  This paper investigates the dynamic voltage support (DVS) control of
inverter-based resources (IBRs) under voltage sags to enhance the low-voltage
ride-through performance. We first revisit the prevalent droop control from an
optimization perspective to elaborate on why it usually suffers from
suboptimality. Then, we formulate the DVS problem as an optimization program
that maximizes the positive-sequence voltage magnitude at the point of common
coupling (PCC) subject to the current, active power, and stability constraints.
The program is inherently nonconvex due to the active power limits, of which
the global optimality is not guaranteed by off-the-shelf solvers. In this
context, we perform the optimality analysis to explore the global optimum
analytically. It is found that the unique global optimum has three
scenarios/stages (S1--S3), which depends on the specific relationship among
grid voltage, grid strength, as well as physical limits of IBRs. The
closed-form solutions in S1 and S3 are derived and the optimality conditions
for S2 are provided, which guarantees the optimality and compatibility with the
fast real-time control. We implement the optimum with a grid-connected
photovoltaic (PV) power plant by integrating a DVS controller. Dynamic
simulations are carried out under different scenarios to test our proposal and
compare it with other existing methods. Additionally, the robustness of
optimality against model errors is discussed and numerically demonstrated.
