A static load model is always equivalent to a constant impedance model. For modelling any different characteristic, you have to switch it over to 100 percent dynamic.

A real constant PQ load model can be obtained by setting all voltage and frequency exponents and also the related time constants to zero; you can additionally specify limits for the described characteristic. If the voltage drops below the limit, the load will have again a constant impedance characteristic. This is necessary, because constant power leads to very large currents in case of very low voltages.