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Coordinated photovoltaic inverter control with centralized coordination of curtailment can increase the amount of energy sent from low-voltage (LV) distribution networks to the grid while respecting voltage constraints. First, this paper quantifies the improvement of such an approach relative to autonomous droop control, in terms of PV curtailment and line losses in balanced networks. It then extends the coordinated inverter control to unbalanced distribution networks. Finally, it formulates a control algorithm for different objectives such as the fairer distribution of PV curtailment and rewarding PV customers for utilizing the excess power locally. The coordinated inverter control algorithm is tested on the 114-node and 906-bus LV European test feeders with cable sizes between 50mm^2 and 240mm^2 and validated with reference to OpenDSS. The results demonstrate that coordinated inverter control is superior when applied to high impedance LV networks and LV networks constrained by the distribution transformer capacity limits compared to autonomous inverters. On the 95mm^2 overhead line, it yields a 2% increase on average in the utilized PV output with up to 5% increase for some PV locations at higher penetration levels. Up to a 20% increase in PV hosting capacity was observed for location scenarios with PV system clustering.
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An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls is establis