On the calibration of the 3/2 model

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An area-time efficient FPGA-implementation of online finite-set model based predictive controllers for flying capacitor inverters

Recently there has been an increase in the use of model-based predictive control (MBPC) for power-electronic converters. Especially for flying-capacitor multilevel converters (FCC) this offers an interesting possibility to simultaneously control output current and the capacitor voltages. The computational burden however is very high and often restrictive for a good implementation. In this paper a time and resource efficient design methodology is presented for the FPGA implementation of FCC MBPC. The control is fully implemented in programmable digital logic. Due to a parallel processing for the three converter phases and a fully pipelined calculation of the prediction stage an area-time efficient implementation is realized. Furthermore, this is achieved by using a high-level design tool. The implementation aspects for 3, 4 and 5-level FC inverters are discussed, with a focus on the 4-level case

On the stator flux linkage estimation of an PMSM with extended Kalman filters

The demand for drives with high quality torque control has grown tremendously in a wide variety of applications. Direct torque control (DTC) for permanent magnet synchronous motors can provide this accurate and fast torque control. When applying DTC the change of the stator flux linkage vector is controlled. As such the estimation of the stator flux linkage is essential. In this paper the performance of the Extended Kalman Filter (EKF) for stator flux linkage estimation is studied. Starting from a formulation of the EKF for isotropic motors, the influence of rotor anisotropy and saturation is evaluated. Subsequently it is expanded to highly isotropic motors as well. In both cases the possibilities to add parameter estimations are evaluated

On extended Kalman filters with augmented state vectors for the stator flux estimation in SPMSMs

The demand for highly dynamic electrical drives, characterized by high quality torque control, in a wide variety of applications has grown tremendously during the past decades. Direct torque control (DTC) for permanent magnet synchronous motors (PMSM) can provide this accurate and fast torque control. When applying DTC the change of the stator flux linkage vector is controlled, based on torque and flux errors. As such the estimation of the stator flux linkage is essential. In the literature several possible solutions for the estimation of the stator flux linkage are proposed. In order to overcome problems associated with the integration of the back-emf, the use of state observers has been advocated in the literature. Several types of state observers have been conceived and implemented for PMSMs, especially the Extended Kalman Filter (EKF) has received much attention. In most reported applications however the EKF is only used to estimate the speed and rotor position of the PMSM in order to realize field oriented current control in a rotor reference frame. Far fewer publications mention the use of an EKF to estimate the stator flux linkage vector in order to apply DTC. Still the performance of the EKF in the estimation of the stator flux linkage vector has not yet been thoroughly investigated. In this paper the performance of the EKF for stator flux linkage is studied and simulated. The possibilities to improve the estimation by augmenting the state vector and the consequences of these alterations are explored. Important practical aspects for FPGA implementation are discussed

An accurate analytical approximation for the price of a European-style arithmetic Asian option.

For discrete arithmetic Asian options the payoff depends on the price average of the underlying asset. Due to the dependence structure between the prices of the underlying asset, no simple exact pricing formula exists, not even in a Black-Scholes setting. In the recent literature, several approximations and bounds for the price of this type of option are proposed. One of these approximations consists of replacing the distribution of the stochastic price average by an ad hoc distribution (e.g. Lognormal or Inverse Gaussian) with the same first and second moment. In this paper we use a different approach and combine a lower and upper bound into a new analytical approximation. This approximation can be calculated efficiently, turns out to be very accurate and moreover, it has the correct first and second moment. Since the approximation is analytical, we can also calculate the corresponding hedging Greeks and construct a replicating strategy.Options; Dependence; Structure; Prices; Hedging; Strategy;

FPGA implementation of online finite-set model based predictive control for power electronics

Recently there has been an increase in the use of model based predictive control (MBPC) for power-electronic converters. MBPC allows fast and accurate control of multiple controlled variables for hybrid systems such as a power electronic converter and its load. The computational burden for this control scheme however is very high and often restrictive for a good implementation. This means that a suitable technology and design approach should be used. In this paper the implementation of finite-set MBPC (FS-MBPC) in field-programmable gate arrays (FPGAs) is discussed. The control is fully implemented in programmable digital logic by using a high-level design tool. This allows to obtain very good performances (both in control quality, speed and hardware utilization) and have a flexible, modular control configuration. The feasibility and performance of the FPGA implementation of FS-MBPC is discussed in this paper for a 4-level flying-capacitor converter (FCC). This is an interesting application as FS-MBPC allows the simultaneous control of the output current and the capacitor voltages, yet the high number of possible switch states results in a high computational load. The good performance is obtained by exploiting the FPGA’s strong points: parallelism and pipe-lining. In the application discussed in this paper the parallel processing for the three converter phases and a fully pipelined calculation of the prediction stage allow to realize an area-time efficient implementation