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.

This work proposes a simulation strategy of the lead sintering process assuming that it takes place in a horizontally moving packed bed with transverse air flow. Some local chemical reactions occur at rates that depend on the temperature, and chemical species formed in one volume stage will flow for further reaction in other stages. To simulate this process, the model reactor is divided into a number of sequential stages. Condensed species flow horizontally, and gaseous species leave each stage vertically. The compositions and temperatures of the species are calculated considering that the local thermodynamic equilibrium is reached in each stage without external heat transfer, apart from the gas flow, before moving on to the next stage. The model calculates the temperature profile along the sintering machine, the compositions of the sinter and the exhaust gas. The results of the proposed model were compared with sinter pot experimental trials and a reasonably good agreement was obtained. This model can be used to optimize the operating conditions of the lead sintering process.