No Arabic abstract
The output impedance matrix of a grid-connected converter plays an important role in analyzing system stability. Due to the dynamics of the DC-link control and the phase locked loop (PLL), the output impedance matrices of the converter and grid are difficult to be diagonally decoupled simultaneously, neither in the dq domain nor in the phase domain. It weakens the effectiveness of impedance-based stability criterion (ISC) in system oscillation analysis. To this end, this paper innovatively proposes the generalized-impedance based stability criterion (GISC) to reduce the dimension of the transfer function matrix and simplify system small-signal stability analysis. Firstly, the impedances of the converter and the grid in polar coordinates are formulated, and the concept of generalized-impedance of the converter and the grid is put forward. Secondly, through strict mathematical derivation, the equation that implies the dynamic interaction between the converter and the grid is then extracted from the characteristic equation of the grid-connected converter system. Using the proposed method, the small-signal instability of system can be interpreted as the resonance of the generalized-impedances of the converter and the grid. Besides, the GISC is equivalent to ISC when the dynamics of the outer-loop control and PLL are not considered. Finally, the effectiveness of the proposed method is further verified using the MATLAB based digital simulation and RT-LAB based hardware-in-the-loop (HIL) simulation.
The output impedance matrices of three-phase grid-connected voltage source converters (VSCs) are widely used in power system stability analysis. Regardless of how the impedance is modeled, there always exist coupling terms in the impedance matrix, which makes the system a multi-input- multi-output (MIMO) system. Some approximation approaches omit the coupling terms so that a three-phase system can be treated like a single-phase one, and the impedance-based stability criterion for a single-input-single-output (SISO) system is applicable. However, such handling may result in analytical errors or even incorrect conclusions in a mirror frequency coupled system. By introducing the concept of generalized- impedances, this letter proposes a new stability criterion based on a virtual SISO system, which can effectively handle the coupling terms. Further, the effects of the phase-locked-loop (PLL) parameters on system stability are studied based on the proposed criterion. The effectiveness of the proposed criterion is verified by a hardware-in-the-loop (HIL) simulation based on RT-LAB.
We apply a novel data-enabled predictive control (DeePC) algorithm in grid-connected power converters to perform safe and optimal control. Rather than a model, the DeePC algorithm solely needs input/output data measured from the unknown system to predict future trajectories. We show that the DeePC can eliminate undesired oscillations in a grid-connected power converter and stabilize an unstable system. However, the DeePC algorithm may suffer from poor scalability when applied in high-order systems. To this end, we present a finite-horizon output-based model predictive control (MPC) for grid-connected power converters, which uses an N-step auto-regressive-moving-average (ARMA) model for system representation. The ARMA model is identified via an N-step prediction error method (PEM) in a recursive way. We investigate the connection between the DeePC and the concatenated PEM-MPC method, and then analytically and numerically compare their closed-loop performance. Moreover, the PEM-MPC is applied in a voltage source converter based HVDC station which is connected to a two-area power system so as to eliminate low-frequency oscillations. All of our results are illustrated with high-fidelity, nonlinear, and noisy simulations.
The modern power system features high penetration of power converters due to the development of renewables, HVDC, etc. Currently, the controller design and parameter tuning of power converters heavily rely on rich engineering experience and extrapolation from a single converter system, which may lead to inferior performance or even instabilities under variable grid conditions. In this paper, we propose an $H_{infty}$-control design framework to provide a systematic way for the robust and optimal control design of power converters. We discuss how to choose weighting functions to achieve anticipated and robust performance with regards to multiple control objectives. Further, we show that by a proper choice of the weighting functions, the converter can be conveniently specified as grid-forming or grid-following in terms of small-signal dynamics. Moreover, this paper first proposes a decentralized stability criterion based on the small gain theorem, which enables us to guarantee the global small-signal stability of a multi-converter system through local control design of the power converters. We provide high-fidelity nonlinear simulations and hardware-in-the-loop (HIL) real-time simulations to illustrate the effectiveness of our method.
Stability of power grids with synchronous generators (SGs) and renewable generation interfaced with grid-forming converters (GFCs) under dc-side current limitation is studied. To that end, we first consider a simple 2-bus test system and reduced-order models to highlight the fundamental difference between two classes of GFC controls -- (A) droop, dispatchable virtual oscillator control (dVOC) and virtual synchronous machine (VSM), and (B) matching control. Next, we study Lyapunov stability and input-output stability of the dc voltage dynamics of class-A GFCs for the simple system and extend it to a generic system. Next, we provide a sufficiency condition for input-to-state stability of the 2-bus system with a class-B GFC and extend it for a generic system. Finally, time-domain simulations from a reduced-order averaged model of the simple test system and a detailed switched model of the GFC validate the proposed conditions.
The grid-forming converter is an important unit in the future power system with more inverter-interfaced generators. However, improving its performance is still a key challenge. This paper proposes a generalized architecture of the grid-forming converter from the view of multivariable feedback control. As a result, many of the existing popular control strategies, i.e., droop control, power synchronization control, virtual synchronous generator control, matching control, dispatchable virtual oscillator control, and their improved forms are unified into a multivariable feedback control transfer matrix working on several linear and nonlinear error signals. Meanwhile, unlike the traditional assumptions of decoupling between AC and DC control, active power and reactive power control, the proposed configuration simultaneously takes all of them into consideration, which therefore can provide better performance. As an example, a new multi-input-multi-output-based grid-forming (MIMO-GFM) control is proposed based on the generalized configuration. To cope with the multivariable feedback, an optimal and structured $H_{infty}$ synthesis is used to design the control parameters. At last, simulation and experimental results show superior performance and robustness of the proposed configuration and control.