Probabilistic Analysis Of Small-Signal Stability Of Power Systems As Affected By Stochastic Variation Of Grid-connected Wind Generation

Power system stability plays a significant role in modern power industries. With increasing wind power penetration, the theory of power system stability needs to be improved, because the performance of power system are no longer only influenced by controllable synchronous generators, but also a large number of stochastic and fluctuating asynchronous generators (wind turbine generators, WTG), which makes the modern power system a complex stochastic-deterministic coupling power system.Deterministic strategies used for small signal stability analysis of power systems as affected by penetration of large scale wind generation are limited since they are carried out based on a specified operating condition. However, since the wind generation is primarily determined by wind speed and thus fluctuating constantly, the operating conditions of the system are stochastically uncertain. Therefore, a more comprehensive probabilistic stability research that considering the uncertainties and intermittence of wind power should be conducted to assess the influence of wind generation on the power system stability from the viewpoint of probability. This dissertation studied and explored the probabilistic analysis of small-signal stability of power systems as affected by stochastic variation of grid-connected wind generation. The primary contents and original contributions of this dissertation are as follows:Dynamic modelling of wind turbine generator is the basis of researching the impact of wind power on power system small signal stability. For this purpose, the status equations of the aerodynamic model, shaft system model, pitch control model, converters model with application of vector control and feed-forward decoupling control strategies of the doubly-fed induction generator (DFIG) are established for analyzing small signal stability. Furthermore, in order to investigate the effects of large scale wind farms connected to an existing power grid on the small signal analysis of power system, the whole wind farm is modelled as an aggregated wind farm model by one equivalent wind generator, whose parameters can be modelled as an equivalent of the parallel connection of single generators. Apart from this, models for synchronous generators, excitation systems, transmission lines and transformers are also presented.The primary task of small signal stability analysis of wind integrated power systems by using the probabilistic method is to reasonably simulate the probabilistic production of wind farms. Therefore, considering the main factors affecting stochastic characteristic of wind power, probabilistic production model of multiple wind farms is developed. This model consists of three parts:wind speed frequency distribution model, wind speed correlation model and wind speed-power output transformation model. By comparing the calculated results getting from different estimation methods, it can be seen that maximal likelihood method was better in fitting the wind speed distribution. The proposed wind speed correlation model is verified from three aspects:goodness of fit test, two-dimensional kernel smoothing density estimate and aggregated power output comparison. The results show that the proposed wind speed correlation model preserves the marginal distribution of wind speed at each wind site and the correlation structure of multiple wind site, which can be applied to small signal stability analysis of power system containing wind farms.Based on the dynamic model of grid-connected wind farms with DFIG type and the probabilistic production model of multiple wind farms, a probabilistic methodology for small signal stability analysis of power system with correlated wind sources is presented. The approach based on the2m+1point estimate scheme and Cornish Fisher expansion, the orthogonal transformation technique is used to deal with the correlation of wind farms. A case study is carried out on two test system and the probabilistic indexes for eigenvalue analysis are computed from the statistical processing of the obtained results. The accuracy and efficiency of the proposed method are confirmed by comparing with the results of Monte Carlo simulation. The numerical results indicate that the proposed method can actually capture the probabilistic characteristics of mode properties of the power systems with correlated wind sources. Test results show that the dampings of local mode and inter-area mode tend to be improved when a synchronous generator involved in these oscillatory modes is replaced by the wind farms within the same area. Additionally, it appears that wind farms do not affect local modes in distant areas. Furthermore, the presence of correlated wind speeds increases the fluctuation of wind farms’output, which leads to a considerable influence on the probability of small signal instability and damping of oscillatory mode. It is necessary to consider the correlation among wind farms in the probabilistic small signal stability problem to build more exact models.At last, author provides an attempt to include probabilistic character of wind power into the power system oscillatory stability margin (OSM) analysis. The probabilistic production model of multiple wind farms is applied to generate the wind speed samples. The mathematical model of OSM for wind farm integrated power system is formulated and is calculated by the integration-based eigenvalue tracing approach. Considering the uncertainties of the wind power, several statistical indices are presented to evaluate OSM. Monte Carlo simulation is used to calculate these statistics. The impact of wind power uncertainty on OSM restricted by inter-area mode is investigated in two test system, respectively, for different wind farm locations, wind power penetration levels and wind speed correlation (WSC) degrees. For both interconnected systems, wind power uncertainty variation is found to have a positive or negative impact on the probabilistic OSM. The impact depends on the locations of the wind farms (the degree of network congestion), the wind power penetration level and wind speed correlation degree. Statistical indices allow visualizing the above phenomena and, which is more important, can be used to assist power system operators and planners in quantitatively assessing the impact of wind generation and certain operating decisions with respect to changing operating conditions. The risk index provides system operators and planners with information necessary for decision making, including risk threshold selection. Hopefully, the analysis presented in this paper can be extended to include possible preventive and remedial measures necessary to improve the probability of oscillatory stability or maintain a certain OSM in the actual system operation.