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In this paper, we develop energy-efficient schemes for multi-user multiple-input single-output (MISO) broadcast channels (BCs), assisted by reconfigurable intelligent surfaces (RISs). To this end, we consider three architectures of RIS: locally passive diagonal (LP-D), globally passive diagonal (GP-D), and globally passive beyond diagonal (GP-BD). In a globally passive RIS, the power of the output signal of the RIS is not greater than its input power, but some RIS elements can amplify the signal. In a locally passive RIS, every element cannot amplify the incident signal. We show that these RIS architectures can substantially improve energy efficiency (EE) if the static power of the RIS elements is not too high. Moreover, GP-BD RIS, which has a higher complexity and static power than LP-D RIS and GP-D RIS, provides better spectral efficiency, but its EE performance highly depends on the static power consumption and may be worse than its diagonal counterparts.