Abstract In recent years, the use of HVdc technology has increased and VSC technology has enabled the realization of HVdc grids. This calls for the development of new tools to solve the transmission network expansion planning (TNEP) model. A detailed representation of the dc grid TNEP problem is highly nonlinear and more complex than the traditional ac grid expansion problem due to extra constraints and additional decision variables from the converter station model. The present day industrial solvers have difficulties to tackle the resultant MINLP problem. Therefore, the linearized ‘DC’ approximation is often used in practice, which may not produce sufficiently accurate answers. In this paper, different relaxations and approximations of the dc grid TNEP problem are presented. The performance of each formulation is evaluated using eight test cases. Although there is no clear formulation that shows the best performance, LPAC approximation and SOC relaxations seem to provide better alternatives to ‘DC’ approximations. The developed formulations do not guarantee feasibility and a second corrective stage is required to obtain feasible solutions.

中文翻译：

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HVdc 电网 TNEP 问题的松弛和近似

摘要 近年来，高压直流技术的应用越来越多，VSC技术使高压直流电网的实现成为可能。这就需要开发新的工具来解决输电网络扩展规划（TNEP）模型。由于来自换流站模型的额外约束和额外决策变量，直流电网 TNEP 问题的详细表示是高度非线性的，并且比传统的交流电网扩展问题更复杂。当今的工业求解器难以解决由此产生的 MINLP 问题。因此，在实践中经常使用线性化的“DC”近似，这可能无法产生足够准确的答案。在本文中，提出了直流电网 TNEP 问题的不同松弛和近似。使用八个测试用例评估每个配方的性能。尽管没有显示最佳性能的明确公式，但 LPAC 近似和 SOC 松弛似乎为“DC”近似提供了更好的替代方案。开发的配方不能保证可行性，需要第二个纠正阶段才能获得可行的解决方案。