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This paper offers non‐linear control for enhancing the transient stability in power systems containing a photovoltaic (PV) and doubly fed induction generator (DFIG) by transient energy function (TEF) method and finite‐time observers. At first, the TEF method is utilized to enhance the transient stability in a power system containing a PV, DFIG, and synchronous generator (SG) by constructing a hybrid Lyapunov function. Then, the derivative terms in control are estimated with finite‐time observers. The main contribution of the research is the application of the TEF technique in the transient stability evaluation of a power system consisting of PV, SG, and DFIG. Another innovation of the research is the simultaneous control of DFIG and PV, whose uncertain parameters are estimated with the use of finite‐time observer. The proposed non‐linear control scheme is robust against changes in the configuration of the power system. In order to show the capability of this control scheme, time domain simulations are performed on the IEEE 9‐bus, and the NEW ENGLAND Standard 39‐Bus power system. Using the obtained result, some comparisons are made with the back‐stepping control scheme to clarify the superiority of the proposed method. The comparisons show that the proposed non‐linear control scheme can properly provide extra damping to reduce the first‐swing fluctuations in less time. The manuscript contains the new original results of the authors' research. In this article, to maintain and improve the transient stability, a new controller with simultaneous management of photovoltaic (PV) and doubly fed induction generator (DFIG) has been developed. The contributions of the paper are as follows. (1) The transient energy function (TEF) is obtained for the power system containing synchronous generator (SG) and DFIG. (2) The control laws are acquired with four PV and DFIG control variables. (3) The derivative parameters of the PV and DFIG controls by a finite‐time observer are estimated. [ABSTRACT FROM AUTHOR]

Mid-long term voltage stability refers to voltage stability concerning the dynamics of the slow dynamic elements and protection devices in power systems. To improve the mid-long term voltage stability, this paper proposes a scheme of model predictive control (MPC) based on Galerkin method. The basic principle of MPC is to solve the optimization problem regarding voltage stability control based on the prediction model periodically. By applying the optimal control scheme to power systems, the mid-long term voltage stability can be enhanced. The Galerkin method-based polynomial approximation approximates the relationship between mid-long term trajectories and control parameters by a polynomial function. The polynomial function acts as a prediction model to predict future system trajectories under different values of control parameters in MPC. The advantage of the proposed method is that its prediction accuracy is relatively high and thus the control efficiency of MPC is improved, as the polynomial function can embody the non-linear characteristics of the power system. In the case study, the 3-machine 10-bus system and the New England 39-bus system are taken as examples to compare the MPC based on the proposed method and the trajectory sensitivity method in terms of prediction accuracy, computation time and control results. [ABSTRACT FROM AUTHOR]