Mixed variable metamodeling and optimization and application to power transfer capability analysis of manitoba-ontario electrical interconnections

现代产品设计，例如飞机或电气系统的设计，是非常复杂的，通常涉及多个学科，以及用于分析和仿真的计算密集型过程。商业分析代码的复杂性，如有限元分析（FEA）和计算流体动力学（CFD），似乎与计算的进步保持同步。近年来，基于近似的优化方法引起了人们的广泛关注。这种方法用简单的分析模型近似计算密集型模型。简单模型通常被称为元模型；构造元模型的过程称为元建模。有了元模型，就可以有效地应用经典的优化方法来寻找最优解。然而，目前对元建模和相关优化技术的研究主要集中在所有优化变量都是连续的问题上。在实践中，离散变量是常见的，例如，一个齿轮的齿数和发电厂的数量。因此，实际的系统分析和优化问题往往涉及连续变量和离散变量，这被称为混合变量元建模和优化问题。在给定系统输入的情况下，电力传输能力分析通常是通过求解多个联立方程来进行的。然而，作为所有输入的函数的传递能力是未知的。随着电力系统放松管制的趋势不断发展，了解这一功能，从而最大限度地提高电力传输能力具有重要的经济意义。本研究尝试发展混合变量元建模和优化方法，并将其应用于马尼托巴水电的输电能力分析问题。本研究密切考察了马尼托巴电网和安大略省电网之间的电力传输。预计研究结果将适用于其他州际电力连接和其他电力供应商。

Modern product design, such as design of an aircraft or electrical system, is very complex, often involving multiple disciplines, and computation-intensive processes for analysis and simulation.  The complexity of commercial analysis codes, such as finite element analysis (FEA) and computational fluid dynamics (CFD), seems to keep pace with computing advances.   In recent years, the approximation-based optimization method has attracted many attentions. This approach approximates computation-intensive models with simple analytical models.  The simple model is often called a metamodel; and the process of constructing a metamodel is called metamodeling. With a metamodel, classic optimization methods can then be effectively applied to search for the optimum.  Current research in metamodeling and associated optimization techniques, however, is focused on problems in which all the optimization variables are continuous.  In practice, discrete variables are commonly seen, e.g., the number of teeth of a gear and the number of power generation stations.  As a result, practical system analysis and optimization problems often involve both continuous and discrete variables, which are referred as mixed variable metamodeling and optimization problems.  Power transfer capability analysis is conventionally performed by solving numerous simultaneous equations, if the system inputs are given. The transfer capability, as a function of all the inputs, is however unknown.  As the trend of power systems' deregulation progresses, to be able to understand such a function and thus maximize the power transfer capability is economically significant.  This research attempts to develop mixed variable metamodeling and optimization methods and then apply them to the power transfer capability analysis problem for Manitoba Hydro. This research examines closely the power transfer between Manitoba power network and that of Ontario.   The results are expected to be able to apply to other inter-state power connections and other electrical power vendors.