Aalborg Universitet Absorption Cycle Heat Pump Model For .
Aalborg UniversitetAbsorption Cycle Heat Pump Model for Control DesignVinther, Kasper; Just Nielsen, Rene; Nielsen, Kirsten Mølgaard; Andersen, Palle; Pedersen,Tom Søndergård; Bendtsen, Jan DimonPublished in:Control Conference (ECC), 2015 EuropeanDOI (link to publication from Publisher):10.1109/ECC.2015.7330870Publication date:2015Document VersionEarly version, also known as pre-printLink to publication from Aalborg UniversityCitation for published version (APA):Vinther, K., Just Nielsen, R., Nielsen, K. M., Andersen, P., Pedersen, T. S., & Bendtsen, J. D. (2015). AbsorptionCycle Heat Pump Model for Control Design. In Control Conference (ECC), 2015 European (pp. 2228 - 2234).IEEE Press. https://doi.org/10.1109/ECC.2015.7330870General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.? You may not further distribute the material or use it for any profit-making activity or commercial gain? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: October 21, 2021
Absorption Cycle Heat Pump Model for Control DesignKasper Vinther1 , René J. Nielsen2 , Kirsten M. Nielsen1 , Palle Andersen1 ,Tom S. Pedersen1 and Jan D. Bendtsen1Abstract— Heat pumps have recently received increasinginterest due to green energy initiatives and increasing energyprices. In this paper, a nonlinear dynamic model of a singleeffect LiBr-water absorption cycle heat pump is derived forsimulation and control design purposes. The model is basedon an actual heat pump located at a larger district heatingplant. The model is implemented in Modelica and is basedon energy and mass balances, together with thermodynamicproperty functions for LiBr and water and staggered gridrepresentations for heat exchangers. Model parameters havebeen fitted to operational data and different scenarios aresimulated to investigate the operational stability of the heatpump. Finally, this paper provides suggestions and examples ofderivation of lower order linear models for control design.I. I NTRODUCTIONEnergy consumption in residential, commercial and industrial buildings has received increasing attention in recentyears due to the rising demand for efficient energy useand higher comfort standards. In industrial buildings, inparticular, energy efficiency is becoming more and moreimportant in order to avoid waste. Due to their attractiveproperties, heat pumps of various types are seeing extensiveuse in modern buildings, see for instance [1], [2], and manyothers. Furthermore, applying heat pumps together with othertechnologies at modern combined heat and power (CHP)plants and using them in combination with district heating,can yield significant economical and practical benefits, asdescribed in e.g. [3], [4], [5], [6], and [7].The town of Sønderborg in the southern part of Denmark isone such case, where two suppliers, Sønderborg Fjernvarme(SFJV) A.m.b.a. and Sønderborg Kraftvarmeværk I/S, collaborate to provide district heating to a fairly large numberof commercial and private consumers in the local area.Together, the two suppliers incorporate burning of waste,natural gas, wood-chips and, of highest relevance to thepresent paper, four interconnected absorption cycle heatpumps primarily driven by geothermal heat.As can be expected, day-to-day operation needs to beadjusted to consumer load changes, weather, fuel prices,etc. In order to operate complex plants under such dynamicconditions, it is necessary to have good knowledge of theThis work was financially supported by the Danish Energy Agencythrough the EUDP project GreenFlex (jn:64013-0133) and the Faculty ofEngineering and Science at Aalborg University1 K. Vinther, K. Nielsen, P. Andersen, T. Pedersen and J. Bendtsen are with the Section of Automation and Control, Departmentof Electronic Systems, Aalborg University, 9220 Aalborg, Denmark{kv,kmn,pa,tom,dimon}@es.aau.dk2 ejle,Denmarkdynamic behavior and constraints of individual units. However, while absorption cycle heat pumps have received someattention in terms of modeling for the purpose of designand operation under steady state conditions, the literatureis quite limited when it comes to modeling for controlpurposes. [8] and [9] provides an overview of the technology,but does not consider dynamic operation; [10], [11], and[12] all provide steady-state models of absorption cycle heatpumps of varying degree of detail, but also do not considerdynamics. [13] and [14] both present models that includedynamics (mass storage and thermal inertia), but the mainfocus remains on steady-state operation.In this paper, we present a single-effect absorption cycleheat pump model for the specific purpose of investigatingcontrol design issues. In our model, the main heat transportis carried out by a chemical absorption/desorption cycleinvolving a mixture of water and Lithium-bromide (LiBr),and we consider both mass storage and heat transfer. Themodel is implemented as interconnected components in thesimulation tool Dymola using the open-source and objectoriented modeling language Modelica [15]. The componentmodels of the absorber and generator are formulated basedon the aforementioned modeling papers, while the evaporatorand condenser models are inspired by [16]. Heat exchangersare modeled using staggered grid models, e.g., see [11],while LiBr properties are modeled according to [17]. Modelparameters are then fitted using actual plant data.The outline of the paper is as follows. Section II givesan overview of the heat pump process. Section III presentsthe main model components, whereupon Section IV presentsthe results of parameter fitting. Next, Section V showssimulations with external water flow control, Section VIdiscusses linearization of the model, and Section VII sums upthe work. Finally, it should be pointed out that a companionpaper, [18], presents an analysis of different control loopconfigurations based on the model presented here.II. D ISTRICT H EATING H EAT P UMP S ETUPAt the highest level of abstraction, a part of the districtheating supply system at SFJV is structured as shown inFig. 1. The main sources of heat are a wood-chip firedboiler (high-value heat) and a geothermal reservoir (lowvalue heat). These two main heat sources supply heat to thedistrict heating system via four absorption cycle heat pumpsinterconnected in a fairly complex way that permits one ormore of the individual heat pumps (of different size) to bedisengaged from the heat supply operation. In the following,we will limit our focus to the largest heat pump (HP1).
Wood-chipburner80 CHP1HP2HP3HP4155 C42 CCitydistrictheatingsystem48 C15 CGeothermal EvaporatorAbsorber1106Solution HEXEvaporator pump19Hot water valve7200.3 0.40.50.60.71100The heat pump in question was delivered by Hope Deepblue Air-conditioner Manufacture Corp., Ltd., and has anoperational weight of 67 ton [19]. An illustration of the heatpump is provided in Fig. 2. The basic absorption cycle workssimilarly to the standard vapor compression cycle except thatthe compressor is replaced by an absorber and a generator,and the working fluid in an absorption refrigeration system isa binary solution consisting of refrigerant and absorbent—in this case, water and LiBr, respectively. This solution ispumped from the absorber to the generator by an electricalpump (1 3). High temperature water from the wood-chipburner is supplied to the generator (11 12) and used toevaporate refrigerant out from the solution. The refrigerantand absorbent are chemically separated as the refrigerantvaporizes, leaving a liquid solution with a high absorbentconcentration in the generator, which is gradually returnedto the absorber (4) when the generator overflows. A utube mechanism then helps maintain a pressure differencebetween the generator and absorber (5 6), see [13] for8010Fig. 1. Bird’s eye view of a district heat supply system at SFJV withindication of typical water flow temperatures.15Solubility limitLiBr concentrationWaterLiBr Water210Pressure (kPa)Absorption cycle heat pumps170 C5u-tubeSolution pump0102030405060 70 80 90 100 110 120 130 140 150Temperature ( C)Fig. 3. Dühring chart illustration of different state points in the absorptioncycle. The four colored dots indicate the initial conditions of the liquidcontent of the evaporator, absorber, generator, and condenser for the datapresented in Section V.further explanation of the u-tube design. The refrigerantvapor from the generator is led to a condenser (7), where astandard condensation occurs, expelling heat to the surroundings (15 16), which in this case is district heating water.Saturated refrigerant is fed to an evaporator through anotheru-tube overflow mechanism (8 9), where it evaporates,consuming heat from the surroundings (17 18). Actually,in this case, heat is taken from the district heating water,but this water is reheated by geothermal water, which can beconsidered as a cheap energy source. An evaporator pumpis used to continuously circulate liquid refrigerant across theheat exchanger pipes. Finally, the vapor is led to the absorber(10), where the solution absorbs refrigerant vapor at lowpressure; this absorption process is an exothermic process.This means that it must reject heat to the surroundings(13 14), which again is district heating water. A solutionheat exchanger (HEX) allows the solution from the absorber(2) to be preheated before entering the generator (3) byusing the heat from the hot solution leaving the generator(4 5). As a consequence, less hot water from the wood-chipburner is required in the generator. Moreover, the size of theabsorber can be reduced as less heat is rejected. The systemalso has a water HEX located after the condenser, whichtransfers heat from the refrigerant to the district heating water(19 20) before it enters the evaporator.Fig. 3 shows a Dühring chart, which is a graphicalrepresentation of the pressure/temperature/concentration atdifferent saturated state points in the absorption cycle. Notethe red curve; it indicates at which combinations of concentration, pressure, and temperature the LiBr solution starts tocrystallize, which can result in clogging of the pipes andinterruption of machine operation. The region of operationbelow this curve should thus be avoided and the critical pointis where the strong solution returns to the absorber.III. A BSORPTION C YCLE H EAT P UMP M ODEL2Fig. 2. Illustration of the absorption cycle heat pump at SFJV. The numbersindicate thermodynamic state points used in the model (adopted from [8]).A sketch of a single-effect LiBr-water absorption cycleheat pump model is shown in Fig. 4. The individual components are drawn in a temperature-pressure diagram toillustrate the relative operating conditions in the four maincomponents (evaporator, absorber, generator, and condenser).
Qc19erateWEvaporator9187Generator3rHateW110Qe 1756Absorber134ntiolu eSo alvvntioluSo HEXQa eThe model is based on the heat pump system shown inFig. 2. However, for simplicity, the evaporator with evaporator pump is replaced by an evaporator model without thepump, where the heat exchanger pipes are submerged in theliquid water. The overflow pipes from the generator and thecondenser together with the u-tube design can alternativelybe replaced by controlled electronic expansion valves. Valvemodels are therefore used, where control loops start to openthe valves, when the level in the generator or the condenserexceeds a predefined upper bound (nominal level).The dynamic model of the absorption cycle used in thiswork is based on mass and energy balances and thermodynamic property functions. Further, the model is implementedin the Modelica modeling language. This allows reuse ofthe standard Fluid and Media libraries and encouragesobject-oriented programming. Fluid flow between individual component models in thermodynamic systems are alsostandardized using the stream connector implementation, see[20], which is also adopted here.In the following it is assumed that the evaporator andabsorber operate at the same low pressure, and that thegenerator and condenser operate at the same high pressure.Further, there are no heat losses to the ambient air and eachof the four main components can be represented by a liquidcontrol volume (subscript l) and a vapor control volume(subscript v). The overall mass balances aredMedtdMaAbs:dtdMgGen:dtdMcCon:dtMi Vi,l ρi,l Vi,v ρi,v(6)d (Xg Vg,l ρg,l ) X3 m3 X4 m4 ,(7)dtwhere X is mass fraction of LiBr. The energy balances areFig. 4. A sketch of the absorption heat pump model drawn in a temperaturepressure diagram. The numbers indicate state points used in the model.Eva:denotes total. The LiBr mass balances ared (Xa Va,l ρa,l )Abs: X6 m6 X1 m1 ,dtGen:2pmPuQg 11128EXlvva16Condenser20QhWpPressure15 m9 m10 ,(1) m6 m10 m1 ,(2) m3 m4 m7 ,(3) m7 m8 ,(4) Vi,l ρi,l (Vi,tot Vi,l )ρi,v (5)where M is mass, V is volume, ρ is density, m correspond tomass flows illustrated with arrows in Fig. 4, i {e, a, g, c}in (5) and (12) denote each component, and subscript tot m9 h9 m10 h10 Qe ,(8) m6 h6 m10 h10 m1 h1 Qa ,(9) m3 h3 m4 h4 m7 h7 Qg ,(10) m7 h7 m8 h8 Qc ,(11) Vi,l ρi,l hi,l Vi,v ρi,v hi,v pi Vi,tot(12)where U is internal energy, Q is heat transfer rate, h isspecific enthalpy, and p is pressure.The water vapor flow out of the generator solution andthe water vapor flow absorbed in the absorber are driven bythe amount of heat transferred through the HEXs assumingthat the solutions are always in a saturated state. It is alsoassumed (see [8]) that the solution that exits the absorberand generator, the water that exits the condenser, and thevapor that exits the evaporator, all are in a saturated state(same state as in the respective components). Additionally,the vapor from the generator interacts with the solutionfrom the absorber in a counterflow way (sprayed in), suchthat the vapor at the outlet is superheated to the saturationtemperature of the solution, see again [8].The mass and energy balances are supplemented with thermodynamic property functions. E.g., to calculate enthalpy ordensity of water we would use a function of the form(h, ρ) f (p, T ),since liquid-vapor equilibrium is assumed. The water property functions are part of the standard Modelica Medialibrary and the LiBr-water solution property functions areimplemented based on the formulations given in [17].Since Modelica.Media does not provide an interface for incompressible solutions the LiBr-water solutionproperties have been implemented in a separate packagewith functions for pressure, p(T, X), density ρ(T, X), specific enthalpy h(T, X), entropy s(T, X) and heat capacitycp (T, X). Their partial derivatives wrt. temperature, T , andconcentration, X, have been symbolically deduced from theexpressions in [17] and are also provided in the package.The HEX in the four main components, the water HEX,and the solution HEX, illustrated in Fig. 4, are such thatpartial differential equations must be used in the descriptiondue to the distributed parameter nature. This is modeledusing 1-dimensional dynamic staggered grid flow modelswith a finite volume model representation with N volumeselements (volume divided equally) and N 1 flow elementsin between the volumes, as shown in Fig. 5. Further, streamconnectors are used to connect each element as indicated
Twall,2Qwall,1p1h1Flow element.Qwall,2p2h2Volume elementheat port.stream connectorFinally, the mass flow through the solution pump m1 isrelated to the pump work Wp via the static equationm1ηp Wp pp,(19)ρpTwall,NQwall,NpNhNFig. 5.Illustration of a Modelica implementation of a 1-dimensionalstaggered grid model connected to a wall.and heat ports are used for the connection of the volumeelements with the wall elements.The energy balance equation for the j’th volume elementin the staggered grid model, j 1, . . . , N , is; tottotρj hj pj VNd VN mj 1 hj 1 mj hj Qwall,j ,dt(13)UAQwall,j (Twall,j Tj ),(14)N 0.8 mj UA UAno,(15)mnowhere UA is a mass flow dependent overall heat transfercoefficient, subscript no defines nominal values, and Twall ispipe wall temperature. Inlet and outlet pressures are equalfor each volume and the outlet temperature of each volumeis equal to the temperature of that volume Tj . Furthermore,the pipe wall temperature is modeled byMwalldTwall,jcp,wall Qwall,in,j Qwall,out,j , (16)Ndtwhere Qwall,in and Qwall,out are the heat transfer rate intoand out of the wall, respectively, and cp,wall is the specificheat capacity of the wall material. To keep the model simple,the water heat exchangers for the four main componentsare assumed to have saturation temperature along the entirelength of the secondary side of the wall (internal heat pumptemperature). Steady state mass balance is also assumed ineach staggered grid model, since only incompressible fluidflows occur in these.The pressure drop pj across the j’th flow element in thestaggered grid model, j 1, . . . , N 1, located between theN volume elements, is calculated asKfmj mj ,(17) pj ρjwhere Kf is a fixed flow coefficient for each flow element.Note that the pressure loss internally in the heat pump cyclebetween state points 2-3, 4-5, and 8 to before the water valveare assumed to be negligible and thus set to zero, togetherwith static mass balances. This reduces model complexityconsiderably and improves simulation speed.A linear static equation is used to describe the mass flowrate through the valves;Kv mv α pv ,(18)where Kv is a fixed flow coefficient, mv is mass flowthrough the valve, α is valve opening degree, and pv isthe differential pressure across the valve.where ηp is a fixed pump efficiency and ρp is the density ofthe incompressible solution.IV. M ODEL PARAMETER F ITTING AND C OMPARISONW ITH O PERATIONAL DATAThe heat pump model described in Section III containsmultiple parameters that can represent the operational characteristics of a given system. Data from the heat pumpdescribed in Section II and a data sheet [19] are used to fitthe parameters to HP1 (Fig. 1) located at SFJV. In additionto identification of parameters, it is necessary to implementand tune basic stabilizing control loops similar to the setupin SFJV, because the available data is obtained from closedloop operation. However, once a basic control setup is foundthat provides a good fit to the closed-loop data it can be usedas a benchmark for design of more advanced control.The mass flow through the solution pump m1 is used tocontrol the LiBr concentration of the strong solution at theoutlet of the generator, while the external water mass flowthrough the generator m11 is used to control the condenserpressure (same pressure as in the generator). The externalwater mass flow through the water HEX m19 is controlledto maintain a constant outlet temperature T20 .Decentralized PI control loops are used for each of themass flows (m1 , m11 , and m19 ) to provide simple setupsthat can be tuned manually. Note that the exact controlalgorithms in the heat pump at SFJV are unknown and thesuggested control implementation is only one out of manypossible ways to control the cycle, see [18] for further detailon potential control setups. However, the suggested controlshave given the best agreement between data and simulation.Finally, the external water mass flow through the evaporator, absorber, and condenser are controlled externally asdescribed in Section V and the data presented in Fig. 6150Mass flow (kg/s)Twall,1m 13m 15m 171251007550250175Temperature ( C)Wall element150T11125T13T15T17T1910075500510Time (hours)1520Fig. 6. Measured external water mass flow and inlet temperatures during20 hours of operation of the heat pump at SFJV.
are used as input to the simulation, along with the initialconditions shown in Fig. 3.Table I contains the most important model parameters.The volumes and HEX wall masses are based on information provided in the data sheet [19]. The relative sizesof the solution HEX and the water HEX are assumed tobe 10% of the generator and condenser sizes, respectively.Furthermore, it is assumed that the nominal liquid filling(level) of the evaporator, absorber, and condenser is 15% oftheir respective total volumes. The generator has a slightlyhigher nominal liquid level of 20%. The resulting masses ofHEX walls, water, solution, and miscellaneous equipmentgives reasonable total shipment and fluid weight values,respectively 54.6 ton and 12.4 ton, when compared with datasheet values. The heat transfer parameters and the controlparameters were found through manual iteration from aninitial guess to give a good visual fit in steady state operationand in the transient behavior during the ramp change incapacity utilization during the 20 hours of operation (seeFig. 6). In addition, 7 volume elements and 8 flow elementsare used to discretize the HEX tubes, which is a trade-offbetween model accuracy and complexity (the improvementin accuracy is negligible with more elements).The simulation result using the manually tuned modelparameters is compared with operational data from SFJVin Fig. 7. Only four measurements are available internally inthe heat pump cycle (T4 , T8 , T10 , and X4 ). This means thatthe initial absorber concentration has also been an iterationvariable in the model tuning process and it was set to55.5% in the presented simulation result. A potential setpoint reference for the concentration X4,ref used at SFJV isunknown and the control loop in the simulation has thereforebeen set to follow the measured concentration at SFJV asreference. However, the reference for the condenser pressurecontrol loop is kept fixed at the initial pressure.Changes in all temperatures are observed when the capacity is ramped up at around 7 hours. The system settles againa couple of hours after the ramping period ends at around 11hours. All the temperatures show good qualitative agreementwith measurement data. The largest offsets are seen in thetemperatures associated with the generator and absorber.These models are relatively simple, where the temperature ofthe solution is assumed to be the same across the entire HEXwall. Models with higher fidelity could be used; however, thiswill increase the model order and the obtained model detailis considered adequate for control design.V. S IMULATION OF E XTERNAL WATER F LOW C ONTROLThe external evaporator water mass flow m17 is used todetermine the desired capacity utilization of the heat pump.Higher external mass flow through the evaporator generatesmore steam, which in turn requires a higher absorber flowto absorb the steam and a higher condenser flow to generateenough condensate for the evaporator. Higher condensationrate in the condenser lowers the pressure and the internalcontrol will thus generate more steam in the generator andpump more solution from the absorber to maintain a suitableTABLE IM ODEL PARAMETERS USED IN SIMULATIONS wallcp,wallTotal eva. volumeTotal abs. volumeTotal gen. volumeTotal con. volumeMass of eva. HEX wallMass of abs. HEX wallMass of gen. HEX wallMass of con. HEX wallMass of wat. HEX wallMass of sol. HEX wallSpecific heat cap. of HEX om13,nom11,nom15,nom19,nom8,nom2,nom4,noNom. eva. HEX heat transf. coef.Nom. abs. HEX heat transf. coef.Nom. gen. HEX heat transf. coef.Nom. con. HEX heat transf. coef.Nom. wat. HEX heat transf. coef.Nom. sol. HEX heat transf. coef.Nom. ext. eva. HEX mass flowNom. ext. abs. HEX mass flowNom. ext. gen. HEX mass flowNom. ext. con. HEX mass flowNom. ext. wat. HEX mass flowNom. int. wat. HEX mass flowNom. weak sol. HEX mass flowNom. strong sol. HEX mass flow1.5 1062.2 1062 1062.5 1061.7 1051.5 kgskgskgskgskgsHeat TransferLiBr concentration in the generator. The heat pump locatedat SFJV is specified to operate with external absorber andcondenser mass flows as a scaling of the evaporator massflow with minimum and maximum margins;0.95ka m17 m13 1.6ka m17 ,(20)0.85kc m17 m15 1.15kc m17 ,(21)with nominal absorber flow scaling ka 1.591 and nominalcondenser flow scaling kc 1.078.In order to keep the heat pump operable it is important thatthe liquid levels (mass distributions) in each of the four maincomponents are kept within a reasonable range from theirnominal values. It is also important that the concentration iscontrollable to be able to prevent potential crystallization.Simulations of the four extreme situations in terms ofabsorber and condenser mass flow are shown in Fig. 8. Thesimulation conditions are the same as presented in Section II,except for the external absorber and condenser mass flows,which are set to be scaled according to Eq. (20) and (21).The levels and concentration are kept within reasonablebounds during the 20 hour simulations in three out of fourextreme cases. The situation with high condenser mass flowand low absorber mass flow exhibits potential problems in
70302826510Time (hours)152005150514020Level (%)7015External water outlet temperaturesAbs. T14 ( C)125Con. T16 ( C)1015Time (hours)20130Eva. T18 ( C)20201451351015Time (hours)6560558075703230282664620510Time (hours)1520Fig. 7. Comparison between 20 hours of data from SFJV and simulationdata from the absorption cycle heat pump model in Dymola.terms of keeping the concentration at the reference andmaintaining decent levels in the evaporator and the absorber.This is due to a too efficient condenser that overflows theevaporator with condensate, while the absorber does notabsorb enough steam from the evaporator to maintain ahealthy liquid level, which raises the concentration in theabsorber and causes the concentration in the generator toraise as well. Note that generally in order to keep theevaporator and the absorber levels controlled at their nominalvalues (15%) it would be necessary to measure or estimateat least one of these levels, see [18]. However, the system isoperable with suitable scaling of external mass flows.051015Time (hours)20X 4,ref65con. 85%abs. 95%64.56463.563051015Time (hours)20051015Time (hours)20051015Time (hours)20051015Time (hours)206564.5con. 115%abs. 95%15Concentration (%)Level (%)20X46463.5636564.5con. 85%abs. 160%7520Le6463.5636564.5con. 115%abs. 160%Eva. T10 ( C)801015Time (hours)Concentration (%)1255Concentration (%)1300Level (%)13515Level (%)Internal concentration and temperatures60140Water HEX T20 ( C)Lc206260LaConcentration (%)640Gen. T12 ( C)LgDymola145Con. T8 ( C)Gen. T4 ( C)Gen. X4 (%)SFJV6463.563Fig. 8. Levels and concentration in simulations on the heat pump modelusing extreme external absorber and condenser water mass flow situationsrelative to their nominal scalings. From top to bottom: low condenser andlow absorber flow, high condenser and low absorber flow, low condenserand high absorber flow, high condenser and high absorber flow.VI. L INEARIZATION OF N ONLINEAR M ODEL FORC ONTROL D ESIGNThe nonlinear heat pump model implemented in Modelicahas the following states: four levels (4), temperature andconcentration in absorber and generator (4), pressure and enthalpy for each volume element in the four main componentHEXs (56), temperature of each volume element and eachwall segment for the solution HEX (21, no pressure loss assumed), temperature of each wall segment and each volumeelement internally in the water HEX (14, no pressure lossassumed), pressure and enthalpy for each volume elementexternally in the water HEX (14). This gives 113 states.A linear lower order model is often preferred for controldesign and Dymola has a built-in linearization functionality,which can linearize the nonlinear model in a given operatingpoint. The output is a state space representation, where modelorder reduction can be performed on the high order modelfor the input/output set of interest, e.g., using the Matlabfunction balred. The linear model can be verified byperturbing the inputs of the nonlinear model with sinusoidalsignals of different frequency and calculating the responsein each output of interest. The test frequencies should bechosen around the desired control bandwidth as lower/higherfrequencies are not as important for the control design.
-20250-40200-60-80-3-2-1101010Frequency (rad/s)-3-2-1101010Frequency (rad/s)01050-20Phase (deg)Magnitude quency (rad/s)010From m11 to Tc-100-410TestFrom m1 to X4Reduced Lin.Phase (deg)Magnitude (dB)Full Lin.0-50-100-410-3-2-1101010Frequency (rad/s)010Fig. 9. Frequency response of a full order and a reduced order linear modelof the SISO systems from solution mass flow m1 to concentration X4 (topgraph) and from water mass flow m11 to condensation temperature Tc . Thefrequency response from tests is performed on the full nonlinear model.The solution pump mass flow m1 and the external generator water mass flow m11 are two internal inputs in theheat pump model. These inputs are used to control thegenerator outlet LiBr concentration X4 and the condensationtemperature Tc (or pressure) a
1K. Vinther, K. Nielsen, P. Andersen, T. Pedersen and J. Bendt-sen are with the Section of Automation and Control, Department of Electronic Systems, Aalborg University, 9220 Aalborg, Denmark fkv,kmn,pa,tom,dimong@es.aau.dk 2R. Nielsen is with Added Values, 7100 Vejle, Denmark RJN@AddedVal
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