调节电力生产中碳排放的平均场模型
Mean Field Models to Regulate Carbon Emissions in Electricity Production
摘要：
对生态系统最严重的威胁是全球气候变化，这是由碳排放的不受控制的增加所推动的。在这个项目中，我们使用平均场控制和平均场对策模型来分析和告知电力生产商在碳税存在的情况下应该使用多少可再生能源的决策。生产带来的较高收入与碳排放的负外部性之间的权衡对每个生产者来说都是量化的，他们需要实时平衡对可靠但污染（化石燃料）的热电站的依赖，以及投资于和依赖不确定的风能和太阳能技术的清洁生产。我们在两种不同的情况下比较这些决策的影响：1）生产者是竞争性的，并有希望达到纳什均衡; 2）他们合作，并达到社会最优。我们首先证明，这两个问题有一个独特的解决方案，使用向前向后系统的随机微分方程。然后，我们用数值实验来说明生产者在每种情况下的行为。我们进一步介绍和分析的影响，监管机构控制的碳税政策，我们研究了由此产生的Stackelberg均衡与生产者领域。
英文摘要：
The most serious threat to ecosystems is the global climate change fueled by the uncontrolled increase in carbon emissions. In this project, we use mean field control and mean field game models to analyze and inform the decisions of electricity producers on how much renewable sources of production ought to be used in the presence of a carbon tax. The trade-off between higher revenues from production and the negative externality of carbon emissions is quantified for each producer who needs to balance in real time reliance on reliable but polluting (fossil fuel) thermal power stations versus investing in and depending upon clean production from uncertain wind and solar technologies. We compare the impacts of these decisions in two different scenarios: 1) the producers are competitive and hopefully reach a Nash Equilibrium; 2) they cooperate and reach a Social Optimum. We first prove that both problems have a unique solution using forward-backward systems of stochastic differential equations. We then illustrate with numerical experiments the producers' behavior in each scenario. We further introduce and analyze the impact of a regulator in control of the carbon tax policy, and we study the resulting Stackelberg equilibrium with the field of producers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
