With widespread access to renewable energy sources and active loads such as electric vehicles, uncertainty problems have gradually become a prominent problem in the power system. However, the conventional stochastic differential equation (SDE) model is not comprehensive in describing the randomness of disturbances, and the solution of novel models generally relies on numerical calculations. To improve the modeling accuracy and the calculation effectiveness, this paper utilizes intervals to model stochastic continuous disturbances and proposes an analytic method based on Taylor series expansion to predict the dynamic response of the power system under interval uncertainty, which may provide a reference for the small disturbance stability analysis of the power system. Furthermore, in order to apply to a more general situation, the case of continuous intervals is considered, and the analytic results are obtained, by which the superposition principle applicable to intervals is summarized. The comparison with the Monte Carlo method and the responses from actual wind power data verify the effectiveness and rationality of the proposed method.
In modern power systems, the impact of random power sources and loads on power systems is increasing, resulting in threatened system frequency security. However, traditional methods are often not comprehensive in modelling randomness, and there is no analytical method to assess the frequency response of power systems under uncertain power disturbances. In this paper, the power disturbance in a power system is regarded as an interval random quantity. Based on a general model of the system frequency response (SFR-G) and the theory of stochastic processes, an analytical prediction method of the power system frequency deviation under uncertain power disturbance is proposed. Through further deduction, the allowable range of power disturbance under the premise of secure frequency deviation can also be defined, which provides a reference for frequency security and accident prevention in power systems. Numerical simulations demonstrate that the proposed analytical method can delimit the response interval of system frequency deviation well, and the backstepping calculation can also delimit the allowable range of power disturbance to ensure the secure operation of the system.
In modern power systems, the impact of random power sources and loads on power systems is increasing, resulting in threatened system frequency security. However, traditional methods are often not comprehensive in modelling randomness, and there is no analytical method to assess the frequency response of power systems under uncertain power fluctuations. Here, the power fluctuation in a power system is regarded as an interval random quantity. An analytical prediction method of the power system frequency deviation under uncertain power fluctuation is proposed. Through further deduction, the allowable range of power fluctuation under the premise of secure frequency deviation can also be defined, which provides a reference for frequency security and accident prevention in power systems. Numerical simulations with the model of the East China Power Grid demonstrate that the proposed analytical method can delimit the response interval of system frequency deviation well, and the backstepping calculation can also delimit the allowable range of power fluctuation to ensure the secure operation of the system.
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