Hybrid Dynamic Phasor Modeling Approaches for Accurate Closed-Loop Simulation of Power Converters

Abstract

Modelling the fast dynamics of power converters is of growing concern in power grids and Microgrids. Dynamic phasor (DP) concept has been widely applied to switched power converter for modelling fast transients efficiently due to the inherent frequency shift property of DPs. The dynamics introduced by the DC/AC power converters depend on the controllers, which are implemented either in the stationary frame or on the synchronous reference frame (SRF). Hybrid closed-loop modelling methods that consider DP-based power converter plant model are not established and the applicability and accuracy of such hybrid approaches are not fully understood. This paper attempts to address this gap by proposing two hybrid closed-loop modelling approaches: Hybrid DP-DQ and Hybrid DP-EMT and discusses the applicability and accuracy for various controller types. Furthermore, this paper presents a DP switched model of single and three phase two level power converter and discusses the selection of harmonics to reduce model complexity. The proposed hybrid approaches were validated against detailed switched power converter models and for a wide range of scenarios, the Hybrid DP-EMT method is found to be superior compared other methods. Finally, application dependent recommendations are made for the selection of suitable hybrid closed-loop model for the accurate simulation of single phase and three phase power converters.

Full-Order and Simplified Dynamic Phasor Models of a Single-Phase Two-Stage Grid-Connected PV System

“…These CV(RMSE) values are supported by the time-domain waveforms in Fig.7and Fig.8which reveal an excellent matching between the responses of DP-Full, DP-Simp, and SW models for 𝑣 𝑑𝑐 and 𝑖 𝑔 . Moreover, the CV(RMSE) of 𝑖 𝑔 from the DP-Full model (1.41%) is lower that obtained in[30] (i.e., 1.77% for a fully DP model with PR based current controller and ideal DC source) thus confirming the high fidelity of the DP-Full model. The CV(RMSE) in 𝑖 𝑠𝑝 for DP-Full and DP-Simp is about 7% because the zerothorder DP of 𝑖 𝑠𝑝 do not precisely track the average of the 50 kHz ripples in the 𝑖 𝑠𝑝 waveform obtained from the SW model.…”

“…The accuracy of the proposed DP-Full and DP-Simp models of a single-phase two-stage grid-connected PV system is quantified by computing the coefficient of variance (CV) of the root-mean-square error (RMSE) (also called root-meansquare deviation (RMSD)) in the DP-Full and DP-Simp models' variables with respect to the detailed switching model's variables. The RMSE and CV of RMSE are [29]- [30]:…”

“…where 𝑥 𝐷𝑃 [𝑖] is the value of the signal predicted by the DP model at 𝑖 𝑡ℎ data point or time step, 𝑥 𝑆𝑊 [𝑗] is the value of the signal obtained from the detailed (or switched (SW)) model at 𝑗 𝑡ℎ data point or time step, 𝑁 𝐷𝑃 is the total number of data points or time steps in the DP model variable, and 𝑥̅ 𝑆𝑊 is the mean value of the signal data obtained from the detailed switching model. Note that for 𝑖 𝑔 , the root-mean-square value is used for normalization (i.e., for computing the 𝐶𝑉(𝑅𝑀𝑆𝐸)) rather than the mean value (which equals zero) while for 𝑄 𝑔𝑓 , the range is used for normalization [30] because the 𝑄 𝑔𝑓 waveform contains both positive and negative values. Also note that we picked values at the same time step for both the DP model and the detailed model to ensure consistency.…”

Coupling of Thermal and Electrical Systems for the Simulation of ECS Architectures

“…Harmonics introduced by the three phase inverter are neglected and the three-phase inverter is modelled as a fundamental phasor. A model that considers switching harmonics can be found in (Gurumurthy et al 2022;Holmes and Lipo 2003;Ruan et al 2018). The dynamic phasor of the phase to neutral voltage of phase A v an is given by (5).…”

“…The electrical system typically requires very small time steps for Electro-Magnetic Transient (EMT) simulations (in the range of 1 to 100 µs) while the VCS time step is significantly larger (about 1 second). The electrical system is modelled in the dynamic phasor domain instead of EMT domain for increasing the time step to the range of 1 second such that it is compatible with the VCS system (Gurumurthy et al 2022;Loka et al 2022;Demiray 2008). To avoid non-smooth changes of torque from the VCS side and non-smooth changes of speed from the electrical side, a non-invasive dynamic relaxation strategy has been introduced.…”