This paper presents a novel method for the solution of the hydrothermal optimal power flow problem. The optimization is decoupled into a primary and a secondary stage. The primary stage is a hydrothermal generation scheduling problem. It is decomposed to individual thermal generation scheduling subproblems, one for each time period, and a hydro generation scheduling subproblem, for the whole time horizon. The thermal subproblem is solved by economic generation scheduling using a generalized power balance constraint. The hydro subproblem is solved by network flow programming. The hydrothermal generation scheduling is obtained by a coordination method between the hydro and thermal subproblem solutions. The secondary stage minimizes the power system losses and calculates a feasible solution for each time period. The thermal generators contribute to the loss minimization according to their economic participation factors. This stage is solved by sparse linear programming subject to control-variable step-limit constraints. A carefully designed step-limit control strategy successfully damps the oscillations that are always present in successive linear programming formulations.

Hydrothermal optimal power flow based on hydrothermal decomposition and coordination

The author presents an advanced simulator with the following features: the transmission line on which switching operations are performed can be untransposed, while the rest of the system is still represented as symmetrical; and the effect of induction motor dynamics can be represented by the time domain simulation of varying speed, slip and machine impedance. The simulator is designed to permit interactive experimentation for examining diverse phenomena in balanced or unbalanced steady state, produced by any sequence of switching, such as fault inception, clearing, temporary overvoltages, effects of compensation, motor starting, and so on. It can be used for educational purposes and for planning and design. Illustrative examples are given for both line and fault switching and for induction motor dynamics.

An interactive power system simulator with enhanced features

Unbalances due to faults and line switching have traditionally been calculated using symmetrical components. By contrast, compensation methods or their mathematical equivalent, the matrix modification lemma (MML), a powerful tool for the solution of modified networks, are still employed primarily for contingency calculations. However, they can be efficiently applied to the calculation of voltages and currents due to faults and/or line switching. In the paper, the MML is applied for closing or opening of a switch which may also represent a fault. For better efficiency, the computations are performed in symmetrical components and sparsity techniques are used. To determine the effect of the switching operations, these are performed interactively and sequentially. Generators and loads are represented by appropriate Norton equivalents. Illustrative results are presented.

An interactive simulator for unbalanced systems

The paper presents a new method for optimal power flow calculations, using the generalized power balance constraint, obtained from the power flow equations by elimination of all state variables. The reduced optimization problem in the control variables is subsequently decoupled into two stages: a primary stage in the primary control variables (generator active power injections) and a secondary stage mainly in the secondary control variables (generator voltages). The primary stage is solved by economic generation scheduling, where the power system losses are accounted for by the coefficients of the generalized power balance constraint. The secondary stage is solved by linear programming, subject to all power system constraints. The linear programming formulation is such that the solution of the primary stage is maintained, if feasible, or otherwise optimally adjusted. Thus, the method takes full advantage of decoupling, if it is applicable, and otherwise inherently reverts to a coupled approach. A step-limit control strategy successfully damps the oscillations that are always present in successive linear programming, and ensures the optimality and feasibility of the solution.

Optimal power flow using a generalized power balance constraint

The field variables (potentials and induced voltages, electric and magnetic fields) in the neighborhood of AC transmission lines are periodic functions of time and can be represented by phasors or temporal complex variables. At the same time, the point in space can be represented by a position vector, a spatial complex variable, and the field quantity as a function of that spatial complex variable. Thus, phasor fields appear as complex variables both in relation to time and space. The use of temporal and spatial complex variables has the advantages of regular complex variables: simple analytical formulations and derivations, and generalizations of real variable procedures (e.g. Taylor series expansions and closed form integration). As an application, the paper presents the calculation of inductive and capacitive effects of a three phase overhead line on a parallel telecommunication line.

Calculation of phasor fields around A.C. transmission lines using temporal and spatial complex variables

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An interactive power system simulator with enhanced features

An interactive simulator for unbalanced systems

Optimal power flow using a generalized power balance constraint

Calculation of phasor fields around A.C. transmission lines using temporal and spatial complex variables