20x-Real Time Modeling And Simulation Of More Electric .

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20x-Real Time Modeling and Simulation of More ElectricAircraft Thermally Integrated Electrical Power SystemsYue Cao1, Student Member, IEEE, Matthew A. Williams2, Student Member, IEEE,Bradford J. Kearbey1, Student Member, IEEE, Andrew T. Smith1,Philip T. Krein1, Fellow, IEEE, Andrew G. Alleyne2, Senior Member, IEEEAbstract—More electric aircraft (MEA) include higher powerratings and more power electronics than conventional aircraft.With electrification comes increased multi-physical interactionbetween power systems, especially in electrical and thermaldomains. It is desirable to develop an accurate and fast systemlevel model that captures the dynamics of multiple energydomains over the course of candidate mission profiles, for thepurpose of trade-off studies, prototyping, and controllerdevelopment. This paper presents comprehensive electricalpower component models that are capable of being assembledinto full electrical system models. Steady-state and dynamicbehaviors of electrical components including electric machines,power converters, batteries, transformers, and loads arecaptured by averaged switching modeling and dq0 referenceframe techniques, without sacrificing computational speed. Anintegrated thermal model within electrical components usespower loss calculations to model temperature variations andidentify system hot spots. Monte Carlo simulation trials on a fivehour realistic mission establish the capability of the electricalsystem models while demonstrating a 50x real-time simulationspeed for a standalone electric subsystem and 20x for a coupledelectrical, thermal, and engine MEA model.Index Terms—more electric aircraft (MEA), power systems,modeling and simulation, power electronics, electric machines,generators, loss modeling, thermal modelingI.INTRODUCTIONThe most common more electric aircraft (MEA)architecture, which is already in commercial production on theBoeing 787, uses a no-bleed architecture, in which traditionalpneumatic systems are replaced by electrically poweredsystems [1]. Environmental control systems (ECS) are nolonger pneumatically powered, and instead the compressors,fans, and pumps are powered by electric motors via powerelectronics converters [2]. Due to this bleed-less architecture,maximum output of around 1.00 MVA comes from fourengine-tied generators. With auxiliary power units (APU) forredundancy, a total of 1.45 MVA is installed on the Boeing787 compared to 0.35 MVA on the Boeing 777 [2]. Increasedelectrical power introduces challenges due to coupledinteractions between aircraft power systems, complexity dueto additional electrical components, especially the powerelectronics and electric machines, and introduces moredegrees of freedom for system control.Major changes in the MEA electrical system include avariable voltage variable frequency 230 (nominal) Vac bus offthe engine generators, a 270 Vdc bus and its attached motordriven loads, and an ac-dc-ac conversion from the 230 Vacbus to a regulated 400 Hz 115 Vac bus, as shown in Fig. 1 [3].This configuration will be used throughout the paper and is themotivation for development of electrical component models1Yue Cao, Bradford J. Kearbey, Andrew T. Smith, and Philip T. Krein arewith the Department of Electrical and Computer Engineering, University ofIllinois, Urbana-Champaign, IL 61801, USA (email: yuecao2@illinois.edu,kearbey2@illinois.edu, atsmith3@illinois.edu, krein@illinois.edu).2Matthew A. Williams and Andrew G. Alleyne are with the Department ofMechanical Science and Engineering, Univ. of Illinois, Urbana-Champaign,IL 61801, USA (email: mwillms4@illinois.edu, alleyne@illinois.edu).highlighted in Section II. Due to the large scale of these powersystems, it is of great interest to rely on accurate modeling andsimulation tools for design and prototyping. Two majorcategories of models exist: high-fidelity detailed switchingmodels within electrical components [4], and system levelaveraged models that capture dynamical interaction betweencomponents [5][6]. This paper develops the latter. Inparticular, the average modeling method pertains totransforming three-phase abc ac signals into a synchronousrotating dq0 frame. Such technique has been proved effectivein accuracy and speed in electric power systems of mobileapplications [5][7]. Recently a dynamic phasor method [8] hasbeen developed to enhance the dq0 approach and addressunbalanced fault conditions. This method will not be appliedin this paper, however, as a balanced three-phase situation isto be explored for mission energy trade-offs.Additionally, it is important to understand and capture thethermal behavior of electrical system components in order toavoid failures due to overheating and thermal runaway. Asuitable thermal model is necessary for hot spot detection andtemperature monitoring. The combined electrical-thermalmodel must run fast while capturing necessary dynamics.Thermal models usually have step sizes of milliseconds orslower, whereas electrical models that capture switchingbehaviors have step sizes of milliseconds or faster. Therefore,switch level models are not suitable when considering systemlevel simulations. An averaged switching modeling approachis able to capture power losses in power electronic convertersand batteries, including device conduction and switchinglosses, based on equivalent steady-state conditions [9][10].Transient dynamics in the generators are captured using d-qmodels that execute with millisecond or faster time steps[9][11]. Previous work [9][12] has tackled the above modelinggoals in part. However, [9] focuses on power system faults,and [12] is heavy on mechanical design. Neither addresseselectrical component thermal modeling. In this paper, theabove criteria will be met. Simulation time versus real timewill be measured to demonstrate the computation speed.Fig. 1. Boeing 787 electrical power system architecture (recreated from [3]).In Section II, electrical and thermal models for individualMEA components are developed. Section III combines thesemodels into two simulation platforms: 1) electrical system inisolation, 2) MEA system architecture with electrically drivenECS and engine power generators. Section IV provides the

results of 1000 Monte Carlo simulations on simulation speeds,electrical system bus voltages, and total generated power.II.ELECTRICAL POWER SYSTEM MODELINGIn this section, the main building blocks of aircraft electricalpower systems including generators, exciters, powerconverters, battery cells, transformers, and electrical loads willbe explained, and modeling details will be presented.Electrical load distributions and power conversionefficiencies in the Boeing 787 at a typical cruising conditionare described in Fig. 2 [13]. This chart provides scalinginformation for modeling development as well as sanity checkdata for simulation results. The electrical power systemcontains the exciter/generator and APU connected to theelectrical distribution system. Electrical component modelsincorporate power loss calculation, which affects thecomponent temperature, and are coupled to ECS models thathandle heat rejection due to electrical losses. Engine modelsprovide low-pressure spool speeds and receive load torquefrom generators. Fig. 3 shows signal flow from the electricalsystem to the engine (black lines) and to the thermal system(red lines). The green lines show the dependency of othersystems on electrical power.frame, can be used. Sinusoidal states are transformed usingPark’s transformation [14], which results in constant steadystate conditions, larger solver time steps, and fastersimulations. The following generator model is derived in thedq0 reference frame. Parameter values are dependent uponspecific machines; however, [15] contains examples of variousmachines and their respective parameters, which can be usedas a baseline for sizing the generator.Fig. 4. Generator system inputs/outputs.Fig. 5. Synchronous generator inputs and outputs.Denoting the direct axis with subscript d and the quadratureaxis with subscript q, the electromotive force E' dynamics forthe stator are modeled as Tdo′ dEq′X d′ X d′′ Eq′ ( X d X d′ ) I d ψ ( X d′ X ls ) I d Eq′ ) E fd2 ( 1dk dt( X d′ X ls ) (1) Tqo′ dEd′X q′ X q′′ Ed′ ( X q X q′ ) I q ψ 2 q ( X q′ X ls ) I q Ed′2 k dt( X q′ X ls ) (2)(Fig. 2. Typical electrical system loads and efficiencies at cruise condition inBoeing 787 (recreated from [13]).Tqo′′ dψ 2 qkA. GeneratorThe generator consists of a synchronous generator, asynchronous exciter, and exciter controls. The input/outputstructure is shown in Fig. 4. The engine speed serves as aninput, and is adjusted based upon a fixed gear ratio. A dcvoltage input provides voltage potential to the exciter, and loadcurrents in the dq0 reference frame impose the total currentload on the generator. The mathematical model outputs providea dq0 line voltage from the generator, current draw by theexciter system, a torque on the engine, and heat produced dueto losses. The synchronous generator and exciter models willbe detailed in this paper. The input/output structure of awound-field synchronous generator is shown in Fig. 5.1) Electrical ModelIn ac machine models, sinusoidal states can lead tocomputationally intensive simulations. Alternatively, a wellknown synchronous, or direct-quadrature-zero (dq0) reference where X is the per-unit reactance, ′ is the per-unit transientis thereactance, ′′ is the per-unit sub-transient reactance,leakage reactance,andare the per-unit transient fieldwinding time constants in their respective axes, and is thecurrent [11].The flux linkage ψ dynamics are defined asTdo′′ dψ 1d ψ 1d E q′ ( X d′ X ls ) I dk dtFig. 3. Electrical power system diagram with input/output dependencies. ) dt ψ 2 q Ed′ ( X q′ X ls ) I q(3)(4)whereandare the sub-transient field winding timeconstants in their respective axes [11].The effect of temperature on electromotive force is capturedby considering the change in electrical resistance due totemperature. The coefficient k in (1)-(4) is defined ask R(T ) 1 αΔTR(T0 )(5)where ΔT is the temperature difference between the generatortemperature T and the nominal temperature T0, and α is thecoefficient of resistance for the field coil windings (for copper,α 3.85 10-3).The scaled field voltage Efd is defined asE fd I fd X mdSBVB(6)where Xmd is the direct axis magnetizing reactance, Ifd is thedirect axis field current, SB is the base generator power whichis equal to the rated three-phase volt-amperes, and VB is basegenerator voltage. The field current is supplied by the excitersystem, and is detailed in the following section.

Voltages in d and q axes can be calculated as algebraicfunctions of the electromotive forces, currents, and fluxlinkages, X '' X lsX ' X d'' ψ1d d'Vq ω X d'' X TL I d ( kRs RTL ) I q ω Eq' d' XXXdlsd X ls () X q'' X lsX q' X q'' Vd ω X d'' XTL I q ( kRs RTL ) I d ω Ed' ' ψ 2q ' X q X lsX q X ls ()(7)(8)where XTL and RTL are the line reactance and resistance, ω isthe rotational speed, and Rs is the stator resistance.Electromagnetic torque TEM of the generator is calculated inTEM ψ d'' I q ψ q'' I d(9)The mathematical model of the exciter is identical to themodel provided in the previous generator’s subsection. Ageneric exciter controller mathematical model will beprovided here. The field-controller converter duty cycle (m) isobtained from(15)r k1 (Vref Vline ( t ) )m k2 ( r k3 m )(16)Vline ( t ) v v(17)2d2qwhere k1, k2, and k3 are controller gains, r is an arbitraryvariable, and m is the dc/dc converter duty ratio. The referenceline voltage is Vref and the measured line voltage is Vline.where'' X '' X 'ls E ' X d X d ψψ ''d d1dq(10) X '' X X ' X ''qls 'qqEd X' X X' Xqlsqls (11) X' X ls d X' X ls dψ ''q ψ 2q Fig. 6. Exciter block diagram and signal flow.Power losses due to inefficiencies are determined as P Ploss S B ω TEM E d I d E q I q 2 (12)where P is the number of pole pairs. Power loss is essentiallythe difference between the shaft input power and the electricaloutput power.2) Thermal ModelA lumped thermal capacitance model is used to representthe overall temperature of the generator. Temperature isaffected by losses from (12) and heat transfers between thegenerator and ambient air as well as between the generator andcoolant. The time rate of change of the generator temperature,Tgen, ism gen C p , gendTgendt Ploss h f A f (T f Tgen ) ha Aa (Ta Tgen )(13)where mgen is the mass of the generator, Cp,gen is the specificheat of the generator lumped thermal capacitance, Aa is theheat transfer area between the ambient air and the generator,and Af is the heat transfer area between the coolant flow andthe generator. Each heat transfer coefficient h is calculatedusing the Nusselt number Nu, the thermal conductivity of thefluid k, and the length over which the heat transfer occurs, byh NukL(14)The Nusselt number for the coolant flowing through thegenerator is calculated assuming turbulent pipe flow and theGnielinski correlation [16]. Similarly, the Nusselt number forthe air moving over the generator assumes turbulent flow overa cylinder, which can be calculated using the ChurchillBernstein correlation [16].B. ExciterThe synchronous machine described above requires a fieldcurrent supply. Commonly another wound-field or permanentmagnet synchronous generator, known as an exciter, coupledto the main generator shaft provides this current. The exciter’soutput terminals are rectified and directly connected to themain generator field terminals. This field current must beprovided independent of the generator and should becontrolled properly to regulate the generator terminal voltage.A battery provides the exciter’s field current, regulatedthrough a dc/dc converter. A generic structural diagram isshown in Fig. 6.C. Inverter1) Electrical ModelThe three-phase inverter block converts the dc bus voltageto ac voltage, which interfaces with the rest of the ac systemdirectly or through a transformer. Since the inverter ismodeled in the dq0 reference frame, the inverter outputvoltages become constant values in steady state due to theabc-dq0 transformation. An averaged switching power lossmodeling technique is used to ensure fast simulation [17]. Theconduction loss is incurred when the IGBT (or equivalent) ison. It can be modeled as an ideal switch in series with aforward voltage drop Von and a series resistor Rds. Von and Rdscan be obtained directly from the IGBT datasheet. Theaverage conduction loss per IGBT pair isPon inv 2 2 I rmsVonπ(18)2Rds I rmsThe averaged switching loss of each IGBT pair can beestimated asPswitch inv 2 2 I rmsVbusπf switch invton toff2(19)where fswitch inv is the inverter switching frequency. Times tonand toff are the switching rise and fall times, respectively, whichare also found in device datasheet. Vbus is the main dc busvoltage.Another input needed to control the three-phase inverter isswitching functions. However, since the inverter is anaveraged model in the dq0 frame, the switching functions qthat determine direct action of the switching devices arereplaced with modulating functions [18]. When sinusoidalpulse width modulation method is used to control the inverterswitches, the output line-line (rms) voltage of the inverter isgiven asVl l ( rms ) 3 qV2 dc(20)The modulating functions for the three-phase inverter becomevoltage rms magnitudes. The phase of the inverter outputvoltages with respect to the rest of the ac system can bechanged by modifying relative values in the d and q axiscontrols.2) Thermal ModelA lumped thermal capacitance model is used to representthe overall temperature of the inverter. It is assumed that the

inverter is cooled under natural convection from a finnedsurface in an electronics bay at temperature Tbay. The rate ofchange of the inverter temperature, Tinv, isminv C p , invdTinv Pon inv Pswitch inv h ( 2 nLH ) (Tbay Tinv ) (21)dtwhere minv is the mass of the inverter and heat sink, and Cp,invis the specific heat of the inverter lumped capacitance. The lastterm is the heat transfer due to an n-finned heat sink with finsthat are H meters tall and L meters long. The heat transfercoefficient h is calculated ash 1.31kS opt(22)where k is the thermal conductivity of the fins. The optimal finspacing Sopt for a vertical heat sink is given by the Rohsenowand Bar-Cohen correlation [16] and is a function of theRayleigh Number Ra and the length L of the finsS opt 2.714LRa1 4(23)D. RectifierThe rectifier block converts ac voltage to dc voltage, whichinterfaces with the rest of the dc system. This is an activerectifier and it is modeled in the synchronous dq0 referenceframe. A voltage-based model is implemented and a dc-linkinductor is assumed. The rectifier is modeled as:di(24)L out m Vline ( t ) Voutdt vq vd (25)θ arctan iq m iout sin (θ )where Vout is the output dc voltage, iout is the output dc current,and m is the modulation depth.Power loss is modeled in a similar fashion as it is in theinverter model [17], since the topology of the rectifier is amirror image of the inverter. Similar thermal models used forthe inverter are also implemented.E. Battery1) Battery Electrical ModelThis subsection deals with the implementation of a lithiumion battery and its mathematical model. In the followingmodel, battery parameters are determined from laboratorytests on a sample lithium-ion battery (PanasonicCGR18650A). The model itself is generic and can be adaptedfor a wide range of batteries, including Li-ion, NiMH andlead-acid batteries. However, the battery circuit modelparameters must be estimated using a battery testing procedure[19]. The battery capacity is a function of the charge/dischargerates i(t), temperature T(t) and cycle number ncycle and a ratefactor f(i(t)) which is a function of current. The rate factor isused to account for undesired side reactions with increase withcurrent magnitude. The dynamic capacity of the batteryrepresented by its state of charge (SOC) is a function of thesefactors and given byt0t iself disch arg e 0t1ζ01ζdt(27)dt SOCinitial f1 [i (t )] f 2 [T (t )] f 3 [ncycle ] i (t ) 6(28)V , R, C exp[ ak lnk (SOC)]k 0The coefficients a0-a6 (exact values can be found in [19])are obtained by a best-fit polynomial expression on theexperimentally determined data points. From the equivalentcircuit, the battery terminal voltage can be calculated asimplemented in fast frequency domain,111(29)V V i (R R R R )tocseriessecsCsecminsCminhoursChourIn addition, a temperature model is developed bymcV 2 (t ) V 2 (t ) V 2 (t )dT (t ) 2 i (t ) Rseries sec min hour - hc A[T (t ) -Ta ]dtRsecRminRhour(30)Mass, m, external surface area, A, and specific heat, c, areinherent battery properties. Applications and thermal designsdetermine the ambient temperature, Ta, and heat transfercoefficient, hc.(26)id m iout cos (θ )SOC (t ) SOCinitial f1 [i(t )] f 2 [T (t )] f 3 [ncycle ] i (t ) The battery is modeled using the notion of multiple scaledtime constants, each at a level such as seconds, minutes andhours. In the electrical equivalent circuit, each time constantcan be modeled as a resistance-capacitance combination, asshown in Fig. 7. Measurements of the circuit parameters arefound by using a battery testing apparatus and recording thetest sequences and data corresponding to open circuit voltage(Voc) and terminal voltage (Vt) versus SOC at multiple ambienttemperatures. Each parameter (resistance and capacitance) inthe model shown in Fig. 7 is a nonlinear function of SOC. Fora practically useable model, in [19] each parameter isrepresented as a polynomial function of the SOC up to sixthorder given as1ζdtFig. 7. Electrical equivalent circuit of the

20x-Real Time Modeling and Simulation of More Electric Aircraft Thermally Integrated Electrical Power Systems Yue Cao1, Student Member, IEEE, Matthew A. Williams2, Student Member, IEEE, Bradford J. Kearbey1, Student Member, IEEE, Andrew T. Smith1, Philip T. Krein1, Fellow, IEEE, Andrew G. Alleyne2, Senior Member, IEEE Abstract—More electric aircraft (MEA) include higher power

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