Control-oriented modeling of the energy-production of a synchronous generator in a nuclear power plant
Highlights
► A dynamic model of a synchronous generator in a Nuclear Power Plant is developed. ► The model has been verified under the usual controlled operating conditions. ► The sensitivity analysis has been applied to determine the model parameters. ► The parameters have been estimated applying the APPS method using measured data. ► The model serves as a basis for controlling the optimal energy production of the generator.
Introduction
A major portion of industrial energy distribution and transportation is performed in the form of electrical energy using large-scale electrical power grids. Both of the energy consumers and producers are connected to this grid that should be operated in a balanced way taking into account the time-varying power demand of the consumers that is difficult to predict. The properties of the consumers are modeled by various types of loads: (i) an resistive one, that represents, for example, heating devices, traditional bulbs, that require active (or resistive) power, (ii) an resistive one with serial inductance representing motors and rotating household appliances (washing machine, lawnmower etc.) and (iii) a capacitive input stage load for representing the simple nonlinear switching mode power supplies. The latter two types of loads need reactive power, that adds to the active one as a vector when the total power is computed.
The power plants, that are the energy sources, can also be of various types including nuclear power plants, wind and solar power plants, just to mention often discussed hypothetical future sources of electric energy(after terminating fossil fuel production). From the viewpoint of the power grid the electric power generation of these plants can be characterized by the operation of the electrical generators, the subject of our study. These power plants should be able not only to follow the time-varying active and reactive power demand of the consumers, but also keep the quality indicators (frequency, waveform, total harmonic distortion) of the grid [1]. This can be achieved by applying proper control methods based on dynamic models of the involved generators.
Reactive power is tightly related to bus voltages throughout a power network, and hence it has a significant effect on system security. Its importance is indicated by the fact that insufficient reactive power of the system may result in the voltage collapse. Therefore, it is widely accepted that the consumer of reactive power should pay for the reactive power support service and the producers of reactive power are remunerated [2]. The problem of controlling the reactive power production as a component of the effective integration of renewable energy sources into the power grid is analyzed and solved in [3] using the dynamic model of the generator of the plant. A simple dynamic model of permanent magnet synchronous generators is reported in [4], that is used to investigate their short-term transient behavior to investigate their direct interconnection to the grid.
The electrical energy generation by power plants using renewable energy (wind, solar, etc.) has attracted a great attention nowadays because of its practical importance. The modeling and analysis of the steady state behavior for various operating conditions of a six phase synchronous generator used as a stand-alone electric energy source is presented in [5] in conjunction with a hydro power plant. The experimental investigation of the same generator is reported in [6].
Because of the specialities and great practical importance of synchronous generators in power plants, their modeling for control purposes is well investigated in the literature. Besides of the basic textbooks (see e.g [7].) that develop general purpose dynamic models for SGs, there are several papers that describe the modeling and use the developed models for dynamic analysis and controller studies [8]. Two SG models are presented and analyzed in [8], that are validated using a 75 kVA salient-pole synchronous machine with damper windings. In [9] a new method of SG modeling is presented taking an infinite inner resistance into account, and a statistical technique for determining the parameters of the synchronous machine is also proposed.
It is well known that integrating distributed generation into electric power systems presents great challenges and opportunities at the same time [10], that does not only need suitable dynamic models for the involved synchronous generators, but also a dynamic model of the power grid with its consumers. Therefore, it is important to emphasize that control-oriented modeling of real industrial generators in power plants presents special requirements and challenges because of the frequent and unforeseen disturbances from the electrical network and the load changes caused by the switching between the high and low production operating mode of the power plant. An optimization study was presented in [11] with constraints for the excitation control in synchronous generators, that aims at damping oscillations in the grid and uses a simple dynamic model of the generators. Another control study of synchronous generators is reported in [12], that focuses on the regulation of the active and reactive power to a set point ordered by the wind farm control system, where also a simple dynamic model of the generators is utilized.
Nuclear power plants (NPPs) generate electrical power from nuclear energy, where the final stage of the power production includes a synchronous generator (SG) that is driven by a turbine. Although nuclear energy is not considered as a promising clean energy source on a world scale [13], the electrical energy produced by the Paks Nuclear Power Plant (Paks NPP) presents 40% of the total electrical energy production in Hungary, thus its efficient and safe operation is vital. Although it is well known that nuclear power plants are operated mostly and efficiently such that their maximal power is produced, the generators of the Paks NPP are required to take part in the reactive power support of the power grid following the demand of a central dispatch center of Hungary. In addition, the operating nuclear power plant units also contribute to the frequency control of the grid by adjusting the nuclear power of the reactor itself. The above grid-wide control functions are partially supported by the operation of three main coupled control loops: the reactor power, turbine and generator controllers.
The refurbishment of the control system of this plant has already been started as part of its lifetime extension project. This gives the possibility to extend and improve the functionality of the present control system to be able to control both of the generated active and reactive power components effectively and simultaneously. Therefore, the aim of this paper is to propose a dynamic model of the SGs in the Paks NPP for control studies that is able to describe its dynamic (transient) behavior in the short term (1 s - 1 h) time range. Furthermore, an optimization-based method is also to be developed for estimating the model parameters from industrial measured data.
Section snippets
The synchronous generator model
In this section a state space model of a synchronous generator is presented. The model development is largely based on [7], but the special circumstances of the generator operation in the considered NPP have also been taken into account. It is important to note, however, that large industrial synchronous generators operating in other (e.g. hydro, gas or coal powered) types of power plant have similar operating conditions and grid requirements, therefore the resulting dynamic model is also
Model analysis
A preliminary analysis of the dynamic properties (i.e. stability and disturbance rejection properties) was first analyzed in order to verify our model against engineering intuition.
Thereafter parameter sensitivity analysis has been performed as a preparatory step for model parameter estimation.
Parameter estimation
The developed model (Eqs. (2), (3), (5), (6), (8)) together with the model equations of the two considered PI controllers have been used for estimating its parameters using measured data from the Paks NPP obtained from load changing transients. The model is nonlinear in its parameters, therefore a special, optimization-based parameter estimation have been used that minimized the estimation error.
Conclusion and further work
A dynamic model of a large industrial synchronous generator commonly applied in power plants is developed in this paper based on first engineering principles that is able to describe the time-varying active and reactive power output of the generator. The model is based on first engineering principles that describes the mechanical phenomena together with the electrical model.
The developed model has been verified under the usual controlled operating conditions in Paks Nuclear Power Plant
Acknowledgment
We acknowledge the financial support of this work by the Hungarian State and the European Union under the TAMOP-4.2.1/B-09/1/KONV-2010-0003 project. This work was also supported in part by the Hungarian Research Fund through grant 83440.
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