  This study proposes a novel stochastic geometry framework analyzing power
control strategies in spatially correlated network topologies. Heterogeneous
networks are studied, with users modeled via the superposition of homogeneous
and Poisson cluster processes. First, a new expression approaching the
distribution of the number of users per base station is provided. This
distribution defines the load associated with each Vorono\"i cell, capturing
non-uniformities in user locations and correlation to BSs positions. The power
allocation is adjusted based on this load, allowing BSs to enter sleep mode
when their activity falls below a defined threshold. Furthermore, the
propagation model features millimeter wave transmission characteristics and
directional beamforming. Considering these aspects, revisited definitions of
coverage probability, spectral efficiency, and energy efficiency are proposed.
Tractable expressions for these metrics are derived and validated using
Monte-Carlo simulations. Asymptotic expressions are also proposed, providing
further understanding on the influence of the system parameters. Our numerical
results finally analyze the impact of the sleep control on the performance and
display the optimal strategies in terms of energy efficiency.
