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Modeling and Analysis of an Avionic Battery Discharge Regulator
Modeling and Analysis of an Avionic Battery Discharge Regulator
Journal of Power Electronics. 2016. May, 16(3): 1218-1225
Copyright © 2016, The Korean Institute Of Power Electronics
  • Received : November 16, 2015
  • Accepted : December 28, 2015
  • Published : May 20, 2016
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About the Authors
Qian, Chen
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Haihong, Yu
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Xiaoming, Huang
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Yi, Lu
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Peng, Qiu
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Kai, Tong
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Jiazhuo, Xuan
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Feng, Xu
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Xiaohua, Xuan
Zhejiang Electric Power Corporation Research Institute, Hangzhou, China
Weibo, Huang
Department of Electronic and Electrical Engineering, Beijing Jiaotong University, Beijing, China
Yajing, Zhang
chenqian05291148@126.com

Abstract
The avionic battery discharge regulator (BDR) plays an important role in a power-conditioning unit. With its merits of high efficiency, stable transfer function, and continuous input and output currents, the non-isolated Weinberg converter (NIWC) is suitable for avionic BDR. An improved peak current control strategy is proposed to achieve high current-sharing accuracy. Current and voltage regulators are designed based on a small signal model of a three-module NIWC system. The system with the designed regulators operates stably under any condition and achieves excellent transient response and current-sharing accuracy.
Keywords
I. INTRODUCTION
The power-conditioning unit (PCU) balances the power among new energy sources to keep the bus voltage constant. According to various bus voltages, PCU is divided into three categories, namely, 28, 42, and 100 V. The avionic battery discharge regulator (BDR), which controls the discharging procedure of a battery, plays an important role in PCU [1] . The non-isolated Weinberg converter (NIWC) is suitable for BDR because of its merits, such as high efficiency, no right-half-plane (RHP) zeroes, and continuous current.
Many scholars have conducted research on NIWC in the past few years. Lei derived a small signal model of NIWC [2] , [3] . Ejea–Marti J. established a small signal model based on peak current control and analyzed stability under a small duty cycle [4] [6] . Chen analyzed the effect of leakage inductance on the steady-state performance of NIWC [7] . However, the small signal model and controller design of parallel NIWC systems have not been analyzed to date.
This paper presents an improved peak current control strategy to achieve excellent current-sharing accuracy and reliability. Based on a 42 V-level PCU, the small signal model and controller design of a three-module NIWC system under current continuous mode (CCM) are presented.
The transfer functions utilized in the following analysis are defined as follows.
  • Gv(s): Voltage regulator
  • Gi(s): Current regulator
  • Req1: Sampling coefficient of peak current
  • Req2: Sampling coefficient of average current
  • Kv(s): Sampling coefficient of output voltage
  • Fm: Current modulator gain
  • Gid(s): Transfer function of
  • Zout(s): Transfer function of output impedance
  • He1(s): Transfer function describing the sampled data effect on peak current
  • He2(s): Transfer function describing the sampled data effect on average current
II. OPERATING PRINCIPLE
The NIWC is shown in Fig. 1 . Couple inductor Lcouple and transformer T make the input and output current continuous by properly controlling Q 1 and Q 2 . The input-damping filter, including Lf , C f1 , C f2 , and Rf , smoothens the input current to make current sampling convenient and extend the battery service life. The operating principle of NIWC is analyzed with Maset E [8] , [9] .
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NIWC.
In consideration of efficiency and reliability, three NIWCs power the main bus in parallel at a rated condition of 1200 W. The control strategy should keep bus voltage stable at 42 V and limit the current-sharing error to 1%.
The control diagram of the three-module NIWC system is shown in Fig. 2 . An improved peak current control strategy that includes a voltage regulator, an average current regulator, and a peak current comparator is proposed to avoid transformer saturation and enhance current-sharing accuracy and reliability. The voltage regulator whose output is the reference of the average current regulator stabilizes the bus voltage. The average current loop significantly enhances current-sharing accuracy. The improved peak current control strategy is suitable for system-level applications that focus on current-sharing accuracy and integrity.
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Three-module NIWC system under improved peak current control.
III. POWER STAGE MODEL
The input filter designed according to the Middlebrook theorem can be neglected in a small signal model [10] . A power stage model of the three-module NIWC system is established in reference to the state-space averaging method, as shown in Fig. 3 . Supposing that the duty cycle disturbance
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of each module is equal, the equivalent inductance is 4 L /3, and the inductance of the single-module power stage model is 4 L [11] . When the disturbance of input voltage
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is zero, control-to-output current transfer function Gid (s) can be derived as Eqn. (1). The power stage model is established in CCM.
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Power stage model of the three-module NIWC system.
The control-to-output current transfer function Gid (s) of the three-module NIWC system is similar to that of the buck converter. Therefore, NIWC easily stabilizes because RHP zeroes do not exist in the transfer functions.
IV. SMALL SIGNAL MODEL OF THE SYSTEM
In reference to the small signal model of peak current control in [12] , the disturbance of duty cycle
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is related to control current
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, output current
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, input voltage
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, and output voltage
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, as shown below.
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where Fm =1/ MaTs , Fg = ( D 2 + 2 D -1) Ts / 8 L , and Fv = (1- 2 D ) Ts / 8 L . D is the sum of the duty cycles of Q 1 and Q 2 , and Ts is half of the period of Q 1 . Ma is the slope of the saw-tooth wave used for slope compensation.
According to Eqn. (2), the small signal model of the three-module NIWC system is built and shown in Fig. 4 . The sampling coefficients of peak and average currents are one-third of those of the single-module small signal model. Fg and Fv can be disregarded if the current ripple is small. With this simplification, the small signal model of the system is constructed in Fig. 5 .
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Small signal model of the three-module NIWC system.
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Modified small signal model of the system.
The additional phase delay and disability at half of the equivalent frequency are reflected in the small signal model by introducing H e1 ( s ) and H e2 ( s ) [13] . The following equation makes the small signal model close to reality.
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where ωn = π / Ts and Qz = -2 / π .
V. CONVERTER DESIGN
The system specifications are described in Table I .
SYSTEM PARAMETERS
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SYSTEM PARAMETERS
In reference to the space engineering electrical and electronic standard established by the European Space Agency (ESA) [14] , the requirements of a 42 V regulated-bus PCU are as follows.
  • Steady-state characteristic: The peak-to-peak ripple of output voltage is required to be lower than 0.1 V.
  • Transient-state characteristic: When the output current changes by 10 A, the voltage spike is required to be lower than ±0.42 V. The duration of the voltage spike over ±0.1 V is required to be less than 7.5 ms.
  • The gain margin is higher than 10 dB.
  • The phase margin is higher than 60°.
  • The closed-loop output impedance is lower than 50 mΩ.
  • The current-sharing error should be less than 1%.
The design of the controller should satisfy the aforementioned requirements. When the input voltage is 26 V and the output current is 30 A, the controller is more difficult to design than in other conditions. Thus, the controller is designed under this condition.
- A. Current Regulator Design
In Fig. 5 , the control object of the average current loop is
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The loop gain of the average current loop is
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The uncompensated loop gain of current loop Tio ( s ) with unity compensator gain Gi ( s ) is depicted in Fig. 6 . The cut-off frequency is 19.4 kHz, the gain margin is 9.9 dB, and the phase margin is 92.1°. The DC gain of Tio ( s ) at a low frequency is not sufficiently high to reduce the steady-state error. Hence, a low-frequency pole should be added to enhance the DC gain. | Tio ( )| dB at high frequencies is higher than 0, which amplifies high-frequency noise. A high-frequency pole should therefore be added to improve anti-interference capability. Based on this analysis, a single-zero double-pole compensator is selected as the current regulator. The current regulator, which is presented in Fig. 2 , is expressed as
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where Ki =1/ R i2 ( C i1 + C i2 ) , ωzi =1/ R i1 C i2 , and ωpi = ( C i1 + C i2 ) / R i1 C i1 C i2 .
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Bode plots of current loop gains Ti(s) and Tio(s).
The parameters are R i1 = 8 k Ω , R i2 =10 k Ω , C i1 = 240 pF , and C i2 = 50 nF .
The compensated loop gain of current loop Ti ( s ) is also shown in Fig. 6 . For Ti ( s ), the cut-off frequency is 14.45 kHz, the gain margin is 12.3 dB, and the phase margin is 91.5°.
- B. Voltage Regulator Design
After designing the current regulator, the control object of voltage loop is derived from Fig. 5 , as shown below.
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The loop gain of the voltage loop is
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The uncompensated loop gain of voltage loop Tvo ( s ) with unity compensator gain Gv ( s ) is depicted in Fig. 7 . The cut-off frequency of Tv ( s ) is designed to be approximately 1 kHz to satisfy the requirement that the cut-off frequency of the voltage loop should be lower than that of the current loop. In Fig. 7 , the amplitude–frequency curve of Tvo ( s ) is lower than 0 dB, which means the system is unstable. A single-zero single-pole compensator is selected as the voltage regulator to enhance DC gain and stability. The voltage regulator, which is presented in Fig. 2 is expressed as
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where Kv =1/ R v2 C v1 and ωzv =1/ R v1 C v1 .
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Bode plots of voltage loop gains Tv(s) and Tvo(s).
The gain of Tvo ( s ) at 1 kHz is −25.5 dB. The cut-off frequency of Tv ( s ) is designed to be 1 kHz; thus, 20log(| Rv1 / Rv2 |)=25.5 dB. If R v2 =10 k Ω, then R v1 ≈300 k Ω. The zero frequency of the voltage regulator is designed to be 100 Hz, so C v1 ≈5.4 n F.
The compensated loop gain of voltage loop Tv ( s ) is also shown in Fig. 7 . For Tv ( s ), the cut-off frequency is 1 kHz, the gain margin is 35.5 dB, and the phase margin is 84.7°, which satisfies the requirements of ESA. Accordingly, the system is stable.
- C. Analysis of Closed-Loop Output Impedance
The small signal model of close-loop output impedance when the disturbance of input voltage
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is zero is shown in Fig. 8 by introducing the disturbance of load current
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The transfer function of close-loop output impedance is
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Small signal model of output impedance.
In Fig. 9 , the maximum output impedance is 41.4 m Ω, which satisfies the requirements. Hence, NIWC has a good load adjustment rate.
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Bode plots of output impedance.
VI. EXPERIMENTAL CONFIRMATION
A 1200 W prototype (shown in Fig. 10 ) is built with a two-layer power printed circuit board to confirm the superiority of the improved peak current control strategy and the rationality of regulator design.
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Experimental platform of the three-module NIWC system.
Fig. 11 shows the drive signal, the voltage of the current transformer, the drain-to-source voltage of the metal–oxide–semiconductor field-effect transistor, and the primary current of the couple inductor when the input voltage is 32 V. Under any condition, the input and output currents are continuous, and the bus voltage is stable at 42 V.
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Key waveforms of NIWC.
The Bode plots of voltage loop gain Tv (s) and output impedance Zout (s) are measured with gain-phase analyzer N4L_PSM1735. Given that the operating frequency of the test transformer is constrained, the test frequency range varies from 100 Hz to 100 kHz. Fig. 12 shows that measured voltage loop gain Tv (s) presents a good agreement with the calculated one in Fig. 7 , which verifies the correction of the small signal model. The magnitude and phase margins satisfy the requirements of ESA, so the system is stable. In Fig. 13 , measured closed-loop output impedance Zout (s) agrees with the calculated results in Fig. 9 . The maximum output impedance is lower than 50 m Ω during the entire frequency band, which satisfies the requirements. Therefore, NIWC has a good load adjustment rate.
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Measured voltage loop gain Tv(s).
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Measured closed-loop output impedance Zout(s).
Table II represents the current-sharing performance without a current-sharing strategy when the input voltage is 32 V. Table III shows the current-sharing performance with the peak current control strategy, and Table IV presents the current-sharing performance with the improved peak current control strategy. The current-sharing error is calculated according to the following equation.
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where
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is the average output current and
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is the maximum difference between the output current of each module and the average output current.
CURRENT-SHARING PERFORMANCE WITHOUT A CURRENT-SHARING CONTROL STRATEGY
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CURRENT-SHARING PERFORMANCE WITHOUT A CURRENT-SHARING CONTROL STRATEGY
CURRENT-SHARING PERFORMANCE WITH THE PEAK CURRENT CONTROL STRATEGY
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CURRENT-SHARING PERFORMANCE WITH THE PEAK CURRENT CONTROL STRATEGY
CURRENT-SHARING PERFORMANCE WITH THE IMPROVED PEAK CURRENT CONTROL STRATEGY
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CURRENT-SHARING PERFORMANCE WITH THE IMPROVED PEAK CURRENT CONTROL STRATEGY
From Tables II IV , conclusions can be drawn as follows.
  • The current-sharing performance without a current-sharing strategy is the worst among all performances.
  • The current-sharing performance with the peak current control strategy is good but still cannot satisfy the 1% requirement.
  • The current-sharing performance with the improved peak current control strategy satisfies the 1% requirement under any condition.
These conclusions demonstrate the superiority of the improved peak current control strategy.
Fig. 14 shows the transient response of the output voltage when the load changes by 10 A. The bus voltage ripple is constrained within 40 mV. When the output current changes from 20 A to 30 A, the voltage spike is 0.28 V. The duration of the voltage spike that exceeds −0.1 V is 1.65 ms. When the output current changes from 30 A to 20 A, the voltage spike is 0.29 V. The duration of the voltage spike that exceeds 0.1 V is 1.68 ms. The steady and transient characteristics of output voltage satisfy the requirements with a large margin.
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Transient response for load changes from 20 A to 30 A.
Fig. 15 shows the transient response of the output current for each module when the load changes by 10 A (20 A to 30 A). Figs. 14 and 15 show that the system gains an excellent transient response and current-sharing accuracy under the improved peak current control strategy.
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Transient current-sharing performance for load changes from 20 A to 30 A.
VII. CONCLUSION
Based on the three-module NIWC system, the power stage model is derived. Improved peak current control strategy is proposed to avoid the saturation of the transformer and enhance the current sharing accuracy and reliability. The current and voltage regulators are designed according to the requirements. Finally, the experimental results are given to verify that the system gains an excellent transient response and current sharing accuracy under improved peak current control strategy by a 1200W prototype. This control strategy is suitable for the system-level application which is strict on the current sharing accuracy and integrity.
BIO
Qian Chen was born in Zhejiang Province, China, in 1987. He received his B.S. and Ph.D. degrees in electrical engineering from Beijing Jiao Tong University, Beijing, China, in 2009 and 2015, respectively. He is currently an engineer at Zhejiang Electric Power Corporation Research Institute, Hang Zhou, China. His current research interests include HVDC, FACTS, and DC grids.
Haihong Yu is the deputy manager of Power Transmission Center of Electric Power Research Institute of Zhejiang Provincial Electric Power Corporation (a subsidiary of SGCC). He worked for four years with the National Grid Power Corporation of the Philippines as the head of the Transmission Planning Department under a technical assistance programmer provided by SGCC. Power transmission planning and modeling are the main areas where he has specialized in for his 22 years with the electric power sector.
Xiaoming Huang received his B.S. degree in electrical engineering from Zhejiang University, Hangzhou, China, in 1991. He is currently the deputy manager at Electric Power Research Institute of State Grid Zhejiang Electric Power Corporation, Hang Zhou, China. His current research interests include relay protection and HVDC.
Yi Lu received his B.S. degree in electrical engineering from North China Electric Power University, Baoding, China, in 2001. He received his M.S. and Ph.D. degrees in intelligence engineering and electrical engineering from the University of Liverpool, Liverpool, U.K., in 2002 and 2007, respectively. In 2008, he joined the Zhejiang Electric Power Corporation Research Institute, Hangzhou, China. He is currently a senior engineer, and his research interests include HVDC and FACTS.
Peng Qiu received his B.S. and M.S. degrees in electrical engineering from Zhejiang University, Hangzhou, China, in 2008 and 2011, respectively. Since 2011, he has been an engineer at Zhejiang Electric Power Corporation Research Institute, Hang Zhou, China. His current research interests include HVDC and FACTS.
Kai Tong received his B.S. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2006. Since 2006, he has been an engineer at Zhejiang Electric Power Corporation Research Institute, Hang Zhou, China. His current research interests include relay protection and HVDC.
Jiazhuo Xuan received his B.S degree in electrical engineering from Zhejiang University, Hangzhou, China, in 2008 and his M.S degree in renewable energy engineering from the University of New South Wales, Sydney, Australia, in 2012. Since 2012, he has been an engineer at Zhejiang Electric Power Corporation Research Institute, Hangzhou, China. His current interests include relay protection and HVDC.
Feng Xu was born in Zhejiang, China, in February 1988. He received his B.S. and Ph.D. degrees in electrical engineering from Zhejiang University, Hangzhou, China, in 2010 and 2015, respectively. He currently works at Zhejiang Electric Power Corporation Research Institute. His research focus is on high power electronics technology, LCC-HVDC transmission systems, VSC-HVDC transmission systems, and DC grids.
Xiaohua Xuan received his B.S. degree in electrical engineering from Zhejiang University, Hangzhou, China, in 1987. He is currently the deputy manager at Electric Power Research Institute of State Grid Zhejiang Electric Power Corporation, Hang Zhou, China. His current research interests include management of power system technology.
Weibo Huang received his B.S. and M.S. degrees in electrical engineering from Beijing Jiaotong University, Beijing, China, in 2012 and 2015, respectively. Since 2015, he has been working for his Ph.D. degree at the Department of Electronic and Electrical Engineering, Beijing Jiaotong University, Beijing, China. His research interests include high-power converters for flexible HVDC applications and protection and control of flexible multi-terminal DC power distribution systems.
Yajing Zhang was born in Hebei Province, China. She received his B.S. degree in Electrical Engineering from the Beijing Jiaotong University, Beijing, China, in 2008; and hers Ph.D. degree in Electrical Engineering from Beijing Jiaotong University, Beijing, China, in 2015. In 2015, she joined the College of Information Science & Technology, Beijing University of Chemical Technology, Beijing, China, where she is presently working as a Post Doctorate. Her current research interests include power systems, Wide band gap semiconductor devices, Wireless power transmission and renewable resource generation.
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