Extreme events can trigger faults in the transmission grid

weakening its support for the active distribution network. This exacerbates the instability risk of intermittent renewable energy sources

various types of distributed resources

and diverse load equipment interfaced with power electronic converters in the network. Ensuring the system reaches a stable operational equilibrium point after a fault is essential for maintaining safe and reliable operation. To address this problem

this paper formulates a steady-state voltage stability measure and corresponding constraints based on Brouwer's fixed-point theorem

ensuring the strict existence of an operational equilibrium point upon connecting a device to the distribution network. Specifically

the study initiates by defining a network characteristic function based on the current balance form

fully capturing the dynamic interactions between the network-connected devices and the infeed device. After that

based on the Brouwer's fixed-point theorem

a sufficient condition is established through the network characteristic function to guarantee the existence of an equilibrium point within the steady-state voltage stability constraint. The proposed measure of distribution network strength is defined based on the sufficient condition

quantifying the voltage support capability and stability margins of the distribution network

respectively. When the distribution network strength at the infeed point exceeds 1

it is sufficient to ensure the existence of an equilibrium point within the voltage operating range after connecting the device to the distribution network. Finally

the simulation results of IEEE 33-bus distribution network demonstrate that when the infeed points satisfy the proposed static voltage stability constraints

the system reaches an operational equilibrium in both single-infeed and multi-infeed scenarios. This validates the correctness and effectiveness of the proposed constraints.