# Mathematical modeling of energy facilities and systems

## Documents

### Bilan T. R., Kaplin M. I. Modelling of energy coal supply by rank for country’s economy at world market conditions and domestic mining decrease

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Board № (full): |
2 (45) 2016 year |

Filesize: |
2.89 MB |

Downloads: |
4293 |

Taking into acount the occupation in steam coal supply model is performed by significant change of supply system structure on state-controlled territory. In particular, the temporarily occupied territory is presented as a source of imports with its own volume and price indices and transport infrastructure elements. Also, the overall demand of the country is corrected by the occupied territory consumption amounts. The possibility of such a modification of the model is provided by network presentation of system.

Significantly different conditions of individual thermal coal ranks supply, both from its own production sources, and on import, are taken into account by inserting to the model separate supply and consumption subsystems of gas and anthracite coal groups, that interact to allocate import amounts among nearby and far abroad exporting countries while meeting the capacity of the national transport infrastructure.

The imports demand of anthracite coal group is significantly higher than the free volumes of this type of coal on the world market. Therefore, providing demand with this type of fuel is impossible without the supply of necessary amounts of anthracite and gas coal from the territories temporarily out of state control.

**steam coal, anthracite, gas group, flow representation, optimization, coal supply system.**

*Keywords:*### Bilodid V.D., Lenchevskyi Ye.A. Modeling of the interaction of a complex of consumers-regulators based on electric heat- generators in the heat supply systems in the processes of equalizing the load curves of electrical power systems

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Board № (full): |
4 (51) 2017 year |

Filesize: |
1.01 MB |

Downloads: |
3002 |

We have proposed a mathematical model for the description of general provisions as to the interaction of a complex of controlled consumers-regulators based on electric heat-generators in the heat supply systems with acting means of providing load regimes in power systems in the processes of equalizing the curves of electrical loads. This model takes info account the features of work of a electrical power system with including, to the conditions of load control, of electric heat-generators located at different towns of the state and allows for the main characteristics of these heat supply systems. We have also formulated algorithms of the restriction of use of electric heat-generators in view of the possibilities of work of separate heat supply systems. The presented results can be used for subsequent development of the idea of using the new method of control of the loading of power systems with applying consumers-regulators based on electric heat-generators and for calculating the optimal parameters of interaction between the electrical power system and complex of district heating, which guarantees the maximal efficiency of their joint operation (economical and technical).

* Keywords:* Ukrainian integrating power system consumers-regulators, electric heat-generators, mathematical model, electric load curve.

### Dobrovolskiy V. C. Economic and Mathematical Model of Formally Formed Prices for Power Sector

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Board № (full): |
2 (3) 2000 year |

Filesize: |
379.04 kB |

Downloads: |
5208 |

Economic and mathematical model of formally formed prices for power sector is presented. Mathematically the model is a linear programming problem with a specific structure, supplemented by algorithms for input data processing and problem optimal solutions. A numeric example is elaborated with data comparable to real one. The prices are calculated for various consumers' groups on voltage and different time ranges over 24-hour period. These formally formed prices can be used for working out the electricity tariffs.** Keywords:** power sector economy, formally formed prices.

### Dremin I. V. Mathematical modeling and analysis of WPP’s rotating parts inertia moment’s influence upon frequency controlling process

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Board № (full): |
1 (36) 2014 year |

Filesize: |
609.19 kB |

Downloads: |
5483 |

The mathematical model of electricity generation on WPP, belonging to the UPS, was elaborated on the basis of the frequency and power controlling universal model by adding the corresponding system of differential-algebraic equations to the source equations set.

The numerical modeling of the automatic frequency controlling processes in the Ukrainian UPS was carried out using generators-controllers and consumer-controllers as controllers. The total capacity of wind power in the power system was established as equal to 3GW.

In the investigated range of WPP’s time constants an acceptable frequency controlling process was proved to be unrealizable even with all HPP capacities (3 GW) involved. However, the use of controller-consumers with total capacity of 3 GW allows frequency controlling in accordance with the requirements of ENTSO-E European energy network regardless of WPP inertia moment.

**wind power plant, wind unit, inertia moment, time constant, power system, mathematical modeling, frequency and power controlling.**

*Key words:*### Dryomin I. V. Account for nonlinear technological limitations at the simulation of transient processes in a power system with AFPC

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Board № (full): |
2 (29) 2012 year |

Filesize: |
885.78 kB |

Downloads: |
5252 |

A mathematical model of AFPC including the system of differential equations complemented by nonlinear terms due to the limitations on the rate of change of the power of a regulator, the level of its power, and the zone of insensibility to a deviation of the frequency is studied. The corresponding numerical calculation within the model is realized by a specially developed software complex.

It is found that the mathematical modeling of transient processes in AFPC without consideration of technological limitations leads to the significant errors of calculations and a low adequacy of appropriate models on the whole.

**power system, automatic system, frequency control, controllable load, regulator-generator, technological limitations.**

*Keywords:*