Modeling large distribution feeders for transient analysis using graph search algorithms

Large penetration levels of distributed renewable resources in the distribution systems impose a paradigm shift in the design, operation, protection and control of the distribution systems. The mandates on the renewable generation component are driving increased penetration of the PV generators in the existing distribution feeders. Large scale implementation of distributed generators in distribution feeders lead to a gradual transition from large centralized generators into a system with a large number of small to medium size distributed generators. For an accurate analysis detailed modeling of the distribution feeders in static, quasi-static and transient tool is required. Very few published material can be even found similar to this paper. Some of the applications of graph search algorithms in the area of power systems are for detection of islands in power grids, network reduction by load aggregation, and optimal placement of capacitor banks in the distribution systems. Whereas this paper applies the graph search algorithm to model large distribution feeders for the purpose of transient analysis. Owing to the computational complexity of an electromagnetic transient program performing a time-series analysis in quasi-static tools can be considered as a quick alternative for electromagnetic transient analysis. With the development of the quasi-static analysis tools for modeling and analysis of the distribution systems, the time-series analysis is a convenient option. Additionally the tools being an open source (OpenDSS [1]/GridLab-D [2]) avoids issues related to the licenses. With the existing distribution system analysis tools the quasi-static analysis with 1 second interval for an hour (3600 simulations) or hourly analysis for a complete year (8760 simulations) can happen in a short duration. However, the concept of the quasistatic analysis is valid presuming that the system parameters (voltages and currents) reach a steady state after a power system disturbance prior to the arrival of the next system state. The quasi-static analysis is explanatory provided either the change in system state is relatively small or sufficient time interval has been chosen to reach a steady state. Hence the accuracy of the study depends on the right choice between quasi-static and transient analyses. The overall time range of power system transients is classified into fast electromagnetic transients and slow electromechanical transients. In a distribution system, the electromechanical transients are not frequently studied. Electromagnetic transients are due to the interaction between the magnetic field of inductors and electrical field of capacitors in the power system components. Electromagnetic Transient Programs (EMTP) are used for detailed simulation of such fast electromagnetic transients. However, with this note, performing a transient analysis on a large distribution system with high penetration of PV generators is extremely time consuming and impracticable. For this purpose, the concept of dynamic phasors or timevarying phasors approach is used in this work [3]–[5]. The main idea behind this method is to represent the periodical or nearly periodical system quantities not by their instantaneous values instead by their time-varying Fourier coefficients (dynamic phasors). Dynamic phasors are based on a Fourier approximation of the system quantities. The analysis of fast electromagnetic transients involves the computation of instantaneous values of voltages and currents. In comparison with the classical time domain analysis, the dynamic phasor formulation has the advantage that the properties of the transients can be directly interpreted in terms of the envelop variation. The dynamic phasors based modeling technique is suitable for solving the large distribution system with high penetration of PV. The inbuilt phasor solver in MATLAB/Simulink will be used to solve the distribution feeder in Simulink. Figure 1 presents the generalized framework of the modeling process. The modeling process starts from the distribution feeder in a quasi-static tool. The proposed algorithm will read the inputs for the quasi-static tools, explore the structure of the feeder, and provide inputs as required for the transient analysis tool. Graph search algorithm will be extensively used for this purpose. SimPowerSystems toolbox of MATLAB/Simulink has an inbuilt dynamic phasor solver. Hence the final model will be developed in MATLAB/Simulink using the SimPowerSystems toolbox. The main idea behind this paper is the development