Dynamic stability analysis of DC microgrid and construction of stability region of control parameters based on Pioncáre map

In the DC microgrid, the difficulty to maintain the stable operation of DC-DC power electronic devices will increase due to the random fluctuations or step changes of power. However, nonlinear dynamics' instability behaviour is very challenging to obtain through an average linearized stability analysis. Therefore, based on the Pioncáre map, this paper derived a global discrete iterative model and its explicit Jacobian matrix in the polynomial form using second-order Taylor series expansion, to detect nonlinear instability behaviour for DC microgrids. A global polynomial Pioncáre map for the microgrid is established, which contains the voltage-current controlled bidirectional DC-DC converter. Then, the derived discrete-time stability analysis method is compared with the average linearized stability analysis method based on the state space average model. Further discussion about the interactive effect on the parameters is conducted through the Jacobian matrix’ eigenvalues, bifurcation diagrams, Pioncáre sections and phase trajectories, leading to the 2-D and 3-D stable regions of operating parameters. Finally, dynamic simulation is carried out on MATLAB/Simulink. Results show that the method proposed can accurately capture the Neimark–Sacker bifurcation critical point in the DC microgrid, construct the stability region of the control parameters, and could help select the controller parameters of DC microgrids.