State-plane Analysis Research Articles

Seamless Control of Full-Bridge and Half-Bridge Topology Morphing LLC Converter Based on State Plane Analysis

Seamless Control of Full-Bridge and Half-Bridge Topology Morphing <i>LLC</i> Converter Based on State Plane Analysis

Decoupled State-Plane Analysis of Series–Series Compensated Bidirectional IPT Systems

Decoupled State-Plane Analysis of Series–Series Compensated Bidirectional IPT Systems

Geometrical State-Plane Analysis of Resonant Switched-Capacitor Converters: Demonstration on the Cascaded Multiresonant Converter

To realize high efficiency and high power density for resonant switched capacitor (ReSC) converters, it is critical to have a thorough understanding of the soft-switching mechanism and design the converter appropriately. However, this can be challenging as the soft-switching operation depends on multiple variables and its design difficulty increases quickly with respect to the topology complexity. This paper demonstrates a framework of using geometrical state-plane analysis to facilitate ReSC converter design. The methodology is first applied to a basic 2-to-1 ReSC converter, and then extended to a new 4-to-1 ReSC converter topology we proposed, herein named cascaded multi-resonant converter. This topology has reduced component count thanks to a new “switching bus” architecture. However, it comes at a cost as the converter has multiple resonances within each switching cycle, complicating the soft-switching design. Despite the high circuit complexity, the state-plane analysis neatly provides analytical equations of all state parameters, which are verified by simulations and experiments. Our hardware prototype achieves 6000 W/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> power density at 48-to-12 V conversion and 80 A continuous output. Its peak efficiency reaches 99.02%, and full-load efficiency reaches 97.67%, including gate drive loss. Both the power density and efficiency are superior to the state-of-the-art 48-to-12 V solutions.

Second Harmonic Voltage Suppression for LLC Converter in Dual-Stage Single-Phase Rectifier Based on Voltage-Oriented State Plane Feedforward Control

Second harmonic output voltage ripple in a single-phase grid-connected rectifier can degrade the system performance. In this letter, a voltage-oriented state plane feedforward (VO-SPF) control is proposed to suppress the second harmonic output voltage ripple for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> converter, which serves as the back-stage of the dual-stage single-phase rectifier. Herein, the desired switching frequency of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> converter is predicted online through geometrically simplified state plane analysis, and thus the voltage control loop gain at the second harmonic frequency can be increased. The proposed control strategy features a fast dynamic response and is immune to a grid frequency deviation. Both simulation and experimental results fully confirm the theoretical analysis.

Fixed Frequency LCC Resonant Converter Modeling and Optimal Design for High-Voltage Capacitor Charging Power Supply in Constant Power Control

LCC resonant converter is widely used in high-voltage capacitor charging power supply(CCPS) due to its high efficiency and utilization of parasitic parameters. Since CCPS generally demand a wide voltage variation range, the conventional frequency modulation is difficult to scale up in constant power control. In this paper, a phase-shift(PS) LCC resonant converter in constant power control is proposed. To solve the deviation of the shifted phase of the traditional method in constant power control, an accurate model based on state plane analysis(SPA) is built. On this basis, an optimal design method of PS-LCC for CCPS is proposed, which is helpful to realize the soft switching and reduce the current peak. Finally, a 10kV CCPS prototype is built. And experiment designed by proposed method realizes the constant power charging in PS-LCC for the first time. Experimental results show that the charging speed is increased by 44.3% compared with the traditional constant current charging. Besides, the current stress is reduced by 24.1% and the soft-switching range is extended by 6.9%. There is valuable engineering guidance for realizing high-efficiency and high-speed CCPS by the design method proposed.

A Variable Frequency Phase-Shift Modulation Constant Power Control Strategy for LCC Resonant Capacitor Charging Power Supply

This article develops the constant power control technology of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> resonant capacitor charging power supply (CCPS) to accelerate the charging speed and use the full capacity of the device at the same time. For the constant power control of the CCPS, variable frequency modulation works in a wide frequency range with large reactive power, and phase-shift modulation (PSM) cannot work with a wide gain range. Therefore, a variable frequency (VF)-PSM constant power control strategy is proposed in this article, which achieves high utilization of transformer and high efficiency of power supply system. Based on state plane analysis, the analytical expressions in different operating modes are derived for the ZVS boundary and the multidimensional relationship between power, output voltage, frequency, and phase-shift angle. Accordingly, a control trajectory of the phase-shift angle and frequency in gain-power plane is calculated. Thus, the problems caused by using the current with large harmonic components to calculate the output power in real time are avoided and the control is simple and accurate. Finally, a 500 W, 1 kV charging experiment was conducted to verify the effectiveness of the VF-PSM constant power control strategy and the feasibility of phase-shift angle and frequency trajectory control in gain-power plane.

Generalized State-Plane Analysis of Bidirectional CLLC Resonant Converter

The <i>CLLC</i> resonant converter is a promising candidate for high efficient, bidirectional power transfer applications, such as vehicle-to-grid on-board charger and hybrid vehicle dc&#x2013;dc converter. Nevertheless, the analysis of <i>CLLC</i> still remains challenging because of its complex multiresonant nature and several storage elements. In this article, a circuit analysis method based on change of variables is presented that maps the state-space equations into two decoupled sets of equations. The analyses are carried out in two state-plane coordinate systems, then the results are mapped onto the original region. The proposed method is then used to thoroughly analyze the <i>CLLC</i> resonant converter operating in the continuous conduction mode (CCM). The voltage and current stresses of components, zero voltage switching condition, output voltage gain, output characteristic diagram, and mode boundary of CCM&#x002F; discontinuous conduction mode are then obtained. The accuracy of the proposed approach is verified by the experiments on a 3 kW bidirectional <i>CLLC</i> resonant converter with GaN transistors as the primary and secondary side switches. The results confirm the accuracy of the proposed state-plane analysis of the <i>CLLC</i> resonant converter operating in either direction of power transferring.

Analysis of Three-Phase Wye-Delta Connected LLC

Three-phase wye–delta LLC topology is suitable for voltage step down and high output current, and has been used in the industry for some time, e.g., for server power and EV charger. However, no comprehensive circuit analysis has been performed for three-phase wye–delta LLC. This paper provides complete analysis methods for three-phase wye–delta LLC. The analysis methods include circuit operation, time domain analysis, frequency domain analysis, and state–plane analysis. Circuit operation helps determine the circuit composition and operation sequence. Time domain analysis helps understand the detail operation, equivalent circuit model, and circuit equation. Frequency domain analysis helps obtain the curve of the transfer function and assists in circuit design. State–plane analysis is used for optimal trajectory control (OTC). These analyses not only can calculate the voltage/current stress, but can also help design three-phase wye-delta connected LLC and provide the OTC control reference. In addition, this paper uses PSIM simulation to verify the correctness of analysis. At the end, a 5-kW three-phase wye–delta LLC prototype is realized. The specification of the prototype is a DC input voltage of 380 V and output voltage/current of 48 V/105 A. The peak efficiency is 96.57%.

Multimode Constant Power Control Strategy for LCC Resonant Capacitor Charging Power Supply Based on State Plane Analysis

A novel constant power charging strategy is proposed for LCC resonant capacitor charging power supply (CCPS) in this article, which combines the advantages of discontinuous current mode (DCM) and continuous current mode (CCM) to increase the charging speed of capacitor and the utilization of input grid capacity. In order to implement the multimode constant power control (CPC) strategy, a steady-state model of LCC series-parallel resonant converter is built by state plane analysis, and the analytical expressions for output voltage, average output current, and switching frequency are derived. By the analytical expressions, this control strategy directly determines the relationship of the output voltage and the switch frequency, so the frequency control curve of the pulse frequency modulation could be realized easily. Accordingly, the converter operating along the control curve can take advantage of high average and low peak current of CCM, small switching loss of DCM. Finally, the accuracy of LCC state plane model and the effectiveness of multimode CPC are verified by the simulation and a 2-kW CCPS experiment.

Near-Time-Optimal Dynamics in PWM DC–DC Converters: Dual-Loop Geometric Control

Traditional voltage-mode and dual-loop current-mode linear schemes are widely used for controlling the fundamental dc–dc converters due to their simple implementation and fixed-frequency. Pulse-Width-Modulation (PWM) operation. While the dynamic response can be improved by pushing the control bandwidth, lower stability margins may lead to unexpected peak deviations in the inductor current and capacitor voltage, causing failures due to magnetic saturation or excessive voltage overshoot. The concept of dual-loop geometric-based control is introduced in this article by combining geometric state-plane analysis for the outer voltage loop with traditional current-control techniques for the inner loop. The traditional linear voltage compensator is replaced by a geometric alternative that can control the time-domain evolution of the state variables, providing a fast and reliable transient response by following a desired geometrical path to reach the steady-state operating point. In this way, stringent dynamic requirements can be successfully addressed by shaping the state variables’ time evolution by employing a simple geometric equation to define the voltage compensator. Circular trajectories are implemented using simple parametric equations resulting in remarkably well-defined, reliable transient behavior. Experimental results of dual-loop geometric controlled platforms validate the proposed control concept and highlight the strong contribution to the applied field made by this innovative controller.

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.

Closed-Loop Design and Transient-Mode Control for a Series-Capacitor Buck Converter

This paper explores the large-signal and small-signal dynamics of a series-capacitor (SC) buck-type converter and introduces an optimal closed-loop control scheme to accommodate both the steady-state and transient modes. As opposed to a conventional buck converter, where time-optimal control is realized by a single on–off cycle, in the SC-buck topology, there is a need to distribute the switching phases to satisfy the charge balance of the SC. The new control method merges a voltage-mode controller for the steady-state operation and a nonlinear, state-plane based transient-mode controller for load transients. A detailed principle of the operation of the SC-buck converter is provided and explained through an average-behavioral model and state-plane analysis. The operation of the controller is experimentally verified on a 20 W 12 V-to-1 V converter, demonstrating voltage-mode control operation as well as minimum-deviation and time-optimal responses for load transients.

A Matrix Presentation of State-Plane Analysis for a Broad Class of Series-Resonant Converters

The trend toward higher switching frequencies and higher power densities in dc–dc conversion led the designers to rediscover resonant topologies. However, the analysis of these converters is often limited to a particular operating mode and/or topology. This paper wants to fill the gap by presenting a state-space-based analysis for a broad class of series-resonant converters including voltage-fed as well as current-fed topologies, either unidirectional or bidirectional. The proposed solution consists of a mathematical framework that solves the trajectory of state variables in the resonant tank, as well as the main characteristic functions such as voltage conversion ratio and transferred power. The matrix approach permits a flexible and compact formulation and easy implementation in computational tools such as MATLAB. The theoretical framework is applied to both voltage-fed and current-fed resonant topologies: the first is used to show the advantages of the proposed model respect to the first harmonic approximation, while a detailed analysis in terms of operating mode boundaries, delivered power, and voltage gain is provided for the second. Simulations and measurements on a 300-W prototype of the current-fed topology are used to validate the correctness of the proposed solution.

Research on Energy Storage Interface Circuit and Its Control Principle Based on the L-LLC Resonant Bidirectional DC-DC Converter

Aiming at the low operating efficiency and poor dynamic response of energy storage interface circuit for flexible interface of connecting microgrid to power grid, the principle of PI or PID and optimal trajectory hybrid control based on the L-LLC resonant bidirectional DC-DC converter (L-LLC BDC) is proposed. It realize zero-voltage switching and zero-current switching for input switches and output rectifiers respectively, besides, it not only significantly reduce the computational complexity and further increase switching frequency, but also improve dynamic response of the converter remarkably. Using state-plane analysis, the operation status and characteristics of L-LLC-BDC are described in detail, based on that, the control system of the energy storage interface circuit is designed. In view of the principle of PI or PID and optimal trajectory hybrid control based on the L-LLC-BDC, the simulation shows that the correctness of theoretical analysis and the superiority of dynamic response and the operation performance of flexible interface of connecting microgrid to power grid is guaranteed.

Fast Response of Deviation-Constrained Hybrid Controllers for Indirect Energy Transfer Converters

This paper introduces and surveys a new family of transient-oriented controllers for indirect energy transfer converters. The controllers incorporate a peak current programmed mode control for steady-state operation and a nonlinear, state-plane-based transient-mode control schemes for load transients. The new controllers facilitate extremely fast convergence from a loading transient to the new steady-state operating point while constraining the output voltage and inductor current deviations to a desired (minimal) value. As a result, the loading transient performance of indirect energy transfer converters can be significantly improved since two control objectives (convergence time and minimal components’ stress) are simultaneously obtained. A detailed principle of operation of the controllers is provided and explained through a state-plane analysis. The operation of the controllers is experimentally verified on a 30 W 3.3 V-to-12 V boost converter, demonstrating a significantly lower output voltage deviation and lower peak inductor current when compared to time-optimal control, allowing for volume reduction of the converter.

Digital Implementation of Soft Start-Up and Short-Circuit Protection for High-Frequency LLC Converters With Optimal Trajectory Control (OTC)

Achieving soft start-up and short-circuit protection have always been challenging for resonant converters due to severe stresses in the resonant tank. Optimal trajectory control (OTC) has been proven to be the most effective control method to optimize energy delivery with given stresses. This paper proposes a method to implement soft start-up and short-circuit protection for LLC converters by using low-cost microcontrollers (MCUs) with minimum stresses and optimal energy delivery. Our current understanding of the relationship between the switching frequency and the output voltage is based on the state-plane analysis, and the requirement for the controllers is significantly reduced when using the lookup table. Further improvement enables the application of the proposed control method to high-frequency LLC converters without increasing the cost for the controllers. This paper proposes a method to protect the LLC converter from abrupt short-circuit with low-cost MCUs, which improves transient response to short-circuit significantly, and investigates limitations when operating the high-frequency LLC converter under short-circuit conditions. The proposed methods minimize the CPU resource requirement and can be further integrated with other state-trajectory control functions within one MCU. Experimental results are demonstrated on a 500-kHz 1-kW 400-V/12-V LLC converter with 60-MHz MCU TMS320F28027.

Constant Resonant Current Limiting Strategy for LLC Converter Without Current Sensing

There are great current shocks in LLC resonant converter during startup and over load condition. Conventional open loop current limiting method suffers from limited effect and complicated design process, while closed loop current limiting method requires extra current sensing. This paper investigates the relationship between resonant current, output voltage, and switching frequency based on state plane analysis, then a constant resonant current limiting strategy without current sensing is proposed, which adjusts switching frequency corresponding to the output voltage. The proposed strategy can realize constant peak value of resonant current during startup, shock load stepping, and over load condition, achieving optimal control of the primary current stress. Together with conventional output voltage regulating strategy, regulation of output voltage under normal load condition is also guaranteed. The maximum available output voltage under current limiting condition is estimated, and simple parameter design method of current limiting strategy is provided.

Analysis and Parameter Optimization of Start-Up Process for &lt;italic&gt;LLC&lt;/italic&gt; Resonant Converter

There is a current spike in LLC resonant converter during start-up and frequency modulation method is adopted to limit the resonant current usually, which controls switching frequency decreasing from specific high frequency to steady-state frequency in exponential pattern with a time constant tau. However, it is hard to determine the crucial parameter of time constant of the exponential switching frequency sweep curve, due to the complexity in analyzing dynamic process of the converter. In this paper, the operation modes and characteristics under continued conductive mode and discontinued conductive mode are analyzed based on state-plane analysis and the boundary of two conductive modes is figured out. Then, the iteration calculation model of the LLC converter is proposed to predict the resonant current during start-up progress, and time constant of the existing soft start method is optimized using iteration algorithm. Using the proposed iterative design method, the current stress of LLC resonant converter is limited, as well as guaranteeing the response speed of output voltage.

DCM-Operated Series-Resonant Inverter for the Supply of DBD Excimer Lamps

This paper presents the study of a series-resonant inverter for the supply of a dielectric barrier discharge excimer lamp. Causal analysis, based on the fundamental properties of the load, is used to detail the reasoning which has led to this topology. In order to effectively control the lamp power, the operating mode of this converter combines discontinuous current mode and soft commutation (zero-current switching), obtaining low electromagnetic emissions and reduced switching losses as well. The model of the lamp is briefly presented, and it allows a simple state plane analysis to calculate all the electric variables involved in the converter and, consequently, to select the components of the supply. The mathematical relationships obtained from this process, for injected power control by means of the available degrees of freedom, are validated with simulations and experimental results.

State-Plane Analysis of Regenerative Snubber for Flyback Converters

The flyback converter is a popular topology for implementing low power and multiple output power supplies. However, the high leakage inductance of the flyback transformer causes high voltage spikes that can damage the main transistor when the switch is turned OFF. Therefore, a turn-off snubber is needed to limit the peak voltage stress. This paper presents the analysis of an energy regenerative snubber using the graphical state-plane technique. The undertaken approach yields a clear-cut design procedure for minimum switch voltage stress. Experimental evaluation of the energy regenerative snubber in comparison with other common snubbers shows that under the same voltage stress the efficiency of energy regenerative snubber has 8% improvement on average over an RCD snubber and 2% improvement over the nondissipative LC snubber.