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Energy 60 (2013) 380e387

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Energy

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

Rajinesh Singh a,*, Michael P. Kearney a, Chris Manzie b

a School of Mechanical & Mining Engineering, The University of Queensland, St. Lucia, Queensland 4072, AustraliabDepartment of Mechanical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia

a r t i c l e i n f o

Article history:Received 21 March 2013Received in revised form4 July 2013Accepted 1 August 2013Available online 6 September 2013

Keywords:Solar thermalSupercritical carbon dioxideClosed Brayton cycleAdaptive controlExtremum-seekingPower maximisation

* Corresponding author.E-mail addresses: r.singh5@uq.edu.au (R. Si

(M.P. Kearney), manziec@unimelb.edu.au (C. Manzie)

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.08.001

a b s t r a c t

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) asthe generator power cycle. Initial investigations into such a CST plant, while promising, have found itspower output and efficiency to be sensitive to fluctuations in solar heat input and ambient temperatureover a day and between seasons. Given the difficulty in developing complete models across all operatingconditions due to non-linearities in CO2 properties, an extremum-seeking controller is proposed tomaximise the power output of the CBC as the solar heat input and cooling-air temperatures change. Thiscontroller achieves this effect by manipulating the CO2 mass inventory in the CBC. Slack variables areintroduced into the extremum-seeking control performance metric to impose constraints on turbineinlet temperature and pressure to protect the CBC from damage. The performance of the proposedscheme is tested through simulations on representative summer and winter days. Simulations indicatethat the performance of the CBC under ESC (extremum-seeking control) based inventory-control com-pares favourably to operation with a fixed-CO2 inventory in both summer and winter and does notrequire retuning between seasons.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fossil fuels presently serve as the main source of electricitygeneration in Australia. In 2010e2011, approximately 90% ofAustralian electricity generated was from fossil fuel sources [1],leading to the nation having one of the highest emissions in-tensities in the world. Concerns over the effects of fossil fuel use onthe environment and its projected future scarcity are fuelling thedevelopment of renewable energy technology. As a further incen-tive, legislation has also been introduced that commits Australia toreductions in CO2 (carbon-dioxide) emissions from the electricitygrid to 20% of 2000 levels by 2050. One option for efficient gener-ation of electricity from solar energy is through CST (ConcentratingSolar Thermal) power plants. Significant opportunities exist forelectricity generation using CST power plants to replace or sup-plement local generation in remote communities and mining op-erations around Australia and achieve savings in fuel and transportcosts [2].

CST power generation technology is still in its infancy, withcurrent generation CST power plants having high capital costs and

ngh), m.kearney@uq.edu.au.

All rights reserved.

high unitized-electricity costs compared to conventional fossil-fuelbased power plants. One approach to reduce both capital andunitized-electricity costs is to use a more efficient and compactpower cycle, such as a cycle based on sCO2 (supercritical-CO2).

The use of sCO2 as a power cycle working-fluid has beengrowing in recent years due to associated benefits such as highlycompact power plant and high cycle thermal efficiencies at turbineinlet temperatures achieved in solar thermal [3] and nuclear powerplants [4]. The simplicity and potential ability of real-gas closedBrayton cycles such as one with supercritical-CO2 to be integratedwith existing inexpensive solar collectors is also an attractivefeature [5]. The supercritical-CO2 CBC is also being considered forpower generation from other medium-grade heat-sourcesincluding waste heat [6] and for integration with post-combustionCO2 capture for efficiency improvements in coal-fired power sta-tions [7].

Experimental campaigns into the Supercritical-CO2 closedBrayton cycle with configurations similar to the one investigated inthis work already exist and preliminary plant performance andstability has been demonstrated [8]. Investigations are also beingconducted into cycle performance during the startup and shut-down phases for power plant peaking [9]. Other experimentaldemonstration campaigns are also being conducted for different

R. Singh et al. / Energy 60 (2013) 380e387 381

components of the sCO2 CBC for application in solar thermal powerplants through programs such as the US Department of EnergySunShot program on concentrated solar power [10]. Some exam-ples include development and experimental demonstration pro-grams for direct-heating supercritical carbon-dioxide solarreceivers in the cycle [11], and turbomachinery and heat exchangerdemonstration programs for the cycle [12].

The increased interest in sCO2 power cycles is also due to CO2being inexpensive, capable of withstanding very high tempera-tures, non-toxic, non-combustible, non-explosive, and abundant.CO2 also has a moderate critical pressure (7.38 MPa) and criticaltemperature (31 �C), which leads to a large operating envelope forsupercritical conditions. A particular advantage of supercritical-CO2to CST power plants is the ability of CO2 to handle high tempera-tures. The high-temperature capability of CO2 allows the powercycle working-fluid to also be directly-heated by the solar collector,rather than rely on a heat-transfer fluid to transfer solar heat to theworking-fluid via an intermediate heat-exchanger. A direct-heatedsCO2 power cycle eliminates the thermal losses associated with thisintermediate heat-exchange as a single-fluid serves as the heattransfer medium and subsequently drives the turbine, in a closed-loop. These factors can potentially contribute to reduced plantcapital costs and generated electricity costs, and higher solar-to-electric conversion efficiencies due to thermodynamic perfor-mance improvements [13].

One potential application of sCO2 as a working-fluid is in adirect-heated and air-cooled CBC (closed Brayton cycle) connectedto PTCs (parabolic-trough collectors) for solar thermal power gen-eration. This approach was investigated in Ref. [14] usinga simulation study for a proposed installation in Longreach,Queensland, Australia in which the sCO2 CBC solar thermal powerplant is supplementing existing diesel based electricity generation

Fig. 1. Schematic of the simulated sCO2 CBC showing major components, s

in the remote community. The water scarcity at this site (and otherpotential CST power plant sites within Australia) requires that thepower plant is air-cooled. The relatively high ambient air temper-atures at such sites when compared to the critical point tempera-ture of CO2 would, however, result in the CBC operating mostly as anon-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 CO2mass-flow rate in the system as indicated by simulations of cycledynamic behaviour on representative summer and winter days inRef. [14]. The high solar heat input and ambient-air temperatures insummer lead to excessive turbine inlet temperatures in the CBC.Additionally, low ambient-air temperatures and solar heat inputleads to subcritical compressor inlet conditions during normalwinter operation. Operation of the plant using the same fixed CO2inventory each day regardless of the solar heat inputs and tem-peratures may lead to plant damage and overly conservativeoperation 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 CO2mass-flow rates and therefore pressures and temperatures in theCBC. Hence, manipulation of CO2 inventory in the sCO2 CBC withESC (extremum-seeking control) is investigated as a control strat-egy in this paper with the objective of maximising power genera-tion while keeping cycle turbine inlet temperature and pressure inproximity to design limits. Inventory control has been investigatedpreviously for achieving part-load operation of the sCO2 CBC innuclear power applications using conventional proportional-integral controllers [15].

The selection of ESC as a control method in the sCO2 CBC isinfluenced by the fact that optimum power generation conditionsof the cycle vary depending on the particular combination of solar

ensor locations, and the point of CO2 inventory addition and removal.

R. Singh et al. / Energy 60 (2013) 380e387382

heat input and cooling-air temperatures. Furthermore, unlikeconventional ideal-gas power cycles, modelling of the sCO2 CBC atlow orders is difficult. This is due to the fine spatial resolution of theheat-exchanger volumes required to capture the highly nonlinearbehaviour of supercritical-CO2.

Extremum-seeking control is a form of non-model basedadaptive control which has received increased interest in recentyears. It uses continuous measurements of a plant performancefunction as inputs to appropriate filters to develop gradient esti-mates of the performance function with respect to the steady stateplant input. This information is then used with an appropriateoptimisation routine to tune the plant inputs and provide conver-gence towards optimal plant operation. The approach is readilyextended to multidimensional input plants. Recent applications ofESC include maximising fuel cell efficiency and power [16], solarphotovoltaic power maximisation [17], chilled-water system opti-misation [18], and maximum power point tracking of wind-turbines [19], although a more complete survey is provided inRef. [20]. Under this framework, ES (extremum-seeking) algorithmsrequire minimal knowledge of the plant being controlled, largelytreating the plant as a ‘black box’, and therefore avoiding thecomplications due to model mismatch that may face other model-based approaches. Alternative ESC variants include methods thatinclude partial plant information [21], in a ‘grey box’ framework. AnESC method with the ability to be tuned for a wide range of oper-ating conditions and independent of the plant map has also beenexperimentally demonstrated for the reduction of thermoacousticoscillations in premixed, gas-turbine combustors [22].

Black box extremum-seeking is subsequently proposed for con-trol of the sCO2 CBC due to its potential to optimally tune multipleparameters in the sCO2 CBC despite fluctuating solar and ambient airtemperature conditions. Critically, it also eliminates the requirementfor a model of the system for controller development, and requiresminimal prior knowledge of optimum conditions of the system. Theperformance of the proposed ESC approach is compared to ad-hocapproaches involving increasing the amount of fixed inventory inthe CBC in summer and maintaining supercritical compressor inletconditions in winter. The extremum seeking controller makes use ofexisting hardware in the plant, so there is minimal or no additionalhardware cost. There may be some additional initialisation costassociated with the programming and implementation of thecontroller, although this will be offset by the reduced calibrationrequirements for the device operating in open-loop.

1.1. Direct-heated supercritical-CO2 solar thermal power plants

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

The compressor and the turbine split the CST plant into a ‘hotside’ and a ‘cold side’. The volumes of sCO2 CBC components be-tween the compressor outlet and turbine inlet in a clockwise di-rection including the high-pressure side of the recuperator,comprise the ‘hot side’ or ‘high pressure’ section of the system. Theremaining volumes between the turbine outlet and compressorinlet including the low-pressure side of the recuperator comprisethe ‘cold side’ or ‘low pressure’ section.

2. Simulation model

2.1. Closed Brayton power cycle model

The performance of extremum seeking-control when applied tothe sCO2 CBC in the solar thermal power plant is demonstratedusing dynamic modelling and simulation; a technique commonlyused to investigate solar thermal energy processes mainly due tothe highly variable nature of the energy source [23]. Modelling andsimulation of the sCO2 CBC was conducted in Dymola� [24]. Thesimulated model of the plant and solar field data was previouslypresented in Ref. [14] and is based on the layout and components inFig. 1. The power cycle model consists of a single-stage radial (orcentrifugal) compressor and turbine, and that of three heat-exchangers; a heater with heat-flux on the external boundary asa simplified form for heat input from the parabolic troughs, arecuperator for heat recovery, and a cooler as a simplified form of adry-cooled cooling-tower for heat rejection. All heat-exchangersare modelled as axially discretised volumes for more accuratetracking of temperature profiles. Reference data from the NISTREFPROP database [25] implemented in the AirConditioning libraryis used for describing fluid properties of carbon-dioxide usingpressure and specific enthalpy as states.

Zero and one-dimensional equations are used to describe thethermal-hydraulic behaviour of themajor components and control-volumes in the CBC along with the conservation laws of mass andenergy. Constant property heat-transfer constitutive equations areutilised to satisfy the mass and energy conservation laws with theassumption of quasi-steady fluid behaviour.

Homogenous mixing is assumed for fluids within control vol-umes and pressure drops are considered negligible using theassumption that the plant is well designed for minimal pressurelosses and considering the high pressures involved. The compressorand turbine are modelled as single-stage radial or centrifugal typeturbomachines using a zero-dimensional model assuming quasi-steady behaviour. Mass accumulation in turbomachinery isconsidered negligible due to the relatively small volumes associ-ated with these components. Compressor performance is calcu-lated using themethod described in Ref. [26] and performancemapdata from a Sandia Laboratories 50 kW sCO2 compressor [8]. Theturbine considered in this research is a single-stage radial (orcentrifugal) turbine and is based on design-point data for a sCO2radial turbine tested at Sandia National Laboratories [8] asdescribed in Ref. [14]. Due to the unavailability of actual sCO2 tur-bine performance data, the turbine (without diffuser) is repre-sented as an adiabatic nozzle. This approach is consistent withprevious system-level modelling of radial turbines for dynamic andoff-design performance studies [26]. A detailed description of themodelled compressor and turbine, and assumptions made waspresented in Ref. [14].

Due to the required discretisation of heat-exchangers into manysub-volumes and the fact that supercritical-CO2 behaves as a real-gas, a lumped control-oriented model of the sCO2 CBC cannot befound readily.

The design point parameters of the simulated sCO2 CBC werepreviously identified in Ref. [14], but are listed here in Table A.1 forconvenience. A hot-side to cold-side volume-ratio of 1 is utilisedin modelling and simulating the sCO2 CBC. This ratio was chosenas it was shown in Ref. [27] to provide the benefit of relativelyfast cycle dynamic response while also reducing the sensitivity ofthe cycle to fluctuations in solar heat input and ambient airtemperatures.

The equations used in modelling of the sCO2 CBC are solved asdifferential algebraic equations using the DASSL (DifferentialAlgebraic System Solver) multistep integration algorithm.

Fig. 2. Net power generated by the sCO2 CBC against turbine inlet temperature whensolar heat input is 4.73 MW, ambient air temperature is 26 �C, and air flow rate is365 kg/s.

R. Singh et al. / Energy 60 (2013) 380e387 383

2.2. Solar field description

The thermal energy output from the solar field applied as theheat-energy input to the sCO2 CBC for the simulated summer andwinter days was determined using NREL’s System Advisor Model(SAM v2011.10.14b). The solar field energy output was determinedfor a solar collector field indirectly (with thermal-oil loop) heating a1 MWe Ormat� power cycle. The field comprises SolarGenix SGX-1single-axis trough collectors with 5 m aperture operating with a2008 Schott PTR70 evacuated tube receiver. The main parametersused in determining the thermal energy output of the solar fieldapplied in simulations are listed in Table A.2. The solar field energyoutput for the representative summer day was applied in simula-tions capped at the design heat input of 4.73 MW assuming fielddefocusing. A detailed description of the solar field includingparasitic electric energy usage and piping heat loss assumptionswas presented in Ref. [14].

3. Control objective

The control objective for the sCO2 CBC is to maximise the netpower delivered by the cycle while ensuring that the cycle remainswithin operational temperatures and pressures. Fig. 2 shows thatthe power generated by the cycle increases with turbine inlettemperature across the operating region. Hence, the desired oper-ating point is at the upper boundary of the operating region at

Fig. 3. Extremum-seeking controller sche

approximately 350 �C. Frequent or extended excursions beyond thistemperature can lead to damage to the cycle due to material tem-perature constraints being exceeded. The pressure in the CBC mustbe kept below 25 MPa due to structural and material limitations.

A further operational requirement for the CBC is that super-critical conditions are maintained at the compressor inlet to avoidthe possibility of turbomachinery damage. In order to keep fullysupercritical conditions at the compressor inlet during winter, abasic controller (such as a proportional-integral controller) couldact to maintain fully supercritical conditions in the CBC by regu-lating the external flow-rate of the cooling-air in the cooler [15]. Asthe development of such a cooling-medium flow-rate controller isbeyond the scope of this work (and will be the subject of futureresearch), the presence of such a controller is simulated by holdingthe ambient air temperature at 32 �C for the winter day, therebyensuring fully supercritical conditions at the compressor inlet. Insummer, ambient air temperatures are generally above 32 �C formost of the day. Hence, the cooling-medium flow-rate controllerwould have little effect and was not used, nor required.

3.1. Proposed fixed inventory approach

A cooling-medium (air) controller is assumed to be present thatis capable of maintaining the ambient temperature at a point wheresupercritical conditions exist at the compressor inlet. The dynamicsof this process is assumed to be significantly faster than those of thesCO2 CBC and so are not considered explicitly in the modelling.Using manual tuning, it was found that a fixed (i.e. open loop) CO2

specific charge of 300 kg/m3 in the sCO2 CBC provided sufficientperformance on the design conditions in Table A.1.

Operating the plant in summer conditions under the same openloop strategy results in the sCO2 CBC exhibiting excessive and rapidturbine inlet temperature rises relatively early in the day. Theseexcessive turbine inlet temperatures result due to the reduced CO2mass flow-rate in the system caused by fluid-property changes andCO2 mass movement between the hot and cold-sides of the cycle.Increasing CO2 mass-flow rate in the CBC with the addition of CO2inventory could aid in alleviating these excessive temperatures[14]. Therefore, the open loop approach is modified by increasingthe amount of CO2 inventory in the CBC from 300 kg/m3 to 382 kg/m3. These open loop strategies serve as a useful benchmark tocompare the performance of the extremum-seeking controller,although it should be noted the fixed inventory approach does notadapt to intra-day or intra-seasonal operating conditions.

3.2. Proposed extremum-seeking approach

The proposed feedback controller applied to the sCO2 CBC isbased on Ref. [28]. Unlike the fixed inventory controller, in the ESC

matic when applied to the sCO2 CBC.

Fig. 4. Cost as a function of CO2 mass-flow rates for different operating conditions.

Table 1Parameters of the extremum-seeking controller applied for both summer andwinter simulations.

Dither frequency, u (rad/s) 0.0017Gain, C 2High pass filter cut-off frequency, h (rad/s) 0.001Dither amplitude, a 10Slack variable weights, a, b 0.5

R. Singh et al. / Energy 60 (2013) 380e387384

approach the CO2 inventory is allowed to vary with time and theplant input is considered to be the inventory rate of change,designated as _q.

In the proposed ES approach, illustrated in Fig. 3, a sinusoidaldither is applied to the plant input to provide persistency of exci-tation in the gradient estimates at the output of the high pass filter.Inventory addition and removal is conducted at the compressorinlet to minimise any involved parasitic power losses, as it is thepoint of minimal pressure and temperature in the sCO2 CBC. CO2inventory addition and removal from the sCO2 CBC is required forstandard operation and for achieving design-point operationalconditions upon cycle startup [14]. It is anticipated that the pro-posed extremum-seeking controller will utilise the same equip-ment as would otherwise be required for inventorymanipulation inthe sCO2 CBC to achieve design-conditions upon startup. The dy-namics of the inventory control system are beyond the scope of thispaper and will be the subject of future research.

The proposed cost function, J, needs to incorporate the net po-wer as well as the operating constraints on turbine inlet temper-ature and pressure. These operating constraints are consideredthrough the introduction of slack variables, which only becomeactive when the constraints are violated. The nonlinear slack vari-able operator is defined as

Gðx; yÞ ¼�

0 if x < yx� y if x > y

(1)

The extremum-seeker may be equally posed as a maximum orminimum seeking scheme by changing the sign of the cost functionand the high-pass filter in Fig. 3. In this work, a maximisationformulation is arbitrarily prescribed, leading to the cost functionbeing proposed as

J ¼ Pnet � aG�Tt;in; Tmaximum

�� bG�Pt;in; Pmaximum

�(2)

Open loop tests were conducted to investigate the shape of thecost function and check feasibility of the proposed approach underdifferent ambient and incident conditions. Fig. 4 shows five com-binations of ambient air temperatures between 26 �C and 32 �C,and solar-heat input of 4.33 MWe5.05 MW. It is clear that the peakperformance varies with operating conditions and in each casethere is a unique maximum with continuous gradients, therebylending credence to the adoption of the proposed extremum-seeking scheme.

4. Results

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

Performance of the sCO2 CBC is evaluated during fluctuations insolar heat energy and ambient air temperatures on summer andwinter solstice days, with heat input on the summer day cappedassuming solar field defocusing. The sCO2 CBC in the solar thermalpower plant is analysed without thermal storage to investigate theability of the extremum-seeking controller to maximise powergeneration from the cycle whilst maintaining turbine inlet tem-perature and pressure operational constraints at or belowapproximately 350 �C and 25 MPa, respectively. Exhaust gas wasteheat from existing diesel-fired generation can be utilised to pro-vide a thermal buffer during periods of low solar insolation for theinvestigated plant and therefore reduce the impact of powerfluctuations on the electrical grid. However, the primary objectiveof the analysis in this paper is to gain an understanding of theability of the extremum-seeking controller in the sCO2 CBC tomaximise cycle power output prior to implementation of anythermal buffer.

4.1. Controller performance

The performance of the proposed ad-hoc (fixed inventory) andextremum-seeking controllers is now compared for both summerand winter operation. The parameters of the extremum-seekingcontroller are listed in Table 1 and were obtained by manual tun-ing. These fixed parameters were used for both the summer andwinter operating conditions, unlike the proposed fixed inventoryapproach that has dedicated feedforward control for eachcondition.

The simulation results are presented in Figs. 5 and 6, for summerand winter respectively and include the trajectories of the plantoutput of interest and states subject to constraints (turbine inlettemperature, net power generated, turbine inlet pressure); and theplant input (CO2 specific charge). Also shown are the solar heatinput and ambient air temperature, which act like disturbances onthe system. It is to be noted that although solar insolation canfluctuate significantly and at high frequencies [29], the actualfluctuations in heat-flux experienced by supercritical-CO2 flowingin the solar collector absorber tubes will be damped and slower dueto the significant thermal inertia associated with the thick-walls ofthe tubes in the solar collectors that are also relatively long.Consequently, hour-averaged data may be used in this workwithout appreciable consequence.

For the summer day the heat input has been saturated throughthe assumption of a secondary control action defocusing the solarfield, as discussed earlier. From Fig. 5, it is clear that the fixed CO2

Fig. 5. Comparison of sCO2 CBC plant dynamic response with and without extremum-seeking control on a representative summer day.

R. Singh et al. / Energy 60 (2013) 380e387 385

inventory strategy in the system results in the avoidance ofexcessive and rapid turbine inlet turbine rises early in the day, andperforms well in achieving close to desired net power output. Thisis expected as the fixed rates have been carefully tuned to achievethis level of performance, although it is worth noting that the netpower decreases away from the design point when the solar heatinput decreases.

Similarly, the proposed extremum-seeking approach is able tomatch or better the performance of the fixed-CO2 strategy over thesummer day, whilst maintaining the turbine inlet temperature andpressurewithin the prescribed levels through the incorporation of theslack variables in the cost function. It is of significant interest toobserve that the slightly improved performance under the extremum-seeking approach is achieved despite reductions in the CO2 specificcharge, implying that the operational costs under this strategymay bedecreased by reducing the initial CO2 charge in the system.

From a quantitative comparison perspective, an average elec-trical energy generation of 8.7 MWh was achieved over the 10 hnormal solar insolation period (between 08:00 and 18:00) with ESCmanipulating CO2 inventory, compared to 7.9 MWh for the fixedinventory approach. Operation with the proposed ESC also resultsin the plant attaining the design net power output of 1 MW muchearlier at the start of the day.

Both controllers are now implemented on conditionsrepresentative of a winter day, with a cooling-medium flow-rate

controller used to keep the effective ambient air temperature at32 �C. The ESC controller parameters and implementation remainidentical to the summer case, however the fixed inventoryapproach utilises a specific charge of 300 kg/m3 (382 kg/m3 forsummer). The results for both schemes are shown in Fig. 6.

The sCO2 CBC when operating with the proposed ESC exhibitsan improvement in net power output and results in slightlyhigher turbine inlet temperatures for most of the normal solarinsolation period when compared to the fixed inventoryapproach. Over the day, an average of 5.7 MWh of electricalenergy is produced over the 7 h normal solar insolation periodusing ESC manipulating CO2 inventory, compared to 5.8 MWh forthe fixed inventory approach. The lower average power genera-tion with ESC when compared to that with the fixed inventoryapproach can be attributed mainly to the startup and shutdownperiods of operation.

The extremum-seeking controller significantly increases CO2inventory to reduce turbine inlet temperature below the targetvalue of 350 �C between 14:30 and 15:00. This results in a largeincrease in CO2 mass-flow rate in the system. Although turbineinlet temperature is subsequently brought below 350 �C, theextremum-seeking controller does not sufficiently reduce CO2 in-ventory between 15:00 and 16:00 to reduce CO2 mass-flow rateand raise turbine inlet temperature again. This decrease in ESCperformance could be attributed to the relatively large plateau in

Fig. 6. Comparison of sCO2 CBC performance with and without extremum-seeking control on a representative winter day.

R. Singh et al. / Energy 60 (2013) 380e387386

the cost function curves and large CO2 mass-flow rate reductionrequirement (and therefore requirement for a significant amount ofCO2 inventory to be removed) at low solar heat input values.

In summarising the capability of both proposed schemes, itis important to note that although the fixed inventory approachhas similar overall performance to the proposed ES controllerfor both days tested, to achieve this has required retuning theinventory flow rates. To maintain consistently high performanceacross the year is likely to require a range of flow rates underthis approach. On the other hand, the single ES approach hasshown to be robust to the likely two extreme operating condi-tions under the same set of parameters, and therefore wouldbe expected to deliver consistently high performancethroughout the year. This represents a significant improvementin the reliability of operation and reduction in initial systemcalibration.

5. Summary and conclusions

The proposed ES feedback controller was found to be capable ofmanipulating CO2 inventory to maintain net power output close toa desired operating point across extreme ambient conditions, andresulted in slight improvements in key factors without violatingspecified operating constraints.

In comparisonwith a fixed inventory approach, the proposed ESalgorithm demonstrated similar or better overall performance but

required significantly less calibration effort. Furthermore, the pro-posed approach was shown to be consistent for the range of fore-seeable environmental conditions, while the fixed inventory mayrequire retuning at interim seasonal conditions within the extremevalues tested. It is to be noted though that experimental testing ofthe closed loop plant is needed to fully ascertain the benefits andvalidate results presented here. This real world validation is thesubject of future research.

Future work directed towards the improvement of ESC perfor-mance in the sCO2 CBCwill also include improving the convergencerate and robustness of the closed loop scheme. This will involveinvestigation of more sophisticated ESC approaches such asNewton-like extremum-seeking [22], and the possible integrationof partial plant information. Attention will be paid to the startupand shutdown phases of operation to improve ESC performanceduring these phases of plant operation. Additionally, the form andtuning of a cooling-side air flow controller and dynamics of theinventory control system will also be investigated in future work.

Acknowledgements

The authors would like to thank Sarah Miller of the Common-wealth Scientific and Industrial Organisation (CSIRO) EnergyTechnology Division for solar field and energy output data. Thisstudy was supported by the Queensland State Government and theUniversity of Queensland.

R. Singh et al. / Energy 60 (2013) 380e387 387

Appendix A. Design point parameters of cycle and solar field

Table A.1Steady-state design point parameters of the sCO2 CBC (adapted from Ref. [10]).

Turbine inlet temperature 350 �CTurbine inlet pressure 20 MPaCompressor inlet temperature 32 �CCompressor inlet pressure 7.8 MPaGenerator/Turbine/Compressor efficiency 1/0.83/0.69CO2 mass-flow rate 19.6 kg/sCooling air mass-flow rate 365 kg/sThermal efficiency with recuperation 23.4%Design net heat input/ambient air temperature 4.73 MW/26 �CNet-power generation 1 MWeCompressor/Turbine rotational speed 60,000 rpmCompressor/Turbine wheel diameter 65.8 mm/92 mmNon-condensing cooler heat exchange

area/approach temperature1510 m2/6 �C

Recuperator heat exchange area/approach temperature 121 m2/10 �CSolar PTC heater heat exchange area 1360 m2

System specific charge at design condition 300 kg/m3

CBC Hot side: Cold side volume-ratio 1

Table A.2Parameters used to determine the solar field thermal energy output used insimulations.

Trough aperture width 5 mCollector reflectance 0.935Solar field temperature (�C) 391Trough aperture area 10,158 m2

Thermal storage (h) 0Evacuated tube receiver Schott PTR70Solar field availability 99%Heat transfer fluid VP-1Solar multiple 1.2Reference direct normal insolation 950 W/m2

Reference wind speed 5 m/sReference ambient air temperature 25 �CCollector SolarGenix single-axis

with 5 m apertureHeat transfer fluid inlet/outlet

temperature293 �C/391 �C

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