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.
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal ...innerapproximation to the region of attraction (ROA). The first theorem addresses linear time-invariant systems, and merges Lyapunov theory with local (sector) quadratic constraints to bound the nonlinear activation functions in the neural network. The second theorem allows the system to include perturbations such as unmodeled dynamics, slope-restricted nonlinearities, and time delay, using integral quadratic constraint (IQCs) to capture their input/output behavior. This in turn allows for off-by-one IQCs to refine the description of activation functions by capturing their slope restrictions. Both results rely on semidefinite programming to approximate the ROA. The method is illustrated on systems with neural networks trained to stabilize a nonlinear inverted pendulum as well as vehicle lateral dynamics with actuator uncertainty.
This study considers the extremum-seeking control problem for double-integrator system that is controlled by using the pulse-width-modulation (PWM) technique. A new class of PWM control law is ...presented that the state trajectories of the closed-loop system are held within a desired range. A trajectory-based analysis approach is also proposed that characterize the influence of the hybrid PWM control input. A novel hierarchical structure is developed that separates the closed-loop extremum-seeking system into the interconnected networked subsystems, which are characterized in the sense of input-to-state practical stability (ISpS) and input-to-output stability (IOpS). By using the nonlinear small-gain theorem, the stability of the ES closed-loop system is ensured so that the PWM-controlled plant can gravitate towards an appropriate region of the maximum (minimum) of the nonlinear map (which can be considered as a gradient field). Finally, numerical examples demonstrate the validity and effectiveness of our proposed design.
Transient stability assessment (TSA) is a cornerstone for resilient operations of today's interconnected power grids. This paper is a confluence of quantum computing, data science and machine ...learning to potentially address the power system TSA issue. We devise a quantum TSA (QTSA) method to enable efficient data-driven transient stability prediction for bulk power systems, which is the first attempt to tackle the TSA issue with quantum computing. Our contributions are three-fold: 1) A high expressibility, low-depth quantum circuit (HELD) is designed for accurate and noise-resilient TSA; 2) A quantum natural gradient descent algorithm is developed for efficient HELD training and 3) A systematical analysis on QTSA's performance under various quantum factors is performed. QTSA underpins a foundation of quantum machine learning-enabled power grid stability analytics. It renders the intractable TSA straightforward and effortless in the Hilbert space, and therefore provides stability information for power system operations. Extensive experiments on quantum simulators and real quantum computers verify the accuracy, noise-resilience, scalability and universality of QTSA.
Power electronic systems are prone to instability. The problem, generally attributed to the constant power load (CPL) behavior of their power electronic controlled loads, can become more acute when ...the systems are subject to parametric uncertainties. The structured singular value (SSV) based μ method has proven to be a reliable approach for assessing the stability robustness of such uncertain systems. Despite its numerous benefits, the μ method is not often applied to electrical power systems (EPS) with multiple uncertainties. This may be due to the mathematical complexity underlying the μ theory. This paper aims to make the μ approach more application-friendly by providing clearer insights into the meaning and usefulness of the robust stability measure μ for EPS with multiple parametric uncertainties. This is achieved by presenting a methodology for translating μ analysis results from the frequency domain to the more perceivable uncertain parameters domain. The method directly demonstrates dependences of system stability on uncertain system parameters. Further, it clearly identifies robust stability domains as subsets of the much wider stability domains. The work is based on a representative EPS connected to an ideal CPL. μ analysis predictions are evaluated and validated against analytical results, for example, CPL system.
Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, ...complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a <inline-formula> <tex-math notation="LaTeX">2\times2 </tex-math></inline-formula> system, and the current control loop of two independent power converters in parallel, a <inline-formula> <tex-math notation="LaTeX">4\times4 </tex-math></inline-formula> system.
High-voltage direct-current (HVDC) transmission systems have been rapidly developing, whereas they also become the crucial factors that affect the power system's stability. The repetitive commutation ...failures (RCF) of the HVDC link will put the sending-end power system at risk of transient instability, which greatly raises the demand of the system to enhance its ability to cope with such events. This paper proposes a flexible control strategy supported by the fast-acting energy storage system (ESS) based on the combination of the model predictive control (MPC) principle and the extended equal area criterion (EEAC) to ensure transient stability of the sending-end system when RCF occurs in a single HVDC link. The formulas to forecast the system's dynamic behavior are constructed. The optimal power expected to be provided by the ESS for each commutation failure (CF) is obtained by assessing the system stability margin. The proposed strategy is to maintain the system's transient stability by the consecutive appropriate responses of the ESS during RCF. Additionally, the blocking conditions of the HVDC link and the required consequent control are studied. The simulation results demonstrate the ability of the proposed strategy to ensure the transient stability of the sending-end power system when the RCF occurs.
Wind turbines (WTs) are prone to transient instability during weak grid faults, which is caused by their complex interactions. However, it is a challenge to analyze the transient stability, due to ...high-order and strong nonlinearity. Moreover, the existing works mainly focus on a phase-locked loop (PLL) system while ignoring current control, which cannot fully reflect the transient instability mechanism. To fill this gap, this article studies the transient stability of type-3 WT considering both PLL and current control. First, to simplify the full model of type-3 WT, a slow-fast subsystem is established using the singular perturbation. Then, the sixth-order full model is simplified as a second-order slow subsystem and its small disturbance (i.e., fast subsystem). Based on it, Lyapunov's direct and indirect methods are adopted to analyze the stability of slow and fast subsystems, respectively. Meanwhile, the influence of various factors (e.g., the fault degree, grid inductance, current references, current controller, and PLL controller) on transient stability of type-3 WT is revealed. In addition, the proposed analytical method combining singular perturbation and Lyapunov methods is a new approach to studying transient stability, which can also be applied to other renewable energy resources. Finally, the analysis is validated by experiments.
The stability problem of low-voltage multi-terminal DC (MTDC) systems has drawn much interest. This paper focuses on the oscillation instability phenomenon of low-voltage MTDC systems and analyzes ...the interaction behavior between each voltage-source converter and the DC network oscillation mode. The typical structure and control strategy of a low-voltage MTDC system under master-slave control is first described, and its equivalent circuit is established. Then, an interaction behavior analytical model is proposed, and the source-network and network-load interaction characteristics are studied. Furthermore, a system stability analysis method is built based on the modularized modeling, which can solve the problem of how to address the complexity of high-order low-voltage MTDC systems. The transfer function of the whole system is conveniently established, revealing the system instability mechanism. The proposed method can provide effective stability assessment for low-voltage MTDC systems. Finally, the results are verified using electromagnetic transient simulation and experimentally validated using a low-voltage three-terminal DC system test platform with AC 0.4 kV/DC 800 V. This research can be flexibly extended to high-order systems for controller design and performance optimization.
Multi-terminal modular multilevel converter (MMC) power transmission is the current development trend in DC transmission. However, owing to its fast control and dynamic characteristics, it may ...interact with the other inductive devices or the grid and cause stability issues. This paper describes the use of the impedance analysis method in the frequency domain to analyze system stability. First, the multi-harmonic linearization method is used to model the impedance of a three-terminal MMC system. To make the model more accurate, the modeling considers the effect of frequency coupling caused by an asymmetric controller and the AC sampling site position. This paper then proposes an equivalent method of the grid impedance for the three-terminal system that can accurately judge the stability of the grid-connected system when the AC side is coupled. This work provides a theoretical basis for the prediction and suppression of the oscillation of MMC grid-connected system with coupling on the AC side. Finally, a three-terminal MMC model is built in Matlab/Simulink and the Nyquist stability criterion is used to verify the correctness of the analysis.
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