Abstract:Grid-synchronizing Stability (GSS) is an emerging issue related to grid-feeding voltage-source converters (VSCs). Its occurrence is primarily related to the non-linear dynamics of a type of vastly applied synchronization unit-Phase-locked Loops (PLL). Dynamic characterization and modeling for the GSS analysis can be achieved using a simplified system model, which is a second-order and autonomous non-linear equation, but with the presence of an indefinite damping term. As revealed and demonstrated in this work,… Show more
“…Numerical problems will have an impact on the results, which may make the continuity condition of the piecewise Lyapunov function on the switching boundary of various control modes unsatisfied. In [14], the SOS method is also used in the analysis of grid‐synchronizing stability of systems with voltage source converters. However, the validation models of the SOS method are still relatively simple, and the dynamic characteristics of renewable generators have not been taken into account.…”
Section: Introductionmentioning
confidence: 99%
“…In the SOS technique, Positivstellensatz (P-Satz) theorem or S-Procedure theorem is often used to construct optimiza-tion problems with SOS constraints. And some LF level set approaches such as V-s iteration can be used to solve the ROA problem [12,14]. Although the method of estimating the ROA based on LF is proven to be effective, there is still the problem of conservative estimation.…”
With large-scale wind farms connected to AC/DC network, the transient stability assessment (TSA) of the power system becomes more and more difficult. Among them, estimating the region of attraction (ROA) of the equilibrium point is a traditional but still challenging problem. Based on the Lyapunov stability theory, this paper proposes a new approach to obtain the enlarged estimation of the ROA. The optimization and updating strategy of shape function in the sum of squares (SOS) optimization problem are studied to reduce the conservatism of estimation result. In the proposed method, the gravitational search algorithm (GSA) is employed to optimize the coefficients of initial shape function to improve estimation performance. Based on the time-domain simulation (TDS) of expected faults, the fitness value for shape function optimization is calculated using the values of state variables at the fault clearing time and the system stability information. Furthermore, the optimal Lyapunov function is computed by introducing the update condition of shape function and adjusting the iteration strategy of the ROA estimation algorithm. Finally, the proposed method is applied to a two-machine-infinite-bus system and a more complex nine-bus AC/DC system with wind power. And the effectiveness of the proposed method is verified by comparing with the existing ROA estimation methods.
“…Numerical problems will have an impact on the results, which may make the continuity condition of the piecewise Lyapunov function on the switching boundary of various control modes unsatisfied. In [14], the SOS method is also used in the analysis of grid‐synchronizing stability of systems with voltage source converters. However, the validation models of the SOS method are still relatively simple, and the dynamic characteristics of renewable generators have not been taken into account.…”
Section: Introductionmentioning
confidence: 99%
“…In the SOS technique, Positivstellensatz (P-Satz) theorem or S-Procedure theorem is often used to construct optimiza-tion problems with SOS constraints. And some LF level set approaches such as V-s iteration can be used to solve the ROA problem [12,14]. Although the method of estimating the ROA based on LF is proven to be effective, there is still the problem of conservative estimation.…”
With large-scale wind farms connected to AC/DC network, the transient stability assessment (TSA) of the power system becomes more and more difficult. Among them, estimating the region of attraction (ROA) of the equilibrium point is a traditional but still challenging problem. Based on the Lyapunov stability theory, this paper proposes a new approach to obtain the enlarged estimation of the ROA. The optimization and updating strategy of shape function in the sum of squares (SOS) optimization problem are studied to reduce the conservatism of estimation result. In the proposed method, the gravitational search algorithm (GSA) is employed to optimize the coefficients of initial shape function to improve estimation performance. Based on the time-domain simulation (TDS) of expected faults, the fitness value for shape function optimization is calculated using the values of state variables at the fault clearing time and the system stability information. Furthermore, the optimal Lyapunov function is computed by introducing the update condition of shape function and adjusting the iteration strategy of the ROA estimation algorithm. Finally, the proposed method is applied to a two-machine-infinite-bus system and a more complex nine-bus AC/DC system with wind power. And the effectiveness of the proposed method is verified by comparing with the existing ROA estimation methods.
“…In this paper, the PLL-based VSC system is mainly studied. For the transient stability analysis, several methods including the time-domain simulation, phase portrait, equal area criterion (EAC), energy function, bifurcation analysis, etc have been developed recently [8]- [17]. Although the time-domain simulation always shows the dynamic process properly and it has been broadly used to verify the accuracy of system modeling [9] and the efficiency of transient stability enhancement strategies [10], it is timeconsuming and inconvenient.…”
Section: Introductionmentioning
confidence: 99%
“…However, this method is difficult to be understood from the physical perspective. In [17], the sumof-squares programming technique was used to improve the accuracy of the stability region by considering the indefinite damping effect, but it was still conservative.…”
As a typical power electronics interface device, the voltage source converter (VSC) usually uses phase-locked loop (PLL) to synchronize with the grid and its transient synchronous dynamics is complicated. Recently it is found that the PLL-VSC system can be described by a generalized swing equation which is similar to the swing equation for the synchronous generator. Differently it has a state-dependent damping term and the basin boundary of the stable operating point can show either a closed-loop or a fish-like pattern under different parameters. To deal with these difficulties, a trajectory reversing method is proposed to efficiently obtain the basin boundary of the post-fault stable operating point, and further the critical clearing angle and the associated critical clearing time. In addition, for the transient stability enhancement, an adaptive control strategy by varying equivalent PI controller parameters of PLL in terms of the system status is proposed. It is found that it can efficiently and quickly damp transient disturbances. Therefore, these two novel methods including the trajectory reversing method and the adaptive control method are expected to be valuable for transient stability analysis and enhancement of the PLL-VSC system.INDEX TERMS Voltage source converter, transient stability analysis, transient stability enhancement, statedependent damping, trajectory reversing method, adaptive control.
“…The rotor motion is represented by the second-order swing equation within the electromechanical timescale (Kundur, 1994). For the transient stability analysis of power-electronic-dominated power systems, several approaches have been developed, including the time-domain simulation (Zhao et al, 2021), energy function (Zhang et al, 2022), equalarea criterion (Xu et al, 2023), phase portrait (Wu and Wang, 2020), hyperplane method (Ma et al, 2023a), basin of attraction (Zhang et al, 2020), and bifurcation analysis (Ma et al, 2022a). Usually, the transient synchronization of the VSC grid-tied systems belongs to the electromagnetic timescale, including the DC voltage control timescale and AC current control timescale (Yuan et al, 2017;Ma et al, 2023b).…”
The integration of large-scale photovoltaics (PVs) into the power grid has significantly altered the transient synchronization dynamics of traditional power systems dominated by synchronous generators (SGs) and posed great challenges to modeling and analysis of PVs integration. In this paper, the transient synchronization stability of the PV-SG system is studied using the singular perturbation technique. Firstly, a nonlinear model of a PV-SG system is established to reveal the multiscale transient synchronization characteristics. Further, the full system is decomposed into a slow subsystem and a fast subsystem by the singular perturbation technique. The fast subsystem containing the dynamics of the DC voltage control, terminal voltage control, and phase-locked loop, and the slow subsystem containing the dynamics of rotor motion can perfectly reflect the dynamics of the full system within the electromagnetic and electromechanical timescales, respectively. The proposed model provides a clearer physical picture of dynamics in the PV-SG system within the electromagnetic and electromechanical timescales. Subsequently, the stability of the slow and fast subsystems is investigated using the energy function and eigenvalue analysis methods, respectively. Meanwhile, the impacts of various operating, control, and structural parameters on the transient synchronization stability are uncovered. Different from the most existing research endeavors on the wide simulations of the PVs integration, the impact of PVs on the synchronization dynamics of SGs without considering the dynamical characteristics of the PV system, and the transient synchronization stability analyses of the PLL-based voltage source converter systems, it is the key contribution to study the transient synchronization dynamical characteristics of the PV system and its interaction with the SG under different timescales. All these are helpful and easy to extend to more complicated PV-SG systems. Finally, the analysis results are validated by extensive simulations.
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