Power System Small-signal Angular Stability Research Articles

Power System Small-Signal Angular Stability Affected by Virtual Synchronous Generators

This paper examines the small-signal angular stability of a power system affected by a virtual synchronous generator (VSG). The examination is based on an interconnected model with two subsystems. The VSG under the examination is modeled as the VSG subsystem. The rest of power system (ROPS) forms the other subsystem. Damping torque analysis is applied to indicate that when an oscillation mode of the VSG subsystem is in the proximity of an electromechanical oscillation mode of the ROPS subsystem on the complex plane, strong dynamic interactions are introduced by the VSG to decrease the small-signal angular stability of the power system. This implies that when the parameters of the VSG are set, modal proximity of the VSG to the electromechanical oscillation mode of the ROPS subsystem should be examined to avoid the detrimental impact of the VSG on power system small-signal angular stability. A method to evade the modal proximity is proposed in this paper for guiding the design of the VSG. Two example power systems with multiple VSGs for the wind power generation and transmission are presented. Study cases demonstrate and evaluate the analysis about the impact of modal proximity and proposed method for guiding the parameters setting of VSGs.

Parameter tuning of the PLL to consider the effect on power system small‐signal angular stability

A phase locked loop (PLL) tracks the phase of the terminal voltage of a grid-connected permanent magnetic synchronous generator (PMSG) for wind power generation. Phase tracking by the PLL is used by the vector control for the grid connection of the PMSG. This study investigates the impact of phase-tracking performance of the PLL on power system small-signal angular stability. Damping torque analysis conducted in this study explains why the impact of the PLL is normally small. The analysis indicates that under the special condition of open-loop modal resonance, however, the effect of the PLL may become significant. It is very likely that the open-loop modal resonance may reduce the power system small-signal angular stability. Hence, in tuning the parameters of the PLL, the open-loop modal resonance should be avoided. In this study, the procedure about the parameter tuning of the PLL to consider the effect of open-loop modal resonance is proposed and demonstrated in an example multi-machine power system integrated with a PMSG. Analysis and conclusions made in this study are evaluated using the example power system.

Small-signal angular stability of power system as affected by grid-connected variable speed wind generators- A survey of recent representative works

This paper reviews the status and progress of the investigation on power system small-signal angular stability as affected by grid-connected variable speed wind generators (VSWGs). The review is carried out on the basis of a survey of recently published representative papers. Strategies of the investigation made in those selected papers are classified into two groups: 1) VSWGs displacing synchronous generators (SGs); 2) VSWGs simply being added in a power system. The diversification of the results of the investigation is highlighted in the survey. Careful analysis on two strategies of the investigation is conducted in this paper. It is revealed that in the strategy of VSWGs displacing SGs, there are two factors which could affect power system small-signal angular stability differently: 1) Withdrawing the SGs' dynamics; 2) adding the VSWGs' dynamics. In the strategy of adding VSWGs in the power system, there are also two affecting factors: 1) Change of load flow brought about by the VSWGs; 2) dynamic interactions with the SGs introduced by the VSWGs. Hence diversified results of the investigation obtained so far are not only due to the dependence of the investigation on sample power systems used, but also caused by the mixture of different affecting factors. This paper is concluded with a summary of key issues of the investigation for future work.

Power System Electromechanical Oscillation Modes as Affected by Dynamic Interactions From Grid-Connected PMSGs for Wind Power Generation

Dynamic interactions between a grid-connected permanent magnet synchronous generator (PMSG) and power system are normally weak. This paper reports a special condition of modal resonance, under which the grid-connected PMSG may dynamically interact with power system strongly to affect power system electromechanical oscillation modes (EOMs). The special condition of modal resonance reported in this paper is that an open-loop converter oscillation mode (COM) of PMSG is close to an open-loop EOM of a power system on the complex plane. Damping torque analysis is carried out to explain why strong dynamic interactions between PMSG and power system may occur under the condition of modal resonance. Results of theoretical analysis in this paper indicate that occurrence of modal resonance may possibly cause the damping of either closed-loop COM or EOM to decrease such that power system small-signal angular stability is affected negatively by grid connection of PMSG. Responsible COMs for modal resonance are found to be related with active/reactive power control systems of a grid-side converter of PMSG. In the paper, an example multimachine power system with PMSGs is presented to demonstrate and validate analysis and conclusions made.

On the impact index of synchronous generator displaced by DFIG on power system small-signal stability

As the maturity of wind power technology and the ageing and retirement of conventional synchronous generators, the displacement of synchronous generators by wind power generators would be a trend in the next few decades. The power system small-signal angular stability caused by the displacement is an urgent problem to be studied. The displacement of the SG by the DFIG includes withdrawing the dynamic interactions of the displaced SG and adding the dynamic interactions of the displacing DFIG. Based on this fact, a new index is proposed to predict the impact of the SG to be displaced by the DFIG on power system oscillation modes. The sensitivity index of the oscillation modes to the constant inertia of the displaced SGs, proposed in early literatures to estimate the dynamic impact of the SG being displaced by the DFIG, is also compared with the proposed index. The modified New England power system is adopted to show various results and conclusions. The proposed index can correctly identify the most dangerous and beneficial displacement to power system small-signal angular stability, and is very useful in practical applications.

Damping torque analysis of power systems with DFIGs for wind power generation

A grid-connected double fed induction generator(DFIG) for wind power generation can affect power system small-signal angular stability in two ways: by changing the system load flow condition and dynamically interacting with synchronous generators (SGs). This study presents the application of conventional method of damping torque analysis (DTA) to examine the effect of DFIG's dynamic interactions with SGs on the small-signal angular stability. It shows that the effect is due to the dynamic variation of power exchange between the DFIG and power system and can be estimated approximately by the DTA. Consequently, if the DFIG is modelled as a constant power source when the effect of zero dynamic interactions is assumed, the impact of change of load flow brought about by the DFIG can be determined. Thus the total effect of DFIG can be estimated from the result of DTA added on that of constant power source model. Applications of the DTA method proposed in this study are discussed. An example of multi-machine power systems with grid-connected DFIGs is presented to demonstrate and validate the DTA method proposed and conclusions obtained in this study.

A Method to Examine the Impact of Grid Connection of the DFIGs on Power System Electromechanical Oscillation Modes

Grid connection of a DFIG for power generation changes the power system load flow and introduces dynamic interactions with the synchronous generators (SGs). A method is proposed in this paper for the separate examination of the impact of those two affecting factors, the change of load flow and dynamic interaction brought about by the DFIG, on the electromechanical oscillation modes of a power system. The method is developed on the establishment of a “closed-loop control system” type of state space model of the power system where the DFIG is treated as the feedback controller. The established model unambiguously indicates that the impact of the DFIG can be examined separately: (1) With the DFIG being modelled as a constant power injection into the system, the impact of the load flow change brought about by the DFIG on the oscillation modes is determined; (2) The impact of the dynamic interactions introduced by the DFIG is estimated by calculating the contribution of the damping torque from the DFIG with its full dynamics being considered. Thus a more detailed examination on and deeper insight into the impact of grid connection of the DFIGs on power system small-signal angular stability is obtained by using the proposed method.

Impact of grid connection of large-scale wind farms on power system small-signal angular stability

The grid connection of a large-scale wind farm could change the load flow/configuration of a power system and introduce dynamic interactions with the synchronous generators (SGs), thus affecting system small-signal angular stability. This paper proposes an approach for the separate examination of the impact of those affecting factors, i.e., the change of load flow/configuration and dynamic interactions brought about by the grid connection of the wind farm, on power system small-signal angular stability. Both cases of grid connection of the wind farm, either displacing synchronous generators or being directly added into the power system, are considered. By using the proposed approach, how much the effect of the change of load flow/configuration brought about by the wind farm can be examined, while the degree of impact of the dynamic interaction of the wind farm with the SGs can be investigated separately. Thus, a clearer picture and better understanding of the power system small-signal angular stability as affected by grid connection of the large-scale wind farm can be achieved. An example of the power system with grid connection of a wind farm is presented to demonstrate the proposed approach.