Elsevier

Energy

Volume 60, 1 October 2013, Pages 380-387
Energy

Extremum-seeking control of a supercritical carbon-dioxide closed Brayton cycle in a direct-heated solar thermal power plant

https://doi.org/10.1016/j.energy.2013.08.001Get rights and content

Highlights

  • Control of a supercritical-CO2 closed Brayton cycle solar power plant is simulated.

  • An ES (extremum-seeking) controller is used to maximise cycle power output.

  • The ES controller manipulates CO2 inventory at the compressor inlet.

  • ES control approach compares favourably to that with a fixed-CO2 inventory approach.

  • Simulations indicate that ES controller retuning is not required between seasons.

Abstract

One promising avenue for the development of next generation CST (Concentrating Solar Thermal) technology focuses on the use of a direct-heated sCO2 (supercritical-CO2) CBC (closed Brayton cycle) as the generator power cycle. Initial investigations into such a CST plant, while promising, have found its power output and efficiency to be sensitive to fluctuations in solar heat input and ambient temperature over a day and between seasons. Given the difficulty in developing complete models across all operating conditions due to non-linearities in CO2 properties, an extremum-seeking controller is proposed to maximise the power output of the CBC as the solar heat input and cooling-air temperatures change. This controller achieves this effect by manipulating the CO2 mass inventory in the CBC. Slack variables are introduced into the extremum-seeking control performance metric to impose constraints on turbine inlet temperature and pressure to protect the CBC from damage. The performance of the proposed scheme is tested through simulations on representative summer and winter days. Simulations indicate that the performance of the CBC under ESC (extremum-seeking control) based inventory-control compares favourably to operation with a fixed-CO2 inventory in both summer and winter and does not require retuning between seasons.

Introduction

Fossil fuels presently serve as the main source of electricity generation in Australia. In 2010–2011, approximately 90% of Australian electricity generated was from fossil fuel sources [1], leading to the nation having one of the highest emissions intensities in the world. Concerns over the effects of fossil fuel use on the environment and its projected future scarcity are fuelling the development of renewable energy technology. As a further incentive, legislation has also been introduced that commits Australia to reductions in CO2 (carbon-dioxide) emissions from the electricity grid to 20% of 2000 levels by 2050. One option for efficient generation of electricity from solar energy is through CST (Concentrating Solar Thermal) power plants. Significant opportunities exist for electricity generation using CST power plants to replace or supplement local generation in remote communities and mining operations around Australia and achieve savings in fuel and transport costs [2].

CST power generation technology is still in its infancy, with current generation CST power plants having high capital costs and high unitized-electricity costs compared to conventional fossil-fuel based power plants. One approach to reduce both capital and unitized-electricity costs is to use a more efficient and compact power cycle, such as a cycle based on sCO2 (supercritical-CO2).

The use of sCO2 as a power cycle working-fluid has been growing in recent years due to associated benefits such as highly compact power plant and high cycle thermal efficiencies at turbine inlet temperatures achieved in solar thermal [3] and nuclear power plants [4]. The simplicity and potential ability of real-gas closed Brayton cycles such as one with supercritical-CO2 to be integrated with existing inexpensive solar collectors is also an attractive feature [5]. The supercritical-CO2 CBC is also being considered for power generation from other medium-grade heat-sources including waste heat [6] and for integration with post-combustion CO2 capture for efficiency improvements in coal-fired power stations [7].

Experimental campaigns into the Supercritical-CO2 closed Brayton cycle with configurations similar to the one investigated in this work already exist and preliminary plant performance and stability has been demonstrated [8]. Investigations are also being conducted into cycle performance during the startup and shutdown phases for power plant peaking [9]. Other experimental demonstration campaigns are also being conducted for different components of the sCO2 CBC for application in solar thermal power plants through programs such as the US Department of Energy SunShot program on concentrated solar power [10]. Some examples include development and experimental demonstration programs for direct-heating supercritical carbon-dioxide solar receivers in the cycle [11], and turbomachinery and heat exchanger demonstration programs for the cycle [12].

The increased interest in sCO2 power cycles is also due to CO2 being inexpensive, capable of withstanding very high temperatures, non-toxic, non-combustible, non-explosive, and abundant. CO2 also has a moderate critical pressure (7.38 MPa) and critical temperature (31 °C), which leads to a large operating envelope for supercritical conditions. A particular advantage of supercritical-CO2 to CST power plants is the ability of CO2 to handle high temperatures. The high-temperature capability of CO2 allows the power cycle working-fluid to also be directly-heated by the solar collector, rather than rely on a heat-transfer fluid to transfer solar heat to the working-fluid via an intermediate heat-exchanger. A direct-heated sCO2 power cycle eliminates the thermal losses associated with this intermediate heat-exchange as a single-fluid serves as the heat transfer medium and subsequently drives the turbine, in a closed-loop. These factors can potentially contribute to reduced plant capital costs and generated electricity costs, and higher solar-to-electric conversion efficiencies due to thermodynamic performance improvements [13].

One potential application of sCO2 as a working-fluid is in a direct-heated and air-cooled CBC (closed Brayton cycle) connected to PTCs (parabolic-trough collectors) for solar thermal power generation. This approach was investigated in Ref. [14] using a simulation study for a proposed installation in Longreach, Queensland, Australia in which the sCO2 CBC solar thermal power plant is supplementing existing diesel based electricity generation in the remote community. The water scarcity at this site (and other potential CST power plant sites within Australia) requires that the power plant is air-cooled. The relatively high ambient air temperatures at such sites when compared to the critical point temperature of CO2 would, however, result in the CBC operating mostly as a non-condensing fully-supercritical Brayton cycle.

The performance of the sCO2 CBC in a direct-heated and air-cooled CST power plant is sensitive to dynamic variations in CO2 mass-flow rate in the system as indicated by simulations of cycle dynamic behaviour on representative summer and winter days in Ref. [14]. The high solar heat input and ambient-air temperatures in summer lead to excessive turbine inlet temperatures in the CBC. Additionally, low ambient-air temperatures and solar heat input leads to subcritical compressor inlet conditions during normal winter operation. Operation of the plant using the same fixed CO2 inventory each day regardless of the solar heat inputs and temperatures may lead to plant damage and overly conservative operation of the plant with low efficiency and power output. However, the results in Ref. [14] also indicate that the amount (inventory) of working-fluid in the CBC influences resulting CO2 mass-flow rates and therefore pressures and temperatures in the CBC. Hence, manipulation of CO2 inventory in the sCO2 CBC with ESC (extremum-seeking control) is investigated as a control strategy in this paper with the objective of maximising power generation while keeping cycle turbine inlet temperature and pressure in proximity to design limits. Inventory control has been investigated previously for achieving part-load operation of the sCO2 CBC in nuclear power applications using conventional proportional-integral controllers [15].

The selection of ESC as a control method in the sCO2 CBC is influenced by the fact that optimum power generation conditions of the cycle vary depending on the particular combination of solar heat input and cooling-air temperatures. Furthermore, unlike conventional ideal-gas power cycles, modelling of the sCO2 CBC at low orders is difficult. This is due to the fine spatial resolution of the heat-exchanger volumes required to capture the highly nonlinear behaviour of supercritical-CO2.

Extremum-seeking control is a form of non-model based adaptive control which has received increased interest in recent years. It uses continuous measurements of a plant performance function as inputs to appropriate filters to develop gradient estimates of the performance function with respect to the steady state plant input. This information is then used with an appropriate optimisation routine to tune the plant inputs and provide convergence towards optimal plant operation. The approach is readily extended to multidimensional input plants. Recent applications of ESC include maximising fuel cell efficiency and power [16], solar photovoltaic power maximisation [17], chilled-water system optimisation [18], and maximum power point tracking of wind-turbines [19], although a more complete survey is provided in Ref. [20]. Under this framework, ES (extremum-seeking) algorithms require minimal knowledge of the plant being controlled, largely treating the plant as a ‘black box’, and therefore avoiding the complications due to model mismatch that may face other model-based approaches. Alternative ESC variants include methods that include partial plant information [21], in a ‘grey box’ framework. An ESC method with the ability to be tuned for a wide range of operating conditions and independent of the plant map has also been experimentally demonstrated for the reduction of thermoacoustic oscillations in premixed, gas-turbine combustors [22].

Black box extremum-seeking is subsequently proposed for control of the sCO2 CBC due to its potential to optimally tune multiple parameters in the sCO2 CBC despite fluctuating solar and ambient air temperature conditions. Critically, it also eliminates the requirement for a model of the system for controller development, and requires minimal prior knowledge of optimum conditions of the system. The performance of the proposed ESC approach is compared to ad-hoc approaches involving increasing the amount of fixed inventory in the CBC in summer and maintaining supercritical compressor inlet conditions in winter. The extremum seeking controller makes use of existing hardware in the plant, so there is minimal or no additional hardware cost. There may be some additional initialisation cost associated with the programming and implementation of the controller, although this will be offset by the reduced calibration requirements for the device operating in open-loop.

The layout of the modelled recuperated sCO2 CBC being heated directly using parabolic-troughs is shown in Fig. 1. In a direct-heated configuration of the cycle, heat from the sun is collected and transferred directly into supercritical-CO2 (working-fluid) by PTCs. A compressor is used to raise the pressure of CO2 after which it is heated in the PTCs. The sCO2 at high pressure and temperature then expands through a turbine after which it is eventually cooled in the cooler with air. A recuperator is also used to recover the residual heat in the sCO2 after the turbine which is subsequently used to preheat sCO2 entering the heater.

The compressor and the turbine split the CST plant into a ‘hot side’ and a ‘cold side’. The volumes of sCO2 CBC components between the compressor outlet and turbine inlet in a clockwise direction including the high-pressure side of the recuperator, comprise the ‘hot side’ or ‘high pressure’ section of the system. The remaining volumes between the turbine outlet and compressor inlet including the low-pressure side of the recuperator comprise the ‘cold side’ or ‘low pressure’ section.

Section snippets

Closed Brayton power cycle model

The performance of extremum seeking-control when applied to the sCO2 CBC in the solar thermal power plant is demonstrated using dynamic modelling and simulation; a technique commonly used to investigate solar thermal energy processes mainly due to the highly variable nature of the energy source [23]. Modelling and simulation of the sCO2 CBC was conducted in Dymola® [24]. The simulated model of the plant and solar field data was previously presented in Ref. [14] and is based on the layout and

Control objective

The control objective for the sCO2 CBC is to maximise the net power delivered by the cycle while ensuring that the cycle remains within operational temperatures and pressures. Fig. 2 shows that the power generated by the cycle increases with turbine inlet temperature across the operating region. Hence, the desired operating point is at the upper boundary of the operating region at approximately 350 °C. Frequent or extended excursions beyond this temperature can lead to damage to the cycle due

Results

The proposed extremum-seeking controller is now applied to the simulations of the sCO2 CBC (non-condensing) in the context of power generation in a solar thermal power plant with air-cooling. The analysis is conducted on the simulated model of a 1-MWe direct-heated (no secondary thermal-oil loop) and air-cooled parabolic-trough solar thermal power plant supplementing diesel generators in a remote community. The parameters of the cycle and solar field are described in the Appendix.

Performance of

Summary and conclusions

The proposed ES feedback controller was found to be capable of manipulating CO2 inventory to maintain net power output close to a desired operating point across extreme ambient conditions, and resulted in slight improvements in key factors without violating specified operating constraints.

In comparison with a fixed inventory approach, the proposed ES algorithm demonstrated similar or better overall performance but required significantly less calibration effort. Furthermore, the proposed

Acknowledgements

The authors would like to thank Sarah Miller of the Commonwealth Scientific and Industrial Organisation (CSIRO) Energy Technology Division for solar field and energy output data. This study was supported by the Queensland State Government and the University of Queensland.

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