Low Switching Frequency Research Articles

A Hybrid Model Predictive Multilayer Control Strategy for Modular Multilevel Converters

This paper presents a novel hybrid model predictive multilayer control (HMPMC) strategy for modular multilevel converters (M2LCs). The proposed hybrid strategy uses a modified model predictive direct slope control (MPDSC) concept to regulate the load current while concurrently minimizing the switching frequency, circulating current, and capacitor voltage variations through a new MPMC concept. The multilayer philosophy uses dedicated control layers to independently evaluate its control variables. As the main advantage, the hybrid strategy enables operation of M2LC at low switching frequencies. Moreover, this paper proposes a hierarchical screening algorithm, which estimates the minimum number of switching states required to be evaluated for each control variable, reducing the computational burden. An execution order for each control layer, in which the variables are assigned to control layers as appropriate, is also incorporated to further reduce the computational burden. Instead of using conventional weighting factors, this paper uses tuning factors for each layer, which is based on the number of switching states of the lowest cost to make the tuning process efficient and adaptable to any operating conditions. To demonstrate the validity, a prototype single-phase, five-level, 380-VA M2LC is designed, built, and controlled through the proposed strategies. The performance of prototype is investigated under both the steady-state and transient conditions, and the experimental results are presented in comparison with simulations and benchmarked against both the conventional finite control set model predictive control (FCS-MPC) and an improved MPC strategy. The results clearly indicate that the proposed strategy enables efficient operation of the converter at both significantly lower switching frequency and reduced computational burden, which is preferred for high-power applications.

State variable derivation with numerical approach and efficiency optimisation method for phase‐shift LLC converters under wide voltage‐gain range

The phase-shift modulation (PSM) brings wider voltage-gain range compared with pulse-frequency modulation (PFM) control to the LLC resonant converter in particular occasions such as battery charging converters. Current researches have less discussion about the converter current transfer gain especially at low voltage-gain range. The switching frequency is much increased and high circulating current occurs under low voltage range, which brings large error in the fundamental harmonic approximation analysis. This work has proposed a numerical derivation method to derive the accurate transfer gain for LLC converters with PSM + PFM control. The accurate model and equations for resonant variables are built by the static state-plane analysis. With the help of the iteration algorithm, numerical solutions are got for the resonant variables. The output current gain and the loss estimations are acquired and discussed at each operating point. The results also indicate that there are multiple solutions for the control variables, switching frequency and phase-shift angle, at the same output point. The loss optimisation method is proposed and the losses on the switches are optimised by using lower switching frequency and greater phase angle. The simulation approach and the experiment prototype test have both proved the theoretical calculations and the optimisation results.

Virtual Positive-Damping Reshaped Impedance Stability Control Method for the Offshore MVDC System

For the offshore medium-voltage direct-current (MVdc) system, the dc-side medium voltage can easily cause high-frequency oscillation and even instability owing to the complex impedance interactions. The virtual-resistance stability control method aiming at rectifier station is first introduced from low-voltage dc micro-grid application for mitigating its dc-side oscillation without affecting the load performance of the inverter station. Viewed from the dc input terminal, the small-signal dc impedance modeling of the overall system is established by considering the influences of dc cable, ac grid inductance, and input-parallel output-series structure of rectifier station. Then, the oscillation mechanism is analyzed by the impedance-based Nyquist stability criterion. It is found that only the virtual resistance deteriorates the stability of the MVdc system under the low switching-frequency condition, because the high-frequency oscillation peak may easily exceed the narrow control bandwidth of the rectifier station and fall into the negative-damping region, resulting in a poor robustness against the dc cable variation. To address this issue, the virtual positive-damping reshaped impedance stability control method is further proposed to maintain a larger positive damper in the actual oscillation frequency range regardless of the variation of dc cable length. Thus, the dc-side oscillation of the offshore MVdc system is effectively mitigated at the low switching frequency. Finally, simulation and experimental results validate the proposed control method.

Generalised optimised design of single‐resonant AC current regulators

This Letter generalises frequency-domain oriented design guidelines for optimised single-resonant three-parameter AC current regulators for grid-connected converters. Unlike in previously established set of design guidelines, possible practical restrictions imposed by relatively low-switching frequency are taken into account in the proposed methodology. In addition, resonant term bandwidth is selected according to the desired robustness to fundamental frequency variations. As a result, a closed set of three non-linear equations is created. The solution maximises the loop gain crossover frequency for a given phase margin while respecting frequency robustness and resonant gain restrictions, set a priori.

Comparison analysis of low‐switching‐frequency‐based IPMSM sensorless drives considering regulators, observer and inverter non‐linearity

This study proposes an integration design of sensorless closed-loop drives for rail transit application employing interior permanent magnet synchronous machine (IPMSM), which works under low switching frequency. Due to the long signal sampling period in high-speed region, the individual back-EMF observer cannot ensure the sensorless closed-loop control stability. In order to increase the speed dynamic response and decouple the d - q axes currents accurately, a fast non-singular terminal sliding mode control is designed. It combines a linear sliding mode factor with conventional non-singular terminal sliding mode and is applied uniformly to position observer, speed and currents regulators. Then, considering the effect of inverter non-linearity on position observer, the observed position error caused by dead-time is analysed, and a compensation method based on q -axis voltage error is proposed. Based on the above methods, a comparison analysis of position observer, speed and currents regulators is given. Finally, a 3.7 kW IPMSM is tested to verify the feasibility of the improved sensorless method.

Global kinetic modeling of rapidly pulsed reductants for lean NOx traps: Frequency domain analysis and impact of mass transfer

In the Rapidly Pulsed Reductants (RPR) process, also known as Di-Air (Bisaiji et al., 2011 [1]), hydrocarbons are injected in rapid pulses ahead of a lean NOx trap (LNT) in order to improve its performance at higher temperatures and space velocities while maintaining a reasonable fuel penalty associated with injecting reductants.In this study, a 23-step global kinetic model is developed to predict the performance and product selectivity of the RPR process using propylene as the reductant over a wide range of pulsing frequencies, particularly for the temperature range of 450–600 °C. Some of the previous studies, (Bisaiji et al., 2012 [2], Perng et al., 2014 [3]) have suggested a reaction mechanism based on the formation of stable isocyanate (NCO) intermediates at high temperatures which promote the NOx conversion efficiency. However, in this study, we are checking whether a global kinetic model based on the conventional (low frequency) NOx storage and reduction mechanism is able to predict the NOx conversion improvements at higher pulsing frequencies at high temperatures, where the stability and role of previously proposed intermediates for NOx reduction is more questionable.A wide range of low frequency switching experiments were used to fit the kinetic parameters to the low frequency response of the RPR process. This model was then used to explore the high frequency performance of the RPR process. The kinetic model can predict the increase in NOx and propylene conversion as well as the change in selectivity of the reaction products, such as NH3 and CO, when the pulsing frequency is increased from conventional LNT to optimal RPR frequencies near 1 Hz corresponding to maximum NOx conversion (Reihani et al., 2018 [4]). However, in order to predict the behavior of RPR above the optimal frequency, it was required to add a model of axial pulse mixing to the kinetic model.The model results indicate that the main mechanism for improvement in NOx conversion at high frequencies and high temperatures is the more efficient utilization of storage sites. Also, the drop in NOx conversion at frequencies higher than the optimal frequency is caused by axial mixing of the reductant pulses. In addition, the model and experimental results provide insights into the importance of washcoat diffusion resistance. Particularly, the NOx reduction step with propylene becomes increasingly limited by washcoat diffusion at high temperatures and pulsing frequencies. The agreement between the model and the experimental results provides strong support for using this model to describe the RPR process.

Design considerations of the multi-resonant converter as a constant current source for electrolyser utilisation

An electrolyser is a current driven device, and the volume of produced hydrogen is proportional to the applied current density. To achieve optimal and efficient hydrogen production, it is necessary to calculate current to feed electrolyser and keep it constant despite the input voltage change, number of stacks, temperature, pressure or resistance change of each stack. A systematic design procedure of high frequency DC-DC multi -resonant converter as a constant current source optimized for interfacing electrolyser stack to DC voltage source is presented. The multi resonant converter can operate in four different modes of operation. Each mode of operation represents a specific four-stage sequence characterized by resonating specific part of multi element resonant network. The advantage of this type of converter is that all major parasitic reactances are included in resonant processes. The converter performs Zero Voltage Switching and Zero Current Switching on all switching components depending on the operation mode. The favourable switching conditions are not achievable throughout the whole operating range. The optimal switching region in DC conversion ratio characteristics is calculated and emphasized. The design presented in this paper is based on the mapping of the desired converter operating area in DC conversion ratio characteristic and the calculation of component values using parameters that derive from the selected operating area. The realized converter prototype operates in Mode I with high full load efficiency. The high partial load efficiency is maintained down to 50% of the full load. The realized converter maintains a constant output current with low switching frequency change. The zero voltage switching is achieved both for the power switches and rectifier diodes throughout the load range.

Unbalanced and Reactive Load Compensation Using MMCC-Based SATCOMs With Third-Harmonic Injection

Modular multilevel-cascaded converter-based STATCOMs are scalable to higher voltages without requiring a step-up transformer with multiple windings and can be realized using a low switching frequency, giving lower harmonic content and, hence, a reduced filtering requirement. This paper presents a new injection technique to extend the operating ranges of modular multilevel-cascaded converters STATCOMs when used for negative sequence and reactive current compensation. A nonsinusoidal voltage or current containing a fundamental and its third-harmonic component is injected to achieve phase cluster voltage balance. This technique reduces the maximum dc-link voltage for the star configuration, and the maximum converter phase circulating current for the delta case, compared to applying only sinusoidal zero-sequence components for mitigating the same degree of load unbalance. The analysis is confirmed experimentally, showing that the third-harmonic injection can allow a significant improvement of STATCOM capability for simultaneous compensation of unbalanced load and reactive current.

A dual-mode cascaded H-bridge multilevel inverter for improving THD

Conventionally, multilevel inverters utilise multi-carrier pulse width modulation or multi-stepped (staircase) modulation to produce high-power quality waveforms. Though multi-carrier modulation schemes reduce total harmonic distortion (THD), they lead to considerable switching loss at higher modulation indexes. The staircase modulation, which operates at low switching frequencies, has a limitation of excessive high THD at low modulation indexes, making it unsuitable at lower modulation indexes. The proposed modulation technique blends the advantages of multi-carrier pulse width modulation and staircase modulation to improve the THD and reduce the switching losses over a wide range of modulation indexes. The proposed multilevel inverter employs a modified level-shifted multi-carrier modulation at lower modulation indexes and shifts to sinusoidally approximated multi-stepped at moderate and higher modulation indexes. The carrier frequency of the multi-carrier modulation is varied according to the switching loss analysis to further enhance the THD. A 1 KW prototype was built to confirm the practicality of the proposed method.

A Radio Frequency Nonreciprocal Network Based on Switched Acoustic Delay Lines

This work demonstrates the first non-reciprocal network based on switched low-loss acoustic delay lines. The 4-port circulator is built upon a recently reported frequency-independent, programmable, non-reciprocal framework based on switched delay lines. The design space for such a system, including the origins of the insertion loss and harmonic responses, is theoretically investigated, illustrating that the key to better performance and low-cost modulation signal synthesis lies in a large delay. To implement a large delay, we resort to in-house fabricated low-loss, wide-band lithium niobate (LiNbO3) SH0 mode acoustic delay lines employing single-phase unidirectional transducers (SPUDT). The 4-port circulator, consisting of two switch modules and one delay line module, has been modularly designed, assembled, and tested. The design process employs time-domain full circuit simulation and the results match well with measurements. A 18.8 dB non-reciprocal contrast between insertion loss (IL = 6.6 dB) and isolation (25.4 dB) has been achieved over a fractional bandwidth of 8.8% at a center frequency 155 MHz, using a record low switching frequency of 877.19 kHz. The circulator also shows 25.9 dB suppression for the intra-modulated tone and 30 dBm for IIP3. Upon further development, such a system can potentially lead to future wide-band, low-loss chip-scale nonreciprocal RF systems with unprecedented programmability.

Stator current harmonic elimination control for the high‐power synchronous motors with online implementation

In order to reduce the switching losses and improve the converter efficiency, the switching frequency of the semiconductor devices is usually kept low. However, the low switching frequency operation could lead to a severe harmonic distortion in the stator current and an undesirable modulation delay, which also affect the current control performance. Here, a stator current harmonic elimination control scheme has been studied for the electrically excited synchronous motor (EESM). First, extracting the stator current amplitudes of the fundamental and harmonic components by the sliding discrete Fourier transform (SDFT) algorithm. Then, these obtained current amplitudes will be taken as a part of the cost function for the current model predictive control strategy along with the switching losses and neutral point potential issues. For the further algorithm simplification and performance improvement, a reduced-order processing has been also introduced to realise a simple digital implementation. Finally, simulation and experiments demonstrate that this kind of stator current control could realise a similar characteristic with the selective harmonic elimination along with an online implementation and nice dynamic performance.

A Novel Eight-Channel Grid-Connected Three Phase Converter

In order to improve power quality to reduce harmonics in ac mains, traditional three phase grid-connected converter was usually working at high switching frequency mode, which caused system’s low conversion efficiency and restricted its application in high power conversion. This paper studied an eight-channel three-phase converter based on space vector modulation (SVM) plus phase shift control strategy in which its main circuit was composed of two groups multipulse converters with the same structure by parallel connection at DC side and series at AC side. This novel converter can output sine wave with very little harmonic content at AC side under three times the fundamental frequency switching mode, thus the high quality of grid current can be obtained with very small filter used at grid side. A 50kW eight-channel grid-connected three phase inverter prototype is developed, experiment results show that the multipulse three phase converter has the advantages of high quality grid current, low switching frequency, good transient performance and system reliability.

Scalable Single-Phase Multi-Functional Inverter for Integration of Rooftop Solar-PV to Low-Voltage Ideal and Weak Utility Grid

Integration of rooftop solar-PV (RTSPV) systems and extensive use of nonlinear loads in the low-voltage distribution system (LVDS) leads to poor power quality (PQ). Therefore, it is necessary to address the issues leading to poor PQ at the point of common coupling of the LVDS. In this article, a multi-band hysteresis current control (MB-HCC) for the multi-functional inverter (MFI) is proposed which improves the efficiency of the MFI and also enhances the PQ of the LVDS. The MB-HCC uses simple switching logic and outperforms in its multi-functional tasks such as active power injection and power conditioning. MB-HCC offers better efficiency over variable double-band HCC (VDB-HCC) as it operates at a lower switching frequency. The performance of the proposed system is simulated by using MATLAB/Simulink and validated by OPAL-RT based real-time simulation studies. During the variation of solar irradiation, the proposed MFI has an average efficiency of 98.5% under the ideal grid and 97.34% under the distorted grid. Moreover, the percentage of Total Harmonic Distortion under ideal and distorted grid conditions is brought down to below 5%, and also, reactive power compensation maintains unity power factor operation complying with the IEEE-519-2014 and 1547 standards. These results substantiate the hypothesis of scalability of the single-phase MB-HCC-based MFI for an LVDS contributing to economy and ecology.

Control of Modular Multilevel Converters Using an Overlapping Multihexagon Space Vector Modulation Scheme

This paper introduces a novel space vector modulation scheme that can be applied for the control of modular multilevel cascaded converters (MMCCs) with any number of levels. This is achieved by using basic two-level or three-level hexagons to determine the switch states and the duty cycles separately within one tier of the converter which is a cascade of three-level ${H}$ -bridge, five-level flying capacitor, or neutral point-clamped inverters. Many such hexagons can be overlapped, with phase shift relative to each other, for the control of a complete MMCC, instead of extending a single hexagon to regions corresponding to the number of levels. This approach simplifies the modulation algorithm and brings flexibility in shaping the output voltage waveforms. Also, this proposed method achieves good waveform quality at low switching frequency, hence resulting in low switching losses. Simulation and experimental results are presented to verify the advantageous features of the method.

Three-Vector-Based Low-Complexity Model Predictive Direct Power Control Strategy for PWM Rectifier Without Voltage Sensors

A voltage sensorless control of low-complexity model predictive direct power control (LC-MPDPC) for pulsewidth modulation (PWM) rectifier is proposed. The conventional LC-MPDPC adopts one or two voltage vectors during one control period, which achieve good steady-state performance and quick dynamic response. In addition, based on the mathematical model of the real system, the conventional method only requires one prediction to find the optimal voltage vector, which reduces the control complexity and computational burden. However, the use of one or two vectors during one sampling interval presents abundant current harmonics and high power ripples, and the switching frequency is variable. In order to solve these problems while preserving all the advantages of the conventional LC-MPDPC, this paper presents a novel control scheme, with the aim of operating at a constant switching frequency and obtaining an excellent steady-state performance at a low switching frequency. The proposed method is based on an optimal application of three voltage vectors in a symmetrical way, which takes advantage of advanced PWM techniques. Furthermore, the virtual flux-based control scheme is introduced to achieve voltage sensorless control. The proposed strategy is compared with the conventional MPDPC methods and its effectiveness is confirmed by both simulation and experimental results from a three-phase PWM rectifier under 1000-W operation condition.

Iterative control method of voltage source converters for various high‐power applications

High-voltage and high-power voltage source converters (VSCs) are usually operated at low switching frequencies to minimise the switching losses. This study presents a new control method suitable for low switching frequencies. It consists of two stages. In the first stage, a simple proportional controller is used to suppress any overvoltage or overcurrent during the transients. Then, after the control variables have settled to steady-state values, the iterative controller is activated to finely adjust the modulation index and firing angle of the converter to fulfil the control objectives. To justify the proposed control method, various control objectives are realised in a 10 MVA VSC system, and the results are validated by PSCAD/EMTDC and hardware-in-the-loop simulation. The results show that state variables converge within a few iterative steps, and the transient response is sufficiently fast. The proposed method is shown to perform better than the conventional PI control for eliminating the power imbalance and DC second harmonics due to the imbalance at the grid voltage.

Model Predictive Pulse Pattern Control for Modular Multilevel Converters

For dc–ac modular multilevel converters (MMCs) in double-star configuration, this paper proposes a fast closed-loop control method based on optimized pulse patterns (OPPs). Thanks to the direct manipulation of the OPP switching instants, OPPs with discontinuous switching angles can be used, and the intrinsic cell capacitor voltage ripple is compensated for to preserve the OPPs’ superior harmonic performance. This model predictive pulse pattern controller is combined with a fast acting dead-beat circulating current controller and linked to an upper layer voltage balancing control scheme. The proposed control and modulation method is particularly suitable for medium voltage MMCs with a low number of cells. Despite operation at very low switching frequencies close to and including the fundamental frequency, a superior harmonic performance can be achieved.

Selective harmonics elimination in multilevel inverter by a derivative-free iterative method under varying voltage condition

Selective Harmonics Elimination Pulse width modulation (SHE PWM) presents an alternative modulation technique to operate medium voltage medium and high power converters as it reduces the switching losses. SHE PWM generates high-quality output waveform at the low switching frequency. Its application to multilevel converters furthers leads to improvement in output waveforms with lower switching losses, lesser dv/dt and lowers switching devices ratings. In this Paper SHE PWM for an asymmetrical cascaded H-bridge multilevel inverter under unequal DC voltage condition for fundamental and multiple switching cases are investigated. More harmonics can be eliminated by considering multiple switching’s. The Solution of the Nonlinear transcendental SHE equation is obtained using an advanced derivative free numerical technique which. The method is simple in implementation with fast calculations per iteration as it avoids the evaluation of Jacobian and its matrix. Also the need for precise initial guess in the proximity of actual solution is not needed as an identity matrix of the size of designed variable serves the purpose. Different inequality in the dc voltages is taken to eliminate the lower order harmonics from the output. Only exact solutions for the switching angles which ensure the complete elimination of targeted harmonics are reported. Simulation and Hardware results are presented to confirm the validity of the proposed technique.

Fuzzy frequency‐selecting sliding mode controller for LLC resonant converter

A fuzzy frequency-selecting sliding mode controller for LLC resonant converter is presented here. Based on the fixed high and low switching frequency of sliding mode controller in the LLC resonant converter, the fuzzy controller is used to generate the corresponding high and low switching frequency according to different power levels. The high or low switching frequency is then selected by the frequency switching signal generated by the sliding mode controller, thus the fuzzy frequency-selecting sliding mode controller is realised. The fuzzy control rules here come from the simulation and artificial summary of the application circuit and load characteristics, and the high and low switching frequencies varied with the load are generated by the fuzzy frequency-selecting sliding mode controller, so as to realise the stable control of the output power of the LLC resonant converter. The fuzzy frequency-selecting sliding mode controller for LLC resonant converter is applied to a 240 W all-digital adaptive dimming power supply prototype, which can effectively reduce the steady-state error of the output power of the LLC resonant converter, and has a consistent low ripple characteristic when the load changes.

DC-DC Converter Design Issues for High-Efficient DC Microgrid

In this article, the electrical properties, as well as the economic aspects of the modular and non-modular solution of the DC-DC photovoltaic converter for DC microgrid subsystem, are described. Principally a theoretical overview of the circuit configuration for the selected DC-DC stage of the DC microgrid system is shown. It is dealt with the comparison of the one non-modular high - voltage SiC-based dual - interleaved converter operating at the low switching frequency and with modular low voltage GaN-based DC-DC converters operating at high switching frequencies. The main focus is given to the research of the dependency that arises from the different module count, overall efficiency, costs, and power density (system volume). High efficiency, reduced overall volume, and maximum power density are important factors within modern and progressive solar systems. It is assumed that with the increase of switching frequency within the modular system the volume reduction of the passive components will be highly demanded, thus PCB dimensions and overall volume can be reduced. This dependency is investigated, while the total volume of the non-modular system is a unit of the measure. For these purposes, the design of variant solution was done, and consequently mutually compared in the way of simulations and experimental measurements.