Abstract
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.
Highlights
Renewable photovoltaic (PV) generation systems represent an attractive and viable alternative of electrical energy supply to decrease the environmental contamination and the global warming effect produced by the consumption of fossil fuels
The rest of the paper is organized as follows: Section 2 deals with the microgrid description, its modelling and the interconnection of PV systems; Section 3 reviews the Numerical Differentiation (ND) method based on the Poincare map and the extrapolation to the limit cycle concepts; Section 4 explains the cubic spline interpolation (CSI) method to adjust the number of time steps per cycle and to define the time step to be used during the electrical system solution; Section 5 details a flowchart of the solution procedure; Section 6 reports the practical application of the methodology through a test case and limitations of the microgrid modelling; Section 7 draws the main conclusions of this research work
A nonlinear power network/component can be mathematically modelled by a set of first-order differential algebraic equations (DAEs), and using some integration routine, such as the trapezoidal rule (TR) or Fourth-Order Runge-Kutta (RK4) algorithm [31], the periodic steady state solution is obtained
Summary
Renewable photovoltaic (PV) generation systems represent an attractive and viable alternative of electrical energy supply to decrease the environmental contamination and the global warming effect produced by the consumption of fossil fuels. The ND method is numerically robust and it has good convergence properties [13] In this contribution, it is used to speed-up the periodic steady state solution of the microgrid with interconnected PV generation, and to reduce the execution time and the computational effort required to obtain the periodic steady state solution in TD. The CSI technique obtains new solution points, adjusted with a smaller error This contribution presents an efficient TD solution process to obtain the periodic steady state of microgrids with PV generation sources. This process incorporates fast and precise mathematical and numerical tools such as Newton Raphson (NR), trapezoidal rule (TR), DN, and CSI, respectively. The rest of the paper is organized as follows: Section 2 deals with the microgrid description, its modelling and the interconnection of PV systems; Section 3 reviews the ND method based on the Poincare map and the extrapolation to the limit cycle concepts; Section 4 explains the CSI method to adjust the number of time steps per cycle and to define the time step to be used during the electrical system solution; Section 5 details a flowchart of the solution procedure; Section 6 reports the practical application of the methodology through a test case and limitations of the microgrid modelling; Section 7 draws the main conclusions of this research work
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