Modeling and Analysis of an Avionic Battery Discharge Regulator

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.

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.

 

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 Q1 and Q2. The input-damping filter, including Lf, Cf1, Cf2, 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].

Fig. 1.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.

Fig. 2.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 of each module is equal, the equivalent inductance is 4L/3, and the inductance of the single-module power stage model is 4L [11]. When the disturbance of input voltage is zero, control-to-output current transfer function Gid(s) can be derived as Eqn. (1). The power stage model is established in CCM.

Fig. 3.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 is related to control current , output current , input voltage , and output voltage , as shown below.

where Fm =1/ MaTs , Fg = (D2 + 2D -1)Ts / 8L , and Fv = (1- 2D)Ts / 8L . D is the sum of the duty cycles of Q1 and Q2, and Ts is half of the period of Q1. 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.

Fig. 4.Small signal model of the three-module NIWC system.

Fig. 5.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 He1(s) and He2(s)[13]. The following equation makes the small signal model close to reality.

where ωn =π / Ts and Qz = -2 /π .

 

V. CONVERTER DESIGN

The system specifications are described in Table I.

TABLE ISYSTEM 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.

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

The loop gain of the average current loop is

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(jω)|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

where Ki =1/ Ri2(Ci1 +Ci2) , ωzi =1/ Ri1Ci2 , and ωpi = (Ci1 + Ci2) / Ri1Ci1Ci2.

Fig. 6.Bode plots of current loop gains Ti(s) and Tio(s).

The parameters are Ri1 = 8kΩ , Ri2 =10kΩ , Ci1 = 240 pF , and Ci2 = 50nF .

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.

The loop gain of the voltage loop is

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

where Kv =1/ Rv2Cv1 andωzv =1/ Rv1Cv1.

Fig. 7.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 Rv2=10 kΩ, then Rv1≈300 kΩ. The zero frequency of the voltage regulator is designed to be 100 Hz, so Cv1≈5.4 nF.

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 is zero is shown in Fig. 8 by introducing the disturbance of load current The transfer function of close-loop output impedance is

Fig. 8.Small signal model of output impedance.

In Fig. 9, the maximum output impedance is 41.4 mΩ, which satisfies the requirements. Hence, NIWC has a good load adjustment rate.

Fig. 9.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.

Fig. 10.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.

Fig. 11.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 mΩ during the entire frequency band, which satisfies the requirements. Therefore, NIWC has a good load adjustment rate.

Fig. 12.Measured voltage loop gain Tv(s).

Fig. 13.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.

where is the average output current and is the maximum difference between the output current of each module and the average output current.

TABLE IICURRENT-SHARING PERFORMANCE WITHOUT A CURRENT-SHARING CONTROL STRATEGY

TABLE IIICURRENT-SHARING PERFORMANCE WITH THE PEAK CURRENT CONTROL STRATEGY

TABLE IVCURRENT-SHARING PERFORMANCE WITH THE IMPROVED PEAK CURRENT CONTROL STRATEGY

From Tables II–IV, conclusions can be drawn as follows.

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.

Fig. 14.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.

Fig. 15.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.