Collaborative Research: EAGER: Renewables: A function space theory for continuous-time flexibility scheduling in electricity markets

当前的电力网操作程序多年来在通过发电的编程变化来补偿电力负载的可变性和不确定性方面工作良好。这有助于向数百万客户提供可靠和经济的电力。然而，注入电网的可再生能源发电量的增加了更高水平的可变性和不确定性。此外，在积极追求绿色能源的几个市场中，大的、快速的和意外的功率变化导致对斜升发电的频繁突然需求，所谓的斜升稀缺事件，同时增加了系统的操作成本。该项目采用了一种新的建模方法，预计将产生用于发电资源调度的算法，该算法对于具有高可再生渗透率的系统更有效。工作的主要重点是什么被称为机组组合问题，其中涉及调度发电机组，以补偿电力需求的变化。虽然目前的机组组合是根据每小时变化的发电计划来考虑的，但该项目考虑了更短时间间隔的调度，以充分跟踪高度可变的电力网络中不断变化的供需。这项研究可以消除大规模可再生能源整合的根本障碍，从而为可再生电力资源的可持续，可靠和经济整合铺平道路。这将有助于实现能源独立和减少温室气体的国家目标。虽然这种方法提供了一个完全不同的观点，但它并没有从根本上改变批发市场的架构，也没有改变调度问题的复杂性，因此，该项目的想法在真实的市场的整合预计是实际可行的。这项工作的主要假设是，斜坡稀缺事件是一个严重的瓶颈，这是在流行的离散时间公式的权力的证据系统运行问题的一般，特别是两个相互依赖的因素：1）的近似背后的结构的机组组合（UC）问题的决策空间，和2）的结构的运行成本函数的发电机组和其他灵活的资源，谁被允许投标的能量，但不为斜坡。当前UC决策空间仅包括每小时承诺决策点和每小时发电计划，其形成每个发电单元的分段恒定发电轨迹。这些轨迹是其高阶连续时间对应物的零阶近似，其填充实际UC决策空间。事实上，在每小时UC模型中，关于净负荷的变化的信息被很差地捕获，并且关于净负荷的变化的大量信息被丢失。为了解决增加的斜升需求，代替将决策空间限制到承诺状态和发电轨迹，还包括发电轨迹的一阶导数（即斜升轨迹）作为自由度中的决策变量将是有利的，从而打开接收在每个时刻捕获发电和斜升的联合成本的竞争性报价的大门。认识到一个连续的时间轨迹承担额外的自由度，可以选择作为优化决策空间的一部分，提出了一种新的方法，包括变量，直接代表额外的自由度，并可以方便适当地定价。所使用的概念是函数空间的成熟概念，其允许UC问题被公式化为当前流行的混合线性规划（MILP）问题，但具有额外的自由度以平衡可变性。初步结果清楚地表明，明确的斜坡轨迹变量的引入改变了优先级给予不同的单位在时间表中，降低了总的运营成本，并大大减少了斜坡稀缺事件。还注意到，与函数空间表示相比，引入亚小时决策变量更复杂，并且导致效率降低，函数空间表示被定制以增加表示目标和约束的准确性。

Current electric power grid operating procedures have worked well for many years in compensating for the variability and uncertainty of electric power load by programmed changes in generation. This has contributed to the reliable and economic delivery of electric power to millions of customers. However, the rising level of renewable generation injected into the power grid adds a higher level of variability and uncertainty. Moreover, in several markets that are aggressively pursuing green energy, large, fast, and unexpected power changes are leading to frequent sudden demands for ramping power generation, so-called ramping scarcity events, while increasing the operating cost of the systems. This project takes a new modeling that is expected to yield algorithms for scheduling of generation resources that is more effective for systems with high renewable penetration. The main focus of the work is what is known as the unit commitment problem, which involves scheduling of generating units to compensate for variability in power demand. While currently unit commitment is considered in terms of generation schedules that change on an hourly basis, the project considers a scheduling over shorter time intervals to adequately track changing supply and demand in highly variable power networks. This research can eliminate a fundamental barrier to large-scale renewable integration, thus paving the way to sustainable, reliable, and economic integration of renewable electricity resources. This would contribute to reaching national targets on energy independence and greenhouse gas reductions. While the approach offers a radically different point of view, it does not fundamentally alter the architecture of the wholesale market, nor the complexity of the scheduling problem, so the integration of the project's ideas in real markets is expected to be practically feasible.The main hypothesis in this work is that ramping scarcity events are evidence of a severe bottleneck that lies in the prevalent discrete time formulation of the power system operation problem in general, and in particular to two interdependent factors: 1) the approximation behind the structure of the unit commitment (UC) problem decision space, and 2) the structure of the operating cost functions of the generating units and other flexible resources, who are allowed to bid for energy but not for ramping. The current UC decision space includes only hourly commitment decision points and hourly generation schedules, which form a piecewise constant generation trajectory for each generating unit. These trajectories are a zero-order approximation of their higher-order continuous-time counterparts that populate the actual UC decision space. In fact, the information about the variability of the net-load is poorly captured in the hourly UC model, and a wealth of information about the variations of the net-load is lost. In order to address the increased ramping demand, instead of limiting the decision space to the commitment state and generation trajectory, it would be advantageous to also include the first derivative of the generation trajectory, i.e. the ramping trajectory, as a decision variable among the degrees of freedom, opening the door to receiving competitive offers that capture the joint cost of generation and of ramping at each time instant. Recognizing that a continuous-time trajectory bears additional degrees of freedom that could be chosen as part of the optimization decision space, a new approach is proposed that incorporates variables that directly represent additional degrees of freedom and can facilitate appropriately pricing them. The notion utilized is the well-established notion of function space that allows the UC problem to be formulated as a Mixed Integer Linear Programming (MILP) problem, currently in vogue, but with additional degrees of freedom to balance the variability. Preliminary results clearly show that the introduction of explicit ramping trajectory variables alter the priority given to different units in the schedule, reduces the total operation cost, and considerably reduces ramping scarcity events. It is also noticed that introducing sub-hourly decision variables is more complex and leads to decreased efficiency compared to the function space representation, which is tailored to increase the accuracy in representing both objectives and constraints.