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A methodology for the modelling and analysis of horizontally-operated power systems, i.e. systems with a high penetration of stochastic renewable generation, is presented. The objective is to obtain insight in the steady-state of the transmission system when a high penetration level of stochastic distributed generation (in this study case wind power), is present in the underlying distribution systems. The results can be used for the adequacy assessment and risk management of the system. For the system stochastic modelling, the methodology proposes the decoupling of the individual (marginal) behavior of the input random variables from the dependence structure between them. The stochastic dependence is shown to be a major factor for the assessment of the aggregated effect of the distributed stochastic generation on the system. In particular, the stress in the system increases in cases of positive dependence between the inputs and the maximum stress, i.e. the worst-case scenario for the system, occurs when extreme positive dependencies are present between the inputs. Based on this modelling principle, the system operational planning and design can be performed by modelling the extreme dependencies in the system. This powerful computational method can be easily applied to large systems with a high number of stochastic generators.