Power load models are significant for power system transient analysis and voltage stability. However, as the load behavior is time varying in nature, the model parameters are also time varying and online parameter estimation algorithms are thus required. In this work we cast static and dynamic load models in linear parametric form and use them as a baseline to develop online parameter identification algorithms. The linear static parametric representation allows the consideration of a wide class of online parameter estimation algorithms. Here we indicatively consider quadratic and integral cost functions. The considered online estimation algorithms are assessed using real data obtained from the Electricity Authority of Cyprus. The simulation results indicate convergence to the expected parameter values.