode. Multiple driving modes can be integrated and switched over to allow high torque and fuel efficiency for different driving conditions, e.g., vehicle launching (high torque, low speed) or highway cruising (low torque, high speed). The collection of driving modes is referred to as an architecture or configuration. Notable architectures include the single-mode Toyota hybrid system (Hermance Reference Hermance1999; Liu, Peng & Filipi Reference Liu, Peng and Filipi2005) and the four-mode Volt plug-in hybrid system (Zhang et al. Reference Zhang, Li, Kum and Peng2012). For a given architecture, a control unit is designed to convert ‘throttle’ signals from the driver to operation commands to the engine and motor(s), so as to achieve near-optimal fuel consumption while meeting performance requirements such as 0–60 mph acceleration. In the vehicle design phase, offline optimal control policies are determined using Dynamic Programming (DP), Pontryagin’s Minimum Principle (PMP) or Equivalent Consumption Minimization Strategy (ECMS), and are implemented into rule-based online control strategies. Existing research has addressed modeling and design of both mechanical and electrical components (Liu et al. Reference Liu, Peng and Filipi2005; Zhang et al. Reference Zhang, Li, Kum and Peng2012; Ahn, Bayrak & Papalambros Reference Ahn, Bayrak and Papalambros2013), architectures (Liu Reference Liu2007; Raghavan, Bucknor & Hendrickson Reference Raghavan, Bucknor and Hendrickson2007; Liu & Peng Reference Liu and Peng2010; Bayrak, Ren & Papalambros Reference Bayrak, Ren and Papalambros2013; Zhang, Peng & Sun Reference Zhang, Peng and Sun2013; Bayrak, Kang & Papalambros Reference Bayrak, Kang and Papalambros2015), and optimal control policies for particular architectures (Paganelli et al. Reference Paganelli, Delprat, Guerra, Rimaux and Santin2002; Delprat et al. Reference Delprat, Lauber, Guerra and Rimaux2004; Liu et al. Reference Liu, Peng and Filipi2005; Ahn, Cho & Cha Reference Ahn, Cho and Cha2008; Kim, Kim & Kim Reference Kim, Kim and Kim2008; Serrao, Onori & Rizzoni Reference Serrao, Onori and Rizzoni2009; Stockar et al. Reference Stockar, Marano, Rizzoni and Guzzella2010; Kim, Cha & Peng Reference Kim, Cha and Peng2011).

2.3 Design for market systems

Design for market systems research emerged from looking at products from the perspective of the producer who aims to maximize expected value (e.g., profit and social welfare) from selling a product rather than the purely engineering perspective of optimizing functional performance metrics, even if including cost (Wassenaar & Chen Reference Wassenaar and Chen2003; Michalek et al. Reference Michalek, Feinberg and Papalambros2005; Lewis et al. Reference Lewis, Chen and Schmidt2006; Michalek et al. Reference Michalek, Ebbes, Adigüzel, Feinberg and Papalambros2011). Product design for market systems is cast as a mathematical optimization problem to find the optimal design that maximizes the expected profit while satisfying engineering and other constraints. To formulate the optimization problem, the relations between functionality and design decisions derived typically in engineering analysis through physics-based models and simulations must be augmented by economic models that link design decisions with profit via product demand and production cost.

Quantitative demand models are used in marketing extensively to express customer preferences (demand) as a function of design attributes and price. To incorporate such demand models in the design problem we must also express the design attributes as functions of the design variables that the designer can control directly. Deriving the mapping from design attributes to design variables is not always straightforward, particularly for subjective attributes such as aesthetics, and is a research problem in its own right. An example of a social constraint is government regulation, such as on vehicle fuel economy and safety.

We now briefly review how design decisions are modeled quantitatively. We represent a product or system design in the market with a vector of design attributes $\mathbf{a}$ that are the product properties perceived by the user. These attributes have a particular set of values for a particular market instantiation of the product. Attributes must be then expressed as functions of the design variables $\mathbf{x}$ that are the actual decisions made by the producer/designer. In EV design, design variables may be the number of battery cells and final drive ratio, while design attributes may be vehicle fuel economy and acceleration. The predicted market demand for a design can be expressed as $q(\mathbf{a})$ where $\mathbf{a}$ includes design attributes and price $p$ . With unit production cost denoted as $c(\mathbf{x})$ , the profit maximization design problem is stated as

(1) $$\begin{eqnarray}\max _{\text{all feasible }\mathbf{x}}q(\mathbf{a})(p-c(\mathbf{x})).\end{eqnarray}$$

The feasibility of $\mathbf{x}$ is expressed by a potentially large and complicated set of constraint functions, possibly computed through simulations, that assure the product’s functionality, manufacturability, and satisfaction of regulatory and other requirements. These constraints are functions of the design variables $\mathbf{x}$ .

The market demand $q(\mathbf{a})$ is forecast by multiplying the market potential (market size) $s$ and the choice probability (expected share of the market) $P(\mathbf{a})$ . Determining the function $P(\mathbf{a})$ is referred to as preference elicitation or preference learning, a subject of study in marketing research. In a market consisting of $M$ pre-existing competing products with design attributes $\mathbf{a}^{(m)}$ for $m=1,\ldots ,M$ , the commonly used logit model estimates the choice probability $P(\mathbf{a})$ for the new product design as

(2) $$\begin{eqnarray}P(\mathbf{a}|\mathbf{w})=\frac{e^{\mathbf{w}^{T}\mathbf{a}}}{e^{V}+\mathop{\sum }_{m=1}^{M}e^{\mathbf{w}^{T}\mathbf{a}^{(m)}}+e^{\mathbf{w}^{T}\mathbf{a}}},\end{eqnarray}$$

where the vector $\mathbf{w}$ contains the individual attribute part worths, a set of weights that reflect the importance of each design attribute for the target customer group. The vector product $\mathbf{w}^{T}\mathbf{a}$ represents the utility of a design, i.e., how much consumers prefer the design. The term $e^{V}$ reflects the utility, $V$ , of choosing none of the products. When a variety of preferences exists in a consumer group (market heterogeneity), the mixed logit model can be used. This model assumes that the individual part worths follow a probability distribution of given type, typically either discrete (latent class) or multivariate normal (McFadden & Train Reference McFadden and Train2000; Train Reference Train2009).

The data required for the choice probability estimation above can be collected through either existing market sales data (revealed preferences) or questionnaires answered by potential customers (stated data). The latter is more common for studying customer response to novel products, such as EVs. A classical questionnaire for part-worth estimation is the Choice-Based Conjoint (CBC) analysis (or discrete choice analysis) (Netzer et al. Reference Netzer, Toubia, Bradlow, Dahan, Evgeniou, Feinberg, Feit, Hui, Johnson and Liechty2008; Train Reference Train2009). The questionnaire consists of a series of choice questions. In each question, a set of designs with different attribute combinations is presented to the participant and one of them must be chosen as a preferred one. In some questionnaires, the participant is also allowed to choose none of the alternatives if none are acceptable.

In the mixed logit model, prior specification of the type of consumer part-worth distribution and the actual participant responses collected from the CBC study are used to estimate the posterior individual-level part-worth distribution. The estimation of the part-worth distribution and inference of individual part worths is done using either hierarchical Bayes estimation (Train Reference Train2001; Rossi, Allenby & McCulloch Reference Rossi, Allenby and McCulloch2005) or convex optimization (Evgeniou, Pontil & Toubia Reference Evgeniou, Pontil and Toubia2007). Accuracy and efficiency of part-worth estimation can be improved by introducing social (Brock & Durlauf Reference Brock and Durlauf2001) and contextual (He et al. Reference He, Chen, Hoyle and Yannou2012) information, and by utilizing adaptive questionnaires (Abernethy et al. Reference Abernethy, Evgeniou, Toubia and Vert2008; Ren, Scott & Papalambros Reference Ren, Scott and Papalambros2013).

While general market share prediction modeling has mature theory and available computational tools, the particular prediction of future EV adoption is an ongoing research challenge, requiring, for example, quantification of consumers’ knowledge in EV technology to measure adoption barriers (Egbue & Long Reference Egbue and Long2012).

The information flow for modeling the profit maximization problem from the EV manufacturer’s perspective is summarized in Figure 2.

Figure 2. Information flow for the EV manufacturer’s profit maximization model.

In a market with multiple stakeholders, each stakeholder has its own objective. Depending on the scenario, the stakeholders could combine their objectives in the optimization formulation (a collaboration scenario) or aim to optimize their own profit (a cooperation scenario that assumes all information is shared by all stakeholders). In the latter case, a game-theoretic model for the market can be set up to reach an equilibrium where no further decisions are made. When the first order optimality conditions of equilibrium can be derived analytically, the solution to these conditions can be found numerically; see Morrow and Skerlos on finding Bertrand–Nash equilibrium prices for product market models based on the mixed logit model (Morrow & Skerlos Reference Morrow and Skerlos2011). However, most engineering models rely on simulations and experimental data, and analytical derivation of first order conditions is rarely possible. In this situation, optimization for each stakeholder can be performed sequentially until no further improvement in any of the individual objectives can be made; see Michalek et al. (Reference Michalek, Papalambros and Skerlos2004), Shiau & Michalek (Reference Shiau and Michalek2009a ,Reference Shiau and Michalek b ), and Frischknecht et al. (Reference Frischknecht, Whitefoot and Papalambros2010) for examples.

2.4 EV product–service system design

Service optimization aims to maximize service profit accounting for consumer preferences with respect to service attributes (Pullman & Moore Reference Pullman and Moore1999; Easton & Pullman Reference Easton and Pullman2001; Goodale, Verma & Pullman Reference Goodale, Verma and Pullman2003). Product–service systems design recognizes that in many instances services are tied to products and consumer preferences are affected by relationships between product and service attributes (Cohen & Whang Reference Cohen and Whang1997; Verma et al. Reference Verma, Thompson, Moore and Louviere2001). Cohen & Whang (Reference Cohen and Whang1997) addressed trade-offs between product price and after-sales service price and quality to design a profit-maximizing product–service ‘bundle’ using game theory to find the equilibrium point between the producer and service operator. Verma et al. (Reference Verma, Thompson, Moore and Louviere2001) proposed a product–service design framework to address operations difficulties in meeting market demand, for example, for a pizza design and delivery system.

Research in design for market systems, initially focused on products, has been expanded to product–service system design. Several recent studies have explored the integration of marketing, engineering, and operations models for product–service system design optimization (Kang Reference Kang2014; Kang et al. Reference Kang, Emmanoulopoulos, Ren, Feinberg and Papalambros2015; Kang, Feinberg & Papalambros Reference Kang, Feinberg and Papalambros2015a ,Reference Kang, Feinberg and Papalambros b ). Kang et al. showed that when multiple product and service providers compete in the same market, trade-offs exist between product and service profits, in which case co-designing products and services can be more profitable than separately designing the product and the service.

In the EV market, products and services are closely related when the refueling service station operations are included in the system. Range anxiety (concern regarding how far one can drive on a single charge) is a major reason for slow EV adoption (Melaina & Bremson Reference Melaina and Bremson2008; Vardera Reference Vardera2010; Egbue & Long Reference Egbue and Long2012). This concern comes not only from the relatively low driving range of current EVs but also from the sparseness of public charging stations. In both US and Chinese markets, EV manufacturers and charging station operators have started to collaborate to overcome this adoption barrier (ChargePoint 2014; ECOtality 2014; JRJ.com 2015). Early studies for a US market indicate that a collaboration between vehicle producers and charging station operators is necessary to reach overall profitability (Kang et al. Reference Kang, Feinberg and Papalambros2015a ,Reference Kang, Feinberg and Papalambros b ). When the two stakeholders work in partnership, the charging station operators can build more stations even with a loss, which is mitigated by profit from EV sales. Aggressive investment in charging station infrastructure can relieve range anxiety of EV users leading to more EV sales (Kang et al. Reference Kang, Feinberg and Papalambros2015b ). Regarding charging service design, specifically, a study of the Beijing market has shown that a distribution of mixed charging services (including charging stations, charging posts, and battery swap stations) will be needed to accommodate the growing EV adoption rate without significant disturbances to the power grid Liu (Reference Liu2012). The relationship between charging capacity and charging service profit has been studied by Li & Ouyang (Reference Li and Ouyang2011), showing that high station load is important for keeping the service profitable.

2.5 Modeling assumptions

Several assumptions are made throughout the modeling framework described here. Some are intrinsic to the models themselves; others are simply parameter values assumed in the application study and can be modified without changing the model itself. In the latter case, the models can be rerun with different values and different conclusions may be reached. Results for some parametric changes are included in the application study. Additional assumptions are noted in the relevant model descriptions.

• ∙ The study focuses only on subsidy-related policies and market equilibria resulting from them; it does not consider other policies such as zero-emission vehicle sales mandates. In addition, the fixed gasoline vehicle design used in the study is assumed to satisfy all fuel economy and emission standards. This is reasonable since the paper does not aim to establish optimal choice of powertrain and emission technologies. Further, behavioral interventions such as energy consumption feedback to users (see Allcott & Mullainathan (Reference Allcott and Mullainathan2010) for example) are not considered as a policy alternative.

• ∙ All models are time-independent, representing a steady state of the market. This assumes that responses to public policies and design decisions are instantaneous, and currency depreciation and loan interests are not modeled. Nonetheless, we will perform parametric studies on the gas price, which is time sensitive in reality and has significant influence on the market equilibrium. We will discuss the validity of major findings of this study for varying gas prices. It should be noted that the steady state assumption sidesteps important dynamics in the EV market, e.g., the existence of early adopter and mainstream consumers, and the rebound effect for improved fuel economy (which is shown to be moderate in the US market, see Greening, Greene & Difiglio (Reference Greening, Greene and Difiglio2000), and Small & Van Dender (Reference Small and Van Dender2007)). However, the proposed framework has the potential to be extended to equilibria of time-dependent decisions optimized for all stakeholders.

• ∙ The market consists of only two manufacturers: one offers a BEV and a PHEV for which optimal designs need to be determined; the other offers a conventional gasoline vehicle with a fixed design. Our model essentially clusters the decisions of manufacturers into two groups, EV and gasoline, and assumes that each group shares the same goal and technology, financial, and manufacturing capabilities; see, for example, Whitefoot, Fowlie & Skerlos (Reference Whitefoot, Fowlie and Skerlos2011) for more discussion in this direction. This largely simplified model allows us to focus on differentiating the main trends in EV market penetration for the US and China markets (different in size, consumer preferences, and policies), without further complicating conclusions by incorporating heterogeneous firm-wise decisions. We acknowledge that adding these details would improve the realism of the study, but it will cause the model to be too complicated (with all parameters characterizing manufacturers) as an initial study to effectively reveal the key factors linking public policies and engineering design decisions that influence the markets. Our analysis focuses on revealing how EVs would be designed at market equilibrium, but does not inform manufacturers on strategies to differentiate their products from competitors.

• ∙ This study focused on the two markets (central area of Beijing and Ann Arbor) where chargers can be installed in public parking spots relatively cheaply. We acknowledge, however, that the actual building and land cost will be high for installing charging stations in suburban areas or along interstate highways, in both USA and China. In addition, all chargers installed in stations use Direct Current (DC) fast chargers that can recharge a battery within 30 min. All charging stations are operated either by a private company or by the government.

• ∙ In the calculations for fuel economy and emissions the driving cycles used are Federal Test Procedure (FTP-75) and New European Driving Cycle (NEDC) for the US and Chinese markets, respectively. The GHG emission values are calculated based on $\text{CO}_{2}$ emission from both gasoline consumption and electricity production (for EVs). For the latter, an existing method for the US market (EIA 2015) is applied to both markets.

• ∙ Baseline tax and plate fees for EVs are the same as the ones for gasoline vehicles. All reductions are considered as a government investment. Tax and plate fees are not considered as government income. Currently, USA has a one-time tax for vehicles, while China has an annual tax.

• ∙ The following parameters are assumed in the comparison study: gas prices for Ann Arbor and Beijing are $2.51/gallon and $4.77/gallon, respectively. One US dollar equals 6.26 Yuan. Discount rate is 10 % per a year. EV use life is set at ten years.

The next section describes how the decisions by the three stakeholders, government, vehicle producer and infrastructure operator, are combined in a single framework to estimate the resulting market equilibrium.

3.1 Public policy model

We model EV-related public policies currently implemented in USA and China according to Mock & Yang (Reference Mock and Yang2014), consisting of EV subsidies for consumers and manufacturers, and subsidies for charging station operators. The total amount of subsidies has an upper bound set to the government’s approved budget limit.

3.1.1 US case policy model

For the US case, four public policies are considered as decision Variables; see Table 2 for definitions and bounds.

Table 2. Public policy decision variables for U.S

Let $S_{\mathit{EV}}$ be the subsidy on unit (kWh) battery energy, $BC_{\mathit{BEV}/\mathit{PHEV}}$ and $D_{\mathit{BEV}/\mathit{PHEV}}$ be the battery capacity and market demand, respectively. The total subsidy allocated to the manufacturer, $I_{\mathit{EV}}$ , can be calculated as

(7) $$\begin{eqnarray}I_{\mathit{EV}}=S_{\mathit{EV}}\times (BC_{\mathit{BEV}}\times D_{\mathit{BEV}}+BC_{\mathit{PHEV}}\times D_{\mathit{PHEV}}).\end{eqnarray}$$

The total subsidy on the charging station operator, $I_{\mathit{CS}}$ , can be formulated as

(8) $$\begin{eqnarray}\displaystyle I_{\mathit{CS}} & = & \displaystyle S_{\mathit{CS}}\times N_{\mathit{CS}}\times (C_{inst}+C_{main})\nonumber\\ \displaystyle & & \displaystyle +\,\mathit{Cut}_{\mathit{EC}}\times C_{\mathit{EC}}\times (\mathit{BC}_{\mathit{BEV}}\times D_{\mathit{CS}_{\mathit{BEV}}}+\mathit{BC}_{\mathit{PHEV}}\times D_{\mathit{CS}_{\mathit{PHEV}}}),\end{eqnarray}$$

where $S_{\mathit{CS}}$ and $\mathit{Cut}_{\mathit{EC}}$ are the unit charging station subsidy and the electricity cost discount, respectively; $N_{\mathit{CS}}$ is the number of stations; $C_{inst}$ and $C_{main}$ are costs for installing and maintaining a charging station; $C_{\mathit{EC}}$ is the electricity cost; $D_{\mathit{CS}_{\mathit{BEV}/\mathit{PHEV}}}$ is the charging demand.

For subsidies allocated to consumers, $I_{cu}$ , we have

(9) $$\begin{eqnarray}I_{cu}=\mathit{Cut}_{tax_{\mathit{EV}}}\times Tax_{gas}\times (D_{\mathit{BEV}}+D_{\mathit{PHEV}}),\end{eqnarray}$$

where $\mathit{Cut}_{tax_{\mathit{EV}}}$ is a one-time tax cut for EV users, and $Tax_{gas}$ is a one-time tax for a gasoline vehicle.

Table 3. Public policy decision variables for China

3.1.2 Chinese case policy model

Seven public policies are considered for Beijing, see Table 3. There are several differences between the Chinese and US cases.

In China, the manufacturer subsidy is proportional to the battery range rather than the capacity, so instead of Eq. (7) we have

(10) $$\begin{eqnarray}I_{\mathit{EV}}=S_{\mathit{EV}}\times (R_{\mathit{BEV}}\times D_{\mathit{BEV}}+R_{\mathit{PHEV}}\times D_{\mathit{PHEV}}),\end{eqnarray}$$

where $R_{\mathit{BEV}/\mathit{PHEV}}$ is the battery range. On the consumer side, issuance of new vehicle license plates is restricted in major cities such as Beijing and Shanghai. In Shanghai, a lottery system is used for conventional vehicles and an amount of 10–15k USD is charged for a plate (Net Reference Net2015c ) upon winning the lottery. In Beijing, lottery participation is restricted based on criteria including city residence and at least 5 years of tax payments. See Net (Reference Net2015b ) for a complete restriction list. In our comparison study, we assume that the ‘effort’ for obtaining a plate in Beijing is the same as for Shanghai. Hence we set the plate cost, $F_{plate\_gas}$ , for a conventional vehicle in Beijing at the same level as in ShanghaiFootnote ¹ .

For EV adopters, a plate discount of $\mathit{Cut}_{plate\_\mathit{BEV}/\mathit{PHEV}}$ percent applies in addition to a $\mathit{Cut}_{tax\_\mathit{EV}}$ percent discount on annual tax and a one-time purchase subsidy of $\mathit{IC}_{\mathit{EV}}$ USD. Therefore, the total government investment on consumer subsidies can be stated as follows:

(11) $$\begin{eqnarray}\displaystyle I_{cu} & = & \displaystyle \mathit{IC}_{\mathit{EV}}\times (D_{\mathit{BEV}}+D_{\mathit{PHEV}})\nonumber\\ \displaystyle & & \displaystyle +\,\mathit{Cut}_{plate\_\mathit{BEV}}\times F_{plate\_gas}\times D_{\mathit{BEV}}\nonumber\\ \displaystyle & & \displaystyle +\,\mathit{Cut}_{plate\_\mathit{PHEV}}\times F_{plate\_gas}\times D_{\mathit{PHEV}}\nonumber\\ \displaystyle & & \displaystyle +\,\mathit{Cut}_{tax\_\mathit{EV}}\times Tax_{gas}\times D_{\mathit{PHEV}},\end{eqnarray}$$

where $F_{plate_{gas}}$ and $Tax_{gas}$ are the license plate fee and the annual tax for conventional (gasoline) vehicles, respectively. For the comparison study, we set $F_{plate_{gas}}$ to 25k USD and $Tax_{gas}$ to 50 USD per engine displacement, respectively.

Business models for charging services in USA and China are still under exploration. Therefore, we use the same CS subsidies, Eqs. (9) and (8), for both cases.

3.2 Engineering functionality model

Our market model assumes one manufacturer designs and sells one BEV and one PHEV product, and competes with another manufacturer who sells a conventional gasoline vehicle with a fixed design. Three vehicle simulation models for BEV, PHEV and gasoline vehicles are built in the AMESim (AMESim 2014) simulation environment, as shown in Figure 5. The vehicle models follow specifications similar to the Nissan Leaf, Toyota Prius (PHEV version), and Volkswagen Jetta. We use battery cell specifications from the Nissan Leaf for both the BEV and the PHEV (EERE 2011a , b ). All component specifications are listed in Table 4. Note that the simulation models are meant to approximate these representative vehicles rather than to provide high-fidelity models for them.

Figure 5. Engineering simulation models.

Table 4. Vehicle component specifications

Each vehicle model has a drive cycle as input and uses a Proportional–Integral–Derivative (PID) controller to represent the driver that follows the drive cycle. The PID controller is a standard control-loop feedback mechanism that attempts to minimize the error between a measured state variable and its desired value (Aström & Hägglund Reference Aström and Hägglund1995). The PID control gains are fixed in all vehicle simulations. Two sources of GHG emission are considered: for the PHEV and the gasoline vehicle, emission from usage of gasoline is accounted for through a driving simulation; for the PHEV and the BEV, emission from electricity production is predicted based on electricity usage (kWh) of EVs during the drive cycles, using the method from (EIA 2015). PHEV uses only battery power at the outset, and switches to the gasoline engine once the battery drains. The PHEV powertrain energy management (control) strategy is tuned to maximize electric-only range for the given drive cycle, rather than for sustaining the State Of Charge (SOC) of the battery. The initial state of charge is set at 80 %, which is the assumed SOC after visiting a fast-charging station.

Because the PHEV initially uses only the battery, and engages the gasoline engine only later, in the model, batteries are not recharged by the engine and emissions are estimated based on gasoline engine usage only. In the operations model, the constraint for charger capacity for both EVs and PHEVs is included because both EV and PHEV users can use charging stations. In the consumer demand model, we assume that PHEV purchasers would not care about availability of charging stations because PHEVs have alternate charging options.

Table 5. Engineering design variables

We consider three design variables within the engineering model as listed in Table 5: the number of battery cells in series in one branch, the number of branches in parallel, and the final drive gear ratio. Other vehicle parameters, e.g., mass and coefficient of drag, are fixed since they can be designed independently from the drive cycles. For a given set of input variable values, the simulation outputs the emissions, range, battery/fuel consumption, top speed, 0–60 mph acceleration, and vehicle manufacturing cost. Emissions minimization is the government objective. Vehicle cost is decomposed into battery cost and cost for other parts, both of which are calculated following Kang et al. (Reference Kang, Feinberg and Papalambros2015b ). From the outputs, range, and battery/fuel consumption are parameters used as inputs to the market demand model, while top speed and acceleration serve as engineering constraints. A feasible design should have a top speed greater than 70 mph, and a 0–60 mph acceleration time less than 20 s. We use the same engineering simulation models for both USA and China but with different drive cycles: the Federal Test Procedure (FTP)-75 drive cycle for USA and the New European Driving Cycle (NEDC) for China. Due to the high computation cost of simulations, metamodels are built from the simulation results and used to speed up the optimization. Specifically, for both BEV and PHEV, we generate 20,000 vehicle designs using Latin Hypercube sampling, each yielding vehicle performance (e.g., MPG, 0–60, range, etc.) through simulation using AMESim. We then create a neural network with 15 hidden neurons through the Matlab Neural Network Toolbox (MathWorks 2015). The resultant models have test R values close to 0.99.

3.3 Charging service model

For each city, the charging service model determines the best station locations and charging fee based on the number of charging stations. The model assumes DC fast-charging stations that can recharge a 24 kWh battery to 80 % capacity within 30 min. We adopt the $p$ -median model (Tansel, Francis & Lowe Reference Tansel, Francis and Lowe1983) to determine the optimal set of stations: the optimal location selection of $p$ stations minimizes the average Euclidean distance between any EV on the map and its closest station. The model then calculates the average distance to the closest station from any EV user, assuming that users are uniformly distributed in a given city area.

Table 6. Optimal charging station locations in Ann Arbor (A to O)

We define the average driving distance for recharging as the aforementioned Euclidean distance multiplied by a parameter $\unicode[STIX]{x1D6FC}$ , which is dependent on city road and traffic conditions (Burns, Jordan & Scarborough Reference Burns, Jordan and Scarborough2013). This distance is used as a parameter in the consumer preference model to estimate market share. The number of stations should be such that every charger can serve at least 12 EV users per day. This lower bound stems from estimates that each public charger will be used 6 h a day (ECOtality 2013) and that each charging service requires 30 min. Consider the total EV demand $D_{\mathit{BEV}}+D_{\mathit{PHEV}}$ as the EV market size, and denote $D_{\mathit{CS}_{daily}}$ as the number of charging services needed by each vehicle per day, $N_{\mathit{CS}}$ as the number of stations, and $N_{charger}$ as the number of chargers per station. This constraint can be written as

(12) $$\begin{eqnarray}(D_{\mathit{BEV}}+D_{\mathit{PHEV}})\times D_{\mathit{CS}_{daily}}\leqslant 12\times N_{\mathit{CS}}\times N_{charger}.\end{eqnarray}$$

3.3.1 US case charging station location model

The US Case model is based on an 11 mile by 11 mile area that approximates the city of Ann Arbor with 15 candidate charging station locations selected among its existing public parking lots. This area and candidate station locations are shown in Figure 6. As a pre-process, the optimal locations are computed for 1–15 stations (see Table 6) and the corresponding average distances are recorded. For example, if we plan to build five charging stations, locations A, B, G, K, and N in the figure will be chosen. This look-up table of optimal charging station locations and average distances is used for system level optimization. We set the proportional parameter $\unicode[STIX]{x1D6FC}=1.2$ based on an estimate for the most ‘straight’ route on Google maps. We assume that each charging station has two chargers.

The total cost of running the charging stations consists of installment, maintenance, and electricity costs (Kang et al. Reference Kang, Feinberg and Papalambros2015b ). For Ann Arbor, we set $75,000 for installing a charger, $5,500 for annual maintenance, and $10.28$ cents per kWh for electricity (Schroeder & Traber Reference Schroeder and Traber2012; EIA 2014).

Figure 6. Candidate charging station locations in Ann Arbor (A to O).

3.3.2 Chinese case charging station location model

While the Beijing downtown area is similar in size to Ann Arbor ( $11\times 11$ miles), charging station operator and public policy decisions could be different. Twenty candidate charging station locations are selected among existing major public parking lots (see Figure 7), and the optimal locations are identified (see Table 7).

Figure 7. Candidate charging station locations in Beijing (A to T).

Table 7. Optimal charging station locations in Beijing (A to T)

We set the parameter $\unicode[STIX]{x1D6FC}$ to $1.4$ , higher than that in the Ann arbor case, to reflect the more complex road structure in Beijing. Each charging station is assumed to have 34 chargers so that the chargers per station ratio between Beijing and Ann Arbor equals that of the potential market sizes (100,000 and 5,800). Installment and annual maintenance costs for one station are set at $300,000 USD (Xinhuanet 2015)Footnote ² and $9,600 USD (Sina 2015)Footnote ³ , respectively. Electricity cost for charging EVs is set at $15$ cents per kWh according to Sohu (2015)Footnote ⁴ .

3.4 Market model

The market model predicts the market shares of a set of products based on product attributes and consumer preferences. We build the US and Chinese Case models based on responses collected from surveys we conducted in the two countries. Specifically, Choice-Based Conjoint (CBC) studies were executed in the two countries; details appear below. We then used a Hierarchical Bayesian (HB) approach (Rossi et al. Reference Rossi, Allenby and McCulloch2005; Orme Reference Orme2009) to estimate the part worths (the weights on product attributes that reflect preferences of the consumer group). The HB analysis leverages responses from all subjects during the estimation of individual part worths, and accounts for preference heterogeneity across subjects. The average market demand is estimated as

(13) $$\begin{eqnarray}q(\mathbf{a})=\frac{1}{I}\mathop{\sum }_{i=1}^{I}sP_{i}(\mathbf{a}),\end{eqnarray}$$

where $q(\mathbf{a})$ is the EV demand based on all design attributes $\mathbf{a}$ , including engineering, price and service, scaled by the market potential $s$ . The choice probability of the $i$ th survey participant, $P_{i}$ , is calculated following Eq. (2), where $I$ is the total number of survey participants. We assumed that the vehicle market size of Ann Arbor is proportional to that of USA as a whole. This gives us an estimated market of 5,800 in Ann Arbor. For Beijing, the market size is approximately 100,000 according to Xinhuanet (2013)Footnote ⁵ . We used $2.51 per gallon for gas price in Ann Arbor and $4.77 per gallon in Beijing, according to market prices on March 23rd, 2015.

3.4.1 US market model

Three price variables are of interest in modeling US market demand: retail prices for BEV and PHEV, and charging station fee. To estimate market demand, our CBC study included seven product attributes: (1) Vehicle type (BEV, PHEV or Gasoline), (2) vehicle price taking EV subsidy into account, (3) registration fee, (4) vehicle range, (5) fuel (electricity) cost to fully refuel (recharge) the vehicle, (6) number of charging stations, and (7) average distance to a station. We gathered responses from 213 subjects living in US cities that have similar population size and area to Ann Arbor. The survey was conducted in November 2014, using Sawtooth Software (Orme Reference Orme2009) for data analysis and ClearVoice Research (Clearvoice 2015) for participant recruitment and screening. Demographic information of the participant group is as follows. The subjects were 41 % male and 59 % female; 3 % were 18 to 24 years of age, 17 % were 25 to 34 years of age, 17 % were 35 to 44 years of age, 23 % were 45 to 54 years of age, 25 % were 55 to 64 years of age, and 15 % were more than 65 years of age. Attribute levels and estimated part worths (means and standard deviations) are summarized in Table 8.

Table 8. Attributes levels and their part worths for US case

3.4.2 Chinese market model

For Beijing, we use the same variables: BEV and PHEV retail prices, and charging fee. The CBC study for this case used eight attributes: (1) Vehicle type (BEV, PHEV or Gasoline), (2) vehicle price taking EV subsidy into account, (3) one-time license plate fee, (4) annual tax, (5) vehicle range, (6) fuel (energy) cost to fully refuel (or recharge) the vehicle, (7) the number of charging stations, and (8) the average distance to the station. We gathered responses from 170 subjects living and working in Beijing or Shanghai. The survey was conducted in April, 2015, using the same tools as in the US case. Demographic information is as follows: the subjects were 68 % male and 32 % female; 3 % were 18–24 years of age, 42 % were 25 to 34 years of age, 30 % were 35–44 years of age, 17 % were 45 to 54 years of age, 7 % were 55–64 years of age, and 1 % were more than 65 years of age.

In this survey we used driving time instead of distance to a station. This is based on the hypothesis that people living in central metropolis areas in China tend to describe driving distances by time, probably because distance does not directly reflect the cost (by taking time into consideration) of travel with the presence of high uncertainty in traffic conditions, while people are commonly sensitive to time. In post-survey analysis, we converted this time attribute back to a distance, using an average driving speed of 7.5 mph in central Beijing according to Tejada (Reference Tejada2015). Attribute levels and resulting part worths (means and standard deviations) are summarized in Table 9.

Table 9. Attributes levels and their part worths for China case

Here we should note some preference differences between consumers in the two countries observed from the survey data, as these will help contextualize optimal policy and market behavior results later on. (1) Chinese consumers prefer PHEVs more than conventional vehicles. We found that PHEVs are well-regarded in Beijing, while in Ann Arbor neither EV type is as well accepted as the gasoline alternative (which is consistent with the recent US studies in Carley et al. (Reference Carley, Krause, Lane and Graham2013), Helveston et al. (Reference Helveston, Liu, Feit, Fuchs, Klampfl and Michalek2015)). However, this result is partially inconsistent with the China market survey reported in Helveston et al. (Reference Helveston, Liu, Feit, Fuchs, Klampfl and Michalek2015) (during 2012–2013), where Chinese consumers strongly preferred HEVs instead of PHEVs. One reason could be the recent policy change that terminated HEV purchase subsidies and license issuance benefits, in addition to the ever-increasing restriction on license plate issuance for gasoline vehicles. One support for our result is a more recent (2015) survey in Shanghai that showed a total of 75.6 % of respondents considering buying PHEVs, compared to 15.0 % for BEVs (Daily Reference Daily2015). (2) US consumers are more sensitive to price and range. While price and range play an important role in purchase decisions across both markets, US consumers are more sensitive to these attributes. For example, the probability for a US consumer to buy an low-range EV (100 miles) is approximately one-third of that for a Chinese consumer. (3) Chinese consumers care about charging service attributes as much as price and range, while US consumers do not (relatively) value these attributes.

Note that, in discrete choice models, part worths reflect not only the importance of various attributes, but the extent to which they drive choice probabilities away from equality across options; the latter interpretation does account for differences in error scale. As such, differences between USA and China can be assessed by parametric differences to the extent that they reflect their relative populations. This is consistent with the work of Louviere and co-authors on the topic, see, e.g., Swait & Louviere (Reference Swait and Louviere1993) and Fiebig et al. (Reference Fiebig, Keane, Louviere and Wasi2010).

3.4.3 Charging demand model

We assume that the charging demand ( $De_{\mathit{CS}\_\mathit{EV}}$ ) is proportional to the number of EVs on the road, which is approximated as the demand for EVs ( $De_{\mathit{EV}}$ ):

(14) $$\begin{eqnarray}De_{\mathit{CS}\_\mathit{EV}}=De_{\mathit{EV}}\times De_{\mathit{CS}\_daily}\times L_{\mathit{EV}}.\end{eqnarray}$$

Here the parameter $De_{\mathit{CS}\_daily}$ is the average daily charging frequency. Following Smart & Schey (Reference Smart and Schey2012), ECOtality (2013), we assume that on average there are 1.05 charging events per vehicle day, while 4.64 % of these events occur at DC fast-charging stations. Therefore, $De_{\mathit{CS}\_daily}=1.05\times 4.64\,\%=4.87\,\%$ . We assume the EV useful life $L_{\mathit{EV}}$ to be ten years. The charging demand is translated into a lower bound of the number of charging stations.