With high renewable penetration, primary frequency regulation (PFR) in low-inertia power systems faces a critical challenge of balancing frequency security with sustainable energy storage system (ESS) utilization. Existing ESS-based PFR studies mainly focus on single-sided resource support or homogeneous modeling, which cannot address the cross-side coordination demands arising from heterogeneous ESS on the source, grid, and load sides. This paper extends ESS-based PFR to a synergistic scenario involving heterogeneous three-sided ESS. A unified modeling framework is established, explicitly incorporating differences in capacity, functional roles, participation priority, and security boundaries. Based on this, a hierarchical decoupling control structure is proposed, separating system-level frequency regulation from side-level energy coordination. The upper level uses a low-dimensional equivalent representation to reduce the optimization burden from modeling numerous ESS units, while the lower level achieves complementary advantages and orderly task allocation among the three sides through differentiated coordination. Simulations show that the method maintains system frequency performance while achieving rational PFR responsibility allocation across source-, grid-, and load-side ESS, effectively leveraging multi-sided heterogeneous ESS for synergistic regulation, and verifying the hierarchical decoupling framework as an effective approach for coordinating multi-side energy storage.

To address the low-voltage violations that may occur in distribution networks with high penetration of distributed photovoltaic (PV) during sunset and evening peak periods under extreme high-temperature conditions, this paper establishes a source–grid–load electro-thermal coupling model that accounts for load thermal accumulation, transient conductor thermal inertia, temperature-dependent line impedance, and PV thermal derating. Based on a soft safety lower bound and a risk-preference utility function, the probability of voltage violation, violation depth, and expected violation duration are introduced to construct node-level and system-level comprehensive risk factors. The cumulant method combined with the Cornish–Fisher expansion is used to reconstruct the probability distribution of nodal voltages, enabling analytical risk calculation. Simulation results on the IEEE 33-bus system at 45 °C show that the proposed method can quantitatively reflect the temporal variations of nodal voltage distributions, physical violation depth, dimensionless severity utility, and expected violation duration, and identify weak nodes in the later part of the evening peak, providing a reference for risk early warning in distribution networks under extreme heat.

Hybrid energy storage systems combining batteries and supercapacitors can effectively mitigate power fluctuations from renewable energy sources by leveraging their complementary energy and power density characteristics. This paper proposes a bilevel optimization framework for simultaneous capacity sizing and energy management of such systems. The upper level employs an improved particle swarm optimization algorithm to determine optimal storage capacities, while the lower level implements a rule-based power allocation strategy with adaptive frequency decomposition. A rainflow counting-based battery degradation model is integrated to capture the coupled effects of state of charge, depth of discharge, and C-rate on cycle life, enabling accurate life cycle cost estimation. The adaptive frequency decomposition method dynamically adjusts the cutoff frequency based on power variance characteristics to improve power allocation efficiency. Case studies demonstrate that the proposed framework reduces life cycle cost by 15.2% compared to conventional approaches, achieves 84.28% power fluctuation reduction, and extends battery lifetime to 8.6 years. The bilevel structure effectively coordinates long-term capacity planning with real-time operational control, providing a practical methodology for renewable energy integration.