Assessment of Energy Transition Policy in Taiwan—A View of Sustainable Development Perspectives

Energy transition has become a priority for adaptive policy and measures taken in response to climate change around the world. This is an opportunity and a challenge for the Taiwan government to establish a climate-resilient power generation mixed to ensure electricity security as well as climate change mitigation. This study adopted a sustainable development perspective and applied optimal control theory to establish a cost-effective model to evaluate a long-term (2050), climate-resilient power generation mix for Taiwan. Furthermore, this study applies the STIRPAT approach to predict the demand of electricity by 2050 for the demand side management. The results not only showed the share of various power generation mixed, but also recommended the trajectory of electricity saving by 2050.


Introduction
The Paris Agreement has set a target of net zero emissions by 2050, which will require rapid reduction of regional and global CO2 emissions, in the order of 5-10% per year (Seto et al. 2016) [1]. The energy transition has become a global response to net zero emissions internationally, indicating that renewable energy will represent a higher share of electricity, and to improve energy efficiency to generally meet energy service demand with lower energy use in energy systems (Intergovernmental Panel on Climate Change, IPCC, 2018) [2]. However, traditional power system planning is still mainly conducted to meet the increasing electricity demand, and this cannot meet the criteria of sustainable power supply, i.e., economic development (reliability and economic feasibility), environmental development (environmental friendliness), and social development (affordability and social acceptability) (World Summit on Sustainable Development, WSSD, 2002), and cannot allow for the achievement of net zero emissions target by 2050. In summary, the power mix that meets environmental effectiveness and cost effectiveness will be a key strategy towards low-carbon emission pathways in a country.
The above studies point out that power mix does indeed pose a challenge for the energy transition in Taiwan. Therefore, it is essential that the electricity resource governing authority considers our sources of domestic electricity (including fossil fuel, Nuclear, and renewable energy) and develops a power supply system that incorporates climate resilience, based on the characteristics of the various types of electricity resources. In response to low carbon emissions, the government set a supply target of as 50% natural gas power, 30% coal-fired power, and 20% renewable energy power by 2025. In short, a power resource planning and management policy in line with the principle of "supply dictates demand" has been established (Huang and Lee,2019) [19]. This article wants to put forward a view from the sustainable development perspective, which evaluates the country's long-term power technology mix. In other words, this study aims to limit electricity demand through long-term optimal power generation. The method is feasible and necessary under the development of net zero emissions, as hydrogen energy and decentralized grids among other innovation energy saving methods continue developing rapidly, and these could be used to greatly reduce electricity demand.
This paper aimed to plan the trajectory of power mix as well as electricity saving rate by 2050 in Taiwan. A cost-effectiveness optimal control model was proposed to explore the optimal power mixed pathways. The modelling of costs involved is most similar to the work of Huang and Lee (2019) [19]. This analysis pays special attention to renewable energy, which is an important alternative power supply to respond to the energy transition and low carbon pathway, but the intermittency cost is generally larger, along with aa higher ratio, which is a key factor for power supply portfolio planning. Furthermore, this study introduced an extended STIRPAT (Stochastic Impacts by Regression on Population, Affluence, and Technology) model (refer to Su and Lee, 2020) [20]; Pan and Zhang (2020) [21]) to project electricity demand by 2050 in Taiwan. This paper is organized into four sections: Section 1 explains the background and purpose of this paper. Section 2 presents a theoretic model power mixed. Section 3 includes the results and subsequent discussion. Section 4 concludes and suggests recommendations.

Methods
This paper establishes a social planner's optimal control model for deriving the cost effectiveness power generation mixed under various objectives, which include greenhouse gas emissions reduction target, economic dispatch risk of power system, and electricity security respectively.

Theoretical Model
Nowadays, Taiwan's domestic power supply comprises primarily fossil fuel (80%), nuclear (15%), and renewable energy (5%), although the development of diversified resources, such as solar PV and wind power have been actively promoted since 2012. This is an opportunity and a challenge for the Taiwan government to establish a climate-resilient power supply portfolio to ensure electricity security as well as to reach the greenhouse gas emissions target by 2050 (Greenhouse gas emissions are required to be cut by 50% compared to the emissions level in 2005 by 2050 in Taiwan).
The objectives for the model were set as follows: (1) Time horizon: the year 2050 was set as the end of the model; (2) Power supply mixed: diversified development (investment) to ensure a reliable power supply, in particular gas fired generation and the renewable power promotion under Nuclear free beyond 2025; (3) Electricity security: ensure that annual electricity supply is no less than electricity demand each year, while the intake of available renewable energy is affected by weather conditions and climate change, which reflects power security; (4) Power technology characteristics: consider the intermittency cost of renewable technology, which reflects reliability; (5) Carbon dioxide emission cost: consider the carbon dioxide emission cost associated with power production, which represents the cost of reducing the carbon footprint of power generation.

Function of Power Supply Costs
The total cost ( it TC ) and unit/average cost ( it c ) of producing the ith type of power technology in the tth year is expressed in Equations (1) and (2): (refer to Huang and Lee, 2019) [19] [ ] where i TC is the total cost of the i th power generation technology, including power generation cost, i i c Q , i c is the average cost of power generation (see Equation (2) CO emissions ( i E ). Ai P , ei P and Fi P are exogenous variables and i ϕ is the intermittency cost of power generation technology, which reflects the instability of the technology, such as renewable energy. Due to the uncertainty of regeneration capacity (such as wind power), the cost of power dispatch and reserve capacity will increase. Therefore, in addition to equipment and operating costs, the cost of renewable energy power generation also needs to reflect intermittent costs (Huang and Lee, 2019) [19]). i ϕ is zero for thermal and nuclear power plants. i R is the radical waste disposal cost of the ith type power generation technology, such as nuclear power generation will produce radical waste. i R is a proxy variable of social communication cost, this reflect the social acceptability for the type of power generation technology, i.e., i R = 0 for renewable energy.

Expected Risk of Power Mixed
Portfolio theory was initially conceived in the context of financial portfolios, where it relates expected portfolio return to expected portfolio risk, defined as the year-to-year variation of portfolio returns. The expected portfolio cost constraint as follows: (refer to Awerbuch and Spencer, 2007) [3].
where ( ) t E σ is the expected portfolio risk of power plants and t σ is the standard deviation of holding period returns (HPR) of power plants. HPR is an important indicator of investment efficiency. It refers to the rate of return within the unique period between purchase and sale. HPR = (EV-BV)/BV. EV means the value in the end; BV means the value at the beginning. In this study, the standard deviation of HPRs calculates the changing rate in costs from year to year (Awerbuch and Spencer, 2007) [3]. The risk of power generation is determined by the holding period returns. This study assumed that the risks of the two power generation technologies are 1 σ and 2 σ , respectively, and 12 ρ is the correlation coefficient of these two power generation technologies. Lower 12 ρ implies higher complementarity between power generation technologies. This shows more reliability of the power system, or lower expected risk. Thus, Equation (3) indicates that the expected portfolio risk of the power generation system is lower than the reasonable ex- Equation (3) indicates that the social planner should control the expected portfolio risk of the power system to be lower than the reasonable expected portfolio risk ( 0 σ ), that is, the social planner should control the expected portfolio risk within the reasonable range. Therefore, Equation (4) is used to reflect the reliability as well as economic feasibility of power generation mixed.

Equation of Capital Accumulation
The motion equation of the model as follows: where it K  is capital stock accumulation for the ith type of power technology in the tth period; it I is the investment in the ith type of power technology in the tth period; i δ is capital depreciation rate for the ith type of power technology (assumed to be constant). It is assumed that in addition to being a function of fuel input, power production is also a function of the capital stock, i.e.,

Greenhouse Gas Emissions Equation
Assuming net greenhouse gas emissions ( it E ) are gross greenhouse gas emissions ( 0 it e F ) minus the emissions abatement ( t A ): where 0i e is the coefficient of unit greenhouse gas emissions for the ith power technology (assumed to be constant). When 0i e lower means that more clean power generation technology is adopted. A higher t A means that carbon-reduction technology, such as carbon capture and storage (CCS), is actively adopted and the net emissions ( it E ) are therefore lower.
Assuming the upper limit of net greenhouse gas emissions for the power generation in the end of the year is T E , T is the end of the year (or target year, i.e., 2050), the net greenhouse gas emissions must satisfy the following equation:

Power Security
Assuming electricity demand for each period is it Q (exogenous variable), the following must be satisfied to achieve power security: This reflects the reliability of the power supply system while capturing either long term demand management actions or the ability to reduce demand in the short term response for peak-load management.

The Optimal Power Portfolio Model
To achieve the power security (Equation (7)) and greenhouse gas emission target (Equation (6)) by 2050, it is necessary ensure power reliability and expected portfolio risk of power system (Equation (3)). The cost effectiveness of the optimal control problem by the social planner is as follows: The current value of Hamiltonian and Lagrangian function (subscript t is omitted) are expressed in Equations (8) and (9): where i m is the co-state variable of capital stock, or shadow price (Shadow price means the market value of capital in each term), while λ , µ , and θ are the Lagrangian multipliers of reasonable expected portfolio risk, greenhouse gas emissions target, and power security, respectively. To quantify the power supply mixed, this study assumes that power generation function is a Cobb-Douglas (C-D) function with constant return to scale (CRTS), i.e., . This is a typical production function in economics and indicates that if all the input factors (capital and fuels) increase t times, then the output (power generation) would be increased t times. α is a constant parameter capturing the role of technology-the output elasticity of input factors, and lies in the interval 0-1, i.e., 0 1 α ≤ ≤ . i ϖ is the power production capacity factor (capturing how much electricity is generated given the capital per year).
With investment Ii > 0, the optimal solution must satisfy the following conditions ( ∀ i): The optimal power generation mixed can be estimated using Equation (10). It is obvious that power production per capacity is affected by various parameters, which include technology factor (α ), depreciated rate ( i δ ), fuel cost ( i F P ), abatement cost ( Ai P ), emissions coefficient ( 0i e ), investment cost ( Ii P ), and discount rate ( r ), respectively. However, for the convenience of calculation, the unit power generation cost of various power generation technologies will be substituted for

The Unit Power Generation Cost Prediction under Uncertainty
This research refers to the risk neutral probability method of real option analysis (ROA) (Copeland and Antikavro (2001) [22], which will incorporate the cost randomness of various power generation technologies, then estimate the pathway of unit power generation costs by 2050.

The Average Growth Rate of Unit Power Generation Cost
This applies the ROA method to estimate the growth rate and decline rate of unit power generation cost of various power generation technologies as follows: This study collected the unit power generation cost (US$/kWh) of various power generation technologies of the Taiwan Power Company (2016) [23] (see Table 1). The unit cost of oil-fired power generation reached 0.15 US$/kWh, which was the most expensive, but the unit cost of nuclear power generation was only 0.04 US$/kWh, which was the cheapest. Further, the study estimates the average annual unit power generation cost growth rate ( g ) of various power generation technologies from 2005 to 2015 (see Table 1). This show that nuclear has the highest average annual growth rate (10.92%) of unit power generation costs, but gas has the lowest average annual growth rate (1.18%) of unit power generation costs.

The Change Rate of Unit Power Generation Cost Estimation
(1 ) where u is the increasing rate of unit power generation cost, d is the decline rate of unit power generation cost, g is the annual average growth rate of unit generation cost and t is the interval of each stage (let t = 5). The u and d values of various power generation technologies are summarized as shown in Table 1.
x and 1 − x are the ascending path allocation ratio and the descending path allocation ratio respectively (refer to Copeland and Antikavro (2001) [22]). This study uses the risk-neutral probability method, such as Equations (11) and (12), to calculate the ascending (x) and descending (1 − x) path allocation rates. Substituting the risk-free interest rate ( 1.18%  (12) and (13), we can get the distribution ratios of various annual growth and decline rate of various unit cost of power generation technology. The results are obtained of various parameter, see Table1.

Capacity Factor and Technology Factor
The study collected the capacity factor ( i ϖ ) of various power generation technology form the Taiwan Power Company (2016) [22], as shown in Table 1. This indicates that nuclear and coal-fire have the highest capacity factors of 89.9% and 88.87%, respectively. This reflects the characteristics of the base load of this two power generation technologies. The capacity factors of pumped-storage and oil-fired are the lowest, 13.5% and 18.6%, respectively.
To simplify the analysis, the research assumes technology factor (α ) as shown in Table 1. Then, a form of long-term random unit cost power generation trajectory is shown in Figure 1.

Long-Term Unit Cost of Power Generation Estimation
Taking the unit coal-fired power generation cost as an example, the growth rate of coal cost is 1.185% and the decline rate is 0.844%. Then, the unit cost at different stages can be calculated. See the calculation method in Figure 1. It could be obtained that the highest unit cost of coal-fired power generation by 2050 can rise to 0.086 US$/kWh, and the lowest can be reduced to 0.025 US$/kWh (see Table 2). The calculation of other power generation unit costs is the same way.
The article divides the random fuel cost of future power generation technologies into high, medium, and low case for analysis. The high case is the average cost of each year greater than or equal to the median value (including the median value), and the medium case is the average of all random costs. The low case is the average cost of each year less than or equal to the median value (including the median value). Taking the unit cost of coal-fired random power generation as an example, there are two cost values in 2020. The high cost is 0.173US$/kWh and the low cost is 0.122US$/kWh. The average cost is 0.147US$/kWh (see Table 2). The calculation of other power generation unit costs is performed the same way.  Table 3).

Reasonable Risk Value by 2050
Reasonable risk value refers to the risk value of the power generation technology portfolio that could maintain sufficient economic dispatch of the power generation system (Awerbuch and Spencer, 2007;Huang and Lee, 2019). The economic dispatch of the power generation system portfolio should get better. This article sets the risk value (0.2537) in 2015, which is the default value of the reasonable risk value. This means that the risk value of the future power generation mixed must be less than 0.257. We calculate the long-term trajectory of the risk value of the power generation technology portfolio as shown in Table  3 3

Optimal Power Generation Mixed
The Taiwanese government has set a goal for a nuclear-free country by 2025. This study assumes that, after 2025, the nuclear power generation ratio will decline to zero. Based on this, the research takes a medium-scenario fuel cost as an example (see Table 2), subject to the conditions and restrictions of each period in Table 3. Putting the relevant parameters into Equation (10)-as data on the marginal cost of carbon reduction in the power generation sector is not easy to obtain, in order to simplify the analysis, the cost of abatement ( A P e ) is not calculated-we obtain power generation mixed by 2050, as shown in Figure 2. Figure 2 was showed the optimal power generation technology mixed during the period 2020-2050 in Taiwan. It indicates that the unit cost of power generation will increase gradually from 2020 to 2050, from 1.81 NT$/kWh to 2.77 NT$/kWh. The share of renewable energy and gas power will increase gradually, as the former will increase from 16.11% (2020) to 52.67% (2050) and the latter will increase from 16.42% (2020) to 17.82% (2050). In contrast, the share of coal-fired power will decrease from 33.43% (2020) to 25.64% (2050).
Renewable energy is carbon-free and complementary to fossil fuels. It has the advantage of reducing risk value, but the disadvantage of high cost. Therefore, it can meet the CO2 target and reasonable risk value at the same time. Under the condition of reasonable risk value, the ratio of renewable energy power generation should be maintained at about 25%. Especially after being nuclear-free by 2025, the ratio of renewable energy is the key power generation technology to support the national low-carbon target and the low risk value of the power generation system. Gas-fired power generation has low-carbon advantage, but high cost and substitution with other fossil fuels, having the disadvantage of increasing the value of risk. Therefore, after being nuclear-free by 2025, although the share of power generation will be greatly increased by 31% (additional low-carbon requirements), it can only be maintained at a ratio of slightly higher than 30%. Coal-fired power generation has low cost, but high CO2 emissions and its substitution with other fossil fuels, this disadvantage for improving risk value. Therefore, after being nuclear-free by 2025, although the share of power generation will be slightly increased by 39% (to supplement the power supply security and low-cost requirements), as the proportion of renewable energy and gas power generation increases, coal-fired power generation will suffer from high CO2 emissions restrictions, as the mixed power generation will drop slightly to 38%.

Optimal Electricity Saving Planning
This article aims to limit the country's electricity demand through long-term optimal power generation. This method is feasible and necessary under the development of net zero emissions, because hydrogen energy and decentralized grids and other energy saving innovation are under schedule in the agenda and could be used to greatly reduce electricity demand.
In the following sections, we will use the STIRPAT model with PLS regression to predict the electricity demand baseline (or business as usual), then provide the optimal electricity saving trajectory by 2050.

STIRPAT Regression Model
Dieta and Rosa (1997) [24] proposed the STIRPAT (Stochastic Impacts by Regression on Population, Affluence, and Technology) model, it has been widely used in forecasting for various economic activities (York et al., 2003) [25]. This study chooses two key variables, GDP per capita and energy intensity, affecting power consumption in the ATIRPAT model. GDP per capita captures both the population and affluence as two variables, and energy intensity describes energy technology. The STIRPAT model can be expressed as Equation (14): where t E is the electricity demand in year t; t GDPP is the GDP per capita in year t; t EGDP is the energy intensity in year t; 0 a is constant term; 1 α and 2 α are the regression coefficients of variables of GDP per capita and energy intensity respectively; t ε is the error term.

Data Collection and Settings
This study uses the "Energy Statistics Manual" published by the Bureau of Energy [26] in 2015 to collect data on electricity demand and energy intensity. It also uses the statistics information network of the Republic of China to collect data on per capita GDP and energy intensity. The year range for the completeness of the data is from 1998 to 2015.
This study aims to predict the medium and long-term electricity demand in Taiwan. It is planned to set the forecast value for each independent variable, as shown in Table 4. Per capita GDP is estimated based on data from the past 10 years (2006 to 2015) and an average annual growth rate of 2.92% is calculated. The energy intensity is estimated based on the data from 1998 to 2015, and the annual average decline rate is calculated to be 1.45%, while electricity demand is estimated by using the model established by the regression results to bring in the predicted values of the respective variables for medium and long-term estimation. Based on this, this study estimates the predicted values of each variable in 2020, 2025, 2030, 2040, and 2050, as shown in Table 5.

Prediction of the Electricity Demand
The correlation of the independent variables of the STIRPAT model is shown in Table  6, where the variables have a high linear correlation. Therefore, this study uses the partial least squares regression (PLS-R) method for regression analysis. The results of PLS regression as shown in Equation (15), which present that all variables are 1% significant (See Table 7). This study further calculated the mean absolute percentage error (MAPE) based on the actual electricity demand from 1998 to 2015. As shown in Figure 3, the MAPE value is very small (0.019), indicating that the regression equation (Equation (15)) has a high accuracy for the electricity demand prediction.

The Trajectory of Electricity Saving by 2050
Under the regression equation of Equation (15), the prediction of electricity demand from 2020 to 2050 is shown in Table 8. It shows the electricity demand going up along with time, from 302,002 GWh in 2020 to 622,358 GWh in 2050. Since electricity saving is the priority strategy to achieve greenhouse gas emissions targets and maintain power supply security, this study can calculate the power saving requirements for each period in the future, such as 52,712 GWh/year (

Conclusions
This research considers long-term power generation portfolio planning that simultaneously meets the requirements for power generation security, greenhouse gas reduction targets, and reasonable risk value. While the model developed is new, it provides significant policy implications. In terms of research methods, this research uses an optimal control model to establish a theoretical basis for calculating the long-term dynamic path of various the power generation mixed, which is innovative in terms of methodology. Meanwhile, this research uses the theory of real options to capture the randomness of long-term unit power generation costs of various power generation technologies. This study points out that the target power generation mix set by the Taiwanese government for 2025 is not consistent with a low-carbon transition. Indeed, the share of renewable energy should be increased to 25% to reflect its complementarity with other power generation technologies for the economic dispatching requirements of a power system. Being environmentally friendly and socially acceptable, the ratio should be maintained at about 25% to maintain the reliability of the power generation system (low risk value). The coal ratio should be adjusted to reflect affordability and economic efficiency, and in the medium and long term, it should be controlled below 40% to match the requirement of affordability. The share of natural gas should be reduced for affordability, and in the medium and long term, it should be maintained at about 30% to reflect the environmental friendliness of lowcarbon energy. Furthermore, we apply the STIRPAT model with PLS regression to predict the electricity demand baseline (or business as usual), providing a feasible electricity saving trajectory by 2050.
This article tries to adopt a viewpoint of sustainable development, which evaluates the country's long-term power mix. Therefore, the research approach is different from the traditional view. This article aims to limit the country's electricity demand through the principle of "supply dictates demand". The result is feasible under the development of low carbon technology, like hydrogen energy and decentralized grids, as well as other developing rapidly innovations in climate finance which could be used to greatly reduce electricity demand.