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The paper presents a hybrid co-simulator comprising EMT and dynamic phasor-based simulators. The EMT simulator models portion(s) of the network wherein fast transients are prevalent and detailed modeling is necessary. The dynamic phasor solver models the rest of the network using extended-frequency Fourier components. Specialized algorithms are developed and presented to accurately map instantaneous EMT and counterpart dynamic phasor samples. Interfacing requirements for co-simulation using different time-steps in the two solvers are also discussed along with implications on accuracy and numerical stability. The paper demonstrates the developed co-simulation algorithm using an example of the IEEE three-phase 118-bus network in which a wind farm is included. The wind farm and the network in its vicinity are modeled in the PSCAD/EMTDC electromagnetic transient simulator, and are interfaced to the rest of the system modeled in a dynamic phasor-based solver. The paper demonstrates the accuracy of the proposed co-simulation for a range of time-step ratios of the two solvers, and also reports the substantial computational time savings obtained using the hybrid simulator. [ABSTRACT FROM AUTHOR]

This paper presents a model for a Modular Multilevel Converter (MMC) using extended-frequency dynamic phasors. The model is based upon a series of harmonic-frequency representations that are obtained for the fundamental and dominant harmonic components. Depending on the requirements of the study to be conducted and the desired level of model accuracy, a low-order model (i.e., average-value) or an arbitrarily wideband model may be constructed. The paper describes the principles of modeling using extended-frequency dynamic phasors, and applies them to an MMC connected to a power system represented using a Thevenin equivalent. The model contains details of the MMC's control system including its high-level control circuitry, as well as voltage balancing and synchronization components. The developed model is then validated by comparing it against a fully-detailed electromagnetic transient (EMT) simulation model developed in PSCAD/EMTDC simulator. Comparisons are made to establish the accuracy of the model (both its low-order and wide-band variants) and to assess the computational advantages it offers compared to conventional EMT models. [ABSTRACT FROM AUTHOR]

This paper presents an average-value model of a line-commutated converter-based HVDC system using dynamic phasors. The model represents the low-frequency dynamics of the converter and its ac and dc systems, and has lower computational requirements than a conventional electromagnetic-transient (EMT) switching model. The developed dynamic-phasor model is verified against an EMT model of the CIGRE HVDC Benchmark. Simulation results confirm the validity and accuracy of the average value model in predicting the low-frequency dynamics of the ac- and dc-side quantities. Merits and applicability limitations of the average model are highlighted. [ABSTRACT FROM AUTHOR]