Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 8180674, 15 pages

http://dx.doi.org/10.1155/2016/8180674

## Evaluating CCS Investment of China by a Novel Real Option-Based Model

School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China

Received 22 September 2016; Revised 4 November 2016; Accepted 9 November 2016

Academic Editor: Leonid Shaikhet

Copyright © 2016 Hongrui Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Carbon capture and storage (CCS) technology is an effective method to mitigate CO_{2} emission pressure; however it is hard to be evaluated due to uncertainties. This paper establishes a real options analysis (ROA) model to evaluate CCS investment from the perspective of the existing thermal power plant by considering the fluctuations of electricity price, carbon price, and thermal coal price. The model is solved by the proposed robust Least Squares Monte Carlo method and China is taken as a case study to assess power plant’s CCS investment revenue. In the case study, robust ROA and ROA are compared under some CCS incentive factors. The results indicate that the proposed robust ROA is more realistic and suitable for CCS evaluation than common ROA to some extent. Finally, a policy schema to promote CCS investment is derived.

#### 1. Introduction

Global greenhouse gas (GHG) emissions exacerbate global warming and make major contribution to climate change. International Panel on Climate Change has reported that approximately 35% of total anthropogenic GHG emissions were attributed to energy supply sector in 2010 [1]. Currently, the mitigation efforts of GHG emissions, especially CO_{2}, have focused on innovations of energy sector, such as renewable energy sources and Clean Development Mechanism [2]. Although those ways can reduce GHG emissions significantly, they are not able to completely replace fossil energy to meet future energy needs. In 2013, 41.3% world electricity is generated by coal. Most countries of the world will still use fossil fuels as their primary energy resource in the future.

Great attention has been paid to carbon capture and storage (CCS) technology which would significantly reduce CO_{2} emission, especially for developing countries which take coal as the primary energy resource. China has become the biggest coal consumer and ranks the first place in terms of CO_{2} emissions due to the rapid development, great pressure of air pollution, and energy security which has been posed to China. According to statistics released by the National Bureau of Statistics [3], China’s coal consumption is about 70% of total energy consumption and more than 75% of electricity is generated by coal combustion. CCS technology is deemed as an important approach to significantly reduce CO_{2} emissions with the purpose of maintaining fossil fuels usage in China power industry. In order to establish a nationwide carbon market and achieve the emission target in 2020, China has launched seven regional pilot carbon trading systems during 2013 to 2014 and drafted the regulations for national CO_{2} market in 2016. Although regional carbon exchanges have been operating for a certain time, trading activities are depressed and companies have little incentive to buy carbon credits.

An integrated CCS system has three distinct components involving capture, transportation, and storage which need large-scale facility investments [4]. However, high operation costs and future revenue uncertainties place power plants in a dilemma to implement CCS retrofit under the stringent CO_{2} emission restrain [5]. In this context, an in-depth cost-benefit analysis of CCS retrofitting is required, and effective economic incentives should be implemented to trigger CCS deployment of electric plants.

There are numerous uncertainties in CCS investment, such as climate policy, CCS cost, fossil energy price, power plant lifetime, and technological feasibility. Those uncertainties are conspicuous obstacle to deployment of CCS technology, particularly in developing country like China. As to climate policy, Australian parliament repealed carbon tax after two years’ fierce debate in 2014; Canada became the first country who announced withdrawing from the Kyoto Protocol in 2011. Therefore, the trend of future climate policy is unpredictable, and it affects the implementation of carbon tax system directly. On the other hand, CCS uses a combination of processes and technologies; some of them have not been proven at large scale or still in the research and development (R&D) stage, so it is hard to predict CCS investment cost. In addition, coal price has ridden a roller coaster of booms and busts around 2009 and has been falling since 2014; it brings a significant effect on generating cost of thermal electric plant. Furthermore, CCS deployment will decrease energy conservation and efficiency of power plant, in turn consume 10–40% more energy, and increase 10–60% more generating cost than the same power plant without CCS [6]. Therefore, it is difficult for power plants to implement CCS investment, and CCS cost is a vital economic challenge that must be overcome.

This paper integrates real options theory with robust technology and then applies it to evaluate the CCS investment from the perspective of electric plants. The uncertainties of electricity output price, fuel input price, and carbon price are taken into consideration in the model establishment; then the investments value of CCS can be evaluated in the simulation period which will help electric plants make a decision of whether to adopt CCS technology. With taking China’s energy plant as a case study, the effects of initial carbon price, operations management cost, generating subsidy, and investment subsidy are analyzed. The proposed model can help electric plants to make investment decision and can also help government trigger energy plants’ CCS investment in current China energy situation.

#### 2. Literature Review

Although CCS technology has not been applied extensively, many researches have paid attention to CCS technology development and CCS policies. For technoeconomic analysis of CCS project, the conventional approach is discounted cash flow method (DCF) with the criterion of net present value (NPV). For example, Sekar et al. [7] performed an NPV analysis to determine the carbon price levels and growth rates which would be used to justify whether to build a baseline IGCC plant. Bohm et al. [8] estimated the lifetime NPV costs of power plants with different carbon capture preinvestment levels; they showed that a baseline PC plant is the most economical choice under low carbon prices while IGCC plant is preferable at higher carbon prices. NPV criteria decision is predicted based on current information and does not have the capabilities to deal with the future uncertainties. However, CCS technologies have not been driven to mature stage; power plants with CCS investment will be influenced by many factors; along with irreversible CCS investment cost, it is clear that NPV is not suitable for CCS investment evaluation.

In practice, companies usually postpone a project instead of making decision immediately to avoid huge sunk costs [9]. Real options analysis (ROA) is a proved effective method to evaluate projects with uncertain future revenue; it gives decision-maker the opportunity to postpone judgment. So ROA is more suitable for large-scale investment project evaluation and received great attention to assess green and sustainable development projects recently. Although investment ROA strategy in the power sector has developed in less than twenty years, there are many excellent research findings. At the earliest, Kaminski [10] pointed out the growing importance and usefulness of real options and risk management in power plant operations and project valuation. Then Hsu [11] first used spark-spread options technique to tackle power plant valuation problem. After that, ROA was widely applied to evaluate power investment, including short-term power plant valuation [12] and Clean Development Mechanism (CDM) project valuation [13].

In order to capture specific characteristics, some researchers have applied ROA to evaluate CCS investment. Classified by real options solving techniques, Abadie and Chamorro [14] used binomial lattice method to assess CCS options value of a coal-fired power plant in a carbon-constrained environment. Fuss et al. [15] used Monte Carlo simulation to solve a real options CCS investment model. And Zhang et al. [16] developed a trinomial tree modeling-based real options approach to analyze the investment of CCS technology. Classified by uncertainties involved in models, both Abadie and Chamorro [14] and Fuss et al. [15] supposed that the carbon emission price and the electricity output price are uncertain. Szolgayová et al. [17] presented a real options model with stochastic electricity and CO_{2} prices; they also analyzed the effect of price gaps. Zhang et al. [16] considered multiple uncertainties such as carbon price and government subsidy. There are also some researchers focusing on types of power plants and CCS technologies, such as Zhou et al. [9] who adopted a real options analysis to estimate the value of the CCS technology application to three kinds of power plants by considering the uncertainties of electricity price, fuel price, and emission allowances price. Heydari et al. [18] developed an analytical real options model for a coal-fired power plant to evaluate the choice between two available emissions-reduction technologies, full CCS technology and partial CCS technology.

Previous researches usually evaluated CCS investment by innovative real options solving methods or considering specified conditions. For CCS technology investment can be seriously affected by the above-mentioned uncertainties, which leads CCS investment options value to change largely; in order to handle this problem, a robust optimization method is used for CCS evaluation in this paper. It is widely recognized that optimal solution is highly sensitive to the perturbation of input data and may even be infeasible in some worse cases, so many approaches are proposed based on parameter uncertainty. One popular approach is robust optimization which assumes that parameters exist in a given “uncertainty set.” After Soyster [19] first studied explicit approaches to solve robust optimization problems, the robust approaches have been extensively studied and extended (see [20, 21]). For robust least squares problems, El Ghaoui and Lebret [22] disposed them by minimizing the worst-case residual error using second-order cone programming, and Chandrasekaran et al. [23] solved total least squares with bounded uncertainty by a Min-Min Model. In this paper, we use robust least squares to improve Least Squares Monte Carlo approach.

This paper adopts robust optimization theory to reform Least Squares Monte Carlo technique for evaluating real options value of power plant’s CCS retrofit. Based on collected data and previous research, CCS investment of China’s electric plants is evaluated in a given observation period. This study attempts to analyze CCS investment in a novel approach which is different from previous studies. At first, this paper considers three uncertainties of CCS investment, fuel price, electricity price, and carbon price, and simulates electricity price by a mean-reverting process which has been verified but rarely used in previous related research. Secondly, we collect historical data of China’s energy sector from reliable institutions and then calculate regression parameters based on the processed data which can ensure the reliability of case study. Thirdly, the proposed robust ROA method presents different results compared with common ROA. And we illustrate that robust ROA is more realistic and suitable for CCS evaluation than ROA to some extent. Then the effects of carbon price, cost reductions, and subsidies for CCS investment are analyzed by three scenarios which provide implications for electric plants and government. At last, a policy approach to trigger CCS investment is proposed for launching an effective national carbon market.

#### 3. Modeling Description

We assume that it should be decided whether a coal-fired power plant be retrofitted with CCS technology when government implements carbon tax system. Based on available research framework, we evaluate CCS cost saving value from the view of power plant. The CCS profit comes mainly from certified emission reduction; the cost refers to investment cost and efficiency penalty. Three sources of uncertainty, electricity output price, fuel input price, and carbon price, are taken into consideration for CCS investment valuation. We take fuel input price as uncertainty instead of generating cost because fuel is the most uncertain factor to generate electricity, and generating cost is usually stable once the power plant is fixed. Price series models of carbon, electricity, and fuel are given in the following before calculating CCS investment options value.

##### 3.1. The Model for Electricity Output Price

Unlike common commodity, whose market prices are compelled by the supply and demand relationship, traded electricity cannot be stockpiled in electricity market. The feature of grid electricity makes its price curve exhibit high frequency, mean reversion, and multiple seasonality effect. There are numerous methods that have been developed for forecasting electricity spot price, and a brief survey given by Geman [24] found that electricity price displays the trends of mean reversion, seasonality, and stochastic volatility which are also recognized in other literatures. Therefore, we assume that the electricity price follows a mean-reverting process:where is electricity price at time , is drift parameter that denotes the long-run equilibrium value, is the speed of mean reversion, and stands for instantaneous volatility. represents the increment of a Wiener process, , where is a random variable of standard normal distribution. Here we ignore the correlation between thermal power price and CCS electricity price.

##### 3.2. The Model for Carbon Price

Carbon credit price is the most important component in carbon trading system and the biggest factor to CCS technology investment; to investigate the effect of carbon price volatility, accurate forecasting model is needed. Geometric Brownian Motion has been employed in most previous CCS investment researches to depict carbon price series; the model can be described by the following equation:where is carbon allowance price at time , stands for the expected growth rate, and represents the instantaneous volatility of the carbon price. is independent increments of the Wiener process, , where denotes a standard normal variable.

##### 3.3. The Model for Fuel Input Price

The costs of power generation mainly contain operational cost and fuel cost. In general, fuel cost has a greater impact on power plant’s revenue than operational cost. Pindyck [25] found that fuel prices have significant mean-reverting effect by examining the prices of oil, coal, and natural gas in the United States. According to Pindyck’s recommendation, Geometric Brownian Motion model is widely accepted to formulate fuel prices in investment analysis (see [18]). In this paper, we also assume that fuel price follows a Geometric Brownian Motion:where is the fuel price for thermal power, is independent increments of the Wiener process, , where is a standard normal random variable, and and represent the drift and variance parameters, respectively.

##### 3.4. Valuation of CCS Cost Saving

The problem of evaluating power plant’s cost saving after retrofitting with CCS technology is usually solved by maximizing the total discounted expected profits over the planning horizon. The electric plant’s annual profit is total revenues minus total costs, the revenues are derived from selling electricity and carbon credit, the costs refer to fuel cost, CCS operational and maintenance cost, and CCS implementation cost. Let denote whether the CCS module is running at time ; is the executed action at time . So the profit of power plant at time can be expressed aswithwhere is electricity generation capacity, represents CCS carbon emission rate, and is fuel conversion efficiency in CCS power plant. , , and represent electricity output price, carbon price, and fuel input price, respectively. refers to operations management cost of CCS; denotes the CCS module deployment cost if CCS technology is adopted; otherwise it equals zero.

##### 3.5. Robust Model for Least Squares Monte Carlo Simulation

The least squares method is a standard approach to estimate parameters in regression analysis by minimizing the mean-squared error over all estimators. For a linear least squares problem, a solution should be found to fit the equation with the given matrices . The least squares method minimizes residual subject to ; is 2-norm. However, the elements of matrix are usually subject to errors since they are measurements. The total least squares solution finds the smallest error subject to the consistency equation and provides Maximum Likelihood estimate for when the errors in and are independent and identically distributed Gaussian noise [26]; is Frobenius norm. Then El Ghaoui and Lebret [22] presented a robust least squares (RLS) by Min-Max techniques to the following optimization problem:

The robust least squares minimizes worst-case residual over a set of perturbations, and the obtained solutions deviate more from the least squares solution when the bound gets larger. If , it recovers the standard least squares problem. For every , can be represented as . El Ghaoui and Lebret [22] proved that when , the worst-case residual can be given bywhich can result in a unique solution by minimizing over and can be formulated as a second-order cone programming (SOCP):

Using duality theorem, the optimal solution of problem (8) is where is the unique optimal point for the problem. denotes the Moore-Penrose pseudoinverse of :

This paper uses robust technique to improve the Least Squares Monte Carlo method for options evaluation, the robust least squares will be embedded for the uncertainty revenue of CCS power plant, and SOCP model (8) is used to calculate options values instead of common least square regression for Least Squares Monte Carlo method.

Before giving the case study, we take a comparison of LSM method and robust LSM method by a simple options pricing example. Considering American style call options, we assume that the asset price , the exercise price , the risk-free interest , and the asset volatility . During period , the holder can exercise the option at time . We calculate the option price with 10,000 paths and duplicate the experiment ten times. The results indicate that robust LSM has higher options value than LSM method under the given parameter setting, in which LSM option price is 36.8683 and robust LSM option price is 38.7645.

#### 4. Assumptions and Data Collection for Case Study

China is taken as a case study to evaluate CCS investment by the models established in Section 3. In Chinese power sector, most electricity is generated by the conventional thermal power plants which confront big challenges from increasingly strict environmental policies. CCS technology could ensure the normal production of thermal power plants without emitting lots of greenhouse gases, but it should be well evaluated before installation for high cost. Before taking the case study, some assumptions are given first.

We choose a conventional coal power plant to evaluate CCS cost saving from 2015 to 2035. We assume that a national carbon market will be launched in 2017 and ignore the deployment time of CCS module. At present, carbon credit is the most common carbon emission mitigation policy; this policy gives enterprises carbon emission limit; each enterprise must buy the credit from carbon market if its carbon emission beyond the threshold, and enterprises also can benefit from selling carbon credits by implementing low carbon technologies. We suppose that carbon credit system with volatile price mechanism will be adopted for carbon market and ignore the effects of other climate policies.

Relevant data is collected from China Energy Statistical Yearbook [3] and China Electric Power Yearbook 2014 [27]. And some other parameters are investigated or estimated based on previous related literatures [9, 28]. Table 1 shows the assumptions of parameters.