Abstract
Due to the increasingly marketized demands of power systems, the dedicated communication channel used by the traditional load frequency control (LFC) scheme is ineluctably replaced by highly open communication networks, which may introduce constant, and time-varying delays. Hereupon, for those two kinds of communication methods, this article explores the LFC problem of power systems in consideration of constant, and time-varying delays. By utilizing the Lyapunov stability theory, and an improved inequality technique, some criteria for guaranteeing the stability, and the specified H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the closed-loop system are obtained, and a PID-type controller with the consideration of time delays and disturbance is designed. The case studies take one-area delayed LFC scheme and the traditional/deregulated three-area LFC scheme as examples to discuss the relationships between the maximum allowable delay, and the controller gain as well as the relationships between time delays, and the minimum H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index, respectively. Finally, the effectiveness of the method proposed is verified, and the comparison results show certain advantages of the method presented in this article over the existing literature.
Highlights
L OAD frequency control (LFC) is a mechanism for maintaining frequency and power interchange with adjacent areas at a predetermined value, which occupies a special position in power systems due to its excellent ability [1]–[4]
2) For the traditional and the deregulated three-area load frequency control (LFC) schemes, the PID-type controller is designed to ensure the stability of the system under the condition that delays are less than the present value, and to guarantee the optimal H∞ performance index of the closed-loop system (CLS)
Defining y(t) =Δ [ y(t) y(t) ]T, K =Δ [ KP KI ], and taking time delays caused by control signal transmission into account, formula (3) can be re-expressed in the following form: u(t) = −Ky(t − d(t))
Summary
L OAD frequency control (LFC) is a mechanism for maintaining frequency and power interchange with adjacent areas at a predetermined value, which occupies a special position in power systems due to its excellent ability [1]–[4]. Apart from that, the Rekasius substitution [20], Schur–Cohn methods [21] are common methods for calculating the upper bound of delays When it comes to the stability analysis and control problems of the systems with time-varying delays, some methods may fail. 1) The stability of the one-area delayed LFC scheme with a PI-type controller is analyzed, and the corresponding stability criterion is improved by using the Lyapunov stability theory and the optimized inequality technique. 2) For the traditional and the deregulated three-area LFC schemes, the PID-type controller is designed to ensure the stability of the system under the condition that delays are less than the present value, and to guarantee the optimal H∞ performance index of the closed-loop system (CLS). Notations: The notations used in this article are standard and consistent with [32]; they are omitted here
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