Dynamic Equivalent Model Research Articles

Integration of distributed energy resource models in the VSC control for microgrid applications

Studies related to the integration of distributed energy resources (DERs) face challenges in considering models for the primary energy source, the conversion equipment, the inverters, and the microgrid. Most of the current approaches only consider some of these models, then the complete modelling is uncommon, leading to simplified system representations. As a solution, this paper presents a three-stage approach to easily integrate the generation and storage system models into the dq0 control algorithm of a voltage source converter (VSC), useful in microgrid studies. The considered DERs, correspond to battery energy storage system (BESS), wind generation and photovoltaic (PV) generation systems; then, the model influence and the variation of the primary energy source modify the control references. This approach allows an appropriate balance between model accuracy and simplicity of steady-state and dynamic equivalent models for converter integrated DER (CIDER). The results show how this modelling facilitates the steady and dynamic state studies, as is evidenced in the tests performed in a CIGRE based microgrid.

A Modified Dynamic Model of Single-Sided Linear Induction Motors Considering Longitudinal and Transversal Effects

This paper proposes a modified dynamic equivalent circuit model for a linear induction motor considering both longitudinal end effect and transverse edge effect. The dynamic end effect (speed-dependent end effect) is based on conventional Duncan’s approach. The transverse edge effect is investigated by using three correction factors applied to the secondary resistance and magnetizing inductance. Moreover, the iron saturation effect, the skin effect, and the air-gap leakage effect are incorporated into the proposed model by using the field-analysis method. A new topology of the steady-state and space-vector model of linear induction, regarding all mentioned phenomena, is presented. The parameters of this model are calculated using both field analysis and the finite-element method. The steady-state performance of the model is first validated using the finite-element method. Additionally, the dynamic performance of the proposed model is studied. The results prove that the proposed equivalent circuit model can precisely predict the dynamic and steady-state performances of the linear induction.

Planetary Gearbox Dynamic Modeling Considering Bearing Clearance and Sun Gear Tooth Crack.

Planetary gearbox systems are critical mechanical components in heavy machinery such as wind turbines. They may suffer from various failure modes, due to the harsh working environment. Dynamic modeling is a useful method to support early fault detection for enhancing reliability and reducing maintenance costs. However, reported studies have not considered the sun gear tooth crack and bearing clearance simultaneously to analyze their combined effect on vibration characteristics of planetary gearboxes. In this paper, a dynamic model is developed for planetary gearboxes considering the clearance of planet gear, sun gear, and carrier bearings, as well as sun gear tooth crack levels. Bearing forces are calculated considering bearing clearance, and the dynamic model equations are updated accordingly. The results reveal that the combination of bearing clearances can affect the vibration response with sun gear tooth crack by increasing the kurtosis. It is found that the effect of planet gear bearing clearance is very small, while the sun gear and carrier bearing clearance has clear impact on the vibration responses. These findings suggest that the incorporation of bearing clearance is important for planetary gearbox dynamic modeling.

Dynamic equivalent modeling for power converter based on LSTM neural network in wide operating range

The internal parameters and topology of the power converter are unknown in some practical cases. Existing modeling methods based on impedance frequency scanning method can only guarantee that the dynamic modeling is effective at a single working point. To make the established dynamic model effective in a wide range, an equivalent modeling method for power converter based LSTM Neural Network is presented. At first, the equivalence of black-box modeling problem and deep loop neural network is studied. Then, dynamic modeling method black-box power converter on wide operating range by using LSTM neural network is proposed. Finally, the simulation results under large disturbance and multi-operating points show that the proposed method is effective under wide operation range.

Equivalent dynamic modeling of flexible morphing aircraft.

A morphing aircraft can maintain optimal flight performance by adaptively changing shape. However, large deformation and fast motion of aircraft modules lead to complicated dynamics during morphing process. This paper proposes a mechanistic equivalent model with parameters identified by optimization method. Based on the dynamics of the aircraft modules with large deformation and fast motion and considering the coupling characteristics of rigid bodies and gimbal joints, an equivalent dynamic model of morphing aircraft is built in this study. Considering the huge amount of highly coupled parameters in the equivalent model, particle swarm optimization algorithm is used to identify the equivalent parameters based on the sample data of flexible model. By comparing the simulation results of proposed model to those of rigid model and flexible model, it can be seen that the accuracy of the proposed equivalent model is comparable to that of the flexible model, but the computational load is only 10% of that of flexible model. Further, based on this high-fidelity model with low computational load, an optimized morphing process is obtained, and the attitude variation during morphing is reduced by 4.23%.

Controlling Two-Legged Mobile Robot

Since the appearance of robots, they have brought many benefits, for example: they can work continuously; they can work in harsh and dangerous environments that cannot be accessed by humans. Thanks to their mobility, mobile robots have a wide and flexible working area, especially two-legged mobile robots that can move in bumpy terrains, go up and down stairs or step over obstacles easily. Nowadays, with the increasing development of science, more and more mobile robots are applied and participated in human activities not only in service activities but also in direct coordination with humans. Robot control methods usually come from robot dynamic model and robot motion differential equation, thereby, calculating driving forces based on the deviation of input and output signals to drive motors on joints in order to ensure that robots moves in the desired trajectory. Two-legged mobile robots have a structure of many phases and joints connected together, besides, due to a large number of degrees of freedom, this type of robot is able to operate flexibly and move easily, however, it has a difficulty in dynamic and kinematic modeling, and robot control. Normally, the differential equation of robot motion will have complex quantities and massive formulas. In order to improve the walk of this robot, this study focuses on researching and surveying the problem of kinetics and dynamics and using a control method to control a specific two-legged mobile robot that moves in a cycle of walking.

Online Identification of Simplified CHP Models

The aim of this article is to develop a simplified equivalent dynamic model capable to capture the transient behavior of a gas-fueled co-generator. To comply with this exigency, an online identification methodology based on the sensitivity theory in conjunction with the Lyapunov function is adopted. By this methodology, stable solutions can be achieved in the online environment, renewing the parameters of the model at every change occurring on the physical system. In order to investigate the effectiveness of the proposed methodology in deriving a simplified dynamic model, several simulations and experimental tests were performed on the Prince Lab microgrid located at the Polytechnic University of Bari.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems.

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

Non-Linear Model and Parameter Extraction for Charge/Discharge Behavior of Valve Regulated Lead-Acid Battery

A dynamic model of a battery is required for the appropriate real-time control during charging/discharging process. Present paper considers the development of nonlinear Dynamic Equivalent Electric Circuit Model (DEECM) of a Valve Regulated Lead-Acid (VRLA) battery based on the data obtained through the experimentation and the available datasheet information. Cases of charging, discharging, and the self-discharging are considered for 12V, 26Ah VRLA battery at room temperature. Accordingly, experimental <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\boldsymbol{v}} - {\boldsymbol{i}}$</tex-math></inline-formula> characteristics of the battery are used to express the nonlinear model parameters as a function of measurable battery current and estimated open-circuit voltage as a part of parameter estimation. Further model is validated through voltage response test with maximum error of 0.4% during discharging and 0.7% during charging under different current levels.

Inertial Response Identification Algorithm for the Development of Dynamic Equivalent Model of DFIG-Based Wind Power Plant

As the wind power penetration increases, the frequency stability of the power system is deteriorating. Thus, it is expected that the wind power plants (WPPs) will be required to produce the inertial response during the short-term large-scale frequency disturbances. To study the effects of the inertial response of the WPP, the dynamic equivalent model (DEM) of the WPP should be able to emulate the inertial response of the actual WPP. Otherwise, the simulated system frequency would be different from the actual one. Therefore, the inertial response identification algorithm (IRIA) is proposed in this article. The IRIA is able to identify the gain of the inertial controller and the inertia constants of the WPP according to the actual system frequency and the active power output of the actual WPP. In this article, the actual WPP is represented by the detailed model. In order to prove the effectiveness of the IRIA, three cases with different gains of the inertial controller are studied. The simulation results demonstrate that the proposed IRIA allows the DEM of the WPP to generate similar response of the active power and lead to close response of the system frequency as the actual WPP does in three different scenarios.

Robustness-Improved Method for Measurement-Based Equivalent Modeling of Active Distribution Network

Accurate equivalent model can be efficient to analyze the dynamic properties of active distribution network (ADN) as well as assess their impacts on stabilities of interconnected power system. However, due to the stochastic nature of renewable resources and time-varying configurations of load conditions, traditional ADN equivalent model may not be robust enough to different operation conditions. To overcome the limitations, this article proposed a robustness-improved method for dynamic equivalent modeling of ADN. To sketch out the most representative operation conditions of ADN, two-step clustering method with fisher discriminant analysis are used for grouping of operation conditions featured characteristic data sets. With the key parameter based identification technique applied, the multiple solution issue in parameter identification process could be effectively avoided. To further enhance the robustness of equivalent model, long short-term memory neural network is adopted to generalize the identified parameters. The performance of proposed modeling method is comprehensively evaluated by an actual ADN based verification cases.

Frequency Response From Solar PV: A Dynamic Equivalence Closed-Loop System Identification Approach

The analysis of the frequency response of integrated transmission-distribution networks with deep penetration of solar photovoltaic (PV) generation faces major challenges due to the complexity emerging from the dynamic models of the numerous and diverse PV units involved. This article proposes converter-based dynamic equivalent models for both distributed (distribution network-connected) and large-scale (transmission network-connected) PV units, which take into account practical issues, such as measurement and coordination delays. Different from the previous work that adopted an open-loop identification, the unknown model parameters are identified here through a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop</i> identification process based on the least-square minimization. This allows capturing the continuous interaction between system and PV responses, thus improving the outcome of the overall frequency response model. The proposed models are validated with the real data from the August 2018 separation event in Australia. The results demonstrate the excellent performance of the proposed models in determining the frequency response from PV in both transmission and distribution networks, hence paving the way to its adoption in the frequency stability analysis in low-carbon grids dominated by frequency-responsive renewables.

A Dynamic Equivalent Model for District Heating Networks: Formulation, Existence and Application in Distributed Electricity-Heat Operation

Coordination efficiency between different energy sectors with privacy preservation has become a technical bottleneck in distributed operation of the integrated electricity and heat systems (IEHS). This article investigates, for the first time, an equivalent model-based non-iterative solution for this issue. An equivalent model of district heating networks (DHNs) retaining the temperature quasi-dynamics is derived. Based on the equivalence, all the state variables in DHNs are explicitly expressed by the heat power generation, and the feasible region of DHNs is projected on the coupling boundaries of the IEHS. The existence of this equivalent model is proved under a mild sufficient condition. The application of the proposed equivalent model is demonstrated via the distributed unit commitment for IEHS. Case studies of two test systems validate the effectiveness and the efficiency of the solution for distributed IEHS operation.

Dynamic Modeling and Active Vibration Isolation of a Noncontact 6‐DOF Lorentz Platform Based on the Exponential Convergence Disturbance Observer

In order to study the vibration isolation and positioning performance of the noncontact 6‐DOF platform in the space microgravity environment, this paper presented a cosimulation model of a virtual prototype. Based on the model driven by biaxial noncontact Lorentz force actuators (NLFAs), an equivalent dynamic model has been established. In the meanwhile, the 6‐DOF sliding mode robust controller with exponential convergence disturbance observer is developed. The mechanical system simulation model was designed using ADAMS, and the corresponding 6‐DOF decoupling control system and disturbance observer programs were developed using MATLAB/Simulink. According to the mechatronics simulation results, the system can enable the floating platform to achieve micron‐level posture positioning within 0.5 s. In vibration isolation simulation, the disturbance observer can predict the external disturbance input and compensate the control force more accurately so that the floating platform can effectively suppress low‐frequency disturbance and step disturbance under the control of the sliding mode controller. And the displacement of the floating platform under the disturbance of 1–100 Hz frequency sweep is less than 1 μm.

Dynamic Equivalent Magnetic Network Analysis of an Axial PM Bearingless Flywheel Machine

A nonlinear dynamic equivalent magnetic network model for an axial permanent magnet bearingless flywheel machine (APM-BFM) is proposed in this paper. The model focuses on analyzing the magnetic field changes at the air gap of the machine. According to the relative position of the stator and rotor, the magnetic circuit between the rotor and the suspension pole (the torque pole) is divided into 7 stages (8 stages), and dynamic equivalent magnetic network models are established. The local saturation coefficient is introduced to characterize the local magnetic saturation phenomenon of the rotor yoke during the rotation of the rotor. Using the proposed model and based on the obtained winding flux, the opposing electromotive forces and inductances of the suspension and torque windings of the APM-BFM are all analyzed and calculated. Finally, the validity of the proposed model is verified by finite element analysis (FEA).

Maximum Probabilistic and Dynamic Traffic Load Effects on Short-to-Medium Span Bridges

The steadily growing traffic load has resulted in lots of bridge collapse events over the past decades, especially for short-to-medium span bridges. This study investigated probabilistic and dynamic traffic load effects on short-to-medium span bridges using practical heavy traffic data in China. Mathematical formulations for traffic-bridge coupled vibration and probabilistic extrapolation were derived. A framework for extrapolating probabilistic and dynamic traffic load effect was presented to conduct an efficient and accurate extrapolation. An equivalent dynamic wheel load model was demonstrated to be feasible for short-to-medium span bridges. Numerical studies of two types of simply-supported bridges were conducted based on site-specific traffic monitoring data. Numerical results show that the simulated samples and fitting lines follow a curve line in the Gumbel distribution coordinate system. It can be assumed that dynamic traffic load effects follow Gaussian distribution and the extreme value follows Gumbel distribution. The equivalent probabilistic amplification factor is smaller than the individual dynamic amplification factor, which might be due to the variability of individual samples. Eurocode 1 is the most conservative specification on vehicle load models, followed by the BS5400 specification. The D60-2015 specification in China and ASSHTO specification provide lower conservative traffic load models.

Coordinated control strategy for mode transition of DM-PHEV based on MLD

In this paper, a hybrid variable cost function model predictive control strategy (HC-MPC) is developed for the mode transition process of a novel motor compound power-split plug-in hybrid electric vehicle (DM-PHEV). Based on the layout of DM-PHEV, the mode transition process from electric driving mode to hybrid driving mode is divided into 5 stages. Considering the hybrid characteristics of mode transition process, the dynamic models under different stages are transmitted into an equivalent mixed-logical dynamical hybrid model. MPC based on hybrid model (H-MPC) is applied as the coordinated controller. Moreover, considering that fixed cost functions for the finite time horizon are not reasonable if stage transition happened during the prediction horizon, so variable cost functions changing with predictable stages is useful for improving the control effect of MPC. H-MPC considering variable cost functions (HC-MPC) is proposed as the coordinate controller in this paper. Simulation and hardware-in-the-loop test show that HC-MPC can efficiently improve the PHEV drivability.

PIO Based Data-Driven Iterative Learning Control for Nonlinear Batch Processes with Nonrepetitive Disturbances Subject to Input Constraints

Abstract This paper proposes a novel proportional-integral observer (PIO) based high-order data-driven iterative learning control (HODDILC) for nonlinear batch processes with non-repetitive disturbances subject to input constraints. First, an equivalent dynamic linearization data model (DLDM) with an uncertainty term arising from the nonrepetitive disturbances is constructed in the batch direction. Based on the established DLDM along with a gradient estimation algorithm, a data-driven PIO is then designed to estimate the uncertainty term along the batch direction, followed by designing a HODDILC law in terms of the tracking errors over more than one previous batches and control inputs in the previous time instants of the current batch. Using the contraction mapping principle and matrix theory, rigorous convergence analysis is conducted in the iteration domain. A notable advantage of the proposed design is that only input and output measurement data are used rather than a process model. Finally, an illustrative example from the literature is given to demonstrate the effectiveness and merit of the proposed method.

Measurement based parameters estimation of large scale wind farm dynamic equivalent model

For the past few decades, the drastic increase in the installed capacity of wind farms (WFs) has necessitated a computationally efficient dynamic equivalent model of a WF, which can be used for accurate power network simulations. Various doubly-fed induction generators (DFIGs) with sophisticated power control, rotor, and grid side converter control based models for wind turbine (WT) exist in the literature. However, these models are computationally burdensome and restrict their application for modeling large WFs. Thus, an equivalent DFIG based model of a WF, with the rotor circuit modeled as a constant current source, is proposed in this paper. The proposed model is simple and computationally efficient as no rotor measurements are required, and voltage and current measurements at the point of common coupling (PCC) of the WF are used in extended Kalman filter (EKF) to evaluate the dynamic parameters of the equivalent DFIG. A Ybus based reduction is also proposed for the equivalent collector system’s impedance. Simulation results on a test WF in MATLAB Simulink and DIgSILENT prove the proposed model’s efficacy over the existing equivalent models for different operating conditions like wake effect and contingencies in the interconnected power system network.

Robust augmented H∞ shift control strategy for power-split system with a two-speed AMT gearbox of a heavy commercial vehicle

The coordination control of a transmission system has gradually attracted more attention with the development of hybrid electric vehicles. However, nonlinear coupling of multiple power sources, superposition of different dynamic characteristics in multiple components, and withdrawal and intervention for a power-split powertrain with a two-speed automated manual transmission (AMT) gearbox can cause jerk and vibration of the transmission system during the shift, which has higher requirements and challenges for the overall performance improvement of the system. This paper designs a novel, robust, augmented H∞ shift control strategy for a power-split system with a two-speed AMT gearbox of a heavy commercial vehicle and verifies the strategy’s effectiveness with simulations and experiments. First, the dynamic plant model and kinetic equations are established, and the shift is divided into five stages to clearly reveal the jerk and vibration problem. Based on augmented theory, a robust H∞ shift control strategy is proposed. Shift coordination is transformed into a speed tracking problem, and state variable and disturbance are reconstructed to obtain a new augmented system. Simulation and hardware-in-the-loop test are carried out to verify the effectiveness of the strategy, which mainly includes simulation of pneumatic actuator and H∞ control strategy. Results show that the proposed H∞ control strategy can greatly reduce the jerk of the transmission system. The jerk produced by the proposed strategy is decreased from 20.4 to 4.07 m/s3, leading to a substantial improvement of 80%. Therefore, the proposed strategy may offer a theoretical reference for the actual vehicle controller during the shift.