This paper presents a systematic review of optimal transformer configuration in weak sending-end distribution networks with high renewable energy penetration. As the primary equipment for voltage transformation and power flow aggregation

transformers face new challenges in their capacity sizing

location selection

tap-changer setting

and number determination under weak-grid conditions. The review is organized around two parallel dimensions: a physical-problem-oriented dimension and a mathematical-method-oriented dimension. From the physical perspective

five key challenges specific to transformer configuration are identified: strong voltage-reactive power coupling

stability constraints under weak-grid conditions

temporal capacity sizing difficulties

multiple sources of uncertainty

and combinatorial explosion from discrete decision variables. The impact of each challenge on the four transformer configuration dimensions (capacity

turns ratio

location

and tap position) is analyzed in detail. From the mathematical perspective

existing approaches are comparatively examined across model formulation

optimization solution

and decision evaluation

with particular emphasis on algorithm suitability for the mixed-integer nature of transformer configuration (discrete tap positions and unit numbers combined with continuous capacity variables). By cross-mapping the two dimensions

a problem-method maturity matrix is developed to identify research gaps and emerging topics. The results indicate that transformer configuration method selection essentially involves a trade-off among modeling accuracy

solvability

and scalability. Existing studies predominantly concentrate on convexifiable problems

whereas scenarios involving implicit nonconvex weak-grid stability constraints in transformer configuration remain insufficiently investigated. Future research should prioritize refined embedding of stability constraints into transformer configuration models

coordinated source-grid-storage-transformer configuration

integration of uncertainty and multi-objective optimization

hybrid physical-data-driven modeling

and computationally efficient solution tools for engineering applications.