Increasing distributed generators (DGs) and flexible loads (FLs) enable distribution systems to provide both active and reactive power reserves (P-Q reserves) in supporting the frequency and voltage regulations of transmission systems. However

such requirements at the interface between the transmission system operator (TSO) and distribution system operator (DSO) affect the distribution system operation security

considering the uncertainties of DGs and FLs. To exploit the reserve potential of distribution systems

this paper investigates the voltage-dependent P-Q reserve capacity (V-PQRC) of such types of distribution systems. V-PQRC reflects the feasible space of P-Q reserves that the DSO can provide to the TSO taking the voltage deviation limit at TSO-DSO interface into consideration

while ensuring the distribution system operation security under uncertainties of DGs and FLs. An evaluation method for V-PQRC at the TSO-DSO interface is proposed. To improve the robust performance of the evaluation method

the DG uncertainty is captured by a generalized ambiguity set and the FL uncertainty is addressed by designing a constrained sliding mode controller (CSMC). Three objectives are considered in the evaluation

i.e.

P reserve capacity

Q reserve capacity

and the voltage deviation limit at the TSO-DSO interface. Then

a multi-objective optimization model integrating the generalized robust chance-constrained optimization and CSMC (GRCC-CSMC) is established for V-PQRC evaluation to obtain the Pareto optimal reserve schemes. Finally

a non-approximated selecting (NAS) method is proposed to build up a simplified V-PQRC linear model

which can be convenient to apply in the transmission-distribution system coordination. Simulation results reveal that the V-PQRC evaluation method can achieve a good performance of accuracy and robustness against uncertainties.