Sparse Control Synthesis for Uncertain Responsive Loads With Stochastic Stability Guarantees

Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability various weather-related end-use behavioral factors often affect demand-side control performance. This work addresses this problem with design a to achieve under load uncertainties. Our approach involves modeling uncertainties via stochastic processes that appear as both multiplicative additive system states closed-loop power dynamics. Extending recently developed mean square exponential stability (MSES) results for systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal synthesis problems not only guarantee stability, but also promote sparsity, enhance transient performance, maximize allowable The fundamental trade-off between maximum ( critical ) levels stabilizing efforts is established. Moreover, sparse generalized realistic systems scenario which partial-state measurements are available. Detailed numerical carried out on IEEE 39-bus demonstrate performance controllers enhancing uncertainties; well illustrate efforts.