In the Nordic countries (Sweden, Norway, Finland and Denmark), many interconnectors are formed by long High-Voltage Direct-Current (HVDC) lines. Every year, the operation of such interconnectors costs millions of Euros to Transmission System Operators (TSOs) due to the high amount of losses that are not considered while clearing the market. To counteract this problem, Nordic TSOs (Svenska kraftnat - Sweden, Statnett - Norway, Fingrid - Finland, Energinet - Denmark) have proposed to introduce linear HVDC loss factors in the market clearing algorithm. The assessment of such a measure requires a detailed model of the system under investigation. In this paper we develop and introduce a detailed market model of the Nordic countries and we analyze the impact of different loss factor formulations. We show that linear loss factors penalize one HVDC line over the other, and this can jeopardize revenues of merchant HVDC lines. In this regard, we propose piecewise-linear loss factors: a simple to implement but highly effective solution. Moreover, we demonstrate how the introduction of only HVDC loss factors is a partial solution, since it disproportionately increases the AC losses. Our results show that the inclusion of AC loss factors can eliminate this problem.

中文翻译：

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北欧电力市场中的高压直流损耗因素

在北欧国家（瑞典、挪威、芬兰和丹麦），许多互连器由长的高压直流 (HVDC) 线路构成。每年，由于在市场出清时未考虑到的大量损失，此类互连器的运营对输电系统运营商 (TSO) 的成本高达数百万欧元。为了解决这个问题，北欧 TSO（Svenska kraftnat - 瑞典、Statnett - 挪威、Fingrid - 芬兰、Energinet - 丹麦）已提议在市场出清算法中引入线性 HVDC 损耗因子。对此类措施的评估需要对所调查系统的详细模型。在本文中，我们开发并介绍了北欧国家的详细市场模型，并分析了不同损失因子公式的影响。我们表明，线性损耗因素对一条 HVDC 线路的不利影响大于另一条，这可能会危及商业 HVDC 线路的收入。在这方面，我们提出了分段线性损耗因子：一种易于实现但非常有效的解决方案。此外，我们证明了仅引入 HVDC 损耗因子是一种部分解决方案，因为它不成比例地增加了交流损耗。我们的结果表明，包含交流损耗因子可以消除这个问题。