  In transmission expansion planning, situations can arise in which an
expansion plan that is optimal for the system as a whole is detrimental to a
specific country in terms of its expected economic welfare. If this country is
one of the countries hosting the planned capacity expansion, it has the power
to veto the plan and thus, undermine the system-wide social optimum. To solve
this issue, welfare compensation mechanisms may be constructed that compensate
suffering countries and make them willing to participate in the expansion plan.
In the literature, welfare compensation mechanisms have been developed that
work in expectation. However, in a stochastic setting, even if the welfare
effect after compensation is positive in expectation, countries might still be
hesitant to accept the risk that the actual, realized welfare effect may be
negative in some scenarios.
  In this paper we analyze welfare compensation mechanisms in a stochastic
setting. We consider two existing mechanisms, lump-sum payments and purchase
power agreements, and we develop two novel mechanisms, based on the flow
through the new transmission line and its economic value. Using a case study of
the Northern European power market, we investigate how well these mechanisms
succeed in mitigating risk for the countries involved. Using a theoretically
ideal model-based mechanism, we show that there is a significant potential for
mitigating risk through welfare compensation mechanisms. Out of the four
practical mechanisms we consider, our results indicate that a mechanism based
on the economic value of the new transmission line is most promising.
