Rigorous decomposition methods for planning and scheduling of energy networks

气候变化、能源安全和公众对可持续发展的认识是推动多能源系统研究和开发的核心因素。多能源系统是由能源生产、转换、运输、储存和消费单元组成的能源网络，涉及燃气、电力和热能等多种能源载体。所提出的研究计划的目标是能源网络的规划和调度，即通过以最优的方式协调网络单元来获得最佳的网络性能。这是一个困难的决策问题，因为该问题需要包括用于准确描述潜在物理化学关系的非线性模型，并且该问题需要包括用于对单元进行是/否和开/关决定的整数变量。现有的决策方法只提供了近似解，这可能是不可行的，也可能远远不是最优的。拟议研究计划的主要目标是开发严格的优化方法，以“分而治之”的理念解决问题。具体地说，这些方法将利用问题的可分解结构，并通过解决一组更容易的子问题来解决问题。方法的严密性保证了解的可行性和最优性。此外，我们还将开发新的建模策略，以平衡模型精度和求解效率。该研究计划包括未来五年的四个主题。在第一个主题中，我们将分别在多区域和单区域水平上建立燃气和电力联合网络的非线性规划和调度模型。在第二个主题中，我们将开发不同的严格优化方法，这些方法可以在时间、空间、逻辑和场景维度上分解问题。在第三个主题中，我们将协调建模和算法开发，即用混合整数线性子模型来逼近模型的部分部分，以达到预定的精度，这样部分逼近模型的算法开发就容易得多。在第四个主题中，我们将建立微电网和由多个微电网组成的区域能源网络的非线性多能量模型。该研究计划的成果将对多个学科做出贡献，包括能源系统工程、规划和调度以及运筹学。该研究计划将产生先进的全球优化软件，该软件将为能源网络的离线设计或实时运营提供可靠而高效的决策工具，帮助加拿大的能源和制造业实现高效、可持续和环境友好的运营。

Climate change, energy security, and public awareness in sustainability are among the central factors that have motivated the research and development of multi-energy systems. Multi-energy systems are energy networks comprising energy generation, conversion, transport, storage, and consumption units, where multiple energy carriers, such as gas, electricity, and heat, are involved. The proposed research program targets planning and scheduling of energy networks, which is to achieve the best network performance by coordinating the network units in an optimal way. This is a difficult decision-making problem, in that the problem needs to include nonlinear models for accurate description of the underlying physical-chemical relationships, and that the problems needs to include integer variables for yes/no and on/off decisions on the units. Existing methods for the decision-making problem only provides approximate solutions, which may be infeasible or far from the best. The primary goal of the proposed research program is to develop rigorous optimization methods that tackle the problem with the notion of "divide and conquer". Specifically, the methods will exploit the decomposable structure of the problem, and solve the problem via solving a set of much easier subproblems. The rigorousness of the methods ensures the feasibility and optimality of the solutions. In addition, we will also develop novel modeling strategies that can balance the model accuracy and solution efficiency. The research program includes four topics for the next five years. In the first topic, we will develop nonlinear planning and scheduling models for combined gas and power networks, at a multi-region level and at a single-region level, respectively. In the second topic, we will develop different rigorous optimization methods that can decompose the problem along temporal, spatial, logical, and scenario dimensions. In the third topic, we will coordinate the modeling and algorithmic development, i.e., we will approximate parts of the model by mixed-integer linear submodels for a predefined precision, such that the algorithmic development for the partially approximated model is a lot easier. In the fourth topic, we will develop nonlinear multi-energy models for a microgrid and a regional energy network consisting of multiple mircrogrids. The results of the research program will contribute to multiple disciplines, including energy systems engineering, planning and scheduling, and operations research. The research program will yield advanced global optimization software, which will enable reliable and efficient decision-making tools for offline design or real-time operation of energy networks, helping Canada's energy and manufacturing industries to achieve efficient, sustainable, and environmentally friendly operations.