Spatial Inertia-Aware Generation Scheduling Optimization Framework with Maximized Inertia-Less VRES Generation Dispatch for Grid Frequency Stability.
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Date
2026-05-02
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Pan African University
Abstract
The global transition toward low-carbon power systems has accelerated the integra-tion of variable renewable energy sources (VRES). While this transition contributes to carbon-emission reduction, it also displaces synchronous generators (SGs) that inherently provide rotational inertia. The resulting decline in system inertia, to-gether with its non-uniform spatial redistribution across the network, can alter frequency dynamics and increase the risk of local frequency instability following disturbances. Conventional operational and planning approaches commonly rely on aggregated system-level inertia metrics, which may obscure locational vulner- abilities and fail to reveal bus-level violations of frequency stability limits even when global indices appear secure.
This thesis proposes and validates a spatially resolved framework for inertia estima- tion and inertia-aware generation scheduling in power systems with high penetration of inertia-less VRES. First, an offline method for estimating bus-level inertia dis- tribution is developed. The method uses steady-state network parameters to quantify the effective inertia reflected at individual buses within the power network.This formulation provides a transparent mapping of spatial inertia distribution without requiring online measurements, time-domain simulations, or disturbance data during the estimation stage, making it suitable for planning and operational studies. Building on this foundation, a multi-objective optimization framework is formulated to maximize inertia-less VRES penetration while maintaining frequency stability. The framework enforces minimum inertia thresholds at each bus, rather than relying solely on aggregated system inertia constraints. Transmission losses and synchronous generator commitment are simultaneously considered using the Non-Dominated Sorting Genetic Algorithm II. The resulting Pareto front reveals trade-offs between VRES penetration, network efficiency, and inertia adequacy,v and identifies operating points that balance these competing objectives. The proposed methods are evaluated on modified IEEE 9- and 39-bus benchmark systems. Results show that, with a bus RoCoF limit of 1 Hz/s, the selected Pareto knee operating point achieves 75% penetration of inertia-less VRES while reducing transmission losses by approximately 56%. Sensitivity analysis performed for RoCoF limits of 1 Hz/s, 2 Hz/s, and 3 Hz/s shows that stricter frequency stability requirements require higher synchronous inertia and consequently limit renewable penetration. Under the 1 Hz/s limit, the maximum achievable inertia- less VRES penetration is approximately 82% with the lowest transmission losses due to reduced line loading. Relaxing the limit to 2 Hz/s increases the achievable penetration to about 86%, while the most relaxed limit of 3 Hz/s permits up to 95% VRES penetration but results in higher transmission losses due to increased line loading. The analytical inertia formulation is benchmarked against kinetic- energy-based frequency stability indicators and time-domain dynamic simulations, showing strong agreement in RoCoF and frequency nadir estimates. In addition, stochastic simulations under time-varying load and VRES conditions indicate that the proposed inertia-aware scheduling framework improves both the average performance and variability of key frequency stability indices relative to the benchmark method. Overall, this thesis extends existing inertia estimation and inertia-constrained scheduling approaches by linking bus-level spatial inertia assessment with multi- objective VRES-aware generation scheduling. The proposed framework provides a planning-oriented approach for identifying frequency-security limits, inertia bottle- necks, and feasible renewable dispatch levels in low-inertia power systems. The findings support the use of spatially informed inertia management as a complemen- tary tool for maintaining frequency stability in future power systems with high levels of converter-interfaced renewable generation.
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This theses was published by Pan African University