key: cord-0173196-w34jytyj
authors: Liu, Yue; Tian, Lixin; Xie, Zhuyun; Zhen, Zaili; Sun, Huaping
title: Option to survive or surrender: carbon asset management and optimization in thermal power enterprises from China
date: 2021-04-10
journal: nan
DOI: nan
sha: 0d1e327ac4963c7103cc77d2d763908235a2da0f
doc_id: 173196
cord_uid: w34jytyj

Carbon emission right allowance is a double-edged sword, one edge is to reduce emission as its original design intention, another edge has in practice slain many less developed coal-consuming enterprises, especially for those in thermal power industry. Partially governed on the hilt in hands of the authority, body of this sword is the prices of carbon emission right. How should the thermal power plants dance on the blade motivates this research. Considering the impact of price fluctuations of carbon emission right allowance, we investigate the operation of Chinese thermal power plant by modeling the decision-making with optimal stopping problem, which is established on the stochastic environment with carbon emission allowance price process simulated by geometric Brownian motion. Under the overall goal of maximizing the ultimate profitability, the optimal stopping indicates the timing of suspend or halt of production, hence the optimal stopping boundary curve implies the edge of life and death with regard to this enterprise. Applying this methodology, real cases of failure and survival of several Chinese representative thermal power plants were analyzed to explore the industry ecotope, which leads to the findings that: 1) The survival environment of existed thermal power plants becomes severer when facing more pressure from the newborn carbon-finance market. 2) Boundaries of survival environment is mainly drawn by the technical improvements for rising the utilization rate of carbon emission. Based on the same optimal stopping model, outlook of this industry is drawn with a demarcation surface defining the vivosphere of thermal power plants with different levels of profitability. This finding provides benchmarks for those enterprises struggling for survival and policy makers scheming better supervision and necessary intervene.

In the global blueprint of carbon emission reduction, China is expected to share a great mission in this campaign [1] , and now is the in the great march towards carbon neutrality. From the establishment of carbon emission trading pilot projects in seven provinces and cities in 2011 to the formal launch of carbon emission system in 2017, the volume of China's carbon trading market has expanded rapidly, with a cumulative trading volume of nearly 400 million tons, and the emission reduction of CCER projects has exceeded 300 million tons. However, behind the booming carbon market, there are huge burdens of carbon emission on the shoulders of industries like steel, petrochemical, cement, and thermal power. Since Chinese coal price was increasing in recent years, thermal power industry is under more pressures, more than one hundred of thermal power enterprises went bankrupt. This trend is growing, thanks to the 'Big up small down' scheme, that is, to put forward the big generator sets and oppress the Carbon emission allowance is the core asset in carbon finance market, it transfers the government's restraint in carbon emission to the enterprises in form of its prices.

Hence for those companies, carbon asset operation becomes a crucial aspect of enterprise operation. To describe the strategy and actions during the carbon asset operation, Markov decision process is applied to simulate the decision-making as in [2] for energy storage system, [3] for management of greenhouses, [4] for optimizing energy conversion and [5] for micro-grid power optimal control. Paralleling to the approach of Markov decision process, optimal stopping model is also usually used to characterize the timing of decision and operation, especially for those financial environments with continuous dynamic of price process, see [6] for asset trading strategy and [7] , [8] , [9] for option pricing. The former has its advantage of describing the decision-making for all points in the time horizon, while the later seeks one or limited several (multiple optimal stopping times) timings for some specific action and it handles both discrete and continuous environment. In the operation modelling of this paper, we mainly focus on the time to suspend or halt production under pressure of profitability and the decision is under consideration of time-continuous price dynamic, hence optimal stopping problem is established after modeling the price process with geometric Brownian motion, which is commonly used to simulate the variable on continuous time horizon, as applied in [10] for price forecasting, [11] , [12] for stock trading, [13] for risk analysis and hedging.

There have been intensive researches on the topics of carbon emission allowance, carbon capital operation and thermal power plants. Thermal power is one of the most signification industries contributing to carbon reduction, especially the clear power resources like solar thermal power, which has been developed fast and taken an increasing share of power industry, as shown by [14] and [15] . More researches were about its technical specialties, like its performance (see [16] and [17] ) and parabolic trough (see [18] - [21] ). Besides, its technical and economic potentials are widely and repeatedly analyzed, as in [22] and [23] . Compared with those above mentioned with researches on traditional thermal power like [24] and [25] , concerns for the coal powered plants are emerging since it appears that the shifting of weight was speeding up in the thermal power industry, which arguments are supported by perspectives from [26] .

Specifically when taking a close check over this industry in China, they tend to believe that survival environment of traditional thermal power plants is shrinking for several reasons, one is increasing in the overall cost (see [27] for more information), influenced mainly by the prices of stream coal and carbon emission allowances, another is the restrained electricity selling price, which is generally not very market-orientated, but more governed by the authority. Under pressures from both ends, hundreds of plants have been squeezed out, survivals may have their distinctive advances in emission reduction technology (as shown by [28] and [29] ), cost control (such as those in [30] and [31] ), efficiency improvement (as proposed by [32] and [33] ), or operation management optimizations (refer to [34] and [35] ). Integrating all aspects from technical escalation, operation management and market impact, we aim to investigate the sur- We proceed as follows. In Section 2, price process of carbon emission allowance is modeled by geometric Brownian motion and the optimization of operation management with carbon asset is modeled as an optimal stopping problem, which is analyzed and algorithmically solved in Section 3. By solving the relevant optimal stopping Finally, Section 7 concludes to the theoretical and case analysis before illustrating some management implications and suggestions.

To formulate the core problem in the scenarios of operation management with carbon asset of a coal-powered plant, we define several variables first. Let M ∈ IR + denote the averaged daily emission, (Y t ) t∈[0,T ] denotes the price of carbon emission right at time t ∈ [0, T ], where [0, T ] is the production cycle. During this cycle, the averaged profit achievable at cost of a unit of carbon emission is denoted as P ∈ IR + .

Hence if the price of carbon emission right Y t is always well above the profit P , this enterprise will consider a reduction or halt of output. This decision might not be taken immediately once the price Y t excesses P since some fluctuation of price may create price peaks occasionally and influence little on the judgement of the long-term behavior of price process. However, in view of the probabilistically expectation of the comparison between price Y t and profit P , if maintenance of production for the whole time horizon [0, T ] will finally yield inferior results, towards the target of ultimate maximization of total net profit, this enterprise will optimize an halting time to quit this process of loss and we assume it will finally sell out the remaining carbon emission right at time T . This stopping time is denoted as τ ∈ [0, T ]. Obviously, an extreme case that τ = T illustrates that production sustains during this whole cycle and the enterprise is in no need of such intervene. In this case, total carbon emission during the production cycle is M T , and the total profit becomes M T P . For the general case with consideration of production halt, total profit R(τ ) will be expressed in the reward formula without excluding the extreme case τ = T . As follows, the reward function of optimal stopping time is defined:

To simulate the carbon emission right price process (Y t ) t∈[0,T ] , we simply apply a geo-metric brownian motion as many existed researches did to capture the price dynamic:

where µ ∈ IR + is the drift factor and σ ∈ (0, ∞) is the volatility factor, (B t ) t∈I R + is a standard Brownian motion, we denote F t as the filtration generated by σ{B s ; s ∈ [0, t]}. The solution to the stochastic differential equation (2.2) is given by

for more details, we refer to [36] .

Since enterprises are aim to maximize the final profit, we search for an optimal stopping time τ * among all possible stopping times τ ∈ [0, T ]. This stopping time τ * is theoretically optimal in a sense of achieving the ultimate profit maximization, which is in form of the following optimal stopping problem:

of which the solution τ * satisfying the equation that V = IE[R(τ * )]. For further investigate this optimal stopping problem, we define the value function V (t, y) as follows for t ∈ [0, T ] and y ∈ IR + :

To justify the existence of the optimal stopping time according to [37] , we need to define a function G(t, y) that

and check some boundedness and smoothness conditions as follows.

a) G(t, y) is lower semicontinuous with respect to y. This is easily checked by expressing G(t, y) after combining (2.1), (2.3) and (2.6): c) G(t, y) < ∞ by checking the expression (2.7).

Following the standard arguments as in [37] , [38] , [39] , we define a stopping set D by 3 Solution to the optimal stopping problem

(3.1) By (3.1) and applying strong Markovian property, we see that

Applying the result of exponential martingale to the formula above and by (2.7) of G(t, y), it follows that For any s ∈ [0, T ] and by the definition of optimal stopping time, by (3.2), we see

Hence we conclude that:

where P ∈ IR + is the averaged profit achievable at cost of a unit of carbon emission, this enterprise will maintain the state of production. Therefore,

In view of Proposition 3.1 and 3.2, a rough draft is drawn as Figure 2 below. The To solve this optimal stopping problem, it is most preferred to have an explicit expres-

However, this is not achievable in most cases. Particularly, for the optimal stopping problem (3.1) we considered, there is no standard approach to solve it by stochastic analysis and to conclude with a closed-from expression. Instead, with all parameters well collected, we can design a backward algorithm to compute b(t) numerically. The basic methodology is to calculate the value function after discretization of time horizon. Particularly, [0, T ] is discretized into a sequence

To solve the optimal stopping problem in (3.2), we consider the discrete optimal stopping problem of sup

The recursion relation is obtained in the following formula for i ∈ {0, . . . , n − 1} that

Accompanied with this formula, we design the algorithm whose pseudocode is attached in the Appendix. according to [40] and [38] below: 2) simulates the price process, which is applied in the model (3.2) . Hence to solve the optimal stopping problem (3.2), all parameters are ready as shown by Table 1 .

Next, implementing a backward recursive algorithm whose pseudocode is attached in the Appendix to solve the optimal stopping problem, we obtain the boundary and

show the actual operation with consideration of the carbon emission price in Figure 4 below. To interpret Figure (4) , we introduce the curves and nodes in this graph. The Table 3 : Parameters of the optimal stopping problem for analyzing the case of Wushashan power plant in 2019

For the above two cases, we implement the backward recursive algorithm whose pseudocode is attached in the Appendix to solve the optimal stopping problem. As shown in Figure 8 , two optimal stopping boundaries are plotted by regressing the computa- Solving the optimal stopping problems for different P values and collecting all boundary lines yield a surface in Figure 11 . Inspecting this graph from a vertical angle, for any state (t, p) that the P value at time t is p, we can find a unique point on the surface, denoted as (t, p, B(t, p)). Surviving or dying is illustrated by whether the carbon price is below or above B(t, p). From another angle, given carbon price Y t and at time t, a minimum value of P is detected on the surface to satisfy the survival condition that B(t, p) > Y t .

It is obviously observed that, for any fixed P ∈ [10, 40] , the boundary curve is decreasing in time t ∈ [0, T ] since the price trend of carbon emission allowance is downward as shown by Figure 10 regrading SHEA hence µ is negative. Besides, by raising the P value, boundary curve is also lifted accordingly, which is consistent with the cases of Wushashan power plant in 2017 and 2019. From another angle, considering the curve with increasing P and fixed t, slope of the curve turns milder. This observation indicates that, it gets comparatively tougher to uplift the optimal stopping boundaries when P is achieving a higher value. Unfortunately, we feel even more concerned when we realize that, this law of diminishing marginal utility is not isolate, it has already existed in the process of raising the P value by technical upgrades.

Comparing with Figure 10 , we seriously concern that, the survival environment of thermal power industry is tough since the high price of carbon emission rights al- 

Pushed by the great cause of carbon neutrality, the survival environment of thermal power industry becomes severer as carbon regulation turns stricter. Intuitionally, two directions towards survival are feasible, one is to reduce absolute quantity of carbon emission as the rule makers wish, another is to boost up the output value with the same consumption of carbon emission. See from several cases we presented above, both approaches can be achieved by technical upgrades and reflected on a key variable P value investigated in the above text, which counts for the averaged net profit generated by consuming per unit of carbon emission.

To illustrate the relation between P value and the viability of thermal power plants, an optimal stopping model is designed to exactly reflect their dynamic connection.

Once the model suggests a stopping, it means that suspending or halting of production right at that circumstance is the optimal choice compared with maintaining operation, this decision is made with respect to the maximization of ultimate profit. Applying the optimal stopping model based on the market data of 2020, we present the outlook of survival environment of thermal power industry in the near future.

By displaying the tipping benchmark of production halts, Figure 11 answers to the question that at least how much is the P value of a thermal power plant to survive under the pressure of high price of carbon emission allowance. The most important observation is, by increasing the P value, optimal stopping boundaries will rise accordingly. Besides, we find that, when the price of carbon emission allowance is in a upward (downward) trend, the boundary curves are also increasing (decreasing) in t ∈ [0, T ].

Given the price of carbon emission allowance continues the existed trend and the SHEA price maintain the level around 45 CNY, thermal power plants are compelled to ensure their P value (namely the averaged net profit generated by consuming per unit of carbon emission) well above 40 CNY. Associated with the stopping surface in Figure  11 , double pressures of diminishing marginal utility implies that, it is increasingly difficult to uplift the P value by technical upgrades as well as to uplift the boundary curves by prising P values. Along this trend, the vivosphere of thermal power plants is shrinking. The ultimate savior for them must be the government conversely, although it will not loosen the carbon regulation by denying the previous efforts. Several solutions are feasible, for one thing, government is able to suppress the carbon price from surging (for instance, SHEA price should be controlled during 35 to 45 CNY), for another, if the above intervention is blamed for disturbing the overall cause of carbon reduction, government can still take its old way by further increasing subsidies for thermal power plants which will also raise their P values immediately. Anyway, those begging for survival will finally be weeded out from the system of laying off the last even when the government offers more subsidies to this industry. Without big generator sets, traditional thermal power plants might be forced to transform towards new energy like solar or photovoltaic power. For them, solar aided coal based power generation is a potential alternative, or to share part of the components with other power generation is a compromise approach. Policy design should be appropriately biased to guide this transformation by resetting the carbon emission tax. Indeed, though the carbon emission tax is not considered separately, it been has already taken account when we measure the profit P . Further research may consider the carbon emission tax as an independent variable in a more profound but also more complex model.

Output: G(t, y) and V (t, y) for each t ∈ {t 0 , t 1

0} backwardly do 7: for each y ∈ {y 0 , y 1 , . . . , y m } increasingly

12: obtain a sample V (t k−1 , y) = V (t k , Y t k ); samples of V (t k−1 , y) to get V

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