A <italic>&#x03BC;</italic>-Synthesis Framework for Multi-Domain Robust Load Frequency Control Under Concurrent Communication Delays and Parametric Uncertainties

The integration of communication networks into modern power systems introduces variable time delays that degrade the performance of traditional Load Frequency Control (LFC), while the shift towards renewable energy sources increases system vulnerability through parametric uncertainties. Existing methods, predominantly based on Lyapunov-Krasovskii Functionals, involve a complexity&#x2013;conservatism trade-off and may not provide a unified and tractable solution for this multi-domain robustness challenge. This paper addresses this gap by proposing a novel control framework based on <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-analysis. The methodology models communication delays as structured uncertainties using a Pad&#x00E9; approximation and integrates them with parametric variations within a unified <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synthesis design process. A detailed comparative analysis indicates that unlike Lyapunov-based approaches, which require guaranteeing system smoothness at every delay subinterval, the proposed method efficiently stabilizes the system under the worst-case conditions, quantified by the structured singular value. Simulation results demonstrate improved robustness compared to conventional H<inline-formula> <tex-math notation="LaTeX">$\infty $ </tex-math></inline-formula> control under concurrent delay and parametric uncertainties. While the conventional H<inline-formula> <tex-math notation="LaTeX">$\infty $ </tex-math></inline-formula> controller exhibits degraded stability margins when delays exceed 15 ms, the proposed <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synthesis controller maintains stability and performance under extreme concurrent disturbances, including time-varying delays of 0.5&#x2013;5 s, 40% load changes, and over 80% variation in tie-line reactance and turbine-governor time constants. The proposed controller drives the Area Control Error (ACE) below 0.01 pu within two minutes for a 40% load change under these conditions. These results indicate that <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-analysis provides a systematic framework for achieving multi-domain robustness in Load Frequency Control under large simultaneous uncertainties.