This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among other issues, of microgrids with PV sources. The results are successfully validated through direct comparison against those obtained with the PSCAD/EMTDC simulator, widely accepted by the power industry.

In this contribution, a harmonic domain (HD) model of grid-connected photovoltaic (PV) generation systems is proposed. The topology of the PV generation system contains a PV array connected to a DC/DC converter and a DC/AC converter, coupled to the grid through a filter. The individual components of the PV system are modeled in the HD. The PV array is represented as a Thevenin equivalent, whereas the DC/DC converter and the DC/AC converter are represented in the HD using switching function matrices. The periodic steady-state solution of the PV system is obtained through simple matrix/vector operations. The results obtained by the proposed model are validated against the response obtained with the PSCAD/EMTDC^® simulator, widely accepted by the power industry.