The research improved conventional methodologies of analysis of power planning and development of a smart city. It takes into account expected cost-effectiveness, efficiency and overall sustainability and uncertainty of relevant variables. The research plan includes characterization of stochastic (aleatory) and knowledge (epistemic) uncertainties of relevant parameters based on available data and assessment. Specific models have been defined to characterize the uncertainty of the parameters of the input variables. Characterization defines statistical probability density functions of the relevant parameters for the calculation ,with or without time-dependent part. It depends on the nature of project implementation and the characteristics of the variable itself. The methodology consists of defining scenarios based on assumptions about the manner of implementation of power solutions of the smart city in terms of financing, implementation dynamics and performance of advanced solutions. The improved methodology of cost-benefit analysis with the characterization of input variables uncertainty better determine the probability success of the planned activities of a smart city. It would allow measuring of the importance of the variables and their impact on the implementation of planned activities, and thus a priority to reduce the risk of unsuccessful implementation of advanced solutions. The developed methodology was applied to the smart city project and the development of energy-efficient solutions in the city of Ludbreg by developing selected units (smart metering infrastructure and smart network components). Scientific contributions are: 1) Improving the conventional methodology of smart city power planning (smart distribution network and electric transport) by including uncertainty and sensitivity of relevant variables. 2) Characterization of stochastic and knowledge uncertainty of variables of the mathematical model of smart city power planning for the dynamics of implementation, realization of planned effects and acceptability of derived advanced solutions. 3) Applicability check of the developed methodology of a smart cities power planning on the example of a city in Croatia and comparison to the conventional approach chosen.