The existing small-signal stability constrained optimal power flow (SC-OPF) generally needs to deduce the sensitivity analytical expression of the small-signal stability index to parameters, which requires a large amount of formula derivation and mathematical computation. In order to overcome the complex problem of sensitivity, this article proposes an approximate sensitivity calculation method based on the back propagation (BP) neural network algorithm in the SC-OPF model. First, the minimum damping ratio of the system is taken as the small-signal stability index, and the algebraic inequality composed of the minimum damping ratio is used as the small-signal stability constraint in this model. Second, the BP neural network is introduced into the SC-OPF to analyze the mapping relationship between the generator power, node power, line power and the minimum damping ratio of the system, and then the numerical differentiation method is used to calculate the approximate first-order sensitivity of the minimum damping ratio in the correction equation. Finally, a series of simulations on the WSCC-9 bus and IEEE-39 bus systems verify the correctness and effectiveness of the proposed model.
Transient stability is an important factor for the stability of a power system. With improvements in voltage levels, and the expansion of power network scales, the problem of transient stability is particularly prominent. When a power system circuit fails, if the operation time of the relay protection device is higher than the critical clearing time (CCT), the relay protection device cannot cut the fault line in a timely manner. It is essential to forecast and adjust the CCT to improve the stability of the system; therefore, a method is proposed in this paper to predict and evaluate the critical clearing time using the broad learning system (BLS). The sensitivity of the critical clearing time can be easily calculated based on the prediction results of the critical clearing time using BLS. Moreover, the critical clearing time can be modified using the BLS correction control model. The proposed method was verified using a 4-machine 11-node system and a 10-machine 39-node system. According to the experimental results, the proposed model can predict, evaluate, and correct the CCT very well.
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