The influence of economic parameters on the optimal values of the design variables of a combined cycle plant

doi:10.1016/j.energy.2009.07.014

Energy

Volume 35, Issue 2, February 2010, Pages 911-919

https://doi.org/10.1016/j.energy.2009.07.014 Get rights and content

Abstract

This paper presents the analysis of the influence of fuel price variation on the optimal values of the design variables of the steam part of a combined cycle plant. The investigated system was a power plant with a triple-pressure heat recovery steam generator and extraction-condensation steam turbine. Fourteen design variables for the steam part were identified. The variables that were optimised were the pressure levels of the working medium in the steam part of the system, and characteristic differences of temperatures in the heat recovery steam generator. Thanks to the development of an optimising programme, based on the genetic algorithms theory, it was possible to find an optimal solution. The indices of economic efficiency, in the form of the break-even price of electricity, were chosen as the objective function in the optimisations. The results of economic optimisations were compared with the results of the optimisation, where the electric efficiency was the objective function. This paper includes an analysis of the sensitivity of the economic objective function to failures in the adherence of the optimal values of decision variables. This analysis allowed the selection of variables such that a failure results in the highest increase of the break-even price of electricity.

Introduction

Combined cycle plants, which utilise gas turbines and heat recovery steam generators (HRSG), are one of the most effective technologies for generating fossil fuel based electricity. With the development of gas turbines, the energy efficiency of these systems has increased, exceeding more than 60% [1]. The steam part is also an important component and its optimisation may considerably improve the energy efficiency and economic performance of the plant [2].

There are many possible configurations of combined cycles including, among others, systems with a single, double, and three-pressure boiler. The latter two can also be used together with a reheater. The solutions used in each configuration may differ from each other, both by the distribution of the heated surfaces in the boiler (in series, parallel or mixed), and by the means of preheating the condensate and feed water [2], [3], [4].

The most complicated configuration of combined cycles utilise three-pressure HRSGs; the power rating of such a system with only one gas turbine is 400 MW. Aside from their high efficiency, combined cycles are characterised by their low emission of noxious substances, short construction times, high disposability, and low capital costs.

In Poland, the incorporation of combined cycle plants has been hampered by the high price of gas fuel. The popularity of these installations is expected to grow, however, as a result of the development of technology to gasify hard coal.

The large fluctuation in gas fuel price (almost doubled since 2003) poses the question: how much do fuel prices influence the optimal values of the design variables of energy systems?

Section snippets

Design variables of the steam part

The electric efficiency in a combined cycle plant is defined by the relation $η_{elCC} = \frac{N_{el}}{(m_{f} \cdot LHV)} = \frac{N_{elGT} + N_{elST} - N_{on}}{(m_{f} \cdot LHV)}$

This relation can be transformed as follows $η_{elCC} = η_{elGT} (1 + α \cdot η_{elST})$

In this equation, η_elST can be interpreted as the electric efficiency in the steam part of the system $(η_{elST} = (N_{elST} - N_{on}) / Q_{4 a})$ , α is equal to $Q_{4 a} / N_{elGT}$ , and η_elST denotes the efficiency of the gas turbine $(η_{elGT} = N_{elGT} / (m_{f} \cdot LHV))$ .

Generally, the steam and gas parts in the combined cycle are not autonomous. Assuming,

Characteristics of the investigated structure

The system presented in Fig. 2 was subjected to multivariable optimisation.

The fundamental installations in the combined cycle are the gas turbine, heat recovery steam generator, steam turbine, condenser, deaerator, condensate extraction pump and feed water pump.

In terms of the analysis in this paper, the most essential element of the system is the HRSG. The structure of HRSG with three pressure levels of the working medium was chosen. Such a system allows for minimal exergy losses during the

Optimisation algorithms

The fundamental design variables of the steam part of the system presented in Fig. 2 were optimised. The design variables of the steam part of combined cycles were reviewed in Chapter 2. In the case of the investigated installation, it was assumed that the pressure of the reheated steam equals the intermediate-pressure of the live steam. An additional variable was the underheating of water at the outlet of the dearation economiser. It should also be noted that the high-pressure economiser was

Assumptions and results of optimisations

Aside from determining the capital costs, many assumptions must be made when analysing an investment economically. The most important of them are:

•
20% of the investment is self-financed and 80% is obtained from commercial credits.
•
The actual interest of the credit amounts to 6%, the repay time is 10 years.
•
The anticipated time of constructing the power plant is 2 years, with a repay of 40% in the first year and 60% in the second.
•
The time of operation – 20 years.
•
The annual time of operation – 7500 h.

Sensitivity analysis of the economical objective function to changes of the optimal values of variables

The presented optimisation, depending on the respective assumptions, has allowed for six sets of optimal values of the selected design variables of the steam part. We consider the question, how essential is it to keep the optimal values of decision variables for the value of the objective function?

In order to answer this question, the sensitivity to changes of the respective decision variables to the attained value of the economic objective function was analysed based on the results of an

Discussion of results and conclusion

1.
Genetic algorithms, constituting one of the stochastic methods of optimisation, permit determination of the optimal values of many design variables of energy installations. In the case of the analysed combined cycle, the derived algorithm permitted optimisation of 14 decision variables. The optimisation was carried out particularly for the economic objective function $(C_{el}^{b-e})$ . The main objective of the research was the analysis of the influence of fuel price on the optimal values of design

Acknowledgements

The investigations presented in this paper have been carried out within the frame of the research project No. 3 T10B 068 30, sponsored by the Ministry of Education and Science.

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The influence of economic parameters on the optimal values of the design variables of a combined cycle plant

Abstract

Introduction

Section snippets

Design variables of the steam part

Characteristics of the investigated structure

Optimisation algorithms

Assumptions and results of optimisations

Sensitivity analysis of the economical objective function to changes of the optimal values of variables

Discussion of results and conclusion

Acknowledgements

Energy

Energy

Energy

Applied Thermal Engineering

Energy

Energy Conversion and Management

Energy Conversion and Management

Energy

Energy technologies