Large-signal Stability Research Articles

Design of a Nonlinear Integral Terminal Sliding Mode Controller for a PEM Fuel Cell Based on a DC-DC Boost Converter

This paper proposes a robust nonlinear controller for a proton exchange membrane fuel cell coupled with a DC-DC boost converter. The key feature is to maintain the desired reference output voltage despite significant disturbances while improving transient stability. In order to do this, a nonlinear robust integral terminal sliding mode controller (ITSMC) is proposed, along with the derivation of the control law, explanation of the reachability analysis, and stability condition. An adapted integral sliding surface is used to capture the dynamics caused by variations in the input voltage and loads. In addition, a modified reaching law is proposed to guarantee the finite time convergence while reducing the chattering. Afterward, the Lyapunov control theory is employed to evaluate the DC-DC boost converter’s large-signal stability while guaranteeing the resilience of the proposed controller. Finally, the applicability of the proposed controller is evaluated through comprehensive analyses on both the simulation platform and the real-time processor-in-loop (PIL) platform under various operating conditions, such as the variation in load resistance, reference output voltage, etc. All of the results, when compared to an existing integral terminal sliding mode controller, indicate quick reference tracking capability with reduced overshoots and robustness against disturbances.

Large-Signal Stability Analysis of Islanded Dc Microgrids with Multiple Types of Loads

Large-Signal Stability Analysis of Islanded Dc Microgrids with Multiple Types of Loads

A Neural Lyapunov Approach to Transient Stability Assessment of Power Electronics-Interfaced Networked Microgrids

This paper proposes a novel Neural Lyapunov method-based transient stability assessment framework for power electronics-interfaced networked microgrids. The assessment framework aims to determine the large-signal stability of the networked microgrids and to characterize the disturbances that can be tolerated by the networked microgrids. The challenge of such assessment is how to construct a behavior-summary function for the nonlinear networked microgrids. By leveraging strong representation power of neural network, the behavior-summary function, i.e., a Neural Lyapunov function, is learned in the state space. A stability region is estimated based on the learned Neural Lyapunov function, and it is used for characterizing disturbances that the networked microgrids can tolerate. The proposed method is tested and validated in a grid-connected microgrid, three networked microgrids with mixed interface dynamics, and the IEEE 123-node feeder. Case studies suggest that the proposed method can address networked microgrids with heterogeneous interface dynamics, and in comparison with conventional methods that are based on quadratic Lyapunov functions, it can characterize the stability regions with much less conservativeness.

Adaptive Stabilization of a Permanent Magnet Synchronous Generator-Based DC Electrical Power System in More Electric Aircraft

Most loads of electrical power systems on a more electric aircraft (MEA) are regulated power converters. These loads behave as constant power loads (CPLs) that can significantly affect system stability. The system will become unstable and will be unable to operate at the rated power. In this article, a novel adaptive stabilization of a permanent magnet synchronous generator-based dc electrical power system in MEA is presented using a nonlinear feedback approach via loop-cancellation technique with a simple equation of feedback gain, which can be calculated from the power level of the CPL. The equation can be derived from a polynomial curve fitting based on the proposed mathematical model derived using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> method. The adaptive stabilization results are validated by a small-signal stability analysis using the linearization technique, a large-signal stability analysis using the phase plane analysis, an intensive time-domain simulation using MATLAB, and experimentation. The results indicate that the proposed adaptive stabilization technique can provide the considered aircraft power system always stable for all operating conditions within the rated power, and the dc bus voltage can adhere to the MIL-STD-704F standard.

A robust passivity based model predictive control for buck converter suppling constant power load

In this paper, the instability problem caused by the constant power load in Buck converter is addressed. In order to solve this instability problem, a composite controller is proposed. Due to the double loop structure of this controller, the passivity based control (PBC) is adopted in the voltage loop to track the reference voltage and make the system stable, while a simplified continuous control set model predictive control (CCS-MPC) is selected as the current controller to track the current reference. Moreover, in order to improve the robustness of the controller and avoid the static error in output, a high order disturbance observer (HODO) is designed out to compensate the negative effects caused by the disturbance and uncertainty. Then, a mixed potential theory based large signal stability analysis is conducted to investigate the large signal stability of the studied system. In order to verify the proposed method, MATLAB simulation, OPAL-RT based hardware in loop and rapid control prototype experiments are conducted.

A novel continuous control set model predictive control to guarantee stability and robustness for buck power converter in DC microgrids

In this paper, an adaptive continuous control set model predictive control (CCS-MPC) is proposed to eliminate the instability problem caused by the constant power load (CPL) in DC–DC​ buck converter applied in DC microgrids. Based on the dynamic model of energy storage elements(inductor and capacitor) in circuit, a parallel feedforward algorithm (PFA) is designed to estimate the variation of the load and input voltage. By supplying the information of the variation to the CCS-MPC controller, the large signal stability and fast recovery performance can be ensured under the existence of disturbances. To verify the control robustness of the adaptive CCS-MPC controller, the MATLAB simulations, hardware-in-loop (HIL) experiments and rapid-control-prototype (RCP) experimental results are conducted. Moreover, the comparative simulations and HIL experiments towards other nonlinear controller are conducted to investigates its dynamic performance.

Takagi-Sugeno Multimodeling-Based Large Signal Stability Analysis of DC Microgrid Clusters

DC microgrid (DCMG) clusters represent interconnections of multiple DCMGs to enable flexible power flow, and hence advantages of high resilience, economic dispatch, loss minimization, and optimal load response with microgrid-based distributed generations can fully be taken. However, small-scale DCMGs are known to be weak in nature due to low inertia and high grid impedance. Meanwhile, dynamic analyses of DCMG clusters have been plagued by their high order dynamic nonlinear system models since numerous state variables are involved. This article proposes large signal stability analysis of DCMG clusters based on Takagi-Sugeno multimodeling approach. With the proposed method, the large signal Lyapunov stability of the DCMG cluster is reduced to the computation of a series of linear matrix inequalities, which will significantly simplify the analysis. The influences of circuit parameters, power flows, and topological change on large signal stability of the DCMG cluster are revealed, and asymptotic stability regions of the network are estimated as well. In addition to simulation verification, a laboratory prototype of a ring topology DCMG cluster with three 48 V DCMGs interconnected is also built to validate the analysis by experimental results.

Extending the Ohtomo Stability Test to Large-Signal Solutions in a Commercial Circuit Simulator

The stability analysis of nonlinear circuits is a central problem in the framework of microwave design, as applied to high-power amplifiers, oscillators, frequency dividers, and multipliers. However, reliable, user-friendly tools for the stability analysis of such components seem to be quite scarce, even within the very commercial suites for high-frequency circuit simulation. This contribution addresses the problem by generalizing Ohtomo’s test—a popular tool born in the context of linear circuits—to the nonlinear case. Specifically, the new technique allows to analyze the characteristic zeros of a linearized large-signal solution resulting from a harmonic-balance (HB) simulation. As well known, the location of these zeros with respect to the imaginary axis of the complex plane is critical in relation to the qualitative nature of the solution, i.e., to its stability. To the best of the authors’ knowledge, for the first time, a large-signal stability test based on the system determinant but not requiring direct access to the nonlinear elements is implemented completely within a commercial circuit simulator (i.e., without requiring an external mathematical environment for data postprocessing). Some limitations still present are discussed. The generalized Ohtomo test was validated against other methods and circuits from the literature.

Region of Attraction Estimation for DC Microgrids With Constant Power Loads Using Potential Theory

The stability issues of DC power grids are attracting researchers' attention, especially with the increasing adoption of power electronic devices and nonlinear loads. Large-signal stability analysis is required to detect and avoid large disturbance and destabilization, which can cause detrimental effects on DC power grids. However, the issue is still unsolved due to the complicated dynamics of large-scale power grids. This paper develops a novel method for estimation of the region of attraction (ROA) with less conservativeness using the Brayton-Moser mixed potential theory. This reliable and robust ROA estimation method provides useful insights into the stable operation of DC power grids. Moreover, this paper reveals the weak correlation between the state variables <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> of branch currents and system stability. It makes it possible to reduce computational cost and lessen the curse of dimensionality by separating these state variables. The case study shows that the proposed approach can obtain a much less conservative ROA compared to traditional methods such as Lyapunov's method.

Large-Signal Stabilization of Power Converters Cascaded Input Filter Using Adaptive Energy Shaping Control

Series connection of input filters with static converters might lead to instability. However, the input filter has rarely taken into account in the stable design of power converters. Indeed, an input LC filter cascaded with a converter can become unstable even if the converter is regulated by a tight controller ensuring its stability alone. This fact is due to the interactions between the filter and the converter. To tackle the instability potential, an adaptive energy shaping control (AESC), which is based on the interconnection and damping assignment passivity-based control (IDA-PBC), is addressed in this article to regulate the cascaded system and achieve the following attractive features: 1) the input filter's dynamics are considered in the control law, so the interactions between the filter and the converter are taken into account during the controller design and 2) the influence between several subsystems, put in cascade, is considered by the proposed method, and the new large-signal stability proof is given accordingly. Simulation and experimental results from a 3.5-kW, 270-200-V buck converter cascaded with an input filter under different load conditions, i.e., constant impedance load (CIL), constant current load (CCL), and constant power load (CPL), are presented to demonstrate the proposed approach.

High-Speed Low-Power Rail-to-Rail Buffer using Dynamic-Current Feedback for OLED Source Driver Applications

In this work, we propose a rail-to-rail output buffer with low static-power and high speed for OLED display applications. To guarantee low static power consumption, low tail-current is designed in the buffer’s first stage and the output stage is cut off in the static operation. To improve the transient response, dynamic-current-bias technique is used, and it also improves the system stability by pushing away the non-dominant pole. Meanwhile, we balance the large-signal slew-rate and system stability with dual-output buffer structure. Placing compensation resistor across the dual outputs creates zero for suitable phase margin, while the real output still behaves with low ON resistance and keeps high slew rate. The proposed design has been verified by a 0.18 μm 1.8 V/5 V CMOS process, which shows that the buffer only draws 2.8-μA static current. Under a 1-nF capacitance load and a 5-V power supply, the buffer achieves 1.18-μs settling time, which is only 41% of the single-output-stage structure with the same chip size (52 μm $$\times$$ 59 μm).

Large-Signal Stability Improvement of DC-DC Converters in DC Microgrid

In DC microgrids, constant power loads (CPLs) reduce the effective damping of the DC-DC converter and may induce destabilizing effects into the DC-DC converter. To overcome such problems regarding CPL and ensure large-signal stability of DC-DC converters in DC microgrids, some feedforward terms are added to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$I$</tex-math></inline-formula> droop-based dual-loop controller for a DC-DC converter based on the large-signal model. It is proven that the feedforward terms can not only improve the transient response but also guarantee the exponential stability of the closed-loop system in the whole operating range in regards to a large-signal manner, which is verified by using a singular perturbation model. Moreover, a disturbance observer is designed to estimate the output current, thereby enabling the removal of the current measurement sensor. The proposed technique can be easily plugged into a pre-defined <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$I$</tex-math></inline-formula> droop-based dual-loop controller without an additional sensor being required. Ultimately, both simulation and experimental tests verify the effectiveness of the proposed method.

Toward Large-Signal Stabilization of Floating Dual Boost Converter-Powered DC Microgrids Feeding Constant Power Loads

In modern dc microgrids (MGs), floating dual boost converters (FDBCs) take the advantages of both interleaved modulations and higher voltage gains, and the FDBC topology has been shown rather suitable for high-power applications. For a given dc MG, those power electronic loads and motor drives would behave as constant power loads (CPLs) that have negative incremental input impedances causing serious stability issues. To make the FDBC-enabled dc MG more adaptable to the increasing penetration of CPLs, this article proposes a compound stabilizer that is capable to stabilize all states in the converter in the large-signal sense. The stabilizer is synthesized by nonlinear disturbance observers and a recursive backstepping controller. The observers provide disturbance estimations to the controller, which neutralizes the disturbances in a feedforward manner and also guarantees the large-signal stabilization of MG under Lyapunov theorems. Practical parameter identification procedures are provided, and it is shown that the proposed stabilizer contributes the wider stability margin to the FDBC than the commonly used proportional–integral (PI) control. Finally, hardware experimentations substantiate the effectiveness and feasibility of the large-signal stabilizer.

Dynamic Analysis of Multimode Buck–Boost Converter: An LPV System Model Point of View

In dealing with the wide voltage range of energy storage components and fuel cell, multimode buck-boost converter (MBBC) serves as a versatile interfacing circuit with multimode operation capability. In this article, dynamic performance of MBBC is analyzed with consideration of converter operation under multiple modes, and a digital control design method is proposed for fast transient response. The dynamic analysis considers two influence factors, including “transition mode selection” and “close-loop control design.” The influences of different Transition mode have been analyzed with the aid of linear parameter varying system, and a new Transition mode has been proposed for the minimum polytopic working region. In “close-loop control design,” the recovery time has been minimized with guaranteed robust stability. Compared with small-signal design method, the proposed method not only ensures large-signal stability across multiple working modes, but also offers new insight for Transition mode selection which is overlooked in existing MBBC dynamic analysis. The designed controller has been applied for three representative transition modes, including the first proposed “double-buck-clamping” mode and comparatively evaluated with existing small-signal PI design method.

Large-Signal Stability of Grid-Forming and Grid-Following Controls in Voltage Source Converter: A Comparative Study

The grid-forming and grid-following controls are adopted in three-phase voltage source converters according to different grid conditions. However, the basic operation principle of the two kinds of control is different and will lead to the instability of the grid-connected system through various paths. In this article, the energy function model of the grid-forming and grid-following controlled converters are established and compared in detail. The influence of system parameters is studied, and the large-signal stability boundaries are derived through a general method. Moreover, compared to the grid-forming controlled converter, the grid-following converter will lose stability by exhibiting a varying damping coefficient transient. The equivalent damping coefficient can be used as a criterion of whether the grid-forming/following control is suitable for the weak/strong grid condition. The simulation and experiment results show the difference of the transient process and validate the control criterion for different grid strength under large-signal disturbance.

Two-Parameter Stability Analysis of Resistive Droop Control Applied to Parallel-Connected Voltage-Source Inverters

The present research work aims to study the large signal stability of two parallel-connected voltage-source inverters operating with resistive droop control through bifurcation analysis. This minimal setup can be considered a prototype of a small islanded ac microgrid studying where droop control acts as a synchronization scheme between inverters. Since switching power converters are strong nonlinear circuits, bifurcation analysis helps to understand nonlinear phenomena more deeply than the standard linear approach. Plenty of complicated nonlinear phenomena have been observed through bifurcation analysis, such as multiequilibria, period-doubling bifurcation, Hopf bifurcation, quasiperiodicity, border collision, bistability, and chaos. Thereby, a set of parameters under certain conditions can influence the equilibrium point and its stability, leading to some of the aforementioned nonlinear phenomena. In this sense, the main contribution of this article is to detect the nonlinear phenomena in considering islanded ac microgrid in order to determine a safe droop parameter region for more robust microgrid operation. This information can be summarized in bifurcation diagrams leading to practical rules for choosing the control and droop parameters. Experimental results are performed to validate the main instabilities predicted by the theoretical models.

Two-Level Stability Analysis of Complex Circuits

A new methodology is proposed for the small- and large-signal stability analysis of complex microwave systems, containing multiple active blocks. It is based on a calculation of the system characteristic determinant that ensures that this determinant does not exhibit any poles on the right-hand side (RHS) of the complex plane. This is achieved by partitioning the structure into simpler blocks that must be stable under either open-circuit (OC) or short-circuit (SC) terminations. Thus, the system stability is evaluated using a two-level procedure. The first level is the use of pole-zero identification to define the OC- or SC-stable blocks, which, due to the limited block size, can be applied reliably. In large-signal operation, the OC- or SC-stable blocks are described in terms of their outer-tier conversion matrices. The second level is the calculation and analysis of the characteristic determinant of the complete system at the ports defined in the partition. The roots of the characteristic determinant define the stability properties. The Nyquist criterion can be applied since, by construction, the determinant cannot exhibit any poles in the RHS. In addition, one can use pole-zero identification to obtain the values of the determinant zeroes. Because the determinant is calculated at a limited number of ports, the analysis complexity is greatly reduced.

Composite Robust Quasi-Sliding Mode Control of DC–DC Buck Converter With Constant Power Loads

To address the stability issues aroused by the negative-resistance effect of constant power loads (CPLs), this article proposes a composite robust discretized quasi-sliding mode control (DQSMC) scheme for stabilization of buck-converter fed dc microgrids with CPLs. In the outer control loop, a robust DQSMC voltage controller is proposed. First, a discrete integral sliding surface is designed to obtain a fast and robust dynamic response of dc-bus voltage. Then, to tackle the varying load disturbances and model uncertainties, a second-order sliding mode disturbance observer is embedded in the voltage controller for disturbance estimation and compensation. The resulting composite DQSMC scheme features enhanced disturbance rejection, inherent chattering suppression, and guaranteed dynamics. Meanwhile, a PI current controller is retained in the inner control loop to realize the current control and limitation. Robustness and stability analysis of the whole composite controller is proved to assure large-signal stability. Simulation and experimental results confirm the superiority of the presented approach.

Stability Improvement of Cascaded Power Conversion Systems Based on Hamiltonian Energy Control Theory

It is well known that the interaction between cascaded individually designed power conversion systems can cause instability. To overcome this issue, a Hamiltonian energy control scheme is proposed, which is based on passivity control theory and port-controlled Hamiltonian framework. A complementary PI adjustment term is also included in the control algorithm to eliminate the steady-state output voltage error caused by the parameter uncertainty. The proposed control approach is applied to three different cascade structures. First, the cascade structure between dc/dc converters is considered, and the detailed controller design is given. Second, the cascade connection of a single converter and its LC filter is studied. By placing the L C filter into the Hamiltonian model of the controlled converter system, the dynamic and potential instability caused by the filter can be adjusted. Finally, the cascade structure between subsystems including filters and converters, which are common in microgrids, is studied. By using the Hamiltonian function (storage function) as the Lyapunov function candidate, the large-signal stability of each controlled converter system is proved. When the cascade structure contains multiple controlled converter systems, the stability of the entire cascaded system is guaranteed by the superposition of multiple Lyapunov functions. A 3.5 kW 220−270−350 V test bench is built in the laboratory to demonstrate the application of the proposed control approach to these three cascade structures.

Vector Measurement-Based Virtual Inertia Emulation Technique for Real-Time Transient Frequency Regulation in Microgrids

The conventional dynamic inertia emulation scheme can desirably prolong the frequency deflection period, sacrificing the frequency restraining time in the microgrid. Therefore, to ensure an elongated frequency deflection period, having a shortened restraining time, the concept of the direction sensitive dynamic inertia emulation (DSIE) technique has been developed in this article. In the proposed DSIE technique, the deflection in the frequency has been measured as a vector quantity to dynamically compute the amount of required virtual inertia. Then, the assessment of the large-signal stability region is provided based on the principle of Lyapunov. The proposed concept has been validated in an experimental hardware testbench to evaluate the performance improvement. To ensure the minimum computational delay and latency, an ARM Cortex A-72-based digital signal processor and BTS-7960 packaged mosfet have been specifically selected. The experimental results have shown that the proposed technique shortens the frequency returning period by 66.68% comparing with the conventional nondirectional scheme in real time.