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This paper considers the turbulent homogeneous mixing of two reactants undergoing a one step, second order, irreversible, exothermic chemical reaction with a rate constant of the Arrhenius type. A statistically stationary turbulent velocity field is assumed given and unaffected by mass or heat production due to the chemical reaction. Relative density fluctuations are neglected. A Hopf-like functional formalism is presented, with application to both statistically inhomogeneous and statistically homogeneous flows. Single and double point probability density function differential equations are derived from those functional equations. The limit of very large activation energies is considered; a low degree of statistical correlation between temperature and concentration fields during the ignition period is hypothesized. After making use of the homogeneity assumption a closure problem is still present due to the nonlocalness of the molecular diffusion term. The problem is rendered closed by assuming a Gaussian conditional expected value for the temperature at a point given the temperature at a neighboring point. The closure is seen to preserve very important mathematical and physical properties. A linear first order hyperbolic differential equation with variable coefficients for the probability density function of the temperature field is obtained. A second Damkohler number based on Taylor's microscale turns out to be an important controlling parameter. A numerical integration for different values of the second Damkohler number and the initial stochastic parameters is carried out. The mixture is seen to evolve towards an eventual thermal runaway, the detailed behavior however being different for different systems. Some peculiarities during the ignition period evolution are uncovered.

This paper describes a new and efficient method for computing a real-time load flow solution of a power system network. The use of line flow measurements is proposed and it is shown that this measurement scheme shows superiority in speed, accuracy and numerical behavior together with advantages in error detection and identification.

An economic schedule for real power generation is obtained by a Lagrangian method and the allocation of reactive power generation is determined by a gradient method. Alternate real and reactive power requirements for economic system operation are computed until the total cost is minimized within the limitations imposed by system constraints. Repeated solutions of the network equations are used to incorporate the effects of transmission losses in lieu of a precalculated transmission loss formula. The computer program provides a means to determine the optimum use of available real and reactive power generation and to plan economically for future requirements.

This paper describes methods for using power system readings to compute a real-time power flow solution of the transmission network. The use of redundant data is discussed and procedures are outlined to detect, identify, and correct for data errors. Several examples are presented and the numerical behavior of the methods is discussed.

Extending the theoretical foundations established in Part I(1), this paper further describes this efficient method of computing the real-time load flow solution for a power system network. An efficient numerical solution technique particularly applicable to this problem is outlined. Relative weighting of the measurements is analyzed in terms of the measurement accuracies. A method is given for dynamic determination of the frequency of the state estimate calculations. The effects of real-time changes in the network are discussed.

There is current interest by many utilities to enhance security of operation through monitoring real time system information. American Electric Power is at this time in the final stages of testing what appears to be the world's first power system state estimation project to obtain a complete real time load flow solution of its EHV system.

This paper describes a method for the optimum scheduling of pumped storage hydro in combination with a steam generating system. It also describes a computer program which determines weekly operating schedules for a pumped hydro station. The techniques developed can be used to evaluate future peaking capacity of this type and to estimate long-term operating costs for different combinations of steam and pumped storage capacity.

The two familiar functional formalisms in turbulence are applied to the simultaneous turbulent mixing and chemical reaction of scalar fields. One‐step, second‐order, irreversible, exothermic chemical reactions with an Arrhenius‐type rate constant are considered. The problem is formally posed in terms of initial and boundary conditions. For the special case of equal mass‐diffusivities and a Lewis number of one the functional equations are decoupled into a turbulent binary mixing study and a reactive problem. The Lewis‐Kraichnan formalism is used in order to obtain exact functional solutions of the binary mixing case in final period turbulence. Driving forces are included in the thermal energy equation. These solutions are used to obtain detailed information about the binary mixing problem and the behavior of very rapidly reacting species in the final period.

The temperature and concentration fields produced by turbulent mixing of two reactants undergoing a one‐step, very rapid, irreversible, exothermic reaction are studied. Temperature and concentration fields decay in two stages: kinetically driven and diffusion controlled. Stochastic solutions are derived for the first stage, the asymptotic state of which displays all the characteristics of species segregration. In particlar, only a weak correlation between the concentration and temperature fields is generated in the first stage. For the special case of equal mass diffusivities and a Lewis number of one the solution to the second stage is obtained in terms of the solution of a nonreacting binary mixing problem. An approximate solution for Lewis numbers different from one is proposed. The temperature field seems to decay with an effective thermal diffusivity determined by the smaller of the molecular mass and thermal diffusivities.