This paper proposes a method to design power system stabilizers (PSSs) based on single-machine infinite-bus system models to mitigate the risk of low-frequency electro- mechanical power oscillations in an N-machine power system. First, models of N fabricated identical-machine power systems are established for the N-machine power system. Analysis in the paper indicates that the electromechanical oscillation mode of fabricated identical-machine power systems with the least damping is of less damping than the electromechanical oscillation modes of N-machine power system. Second, it is proved that models of fabricated identical-machine power systems are dynamically equivalent to the single-machine infinite-bus system models. Finally, it is suggested that the PSSs are designed using single-machine infinite-bus system models to enhance the least damped electromechanical oscillation mode of fabricated identical-machine power systems. This eventually improves the damping of electromechanical oscillation modes of N-machine power system, thus mitigating the risk of low-frequency electromechanical power oscillations. In the paper, the proposed method is demonstrated and evaluated by using three well-known example multi-machine power systems. Effectiveness of PSSs is confirmed by the results of modal computation and simulation.

Case-by-case study in the literature has found from the results of numerical computation and simulation that a grid-connected virtual synchronous generator (VSG) can maintain the stability under the condition of extremely weak grid connection. This paper presents the theoretical proof to the finding and thus, generally concludes that the grid-connected VSG is immune to the instability risk under the condition of weak grid connection. In addition, the paper extends the theoretical proof to the case of a grid-connected PMSG wind farm with multiple VSGs. An example grid-connected PMSG wind farm with twenty VSGs is presented to demonstrate and evaluate the theoretical analysis and conclusion made in the paper.

This paper compares three methods, the impedance model based analysis, the positive net damping analysis and the open-loop modal resonance analysis. The differences and connections among three methods are revealed, which helps to gain better understanding on the limitations of the methods for studying the mechanism of sub-synchronous oscillations (SSOs) caused by grid-connected wind turbine generators (WTGs) in a power system. Following useful conclusions are obtained, which are evaluated and demonstrated by study cases: (1) Both the negative resistance and negative net damping are highly related with strong dynamic interactions between the WTGs and AC grid under the condition of modal resonance. This explains why resistance and net damping may become negative from the standpoint of system modal condition. (2) It is possible that results of IMA and PDA may not reflect correctly the system SSO instability risk brought about by the WTGs. The reason is that the IMA and PDA are based on the sufficient condition of system stability. Assessment made by the IMA or PDA may be very conservative. In study cases, three methods are compared in the parameter space of converter controllers of the WTGs such that all the parameter conditions are covered in comparison.

This paper investigates the modal repulsion between a grid-connected wind farm and power system to cause the sub-synchronous oscillations (SSOs), without using the reduced-order aggregated representation of the wind farm as a single wind generator. Since the dynamic interactions between the wind farm and power system are multivariable, a multi-input and multi-output closed-loop model of the power system with the wind farm is established, which is comprised of the wind farm subsystem and the subsystem of rest of power system (ROPS). Analytical proof is presented in the paper to indicate that when an open-loop SSO mode of wind farm subsystem is close to an open-loop SSO mode of ROPS subsystem on the complex plane, modal repulsion of corresponding closed-loop SSO modes occur which degrades the SSO stability of the power system. Hence, the mechanism about why the wind farm may cause the SSOs in the power system is revealed from the perspective of modal repulsion. Subsequently, a method of open-loop modal analysis is proposed. Application of the proposed method of open-loop modal analysis to study the SSOs caused by the wind farm under the condition of modal repulsion is demonstrated and evaluated by example power systems.

This paper analytically examines how the condition of weak grid connection affects the torsional sub-synchronous oscillations (SSOs) induced by a grid-connected DFIG in a power system. The examination focuses on the SSO mode of grid-connected DFIG, which is dominated by the phase locked loop (PLL) or DC voltage control. Theoretical analysis is carried out to prove that the condition of weak grid connection amplifies the impact of modal resonance between the DFIG and torsional dynamics of synchronous generators. The amplifying effect of weak grid connection exhibits as the decrease of damping of SSO mode of DFIG and increase of the associated residue when the grid connection weakens. Consequently, the DFIG is more likely to induce torsional SSOs under the condition of weak grid connection, leading to system instability in the worst case. Analytical examination presented in the paper reveals the mechanism about how the condition of weak grid connection plays a key role for the DFIG to induce the torsional SSOs. An example multi-machine power system with the grid-connected DFIG is presented. Results of modal analysis and non-linear simulation using detailed model of DFIG validate the analysis and conclusions made in the paper.

This paper analytically derives oscillatory stability criteria of a grid-connected PMSG based on the block diagram model. The derivation reveals the general mechanism about how the condition of grid connection, loading and converter control parameters setting of the PMSG jointly affect the oscillatory stability of the PMSG. It logically explains why the condition of weak grid connection and heavy loading may cause destabilization. In addition, computationally simple and modal-computation free indices are proposed to identify the instability risk caused by the “improper parameters setting” of the control system of grid side converter (GSC) and the phase locked loop (PLL). Following analytical conclusions are obtained: (1) When the PLL is of high-frequency bandwidth, high-frequency oscillations are mainly caused by the PLL or the open-loop modal resonance between the PLL and current control of the GSC. In addition, the low-frequency oscillations may also occur as caused by the power control of the GSC. (2) When the PLL is of low-frequency bandwidth, low-frequency oscillations may be caused jointly by the power control of GSC and the PLL. An example grid-connected wind farm with eighteen similar PMSGs is presented to demonstrate and evaluate the stability criteria derived and analytical conclusions obtained in the paper.