Applied Mathematics for Deregulated Electric Power Systems: Optimization, Control, and Computational Intelligence

The achievements in system engineering in the analysis and control of power system reliability and security over the last three decades, accomplished by taking full advantages of advances in computer, communication, and control technologies, are truly remarkable. For example, the economic generation commitment and dispatch for large power systems are now routinely solved using efficient Lagrangian-relaxation methods [1] and interior-point methods [2]. State estimation with bad data and topology detection capability [3], has become a mainstay in control room, and has gone from being an advisory tool to being used in real-time energy price calculation [4]. Fast stability analysis has benefited from energy function analysis [5,6,7], which also contributed to enhanced understanding of modes of instability. Tools for analyzing voltage stability, a phenomenon not noted until the 1970’s, have been well-developed [8,9] that it is common for control center operators to rely on the power-voltage sensitivity curve in determining admissible power transfer across some major congested interfaces. Smallsignal stability has evolved from a power system stabilizer adding damping to the local swing mode to the need to understand interarea mode oscillations based on coherency analysis [10,11], which drives the development of the wide-area monitoring system (WAMS) installed in the western US system [12]. Flexible AC Transmission Systems [13], based on advances in high-voltage power electronics, allow a system operator to control voltage and line power control on transmission systems, as well as provide damping enhancement [14]. More recently, artificial neural network and genetic algorithms have been applied to several power system problems, including damping control design [15-17]. From a public policy viewpoint, the work in [18] was singularly significantly in the restructuring of the power industry organized as regional monopolies [19,20].