This paper studies and analyses the impacts introduced on Distribution Transformer (DT) overload due to the integration of nearly Zero-Energy Buildings (NZEBS) into existing distribution Low Voltage Grids (LVG). The negative impacts on the DT are studied and explained. For high nZEB integration levels, this study reveals that the subsequent reverse power flows can achieve higher values, especially around noon, than the DT rated (and overload limit) power thus accelerating its aging. A power electronics based Energy Storage System (ESS) is considered to mitigate these negative effects. The paper also analysis the mitigation of the negative DTs impact by considering this ESS solution. The established control laws prevent the transformer to be exposed to excessive reverse power flow levels.