# Degenerate optimization problems of economics and power engineering

10/23/2015 2015 - #03 Economics of nuclear power

https://doi.org/10.26583/npe.2015.3.15

### UDC: 519.87:621.039.5

Optimization of large economic and power engineering systems leads to degenerate solutions of high dimension. This is a very strong mathematical complication. However it allows to consider future development of the power industry based on simultaneous use of nuclear power plants (NPPs) together with coal- and gas power plants, or solely on NPPs. This requires system optimization of NPP parameters.

Calculations of optimal systems of high dimension have shown that the degenerate space of possible solutions for economics and power engineering can be seen as a set of points on a lunar surface pitted with a finite number of craters. This degenerate space can be referred to as «non-convex, non-concave».

In other words, the N-dimensional degenerate «non-convex, non-concave» space of large dimension (N ≥ 10 000) resembles a «lunar surface» with craters of different depth. Craters are the neighborhoods of locally-optimal solutions, the latter being at the crater’s bottom. The crater’s depth defines the value of the optimization functional. Among the most deep, but otherwise different craters, there are craters of equal depth, i.e. craters with the same value of the locally-optimized optimization functional. Local optima (local plans) in different craters can differ by the structure but have the same value of the optimization functional.

Calculations show that among the craters of equal size (with the same values of the functional at the locally-optimized plans of economics and power engineering development) there are craters with locally-optimal plans of development (among other possible heterogeneous combinations of economics and power technologies) only with coal and gas, or coal, gas and nuclear facilities, or only with NPPs. Comparing the values of the optimization functional in different craters, one can find the optimal solution – a locally-optimal plan with the best value of the functional (for example, in the case of minimization – with the minimal value of the functional among all craters).

### References

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degenerate optimization problem economy power electric power system power plant nuclear power plant an optimality non-optimality rate of discounting lunar surface crater