State Space Average Method Research Articles

Applying Particle Swarm Optimization for Investigating the Stability of DC-DC Buck-Boost Converter: A Software Based Approach

ABSTRACT Stability of power converters has always been a major concern when dealing with nonlinear behavior of the system and swarm-based optimization techniques are proven to be handy as they are widely employed. Hence, this study presents an investigative approach to explore the compatibility of applying different variants of Particle Swarm Optimization (PSO) to design an optimized PID controller for DC-DC Buck-Boost converter. This work assesses converter stability through optimization of the PID controller using classical PSO (cPSO), Time-Varying Inertia Weight PSO (TVIW-PSO), Chaotic Descending Inertia Weight PSO (CDIW-PSO), Self-organizing Hierarchical PSO (HPSO) and Random inertia weight PSO (RIW-PSO). The State Space Average (SSA) method is utilized to model and attain the transfer function; eigenvalue analysis and time domain simulation analysis are considered to investigate the stability. Moreover, four objective functions and various performance parameters such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated to assess the system’s efficiency and the outcomes of different approaches are compared extensively. Amongst all, CDIW-PSO showcased better performances e.g. overshoot of 1.08%, settling time 0.000228s and rise time 0.000143s. The findings illustrate algorithm’s capacity to reduce transient and steady-state faults and makes it compatible with more nonlinear applications.

Voltage Equalizing Strategy for Cascaded Constant Current Power Supply

In order to detect the underground medium with large depth, the transmitter of electromagnetic sounding instrument has higher and higher power and voltage. A novel voltage equalizing strategy for cascaded constant current power supply using in electromagnetic transmitter was proposed in this paper. The cascaded topology of the transmitter has two isolated full‐bridge AC/DC converters, which had same input source and were connected in series on the output side. The mathematical model based on state space average method was analyzed. After simplifying the circuit, the state space equation was used to describe the circuit model. The stability and frequency characteristics of the system were analyzed. Aiming at the constant current output and the output voltage balance of the two converters, the system coupling model was established. The constant current controller and voltage equalizing controller were designed with decoupling method. A 300 W prototype was built and the experimental results verified the performance of the proposed method. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

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.

Improvement of circuit oscillation generated by underwater high voltage pulse discharges based on pulse power thyristor

High voltage fracturing technology was widely used in the field of reservoir reconstruction due to its advantages of being clean, pollution-free, and high-efficiency. However, high-frequency circuit oscillation occurs during the underwater high voltage pulse discharge process, which brings security risks to the stability of the pulse fracturing system. In order to solve this problem, an underwater pulse power discharge system was established, the circuit oscillation generation conditions were analyzed and the circuit oscillation suppression method was proposed. Firstly, the system structure was introduced and the charging model of the energy storage capacitor was established by the state space average method. Next, the electrode high-voltage breakdown model was established through COMSOL software, the electrode breakdown process was analyzed according to the electron density distribution image, and the plasma channel impedance was estimated based on the conductivity simulation results. Then the underwater pulse power discharge process and the circuit oscillation generation condition were analyzed, and the circuit oscillation suppression strategy of using the thyristor to replace the gas spark switch was proposed. Finally, laboratory experiments were carried out to verify the precision of the theoretical model and the suppression effect of circuit oscillation. The experimental results show that the voltage variation of the energy storage capacitor, the impedance change of the pulse power discharge process, and the equivalent circuit in each discharge stage were consistent with the theoretical model. The proposed oscillation suppression strategy cannot only prevent the damage caused by circuit oscillation but also reduce the damping oscillation time by 77.1%, which can greatly improve the stability of the system. This research has potential application value in the field of underwater pulse power discharge for reservoir reconstruction.

Research on Current Distribution Strategy Based on Interleaved Double Boost Converter

In the new energy DC microgrid system, most of the new energy outputs DC power with a low voltage level and a large fluctuation range, which cannot be directly connected to the network. It needs to be boosted by a DC–DC converter, then connected to the power grid or supplied with a DC load. On the premise that the traditional DC–DC converter cannot meet the requirements of high-power applications, the interleaved dual boost converter (IDBC) has been widely used because of its low input current ripple, low device stress and high-power density. It is necessary to maintain the current balance of each phase of the converter during a heavy load and to improve the efficiency during a light load. This paper analyzes the working principle of the six-phase IDBC and reduces the high order model to the low order model according to the symmetry. Due to the current imbalance caused by the mismatch of the parasitic parameters of each phase, two current distribution strategies are designed for different operating. To balance the current of each phase when the converter is overloaded, the relationship between the phase current, parasitic parameters and duty cycle is analyzed based on the state space average method. The estimated parasitic parameters are used to obtain the duty cycle compensation of each phase to eliminate the current imbalance. In addition, to improve the overall efficiency of the converter when the converter connects with a light load, the optimal power distribution coefficient is obtained according to the parasitic parameters to achieve the optimization of the input power, so as to improve the efficiency of the converter. Finally, the simulation results verify the feasibility and effectiveness of the proposed control strategy.

Simulation research on sliding mode PID control of Buck converters with improved approaching law

To solve the problem that Buck converters under traditional control strategies will be affected by various disturbances, resulting in poor stability, a new sliding mode PID control strategy based on improved power exponential reaching law is proposed. The sliding mode PID control model of Buck converter is constructed by using the state space average method. On this basis, the traditional reaching law is improved, and the system equivalent control expression of the improved reaching law is obtained by calculation. Finally, according to the equivalent control expression, the control models are built in Matlab/Simulink simulation software, and compared with the PWM-based sliding mode PID control strategy. The simulation results show that the controller with improved reaching law can effectively reduce chattering, steady-state error and overshoot of the system. Besides, the improved controller can make the robustness of the system better.

Dynamic Modeling and Closed-Loop Control of a Tapped Inductor Buck Converter

Modern smart electronic and information technology (IT) devices require a low DC voltage for operation. The low supply voltage is typically provided by a dedicated DC−DC converter by stepping down the system’s bus voltage (e.g., 12 V). It is essential that the converter possesses a large voltage step-down gain and, at the same time, operates at high efficiency. A tapped inductor buck converter (TIBC) is a topology that has a potential to meet these requirements. It has a simple circuit structure and high efficiency similar to a buck converter, but can give a larger voltage step-down gain. This paper presents a dynamic modeling and closed-loop control of a TIBC. The state space averaging (SSA) method is adopted for the dynamic modeling to derive small-signal transfer functions of the converter. Based on the duty-cycle-to-output voltage transfer function, a closed-loop control is designed to keep the converter’s output voltage constant. To verify the design, a prototype TIBC with closed-loop control is implemented. Experimental results show that the prototype converter has good output voltage regulation and fast transient response when subject to a step load. The effect of the crossover frequency and phase margin on the converter’s transient response is also illustrated.

МОДЕЛЮВАННЯ ПРОЦЕСІВ НА ОСНОВІ УСЕРЕДНЕННЯ В ПРОСТОРІ СТАНІВ У ПІДВИЩУВАЛЬНОМУ ПЕРЕТВОРЮВАЧІ З МАГНІТОПОВ’ЯЗАНИМИ ЕЛЕМЕНТАМИ

The features of the state-space average method using Lagrange's theorems for calculation of processes in the boost converter with magnetically coupled elements (with autotransformer connection of inductors) in continuous currents mode are considered. A mathematical model of the converter based on relative variables has been developed, which makes it possible to calculate processes in a wide range of parameters taking into account the degree of magnetic coupling between inductive elements, including the definition of constant and pulsating components. It is shown that to obtain a complete system of the algebraic equations as a mathematical model of converters, which provides its single solution, it is advisable to additionally use the ratio according to energy balance in reactive elements in a steady state at the operation intervals of the converter during commutation period. The boundary dependences of boost converter parameters with magnetically coupled elements between the modes of discontinuous and continuous currents are calculated. The relative characteristics of the converter have been studied, which demonstrate the influence of imperfection of the magnetic coupling in the regulation zone of the relative duration value of switching interval. Ref. 21, fig. 6.

Optimum Parametric Identification of a Stand-Alone Photovoltaic System with Battery Storage and Optimization Controller Using Averaging Approach

The dimensioning of photovoltaic systems is the major concern of researchers and power industry practitioners. This aims to improve energy efficiency and protect the conversion units by a consistent assessment of power conditioning circuits and interconnections for the PV application. In this context, this paper sets out to fulfill detailed modeling and control steps of a standalone photovoltaic (PV) power system with energy storage, according to practical specifications of the load, PV generation unit, and battery pack. The main goal is to estimate all unknown parameters, as the diode ideality factor and revers saturation current, the controller, and the PV link. The PV link interfacing the PV source circuit to the PV-side converter (PVSC) provides a filtering function to maintain a steady voltage at the link. The charge controller used in the PV-side converter is a DC/DC buck converter. It transfers the PV power to the battery and supplies the load. Using pulse- width modulation (PWM) technical, of which the switching duty cycle is the control-input variable; the PVSC power-conditioning circuit is permanently controlled by the maximum power point tracking (MPPT) algorithm to achieve the maximum energy. The battery pack voltage is properly maintained by the charge controller and specified to match the load voltage rating, to avoid a high ratio of voltage conversion. A method is proposed to integrate both the MPPT function and the battery cycle charge. The PV generator output and the power conditioning circuits, mainly constructed from switching- mode power converters, are nonlinear. An averaged model is then derived for dynamic analysis and controller synthesis, using the state-space averaging and linearization method. A PV array of nine PV modules configured into three strings is used in this application to demonstrate the effectiveness of modeling, design, control, and simulation. Simulation model for the controller and power interface is built and developed in short term, using the fundamental blocks of Matlab Simulink.

Photovoltaic Off-Grid Inverter and Maximum Power Point Tracking Technology

The photovoltaic cells’ output characteristics and maximum power point tracking (MPPT) technology are studied to design a two-stage cascaded photovoltaic off-grid inverter, including the front-end Boost converter and the rear-end three-phase inverter. The state-space averaging method is adopted in front-end Boost converter modeling, and space vector pulse width modulation (SVPWM) technology is adopted in the rear-end three-phase inverter. The simulation drive model is obtained through research principles and algorithm realization. Based on the theoretical analysis and simulation, front-end Boost converter’s and the back-end inverter’s hardware are designed. The main circuit includes the front-end Direct Current (DC)-DC topology and the back-end DC-AC topology. The TMS320F28027 digital signal processor is the core of the front-end DC-DC topology’s control system, and LabView is the core of the back-end DC-AC topology’s control system. The front-end Boost converter’s analog output voltage is 32 V, stable at the maximum operating point in the test. The maximum power point can be effectively tracked in the proposed inverter. The rear-end three-phase inverter’s total harmonic distortion (THD) of phase voltage is less than 3%. Less harmonic wave meets the circuit harmonic distortion rate’s design requirements.

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.

New Optimal Control Algorithms for Battery-Supercapacitor HESS Based on Wirtinger-Based Integral Inequality

This paper focuses on the design of new optimal control algorithms for battery-supercapacitor hybrid energy storage system (HESS) with input saturation and time delay. Different from the existing research results, a new state feedback system to track the output DC bus voltage and battery current is developed via the state-space averaged model method. By fully considering the state delay information, a proper Lyapunov–Krasovskii functional (LKF) is constructed. In order to reduce the inherent conservation, Wirtinger-based integral inequality is firstly employed to establish novel stability criteria of battery-supercapacitor HESS. Meanwhile, for the sake of shortening the transition time and realizing the smooth transition of some key variables during the load switch, new optimal control algorithms with actuator saturation can be achieved in terms of linear matrix inequalities (LMIs). Finally, numerical results are presented to verify the effectiveness and superiority of the analysis results.

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.

Research on a single-stage isolated electrolytic capacitor-less LED driver

The lifetime of traditional light-emitting diode (LED) drivers is mainly affected by electrolytic capacitor. Therefore, a single-stage isolated electrolytic capacitor-less LED driver is proposed, with which the electrolytic capacitor is eliminated and the output current ripple is reduced. Firstly, the operation principle and switching mode of the topology are analyzed. Then, the feasibility of the topology is analyzed by using the state space average method. Finally, an experimental prototype of 60 W output power is built to verify the correctness of the scheme.

Mathematical Modeling of Current Source Matrix Converter with Venturini and SVM

The study of Current Source Matrix Converter (CSMC) static properties using the averaged state-space method for two modulation strategies Venturini and Space Vector Modulation (SVM) is the subject of this article. The converter properties for both modulation strategies have been examined and compared. The modeling approach based on the averaged state space method presented in this paper is relatively simple and requires only a small number of mathematical transformations. The averaged set equation is obtained directly from the three-phase schematic circuit, taking into account the sequences of switching patterns and modulation strategies. All the obtained results have confirmed that CSMC has some interesting properties, such as buck–boost output voltage regulation unlike the classic Matrix Converter (MC), in which the maximum voltage gain is 0.866.

Design of backstepping controller for T-type network inverter

In the process of power conversion of new energy generation, complex two-stage converter is needed. T-type network inverter is a kind of transformer that can realize three-phase power output from two single-phase output inverters. Functional Topology, the purpose of this paper is to design the circuit topology and controller so that the inverter output voltage meets the power supply requirements. First, the DC power input circuit and transformer structure are designed according to the principle of voltage vector synthesis. Then the controller is designed by state space average modeling method and backstep method. Finally, the system model is built by Matlab/Simulink simulation software. The conversion of 27V DC power to 220V / 50Hz three-phase power for market power supply verified The effectiveness of The design content of this paper.

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.

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.

Design of a distributed non‐linear stabiliser in MG using synergetic control theory

Stability of inverter-dominated microgrids (MGs) faces many challenges such as inertia shortage, mutual interactions among converters and sudden external disturbances. To enhance the stability of MGs, a distributed non-linear stabiliser is designed in this study based on synergetic control theory. First, inverter interfaces are uniformly modelled as virtual synchronous generators, whose small-signal stability is then analysed with the state-space average method. Also, the objective of the following control strategy, i.e. the system unstable domain, is obtained. Second, macro-variables applicable to droop control are constructed based on the typical dynamic model and then the analytic expression of the controller output could be derived. When external disturbances occur, or droop coefficients with high gains are chosen, power system stability could be guaranteed by adding a non-linear stabiliser. Finally, taking a 9-node MG as an example, simulation verifies the feasibility of the proposed strategy in cases of small disturbances, large disturbances and mode transition.

Frequency response analysis of periodically time varying circuits

PurposeThe purpose of this paper is to introduce a method for the analysis of steady-state processes in periodically time varying circuits. The method is based on a new definition of frequency responses for periodic time-varying circuits.Design/methodology/approachProcesses in inverter circuits are often described by differential equations with periodically variable coefficients and forcing functions. To obtain a steady-state periodic solution, the expansion of differential equations into a domain of two independent variables of time is made. To obtain differential equations with constant coefficients the Lyapunov transformation is applied. The two-dimensional Laplace transform is used to find a steady-state solution. The steady-state solution is obtained in the form of the double Fourier series. The transfer function and frequency responses for the inverter circuit are introduced.FindingsA set of frequency characteristics are defined. An example of a boost inverter is considered, and a set of frequency responses for voltage and current are presented. These responses show a resonance that is missed if the averaged state-space method is used.Originality/valueA new definition of frequency responses is presented. On the basis of frequency responses, a modulation strategy and filters can be chosen to improve currents and voltages.