Power system simulation: Difference between revisions

Revision as of 21:27, 4 October 2022

Revision as of 21:50, 11 November 2022

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These programs typically make use of [[mathematical optimization]] techniques such [[linear programming]], [[quadratic programming]], and [[mixed integer programming]].

Multiple elements of a power system can be modelled. A [[power -flow study]] calculates the loading on transmission lines and the power necessary to be generated at generating stations, given the required loads to be served. A short circuit study or fault analysis calculates the [[Prospective short-circuit current|short-circuit current]] that would flow at various points of interest in the system under study, for short-circuits between phases or from energized wires to ground. A coordination study allows selection and setting of [[protective relay]]s and fuses to rapidly clear a short-circuit fault while minimizing effects on the rest of the power system. Transient or dynamic stability studies show the effect of events such as sudden load changes, short-circuits, or accidental disconnection of load on the synchronization of the generators in the system. Harmonic or power quality studies show the effect of non-linear loads such as lighting on the waveform of the power system, and allow recommendations to be made to mitigate severe distortion. An optimal power -flow study establishes the best combination of generating plant output to meet a given load requirement, so as to minimize production cost while maintaining desired stability and reliability; such models may be updated in near-real-time to allow guidance to system operators on the lowest-cost way to achieve [[economic dispatch]].

There are many power simulation software packages in commercial and non-commercial forms that range from utility-scale software to study tools.

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==Optimal power flow==

Electricity flows through an AC network according to [[Kirchhoff's circuit laws|Kirchhoff's Laws]]. Transmission lines are subject to thermal limits (simple megawatt limits on flow), as well as voltage and [[electrical stability]] constraints.

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where ''u'' is a set of the control variables, ''x'' is a set of independent variables, and the subscript 0 indicates that the variable refers to the pre-contingency power system.

The SCOPF is bound by equality and inequality constraint limits. The equality constraint limits are given by the pre and post contingency power -flow equations, where ''k'' refers to the ''k''th contingency case:

: <math> g^k(u^k, x^k)=0 \qquad\text{for }k=1,2,\ldots,n \, </math> <!-- Should those be subscripts instead of superscripts? -->

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==Models of competitive behavior==

The cost of producing a megawatt of electrical energy is a function of:

#fuel price