Intelligent Control and Optimal Operation of Complex Electric Power Systems Using Hierarchical Neural Networks

Introduction

The derivation of a mathematical model from physical laws according to the use of the model (e.g., for control), is most basic here to determine the mathematical structure. For example, it is shown (Laszlo, 1972) that a close connection exists between dynamic identification of an environment and its control. System identification itself is a well developed area of system theory. The need of mathematical representations in many aspects of the real world dictates the importance of system identification. In a way, it may be said that identification is a link between the mathematical-model world and the real world. For characterization of the cause and effect links of an observed plant, it is often assumed that the plant can be described by a model whose structure is known, or in other words, the plant is associated with a given form of parameterization, but the values of the parameters are assumed to be unknown. The parameters of the model are tuned in such a way that the behavior of the model approximates that of the plant. Differential equations, difference equations, and state-space representations are some examples of most widely used models. An excellent treatment of system identification in theory and applications may be found in (Ljung & Söderström, 1983), (Ljung, 1987). Note that identification may be categorized into off-line identification and on-line identification. The former one refers to a separate procedure by which a model (usually of given structure) is constructed based on a batch of data collected from the real system. The latter one refers to a procedure by which a model (again usually of given structure) is constructed and updated based on the most recent available data collected from the system in operation. Off-line identification may be sufficient for time-invariant systems. The need for on-line identification is seen in cases where the properties of the observed object are time-varying. For control purposes, two different approaches exist. One is the so-called indirect control by which the control action is adjusted based on the on-line identification of the plant. The other is the so-called direct control by which the control action is adjusted to improve a performance index involving implicit identification. Note that for both approaches, efforts have to be made for identification of the behavior of the plant even when control action is being taken based on the most recent available information about the plant. In a way, it may be said that control and identification are inter-dependent (Irwin, et al. 1995), (Haykin, 2001).