# Degenerate optimization problems and optimality of NPPs

12/25/2015 2015 - #04 Economics of nuclear power

https://doi.org/10.26583/npe.2015.4.14

### UDC: 519.87:621.039.5

Optimization of major systems of economy and power leads to degenerate high dimensionality solutions. This very strong mathematical complicating. However it allows to consider the future development of power as teamwork of nuclear power plants (NPPs), power plants (PPs) on coal, PPs on gas. Besides, it allows to consider development of power of the country only on NPPs. System optimization of parameters NPPs is For this purpose necessary.

Rated examinations of optimum systems of high dimensionality have led to understanding degenerate spaces of admissible solutions of economy and power as point sets on the lunar surface pitted by a terminating amount of craters. Locally-optimum solutions of such tasks are given at the bottom of craters. Accounts show, that among equal craters (craters with identical meanings of objective functionals of locally-optimum plans for development of economy and power) meet craters locally-optimum plans for development of economy and power (among other possible heterogeneous combinations of states of economy and energy process engineerings) only on coal and gas PPs; only on coal, gas, nuclear PPs; only on NPPs.

In optimum development strategies of an electric power system sharp transitions from one energy production engineering to other are observed. This consequence of usage in an optimization method of control functions in the form of switching. Such control functions depending on the moments of put of installations of energy production engineering into operation, a placed installed capacity of installations in operation (major or equal to null) is. But so complicated control functions consider all possibilities of optimization. Usage of such control function gives the chance to optimization of the moments of put of installations into operation (and as consequence, switching torques of installations from one mode of operation on other). The model with optimization of the moments of put of installations (power-generating units) into operation displays what more often more favourably to place power-generating units in operation not continuously and annually, and intermittent series (often major) is simultaneous in optimum instants.

Optimality tags PPs are that. PP (in particular, NPP) then it is possible to consider optimum designed when it is included the optimum plan of functioning of an electric power system for an infinite planning interval for a wide gamut of economic situations (from economy with rate of discount of close to null to economy with rate of discount about 30 %/year) in competitive environments with all known types PPs, and there are no reasons, at which it is possible to refine the optimum plan (to refine an optimization objective functional), having changed properties or parameters of this PP. Otherwise, PP (in particular, NPP) it is necessary to recognize this non-optimal.

Problem of system optimization NPP (as well as any PP) in an electric power system – iterative.

If different NPPs (simultaneously jointly) work on any section of a time of the locally-optimum plan it means, that specific (on produced kW·h) profit in the form of the differential rent concrete NPP (the difference between the optimum price of produced energy an electric power system and the cost of production of energy concrete NPP) can differ from that for others together with it working NPPs, but for all it is non-negative. And, for NPP which share in total energy production on this section of a time the greatest, specific profit will be the greatest.

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degenerate optimization problem economy power electric power system power plant nuclear power plant an optimality non-optimality rate of discount