Using the panel unit tests with and without structural break(s), the convergence hypothesis in relative per capita electricity consumption series is tested across Croatian regions during the period 2001-2013. The results are mixed, depending primarily on the consumption sector considered and the test applied. They indicate the necessity to conduct analysis and formulate energy policy measures on the sector-disaggregated and regional specific electricity consumption time series. The Croatian electricity markets are not fully integrated, and some regions are faced with statistically significant structural break(s), demonstrating thereby the Croatian gradual energy reform process with several sudden innovations, significant regional differences, and the market dependence on expectations, domestic and international economic and non-economic innovations. The impacts of innovations are likely to be permanent for most of the regions, and their electricity consumption behaviours are likely to be path dependent. Consequently, innovations into the energy markets, including government interventions, may have long-run effects, indicating that space and time for experimenting with alternative mechanisms are quite limited.