energies Article Model-Based Condenser Fan Speed Optimization of Vapor Compression Systems Sebastian Angermeier 1,2,* and Christian Karcher 1 1 Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, 98684 Ilmenau, Germany; [email protected] 2 MAHLE GmbH, Pragstr. 26–46, 70376 Stuttgart, Germany * Correspondence: [email protected]; Tel.: +49-1703724441 Received: 1 October 2020; Accepted: 11 November 2020; Published: 17 November 2020 Abstract: Vapor compression systems (VCS) cover a wide range of applications and consume large amounts of energy. In this context, previous research identified the optimization of the condenser fans speed as a promising measure to improve the energy efficiency of VCS. The present paper introduces a steady-state modeling approach of an air-cooled VCS to predict the ideal condenser fan speed. The model consists of a hybrid characterization of the main components of a VCS and the optimization problem is formulated as minimizing the total energy consumption by respectively adjusting the condenser fan and compressor speed. In contrast to optimization strategies found in the literature, the proposed model does not relay on algorithms, but provides a single optimization term to predict the ideal fan speed. A detailed experimental validation demonstrates the feasibility of the model approach and further suggests that the ideal condenser fan speed can be calculated with sufficient precision, assuming constant evaporating pressure, compressor efficiency, subcooling, and superheating, respectively. In addition, a control strategy based on the developed model is presented, which is able to drive the VCS to its optimal operation. Therefore, the study provides a crucial input for set-point optimization and steady-state modeling of air-cooled vapor compression systems. Keywords: coefficient of system performance; steady-state modeling; set-point optimization; ideal condensing pressure; air-cooled chiller; refrigeration 1. Introduction Vapor compression systems (VCS) are used in many technical applications, such as the air conditioning of buildings, food temperature control, automotive applications, etc., and consume a considerable amount of energy. For instance, air conditioning and refrigeration account for about 24% of household energy consumption in the USA [1] and for hot and high humid countries like Singapore this consumption can represent over 50% [2]. Therefore, increasing the energy efficiency of VCS through optimization and control appears to be a key issue [3]. One prospective possibility for energy saving is the quasi-stationary control, which aims to achieve the highest possible efficiency within one operating condition, i.e., set-point optimization. 1.1. Ideal Condenser Fan Speed According to Jensen and Skogestad [4], the optimal energy efficiency of a VCS can be obtained by adjusting the five degrees of freedom: refrigerant mass flow rate, superheating, subcooling, condensing, and evaporating pressure. These theoretical degrees of freedom can be influenced by the actuators of the given system. Considering a conventional air-cooled chiller with a thermostatic expansion valve (TXV), as shown in Figure1, the compressor and condenser fan speed are available actuators to set the five degrees of freedom. Hence, an infinite number of combinations of the compressor and condenser Energies 2020, 13, 6012; doi:10.3390/en13226012 www.mdpi.com/journal/energies Energies 2020, 13, 6012 2 of 26 Energies 2020, 13, 6012 2 of 26 fanactuators speed can to meetset the the five load degrees demand, of but freedom. with di ffHencerente, energyan infinite efficiency number [5,6 ].of Thereby, combinations the energy of the efficompressorciency can beand quantified condenser by fan the speed coeffi cancient meet of system the load performance demand, but with different energy efficiency [5,6]. Thereby, the energy efficiency can be quantified by the coefficient of system performance . COSP = Qe/(Pcom + PF) (1) = ⁄( +) (1) . where , , and are refrigeration capacity, compressor power, and condenser fan power. where Qe, Pcom, and PF are refrigeration capacity, compressor power, and condenser fan power. TheThe optimization optimization problem problem of of the the ideal ideal condenser condenser fan fa speedn speed occurs occurs because because of of a tradeoa tradeoffff between between the the compressorcompressor and and fan fan power power consumption consumption [5 ].[5]. For For instance, instance, rising rising fan fan speed speed increases increases the the fan fan power power consumption,consumption, but but decreases decreases the the condensing condensing pressure pressure due du toe to higher higher heat heat rejection, rejection, which which in in turn turn leads leads toto lower lower compression compression work. work. Figure Figure1 shows 1 shows the the power power consumption consumption of compressor, of compressor, fan, andfan, theand sum the ofsum of both against the fan speed at constant cooling load, coolant inlet temperature ( ), and both against the fan speed at constant cooling load, coolant inlet temperature (Tcool,in), and condenser, aircondenser inlet temperature air inlet (temperatureTair,in) to illustrate ( , the) to tradeoillustrateff. the tradeoff. air outlet P fan Q condenser compressor P Compressor TXV air inlet Fan Compressor + Fan Electric power/ kW evaporator Q Condenser fan speed / rpm coolant circuit (a) (b) FigureFigure 1. Air-cooled1. Air-cooled vapor vapor compression compression system (VCS)system comprising (VCS) comprising compressor, condenser,compressor, thermostatic condenser, expansionthermostatic valve expansion (TXV), evaporator, valve (TXV), and evaporator, condenser fanand ( a).condenser Electric powerfan (a). of Electric the condenser power of fan, the compressor,condenser and fan, the compressor, sum of both forand constant the sum air inlet of temperature,both for constant coolant temperature,air inlet temperature, and refrigeration coolant capacity.temperature, The characteristic and refrigeration of the compressor capacity. The and char condenseracteristic fan of power the compressor results in an and energy condenser efficiency fan optimum.power results A low in curvature an energy in efficiency the vicinity optimum. of the minimum A low curvature can be observed in the vicinity (b). of the minimum can be observed (b). The ideal condenser fan speed exhibits a strong dependence on the ambient temperature and the refrigerationThe ideal condenser capacity [7 fan,8]. speed Consequently, exhibits a the strong speed dependence of the condenser on the fanambient must temperature be adjusted inand accordancethe refrigeration with the capacity operating [7,8]. conditions Consequently, in order the to achievespeed of optimum the condenser performance. fan must be adjusted in accordance with the operating conditions in order to achieve optimum performance. 1.2. Optimization of the Condenser Fan Speed Control 1.2.A Optimization key aspect of of the the condenser Condenser fan Fan speed Speed optimization Control is the VCS modeling, which can be separated into blackA key box aspect and component-based of the condenser [ 9fan]. 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[9boundary,] and Zhang and et al.hybrid [12]. or The lumped VCS modelsmodels are [10,11]. usually An assessed overview on of the steady-state basis of the VCS prediction modeling accuracy is given of by the Wan coeffi etcient al. [9] of and performance Zhang et al. (COP).[12]. The In this VCS context, models Scarpaare usually et al. assessed [13] have on stated the basi thats of the the mostprediction accurate accuracy models of leadthe coefficient to a COP of estimationperformance error (COP). of 5%, In andthis context,10% can Scarpa be considered et al. [13] ashave a high stated level that of the accuracy. most accurate In fact, models the most lead ± ± modelsto a COP for set-pointestimation optimization error of ±5%, perform and ±10% a COP can estimationbe considered accuracy as a high of about level of10% accuracy. [14–20 ].In fact, the ± most models for set-point optimization perform a COP estimation accuracy of about ±10% [14–20]. Energies 2020, 13, 6012 3 of 26 Using different modeling approaches, various optimizing system controls of varying complexity are proposed in the literature [21,22]. As a simple solution, the ideal condenser fan speed can be determined in advance to derive a linear function [7,8] or a regression [19,23] for control. In 2004, Chan and Yu [8] published a control of the condensing temperature as a linear function of the ambient temperature. In a further publication, Yu and Chang [19] suggested a load-based speed control for a small ambient temperature range. These solutions can provide a significant improvement compared to