State-space Averaging Technique Research Articles

Detailed analysis and modeling of improved cascade buck converter

ABSTRACT – This paper presents ready-to-use nonlinear and linear averaged models of an improved cascade buck converter (ICBC) for the first time. A detailed steady-state analysis is also given, providing its operating modes, equilibrium values, and design guidelines. The modelling process consists of two stages. First, the nonlinear model is obtained using the state-space averaging technique. Subsequently, the averaged model is linearised by applying the small-ripple approximation and the small-signal model is achieved. Furthermore, the developed small-signal model is employed to derive three significant transfer functions of the converter. The proposed converter model is valid for the continuous conduction mode (CCM) when the duty cycle is lower than . To be used in validation studies, an exemplary converter with rated power that steps down input voltage to is designed. The accuracy of theoretical analyses is confirmed by the simulation results of the designed converter. Similarly, all proposed models are validated with the simulations done in both frequency-domain and time-domain. The results show that the proposed parametric model response closely matches that of the switching (non-parametric) model and hence it can be safely used for controller design in feedback systems.

Modelling and Analysis of Non-ideal Two stage Lift Luo Converter with Positive Output

High power applications such as motor drive control requires a higher voltage level of the DC-DC power converter fed from low-level DC input sources. For increasing the output voltage, a gain of the converter is increased using the pump circuit consisting of inductors and capacitors connected in different forms. The effect of adding the energy storage elements includes the parasitic resistances in the converter and affects the performance. This research paper is intended to model and investigate the effects of non-idealities in two stages cascaded lift circuit type Luo converter with positive output voltage. To analyze the non-ideal effects, state-space averaging (SSA) technique is used to model the converter. The converter is modeled in the presence of equivalent series resistance (ESR) of inductances and capacitances to study the effect of parasitic resistances on the converter performances. The transient and frequency response of the converter is plotted using the MATLAB simulation and observed that the ringing in the transient response is damped and oscillation at corner frequency is mitigated. The effect of ESR reduces the voltage gain and improves the stability of the system by increasing the gain and phase margin. Step response and bode plot of the converter is plotted at ideal and non- ideal condition.

Studying the Applicability of Swarm Intelligence in Designing Optimized PI Controller for DC-DC Zeta Converter: A MATLAB-Based Approach

Studying the stability of power converters and improving the performance is a major concern for researchers in the domain of power electronics. In this context, the DC-DC Zeta converter is studied in this paper and the closed-loop operation is comprehensively investigated by employing swarm intelligence (SI) algorithms with a view to design an optimized proportional-integral (PI) controller. These algorithms have been increasingly used to develop and optimize power converters in recent years. The state-space averaging technique was used to design the converter’s closed-loop transfer function. Hence, the traditional and SI algorithm-based PI controllers are inspected, and comparative analysis is presented. Four objective functions termed as integral absolute error, integral time absolute error, integral square error, integral time squared error, gain values, and different performance parameters such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated to examine the stability of the system. Furthermore, eigenvalues have been analyzed for determining the stability of the system extensively. Finally, a detailed comparative study is shown to provide a detailed evaluation of the performances where ant colony optimization for continuous domains (ACOR)-based PI controller has shown promising results than other SI-based controllers in terms of percentage of overshoot (2.27%), rise time (1.54 μs), and settling time (0.103 μs). All the simulation results and analysis are obtained using the MATLAB-Simulink.

Nonlinear droop compensation for current waveforms inMRI gradient systems.

Providing accurate gradient currents is challenging due to the gradient chain nonlinearities, arising from gradient power amplifiers and power supply stages. This work introduces a new characterization approach that takes the amplifier and power supply into account, resulting in a nonlinear model that compensates for the current droop. The gradient power amplifier and power supply stage were characterized by a modified state-space averaging technique. The resulting nonlinear model was inverted and used in feedforward to control the gradient coil current. A custom-built two-channel z-gradient coil was driven by high-switching (1MHz), low-cost amplifiers (<$200) using linear and nonlinear controllers. High-resolution (<80 ps) pulse-width-modulation signals were used to drive the amplifiers. MRI experiments were performed to validate the nonlinear controller's effectiveness. The simulation results validated the functionality of the state-space averaging method in characterizing the gradient system. The performance of linear and nonlinear controllers in generating a trapezoidal current waveform was compared in simulations and experiments. The integral errors between the desired waveform and waveforms generated by linear and nonlinear controllers were 1.9% and 0.13%, respectively, confirming the capability of the nonlinear controller to compensate for the current droop. Phantom images validated the nonlinear controller's ability to correct droop-induced distortions. Benchtop measurements and MRI experiments demonstrated that the proposed nonlinear characterization and digitally implemented feedforward controller could drive gradient coils with droop-free current waveforms (without a feedback loop). In experiments, the nonlinear controller outperformed the linear controller by a 14-fold reduction in the integral error of a test waveform.

Linear Quadratic Regulator-Based PI Control of a Non-Ideal Quadratic Boost PFC Converter for Low-Power Wind Energy Conversion Systems Supplying Uninterruptible DC Power

DC–DC converters are efficient in providing a regulated power with power factor control in switch-mode power supplies and also in electric vehicle charging stations. The aim of this research work is to design an efficient DC–DC quadratic boost power factor correction converter for Wind Energy Conversion Systems (WECS) to provide uninterruptible DC power in case of one or two modules loss for low-power applications. The state-space model of the converter is derived using a state-space averaging technique through small signal modeling by considering the non-linearities. The reduced-order model is obtained using Routh-Pade's approximation method to reduce the complexity involved in the design of the controller parameters for the outer and inner loops. The outer voltage is regulated using an Internal Mode Control (IMC)-based proportional integral (PI) controller to overcome the effect of right-half plane zero (RHP) and three-phase currents are shaped by using three PI controllers. The three inner PI controllers for each phase are tuned using three methodologies like Zieglar Nichols, Skogestad and Linear Quadratic Regulator (LQR)-based PI control. The transient and steady-state performances of the closed-loop system are analyzed for variations in the load and set point using extensive computer-based simulation studies. The results reveal that the LQR-based PI controller show considerably better performance in terms of less settling time, overshoot, power factor and %THD, including parasitic parameters of the components.

Design, Modeling and Hardware Implementation of Regenerative Braking for Electric Two-Wheelers for Hilly Roads

The electric vehicles which operate in hilly region gain potential energy while moving uphill. Some of this energy can be recuperated to charge the battery while the vehicle moves downhill by using regenerative braking. The speed of the electric vehicle while descending the slope of hilly roads is often low to ensure the safety of the passenger, hence requiring regenerative braking at low speed. Braking at low speed is quite challenging due to the low level of back electromotive force (EMF) during regenerative braking. This paper presents a modular regenerative braking circuit for electric scooters operating at low speeds. The proposed modular regenerative braking circuit’s configuration, operation, and control scheme are explained in the paper. Here using the state-space averaging technique, the small-signal modeling of the braking circuit was done, and a Type-II current controller was designed to track the braking current reference. The proposed configuration also suggests fast switching between the motoring and regenerative modes by enabling or disabling the gate pulses to the inverter or DC/DC boost converter. This removes the need for a separate switch in the power circuit, hence increasing reliability and reducing cost. The operation of the proposed regenerative braking circuit, along with the overall motor drive-train of the vehicle, was simulated in MATLAB/Simulink. Its hardware implementation was conducted on a scaled-down laboratory test set-up. The simulation and experimental results verify the working of the proposed regenerative braking circuit and the effectiveness of the proposed control scheme.

Port-Controlled Hamiltonian Based Controller for Three-Level Ćuk PFC Converter for Battery Charging Application

This paper reveals energy shaping passivity-based control methodology for a three-level (TL) Ćuk PFC converter. The proposed control methodology is based on the dynamic model of the system along with the idea of energy shaping and damping injection. First, a dynamic model of the TL Ćuk PFC converter is developed using the port-controlled Hamiltonian formulation and the state-space averaging technique. Then, the PCH control technique is implemented in the system and the stability analysis is carried out. In order to eliminate the steady state error, a PI controller is integrated with the PCH-PBC control scheme. Further, the performances of aforesaid system are investigated for battery charging application with the help of MATLAB/Simulink. To validate the simulation study, a prototype model of TL Ćuk PFC converter with proposed controller is built using OP-5142 real-time simulator and test results are recorded. Furthermore, the power quality features of TL Ćuk PFC converter are assessed through monitoring of input current THD under different operating conditions. To assess the system performance in terms of efficiency, input p.f., input current THD, and controller parameters, the proposed controller is compared with benchmark PI controller under dynamic variations at the input voltage and the load.

Hopfield Neural Network-Based Average Current Mode Control of Synchronous SEPIC Converter

ABSTRACT Average Current Mode (ACM) controlled synchronous DC–DC converters are increasingly required for computer power supplies and electric vehicle battery chargers. In this study, Generalized Hopfield Neural Network (GHNN) tuned PI controllers has been proposed for ACM control of synchronous single ended primary inductance converter (SEPIC). The dynamic converter model, required for designing the controllers, is derived using the state-space averaging technique considering all the converter non-idealities. In addition, modified Hankel matrix method is applied to reduce the derived converter model to its first-order equivalent to minimize the design complexity. Using the reduced-order model, the control loop errors are formulated as objective functions in terms of their PI controller parameters. These objective functions are then solved using GHNN to obtain the optimal PI controller parameters. The transient and steady-state performance of the converter with the proposed controller is studied and compared with controllers tuned using Zeigler Nicholas (ZN) method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Reduced-Order Linear Quadratic Regulator (ROLQR) control scheme for variations in the input voltage, reference voltage and load using MATLAB/ Simulink R2015b software tool. Results revealed that the proposed GHNN based controller has fast dynamic performance with less settling time, % overshoot, and steady-state error than existing control methods. A 100W converter prototype is also constructed and tested using TMS320C2000TM microcontroller to verify the effectiveness of the GHNN control algorithm.

Novel distortionless dimming in high power LED lighting using isolated SEPIC converter

A new low-cost energy-saving concept in the modern light-emitting diode (LED) illumination system is developed and implemented using an isolated single-ended primary inductance converter (SEPIC). The dimming scheme presented in this study is a single-step with negligible distortion in the AC mains current as compared to the traditional low-cost triode for alternating current (TRIAC) dimming system, which distorts the AC mains current wave-shape beyond sinusoidal nature due to the phase-cut techniques. This dimming concept is completely retrofitted, no additional arrangement is required to initiate the dimming as compared to a TRIAC dimmer or other controllers. The isolated SEPIC converter is modelled and analysed in detail using the state-space average technique. The stability of the designed converter and overall closed-loop control are verified using Bode-plot analysis. The full load converter efficiency is found around 93%, which is much higher than the conventional flyback topology-based LED driver. The concept presented in this study is tested with the help of a laboratory prototype with an LED load of 60 W.

STABILITY ANALYSIS OF HYBRID ENERGY STORAGE BASED ON SUPERCAPACITOR AND BATTERY

The aim of the work is to analyze the stability of the battery-supercapacitor hybrid storage of power supply for resistance micro-welding equipment, considering the possible variation of the system parameters and taking into account parallel series resistance of the circuit components. Methodology. The sufficient accurate mathematical model of the hybrid energy storage system to stability analysis has been obtained by the state-space average method. According to the state-space averaging method, PWM switching converters are described by separate circuit topologies for each switching period. The system of differential equations for each time interval has been derived by use of the Kirchhoff rules. The small-signal model transfer function of the SEPIC converter has been obtained by applying the Laplace transform to linear state equations averaged over one switching cycle. Finally, the Nyquist stability criterion has been considered to evaluate the stability of the proposed energy storage system. Results. Bode diagrams of an open-loop system for different values of the duty cycle, average load current, and input voltage have been obtained by using MATLAB software. The gain margin ranges from 14.6 dB to 26.4 dB and the phase margin ranges from 45.4 degrees to 54.8 degrees. From these results, it is obvious that the proposed system meets the stability criteria regardless of the aforementioned parameter fluctuations. Originality. The high-efficiency energy storage system for micro resistance welding technology has been proposed. Developing of the energy storage system according to the battery semi-active hybrid topology enables to control the Li-ion battery discharge current within the maximum allowable value. SEPIC converter utilization ensures the high-efficient operation of the power supply despite the battery charge state. Moreover, this topology allows implementing series and parallel configuration of both batteries and supercapacitors to obtain the required value of voltage and current. Practical significance. The mathematical model of the SEPIC converter has been developed by applying the state-space averaging technique. The stability analysis for parameter variation, such as duty cycle and the average load current, the input voltage has been performed by using Nyquist criteria.

Performance Assessment of Large Photovoltaic (PV) Plants Using an Integrated State-Space Average Modeling Approach

Distributed power converters represent a technical solution to improve the performance of large or utility-scale photovoltaic (PV) plants. Unfortunately, evaluation of the yield obtained in large PV fields by using distributed converters is a difficult task because of recurring partial unavailability, inaccuracy of power analyzers, operating constraints imposed by the Power Plant Controller and so on. To overcome such issues in real operating scenarios, a new modeling strategy has been introduced and validated in terms of computational complexity and accuracy. This approach is based on the state-space averaging technique which is applied to large PV plants with multiple conversion stages by performing some elaborations in order to get a final integrated model. The new modeling strategy has been tested in MatLab Simulink environment using data coming from a 300 MW PV plant located in Brazil representing the case study of this work. In this plant, one subfield is equipped with central inverters while another is with string inverters. The proposed model, whose accuracy is in the range from 2.2 to 2.7% with respect to the measured energy, effectively supports data analysis leading to a consistent performance assessment for the distributed conversion system. Final results highlight that string inverters ensure a gain of about 2% in terms of produced energy.

Analysis of an efficient interleaved ultra‐large gain DC–DC converter for DC microgrid applications

This study deals with steady-state analysis and control of a step-up interleaved winding cross-coupled inductor DC–DC converter with high voltage gain and reduced voltage stress across semiconductors using voltage multiplier cells (VMCs). Because of the interleaved scheme, the thermal stress is reduced and the input current ripple is minimised. The leakage energy is recycled by passive lossless clamp circuit to the output. Meanwhile, the voltage stress across the semiconductors is substantially low. Hence, MOSFETs with less ON-state resistances and diodes with a less forward voltage drop can be utilised that improves the circuit performance. The operation principle and the steady state are discussed. Small-signal modelling of the proposed converter is derived via state-space averaging technique and a dual loop controller for output voltage regulation is designed. The adopted strategy utilises a fast dynamical inner loop to control the input current and an outer loop for the output voltage regulation. Finally, a 1 kW prototype with 60 V–1 kV voltage conversion is fabricated and tested to probe the carried analysis.

A new effective robust nonlinear controller based on PSO for interleaved DC–DC boost converters for fuel cell voltage regulation

Output voltage regulation of DC–DC converters has recently gained an increasing attention to face the many system nonidealities. The fast switching behavior is nonlinear time varying, the presence of model and measurement uncertainties, and large variations, are all inherited challenges. The aim of the present work is to design a robust nonlinear controller that ensures satisfactory and robust output voltage regulation for a proton-exchange membrane fuel cell (PEMFC) based on a DC–DC Interleaved Boost Converter (IBC). A state-space model of the DC–DC IBC is first derived using the state-space averaging technique, and a mathematical model is constructed for the PEFMC. In this regard, a robust nonlinear controller and a proportional integral controller are proposed. The controllers are tuned though particle swarm optimization algorithm to estimate their good parameters assuring the desired performance is met. The integral of absolute error criterion is used to improve the dynamic performance of the overall controlled system. Furthermore, the closed-loop stability is analyzed using the Lyapunov stability theorem, and the effectiveness of the closed-loop system is validated under various operating conditions of the PEMFC and load perturbations. Compared to other methods, the obtained results demonstrate a superior performance of the proposed control strategy in terms of its robustness to variations and uncertainties, smooth tracking of a varying set-point and faster transients.

Analysis and Modeling of a New Coupled-Inductor Buck–Boost DC–DC Converter for Renewable Energy Applications

A new coupled-inductor buck–boost converter (CIBuBoC) is proposed in this article. In the proposed CIBuBoC, an ultra-high step-up/step-down voltage conversion ratio and step-up/step-down boundary adjustment are achieved compared to the other related buck–boost converters using two power switches with simultaneous operation along with a coupled inductor. This circuit has a simple structure with two cascade semistage and some features including ultra-extended output voltage, continuous input current with low ripple, positive polarity of the output voltage, and common ground. These features make the CIBuBoC more suitable for many applications such as photovoltaic systems. Moreover, the voltage stress across each power switch is much lower than the other buck–boost converters, which led to power mosfet s selection with lower drain-source on -resistance ( R ds). Therefore, the proposed converter has also enough high efficiency. All steady-state and stress analysis, and also, comparisons with other related converters in continuous conduction mode are provided in detail. Also, using the state-space averaging technique, the low-frequency behavior of the proposed CIBuBoC is studied completely. Experimental results of a 100-W step-up 30–200 V and a 35-W step-down 30–22 V confirm the theoretical advantages of the proposed circuit.

Small Signal Analysis and Control of Snubberless Naturally-Clamped Soft-Switching Current-Fed Push-Pull DC/DC Converter

This article presents detailed small-signal modeling and closed-loop control design for transient performance evaluation of a high-frequency snubberless isolated current-fed push-pull dc-dc converter. The topology attains the natural commutation of semiconductor devices through zero current switching. The state-space averaging technique is employed to derive the transfer functions. A two-loop average current controller is designed and implemented on a digital signal processor to evaluate and demonstrate the transient performance of the converters. A complete procedure for a closed-loop control design is illustrated. Simulation results using PSIM 11.1.64 with the designed controller are shown to validate the stability of the system. Experimental results demonstrated satisfactory transient performance at various load conditions of the converter and validated the derived model and the control design.

A New Multilevel Inverter Topology With Reduced Power Components for Domestic Solar PV Applications

Power electronic converters are used to nullify the input fluctuations from a solar photovoltaic unit because of intermittent solar irradiance and to make the terminal voltage grid compatible with the desired frequency. The conventional two-level converters suffer from low power quality and high voltage stress. In this article, a new multilevel inverter topology called Dual Source Multilevel Inverter (DS-MLI) with fewer power switches is proposed for solar PV power conversion systems. It can operate in symmetric and asymmetric operating modes with no cascading. This reduces the switching components required to produce several levels in the staircase voltage waveform. A closed-loop control algorithm is designed using the state-space averaging technique, and we assess the dynamic behaviour of the system under step change. We carry the simulation out in MATLAB environment. The experimental prototype of DS-MLI rated 1 kW is fabricated using FGA25N120-ANTD IGBTs, and an eco-sense made solar PV emulator is used for analysing the performance of DS-MLI while interfacing with solar PV unit. We compare the suggested scheme with its conventional counterpart in the aspects of components required, cost and efficiency, and the results are presented.

Modelling, design and implementation of quadratic buck converter for low power applications

This paper discusses the modelling, design and implementation of quadratic buck converter (QBC) for low voltage CPU voltage regulator applications. The small-signal modelling of QBC is characterised by state-space averaging technique. The QBC has been applied with average current-mode (ACM) control strategy in order to evaluate steady sate as well as dynamic performance. The hardware development of QBC is exploited using FPGA controller. The PSIM simulation results are validated with the experimental results in terms of line and load regulations. It can be verified from results that the system stability is guaranteed for a wide range of operating conditions.

Mathematical modelling and analysis of voltage super-lift power dc-dc converter for enhanced dynamic characteristics in CCM

PurposeThe purpose of this paper is to propose a mathematical model for voltage super-lift dc-dc power converter in continuous conduction mode (CCM). Using the presented mathematical model, the analysis of dynamics of power stage for voltage super-lift dc-dc power converter can be performed.Design/methodology/approachThe proposed method is based on the average state space model using the state equations of the dc-dc power converter. In the proposed method, the converter is represented as a set of differential equations derived for each switching state of the power switch in terms of inductor current and capacitor voltage. The proposed method describes the dynamic behaviour of the system. The controller is designed to meet performance requirement of the system such as to maintain the dynamics such as stability, steady-state accuracy and the speed of response of the system. Using the obtained model, the analysis of dynamic response of the voltage super-lift dc-dc power converter can be performed.FindingsThe converter is modelled and verified using conventional circuit analysis method employing state-space averaging technique, and their corresponding transfer function is also derived. The dynamics of the converter is investigated using frequency response characteristics obtained using MATLAB programming environment. In addition, to improve the stability of the converter, proportional-integral controller is designed using Ziegler–Nichols tuning rules, and the effect of the compensator in the plant is also investigated.Originality/valueThe proposed method can be used for analysing the dynamics of power stage for voltage super-lift DC-DC power converter.

Advanced small‐signal‐based analytical approach to modelling high‐order power converters

This study devises an advanced small-signal based approach (SSA) to model high-order power converter system (HOPCS); in detail, a 3-Z-network converter which employs a single switch to achieve high voltage gain is utilised as a typical example of HOPCS. Therein, four operating modes are detailed in terms of the states of electric current flowing through the inductors. The proposed SSA is performed by means of the state-space averaging technique and small-signal equivalent circuits in frequency domain. Based on the proposed approach, the derived transfer functions for input voltage, output voltage and control input yield deep insight into the dynamic responses of the converter in each working mode. In order to well validate the effectiveness of the proposed approach, numerical results and experimental prototype are conducted and measured, the results agree well with the theoretical analyses.

A Non-Isolated Hybrid-Modular DC-DC Converter for DC Grids: Small-Signal Modeling and Control

This paper presents small-signal modeling, stability analysis, and controller design of a non-isolated bidirectional hybrid-modular DC-DC Converter for DC grid applications. The DC-DC converter can be used to interconnect two different DC voltage levels in a medium-/high-voltage DC grid. Half-bridge Sub-Modules (SMs) and a high-voltage valve are the main components of the converter. The high-voltage valve can be implemented via employing series-connected Insulated-Gate Bipolar Transistors (IGBTs). Operation with zero voltage switching of the involved high-voltage valve is feasible, i.e., there is no concern pertinent to dynamic voltage sharing among the series-connected IGBTs. The power is transferred from one side to another through the involved SMs, where their capacitors are connected in series across the high-voltage side, while they are connected sequentially across the low-voltage side. In this paper, the state-space averaging technique is employed to derive the small-signal model of the presented converter for controller design. Closed-form expression of the duty cycle-to-inductor current transfer function is extracted. Comparison between simulation results of the small-signal model and the detailed circuit model is presented to authenticate the accuracy of the derived small-signal model. Finally, a scaled-down prototype is used to verify the accuracy of the small-signal model.