A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses. The solution is feasible with respect to constraints on control variables and dependent variables such as load voltages, reactive sources, and tie line power angles. The method is based on power flow solution by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints. A test program solves problems of 500 nodes. Only a small extension of the power flow program is required to implement the method.

Optimal Power Flow Solutions

A survey is presented of publications in the fields of optimal power flow and dispatching. It suggests a classification of methods based on the choice of optimization techniques. The survey is summarized in a single flow-chart-type figure, which indicates the relationship between methods, their chronology, and their popularity. This figure is based on a compilation of over three hundred publications. >

A survey of the optimal power flow literature

This paper reviews the progress of optimal dispatch, also called economic dispatch, since its inception to the present in chronological sequence. The classic single area as well as multiarea cases are summarized, and the important theoretical work in optimal load flows suggested to date reviewed. Approaches to the optimal load flow taken by industry are also reported, as well as an itemization of problems that still remain to be solved.

Optimal power dispatch&#2014;A comprehensive survey

This paper presents an economic dispatch procedure for allocating generation in a power system by the use of the Jacobian matrix. The major advantage of the procedure over other optimal dispatch procedures is its inherent simplicity and rapid convergence behavior which are characteristics particularly omportant for on-line implementation. Results obtained from an investigation of its convergence for the 118 bus IEEE system are given. Comparisons with the classical approach are conducted and logic for on-line implementation is presented.

Optimal Power Dispatch

Economic Dispatch of Generation Directly Rrom Power System Voltages and Admittances

In this paper the power losses are studied for an electrical utility. The power and reactive volt-amperes may be specified at the loads. If so, either the voltage or the current vector at the load is also specified. A similar set of specifications may be made for certain of the generator inputs to the electric network. In addition, voltage current vector inputs may be established at other generator nodes. It is presumed that the foregoing restrictions do not preclude the possibility of varying either the voltage or the current vector at several other generator locations. It should be noted that the electric network is assumed to be passive and, if desired, may be grounded at one or more points in addition to those ground connections assumed at the loads and generators. With these restrictions established and the remaining free or manipulative generator voltage or current vectors chosen, loss minimization may be studied. First, the electric network is considered by itself. The necessary and sufficient conditions to be met with the manipulative variables in order to minimize the losses in the electrical network are established. Second, the generator station losses are considered in conjunction with the electric network. This time, the necessary conditions, and also a set of sufficient conditions, are established for the same manipulative variables in order that the over-all loss be minimized. In the latter approach, allowance is made for the fact that the cost per kilowatt-hours is not the same at each station and in the network.

J. F. Calvert

Papers

A New Approach to Loss Minimization in Electric Power Systems