Abstract: Global climate change is the most severe challenge facing humanity today, affecting the sustainable development of the economy and society seriously. Anthropogenic carbon emissions are the mainspring of global climate change. To control carbon emissions, the Chinese government announced a target in the Copenhagen Climate Conferencein December 2009 to reduce carbon intensity by 40-45%, lower than that of the year of 2005 by 2020. In June 2015, China submitted its “Enhanced Actions on Climate Change—China’s Intended Nationally Determined Contributions”, which set a target of reducing carbon intensity by 60-65%,lower than that of the year of 2005 by 2030. To achieve China’s increasingly ambitious nationally determined contributions, a systematic emission reduction plan must be formulated, and a market-based effective emission control tool, such as “carbon trading”is used. The national carbon trading market was officially launched in July 2021, and the carbon trading price is the key element of carbon trading.If the carbon trading price is set too low, the real-world emissions may be higher than expected levels, making it difficult to achieve emission reduction targets. If the carbon trading price is set too high, the carbon trading market may not be able to optimize resource allocation. Therefore, it is necessary to scientifically formulate the future carbon trading price. Developing a coherent emission reduction plan and a reasonable carbon trading price can provide theoretical basis for China to achieve its carbon emission reduction targets through market-based approaches, and provide a pricing benchmark for carbon emission allowances in the national carbon market.
This article focuses on power companies participating in the national carbon trading market and constructs a stochastic optimal control model that minimizes the total compliance cost, including the cost of clean energy replacing non-clean energy generation, depreciation cost of emission reduction equipment, carbon trading cost, and transaction friction cost. In this model, the optimal emission reduction and trading quantities are control variables, and the expected emission reduction, carbon quota price, and energy conversion price are state variables, with the boundary constraint that the expected emission reduction at the end of the compliance period is equal to zero, in order to realize the government’s promised emission reduction target from 2021 to 2030. This study uses Hamilton-Jacobi-Bellman (HJB) equation to convert optimal control problem to solving partial differential equation problem. By solving HJB equation, the optimal abatement and trading strategy for enterprise are derived. Then, we obtain analytical solutions of equilibrium prices of carbon emission permit and aggregate abatements.
To validate the model, scenario analysis and sensitivity analysis are performed using real-world data. Through scenario analysis, the equilibrium carbon emission allowance price and the socially optimal emission reduction within the compliance period are obtained. Through sensitivity analysis, the marginal emission reduction cost of various clean energy sources replacing non-clean energy generation are compared, and it is found that the priority order for energy fuel usage by power generation companies is hydropower, solar, onshore wind, nuclear, offshore wind, and natural gas. Based on this, further research is needed on energy structure optimization in the power market, under the constraints of economic optimization and dual carbon targets, including the optimal proportion of wind power, solar power, hydropower (subject to water resource constraints), nuclear power, and fossil energy for power generation, the optimum usage ratio for various energy sources, and the optimal installation ratio of various energy sources for power generation.

Key words: stochastic equilibrium model, Hamilton-Jacobi-Bellman equation, equilibrium price of carbon emission permit, aggregate abatement

摘要： 为了实现政府承诺的减排目标,亟需完善碳定价机制并制定连贯的减排计划。本文以发电企业为研究对象,建立总合规成本最小化的随机均衡模型,在2021—2030年减排目标的约束下,使用哈密顿-雅可比-贝尔曼(HJB)方程将构建的最优控制问题归结为解偏微分方程问题,获得企业的最优减排量和最优交易量,进而得到碳排放权均衡价格及全社会最优减排量的解析解。为了验证模型,使用实际数据进行情景分析和敏感性分析。通过情景分析,得到合规期内的碳排放权均衡价格和全社会最优减排量。通过敏感性分析,比较各种清洁能源替代非清洁能源发电的边际减排成本,发现发电企业能源燃料优先使用顺序为水能、太阳能、陆上风能、核能、海上风能、天然气。研究结果为全国碳市场碳排放权提供定价基准,同时为中国通过市场化手段实现碳减排目标提供理论依据。

关键词: 随机均衡模型, 哈密顿-雅可比-贝尔曼方程, 碳排放权均衡价格, 全社会最优减排量