Optimizing Risk in a Gauss-Markov Process - Energy Storage Strategies for Renewable Integration

所有来自风能和太阳能等可再生能源的电力都取决于天气。来自可再生能源的电力变化可以是可预测的，例如由于太阳的升起和落下-或者可能难以预测，例如由于云层遮挡太阳。同样，消费者对电力的需求总是部分可预测，部分随机。公用事业必须产生的电力量是消费者需求减去产生的可再生电力。随着可再生能源发电量的增加，所需发电量中不可预测的部分也在增加。公用事业公司已经开始通过投资电池存储和快速启动发电机来应对这种增加的风险。然而，目前还没有办法量化可再生能源造成的风险，这意味着公用事业公司不知道要购买多少电池或如何有效地使用它们。例如，公用事业公司可能会购买1 GWh的电池存储。然而，如果在一天中过早放电，并且当风暴来袭并意外减少太阳能发电时无法使用，则1 GWh是无用的。因此，该项目的目标是开发准确的基于天气的模型，以预测可再生能源发电机产量大幅下降的可能性。然后，该项目提出了使用这些风险模型的算法，以确定消费者和公用事业公司的最佳电池充放电计划。此外，该项目使用这些模型来确定最佳的电力定价结构，包括受监管的公用事业的需求费用。该项目包括若干教育和外联活动。亚利桑那州立大学一个名为“科学是乐趣”的既定项目将用于向K-12学生推广。第一个重点是开发有用的高斯-马尔可夫（G-M）模型的太阳能发电。这些模型基于Wunderground和Arizona utility SRP提供的数据集，并以压力变化，湿度和温度为条件。然后使用机器学习将每日预测数据映射到最有效降低成本的模型。第二个重点是解决目标函数不可分离的随机动态规划（DP）问题。具体地说，最小化G-M过程的期望最大值和计算G-M过程的最大值在有限时间区间上的概率分布。这样的随机DP重新制定使用最近提出的自然向前可分离（NFS）的框架，使他们能够递归地解决使用贝尔曼方程的计算时间最少。第三个重点是将NFS DP框架应用于新开发的太阳能发电模型，并产生用于最佳电池编程和相关旋转储备的算法。 这些算法，然后提出了一个模型的基础上反馈的原则，而不是基于边际定价的消费和需求费用的最优公用事业定价。该算法还用于评估公用事业拥有的太阳能与屋顶太阳能的风险和成本的影响。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

All power derived from renewable energy resources such as wind and solar depends on the weather. Changes in power from renewables can be predictable, e.g. due to the rising and setting of the sun - or can be hard to predict, e.g. due to clouds blocking out the sun. Consumer demand for power, likewise, has always been partly predictable and partly random. The amount of power a utility must generate is the consumer demand minus the renewable power generated. As power from renewables increases, the unpredictable part of this required generation also increases. Utilities have begun to respond to this increased risk by investing in battery storage and quick-start generators. However, there is currently no way to quantify the risk caused by renewable energy resources meaning utilities don't know how many batteries to buy or how to use them efficiently. For example, a utility might buy 1 GWh of battery storage. However, the 1 GWh is useless if it is discharged too early in the day and is unavailable when a storm blows in and reduces solar production unexpectedly. The goal of this project, then, is to develop accurate weather-based models to forecast the probability that renewable generators will experience large drops in production. The project then proposes algorithms to use these risk models to determine optimal battery charge-discharge programs for both consumers and utilities. In addition, the project uses these models to determine optimal electricity pricing structures including demand charges for a regulated utility. The project includes several educational and outreach activities. An established program at Arizona State University called Science is Fun will be utilized for outreach to K-12 students.This project has three areas of focus. The first focus is to develop useful Gauss-Markov (G-M) models of solar generation. These models are based on datasets provided by Wunderground and Arizona utility SRP and condition on pressure changes, humidity and temperature. Machine Learning is then used to map daily forecast data to the model which is most effective at reducing cost. The second focus is to solve stochastic Dynamic Programming (DP) problems with non-separable objective functions. Specifically, minimizing the expected maximum of a G-M process and computing the probability distribution of the maximum of a G-M process over a finite time-interval. Such stochastic DPs are reformulated using the recently proposed Naturally Forward Separable (NFS) framework which allows them to be solved recursively using the Bellman equation with minimal computation time. The third focus is to apply the NFS DP framework to newly developed models of solar generation and produce algorithms for optimal battery programming and associated spinning reserve. These algorithms are then used to propose a model for optimal utility pricing of consumption and demand charges based on principles of feedback and not based on marginal pricing. The algorithms are also used to evaluate the impact on risk and cost of utility-owned solar vs rooftop solar.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.