Pv-energy storage coordinated planning based on moment difference analysis theory and decentralized adaptive control

• Proposes MDAT transforming PV integration as balance equations. • Approximate CMD enables fast assessment with bounded errors at engineering grade. • Developed communication-free, depth-based adaptive control for PV-cluster MPPT. • Reduce ESS requirements by over 50% through PV-ESS coordinated planning framework. The large-scale integration of distributed photovoltaic (DPV) systems into active distribution networks (ADNs) can cause voltage violations and reverse power flow. While energy storage systems (ESS) can mitigate these issues, their high cost limits large-scale deployment. This paper develops the Moment Difference Analysis Theory (MDAT), which reformulates DPV consumption as a moment difference balance equation. Through rigorous derivation and validation, the critical moment difference (CMD) is shown to be approximately constant, determined chiefly by the voltage level and the allowable deviation. Theoretical bounds of CMD across different voltage levels are derived, and a global CMD statistical framework is established to verify its universality. Further analysis indicates that as the number of network nodes increases, the CMD converges to its lower limit. Building on the precise CMD calculation method proposed in our previous work, this study introduces an approximate CMD calculation approach. Compared with the precise method, the approximate method enables rapid evaluation of DPV consumption capability in ADNs, supporting statistical standard formulation and rational method selection in engineering applications. Based on MDAT, the depth of DPVs is defined with a DAC strategy, achieving MPPT (Maximum power point tracking) through depth-based delay and active-reactive power coordination. This study proposes a PV-ESS coordinated planning framework, which further reduces ESS cost and enhances utilization under limited curtailment. Case studies on Sichakou Substation and IEEE 33-bus system show DAC achieves over 97.7% MPPT effectiveness, and the coordinated planning cuts ESS cost by nearly 50%, demonstrating strong engineering practicality.