Are locational marginal prices a good heuristic to divide energy market into bidding zones?

By means of a constructive example we show that clustering of Locational Marginal Prices (LMPs) might give unsatisfactory results of zonal division of energy market. Specifically, we find that the division obtained from clustering of LMPs in some cases may not place the congested lines on the zones' borders. This results in a need for costly readjustments after the Market Coupling mechanism has found the supply/demand equilibrium in order to prevent intra-zonal congestion.