energies

Article Multi-Objective Optimisation-Based Design of an Electric Vehicle Cabin Heating Control System for Improved and Driving Range

Ivan Cvok , Igor Ratkovi´c* and Joško Deur

Faculty of and Naval Architecture, University of Zagreb, 10000 Zagreb, Croatia; [email protected] (I.C.); [email protected] (J.D.) * Correspondence: [email protected]

Abstract: Modern electric vehicle heating, ventilation, and air-conditioning (HVAC) systems operate in more efficient mode, thus, improving the driving range under cold ambient conditions. Coupling those HVAC systems with novel heating technologies such as infrared heating panels (IRP) results in a complex system with multiple actuators, which needs to be optimally coordinated to maximise the efficiency and comfort. The paper presents a multi-objective genetic algorithm-based control input allocation method, which relies on a multi-physical HVAC model and a CFD-evaluated cabin airflow distribution model implemented in Dymola. The considered control inputs include the cabin inlet air temperature, blower and air mass flows, secondary loop pump speeds, and IRP control settings. The optimisation objective is to minimise total electric power consumption and thermal comfort described by predictive mean vote (PMV) index. Optimisation

 results indicate that HVAC and IRP controls are effectively decoupled, and that a significant reduction  of power consumption (typically from 20% to 30%) can be achieved using IRPs while maintaining

Citation: Cvok, I.; Ratkovi´c,I.; Deur, the same level of thermal comfort. The previously proposed hierarchical HVAC control strategy is J. Multi-Objective Optimisation-Based parameterised and extended with a PMV-based controller acting via IRP control inputs. The perfor- Design of an Electric Vehicle Cabin mance is verified through simulations in a heat-up scenario, and the power consumption reduction Heating Control System for Improved potential is analysed for different cabin air temperature setpoints. Thermal Comfort and Driving Range. Energies 2021, 14, 1203. https:// Keywords: control; electric vehicle; heat pump; multi-objective optimisation; optimal allocation; doi.org/10.3390/en14041203 thermal comfort

Academic Editor: Hugo Morais

Received: 19 January 2021 1. Introduction Accepted: 18 February 2021 Consumer acceptance of electric vehicles is increasing strongly [1], with the trend Published: 23 February 2021 bound to continue due to imposed emissions and carbon tax legislation, e.g., in the Eu- ropean Union [2] and China [3]. Although the declared range of current battery electric Publisher’s Note: MDPI stays neutral vehicles (BEV) is typically between 300 km and 500 km, the mass market share is still with regard to jurisdictional claims in hindered due to long and widely unavailable charging and end-users’ perception of BEVs, published maps and institutional affil- having limited driving range compared to conventional vehicles. iations. The EV range significantly drops below the declared one when considering extremely hot or cold weather conditions since the heating, ventilation, and air-conditioning (HVAC) system has the highest energy consumption of all auxiliary systems [4,5]. In cold weather, the vehicle range can be decreased by up to 60% [6,7] when compared to the declared range Copyright: © 2021 by the authors. obtained at . This is especially emphasised in BEVs, which utilise high- Licensee MDPI, Basel, Switzerland. voltage positive thermal coefficient (HV-PTC) resistive heaters for cabin air heating with a This article is an open access article power rating of up to 5 kW for passenger vehicles. Since the coefficient of performance of distributed under the terms and HV-PTC heaters is 1 at maximum [8], this can lead to the high energy consumption of the conditions of the Creative Commons Attribution (CC BY) license (https:// HVAC system. creativecommons.org/licenses/by/ New heating concepts have been developed recently for improved BEV heating effi- 4.0/). ciency in cold weather. These particularly relates to vapour-compression cycle (VCC)-based

Energies 2021, 14, 1203. https://doi.org/10.3390/en14041203 https://www.mdpi.com/journal/energies Energies 2021, 14, 1203 2 of 24

heat pump systems with integrated cabin and battery/powertrain thermal management [9], which support operation in both heating and cooling mode with the coefficient of per- formance being considerably higher than 1 [10]. Such heat pump systems can improve the fuel economy and reduce emissions of hybrid electric vehicles (HEVs) [11], as well as boost the electric driving range of plug-in HEVs (PHEVs) [12]. When concerning BEVs, the driving range can be increased by 18% at the ambient temperature of −10 ◦C by opting for heat pump system instead of a PTC system, as demonstrated in Fiat 500e [13]. Additionally, to boost the efficiency, novel HVAC systems utilise new types of , e.g., CO2 or propane (R290; see [14] for details and a broader discussion of refrigerant selection). The latest trends in automotive HVAC development place emphasis on localised heating and cooling by forming microclimate zones around the passengers, instead of conditioning the entire cabin volume in the same way. For instance, heating the seats at the temperature of 37 ◦C allows for reduction of operative cabin air temperature from the nominal value of 20 ◦C by about 3 ◦C[15], thus, reducing convective heat load on HVAC. The operative cabin air temperature can be reduced by 6 ◦C when combining heated seats with radiative foot heaters [15]. Installing infrared heating panels (IRPs) throughout the cabin can reduce the energy consumption by 50% compared to convective heating [16], but to achieve adequate thermal comfort they need to be combined with the classic HVAC system. Reference [17] considers extending the aforementioned HVAC system of Fiat 500e with heated seat and radiation heating. The analysis shows that using the localized heating reduces average battery power consumption from 2.3 kW to around 0.9 kW at the ambient temperature of 0 ◦C and New European Driving Cycle (NEDC). The advanced BEV HVAC systems are characterised by an increased number of actuators, which makes the energy management/control system design more challenging. To minimise the power consumption at a favourable level of thermal comfort, it is necessary to develop new HVAC control systems that optimally coordinate multiple, often redundant actuators. Fuzzy-logic control of cabin thermal comfort presented in [18] relies on feedback information of simplified predicted mean vote (PMV) model, and it improves both thermal comfort and energy efficiency when compared to using cabin air temperature as a feedback signal of the conventional air-conditioning (A/C) system. A multi-input/single-output proportional-integral (PI)-like controller is proposed in [19] for the conventional A/C system to improve the HVAC efficiency and a PMV-based thermal comfort criterion in a feedback loop manner. It is shown, therein, that the fuel consumption can be reduced by 4.3% compared to conventional control algorithms for the same level of thermal comfort. An optimal allocation-based control strategy presented in [20] allocates low-level A/C control inputs by means of instantaneous on-line optimisation (maximisation) of efficiency and thermal comfort, subject to cooling capacity demand constraint. Alternatively, the model predictive control proposed in [21] and [22] optimises control inputs over prediction horizon to achieve optimal cooling performance of HEV and BEV, respectively. Such an on-line optimisation is computationally demanding, particularly for the case of increased number of actuators. For improved computational efficiency, it is possible to use off-line optimised allocation control law or maps [23]. In this paper, the genetic algorithm-based optimisation method from [23] is extended to multi-objective optimisation and applied to obtain optimal control input allocation maps of an advanced BEV HVAC system comprising also IRPs. The aim is to minimise the total power consumption and the PMV thermal comfort index in the heat pump operating mode. The optimal control input allocation maps are used within a hierarchical cabin temperature control system, which is extended with a proportional-like PMV controller that commands the IRP power setting. The main contributions of the paper are twofold. The first contribution relates to the multi-objective optimisation method itself, which is targeted at providing a favourable trade-off between thermal comfort and power consumption for specified heating power demand and actual cabin air conditions. The method results in computationally efficient optimisation by relying on a simplified computational fluid dynamics (CFD) model-based cabin airflow distribution model and replacing the cabin Energies 2021, 14, 1203 3 of 24

thermal dynamics and thermal load disturbance by cabin air condition sources. The second contribution concerns analysis of optimisation results and establishing a related optimal control strategy to quantitatively recognise and exploit IRP benefits for both steady-state and emphasised transient conditions. The steady-state analysis is more comprehensive than analyses presented in available literature (see e.g., [16,17]) in terms of analysing a wide range of HVAC-only and HVAC+IRP cabin air temperature targets using both optimisation and simulation. Moreover, unlike in the available references (e.g., [17,23]), the optimisation and simulation analysis results are exploited to design an optimal HVAC+IRP control system, which is tested under heavily transient heat-up conditions, as well. The presented study includes the following main steps: (i) multi-physical modelling of the HVAC system and passenger cabin (Section2), (ii) setting the model-based control input allocation map optimisation framework (Section3), (iii) analysing the optimisation results and related power consumption reduction potential based on using infrared panels (Section4), and (iv) revealing the structure of optimal control strategy and presenting corresponding simulation verification results for steady-state and transient conditions, again with the emphasis on power consumption reduction potential (Section5). Section6 discusses the main results and open problems, while concluding remarks are given in Section7.

2. HVAC System Model 2.1. HVACSystem Configuration The considered R290-based HVAC system configuration, operating modes, and ther- mal energy exchange principles are described in detail in [14] and [23]. The emphasis in this work is on the heat-pump operating mode of the HVAC system, where no use of powertrain/battery waste-heat is considered since it is insufficient for cabin heating [24]. The heat pump mode comprises of three distinct thermal energy exchange loops (see Figure1): the core vapour-compression-cycle (VCC) refrigerant loop (green line), which exchanges thermal energy with a low temperature secondary coolant loop (blue line) and a high-temperature secondary coolant loop (red line). The secondary coolant loops serve as intermediary between VCC and ambient and cabin air (coloured arrows). The VCC actuators include the electric and the electronic expansion valve (EXV). The secondary coolant loops are equipped with multiple pumps and proportional three-way valves, which allow for implementing more complex operating modes such as dehumidification. In the considered heat-pump operating mode, the low-temperature coolant is at lower temperature than the ambient air and it receives thermal energy through the main radiator and heats the refrigerant in a (EVAP), while the high-temperature coolant loop is heated by a condenser (COND). The high-temperature coolant flows through the heater core (HC) where it heats up the cabin inlet air. The ambient air is forced through the front main radiator by means of a fan and ramming flow due to vehicle velocity, while the air flow into the cabin is achieved by the blower fan. The air properties at the blower fan inlet are influenced by the cabin air recirculation setting, which allows mixing of the fresh air and cabin air in a specified ratio. The HVAC system is equipped with multiple refrigerant pressure and refrigerant and air temperature sensors to allow for implementation of the complex automatic climate control system considered. The cabin inlet air temperature is controlled by a PI controller, which commands compressor speed, and the superheat temperature is controlled by a PI controller, which commands the EXV position (dashed black lines). The superheat temperature control ensures that the refrigerant at the compressor inlet is in gas state. Energies 2021, 14, 1203 4 of 24 Energies 2021, 14, 1203 4 of 24

Figure 1. System schematic for heat pump (HP) mode.mode.

2.2. Dymola-Based HVACandHVAC and CabinCabin AirAir FlowFlow DistributionDistribution ModelsModels The multi-physicalmulti-physical HVAC HVAC system system model model has has been been implemented implemented in Dymola, in Dymola, parametrised para- using available system design data, technical datasheets, and component test bench data, metrised using available system design data, technical datasheets, and component test and partly validated using test rig data [25]. bench data, and partly validated using test rig data [25]. Figure2 depicts the passenger cabin model with associated HVAC inputs (red outline) Figure 2 depicts the passenger cabin model with associated HVAC inputs (red out- and the airflow distribution subsystem (green outline). The cabin (red outline) is modelled line) and the airflow distribution subsystem (green outline). The cabin (red outline) is as a single-zone humid air volume enveloped by a lumped-parameter of modelled as a single-zone humid air volume enveloped by a lumped-parameter thermal interior elements such as seats, ducts, panels, and car body [26]. The lumped body thermal mass of interior elements such as seats, ducts, panels, and car body [26]. The lumped body mass exchanges heat via with the ambient due to vehicle traveling at thermal mass exchanges heat via forced convection with the ambient due to vehicle trav- velocity vveh and with the interior cabin air volume. The cabin air volume is additionally eling at velocity vveh and with the interior. cabin air volume. The cabin air volume. is addi- subject to various thermal loads Qload, includinġ passenger metabolic load Qmet anḋ the tionally subject. to various thermal loads Qload, including passenger metabolic. load Qmet and solarthe solar load loadQsol Q.̇ sol The. The cabin cabin inlet inlet air air properties properties including including mass mass flow flow rate ratem ṁbfbf,, temperaturetemperature T RH Tcab,incab,in, ,and and relative relative humidity RHcab,incab,in areare determined determined by by the the HVAC HVAC system. system. The The inlet inlet air air is isassumed assumed to toideally ideally mix mix with with the the cabin cabin air airat a at constant a constant pressure. pressure. Therefore, Therefore, the cabin the cabin out- outletlet air airmass mass flow flow rate rate comprised comprised ofof the the mass mass flow flow going going to to the the ambient ambient and recirculated mass flowflow (depending onon thethe set recirculation ratio)ratio) isis equalequal toto thethe inletinlet airair massmass flow.flow. TheThe recirculation ratio used for heatingheating is set,set, herein,herein, toto 90%90% ofof freshfresh airair intakeintake andand 10%10% ofof recirculated cabincabin air.air. The passenger thermal comfort is evaluated using the Predicted Mean Vote (PMV)(PMV) index [27] whose inputs are provided by a look-up table-based cabin airflow distribution index [27] whose inputs are provided by a look-up table-based cabin airflow distribution model described in [26]. The flow distribution model shown in Figure2 (green outline) model described in [26]. The flow distribution model shown in Figure 2 (green outline) is is comprised of four main zones (driver, co-driver, and the two backseat passengers) and comprised of four main zones (driver, co-driver, and the two backseat passengers) and each zone is further divided in three body-specific parts: head, torso, and legs. Such each zone is further divided in three body-specific parts: head, torso, and legs. Such dis- discretisation enables the PMV evaluation for different body parts and, therefore, the cretisation enables the PMV evaluation for different body parts and, therefore, the imple- implementation of localised heating by means of spatially distributed infrared panels. mentation of localised heating by means of spatially distributed infrared panels. Negative Negative PMV values correspond to the occupant feeling cold, while positive PMV values PMV values correspond to the occupant feeling cold, while positive PMV values indicate indicate that the occupant is feeling hot. The best (neutral) thermal comfort is achieved that the occupant is feeling hot. The best (neutral) thermal comfort is achieved at the PMV at the PMV value of zero, while the favourable thermal comfort range is defined by PMV value of zero, while the favourable thermal comfort range is defined by PMV values lying values lying between −0.5 and +0.5. betweenThe − airflow0.5 and distribution+0.5. model is extended with six infrared heating panel (IRP) The airflow distribution model is extended with six infrared heating panel (IRP) clus- clusters (Figure2), i.e., those for driver ( uIRP1,2) and co-driver (uIRP3,4) upper body (torso, ters (Figure 2), i.e., those for driver (uIRP1,2) and co-driver (uIRP3,4) upper body (torso, head) head) and lower body (four clusters in total), and also backseat passengers (uIRP5,6; two in total).and lower Each body cluster (four is modelled clusters in by total), a thermal and massalso backseat heated by passengers an internal (u panelIRP5,6; two temperature in total). controllerEach cluster that is commandsmodelled by heating a thermal power, mass and heated each panelby an exchangesinternal panel convective temperature heat withcon- cabintroller air. that The commands maximum heating IRP heating power, power and depends each panel on the exchanges panel size, convective and it equals heat 390 with W cabin air. The maximum IRP heating power depends on the panel size, and it equals 390 and 160 W for driver clusters 1 and 2, respectively. The IRP control level setting uIRP sets W and 160 W for driver clusters 1 and 2, respectively. The IRP control level setting uIRP the panel target temperature command, which is equal to air temperature for uIRP = 0% sets the panel target temperature command, which is equal◦ to air temperature for◦ uIRP = and the maximum panel temperature for uIRP = 100% (80 C for head panels, and 60 C for other0% and panels). the maximum panel temperature for uIRP = 100% (80 °C for head panels, and 60 °C for other panels).

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TheThe inlet inlet air air distribution distribution in in the the cabin cabin is is determined determined by by air air vent vent outlet outlet locations. locations. In In the the heatingheating mode, mode, the the air air distribution distribution mode mode HEAT HEAT redirects redirects 75% 75% of the of inletthe inlet air to air the to legs, the 15%legs, of15% the of inlet the airinlet to theair to torso, the torso, while while the rest the of rest the of air the mass air flowmass rate flow is rate redirected is redirected towards to- thewards windshield the windshield area (see area [25 (see,26] [25,26] for details for detail ands also and definition also definition of other of other air distribution air distribu- modes).tion modes). The inputs The inputs to the to airflow the airflow distribution distribution model model are cabin are inlet cabin air inlet temperature air temperatureTcab,in . cab,in q̇ cab andT volumetric and volumetric inlet air inlet flow airq flowbf (outputs bf (outputs of HVAC of HVAC model), model) cabin, aircabin temperature air temperatureTcab and T humidityand humidityRHcab ,RH andcab infrared, and infrared panel control panel settingscontrol usettingsIRP,1–6. Metabolic uIRP,1-6. Metabolic activity and activity clothing and factorsclothing are factors considered are considered to be constant to be parameters.constant parameters. The cabin The air temperature,cabin air temperature, the inlet airthe temperatureinlet air temperature and the inlet and air the volume inlet air flow volume determine flow the determine actual air the temperature actual air andtemperature velocity forand each velocity body for part each used body as inputspart used for PMVas inputs calculation, for PMV and calculation, they are and determined they are usingdeter- CFDmined model-based using CFD look-upmodel-based tables look-up for the tables given for ventilation the given and ventilation recirculation and recirculation mode [26]. Themode mean [26]. radiant The mean temperature, radiant temperature, required by requ theired PMV by model, the PMV is determinedmodel, is determined as a linear as combinationa linear combination of cabin airof cabin temperature air temperature and IRP temperatureand IRP temperature [26]. [26].

FigureFigure 2. 2.Block Block diagram diagram of of cabin cabin thermal thermal systemsystem modelmodel includingincluding airflowairflow distributiondistribution modelmodel usedused for Predicted Mean Vote (PMV) evaluation. for Predicted Mean Vote (PMV) evaluation.

ForFor the the purpose purpose of of computationally-efficient computationally-efficient control control input input allocation allocation optimisation, optimisation, the cabinthe cabin thermal thermal model model (Figure (Figure2, red 2, outline) red outline) is replaced is replaced with the with boundary the boundary conditions conditions that that determine the cabin air properties (Tcab and RHcab) and required thermal heating determine the cabin air properties (Tcab and RHcab) and required thermal heating power . power demand Q̇ hR, where the latter accommodates for various cabin thermal loads and demand QhR, where the latter accommodates for various cabin thermal loads and the heat transferredthe heat transferred into thermal into masses thermal [23 masses]. The [23]. airflow The distributionairflow distribution model inputs model related inputs tore- lated to cabin air properties (Tcab and RHcab) are defined by the same boundary conditions, cabin air properties (Tcab and RHcab) are defined by the same boundary conditions, while . while the blower fan air mass flow ṁbf and the inlet air temperature Tcab,in are provided by the blower fan air mass flow mbf and the inlet air temperature Tcab,in are provided by the HVACthe HVAC model. model. TheThe optimisationoptimisation model structure structure is is shown shown in in Figure Figure 3a.3a. The The considered considered HVAC HVAC con- trol inputs are (Figure 1): the low-temperature coolant pump speed np2, the high-temper- control inputs are (Figure1): the low-temperature coolant pump speed np2, the high- ature coolant pump speed np3, the main radiator fan power level setting P̅ rf and the blower temperature coolant pump speed np3, the main radiator fan power level setting Prf and the . fan air mass flow rate ṁbf, which is transformed to blower fan input voltage using polyno- blower fan air mass flow rate mbf, which is transformed to blower fan input voltage using mial functions Vbf = fbf−1(ṁbf, T−bf,in1 ) .as described in [23]. The radiator fan air mass flow and polynomial functions Vbf = fbf (mbf,Tbf,in) as described in [23]. The radiator fan air mass power consumption are determined by three discrete input settings P̅ rf ϵ {0, 0.5, 1} corre- flow and power consumption are determined by three discrete input settings P  {0, 0.5, sponding to different fan power levels (turned off, at half power, and at full power).rf The 1} corresponding to different fan power levels (turned off, at half power, and at full power). blower fan power consumption is described by a look-up table. Another HVAC control The blower fan power consumption is described by a look-up table. Another HVAC control input is the cabin inlet air temperature reference Tcab,in,R, which is feedback-controlled by input is the cabin inlet air temperature reference Tcab,in,R, which is feedback-controlled by varying the compressor speed. Other inputs include the ambient air temperature (Tamb) varying the compressor speed. Other inputs include the ambient air temperature (Tamb) and relative humidity (RHamb), as well as the cabin air properties inputs (Tcab, RHcab) that and relative humidity (RHamb), as well as the cabin air properties inputs (Tcab, RHcab) that replacereplace the the cabin cabin model, model, as as described described above above and and in in [ 23[23].]. TheThe cabin cabin airflow airflow distribution distribution model model control control inputs inputs include include the the driver-related driver-related IRP IRP cluster control settings uIRP,1 and uIRP,2, while other PMV calculation-related inputs are ob- cluster control settings uIRP,1 and uIRP,2, while other PMV calculation-related inputs are . tained from the HVAC model (q̇ bf and Tcab,in) and the cabin boundary conditions (Tcab and obtained from the HVAC model (qbf and Tcab,in) and the cabin boundary conditions (Tcab RHcab). The recirculation mode is set to fresh air mode and the ventilation mode corre- sponds to the above-described HEAT mode.

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Energies 2021, 14, 1203 6 of 24

and RHcab). The recirculation mode is set to fresh air mode and the ventilation mode corresponds to the above-described HEAT mode. TheThe relevant relevant outputs outputs are are the the total total po powerwer consumption of HVAC+IRP system Ptot andand driver’sdriver’s comfort comfort index PMV𝑃𝑀𝑉dr (Figure3 3a),a), where where the the former former is is expressed expressed as as (see (see Figure Figure1): 1): Ptot = PHVAC + PIRP (1) Ptot = PHVAC + PIRP (1) PHVAC = Pcom + Pbf + Prf + Pp2 + Pp3 (2) PHVAC = Pcom + Pbf + Prf + Pp2 + Pp3 (2) PIRP = PIRP1 + PIRP2 (3) PIRP = PIRP1 + PIRP2 (3) The power consumption of other, low-power, positioning HVAC actuators, such as The power consumption of other, low-power, positioning HVAC actuators, such as the EXV stepper motor and cabin air distribution flaps, is not modelled and, therefore, not theaccounted EXV stepper for. motor and cabin air distribution flaps, is not modelled and, therefore, not accountedThe driver’s for. comfort is evaluated by an arithmetic mean of the three individual body partThe PMV driver’s values comfort (head, torso, is evaluated legs): by an arithmetic mean of the three individual body part PMV values (head, torso, legs): 1 3 = 1 PMV𝑃𝑀𝑉dr = 𝑃𝑀𝑉∑ PMVi (4)(4) 33 i=1

FigureFigure 33bb showsshows the the driver’s driver’s mean mean PMV PMV map map obtained obtained for the for HEAT the HEAT ventilation ventilation mode, mode,driving driving activity activity (metabolic (metabolic rate of rate 1.2), of typical 1.2), typical winter clothingwinter clothing factor of factor 1.2, and of 1.2, with and no withuse ofno IRPs use (i.e.,of IRPs the (i.e., mean the radiant mean temperatureradiant temperature is equal tois equal the cabin to the air cabin temperature). air tempera- The ture). The driver’s PMV is primarily determined by the cabin air temperature Tcab and the driver’s PMV is primarily determined by the cabin air temperature Tcab and the blower . blower fan volumetric flow q̇ bf, while the effect of cabin air relative humidity RHcab is of fan volumetric flow qbf, while the effect of cabin air relative humidity RHcab is of minor minorinfluence. influence. For the For particular the particular CFD model-based CFD model-based look-up look-up tables, thetables, ideal the thermal ideal thermal comfort comfort(PMV = ( 0)PMV is achieved = 0) is achieved at around at around 22.5 ◦C, 22.5 while °C, the while comfortable the comfortable range(| rangePMV (||PMV < 0.5)| is< 0.5)achieved is achieved for the for cabin the aircabin temperatures air temperatures lying between lying between 19 ◦C and 19 °C 24 and◦C for 24 moderate°C for moderate blower blowerair mass air flows. mass flows.

FigureFigure 3. 3. SystemSystem model model used used within within optimisation optimisation framework framework (a) and (a) anddriver’s driver’s average average thermal thermal comfortcomfort index index (PMV) (PMV) map map in in dependence dependence of of cabin cabin air air temperature temperature and and inlet inlet air air mass mass flow flow rate rate ( (b).).

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3. Control Input Optimisation Framework The control input optimisation framework has been built around the one developed in [23], where the main extension relates to incorporating the IRPs model and controls.

3.1. General Aim The optimisation is aimed at obtaining optimal control input allocation maps, which minimise total power consumption while maintaining high passenger thermal comfort. As a part of the hierarchical control strategy (see Section5 and [ 23] for details), the op- . timised allocation maps transform the heating power demand QhR, commanded by a superimposed cabin air temperature controller, to low-level controller inputs/references for the given cabin air conditions (Tcab and RHcab). As described in Section2 and [ 23], the above formulation of allocation optimisation problem allows for omitting the passenger cabin dynamics model, thus, leading to a straightforward and computationally efficient optimisations [23]. It should be noted that strictly speaking the optimal allocation ensures optimal control system performance only for quasi-steady-state operation, under which the actual HVAC variables (e.g., Tcab,in) accurately follow the optimal allocation commands (e.g., Tcab,in,R). This is not a major constraint since the (quasi)-stationary HVAC operation usually has a dominant influence on power consumption, because its share of a driving cycle is typically dominant over distinct transient operation (e.g., heat-up transient for which Tcab,in can considerably differ from Tcab,in,R due to HVAC system thermal inertia) [23].

3.2. Objectives and Constraints The optimisation problem is to find an optimal set of control inputs, which simultane- ously minimises the following conflicting optimisation objectives: the total actuator power consumption (J1) and the absolute value of driver’s mean PMV (J2):

J1 = min(Ptot) (5)  J2 = min PMVdr (6)

The control inputs are the cabin inlet air temperature reference Tcab,inR, the radiator fan setpoint Prf, two pump speeds np2 and np3, and the IRP control level settings uIRP1,2 (see Figure3a and also blue box in Figure4). For the optimised control inputs, the blower . fan air mass flow rate mbf can be determined directly from the following relation:

. . QhR mb f = , (7) cp(Tcab,in,R − Tcab)

The cost functions J1 and J2 are subject to various hardware and controller setpoint tracking constraints. The control input constraints (left column of Table1) relate to ac- tuator hardware limits (those of pump speeds and IRP control level settings, as well as discrete states of radiator fan power setting) and software limits of cabin inlet air tem- perature reference for comfortable operation. Additional hardware-related constraints, such as compressor speed, EXV position, and blower fan control voltage limits, are not included in Table1, as they are realised within the HVAC model as saturations of low-level feedback controllers. The controller setpoint tracking constraints (right column of Table1) are applied to ensure that the reference values of cabin inlet air temperature and superheat temperature are achieved for the optimised set of control inputs under steady-state conditions. In both cases the temperature tracking error of up to 1 ◦C is tolerated, as defined in Table1. The third setpoint tracking constraint is related to the requested heating power, where the heating power error of 100 W is tolerated. Energies 2021, 14, 1203 8 of 24

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Table 1. Optimisation constraints.

Table 1.ControlOptimisation Input constraints. Constraints Setpoint Tracking Constraints 40°≤ CT ≤ 65 ° C Controlcab,, Input in R Constraints Setpoint Tracking Constraints ≤≤ Δ−Δ<°TT1C 1600 rpm◦ np2 8000 rpm◦ SH, R SH 40 C ≤ Tcab,in,R ≤ 65 C ◦ ≤≤ −<°|∆TSH,R − ∆TSH| < 1 C 16001600 rpm rpm n≤p3np2 8000≤ 8000 rpm rpm TT 1C ◦ cabinR,, T cabincab ,,in,R − Tcab,in < 1 C 1600 rpm ≤ n ≤ 8000 rpm . ∈{}p3 .  Prf 0, 0.5, 1 QmcT&QhR−−<−&mb f ,mc()p,a Tcab,in T− Tcab 100< W100 W Pr f ∈ {0, 0.5, 1} hR bf,, m p a cab , in cab ∈ uP1,2 [0,1]uP1,2 ∈ [0, 1]

3.3.3.3. Optimisation Optimisation Method Method OptimisationOptimisation of of HVAC HVAC control control inputs inputs has has been been carried carried out out by by using using a a multi-objective multi-objective geneticgenetic algorithm algorithm (GA) (GA) called called MOGA-II, MOGA-II, which which is is built built in in software software modeFrontier. modeFrontier. MOGA-II MOGA- employsII employs an an effective effective multi-search multi-search elitism elitism method method and and preserves preserves good good (Pareto (Pareto or or non-non- dominated) solutions without converging prematurely to a local optimum [28]. The dominated) solutions without converging prematurely to a local optimum [28]. The im- implemented workflow is shown in Figure4, with the MATLAB node placed at the centre. plemented workflow is shown in Figure 4, with the MATLAB node placed at the centre.

Figure 4. Optimisation framework implemented within ModeFrontier environment. Figure 4. Optimisation framework implemented within ModeFrontier environment.

TheThe MATLABMATLAB nodenode isis usedused asas anan intermediaryintermediary interface between the the Dymola Dymola simu- sim- ulationlation model model and modeFrontier. It It feeds the controlcontrol inputsinputs determineddetermined byby thethe GAGAto to DymolaDymola simulation simulation model model in in an an executable executable form, form, calculates calculates the the steady-state steady-state performance performance andand constraint-related constraint-related indices indices after after the the simulation simulation is is executed, executed and, and feeds feeds them them back back to to the the GA.GA. The The model model simulation simulation is is controlled controlled as as described described in in [ 29[29],], where where the the model model is is initialised initialised inin accordance accordance with with the the GA-set GA-set control control inputs inputs and and the the simulation simulation timetime isis set set to to be be large large enoughenough to to ensure ensure that that the the steady-state steady-state condition condition is is reached reached (1200 (1200 s). s). InIn this this study, study, the the initial initial design design of of experiments experiments for for the the GA GA is populated is populated with with 20 genera- 20 gen- tionserations of control of control input input values values obtained obtained using ausing quasi-random a quasi-random Sobol method Sobol method and optimisation and opti- runsmisation for 512 runs GA for iterations. 512 GA iterations. Execution Execution of such an of optimisation such an optimisation setup for setup a single for operat-a single . operating point defined by Tcab, RHcab, and Q̇ hR takes about 40 min when running on a PC ing point defined by Tcab, RHcab, and QhR takes about 40 min when running on a PC basedbased on on 3.5 3.5 GHz GHz Intel Intel Xeon Xeon central central processing processing unit unit and and when when using using three three parallel parallel design design evaluations.evaluations. The control input constraints from the left column of Table 1 are implemented in the form of limited GA search space. All optimisation inputs have continuous values between the set bounds, with the exception of the main radiator fan power settings where only

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The control input constraints from the left column of Table1 are implemented in the form of limited GA search space. All optimisation inputs have continuous values between the set bounds, with the exception of the main radiator fan power settings where only three distinct values are given to GA to choose from. The controller setpoint tracking constraints are implemented using the modeFrontier’s constraint node. The MOGA-II algorithm handles these hard constraints as soft constraints in the GA cost function by proportionally penalizing constraint violation [30]. The above described optimisation procedure has been repeated in a loop for the full . set of cabin air conditions and heating power demands (Tcab, RHcab, QhR). The considered operating set range, optimisation setting parameters and main simulation parameters are given in Table2. The following scenario is considered: the driver (with the metabolic rate activity of 1.2 and the clothing factor of 1.2) is the only passenger in the vehicle that ◦ is travelling at the velocity of 60 km/h and at the ambient temperature of Ta = −10 C. Without the loss of generality, the cabin relative humidity was kept at the value RHcab = 10%, which was obtained by open-loop simulations of cabin thermal dynamics model. Recall that the cabin air relative humidity has negligible impact on PMV thermal comfort index.

Table 2. Basic optimisation and simulation model setting parameters.

Parameter Value . Heating power demand grid QhR ∈ {1:0.5:6} kW ◦ Cabin air temperature grid Tcab ∈ {−10:5:25} C Cabin relative humidity RHcab = 10% ◦ Ambient conditions Tamb = −10 C, RHamb = 60%, pamb = 101.3 kPa Dassl solver tolerance 0.0001

4. Optimisation Results and Related Power Consumption Reduction Analysis 4.1. Optimisation Results Figure5 shows the optimisation results in the form of Pareto frontiers obtained for two characteristic scenarios: without (squares) and with use of IRPs (circles). These results show that by using IRPs (circles) it is possible to significantly improve the thermal comfort (the driver’s absolute mean PMV is reduced by around 1 to 1.5 point) in the cold ◦ cabin environment (below Tcab = 22 C) at the expense of somewhat increased power consumption. This is especially advantageous at cabin temperatures that marginally fall outside the comfortable PMV range (e.g., 15 ◦C, Figure5d), since using IRPs can bring the PMV into the comfort range in that case. On the other hand, the impact of solely HVAC system optimisation on the thermal comfort enhancement is marginal (squares in Figure5), i.e., there is a possibility to reduce the PMV by only up to 0.2 points. This is achieved by changing the cabin inlet air tempera- ture and flow rate, while satisfying Equation (7) (a more detailed discussion on the effect is given with Figure 7). Not only the thermal comfort improvement is marginal, but the power consumption needed to achieve this improvement is rather excessive, particularly . for high thermal energy demands QhR and low cabin air temperatures Tcab. Energies 2021, 14, 1203 10 of 24 Energies 2021, 14, 1203 10 of 24

FigureFigure 5.5. Comparison of multi-objective Pareto Pareto optimal optimal results results for for cases cases with with (circles) (circles) and and without without use of infrared heating panels (IRPs) (squares) at different cabin temperatures (a–f). use of infrared heating panels (IRPs) (squares) at different cabin temperatures (a–f).

FigureFigure6 6 showsshows the trade-off trade-off between between PMV PMV and and HVAC-only HVAC-only power power consumption. consumption. In Inthe the majority majority of cases of cases the HVAC the HVAC power power consumption consumption does not does depend not depend on the IRP on control the IRP controlinput (circles input (circlesin Figure in Figure6), i.e.,6 it), i.e.,coincides it coincides well with well the with minimum the minimum HVAC HVAC power power con- consumptionsumption obtained obtained for zero for zero IRP IRPcontrol control input. input. Only Onlyat the at low-PMV the low-PMV endpoints, endpoints, the opti- the optimisermiser chooses chooses to increase to increase the the HVAC HVAC power power consumption consumption to togain gain marginal marginal improvement improvement . of thermal comfort (see e.g., Tcab = −10 °C and Q̇ hR = 5.5 kW). This indicates that the HVAC of thermal comfort (see e.g., T = −10 ◦C and Q = 5.5 kW). This indicates that the HVAC and IRP controls can be effectivelycab decoupled withhR a very marginal effect on system per- and IRP controls can be effectively decoupled with a very marginal effect on system formance. The HVAC system should be optimised for minimum power consumption due performance. The HVAC system should be optimised for minimum power consumption to its marginal impact on PMV, while the IRPs should be used for improving the thermal due to its marginal impact on PMV, while the IRPs should be used for improving the comfort as much as needed due to its relatively minor effect on the total power consump- thermal comfort as much as needed due to its relatively minor effect on the total power tion (Figure 5). consumption (Figure5).

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FigureFigure 6.6. Pareto frontiers frontiers expressed expressed in in terms terms of ofHVAC-only HVAC-only power power consumption consumption for cases for cases with with (circles) and without use of IRPs (squares) at different cabin temperatures (a–f). (circles) and without use of IRPs (squares) at different cabin temperatures (a–f).

FigureFigure7 ,7, in in its its left left and and right right column, column, shows shows the the optimised optimised control control inputs inputs corresponding correspond- ing to the Pareto frontiers shown in Figure 5a (Tcab = −10◦ °C) and Figure 5e (Tcab = 20 °C),◦ to the Pareto frontiers shown in Figure5a ( Tcab = −10 C) and Figure5e ( Tcab = 20 C), respectively.respectively. Figure Figure7 a7a shows shows the the blower blower fan fan air air mass mass flow flow vs. vs. the the cabin cabin inlet inlet air temperatureair temper- . ature for different heating power demands Q̇ hR and the corresponding total power con- for different heating power demands QhR and the corresponding total power consumption sumption Ptot. At the considered low cabin air temperature, the spread of cabin inlet air Ptot. At the considered low cabin air temperature, the spread of cabin inlet air temperatures temperatures and blower fan air mass flows for the case of no infrared panels used is and blower fan air mass flows for the case of no infrared panels used is rather wide. The rather wide. The lowest power consumption is achieved at the left end points (low inlet lowest power consumption is achieved at the left end points (low inlet temperature/high temperature/high mass flow; see squares in Figure 7a), while the maximum comfort (and mass flow; see squares in Figure7a), while the maximum comfort (and the highest power the highest power consumption) is achieved with low air mass flow and high inlet tem- consumption) is achieved with low air mass flow and high inlet temperature (star symbols). perature (star symbols). The optimisation results for the case of infrared panels included The optimisation results for the case of infrared panels included (diamonds) are mostly (diamonds) are mostly grouped around the lowest total power consumption end (low in- grouped around the lowest total power consumption end (low inlet temperature/high let temperature/high mass flow). mass flow). The optimised and condenser pump speed control inputs np2 and np3 are The optimised evaporator and condenser pump speed control inputs np and np are given in Figure 7b,c, respectively. Higher pump speeds are preferred for better2 thermal3 given in Figure7b,c, respectively. Higher pump speeds are preferred for better thermal

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. comfort for most of the heating power demands Q . However, this increase in pump comfort for most of the heating power demands Q̇ hRhR. However, this increase in pump speedsspeeds has has a a major major impact impact on on the the HVAC HVAC powe powerr consumptions, consumptions, since since it itcorrelates correlates with with higher cabin inlet air temperatures and, thus thus,, higher speeds of the compressor as the largestlarg- estHVAC HVAC consumer. consumer. TheThe optimised optimised radiator radiator fan fan control control input input plot plot is is shown shown in in Figure Figure 7d.7d. The The radiator radiator fan fan is turned off for the majority of operating points, while half or full power is demanded only is turned off for the majority of operating. points, while half or full power is demanded onlyat high at high heating heating power power demands demandsQhR, withQ̇ hR, with an exception an exception of heating of heating demands demands of 2000 of W2000 and W2500 and W 2500 and W the and maximum the maximum comfort comfort case. case. For theFor consideredthe considered constant constant vehicle vehicle velocity veloc- of ity60 km/h,of 60 km/h, this meansthis means that thethat rammingthe ramming air mass air mass flow flow through through the mainthe main radiator radiator is high is highenough enough for sufficient for sufficient thermal thermal energy energy exchange. exchange.

Figure 7. 7. OptimisedOptimised control control inputs inputs corresponding corresponding to Pareto to frontiers Paretofrontiers from Figure from 5a ( Figurea–d, T5caba = ( a–d, −10 °C) and◦ Figure 5e (e–h, Tcab = 20 °C). ◦ Tcab = −10 C) and Figure5e ( e–h, Tcab = 20 C).

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Figure 7e shows the blower fan air mass flow vs. the cabin inlet air temperature for Figure7e shows the blower fan air mass flow vs. the cabin inlet air temperature for the near-neutral comfort cabin temperature of 20 °C. The trade-off between cabin inlet air the near-neutral comfort cabin temperature of 20 ◦C. The trade-off between cabin inlet mass flow and temperature is narrower compared to low cabin air temperature, and the air mass flow and temperature is narrower compared to low cabin air temperature, and theminimum minimum total total power power consumption consumption is achieved is achieved at lower at lower air mass air mass flow flow rate, rate, unlike unlike at low at lowcabin cabin air temperature. air temperature. Similarly, Similarly, the the spread spread of of pump pump speeds speeds is is narrower narrower (Figure (Figure 77f,g),f,g ), whichwhich is connected with with the the narrower narrower spread spread of of inlet inlet air air temperatures. temperatures. The The ramming ramming air airmass mass flow flow through through the themain main radiator radiator is sufficient is sufficient for the for conditions the conditions of high of highcabin cabin air tem- air temperatureperature and and the theradiator radiator fan fancontrol control input input is set is setto zero to zero (Figure (Figure 7h).7h). TheThe optimised IRP IRP control control input input plots plots are are sh shownown in in Figure Figure 8,8 ,again again for for the the cabin cabin air airtemperatures temperatures of − of10 −°C10 and◦C 20 and °C. 20 The◦C. total The consumption total consumption of the two of the IRP two clusters IRP clusters (colour axis) is subject to both IRP control inputs (uIRP1 and uIRP2) and the local (cabin) air temper- (colour axis) is subject to both IRP control inputs (uIRP1 and uIRP2) and the local (cabin) air temperature.ature. To achieve To achieve the IRP the control IRP control input-dema input-demandednded target target radiant radiant surface surface temperature temperature at atthe the lower lower cabin cabin air air temperature, temperature, the the IRPs IRPs require require greater greater input power whenwhen comparedcompared withwith warmwarm cabincabin airair temperaturetemperature (cf.(cf. leftleft andand rightright columnscolumns ofof FigureFigure8 8).). ThisThis is is due due to to convectiveconvective thermalthermal heatheat exchangeexchange ofof IRPIRP surfacesurface withwith thethe surroundingsurrounding air.air. AsAs discusseddiscussed withwith FigureFigure5 5,, increasing increasing IRP IRP control control input input (and (and consequently consequently the the IRP IRP powerpower consumption)consumption) results results in in reduced reduced PMV, PMV, i.e., i.e., improved improved thermal thermal comfort. comfort. The The spread spread of PMVof PMV values values at aat given a given IRP IRP control control input input level level (vertical (vertical spread spread in eachin each subplot subplot of Figureof Figure8 ) can8) can be be explained explained by by the the fact fact that that the the Cluster Cluster 1 (chest1 (chest and and head; head;u IRPuIRP11)) andand ClusterCluster 22 (legs;(legs; uuIRPIRP22)) can can operate operate at at different different control control input input settings. settings. ◦ AtAt thethe lowlow cabincabin airair temperaturetemperature ( T(Tcabcab == −1010 °C),C), the the maximum maximum comfort (star symbols) isis achievedachieved for for both both panels panels operating operating at at the th maximume maximum IRP IRP control control input. input. At At the the near-neutral near-neu- ◦ cabintral cabin temperature temperature (Tcab =(T 20cab C),= 20 the °C), maximum the maximum (lumped (lum PMV-based)ped PMV-based) comfort iscomfort achieved is byachieved setting theby IRPsetting control the inputsIRP control to approximately inputs to 25%approximately and 50% for 25% the head/chest and 50% andfor legthe area,head/chest respectively. and leg area, respectively.

FigureFigure 8. OptimisedOptimised IRP IRP control control inputs inputs corresponding corresponding to Pareto to Pareto frontiers frontiers from from Figure Figure 5a (a5,ba, (Tacab,b =, ◦ ◦ T−cab10 =°C)− 10and C)Figure and Figure5e (c,d5, eT (cabc ,=d 20, T cab°C).= 20 C).

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Energies 2021, 14, 1203 14 of 24 4.2. Power Consumption Reduction Analysis The Pareto optimal results presented in Section 4.1 have indicated that HVAC and IRP4.2. controlPower Consumption actions for Reduction a given cabin Analysis air temperature and heating demand are strongly decoupled,The Pareto where optimal the HVAC results system presented should in beSection tuned 4.1 for have minimum indicated power that consumption HVAC and whileIRP control the IRPs actions should for be a adjusted given cabin for favourable air temperature thermal and comfort. heating This demand opens theare possibilitystrongly ofdecoupled, reducing where the total the powerHVAC consumption system should by be reducing tuned for the minimum cabin air power temperature consumption target belowwhile the nominalIRPs should one be and adjusted compensating for favourable for the lossthermal of thermal comfort. comfort This opens by engaging the possi- the IRPsbility [ 17of]. reducing The optimisation the total power results consumption are further analysed by reducing for steady-state the cabin air conditions temperature to verify tar- if this possibility is viable. get below the nominal one and compensating for the loss of thermal comfort by engaging◦ The considered scenarios relate to the cabin air temperatures Tcab = 15 C and the IRPs ◦[17]. The optimisation results are further analysed for steady-state conditions to Tcab = 20 C and the cases with and without the use of IRPs, respectively. In Section 4.1, the verify if this possibility is viable. . optimisationThe considered results are scenarios presented relate for to a widethe cabin range air of temperatures heating demands Tcab = Q15hR °C, thus, and T coveringcab = 20 the transient and steady-state conditions for proper control strategy formulation. In order °C and the cases with and without the use of IRPs, respectively.. In Section 4.1, the optimi- ̇ tosation obtain results steady-state are presented condition-related for a wide range values of heating of QhR, closed-loopdemands QhR simulations, thus, covering of cabin the . thermaltransient model and steady-state (with no solar conditions load) have for proper been conducted, control strategy which formulation. gives QhR = In 1033 order W to for . obtain steady-state◦ condition-related values of◦ Q̇ hR, closed-loop simulations of cabin ther- Tcab = 15 C and QhR = 1201 W for Tcab = 20 C. The thermal comfort of |PMVdr|= 0.36 mal model (with no solar◦ load) have been conducted, which gives Q̇ hR = 1033 W for Tcab = obtained at Tcab = 20 C is taken as the setpoint for determining the IRP control input at 15 °C and◦ Q̇ hR = 1201 W for Tcab = 20 °C. The thermal comfort of |𝑃𝑀𝑉dr|= 0.36 obtained at Tcab = 15 C, both based on optimisation results. Tcab =Figure 20 °C9 isa,b taken show as the the Pareto setpoint optimal for determining fronts, which the areIRP redrawn control input from Figureat Tcab =5 d,e15 °C, for both based on optimisation .results. . the heating power values Q = 1000 W and Q = 1500 W in a form with substituted Figure 9a,b show the ParetohR optimal fronts, hRwhich are redrawn from Figure 5d,e for x-axis and colour bar. The total power consumptions for the aforementioned, steady-state . Q̇ Q̇ . the heating power values hR = 1000 W and hR = 1500◦ W in a form with substituted x◦-axis heating power values QhR = 1033 W for Tcab = 15 C and QhR = 1201 W for Tcab = 20 C are and colour bar. The total power consumptions for the aforementioned,. steady-state heat- calculateding power byvalues linear Q̇ hR interpolation = 1033 W for of Tcab the = 15 charts °C and corresponding Q̇ hR = 1201 W to forQ hRTcabof = 100020 °C and are 1500calcu- W forlated the by comfort linear interpolation level |PMV ofdr |the= 0.36charts (see corresponding horizontal lines to Q̇ hR and of 1000 hollow and star1500 symbols W for the in Figurecomfort9a,b). level |𝑃𝑀𝑉dr|= 0.36 (see horizontal lines and hollow star symbols in Figure 9a,b). FigureFigure9 9cc showsshows thethe obtainedobtained powerpower consumptionsconsumptions for different scenarios and the the samesame thermalthermal comfortcomfort level. The The total total powe powerr consumption consumption (green (green bars) bars) at at the the reduced reduced ◦ cabincabin temperaturetemperature of 15 °CC and IRPs engaged is is almost almost 20% 20% lower lower than than at at the the cabin cabin air air ◦ temperaturetemperature ofof 2020 °CC and convective heating heating only. only. This This is is because because the the saving saving in in HVAC HVAC ◦ powerpower consumptionconsumption whenwhen reducingreducing thethe targettarget cabin cabin air air temperature temperature to to 15 15 C°C (blue (blue bars) bars) is greateris greater than than extra extra power power consumption consumption taken taken by by IRPs IRPs in in that that case case (red (red bars). bars).

FigureFigure 9.9. PowerPower consumption reduction analysis (c) based on optimisation results results ( (a,,b)) for for the the same thermalsame thermal comfort comfort level andlevel different and different cabin cabin air temperatures air temperatures under under steady-state steady-state conditions. conditions.

5.5. SimulationSimulation Results 5.1.5.1. ControlControl Strategy OptimisationOptimisation results results presented presented in inthe the prev previousious section section demonstrated demonstrated that HVAC that HVAC and andIRP IRPcontrols controls are effectively are effectively decoupled. decoupled. Theref Therefore,ore, the HVAC the HVAC control control strategy strategy can be based can be on the hierarchical structure proposed in [20] and refined in [23], with the control input

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Energies 2021, 14, 1203 15 of 24 based on the hierarchical structure proposed in [20] and refined in [23], with the control input allocation maps set for minimal HVAC power consumption. Such HVAC control system is shown in Figure 10 and extended with IRP control based on PMV feedback for allocationimproved maps comfort. set for minimal HVAC power consumption. Such HVAC control system is shownThe high-levelin Figure 10 HVAC and controlextended subsystem with IRP consistscontrol ofbased a superimposed on PMV feedback cabin airfor tem-im- provedperature comfort. controller and optimal HVAC control input allocation maps. A superimposed PI controller regulates the cabin air temperature Tcab by commanding the heating power The high-level. HVAC control subsystem consists of a superimposed cabin air tem- peraturedemand controllerQhR. The and heating optimal power HVAC demand control is limitedinput allocation based on maps. time-varying A superimposed maximum PI controllerfeasible heating regulates power the cabin for the air given temperature cabin air T temperaturecab by commanding and relative the heating humidity, power which de- mandis obtained Q̇ hR. The from heating the optimisation power demand results is andlimited implemented based on time-varying in the form of maximum a look-up feasi- table. The optimal HVAC control input allocation maps are implemented in the form of look-up ble heating power for the given cabin air temperature and relative. humidity, which is obtainedtables with from the the cabin optimisation air temperature resultsTcab andand implemented heating demand in theQhR formused of as a thelook-up map inputs.table. TheThese optimal look-up HVAC tables control are obtained input directlyallocation from maps optimisation are implemented results presented in the form in Sectionof look-4 upby choosingtables with the the design cabin that air correspondstemperature toTcab minimal and heating HVAC demand powerconsumption Q̇ hR used as the (see map [23] inputs.for details These of allocationlook-up tables map generation).are obtained directly from optimisation results presented in SectionThe 4 by cabin choosing air inlet the temperaturedesign that corr andesponds the superheat to minimal temperature HVAC power are controlledconsumption by (seePI controllers, [23] for details which of allocation are given map in a generation). modified form with the P action moved into the feedbackThe cabin path. air All inlet of the temperature PI controllers and are the extended superheat with temperature gain-scheduling are controlled maps and by anPI controllers,anti-windup which algorithm. are given The in gain-schedulinga modified form with maps the of P low-level action moved controllers into the have feedback been designed based on the controller parameter optimisation method described in [20] and [23], path. All of the PI controllers are extended with. gain-scheduling maps and an anti- windupand they algorithm. involve the The heating gain-scheduling power demand maps ofQ low-levelhR and cabin controllers temperature have beenTcab asdesigned inputs. ◦ basedThe superheat on the controller temperature parameter reference optimisation∆TSH,R is typically method set described to a fixed in value [20] and (5 C, [23], herein). and theyAdditionally, involve the pressure heating limit power controllers demand of Q Ṗ hR type and are cabin added temperature to reduce T compressorcab as inputs. speed The superheatif the compressor temperature outlet reference pressure Δ orTSH,R the is compressor typically set outlet/inlet to a fixed value pressure (5 °C, ratio herein). exceeds Ad- a ditionally,certain safety pressure threshold. limit controllers of P type are added to reduce compressor speed if the compressorThe PMV feedbackoutlet pressure controller or the commands compressor the outlet/inlet driver-side pressure IRP control ratio exceeds setting. a Thecer- taincontroller safety isthreshold. of a proportional type with a dead-zone and output saturation, as described by: The PMV feedback controller commands the driver-side IRP control setting. The con-  sat(k e , u ), for e > ∆PMV > 0 troller uis of a= proportionalPMVi typePMV withIRP a dead,max -zone andPMV output saturation,, asi ∈described[1, 2] by:(8) IRPi 0, otherwise sat𝑘𝑒,𝑢,, for 𝑒 > Δ𝑃𝑀𝑉>0 𝑢 = , 𝑖 ∈ [1, 2] (8) where ePMV = PMVR − |PMVdr| is0, the otherwise driver’s absolute mean PMV error (which is positive for cold conditions, see Figure3), PMV is the PMV reference (set to the ideal where ePMV = PMVR − |𝑃𝑀𝑉dr| is the driver’s absoluteR mean PMV error (which is positive value of zero), kPMV is the PMV controller gain, uIRP,max is IRP control setting limit (set to for cold conditions, see Figure 3), PMVR is the PMV reference (set to the ideal value of 1 or 100%), and ∆PMV is the PMV control error threshold for turning off the IRPs (set to zero), kPMV is the PMV controller gain, uIRP,max is IRP control setting limit (set to 1 or 100%), 0.5, herein). and ΔPMV is the PMV control error threshold for turning off the IRPs (set to 0.5, herein).

FigureFigure 10. 10. OverallOverall hierarchical hierarchical structure structure of of HVAC HVAC co controlntrol system system including including decoupled decoupled IRP-based IRP-based PMV controller. PMV controller.

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5.2. Simulation Analysis of IRP-Based Steady-State Power Consumption Reduction Potential The potential of employing IRP heating for powerpower consumptionconsumption reduction while maintaining the thermal comfort has been investigated in more detail using the overalloverall simulation model consisting of of plant plant model model (Section (Section 22)) andand controlcontrol strategystrategy ((SectionSection 5.1).5.1). Similarly, as in the case of optimisation-based analysis, the steady-state operation is is con- sidered. In In the first first scenario, the difference between the cabin air temperature targets of ◦ HVAC-only and HVAC+IRP systems is kept at the constant value of 5 °C.C. In the secondsecond ◦ scenario, the cabin air temperature target is setset to the fixed,fixed, high-comforthigh-comfort value of 2222 °CC for the the HVAC-only HVAC-only system, system, while while in in the the HVAC+I HVAC+IRPRP system system the the target target temperature temperature is re- is ◦ ◦ ◦ ducedreduced from from 22 22 °CC in in increments increments of of 1 1 °CC down down to to 14 14 °C.C. The The PMV PMV reference (PMV R)) of the HVAC+IRP system is set to the value obtained in the HVAC-only HVAC-only case, in order to provide a fair power consumption comparison for the two cases. The ambient conditions and other parameters remain the same as in the optimisation studystudy fromfrom SectionSection4 4.. Figure 11 shows the simulation results obta obtainedined in in the the first first scenario, scenario, where where the the tem- tem- ◦ perature target difference equals 5 °C.C. Figure 11a11a indicates that both total and HVAC power consumptions,consumptions, withwith oror without without IRP IRP heating, heating, increase increase with with the the cabin cabin air air temperature tempera- T , which is due to increased cabin thermal load. On the other hand, the IRP power turecab Tcab, which is due to increased cabin thermal load. On the other hand, the IRP power consumption is largely independent of cabin temperature. The thermal comfort is best consumption is largely independent of cabin temperature. The thermal◦ comfort is best (PMV is close to 0) at the HVAC-only systemsystem cabincabin temperaturetemperature ofof 2222 °CC (see Figure 1111bb and cf. Figure 33).). ForFor allall consideredconsidered cabincabin airair temperatures,temperatures, thethe useuse ofof IRPIRP heatingheating resultsresults in power consumption reduction by roughly 300–400 W or 26–32%. In the best thermal in power consumption reduction by roughly 300–400 W or 26–32%. In the best thermal comfort point, the power consumption saving is 360 W or 28.6%. comfort point, the power consumption saving is 360 W or 28.6%.

Figure 11. Simulation results of HVAC-only and HVAC+IRPHVAC+IRP systems for scenario ofof constantconstant cabin cabinair temperature air temperature target target difference difference of 5 ◦C. of 5 °C.

Figure 12 shows the results obtained for the second scenario characterised by the best ◦ thermal comfort setting of HVACHVAC onlyonly systemsystem ((TTcabcab = 22 °C).C). Figure 12a12a indicates that the total power consumption of HVAC+IRP system decreases with the fall of correspondingcorresponding cabin airair temperaturetemperature target, target, as as it it is is associated associated with with the the fall fall of cabin of cabin thermal thermal load load and, thus,and, thus,the HVAC the HVAC power power consumption. consumption. However, However, the decreasing the decreasing cabin target cabin temperature target temperature requires requireshigher IRP higher power IRP consumption power consumption (Figure 12 a)(Figure to maintain 12a) to the maintain thermal comfortthe thermal (Figure comfort 12b), ◦ which(Figure is 12b), feasible which up tois feasible the temperature up to the target temp differenceerature target of 6 differenceC; otherwise, of 6 the°C; IRPotherwise, power

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thesaturates, IRP power and saturates, the thermal and comfort the thermal degrades. comfort The degrades. total power The consumptiontotal power consumption saving due to the use of IRP heating is 150 W or 12% for the temperature target difference of 2 ◦C, saving due to the use of IRP heating is 150 W or 12% for◦ the temperature target difference ofand 2 °C, 420 and W or 420 34% W foror the34% temperature for the temperatur differencee difference of 6 C. Althoughof 6 °C. Although the thermal the comfortthermal decreases towards cold when the temperature difference is increased beyond 6 ◦C, it still comfort decreases towards cold when the temperature difference is increased beyond 6 remains within the comfortable range PMV > −0.5 for the cabin air temperature of 14 ◦C, °C, it still remains within the comfortable range PMV > −0.5 for the cabin air temperature for which the power consumption reduction is 540 W or over 40%. of 14 °C, for which the power consumption reduction is 540 W or over 40%.

Figure 12. SimulationSimulation results of HVAC-only andand HVAC+IRPHVAC+IRP systems systems for for scenario scenario of of increasing increasing cabin cabinair temperature air temperature target target difference. difference.

5.3. Heat-up Heat-Up Scenario Scenario Simulation Simulation Results Results The IRP-based IRP-based power power consumption consumption reduction reduction analysis analysis presented presented in inSection Section 5.2 5.2is re- is latedrelated to tosteady-state steady-state conditions. conditions. Another Another opportunity opportunity of of improving improving the the system system efficiency efficiency based on IRP useuse correspondscorresponds toto heavy heavy transient transient conditions, conditions, such such as as those those occurring occurring during dur- ingthe the heat-up heat-up process process from from a low a low ambient ambient temperature. temperature. In the In particular the particular heat-up heat-up simulation simu- test, the cabin and HVAC system are initialised with respect to ambient conditions given lation test, the cabin◦ and HVAC system are initialised with respect to ambient conditions by Tamb = −10 C and RHamb = 60%, and the goal is to reach the cabin air temperature given by Tamb = −10 °C◦ and RHamb = 60%, and the goal is to reach the cabin air temperature setpoint Tcab,R = 22.5 C in 10 min. The vehicle velocity is set to 60 km/h and no solar load setpoint Tcab,R = 22.5 °C in 10 min. The vehicle velocity is set to 60 km/h and no solar◦ load is set. In the case of using IRPs, the case of reduced target temperature (Tcab,R = 17.5 C) is is set. In the case of using IRPs, the case of reduced target temperature (Tcab,R = 17.5 °C) is additionally considered. additionally considered. In all cases, the considered control performance metrics (Table3) include: In all cases, the considered control performance metrics (Table 3) include: • Total energy consumed (Eel); • Total energy consumed (Eel); • Two thermal comfort indices: (i) time to reach the comfortable range defined by • Two thermal comfort indices: (i) time to reach the comfortable range defined by |PMVdr | < 0.5 (tPMV,05), and (ii) integral of absolute value of mean PMV in uncom- |𝑃𝑀𝑉dr | < 0.5 (tPMV,05), andR (ii) integral of absolute value of mean PMV in uncomfort- fortable range C2 [min] = |PMVdr|/60 dt, if |PMVdr| > 0.5 [20]. able range C2 [min] = ∫|𝑃𝑀𝑉dr|/60 dt, if |𝑃𝑀𝑉dr| > 0.5 [20]. Figure 13 shows the comparative heat-up simulation results for the HVAC-only and Figure 13 shows the comparative ◦heat-up simulation results for the HVAC-only and HVAC+IRP systems for Tcab,R = 22.5 C. Since the cabin air temperature is not affected HVAC+IRP systems for Tcab,R = 22.5 °C. Since the cabin air temperature is not affected by by the IRPs, its response and the response of allocated HVAC control inputs are the the IRPs, its response and the response of allocated HVAC control inputs are the same for same for both systems. The cabin inlet air temperature reaches the value of 40 ◦C in both systems. The cabin inlet air temperature reaches the value of 40 °C in approximately approximately 4 min and approaches its reference value in 6 min (Figure 13a, blue and 4red min lines). and approaches During this its transient, reference the value compressor in 6 min speed(Figure is 13a, saturated blue an (Figured red lines). 13e) andDuring the thispower transient, consumption the compressor (Figure 13 speedh) is significantlyis saturated (Figure increased 13e) compared and the power to that consumption occurring in (Figurethe steady-state 13h) is significantly condition (i.e.,increased in the compared final stage to of that response). occurring For in thethe samesteady-state reason, con- the dition (i.e., in the final stage of response). For the same reason, the actual heating power

Energies 2021, 14, 1203 18 of 24

actual heating power differs from the demanded heating power (Figure 13c), and, therefore, the optimal allocation may be suboptimal during the transient phase. In both cases, the cabin air temperature reaches 22 ◦C in 10 min (green plot in Figure 13a). However, it takes around 8 min for thermal comfort (Figure 13g) to reach the comfortable range (|PMV| < 0.5) in the HVAC-only case (dashed line), while when employing IRP heating the comfort range is reached in 5 min. The IRP control inputs are initially saturated to their maximum value (Figure 13d) and they then decrease as the PMV is approaching its target (zero) value (Figure 13g). The saturated IRP control inputs corresponds to the maximum IRP target temperatures of 60 ◦C for Cluster 2 (legs) and 80 ◦C for Cluster 1 (head and chest; Figure 13b). The panels have certain thermal inertia and it takes them around 3 min to reach 45 ◦C and 6 min to reach 60 ◦C. Moreover, once the IR panels are turned off, their temperature slowly decreases due to slow convection cooling by cabin air. During the transient stage, the total power consumption is increased by 500 W when using the IRPs (Figure 13h). Nevertheless, the indices listed in Table3 under Case 2 indicate that the total energy consumption is only 9% higher, while the cumulative thermal comfort index C2 is reduced by 23% and the time to reach the comfortable PMV range is decreased by 36%. The remaining allocated control inputs are dependent on the heating power demand and the cabin air temperature. The pump speeds (Figure 13e) are increased at the start and decrease once the steady-state condition is reached. Similarly, the blower fan (Figure 13f) is high at the start to achieve greater heating power demand. The radiator fan (Figure 13f) is mostly turned-off for the considered velocity of 60 km/h (cf. Figure7g). Table3 also shows the comparison of thermal comfort and energy consumption indices for the case of reduced target cabin air temperatures of 17.5 ◦C. Setting the lower cabin air temperature reference reduces energy consumption by 21% in the HVAC only case (Case 3), but results in the worst thermal comfort performance—thermal comfort range is not reached. When adding IRP heating (Case 3), the thermal comfort remains similar or even better than in Case 2, but the energy consumption is now reduced by (6 + 9)/109 = 14%.

Table 3. HVAC system performance indices obtained from heat-up scenario simulation results.

Case Tcab,R [degC] IRP Eel [Wh] tPMV,05 [s] C2 [min] 433.4 493 23 1 22.5 w/o IRP (0%) (0%) (0%) 473.1 314 17.8 2 22.5 w/IRP (+9%) (−36%) (−23%) 341.1 N/A 31.0 3 17.5 w/o IRP (−21%) (+35%) 407.9 315 15.9 4 17.5 w/IRP (−6%) (−36%) (−31%) Energies 2021, 14, 1203 19 of 24 Energies 2021, 14, 1203 19 of 24

Figure 13. Comparative heat-up responsesresponses ofof HVAC-onlyHVAC-only system system (solid (solid line) line) and and HVAC+IRP HVAC+IRP system sys- (dashedtem (dashed line) line) for target for target cabin ca airbin temperature air temperature of 22.5 of ◦22.5C. °C.

6. Discussion The presented optimisation and simulation results results indicate indicate that that HVAC HVAC and IRP con- con- trols can effectively be decoupled, where th thee HVAC controlcontrol systemsystem shouldshould bebe optimisedoptimised for best efficiency,efficiency, whilewhile thethe IRPIRP heatingheating improvesimproves thethe thermalthermal comfort.comfort. The benefitsbenefits of thermal comfort improvement are present under both steady-state and transient (heat-up) conditions. In the former case, IRP heating allows for reducing the cabin air temperature conditions. In the former case, IRP heating allows for reducing the cabin air temperature reference for the HVAC system without compromising thermal comfort, thus, resulting in reference for the HVAC system without compromising thermal comfort, thus, resulting considerable energy savings (around 350 W or 30% for the particular system). In the latter in considerable energy savings (around 350 W or 30% for the particular system). In the case, the IRPs can improve thermal comfort by locally heating the passenger compartment latter case, the IRPs can improve thermal comfort by locally heating the passenger com- until the slower, HVAC system reaches regular operation. partment until the slower, HVAC system reaches regular operation. The proposed IRP controller relies on PMV feedback, which cannot be directly mea- The proposed IRP controller relies on PMV feedback, which cannot be directly meas- sured. For in-vehicle implementation, the PMV should be estimated from available mea- ured. For in-vehicle implementation, the PMV should be estimated from available meas- surements based on available sensors (see Section 2.1. for details) such as cabin air temper- urements based on available sensors (see Section 2.1. for details) such as cabin air temper- ature and relative humidity and cabin inlet air temperature and flow. This requires special ature and relative humidity and cabin inlet air temperature and flow. This requires special attention and calibration due to (i) unmeasurable factors such as passenger’s activity and attentionclothing, whichand calibration should be due carefully to (i) unmeasurable set based on season factors or such ambient as passenger’s temperature; activity (ii) lack and of clothing, which should be carefully set based on season or ambient temperature; (ii) lack

Energies 2021, 14, 1203 20 of 24

the air velocity measurement, which should be replaced by an estimate determined from the commanded blower air mass flow, air distribution flap positions and calibrated air flow distribution models; and (iii) lack of mean radiant temperature, which should then be estimated from available air temperature sensors and calibrated 3D cabin models. When multi-zone heating is considered, PMV should be estimated locally, and localised PMV control should be implemented taking into account different passengers’ preferences. Vehicle velocity and ambient air conditions could potentially impact the performance of the HVAC system. The presented optimization results were obtained for the fixed values of vehicle velocity vveh = 60 km/h and ambient air conditions (Tamb = −10, RHamb = 60%). However, the optimisation method is readily applicable for any external conditions, and the input parameter space can be extended with additional ‘disturbance’ inputs such as vehicle velocity or ambient air temperature. A preliminary study on ‘disturbance’ inputs influence has been conducted, and the results point out that varying the ambient relative humidity has no impact on the HVAC system, while varying the ambient air temperature and vehicle velocity have a marginal influence on allocation maps. Namely, varying vehicle velocity changes ramming air flow through the main radiator and in turn changes the total air flow. However, it is possible to empirically correct radiator fan power level with respect to vehicle velocity to counteract for this disturbance effect. Similarly, higher ambient air temperature slightly affects the cabin inlet air temperature reference, and this can also be accounted for through an empirical correction. Due to the thermal inertia of both HVAC and IRP system components, the control system could be extended with predictive information to anticipate the transient effects, especially slow cooling of IRPs when its command is set to zero. A method worth consider- ing is model predictive control, as it is capable of handling the process dynamics, limits, and predictive information. It should be noted that the HVAC system and airflow distribution models used in this study have been systematically built up, parameterised, and partly validated based on the available test bench data [25]. The models can be further refined/re-parameterised after performing in-vehicle tests if experimental results show considerable discrepancies with respect to simulation results. Similarly, the control strategy can be re-calibrated to improve the performance for final implementation. Experimental validation is an on-going activity conducted both in climate chambers with dynamometers and also through on-road tests, whose results and recommendations are subject of future publications. Finally, the optimisation and subsequent analyses were performed for extreme ambient conditions (−10 ◦C) where high power consumption occurs. The system should be tested and/or optimised in less severe ambient conditions to fully exploit the infrared panel heating control strategy.

7. Conclusions A multi-objective genetic algorithm-based method for obtaining optimal control inputs has been proposed and applied to an advanced battery electric vehicle HVAC system, equipped with infrared panels (IRP), for the heat pump operating mode. The obtained Pareto frontiers have indicated that HVAC and IRP control actions are effectively decoupled. The HVAC system should be controlled to achieve minimum power consumption, as its tuning has a relatively minor impact on thermal comfort both in heat pump and A/C mode (AppendixA); on the other hand, the IRP heating effectively improve thermal comfort with a modest effect on power consumption. Based on these findings, the hierarchical control strategy from [23] has been param- eterised and extended with a superimposed, proportional-like PMV controller acting through IRP control channel. The control strategy has been verified by simulation, both for various steady-state conditions and a heat-up transient scenario. The steady-state, simulation-based analysis has showed that decreasing the cabin air temperature target by 6 ◦C from the nominal target of 22 ◦C reduces the power consumption by 420 W or 35% and maintains the ideal thermal comfort, in extreme ambient conditions of −10 ◦C. Energies 2021, 14, 1203 21 of 24

Moreover, the results point out that IRPs can significantly improve driver’s thermal comfort during the heat-up transient, where the combined HVAC+IRP system reaches the comfortable range in 314 s (36% faster) compared to HVAC only case, where the comfort settling time is 493 s. This comfort improvement is at the expense of increased energy consumption by 9%. However, if the target cabin air temperature is reduced by 5 ◦C, the energy consumption can, in fact, be reduced by 6% without affecting the thermal comfort gain. The ongoing work includes experimental verification of the proposed control strategy, while the future work will concern development of model predictive controller to account for HVAC and IRP actuator transient behaviours, actuator limits, and possibly predictive information about various disturbances.

Author Contributions: Conceptualization, J.D., I.C. and I.R.; methodology, I.C., I.R. and J.D.; soft- ware, I.R. and I.C.; writing—original draft preparation, I.C. and I.R.; writing—review and editing, J.D.; visualization, I.R. and I.C.; supervision, J.D. All authors have read and agreed to the published version of the manuscript. Funding: The QUIET project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 769826. The content of this publication is the sole responsibility of the QUIET consortium partners and does not necessarily represent the view of the European commission or its services. Acknowledgments: It is gratefully acknowledged that the research work of the first author has been partly supported by the Croatian Science Foundation through the “Young researchers’ career development project-training of new doctoral students”. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

Abbreviation Description HVAC Heating, ventilation and VCC Vapour-compression cycle A/C Air conditioning EXV Electronic expansion valve CFD Computational fluid dynamics HC Heater core LTR Low temperature radiator IRP Infra-red panel PMV Predictive mean vote MOGA Multi-objective genetic algorithm

Nomenclature

Symbols Unit Description RH % Air relative humidity T ◦C Temperature . m kg/s Fluid mass flow rate n rpm Rotational speed P W Power consumption P - Discrete actuator power setting V V Voltage av - Electronic expansion valve steps . Q W Heat flow PMV - Mean PMV index −1 −1 cp Jkg K Isobaric specific mass capacity e - Control error k - PMV Controller proportional gain Eel Wh Total energy consumption Energies 2021, 14, 1203 22 of 24

Subscripts Description Subscripts Description amb Ambient SH superheat cab Cabin IRP Infra-red panel in Inlet veh Vehicle out Outlet met Metabolic rf Main radiator fan sol Solar bf Blower fan rec Recirculation p Coolant pump dr Driver com Compressor h Heating R reference

Appendix A Multi-objective optimisation of the HVAC control input allocation maps has also been carried for the air-conditioning (A/C) mode originally considered in [23]. The optimisation framework described in Section3 is subject to the following modifications: • The air recirculation is set to 100%. This means that the blower fan inlet air temperature and the relative humidity correspond to the cabin air conditions, i.e., Tin = Tcab and RHin = RHcab. • The ambient air temperature is set to 40 ◦C and the relative humidity is 60%. • The air distribution vents are set to “VENT” mode, where the air is only distributed at chest-height positioned air vents (see [25] for details). • The lower limit of cabin inlet air temperature is set to 5 ◦C, while the upper limit is ◦ equated with the cabin air temperature to prevent heating, i.e., 5 C < Tcab,in,R < Tcab. • The control inputs are allocated with respect to three inputs: the cooling power . demand QcR, the cabin air temperature Tcab, and the cabin relative humidity RHcab, where the latter is relevant in the A/C mode due to the dehumidification effect. The Pareto optimal solutions are shown in Figure A1 for two cabin temperatures ◦ ◦ (25 C and 40 C) and RHcab = 20%. These results indicate that for lower cabin air temper- ◦ ature Tcab = 25 C (Figure A1a), the HVAC system can achieve comfortable PMV range. Figure A1c shows that high blower air mass flow rate is preferred when aiming for maxi- mum comfort (star symbol), while lower blower fan mass flow rate is suitable for low total power consumption (square symbol). However, similarly as with the heat-pump mode (cf. Figure5 ), the Pareto frontiers are relatively narrow, particularly for higher cooling demands, i.e., the trade-off of efficiency and comfort is rather modest. ◦ The Pareto frontiers are even narrower for high cabin air temperature (Tcab = 40 C, Figure A1b), and the PMV gain when using higher air mass flows is only 0.1 point on the scale of 4. On the other hand, the power consumption is strongly influenced by the control inputs, which should, therefore, be selected for minimum power consumption (square symbols in Figure A1d). Unlike the case of lower cabin air temperature (Figure A1c), the lowest total power consumption is achieved at higher blower fan mass flow rates. The optimisation results are influenced by the cabin relative humidity, as the cabin air is recirculated, and water condensation occurs on low-temperature radiator (LTR). This affects the performance of HVAC system in A/C mode, especially at high relative humidity due to higher loss on LTR. For more details, the interested reader is referred to [23]. Energies 2021, 14, 1203 23 of 24 Energies 2021, 14, 1203 23 of 24

FigureFigure A1.A1. Multi-objectiveMulti-objective optimisationoptimisation resultsresults forfor A/CA/C mode.

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