Transcript
Subsystem Interaction Analysis in Power Distribution Systems of Next Generation Airlifters Sriram Chandrasekaran, Douglas K. Lindner, Konstantin Louganski and, Dushan Boroyevich Center for Power Electronics Systems, Virginia Tech Blacksburg, VA 24061. Corresponding Author : D. K. Lindner, e-mail :
[email protected] To be presented at the European Power Electronics Conference, Lausanne, Switzerland, Sept 7-9, 1999
Acknowledgements The research reported in this paper is supported by the AFOSR under grant number: F49620-97-1-0254. The authors gratefully acknowledge the help and guidance of Ms. Catherine Frederick, Mr. George Korba and Ms. Quan Keenan of Lockheed Martin Control Systems, Johnson City, New York, in providing the models of the electromechanical actuators used in the analysis.
Keywords «Airplanes», «Power quality», «Control», «High frequency power converters», «Converter machine interactions».
Abstract Subsystem interaction in a simplified power distribution system of a next generation transport aircraft is addressed. Detailed analysis of interaction between an ElectroMechanical Actuator (EMA) connected to the DC bus of the power distribution system in a next generation transport aircraft with the bus regulator is presented. The classical impedance ratio criterion is used to determine local stability around an equilibrium point of each interface by observing the impedance characteristics of the source and load subsystems. Critical parameters that determine the local stability of the integrated system are identified. The loss of stability under large disturbances is presented to motivate the use of nonlinear stability analysis methods. Preliminary results of nonlinear stability analysis are presented.
Introduction The research reported in this paper is concerned with the analysis of subsystem integration in power distribution systems of next generation transport aircraft. It is projected that in future aircraft, all power, except propulsion, will be distributed and processed electrically. In other words, electrical
power will be utilized for driving aircraft subsystems currently powered by hydraulic, pneumatic or mechanical means including utility and flight control actuation, environmental control system, lubrication and fuel pumps, and numerous other utility functions. These concepts are embraced by what is known as the “More Electric Aircraft (MEA)” initiative. The MEA emphasizes the utilization of electrical power as opposed to hydraulic, pneumatic, and mechanical power for optimizing aircraft performance and life cycle cost. Increasing use of electric power is seen as direction of technological opportunity for aircraft power systems based on rapidly evolving technology advancements in power electronics, fault tolerant electrical power distribution systems and electrically driven primary flight control actuator systems. The aircraft power distribution system plays a central role in the development of concepts of “Power-By-Wire” and “More Electric Aircraft”. The MEA will need a highly reliable, fault tolerant, autonomously controlled electrical power system to deliver high quality power from the sources to the load [1].
Baseline Power System Architecture The proposed power distribution system is built around a 270V DC distribution bus. The typical
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baseline power system architecture for a next generation aircraft is shown in Fig. 1. It can be seen that the key components that control the power are the bidirectional power converters (BDCs). A bus regulator provides an interface between the starter/generator and the distribution bus. Most of the loads, including the actuators, are regulated using bidirectional power converters, which control and condition the power from the DC bus. 200 kW
500 kW Electric Load Management System
GCU
APU S/G
GCU
RS/G
GCU
3-Φ Φ L-BDC
L-EPCU
3-Φ Φ APU-BDC
APU-EPCU
3-Φ Φ R-BDC
R-EPCU
270V APU-DC bus (essential bus)
Hydraulic linkage
Smart Actuators
Surface deflection
Surface deflection
LS/G : Left-Starter Generator RS/G : Right-Starter Generator APU : Auxiliary Power Unit
ECS
Utility
1-Φ Φ BDC
MOTOR
3-Φ Φ BDC
DC-DC BDC Induction motor
ECS Coolant pump pump
Electronically commutated motor 270V battery
Cargo temp
GCU : Generator Control Unit EPCU : Electronic Power Control Unit BDC : Bidirectional Converter
MOTOR
ECS pump
Cargo pressure
3-Φ Φ BDC
negative impedance avionics
1-Φ Φ BDC
PUA
Smart Actuators
Mechanical linkage
Surface deflection
Surface deflection
Electromechanical actuator
PUA
3-Φ Φ BDC
Flight control
negative impedance avionics
Utility
3-Φ Φ BDC
270V R-DC bus ECS
Flight control
270V L-DC bus
Electrohydrostatic actuator
500 kW
LS/G
PUA : Power Unit Actuator ECS : Environmental Control System
Fig. 1. Baseline Power System Architecture
With the proliferation of bidirectional power converters and advanced actuators in the power distribution system, it is important to develop methods to analyze the interaction between the different subsystems. Due to the complexity of the baseline power system and the large number of subsystems, a sample power distribution system, which captures the essential features of the baseline system but is not as complicated is introduced. The sample power system is represented as a interconnection of a source and load subsystem. To start with, the classical impedance ratio criterion proposed in [2] is used to determine the stability properties of the interconnected system. The impedance ratio criterion, however, guarantees only local stability in a small neighborhood of an equilibrium point. The critical parameters that affect the stability of the interconnected system are identified and local stability is verified against the variation of these parameters. A simulation example is presented to show the effect of large disturbances on the stability of the system. This motivates the application of nonlinear methods to obtain a global understanding of the behavior of the system in the
presence of large disturbances. Bifurcation methods to study the global behavior of the system are then introduced. Preliminary results of the bifurcation analysis of a modified sample system are presented.
Sample Power Distribution System The sample power distribution system is shown in Fig. 2. The source subsystem represented by subsystem 1 consists of an ideal three phase voltage source, a three-phase boost rectifier to provide the regulated 270V DC required by the DC bus. The load subsystem represented by Subsystem 2 is an electromechanical actuator used to control the secondary flight control surfaces on the aircraft. The other loads on the DC bus are modeled by a current source, or a simple resistance. Ideal 3-φ voltage source
Rectifier 3-φ -to- DC
Input Filter
DC Bus
DC-DC Converter
DC Motor
Actuator (EMA) EMA Drive
Load (R, Io)
Subsystem 1
Subsystem 2
Fig. 2. Sample Power System Architecture
The three-phase boost rectifier is represented by its dq-average model in rotating coordinates synchronized with the input line voltages [3]. A multi-loop controller for the three-phase boost rectifier consists of an outer loop to regulate the output voltage and two inner current loops, one each for the d- and q- axis input currents. The dqequivalent circuit model of the three-phase boost rectifier and the corresponding control block diagram are shown in Fig. 3. vd,vq, idc dd dq id
L
idc
dd vo +
vd iq vq
ωLiq +
L
1 d q iq 2
ωLid + dq vo
+
(a)
1 dd d i 2
+ C vc Rc
+ Σ_
v dq-Model of o id 3-Φ Boost iq Rectifier I =0 + q(ref) Kdq Σ _ _ VREF Σ +
ωL V REF
vo + Σ +
ωL V REF
Kdq
_ Σ
+
1 + s wz ho 1 + s wp Hv(s)
(b)
Fig. 3. (a) DQ-equivalent circuit model of three phase boost rectifier (b) Control block diagram
2
Fig. 6. Schematic of input filter
The ElectroMechanical Actuators (EMAs) drive the secondary flight control surfaces consisting of 14 inboard (IB) and outboard (OB) spoiler panels. Fig. 4 shows the secondary control surfaces and their actuator locations. The EMA is driven by a three-phase brushless DC or permanent magnet synchronous motor drive. The inverter-motor drive is modeled in rotating dq-coordinates that are synchronized with the rotor position. This modeling approach essentially reduces the motor currents and voltages to DC and the resulting model to that of a DC motor. IB Spoilers (6-7)
IB Spoilers (8-9)
OB Spoilers (1-5)
vap
d.vap
vin
iL
Fext
iin
Text
ωm
ωm
ic Average Model of BDC
Text xa xact
Motor Position
HM
F
ωm
θ
Surface Dynamics
EMA
DC Motor
Wind Loading
im ωm xact
d
θref EMA Controller
Fig. 5. Control Block Diagram of EMA Drive System Lf
vin
Typical simulation results for one actuator deflection cycle are shown in Fig. 7. It can be seen that the voltage at the DC bus suffers some spikes due to the transient disturbances caused by the surface deflection command to the actuator. It is critical that the magnitude of the voltage spikes be limited between specified limits. The limits on the transient spikes and the distortion spectra on the DC bus voltage are defined by the specification MIL-STD-704E [4].
RLf
Time in seconds
Fig. 7. Simulation of One Actuator cycle
The input filter in addition to attenuating the switching ripple, reduces the magnitude of the voltage spike seen on the DC bus according to the size of the filter capacitance and the damping. Other factors that determine the magnitude of the voltage excursions are the regulation bandwidth of the boost rectifier and, the other loads on the bus. It is critical that the stability of the interconnected system is verified against the variation of the parameters mentioned above. The stability analysis is presented in the next section.
Stability Analysis
io
Impedance Ratio Criterion
Cf1 RCf
DC Bus Voltage
Hence, the EMA model shown in Fig. 5 is shown to include a DC motor with constant field, a ball screw transmission between the motor and the control surface, and a model of the surface dynamics. The motor voltage is controlled by a PWM bidirectional buck converter with an input filter. The EMA is controlled by a multi-loop controller, which includes a motor current, motor speed, and the ball screw position feedback loops. All of the other loads on the bus are modeled by a resistor or a current source.
d
Simulation Results
OB Spoilers (10-14)
Fig. 4. Secondary Actuator Configuration
Vbus
The circuit schematic of the input filter used for the EMA drive in subsystem 2 is shown in Fig. 6.
Cf2
vo
A generic subsystem interface is shown in Fig. 8a. Subsystems 1 and 2 in Fig. 8a are represented by their small signal models linearized around an equilibrium point. The interconnection results in 3
subsystem 1 to be loaded by subsystem 2. The interface variables vI and iI are given by:
i I = −(Yi 2 v I + Ai 2io )
….. (1)
v I = Av1v s + Z o1i I
where, Zo1 and Yi2 are the output impedance of the load subsystem and input admittance of the source subsystem respectively. Equation 1 shows the presence of a feedback loop shown in Fig. 8b. The stability of the feedback loop determines the stability of the interconnected system. The stability of the feedback loop can be determined by counting the number of counterclockwise encirclements of the (-1,0) point by the Nyquist contour of the minor loop gain Zo1Yi2. If the individual subsystems are stable, then the stability of the interconnected system is guaranteed if and only if there are no encirclements of the (-1,0) point by the Nyquist contour of the minor loop gain. The sufficient condition for stability is obtained from the small gain theorem, and is given by, Z Z o1Yi 2 = o1 < 1 ⇒ Z o1 < Z i 2 Zi2
….. (2)
Equation 2 is the classical impedance ratio criterion that guarantees stability of the interconnected system and minimal interaction between the two subsystems. iI
Zo1 vs
Yi1 Ai1iI
Zo2 Ai2io
+ -
vI Yi2
+ -
io
Av2vI
Av1vs
Subsystem 1
Σ +
Zo1
Yi2
The Nyquist contours of the minor loop gain for various values of filter capacitance and damping resistance are shown in Fig. 10. Input Filter
3-φ -to-DC Rectifier
Load
Zo1
Yi2
EMA Drive Subsystem 2
Subsystem 1
Fig. 9. Identification of output impedance and input admittance in sample power system.
The effects of changes in the capacitance and the damping, on the phase and gain margins of the minor loop gain can be seen in Fig. 10. (The unit circle shown in Fig 10b cannot be used to measure the phase margin because of the unequal scales on the real and imaginary axes and is shown only to illustrate the variation of the stability properties with the damping resistance in the filter). Fig. 11 shows the Nyquist contour of the minor loop gain for a given set of parameters and the corresponding time domain simulations of the sample power distribution system for a single actuator cycle similar to that shown in Fig. 7.
Subsystem 2
(a)
Ai2io +
The impedance ratio criterion presented in the previous section is used to determine the local stability of the sample power distribution system. The output impedance of subsystem 1 and input admittance (impedance) of subsystem 2 are identified in Fig. 9.
- Av1vs Σ +
(b) Fig. 8. (a) Generic Subsystem Interface (b) Equivalent Feedback Representation
Although the Nyquist contour in Fig. 11a indicates that the equilibrium point is stable, the surface deflection command induces a disturbance that is large enough to drive the system into sustained limit cycles as shown in Fig. 11b. This behavior cannot be predicted by the impedance ratio criterion. The simulation results shown in Fig. 11 indicate the manifestation of the nonlinear nature of the sample system and entail the application of nonlinear methods to analyze the stability of the system. Nonlinear methods, to determine the stability of power distribution systems, were used in [5,6,7]. In [7], a modified version of the sample power system as shown in Fig. 12 was used. The
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load converter shown in Fig. 12 was, however, represented as a constant power load. Im Im
Unit Circle 10 p.u
Unit Circle
1 p.u
+
0.1 p.u
+
Re
(a) Re
Im
DC Bus Voltage
(a)
Actuator Duty Cycle
0.16 p.u
1 p.u
+ Unit Circle
Time in seconds
(b) Re
(b) Fig. 10. Nyquist Contours of minor loop against variation in (a) Filter capacitances, Cf1, Cf2 (b) Resistance RCf.
The bifurcation behavior of the modified sample system was studied as a function the control parameter ho of the boost rectifier (Fig. 3b). The complete bifurcation diagram is shown in Fig. 13. The bifurcation diagram shown in Fig. 13 shows nature, type and multiplicity of operating trajectories of the modified power system as a function of the control parameter, ho. For example, the modified power system has an unstable equilibrium solution for ho corresponding to point shown by “X” in Fig. 13. On perturbing the system from this equilibrium point, the system jumps to a periodic solution represented by the trajectory “Period-1 solution”. This information cannot be obtained from the linear analysis methods.
Fig. 11. Loss of Stability under large disturbances (a) Nyquist Contour of minor loop gain (b) Limit cycle behavior of sample power system
Ideal 3-φ voltage source
Rectifier 3-φ -to- DC
270V DC Load (R, Io)
Input Filter
DC-DC Converter Subsystem 2
Subsystem 1
Fig. 12. Modified sample power system used for bifurcation analysis
The bifurcation diagram shown in Fig. 13 was generated under the assumption that the system is represented by a set of differential equations with differentiable right hand sides. In other words, the limiters in the controllers are not taking into account in determining the bifurcation diagram. But the limit cycle behavior shown in Fig. 11b is caused by the saturation of the duty cycle of the converter that drives the actuator. Hence, the 5
bifurcation analysis has to be extended to include the saturation of controller outputs to be able to predict limit cycles as shown in Figure 11b. Period-4 solution
4. 5.
Period-2 solution Period Doubling Bifurcation
6.
P so erio lu dtio 1 n
vo
stable equilibrium solution
Hopf Bifurcation Point
7.
X
Unstable equilibrium solution
Proceedings of the 15th VPEC Seminar, 1994, pp. 63-70. MIL-STD704E, Military Standard, Aircraft Electric Power Characteristics, May 1, 1991 Abed, E.H. et al, “Stability and Dynamics of Power Systems with Regulated Converters”, Proceedings of the IEEE Symposium on Circuits and Systems, vol. 1, 1995, pages 143-145. M. Al-Fayyoumi, “Nonlinear dynamics and Interaction in Power Electronics Systems”, M.S. Thesis, Department of Electrical and Computer Engineering, Virginia Tech, 1998. Sriram Chandrasekaran, Douglas. K. Lindner, Dushan Boroyevich, “Analysis of Subsystem Integration in Aircraft Power Distribution Systems”, International Symposium of Circuits and Systems, ISCAS ’99, Orlando, Florida, May 1999.
ho
Fig. 13. Bifurcation diagram of modified sample power system
Conlusions Stability analysis of a sample power distribution system of a next generation aircraft was presented in this paper. The classical impedance ratio criterion was used to determine the local stability of the sample power system in a small neighborhood of an equilibrium point. However, the behavior of the system under large disturbances cannot be predicted by linear analysis methods. Bifurcation methods were proposed to obtain an understanding a global understanding of the system behavior. The preliminary results presented did not account for the saturation of the controller outputs. Future work will include incorporating the limiters and extending the analysis to a more complex power distribution system.
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2.
3.
Weimer J. A, “Power management and distribution for the More Electric Aircraft”, Proceedings of the 30th Intersociety Energy Conversion Engineering Conference, vol. 1, July 1995, pp. 273-277. Middlebrook, R. D., “Input Filter Considerations in Design and Application of Switching Regulators,” IEEE Industry Application Society Annual Meeting, October 11-14, 1976, Chicago, Il. S. Hiti, D. Borojevic, “Small-signal modeling and control of three-phase PWM converters”,
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