Optimal Economic Operation of Electric Power Systems

active power balance AIEE Trans algorithm assumed Chapter coefficients colſ computational Conf considered constant contraction mapping control vector coordination equations cost functional defined denoted dynamic programming Economic dispatch economic operation El-Hawary electric network electric power systems elements expression forebay elevation formulation fuel cost functional analysis given by Eq Hilbert space hydro plants hydro-thermal hydrograph i e Rh i e RN IEEE IEEE Trans inequality constraints inner product iteration Kirchmayer Lagrange multiplier linear loss formula matrix maximum principle method minimize minimum norm approach multiplier nonlinear nonlinear programming obtained optimal control optimal load flow optimal operation optimal solution output Power Appar power balance equation power demand Proc pseudoinverse quadratic reservoir result satisfied scheduling shown in Fig ſº Syst thermal plant transformation transmission losses turbine upstream plant variables variational calculus voltage volume of water water discharge