  Moving towards regional Supergrids, an increasing number of interconnections
are formed by High Voltage Direct Current (HVDC) lines. Currently, in most
regions, HVDC losses are not considered in market operations, resulting in
additional costs for Transmission System Operators (TSOs). Nordic TSOs have
proposed the introduction of HVDC loss factors in the market clearing
algorithm, to account for the cost of losses and avoid HVDC flows between zones
with zero price difference. In this paper, we introduce a rigorous framework to
assess the introduction of loss factors, in particular HVDC loss factors, in
nodal and zonal pricing markets. First, we focus on the identification of an
appropriate loss factor. We propose and compare three different models:
constant, linear, and piecewise linear. Second, we introduce formulations to
include losses in market clearing algorithms. Carrying numerical tests for a
whole year, we find that accounting only for HVDC or AC losses may lead to
lower social welfare for a non-negligible amount of time. To counter this, this
paper introduces a framework for including both AC and HVDC losses in a zonal
or nodal pricing environment. We show both theoretically and through
simulations that such a framework is guaranteed to increase social welfare.
