National strategic investments in electricity transmission capacity in Europe
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Optimal transmission expansion plans can be determined from a pan European point of view, but investments in transmission capacity are likely to cause re-allocations of welfare. Thus the optimal plan determined by a supranational planner is not necessarily optimal for each individual nation. Moreover, network planning is mainly done at a national level in Europe. This makes it possible for nations to plan investments strategically to maximize the welfare in their country. We present a bi-level model with time periods to study national strategic investments in transmission infrastructure. The model has a transmission planner on the upper level and an electricity market on the lower level. We compare a supranational planner and a zonal planner. The supranational planner maximizes the welfare of the entire market and the zonal planner maximizes the welfare of her zone. For the latter case we consider a situation where the zonal planner incurs the full cost of the planned network upgrades and a bilateral cost sharing situation. The model for the supranational planner can be reduced to a quadratic optimization program, but the zonal planner is modeled using a mathematical program with equilibrium constraints (MPEC) and a non-linear and non-convex objective function. We reformulate the complementary constraints of the feasible region using disjunctive constraints. The models are implemented in GAMS and solved using the CONOPT and BARON solvers. We apply the models to a four- and six-node network representing countries in Northern Europe, and time periods representing the years 2010 and 2020. The MPEC is solved to optimality for small problem instances.The results illustrate that different planners create dissimilar optimal plans. The various plans result in different allocations of social welfare, however the results from the zonal planner comes closer to the supranational results when the costs of transmission investment are shared bilaterally. The importance of time periods to include a long term perspective in transmission planning models is illustrated by showing that a plan for the current system state is no longer optimal in a future system state. Research effort should be put into understanding the welfare reallocations associated with network upgrades and compensation mechanisms should be designed in order to make the supranationally optimal solutions incentive compatible for national transmission planners.