Equivalent circuit models (ECMs) have been widely used to describe the electrical dynamics of lithium-ion batteries. A high model accuracy is important for effective simulation and control of the battery system. The model accuracy depends on the design of experiment (DoE) method for battery test and the optimisation approach for ECM parameter identification. While many optimisation approaches have been proposed in literature to identify the parameters, the effect of DoE on the model accuracy is usually overlooked and undervalued. A novel DoE method is proposed in this paper which uses both partial discharge test (PDT) and deep discharge test (DDT) for battery testing. It is shown through careful test data analysis that, the conventional DoE methods using either PDT or DDT cannot capture the battery's dynamics to sufficient accuracy. Experimental data are collected using a commercial lithium ion battery. Results show the new DoE method can significant improve the ECM accuracy, i.e., reducing the root mean square error by ~70% in comparison with conventional DoE approach. In addition, the improved model accuracy contributes to a significant increase in the SoC estimation accuracy using extended Kalman filter.