Impedance identification is an important tool for the evaluation of grid-converter interactions, and it is based on the injection of a controlled small signal perturbation and in the analysis of the corresponding system response. Using already installed grid-connected converters as perturbation sources offers the advantage of avoiding additional dedicated hardware, but faces some implementation challenges caused by the limited voltage reserve that is normally available in such equipment. To overcome this limitation, this work presents perturbation injection signals that, by considering asymmetric voltage limits, can make the best use of the limited voltage reserve available in the system. The developed approach is first presented for a periodic multi-tone perturbation injection, and then it is extended for narrow-band and wide-band perturbations. Analytical, numerical and experimental results prove that the proposed solution can provide perturbation injections with considerably higher magnitudes compared to other conventional approaches, which makes it ideal to enhance the perturbation injection capabilities of existing grid-connected converters.