Generalized State Space Averaging Research Articles

H‐infinity loop shaping control of wireless power transfer system based on generalized state space averaging model

SummaryThe transmission distance and the output load of wireless power transfer (WPT) system are particularly prone to change, which results in higher requirements for the robustness and dynamic performance of the control. In order to reduce the influence of these characteristics, an H∞ loop shaping controller based on generalized state space averaging (GSSA) method is proposed in this paper. Based on the GSSA model, an appropriate compensation function is constructed for the WPT system to the target loop transfer function. The nominal coprime factorization of WPT system is carried out, and on this basis, H∞ controller is achieved by Riccati equation to minimize the infinite norm from disturbance to error output. The designed controller meets the requirements of robust. Furthermore, the obtained high‐order controller is discretized by a reasonable discretization method, and the details and limitations of its practical application are discussed based on the hardware computational capacity. The experimental results show that the proposed controller has better robustness and dynamic performance and flexibility than the mixed sensitivity H∞ controller and the Z‐N PI controller.

Modeling of the Resonant Inverter for Wireless Power Transfer Systems Using the Novel MVLT Method

Wireless power transfer (WPT) is a power transfer technique widely used in many industrial applications, medical applications, and electric vehicles (EVs). This paper deals with the dynamic modeling of the resonant inverter employed in the WPT systems for EVs. To this end, the Generalized State-Space Averaging and the Laplace Phasor Transform techniques have been the flagship methods employed so far. In this paper, the modeling of the resonant inverter is accomplished by using the novel Modulated Variable Laplace Transform (MVLT) method. Firstly, the MVLT technique is discussed in detail, and then it is applied to model a study-case resonant inverter. Finally, a study-case resonant inverter is developed and utilized to validate the theoretical results with MATLAB/Simulink.

Duty Cycle Control Strategy for Dual-Side LCC Resonant Converter in Wireless Power Transfer Systems

The dual-side inductor–capacitor–capacitor (LCC) topology circuit has been widely adopted in wireless power transfer (WPT) systems due to its constant output current characteristic. However, most conventional control methods need specific synchronization techniques between the primary and secondary sides to avoid the oscillation in the system, which increases the cost and control complexity. To solve this issue, this article proposes a new duty cycle control (DCC) strategy for a dual-side LCC resonant converter with a semibridgeless active rectifier (SAR). With such a control strategy, gate signals of the primary- and secondary-side circuits do not need to be synchronized, which could reduce the complexity and the cost of the WPT system. Besides, the switching frequency of the secondary side can be decreased significantly. This article first presents the modal analysis of phase shift control (PSC) and DCC. Then, generalized state-space averaging (GSSA) modeling with PSC and the hybrid average modeling with DCC are performed. In addition, controllers’ design for both strategies is conducted to achieve the constant output voltage. Finally, the eigenvalues’ analysis is used to determine the stability region of the WPT system. The theoretical analysis has been validated by both simulation and experimental results.

Reliable [formula omitted] filtering for the SP resonant ICPT system with stochastic multiple sensor faults

The inductively coupled power transfer (ICPT) system is one of the most important system in the wireless power transfer field. In this paper, the reliable H∞ filtering problem is considered for the ICPT system based on the series–parallel (SP) resonant compensation network. A more general SP resonant ICPT system model is proposed with considering external disturbances and multiple sensor faults. The sensor faults are assumed to happen in a random way, which are described by a set of stochastic variables satisfying certain statistical features. The main purpose of the addressed problem is to design an H∞ filtering scheme such that the filtering error dynamics are asymptotically mean-square stability (AMSS). For this purpose, a generalized state-space averaging (GSSA) model is built to characterize dynamical behaviors of the SP resonant ICPT system first. Then the filtering-error system with stochastic sensor faults is established via the GSSA model. By virtue of an extended Lyapunov function, a sufficient condition is given to achieve the AMSS of the system and H∞ performance requirement. Subsequently, the H∞ filtering gains are obtained by solving a set of linear matrix inequalities. Finally, a simulation example is provided to verify the availability and reliability of the proposed filtering scheme.

Stabilization of DC MicroGrid Systems Using the Loop-Cancellation Technique

DC microgrid systems (DCMGs) feed power to constant power loads (CPLs) via transmission lines. Although these systems are commonly used worldwide, CPLs have negative impedance effects. These loads can significantly degrade the system stability. Therefore, stability study is very important to avoid inefficient operations. The model proposed in this article can be derived using a combination of the direct quadrature (DQ) method and the generalized state-space averaging (GSSA) method. This model is suitable for analyzing the system stability using the eigenvalue theorem. For stability analysis, the proposed (DCMGs) will be unstable before reaching the rated power when the irradiance is equal to 0 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Consequently, the loop-cancellation technique is applied to mitigate the unstable operation until the operation at the rated power can be achieved. Experimental and simulation results were used to confirm the theoretical analysis. The system performed well, and the results proved that the system could be stabilized using the proposed technique.

A Bidirectional Wireless Power Transfer System Control Strategy Independent of Real-Time Wireless Communication

For the bidirectional wireless power transfer (BWPT) technology, the phase synchronization between the transmitting and receiving converters is very essential and difficult to achieve by wireless communication between two sides because the delay and data transfer interval of wireless communication severely influence the control performance. This article proposes a novel control strategy for BWPT, which can achieve the phase synchronization and maximum efficiency point tracking independent of the real-time wireless communication. To solve the overshoot and oscillation problem incurred by the proposed control strategy and the nature of the system itself, the dynamics of a series-series compensated BWPT system is then analyzed and a small-signal model of this system is derived based on the generalized state space averaging and extended describing function methods. Using the small-signal model, a BWPT control system based on the proposed control strategy is designed and optimized. The validity of the proposed strategy and the performance of the control system are verified experimentally using a 3.3-kW prototype system.

The Analysis of Power supply Characteristics of Aircraft Power supply System

With the rapid development of multi-electric aircraft technology, the aircraft electrical power system is becoming more and more complex and significant. This paper analyzes power supply characterisitics of aircraft power supply system. First, the Generalized State Space Averaging (GSSA) technique is adopted to realize the digital simulation of complex aircraft electrical system. Next, AC vector coordinate transformation, digital zero-crossing detection and least squares polynomial fitting are used to analyze power supply characteristics of aircraft power supply system. Finally, the power quality of the power supply system is analyzed in the time domain and the trend analysis diagram of these power quality parameters with the variation of time is given.

Electromagnetic Transient Modeling and Simulation of Power Converters Based on a Piecewise Generalized State Space Averaging Method

Large-scale photovoltaic (PV) power plants connected to the grid leads to the complex calculations in modeling and simulation of the power system, especially in the electromagnetic transient progress. Common averaging methods are studied for modeling a grid-connected converter to simplify the calculation and balance accuracy and efficiency in the simulation. The piecewise technique is applied to the generalized state space averaging model of converters, which combine time segment with similar operating characteristic. In addition, a new piecewise generalized state space averaging (P-GSSA) model is derived and a multi time scale modeling is achieved for the grid-connected converters in PV systems. The model error and accuracy of the P-GSSA model are analyzed, the physical significance and the influence factors in the model error of P-GSSA model are discussed. The proposed P-GSSA model is flexible to be used in a PVs system simulation, and it can accurately reflect the steady-state and transient characteristics of a converter. The research shows that P-GSSA model improved the simulation efficiency over 20% by the index of consumed time, meanwhile, the model error analysis is under 5%. The analysis of the P-GSSA model is verified by simulating a DC/AC converter and a photovoltaic system.

Robust $\mu$ -Synthesis Control of Dual LCL Type IPT System Considering Load and Mutual Inductance Uncertainty

The output voltage of a dual LCL inductive power transfer (IPT) system varies with the load and mutual inductance, which can affect the system performance, e.g., the charging speed of electrical equipment. This paper proposes a robust controller to maintain constant output voltage against the load and mutual inductance variations. A μ-synthesis method is proposed based on structured singular value to design the dual LCL IPT closed-loop system. The frequency-domain nominal model of the system is established by using the generalized state-space averaging (GSSA) method. A standard M-Δ configuration is generalized through separating the nominal and uncertain block by upper linear fractional transformation (LFT). The μ-controller is finally obtained by D-K iteration. The robust performance analysis and time-domain performance analysis are also carried out. The simulation and experimental results verified the effectiveness of the proposed modeling and controller design, and demonstrated the robust stability and robust performance of the dual LCL IPT system.

Robust Control for Inductively Coupled Power Transfer Systems With Coil Misalignment

Coil misalignment in inductively coupled power transfer (ICPT) systems will lead to fluctuation of transferred power, and even instability of the ICPT systems. To obtain robust control for ICPT system with coil misalignment, a μ-controller based on structured singular value (SSV) is used to set up a closed-loop system in this paper. A generalized state-space averaging (GSSA) model is established using GSSA method first. Then a standard M-Δ configuration is obtained by a linear fractional transformation of the nominal and uncertainty parts of the GSSA model. Finally, a μ-controller is designed by D-K iteration. Besides, the theoretical results are validated by computer simulations and practical experiments.

Hybrid Average Modeling of Three-Phase Dual Active Bridge Converters for Stability Analysis

The three-phase dual active bridge (3p-DAB) converter is widely addressed in emerging power systems applications such as solid-state transformer and dc microgrids. Its successful integration requires accurate modeling of its small-signal characteristics. Due to its dc–ac–dc structure, the DAB converter brings many challenges to small-signal modeling. The state-space averaging (SSA) has been the first proposed methodology to approximate the control-to-output and line-to-output transfer functions of the 3p-DAB. However, as shown in this paper, SSA is not precise for the stability analysis of 3p-DAB converters. A generalized state-space averaging (GSSA) model based on the dynamic phasor concept is developed in this paper for the Y-Δ 3p-DAB. A hybrid SSA and GSSA model representation is then proposed for the evaluation of all the converter transfer functions. The developed models are validated with detailed time-domain switch-level simulations in an electromagnetic transient-type (EMT-type) program. They are also used for the accelerated stability prediction in an EMT-type program.

Dynamic modeling, control design and stability analysis of railway active power quality conditioner

Two-phase three-wire converter has been proposed to compensate the power quality issues in AC electrified railway systems. In this paper, a step-by-step modeling procedure is presented and applied to the compensator to obtain a linear model. The model is then used in a linear control system design and stability analysis of the compensator. The first step is to obtain the bi-linear form of the exact (switched) model of the compensator representing the high and low frequency behavior of the converter. Then, the generalized state space averaging is applied to the bi-linear model to obtain the continuous time model of the compensator. The linear small signal model is derived by differentiating the averaged model around its equilibrium point. Linear control system design is established based on the linear small-signal model to improve DC-link voltage performance. The simulated model of compensator is verified by quantitatively comparing to the previously reported experimental results. The verified simulation model is used to validate the obtained models. Finally, the open loop stability analysis is performed by studying the locus of system eigenvalues with respect to the circuit parameters variations.

Modeling and Analysis of 12-Pulse Inverter in Shipboard or Aircraft

Abstract With the development of DC distribution system within the isolated power system of a ship or an aircraft, more constant frequency loads will be supplied by inverters connected to DC main bus. In the operating mode conversion process of an isolated power system, inverters will inevitably suffer from serious disturbance and affect the stability of the system. Therefore, it is important to establish a model of the inverter that reflects its dynamic characteristics and based on which to conduct the stability analysis. This paper proposes a 12-pulse inverter model based on the generalized state space averaging (GSSA) method. This model can overcome the limitations of 12-pulse inverter state space averaging (SSA) model in transient analysis with good accuracy and fast analysis ability effectively. Three kinds of models for a 12-pulse aircraft inverter are built in MATLAB, namely GSSA model, SSA model and detail device model. The simulation results show the high accuracy of GSSA model in stability analysis. This study provides an effective analytical tool for stability analysis of 12-pulse inverter and also provides a reference for inverter modeling research of isolated power system such as in aircraft or ship.

High Robustness Control for Robotic Wireless Power Transfer Systems with Multiple Uncertain Parameters Using a Virtual Buck Converter

Aiming at achieving high robustness performance in Wireless Power Transfer (WPT) systems for moving robot power supply, this paper proposes a H∞ robust control method with multiple parameters that vary randomly, including the mutual inductance, load parameter, and operating frequency. These uncertain parameters make the system control extremely difficult. A composite Upper Linear Fractional Transformation (LFT) method is proposed to deal with the system uncertainty, particularly for the mutual inductance detachment, which is very unique and important for WPT systems. A suboptimal H∞ controller design method is proposed based on Generalized State Space Averaging (GSSA) model in order to simplify the system structure. In controller implementation, a virtual buck converter for phase shifted regulation is proposed to replace real input buck converter. The proposed H∞ control method is easy to implement because only the output voltage of the WPT system needs to be sampled, and based on which a simple DSP control algorithm is developed. Simulation and experimental results have demonstrated that the proposed control method can achieve less than 15 ms response speed with 70% mutual inductance variation and 50% load variation tolerance respectively.

A novel Generalized State-Space Averaging (GSSA) model for advanced aircraft electric power systems

The growing complexity of Advanced Aircraft Electric Power Systems (AAEPS) has made conventional state-space averaging models inadequate for systems analysis and characterization. This paper presents a novel Generalized State-Space Averaging (GSSA) model for the system analysis, control and characterization of AAEPS. The primary objective of this paper is to introduce a mathematically elegant and computationally simple model to copy the AAEPS behavior at the critical nodes of the electric grid. Also, to reduce some or all of the drawbacks (complexity, cost, simulation time…, etc) associated with sensor-based monitoring and computer aided design software simulations popularly used for AAEPS characterization. It is shown in this paper that the GSSA approach overcomes the limitations of the conventional state-space averaging method, which fails to predict the behavior of AC signals in a circuit analysis. Unlike conventional averaging method, the GSSA model presented in this paper includes both DC and AC components. This would capture the key dynamic and steady-state characteristics of the aircraft electric systems. The developed model is then examined for the aircraft system’s visualization and accuracy of computation under different loading scenarios. Through several case studies, the applicability and effectiveness of the GSSA method is verified by comparing to the actual real-time simulation model obtained from Powersim 9 (PSIM9) software environment. The simulations results represent voltage, current and load power at the major nodes of the AAEPS. It has been demonstrated that the obtained results from GSSA model in Matlab® closely agree with those of obtained in an actual AAEPS implemented in PSIM9 software.

Modeling and Simulation of Full-Bridge Series Resonant Converter Based on Generalized State Space Averaging

The small signal modeling technique based on the generalized state space averaging method is applied to single phase full-bridge resonant DC/DC converter .According to the simulation, the frequency characteristic curve is obtained from MATLAB, this paper analyzes the influence of the duty ratio, input voltage to frequency characteristics, then builds a closed loop simulation circuit with PSIM software, the simulation results show that, the small signal model has good controllability and anti disturbance resistance, generalized state space averaging method is more accurate to series resonant converter modeling.

Validation of Generalized State Space Averaging Method for Modeling and Simulation of Power Electronic Converters for Renewable Energy Systems

This paper presents an advanced modeling and simulation technique applied to DC/DC power electronic converters fed through renewable energy power sources. The distributed generation (DG) system at the Illinois Institute of Technology, which employs a phase-l system consisting of a photovoltaic-based power system and a phase-2 system consisting of a fuel cell based primary power source, is studied. The modeling and simulation of the DG system is done using the generalized state space averaging (GSSA) method. Furthermore, the paper compares the results achieved upon simulation of the specific GSSA models with those of popular computer aided design software simulations performed on the same system. Finally, the GSSA and CAD software simulation results are accompanied with test results achieved via experimentation on both, the PV-based phase-l system and the fuel cell based phase-2 power system.

Robust controller for a full-bridge rectifier using the IDA approach and GSSA modeling

An interconnection-and-damping assignment passivity-based control (IDA-PBC) for a full-bridge rectifier is presented in this paper. The closed-loop system performance fulfils unity power factor in the ac mains and output dc voltage regulation. The controller design takes advantage of the generalized state space averaging (GSSA) modeling technique to convert the quoted nonstandard problem (in actual variables) into a standard regulation one (in GSSA variables). In this approach, the output current is the measured signal instead of the line current; therefore, the number of sensors does not increase in comparison with traditional approaches. The whole system is robust with respect to load variations.

GENERALIZED STATE SPACE AVERAGING FOR PORT CONTROLLED HAMILTONIAN SYSTEMS

Generalized state space averaging (GSSA) is a powerful way to treat analysis and control problems for variable structure systems (VSS). On the other hand, port-controlled Hamiltonian systems (PCHS) describe, in a modular, network-like way, the interconnection of physical systems using the transfer of energy as the unifying concept. In this paper, a relationship between the PCHS structures of a system and its GSSA expansion is established for a class of Hamiltonians (which includes the quadratic ones), and this is used to design controls from a GSSA truncation which, under certain restrictions, can be used for the full original system.

A unified averaging technique for the modeling of quasi-resonant converters

A unified averaging technique, here called the generalized state-space averaging (GSSA) technique, for the analysis of a class of periodically switched networks is proposed in the present paper. The basic assumption of GSSA is that the switching frequency must be much higher than the highest natural frequency of the networks, while the input variables can be bounded fast time-varying functions. It is shown in this paper that the GSSA approach generalizes the idea of the averaging technique to overcome the limitations of the conventional state-space averaging method, which prevents us from applying it to quasi-resonant converters (QRCs). The application of GSSA to the analysis of QRCs has been illustrated via examples of the zero-current switching QRC buck converter and zero-voltage switching QRC boost converter. Its accuracy has been verified by numerical simulation and experimental results.