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Determination of the sources of oscillations in the power system helps operators take appropriate preventive actions. In recent years, the dissipating energy flow (DEF) method has emerged as a promising tool for the online localization of low-frequency oscillation sources. In literature, the mathematical foundation of the DEF method is well-studied for networks with synchronous generators. In this paper, we extend the analysis to flexible AC transmission systems (FACTS). We derive the DEF-expressions for a thyristor controlled series capacitor (TCSC) and a static synchronous compensator (STATCOM) operating with conventional control strategies. Specifically, TCSC with both fixed and variable compensation, and STATCOM in grid-following mode with dc-link voltage and ac voltage-reactive power droop control are considered. Analyzing their respective DEFs, we obtain the conditions for which these FACTS devices could appear as the sources of low-frequency oscillations. Our findings are structured into propositions and are supported through numerical case studies on IEEE test systems.