Modeling of Deadtime Events in Power Converters with Half-Bridge Modules for a Highly Accurate Hardware-in-the-Loop Fixed Point Implementation in FPGA

Abstract

Hardware-in-the-loop (HIL) simulations of power converters must achieve a truthful representation in real time with simulation steps on the order of microseconds or tens of nanoseconds. The numerical solution for the differential equations that model the state of the converter can be calculated using the fourth-order Runge–Kutta method, which is notably more accurate than Euler methods. However, when the mathematical error due to the solver is drastically reduced, other sources of error arise. In the case of converters that use deadtimes to control the switches, such as any power converter including half-bridge modules, the inductor current reaching zero during deadtimes generates a model error large enough to offset the advantages of the Runge–Kutta method. A specific model is needed for such events. In this paper, an approximation is proposed, where the time step is divided into two semi-steps. This serves to recover the accuracy of the calculations at the expense of needing a division operation. A fixed-point implementation in VHDL is proposed, reusing a block along several calculation cycles to compute the needed parameters for the Runge–Kutta method. The implementation in a low-cost field-programmable gate arrays (FPGA) (Xilinx Artix-7) achieves an integration time of 1μs. The calculation errors are six orders of magnitude smaller for both capacitor voltage and inductor current for the worst case, the one where the current reaches zero during the deadtimes in 78% of the simulated cycles. The accuracy achieved with the proposed fixed point implementation is very close to that of 64-bit floating point and can operate in real time with a resolution of 1μs. Therefore, the results show that this approach is suitable for modeling converters based on half-bridge modules by using FPGAs. This solution is intended for easy integration into any HIL system, including commercial HIL systems, showing that its application even with relatively high integration steps (1μs) surpasses the results of techniques with even faster integration steps that do not take these events into account.

Efficient Hardware-in-the-Loop Models Using Automatic Code Generation with MATLAB/Simulink

“…To avoid miscalculations during a change from Mode 1 or 2 to Mode 3 during a dead time, Reference [19] suggested different techniques, including saturating the inductor current to zero amperes. This is a simple and effective solution when using the Forward Euler method, as in this case.…”

“…The implementation of the full-bridge uses a K-calculator similar to the one proposed in [19]. The K-calculator is a computing block that produces the different K i terms of the Runge-Kutta method-K 1 terms when the inputs are zero and K 2 when the inputs are the K 1 terms.…”

Special Issue on Power Converters: Modelling, Control, and Applications

“…It is important research because the thermoelectric generator is perfectly designed for energy harvesting. Saralegui et al [5] presented the model of the half-bridge that can be used in hardware-in-loop simulations with the implementation of the dead-time events increase the accuracy of the model. Zhang et al [6] presented sensorless PI passivity-based control for a DC/DC boost converter to avoid the need for the current sensor.…”

“…Summarizing the first Special Issue edition, papers [1,5,7,9] referred to the design and modelling of the inverters including motor drives, papers [3,4] concerned the implementation of renewable energy sources, papers [2,3,6] described DC/DC converters and their control, and [2] was devoted to the electromagnetic compatibility of the power factor corrector, and paper [8] presented electrothermal model of the components of the power converters. All the expected key areas were presented in the first Special Issue.…”

Impact of the Noise on the Emulated Grid Voltage Signal in Hardware-in-the-Loop Used in Power Converters

“…Studies of available technology have detected associated problems and sources of errors with the development of models in emerging applications, and they have been delved into.For example, different mathematical methods have been proposed for modeling power converters, such as the Euler method, which is popular for its simplicity and reduction of latencies, and more advanced ones, such as Runge-Kutta, which under the conditions in [8] results in the most accurate model. Some HIL converter topologies connected to the grid present errors in the zero crossings of the emulated signals, with two main proposals to solve this problem: (i) forcing the mathematical model through code so that the signal takes the appropriate values, or 2 of 14 (ii) performing a subdivision of integration steps from linear approximations around the operating point [9]. This last proposal is not accidental.…”