Jef Beerten

Predictive Direct Torque Control for Flux and Torque Ripple Reduction

In this paper, a prediction scheme is presented to diminish both the torque and flux ripples in a direct torque control (DTC) induction motor drive. In a discrete implementation of the classical DTC scheme, the time delay associated with data processing results in additional torque and flux ripples. This part of the ripples can amount to a significant fraction of the overall ripple if the hysteresis bands are comparable to the maximum torque and flux variations in one sampling interval. This paper presents a prediction scheme with low computational complexity and low parameter sensitivity, both comparable to the standard DTC scheme. The prediction scheme can easily be extended to compensate for multiple time delays when the sampling frequency is raised but the computation time remains unchanged. Experimental results show the diminishing effect of the prediction scheme on the torque and flux ripples.

Generalized Steady-State VSC MTDC Model for Sequential AC/DC Power Flow Algorithms

In this paper, a steady-state multi-terminal voltage source converter high voltage direct current (VSC MTDC) model is introduced. The proposed approach is extended to include multiple AC and DC grids with arbitrary topologies. The DC grids can thereby interconnect arbitrary buses in one or more non-synchronized AC systems. The converter equations are derived in their most general format and correctly define all set-points with respect to the system bus instead of the converter or filter bus, which is often done to simplify calculations. The paper introduces a mathematical model to include the converter limits and discusses how the equations change when a transformerless operation is considered or when the converter filter is omitted. An AC/VSC MTDC power flow is implemented using MATPOWER to show the validity of the generalized power flow model.

Generalized Dynamic VSC MTDC Model for Power System Stability Studies

In this paper, a new general voltage source converter high voltage direct current (VSC MTDC) model is derived mathematically. The full system model consists of the converter and its controllers, DC circuit equations, and coupling equations. The main contribution of the new model is its valid for every possible topology of the DC circuit. Practical implementation of the model in power system stability software is discussed in detail. The generalized DC equations can all be expressed in terms of matrices that are byproducts of the construction of the DC bus admittance matrix. Initialization, switching actions resulting in different topologies and simulation of the loss of DC lines amount to a simple calculation or recalculation of the DC bus admittance matrix. The model is implemented in Matlab. Examples on a two- and six-terminal system show that the new model is indeed capable of accurately simulating VSC MTDC systems with arbitrary topology.

Modeling of Multi-Terminal VSC HVDC Systems With Distributed DC Voltage Control

This paper discusses the extension of electromechanical stability models of voltage source converter high voltage direct current (VSC HVDC) to multi-terminal (MTDC) systems. The paper introduces a control model with a cascaded DC voltage control at every converter that allows a two-terminal VSC HVDC system to cope with converter outages. When extended to an MTDC system, the model naturally evolves into a master-slave set-up with converters taking over the DC voltage control in case the DC voltage controlling converter fails. It is shown that the model can be used to include a voltage droop control to share the power imbalance after a contingency in the DC system amongst the converters in the system. Finally, the paper discusses two possible model reductions, in line with the assumptions made in transient stability modeling. The control algorithms and VSC HVDC systems have been implemented using both MatDyn, an open source MATLAB transient stability program, as well as the commercial power system simulation package EUROSTAG.

VSC MTDC systems with a distributed DC voltage control - A power flow approach

In this paper, a power flow model is presented to include a DC voltage droop control or distributed DC slack bus in a Multi-terminal Voltage Source Converter High Voltage Direct Current (VSC MTDC) grid. The available VSC MTDC models are often based on the extension of existing point-to-point connections and use a single DC slack bus that adapts its active power injection to control the DC voltage. A distributed DC voltage control has significant advantages over its concentrated slack bus counterpart, since a numbers of converters can jointly control the DC system voltage. After a fault, a voltage droop controlled DC grid converges to a new working point, which impacts the power flows in both the DC grid and the underlying AC grids. Whereas current day research is focussing on the dynamic behaviour of such a system, this paper introduces a power flow model to study the steady-state change of the combined AC/DC system as a result of faults and transients in the DC grid. The model allows to incorporate DC grids in a N-1 contingency analysis, thereby including the effects of a distributed voltage control on the power flows in both the AC and DC systems.

A sequential AC/DC power flow algorithm for networks containing Multi-terminal VSC HVDC systems

In this paper, a sequential AC/DC power flow algorithm is proposed to solve networks containing Multi-terminal Voltage Source Converter High Voltage Direct Current (VSC MTDC) systems. In VSC HVDC technology, the converter losses add up to a significant fraction of the overall system losses. However, they are often neglected or not taken into account in a proper manner in VSC HVDC power flows. The algorithm put forward in this paper takes the converter losses into account using a generalized converter loss model. The converter steady state equations are derived in their most general format, with the AC network power injections as controlled quantities. It is shown that correctly defining the power setpoints with respect to the system bus instead of the converter bus, as is often done to simplify calculations, requires additional iterative calculations. The DC system modelling method proposed in this paper does not impose any restriction on the HVDC grid topology. A VSC MTDC power flow solver is incorporated into MATPOWER to show the validity of the proposed algorithm.

Analysis of Power Sharing and Voltage Deviations in Droop-Controlled DC Grids

This paper analyzes the influence of the converter droop settings and the dc grid network topology on the power sharing in a dc grid based on voltage source converter high voltage direct current technology. The paper presents an analytical tool to study the effect of the droop control settings on the steady-state voltage deviations and power sharing after a converter outage, thereby accounting for dc grid behavior. Furthermore, an optimization algorithm is developed, taking into account two conflicting optimization criteria. The simulation results show that, when selecting appropriate values for the converter gains, a tradeoff has to be made between the power sharing and the maximum allowable dc voltage deviation after an outage.

Optimizing DC Voltage Droop Settings for AC/DC System Interactions

In this paper, a methodology is presented to optimize the dc voltage droop settings in a multiterminal voltage-source converter high-voltage direct-current system with respect to the ac system stability. Implementing dc voltage droop control enables having multiple converters assisting the system in case of a converter outage. However, the abrupt power setpoint changes create additional stress in the ac system, especially when multiple converters are connected to the same interconnected ac system. This paper presents a methodology to determine optimized converter droop settings in order to not compromise the ac system stability, thereby taking into account the adverse effect the droop control actions have on the interconnected ac system. Developing a disturbance model of the interconnected ac/dc system, the principal directions indicate the gain and directionality of the disturbances; from this, optimal droop settings are derived to minimize the disturbance gain.

Identification and Small-Signal Analysis of Interaction Modes in VSC MTDC Systems

In this paper, a methodology is presented to identify and analyse interaction modes between converters in Voltage Source Converter Multi-Terminal High Voltage Direct Current (VSC MTDC) systems. The absence of a substantial level of energy stored in such power electronics based systems results in fast system dynamics, governed by electromagnetic phenomena. Moreover, interactions between converters are largely influenced by the control parameters and in general, an a-priori identification of interaction modes based on associated time constants is less straight-forward than in AC systems. Furthermore, the extent to which converters interact not only depends on the controller parameters, but is also influenced by the physical characteristics of the HVDC system. The methodology introduced in this paper is based on aggregated participation factors to distinguish between local modes, primarily associated with one terminal, and interaction modes involving multiple terminals. To illustrate the proposed methodology, the influence of droop control parameters, as well as DC breaker inductors, on the system dynamics and the participation of the terminals in system interactions are investigated for a three-terminal MTDC system.

Nonunit Protection of HVDC Grids With Inductive DC Cable Termination

This paper deals with nonunit protection of HVDC grids by proposing a set of parameters that characterizes the open protection zones together with an efficient method to determine the thresholds on these parameters. Selective HVDC grid protection schemes must detect and discriminate faults within the first milliseconds of the fault transient and consequently differ considerably from existing ac protection schemes. Due to the accompanying speed requirement, primary protection is expected to be based on open protection zones as communication delay impedes fast operation. In this paper, the principles of the nonunit protection scheme are developed based on reflection of a traveling wave at an inductive termination. Next, the method to obtain the protection scheme thresholds is elaborated. The method accurately calculates the thresholds for HVDC grids with an arbitrary topology. A sensitivity analysis of these thresholds toward grid and fault parameters demonstrates the applicability of the proposed protection scheme in cable-based HVDC grids with inductive cable termination. The results obtained with the reduced grid model are validated by comparison against simulations using a detailed model implemented in PSCAD.