State-space Averaged Model Research Articles

Multiscale Change Point Detection for Univariate Time Series Data with Missing Value

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data.

State Space Average Modeling, Small Signal Analysis, and Control Implementation of an Efficient Single-Switch High-Gain Multicell Boost DC-DC Converter with Low Voltage Stress

This paper presents the closed-loop control of a single-switch high-gain multicell boost DC-DC converter working in a continuous conduction mode (CCM). This converter is particularly designed for applications in photovoltaic systems. One of the main advantages of the proposed converter is that it only employs one active semiconductor switch, which decreases the converter losses and cost, increases the efficiency, and simplifies the control circuit. Moreover, the multicell nature of the proposed converter offers the possibility of obtaining the required voltage gain by selecting the number of cells. State space average (SSA) modeling and small-signal analysis are used to model the switching converter power stages of the proposed converter. The parasitic series resistances of the passive elements of the converter circuit are considered to improve the accuracy of the modeling. Small-signal analysis is used to derive the open-loop transfer functions, input-to-output and control-to-output transfer functions of the proposed converter to examine its dynamic performance. The stability of the converter is analyzed to design the parameters of the voltage controller using the proposed modeling method. The experimental prototype of the proposed single-switch two-cell boost DC-DC converter was implemented. The simulation and experimental results proved the effectiveness of the proposed boost DC-DC converter under different working conditions. It has a fast dynamic response without overshoots. A comprehensive comparison between the proposed converter and previous boost converters is provided. It guarantees a required variable and constant high voltage gain with a wider duty ratio range. It compromises between the required performance, the low number of components, low voltage stress on the components, and cost-effectiveness. The experimental efficiency of the proposed converter is about 96% at a 100 W load.

A stability improvement control strategy research for LLC resonant converter with single neuron PI-I double closed loop control

LLC resonant converters are widely used in the aerospace field. However, under traditional single-loop control, LLC resonant converters are prone to instability in the face of high-power load disturbances, which fails to meet the high stability requirements of the aerospace field. In order to enhance the stability and disturbance rejection capability of the LLC resonant converter, this paper proposes a stability improvement strategy with additional resonant voltage integral control based on the generalized state-space aver-aged model of the LLC resonant converter. By combining eigenvalue sensitivity analysis and eigenvalue analysis theory, the system stability is further optimized. To achieve control parameter adaptive adjustment, a single neuron algorithm is introduced, resulting in an LLC resonant converter with a single neuron PI-I double closed-loop control. Simulation results indicate that the proposed LLC resonant converter with single neuron PI-I double closed-loop control exhibits improved stability compared to the LLC resonant converter under traditional single-loop control.

A novel modulation for four‐switch Buck‐boost converter to eliminate the right half plane zero point

AbstractThe four‐switch Buck‐Boost (FSBB) converter are widely used in combination with other isolated converter to extend the voltage range capability of the overall structure. When the converter operates in buck‐boost mode and boost mode, it exhibits a right half plane zero (RHPZ) in the control to output transfer function. This characteristic would cause negative impact to stability of the converter. In order to eliminate the RHPZ, a novel modulation method is proposed in this paper. The buck mode is introduced to the modulation to adjust the voltage gain, and the corresponding average state space modeling for the FSBB with the proposed modulation is established. The simulation of the converter with the proposed modulation method and traditional modulation are presented. Finally, experiment results by hardware in the loop (HIL) platform is employed to verity the correctness of theoretical analysis results.

Fractional-Order Modeling and Nonlinear Dynamic Analysis of Forward Converter

To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. And nonlinear dynamical bifurcation maps which use PI controller parameters and a reference current as bifurcation parameters are obtained. The nonlinear dynamic behavior is analyzed and compared with that of an integral-order forward converter. The results show that under certain operating conditions, the fractional-order forward converter exhibits bifurcations characterized by low-frequency oscillations and period-doubling as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the forward converter. The stable zone of the fractional-order forward converter is larger than that of the integral-order one. Therefore, the circuit struggles to enter states of bifurcation and chaos. The stability domain for low-frequency oscillations and period-doubling bifurcations can be accurately predicted by using a small signal model and a predictive correction model of the fractional-order forward converter, respectively. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified.

Generalized state‐space averaging modeling to fourth‐order power converters operating in DCM

AbstractThis paper presents a novel methodology for correcting the state‐space averaging (SSA) modeling for DC‐DC power converters represented for fourth‐order systems operating in discontinuous conduction mode (DCM). SSA modeling has been widely employed for converters operating in continuous conduction mode (CCM), obtaining a good similarity between the switched converter and the mathematical model. In contrast, when the converters work in DCM, significant deviations between the average and RMS values imply errors in the SSA model. Hence, the proposed generalized SSA modeling methodology provides an accurate model to aid the controllers and system design. Consequently, the proposed technique can be applied to distinct fourth‐order power converters such as Zeta, Ćuk, and SEPIC in several applications. Additionally, SSA corrections can be associated with different techniques for obtaining the small‐signals representation. Simulation and experimental results and mathematical analyses that prove the feasibility and functionality of the proposal are addressed.

Fractional order modelling and optimal control of dual active bridge converters

As the construction of new power systems centred around renewable energy gains traction, the installed capacity of new energy sources has experienced explosive growth. Research has shown that the actual external characteristics of inductors and capacitors in circuits exhibit fractional order characteristics. As a core device in dual active bridge converters, the non-integer order of inductors and capacitors has an important impact on their dynamic performance, frequency domain characteristics, and control system design. This paper conducts modelling and control research on dual active bridge converters based on fractional-order calculus theory. First, based on the definition of fractional-order calculus, according to the operating mode of the fractional-order dual active bridge converter and the characteristics of fractional-order components, The fractional-order state space average model was established, and the influence of the order of inductance and capacitance on the amplitude frequency characteristics, phase frequency characteristics and dynamic performance of the converter was analyzed. Secondly, the average model and circuit model were built on the MATLAB/Simulink simulation platform, and the simulation results under different fractional orders were compared. Finally, in order to further improve the control performance of the converter, a fractional-order P I λ control strategy is designed based on the established state space average model of the fractional-order dual active bridge converter and based on the transfer function from the control to the output of the fractional-order dual active bridge converter. The research results show that the fractional-order model can more accurately describe the actual characteristics of the converter. In addition, the fractional-order controller P I λ enables the fractional-order dual active bridge converter to obtain better robustness and improve the dynamic performance of the converter.

A high gain Z-source boost DC–DC converter with common ground for solar PV applications

This paper proposes a high-gain dc–dc converter with common ground utilizing a Z-source network for low voltage solar photovoltaic (PV) applications. This converter features a common ground and a high output–input voltage conversion factor at a low duty cycle. These converters find their most common application in grid-tied or stand-alone solar photovoltaic systems, particularly those with low output voltages that must be increased to the required level. The presented converter operating duty ratio is within 0–0.5 and maintains similar voltage stress on Z-network components since it employs the conventional Z-source configuration. The presented converter provides a common ground between source and load, unlike conventional Z-network converter. A type-2 closed-loop voltage controller and state–space average model evaluate the converter’s dynamic behavior for reliable and steady performance. A laboratory hardware prototype of 250 Watts is built and low gate signals are generated by using a ARM cortex M4 Microcontroller (STM32F407VGT6). The experimental results confirm that the proposed converter, with a gain of 10.46 and a power of 250 Watts, has a maximum efficiency of around 93%. The experimental results validates the effectiveness of the proposed converter under both constant and shifts in amounts of solar irradiation.

A new generalized state-space averaged model, control design and stability analysis for three phase grid-connected quasi-Z-Source inverters

A comprehensive dynamic model of the three-phase grid-connected quasi Z-Source inverter (qZSI) with LCL filter is presented based on the generalized state-space averaging (GSSA) method. The developed model mathematically describes (i) the dynamic interaction between DC and AC side variables of converter and (ii) good dynamical precision that ensures a good description of the input–output dynamics, as well as the internal. Then, based on the developed model, a cascaded PI controller by nesting multi-control loops to regulate DC side capacitor voltage and inductor current is proposed. The PI controllers determine the grid and inverter current references in the d- and q-axes by regulating the DC side capacitor voltage. An LMI approach for stability analysis of the proposed controller, reliability calculations and switching losses are investigated. The accuracy of the developed qZSI inverter model and the effectiveness of proposed controls are verified by time-domain simulations of a study system in the MATLAB/SIMULINK environment and hardware-in-the-loop (HIL) simulation.

Applying k‐nearest neighbors to time series forecasting: Two new approaches

AbstractThe k‐nearest neighbors algorithm is one of the prominent techniques used in classification and regression. Despite its simplicity, the k‐nearest neighbors has been successfully applied in time series forecasting. However, the selection of the number of neighbors and feature selection is a daunting task. In this paper, we introduce two methodologies for forecasting time series that we refer to as Classical Parameters Tuning in Weighted Nearest Neighbors and Fast Parameters Tuning in Weighted Nearest Neighbors. The first approach uses classical parameters tuning that compares the most recent subsequence with every possible subsequence from the past of the same length. The second approach reduces the neighbors' search set, which leads to significantly reduced grid size and hence a lower computational time. To tune the models' parameters, both methods implement an approach inspired by cross‐validation for weighted nearest neighbors. We evaluate the forecasting performance and accuracy of our models. Then, we compare them to other approaches, especially, Seasonal Autoregressive Integrated Moving Average, Holt Winters, and Exponential Smoothing State Space Model. Real data examples on retail and food services sales in the United States and milk production in the United Kingdom are analyzed to demonstrate the application and efficiency of the proposed approaches.

Normalized Error-Based PI Controller and Its Application to the DC–DC Buck Converter

In this article, the structure of the normalized error-based proportional-integral (PI) controller is presented and its application to the DC–DC buck converter is discussed. The main motivation is to overcome the drawbacks of saturation and the limited range of controller gains offered by the traditional PI controller. Initially, the theoretical structure and advantages of an improved PI controller are shown. Next, the problem of regulation of the step-down DC–DC converter is addressed using the proposed controller. The objective is to keep the load voltage constant even when the converter parameters vary. The averaged state-space model of the converter is presented and a detailed stability analysis based on the Lypunov indirect method is carried out. The results show an improved range of controller parameters when the proposed controller is employed. Finally, some simulation results are shown to illustrate the effect of controller parameter variations on the output response. These results also verify the ability of the proposed controller to handle the changes in the load, input voltage, and reference voltage of the converter. Moreover, a comparative simulation study validates the superior transient response of the proposed normalized error-based PI controller over the traditional PI controller.

State-Space Averaged Model of Three-Phase Four-Wire Shunt Active Power Filter Based on Current-Controlled VSI

This work presents a universal state-space average model of three-phase four-wire shunt active power filter based on current-controlled voltage-source inverters. In this type of inverters two topologies are commonly used, namely the Four-Leg Full-Bridge (FLFB) topology, and the Three-Leg Split-Capacitor (TLSC) topology. Combining these topologies, a third topology can be obtained, namely the Four-Leg Split-Capacitor (FLSC) topology. This last topology exhibits very interesting characteristics for active filter applications. By means study of FLSC topology a state-space average model can be obtained, which will allow long-time simulations with a low cost of computation time. The behaviour of FLFB and TLSC converters can be obtained as particular cases of this universal model. Likewise, a generic technique for injected current control is proposed, offering as main advantage a decoupled control of the different legs, so full-bridge converters can be implemented without using space-vector based current control techniques.

State-Space Modeling, Design, and Analysis of the DC-DC Converters for PV Application: A Review

Small-signal models of dc-dc converters are often designed using a state-space averaging approach. This design can help discuss and derive the control-oriented and other frequency-domain attributes, such as input or output impedance parameters. This paper aims to model the dc-dc converters for PV application by employing a capacitor on the input side. The modeling, design, and analysis of the dc-dc converters regarding the input capacitor is limited in the literature. Five dc-dc converters, including buck, boost, buck-boost, ĆUK, and SEPIC converters, are designed and implemented using the state-space average modeling approach in MATLAB/Simulink. The circuit topology of each converter and the state-space matrices are derived considering every constraint. A rigorous and compelling analysis of the dc-dc converters is carried out to compare system stability and, ultimately, the dynamic performance. The output of the resulting small-signal models has been demonstrated in the time-domain against topology simulations. All the converters are exposed to unpredictable weather conditions and the simulations are carried out in the PSIM software. The perturb and observe (P&O) maximum power point tracking (MPPT) algorithm is applied in all the converters to ensure maximum power point (MPP) achievement. The results showcase that the boost converter outperforms all other converters in terms of stability, settling time, and overshoot.

Model of quasi-Z-source inverter-based PV power systems for stability studies of multi-terminal AC grid-connected PV power systems

Photovoltaic (PV) power systems are becoming one of the most popular green power systems. Power converters are used in these systems. Among them, quasi-Z-source inverters (qZSIs) are currently on the rise. However, instabilities can appear in multi-terminal AC grid-connected power electronics, such as PV power systems, due to the interaction between power electronic controls and the grid. Modeling of qZSI-based PV power systems is lacking in the literature and stability assessment of grid-connected qZSI-based PV power systems is not yet well understood. Accordingly, the present paper contributes with an s-domain dq-real admittance transfer matrix model of qZSI-based PV power systems derived from their small-signal state-space averaged model. The paper also describes a systematic procedure to study multi-terminal AC grid-connected qZSI-based PV power systems by the nodal admittance method, where the proposed qZSI-based PV power system model is incorporated into the nodal admittance matrix to study stability concerns. Thus, AC grid dynamics in the presence of qZSI-based PV power systems can be investigated using impedance-based stability criteria. The proposed model and the procedure are applied in a stability study of two applications where solutions for improving stability issues are presented. In these applications, the two main causes of instabilities in AC-grid connected PV-qZ systems are analyzed in detail. The study is validated by PSCAD/EMTDC simulation. .

Voltage Stability Control of Boost Converter Using Linear Quadratic Integrator

This paper proposes an optimal control design to regulate output voltage of DC/DC boost converter. Linear Quadratic Integrator (LQI) was designed by determining Q and R weighting matrices in order to minimize error output voltage on several disturbance scenarios. The state-space average model of the boost converter is generated using MATLAB/Simulink, while the controller gain is obtained using LQI function on MATLAB/M-file. We also conduct simple hardware experiment using Arduino board as the main controller. The simulation results for the two test scenarios, namely changing input condition and changing load condition show an IAE value was less than 0.2. In the hardware experiment result, the steady-state error value was less than 9.5% for the both test scenarios.

A Backflow Power Suppression Strategy for Dual Active Bridge Converter Based on Improved Lagrange Method

Dual-active bridge (DAB) converters are receiving increasing attention from researchers as a critical part of the power transmission of energy routers. However, the DAB converter generates a large backflow power in conventional control mode, and when the load is mutated, its output voltage takes longer to return to the reference value accompanied by large fluctuations. To solve the above problems, a hybrid strategy is proposed in this paper to optimize the converter. The mathematical models of the transmitted power and the backflow power were firstly derived through in-depth analysis of the DAB converter under extended-phase-shift (EPS) modulation, and the suppression of the backflow power was performed according to the improved Lagrange method utilized in the obtained results. Moreover, considering the poor dynamic characteristics of DAB converters under PI control, according to the state space average model of output voltage in the paper, a model prediction control equation is established to improve the dynamic response of the converter by predicting the output voltage value at the next moment. The simulation results verify the effectiveness of the optimization strategy presented in the text.

A Unified Switched Nonlinear Dynamic Model of an Electric Vehicle for Performance Evaluation

The advanced modeling and estimation of overall system dynamics play a vital role in electric vehicles (EVs), as the selection of components in the powertrain and prediction of performance are the key market qualifiers. The state-space averaged model and small-signal transfer function model are useful for assessing long-term behavior in system-level analysis and for designing the controller parameters, respectively. Both models take less computation time but ignore the high-frequency switching dynamics. Therefore, these two models could be impractical for the development and testing of EV prototypes. On the other hand, the multi-domain model in available simulation tools gives in-depth information about the short-term behavior and loss analysis of power electronic devices in each subsystem, considering the switching dynamics in a long computation time. In this paper, a general mathematical framework for the dynamical analysis of complete EVs is presented using a unified, switched nonlinear model. This equation-based model runs faster than the available module-based simulation tools. Two other models, namely the time domain state-space averaged model and frequency domain small-signal transfer function model, are also developed from the switched nonlinear model for the analysis with less computation time. The design and performance of an EV with two different motors and its controllers are evaluated using the general mathematical framework.

A Novel Carrier Based Precharging Technique for Single-Phase Odd-Level Flying Capacitor Multilevel Converters (FCMCs)

Flying Capacitor Multilevel Converter(FCMC) needs all its flying-capacitors charged to the appropriate voltage levels during stat-up. This paper presents a novel carrier based precharging technique for single-phase odd-level FCMCs. A new set of modified phase-shifted carrier signals are derived for precharging. These carrier signals when compared to zero modulation signal, ensure the synthesisation of sufficient number of zero output voltage switching modes (zero-modes) of the converter. The proposed precharging technique is detailed using a five-level FCMC and then generalized to higher odd-level FCMCs. State-space averaging models are derived to validate the proposed technique mathematically. Extensive simulation and experimental results are provided to validate the functionality of the proposed technique.

Cascade sliding mode control implementation in photovoltaic power supply for camping-car applications

A cascade proportional integral sliding mode control for a two-stage interleaved boost converter (2IBC) serving as a reliable supplementary power source for camping-car applications is reported. Unlike the active fault-tolerant control approaches used for interleaved boost converters, which require controller reconfiguration, the proposed control scheme is passive fault-tolerant and does not require reconfiguration in the event of a faulty stage. The 2IBC model is analyzed together with the most important parasitic parameters, then, the averaged state-space model is derived to implement the control scheme. The appropriate linear cascade control is determined by using the small-signal equivalent model and improving the robustness and dynamic performance, thereby a proportional integrator controller is replaced by a sliding mode controller. The prototype system uses a signal processor and a low-power solar panel. The control code is generated by a PSIM software and loaded to the via a code composer tool. The experimental results validate the control design and demonstrate the efficiency of the proposed control scheme. In addition, the proposed controller ensures the continuity of service in the event of a faulty stage by verifying the reliability of the power supply.

A Comprehensive Small-Signal Model Formulation and Analysis for the Quasi-Y Impedance-Source Inverter

This paper presents a detailed derivation of the small-signal model and components design considerations for the Quasi-Y-Source inverter. The design methodology is based on the converter steady-state operation, considering the impedance network inductor and capacitor voltage and charge balances, respectively. Moreover, the additional design criteria for component selection, considering control constraints and performance compromise, are given by parametric variation analysis based on converter dynamic response. The small-signal model and transfer functions are obtained using a state-space averaged model, including converter non-ideal characteristics given by equivalent-series resistances (ESR), which makes possible the proposition of different control strategies, using both single or multi-loop schemes. To demonstrate the usefulness of the proposed small-signal model, a DSP-based single-loop type-II PI control strategy is used in which the peak DC-link voltage is indirectly controlled through the measurement of the impedance network capacitor voltage. The controller and converter performances are verified with simulation and experimental results and successfully confirm the validity of the proposed dynamic model. Finally, the obtained results are validated with a built small-scale three-phase/three-wire inverter prototype.