Universities of Leeds, Sheffield and York

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1 promoting access to White Rose research papers Universities of Lees, Sheffiel an York White Rose Research Online URL for this paper: Conference paper Griffo, Antonio, Wang, J. an Howe, D. (28) Stability analysis of electric power systems for more electric aircraft. In: 3r International Conference From Scientific Computing to Computational Engineering". 3r IC-SCCE, 9-12 July 28, Athens, Greece. White Rose Research Online

2 3 r International Conference From Scientific Computing to Computational Engineering 3 r IC-SCCE Athens, 9-12 July, 28 IC-SCCE STABILITY ANALYSIS OF ELECTRIC POWER SYSTEMS FOR MORE ELECTRIC AIRCRAFT Keywors: Power systems, stability, linearization Antonio Griffo 1, Jiabin Wang 1, Davi Howe 1 1 Department of Electronic an Electrical Engineering University of Sheffiel Mappin Street, S1 3JD Sheffiel, UK a.griffo@sheffiel.ac.uk, j.b.wang@sheffiel.ac.uk Abstract. This paper presents a comprehensive assessment of small-signal stability for a more-electric aircraft power system consisting of a synchronous variable-freuency generator which supplies several power electronic controlle loas via an 18-pulse autotransformer rectifier unit (ATRU) for AC-DC conversion. Functional moels for key power system components an loas are erive. Numerical tools employe for the automatic calculation of linearize euations an operating points are escribe, an the influence of leaing esign an operational parameter on system stability is evaluate *. 1 INTRODUCTION Future more electric aircraft power systems will be base on the interconnection of a wie range of components, resulting in a significantly more complex electrical istribution system with multiple istribute loas most of which are supplie an controlle by power electronic converters [1][2]. Negative impeance behaviour [3][4] resulting from constant power characteristic of tightly regulate power electronic loas can be a serious threat to system stability. The necessity to optimize system architecture, as well as the nee to improve ynamic behaviour an avoi system instability reuires a comprehensive unerstaning of the influence of esign an control parameters an operating conitions on stability margins. In general, time-omain simulation using etaile non-linear, time varying power system moels, incluing system protection, control an operational limits, can be employe for accurate transient performance evaluation an stability assessment. This approach, however, is time consuming, reuires vast computation resources an oes not provie useful insights into the influence of the esign, control, an operational parameters on the system ynamics an performance. The application of computational efficient methos for assessing stability are mae possible base on the fact that the majority of fast transient, time varying elements in a multiple-converter base power system are ue to switching of power electronic evices, an the resulting switching harmonics will not have a significant influence on the system stability. By employing a state-space averaging techniue, it is possible to erive an euivalent non-linear, time invariant system moel an the small-signal stability of the power network uner a given operating conition can be assesse either in freuency omain using Nyuist stability criteria [5]-[9] or by evaluating the eigenvalues of the linearise Jacobian matrix [1]-[11]. Inustry application of these small signal stability analysis techniues is reliant on the establishment of a time-invariant state-space moel which entails (i) erivation an valiation of state-space averaging (SSA) moels of power system components an subsystems, (ii) integration of SSA moels to form a given power system architectures using an appropriate tool or simulation environment. The tool also has to be capable of computing the operating point for a given set of inputs an operating conitions, performing linearization an formulating the Jacobian matrix. Further, in orer to perform the analysis efficiently, the entire process has to be execute automatically. At the present, however, valiate state-space moels suitable for stability assessment have not been extensively reporte an no simulation tool that can perform the reuire proceures an operations is commercially available. This paper presents a comprehensive small-signal stability assessment of the power system for moreelectric aircraft consisting of a synchronous variable-freuency generator which supplies several power electronic loas connecte via passive filters to a local high voltage c bus, an employs an 18-pulse Autotransformer Rectifier Unit (ATRU) for AC-DC conversion. Numerical tools employe for the automatic calculation of linearize euations an operating points are escribe, an the influence of leaing esign an * This research is being conucte in the framework of the MOET project (More-Open Electrical Technologies), a FP6 European Integrate Project.

3 operational parameter on system stability is evaluate. Antonio Griffo, Jiabin Wang, an Davi Howe 2 DESCRIPTION OF MODELLING AND SIMULATION ENVIRONMENT The high-voltage DC subsystem uner consieration consists of five motor rive loas which are connecte to a common ±27V DC bus via 4 th orer LC filters. The filters are use to attenuate harmonics so as to meet the power uality stanar, an to provie a stabilizing effect for the motor rive loas which exhibit negative resistance behaviour. The DC bus is powere by an 18-pulse autotransformer rectifier unit (ATRU) whose AC inputs are irectly connecte to the output of a three-phase synchronous generator via fee cables. The AC bus voltage is regulate by the generator voltage controller at the point of regulation. In orer to provie a systematic an computationally efficient tool for stability assessment of more electric aircraft power systems, functional moels for key power system components an loas have been evelope an moelle using Moelica language [12]. Small-signal stability analyses, as well as time-omain simulations have been carrie out in Dymola simulation environment. A library of components for stability analysis has been establishe as the outcome of on-going collaboration between the University of Sheffiel an DLR. 2.1 Synchronous generator A classical six-orer moel of the synchronous generator has been use [13]. In aition to the excitation wining, amper winings have been consiere on both - an - rotor reference frame together with stator flux ynamics. The resulting ifferential-algebraic system of euations is given in es (1)-(4). The rotor voltage euations are: V R I kd RkDIkD (1) R I where V an I are the exciter fiel voltage an current, R is the fiel wining resistance, R kd an R are euivalent - an -axis amper wining resistance, an ψ, ψ kd an ψ are the flux-linkages of the fiel wining an the - an -axis amper winings, respectively. The rotor flux-linkage euations are: ψ L + L I + L I + I ψ ψ kd ( m ) m ( kd ) ( LkD + Lm ) I kd + Lm ( I + I ) ( L + Lm ) I LmI where I an I are the - an -axis stator currents, I kd, an I are the - an -axis rotor amper wining currents, L m an L m, are the - an -axis magnetising inuctances, an L kd an L are the - an -axis leakage inuctances of the rotor amper winings.the stator voltage euations are: V + RsI + ω sψ (3) V + R I ω ψ where, V an V are the - an -axis stator output voltages, R s is the phase resistance of the stator wining, ψ,an ψ are the - an -axis flux-linkages of the stator wining, an ω s is the synchronous angular freuency of the generator. The stator flux-linkage euations are: ψ ψ ( Ls + Lm ) I + Lm ( I + I kd ) ( Ls + Lm ) I + LmI where L s is the leakage inuctance of the stator wining. Fig. 1 shows the Dymola component moel of the synchronous generator. The inputs are electrical angular freuency, an file excitation voltage, an the outputs are - an -axis voltages an currents. V_ s s V_ref (2) (4) welec_in ~ Q_Plug + -. Figure 1 Synchronous generator moel in Dymola library V_ Figure 2 PI excitation control in Dymola library with anti-winup controller

4 2.2 PI excitation control A PI controller with anti-winup limitation is assume for the voltage regulation, as epicte in Fig. 1. Its parameters are erive by assuming the generator being represente as a simplifie first orer voltage behin transient reactance moel [13] given in euation (5) ωslm R ' E V ' (5) T where E an T are the euivalent back emf an time constant of the moel, respectively. This allows for ω specifying controller gains as a function of the reuire banwith n an amping ratio ξ as follows. R ' K p ( 2ξω nt 1) ω s Lm ' (6) T R 2 K i ω n ω L pulse Autotransformer-Rectifier unit s m Several ifferent arrangements of 18-pulse autotransformer rectifiers have been propose [14]-[15]. In this stuy the so-calle irect symmetric ATRU topology has been aopte, whose Dymola moel is epicte in Fig. 3. The ATRU consists of three six-pulse ioe rectifiers, one of which is supplie by a three-phase voltage set in phase with the primary AC voltage, an the others by three-phase voltages isplace with respect to the AC input by 4 electrical egrees leaing an lagging, respectively. Since at each time instant only one ioe-brige is conucting the positive current an one conucting the negative current, the three outputs are irectly connecte to the loa without the nee for interphase reactors. An analytical average value moel of the ATRU has been erive an valiate by comparison with SABER simulation of the etaile ATRU moel [17]. The evelope analytical moel is represente in Dymola as a library component, as shown in Fig. 3 ~ acplug_a Figure 3 18-pulse ATRU in Dymola library UDC Figure 4 Motor rive loa moel in Dymola library Tl 2.4 Motor rive loa If the DC voltage feeforwar compensation is not employe, a motor rive loa may eviate significantly from a constant power loa, an its behaviour is influence by the current an spee/position control banwiths as well as operating conitions. A etaile Dymola motor rive loa has been establishe as shown in Fig. 4. The moel inclues the ynamics of brushless permanent magnet rives in the - axis reference an an inner PI current control loop an an outer PI spee control loop [18]. This moel provies a means to stuy the influence of the current an spee control loop banwiths on the stability of the interconnecte power system. 3. SMALL-SIGNAL STABILITY ANALYSIS OF HVDC NETWORK Using the components establishe in the Dymola library escribe in section 2, the complete system of the HVDC network consisting of 5 power electronic controlle (motor-rive) loas fe by a variable freuency synchronous generator via the ATRU has been establishe, as shown in Fig. 5. Thanks to the powerful linearization capabilities of the Moelica language [12], it allows the small-signal stability analysis of the complete system to be carrie out in an automatic manner. For the sake of simplicity, the power electronic controlle loas are represente as ieal constant power loas. For a given set of parameters an operating conitions the system contains 28 state-space variables. Small-signal stability analysis at a given operating point yiels 28 eigenvalues

5 HVDC filters an loas Generator & control ARTU Figure 5 Dymola moel of HVDC system which are associate with the system components as follows: 4 for each filter-loa combination 5 for synchronous generator 1 for voltage regulator 1 zero eigenvalue ue to the angular reference 1 for ATRU The system stability is ominate by five high freuency pairs of eigenvalues associate with each loa, an one low freuency pair associate with the voltage regulator. Fig. 6 shows the eigenvalues loci as the generator operating freuency is varie from 2 to 8 Hz. For the sake of clarity only the moes with real part less than 5(1/s) are plotte. As can be seen, the increase in operating freuency ecreases the amping of the ~19 Hz moes which, accoring to moal analysis unertaken subseuently, are associate with filter-loas 3 an 5. The reuce stability margins that result from the increase in operating freuency can be explaine as the effect of the ecrease in steay-state DC bus voltage at the output of the rectifier as the operating freuency increases, as shown in Fig. 7. Because of the constant power nature of the loas, the ecrease in steay-state DC bus voltage ue to the so calle reactive voltage rop results in an increase in steay-state DC bus current, as epicte in Fig x 1 4 f 2 Hz f 8 Hz 1.5 Imag (ra/s) Real (1/s) Figure 6 Influence of operating freuency on eigenvalue loci

6 DC voltage (V) Freuency (Hz) Figure 7 DC bus voltage vs. operating freuency DC current (A) Freuency (Hz) Figure 8 DC bus current vs. operating freuency The combine effect of the ecrease in DC bus voltage an the increase in DC bus current results in an increase in the euivalent resistance of the ATRU, as shown in Fig. 9, which moels the reactive voltage rop, given by: R e V e V I DC DC (7) The euivalent voltage, V e, is relate to the magnitue of the AC phase voltage V m by [16]: π 9 π V e 2 cos Vm 2sin (8) 18 π 18 Although the increase in the euivalent resistance shoul result in an improvement in stability margins, in this particular case, the estabilizing effect ue to the reuction in DC voltage is more ominant. 8 7 Euivalent resistance (mω) Freuency (Hz) Figure 9 Euivalent resistance vs. operating freuency Figure 1 shows the eigenvalues loci as the combine AC cable an transformer leakage inuctance, which are assume to be lumpe together, is varie in the range 1μH-2μH. The increase of AC inuctance has the effect of reucing the stability margins an the amping of the ~19 Hz moes which become unstable when the leakage inuctance L ac is larger than 15 μh. Finally, Fig. 11 shows the influence of AC voltage controller banwith an amping factor on the low freuency pair eigenvalues associate with the AC voltage regulator. Their influence on the other ominant pair eigenvalues is insignificant an therefore not shown.

7 1.5 1 x 1 4 L ac 1μH L ac 2μH ra/s 2ra/s ξ.8 2ra/s ξ.6 2ra/s ξ.4 ξ.2 Imag (ra/s) Imag (ra/s) 5-5 ξ1 2ra/s 5ra/s Real (1/s) Figure 1 Influence of AC cable/transformer leakage inuctance on the root locus Real (1/s) Figure 11 Influence of control parameters on the root locus The moes associate with loa voltages have been ientifie using selective moal analysis [18]-[19]. Table 1 lists the participation factors of the five loa voltages with respect to each of their five moes. Table 1 Participation factors of loa voltages λ 5, ±j7137 λ 13,14 25± j7277 λ 11,12 131±j1181 λ 15,16 417±j3672 λ 9,1 162±j11828 P(v CPL1,λ i ) e-3.28e-3 7.5e-6.15e-3 P(v CPL2,λ i ) 3.48e e-3.6e-4 2.2e-3 P(v CPL3,λ i ) 1.89e e e-3.28 P(v CPL4,λ i ) 9.49e-5.4e-3 1.2e e-5 P(v CPL5,λ i ) 1.91e e e-3.61 As is evient from the very low values of the off-iagonal participation factors, the coupling among ifferent loas is negligible, except for the filter-loas 3 an 5, which show a certain egree of coupling ue to the similar value of the loas an the eual values of filters parameters. The effect of the DC cable on the system stability can be investigate by using the lumpe parameter moel shown in Fig. 12. Figure 12 Lumpe parameter moel of DC cable The euivalent capacitance an inuctance can be etermine accoring to the cable length an its characteristic parameters. The effect of the cable can be taken into account by inserting the euivalent circuit between the HVDC bus an the loa filter in Fig. 5. It can be shown that as the cable length increases, the amping ratio of the eigenvalues associate with the loa ecreases, which implies a ecrease in stability margin. 4. TIME DOMAIN SIMULATIONS Time-omain simulations have been unertaken to valiate the finings of the small signal stability analysis escribe in the previous sections. A step variation in the power eman from 14kW to 15kW at Loa #3 has been applie at t.5s, an the transient responses have been simulate. Figure 13 shows the resultant waveforms of the HVDC output voltage with two ifferent values of the AC cable an transformer leakage inuctances. As is evient, the system is stable when the AC cable an transformer leakage inuctance is 15μH. However, instability of the system occurs when the AC cable an transformer leakage inuctance is increase to

8 16μH. These results are consistent with those preicte by the small signal stability analyses, shown previously in Fig. 1. Simulations with ifferent parameters an uner ifferent operating conitions have been performe an similar results have been observe. Lac 15μH DC bus voltage [V] Lac 16μH Time [s] Fig. 13 DC bus voltage waveforms 5. CONCLUSIONS Functional moels for key power system components (Generator & control, ATRU, MCU, an filters, etc) suitable for stability analysis have been erive an a computational efficient tool in the Dymola simulation environment for small- an large-signal stability analysis has been establishe, an its utility emonstrate on a more electric aircraft power system comprising of a variable freuency AC generator, an 18-pulse ATRU an various power electronic controlle loas. Moal analysis has shown that the interaction between some loas is not significant. However system stability margin ecreases as the generator operating freuency an AC leakage inuctance increases. It has also been shown that the loa filter parameters have crucial influence on the system stability. However, the influence of generator control on the system stability is limite. ACKNOWLEDGEMENT The authors woul like to thank the European Commission for the financial support an the MOET Consortium for the permission of publishing the paper. REFERENCES [1] A. Emai an M. Ehsani, Electrical system architecture for future aircraft, Proc 34 th Intersociety Energy Conversion Engineering Conference, British Columbia, Aug [2] A. Emai, B. Fahimi, an M. Ehsani, On the concept of negative impeance instability in more electric aircraft power systems with constant power loas, SAE Journal, [3] L. Han, J. Wang, an D. Howe, Small signal stability stuies of a 27V DC more electric aircraft power system, Proc. IEE PEMD26, Dublin, pp , 4-6 April, 26. [4] A. Emai, an M. Ehsani, Negative impeance stabilising controls for PWM DC/DC converters using feeback linearization techniues, Proc. IECECE2, pp [5] R. D. Milebrook, Input filter consierations in esign an application of switching regulators, Proceeing of IEEE Inustrial Application Society Annual Meeting, IAS76, 1976, pp [6] S. S. Kelkar, an F. C. Lee, Stability analysis of a buck regulator employing input filter compensation, IEEE Trans. Aerospace Electronic Systems, vol. 2, 1984, pp

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