Passivity-Based Control of Buck-Boost Converter for Different Loads Research

Zhang, Feng; Li, Jianguo; Zhu, Gejun; Hu, Rongyuan; Qu, Yaping; Zhang, Yujiang

doi:https://doi.org/10.1155/2023/5558246

Journal of Electrical and Computer Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 5558246 | https://doi.org/10.1155/2023/5558246

Passivity-Based Control of Buck-Boost Converter for Different Loads Research

Feng Zhang,¹Jianguo Li,²Gejun Zhu,¹Rongyuan Hu,¹Yaping Qu,³and Yujiang Zhang³

Academic Editor: Ramani Kannan

Received19 Jan 2023

Revised05 May 2023

Accepted03 Jun 2023

Published09 Jun 2023

Abstract

Normally, the buck-boost converter adopts single or double closed-loop control, and there are differences in control and parameters for different working modes and loads. In this study, a unified control method, the passivity-based control (PBC), is applied to a buck-boost converter for different loads, including constant resistance load (CRL), constant power load (CPL), and battery load. The PBC is a nonlinear control based on energy dissipation principle, and it has strong robustness to parameter interference and external disturbance, and it also has the advantages of simple design and simple implementation. Although many research studies have been conducted before, the voltage and current-related power losses are considered, and different load models are also compared in this research. The detailed mathematical model, control principle, and controller design of the buck-boost converter are thoroughly analysed. In addition, SIMULINK-based simulation results and experimental verification results of different loads are also given in the paper. Also, the PBC has smaller current overshot and smaller current ripples compared with PI control in different loads condition.

1. Introduction

A DC microgrid is usually composed of photovoltaic (PV) generator, battery energy storage system (BESS) and DC loads, and a PV generator; a BESS or a DC load requires either a higher or lower output voltage. To achieve a lower output voltage, a buck converter is used, and a boost converter is used when a higher output voltage is required. A buck-boost converter is used when a higher or lower DC output voltage is required at different times [1].

A buck-boost converter is either buck (lower) or boost (higher) converter, and it can transfer electrical energy bidirectionally. It has the advantages of simpler structure, lower cost, and higher reliability, and it is usually used to control the charging and discharging process in BESS, and a BESS converter is used to serve battery load [2].

Besides, when a PV converter is tightly regulated to stabilize the DC bus voltage, the DC bus will have a one-to-one voltage-current characteristic, and a PV converter is loaded with constant power load (CPL) [3]. Also, when a DC load has a constant resistance value, the DC load converter loads constant resistance load (CRL). In sum, the load of buck-boost converter may be battery load, CPL load, or CRL load, and different loads reveal different characteristics, so it is necessary to conduct the research of buck-boost converter in different loads condition.

The proportional integral differential control (PID) is most widely used in buck-boost converter to realize single closed-loop or double closed-loop control. It has the advantages of simple principle, easy implementation, and independence of system model [4, 5]. However, the buck-boost converter is a nonlinear time-varying system, and a PID cannot achieve the desired control effect, especially when the power source or load changes suddenly in a large range, and it even makes the converter unstable [6, 7].

To improve buck-boost converter’s stability, some nonlinear controllers are developed and applied to the converter. In 1983, the sliding mode variable structure control (SMVS) was first applied to DC/DC converter by Sabanovic et al. [8, 9]. After this, many improvements have been made to improve the converter’s performance, such as elimination of variable switching frequency’s influence, improvement of anti-interference capability, and reducing the natural buffeting. Despite all these improvements, SMVS has to determinate speed, inertia, acceleration, and switching surface parameters, and it is complex to implement online real-time control with a large amount of computation [10].

The adaptive control (APC) was also used in DC/DC converter [11–14]. The APC is a control method with online parameter identification, and it includes model reference adaptive control, self-tuning control, and parameter adaptive control. The APC also has strong robustness to parameter deviation and inaccurate model, but it is not widely used because of its serious lack of generality and openness. The optimization-based control was also used in DC/DC converter to attain the optimal droop resistances to minimize the error in the current sharing [15].

The neural network control (NNC) is the combination of neural network theory and control theory, and it is a control method by imitating biological neural system to process information. A NNC was also used in DC/DC converter to improve the transient performance of the converter. Although a NNC has the advantages of high nonlinear mapping capability, autonomous learning capacity, and fault tolerance capacity, it also has insufficient performance, such as low convergence speed, high sample dependence, and high initial network weight dependence [16, 17].

The passivity-based control (PBC), which was proposed by Ortega and Spong in 1989 [18], is a nonlinear control based on energy dissipation, and it utilizes energy dissipation to control stability and track given objects by means of damping injection. A PBC has the advantages of simple design and simple implementation, and it is already used in nonlinear system, such as motor control and power electronic devices. A PBC was also applied in DC/DC converter, and some measures have been made to eliminate steady-state error, which is caused by parasitic resistance, to improve the stability of CPL load [19–21]. However, the voltage and current-related loss are often ignored, and a unified PBC control strategy for different loads is not considered.

In the study, a unified PBC control strategy is applied to buck-boost converter, the voltage and current-related losses are considered independently, and battery load, CRL load, and CPL load are studied, respectively. Compared with previous research studies, the proposed control method is applied to different working modes and different loads, and it also has the advantages of simple design and simple implement. The buck-boost converter and different loads are analysed thoroughly, and the mathematical model in Euler–Lagrange (EL) form is deduced. In addition, the passivity characteristic is demonstrated, and a unified PBC controller is designed. Besides, the simulation and experimental verifications are carried out.

The rest of this study is organized as follows. In Section 2, the buck-boost topology is introduced and analysed thoroughly. In Section 3, the mathematical model based on EL equation is proposed. In Section 4, the unified PBC controller is designed according to the EL model. In Section 5, the different load models are given, Later in Sections 6 and 7, the results of simulation and experimental verification are given separately. Finally, Section 8 concludes the study.

2. Buck-Boost Converter Analysis

A buck-boost converter is made up of S_d1, S_d2, VD₁, VD₂, L_d, C₁, and C₂, as depicted in Figure 1. Here, S_d1 and S_d2 are all-controlling power switches, for example, MOSFET and IGBT. VD₁ and VD₂ are antiparallel power diodes. L_d is a DC inductor. R₁ and R₃ are used to simulate voltage-related loss, and R₂ is used to simulate current-related loss. A buck-boost converter can realize voltage conversion between different DC voltages, and it can exchange bidirectional power at the same time.

3. Buck-Boost Converter Mathematical Model

3.1. Buck State Model

When the power switch S_d2 is turned off all the time and S_d1 is controlled to turn on and off periodically, a buck converter is realized. Also, it converts constant voltage into variable voltage, such as charging the battery from DC bus.

In Figure 2, it shows the buck converter current path. When S_d1 is turned on, the power diodes VD₁ and VD₂ are all turned off, and the current path is -S_d1-L_d--- as shown in Figure 2(a). At the time, the power supply transmits energy to the load , while the inductor L_d stores energy, and the current i₂ increases.

(a)

(b)

When S_d1 is turned off and the power diode VD₁ is also turned off, the current path is ---- as shown in Figure 2(b). At the time, the inductor L_d releases energy and transmits energy to the load , and the current i₂ decreases.

According to Kirchhoff’s voltage law, we can obtainwhere D₁ is the duty ratio of power switch S_d1. D₁ is 0 when the switch is off, D₁ is 1 when the switch is on, and the duty ratio range is 0 ≤ D₁ ≤ 1.

By writing the current equation for the output node, we can obtain

Synthesizing (1) and (2), where I₁ and I₂ are mean currents of input and output, respectively.

3.2. Boost State Model

When the power switch S_d1 is turned off all the time and S_d2 is controlled to turn on and off periodically, a boost converter is realized. Also, it converts variable voltage into constant voltage, such as discharging the battery to DC bus.

In Figure 3, it shows the boost converter current path. When S_d2 is turned on and the power diodes VD₁ and VD₂ are all turned off, the current path is as shown in Figure 3(a). Compared with Figure 2(b), the current flows S_d2 in the opposite direction. At the time, the power supply stores energy in the inductor , and the current i₂ increases, which also meets (2).

(a)

(b)

When S_d2 is turned off and the power diode VD₂ is turned off, the current path is as shown in Figure 3(b). Compared with Figure 2(a), the current flows VD₁ in the opposite direction. At the time, the power supply transmits energy to the microgrid , the inductor releases energy, and the current i₂ decreases, which also meets (1).

If the duty ratio of the power switch S_d2 is set as D₂, D₂ is 0 when the switch is off, D₂ is 1 when the switch is on, and the duty ratio range is 0 ≤ D₂ ≤ 1.

The buck-boost converter can be expressed as follows:

If the state variable is X = (i_d, )^T and the input variable is V = (D₁, −i₂)^T, (4) can be sorted into Euler equation in the form ofwhere M is a positive definite symmetric coefficient matrix, i.e., M^T = M. J is an antisymmetric coefficient matrix, i.e., J^T = −J. R is a positive coefficient matrix, i.e., R^T = R > 0, which means that the converter has dissipative characteristic.

4. Passivity-Based Controller Design

It is assumed that the target values of state variables are and , respectively, that is, = (, )^T, and the error variable is X_e = X − ; according to (5), we can obtain

To accelerate the convergence rate of X_e to 0, a damping coefficient matrix R_d = diag{r₁₁, } is used to accelerate X approach to ; therefore, it can be rewritten as follows:where r₁₁ and are the injection damping coefficients.

According to the theory of PBC [19], the PBC controller can be designed as follows:

The matrix equation can be further expressed as the following differential equation form:

4.1. Constant Current Control

When a buck-boost converter works in constant current control (CCC) mode, the reference is used as control target. So the first control equation with is selected, and is replaced by the sampling voltage . So, we can obtain

4.2. Constant Voltage Control

When a buck-boost converter works in constant voltage control (CVC) mode, the current reference and voltage reference are all used as control target. So, we can obtain

Normally, the voltage reference is manually set directly, and the current reference is gotten by a PI controller indirectly in the CVC mode, that is,where k_p and k_i are proportional and integral coefficients, respectively.

The current response is derived as follows:where A_d is the initial values of transient components and τ is the time constant.

It implies that when τ is greater than 0, i_d converges to . Also, when r₁₁ is larger, the convergence speed is faster, and current transfer function iswhere T_s is the sampling delay time. According to control theory, when Re|G(jω)| is greater than 0, the system is internally stable, so we can get the range of damping coefficient r₁₁.

Figure 4 shows the buck-boost converter’s control diagram. When a buck-boost converter supplies CRL loads or CPL loads, the CVC mode is usually used. Also, when a buck-boost converter supplies battery loads, the CCC mode and CVC modes are used according to the state of charge (SOC) of the battery.

It can be seen that only L_d is used in the controller, and it only affects the derivative of current reference (/dt). The current reference usually comes from a PI controller, and its output has a relatively large range, so the parametric uncertainty of L_d has almost no significant impact on the system. In addition, the load current i_d only appears in the damping term, and the load disturbance also has no significant impact on the system. The PBC has inherent strong robustness against parametric uncertainties and load disturbances.

5. Different Loads Model

5.1. Constant Power Load Model

A CPL consumes constant power within a certain voltage range, and the voltage and current can be expressed as follows:where is the constant power, and its incremental resistance is negative, which means that the current drawn by the load increases or decreases with the decrease or increase of voltage, that is

The voltage and current characteristic of the CPL, which is shown in Figure 5(a), can be expressed as follows [19]:where V₂ is steady state voltage, and CPL can be equivalent to the parallel connection of a controlled current source and a negative resistor, as shown in Figure 5(b).

(a)

(b)

5.2. Battery Load Model

The battery can be equivalent to a variable voltage source with a variable internal resistance, and the variable equivalent voltage is related to the battery’s state of charge (SOC), and the variable internal resistance is related to battery’s ohmic resistance and polarization resistance. The ohmic resistance is constant for a particular battery, but the polarization resistance changes all the time according to the battery’s working conditions. Figure 6 gives the battery’s equivalent circuit, and it can be expressed as follows:

6. Simulation Verification

To validate the superiority of PBC over PI in different loads, simulations based on SIMULINK are carried out. The main circuit parameters of the buck-boost converter are shown in Table 1, and the control coefficients are listed in Table 2.

6.1. Battery Load Simulation

In Figure 7, it shows the current waveforms compared with PI control with battery load. At the time t = 0, the buck-boost converter starts to go to CCC mode with 20 A charging current reference, then go to CVC mode with 705 V charging voltage reference at the time t₁, finally go to CCD mode with −20 A discharging current reference at the time t₂. Whatever with PI control or PBC control, the buck-boost converter tracks the control command quickly.

(a)

(b)

Compared with PI control, the PBC control has no obvious current overshot in the transient processes, and it also has smaller current ripples in the steady state. Also, it shows that PBC has better transient and steady characteristics in battery load condition.

6.2. Constant Power Load Simulation

In Figure 8, it shows the current waveforms compared with PI control with CPL load. At the time t = 0, the buck-boost converter supplies 10 kW rated CPL load, the CPL load increases to 15 kW at the time t₃, then the supplied voltage is reduced to 600 V at the time t₄, after that the CPL load decreases to 10 kW at the time t₅, finally the supplied voltage is restored to 705 V at the time t₆. Whatever with PI control or PBC control, the buck-boost converter works well to response the control command.

(a)

(b)

Compared with PI control, the PBC control has smaller current ripples, which has been reduced by 67.23%, throughout the process. And, it shows that the PBC control has better characteristics over PI control in CPL load condition.

6.3. Constant Resistance Load Simulation

In Figure 9, it shows the current waveforms compared with PI control with CRL load. At the time t = 0, the buck-boost converter supplies 70 Ω resistance load, another 70 Ω resistance is connected at the time t₇, then the supplied voltage is reduced to 600 V at the time t₈, finally the supplied voltage is restored to 705 V at the time t₉.

(a)

(b)

Compared with PI control, the PBC control has smaller transient current overshot, which has been reduced by 14.29%, and it also has smaller current ripples in steady state. And, it shows that a PBC control has better transient and steady state characteristics over PI control in CRL load condition.

Through the simulation comparation of buck-boost converter with battery load, CPL load, and CRL load, the PBC control has smaller current overshot and smaller current ripples, and it has better transient and steady state characteristics over PI control.

7. Experimental Verification

To further verify the PBC control of buck-boost converter with different loads, a downsize buck-boost converter is built, and a bidirectional DC power of PSB9750-20 (Elektro Automatik company) is used as power supply, an electronic load of MWBPF2-1040 (MyWay company) is used as CPL load and CRL load, and 4 lead-acid battery cells are used as battery load, as shown in Figure 10.

7.1. Battery Load Verification

In Figure 11, it shows experimental waveforms with battery load. The input voltage is 50 V, and the buck-boost converter works in constant current state with battery load. At the time t₁, the buck-boost converter starts to change from CCC state to CCD state, the current changes from 1 A to −1 A, and the voltage changes from 44 V to 32 V. At the time t₂, the reverse change process from CCD state to CCC state occurs. The dynamic response time is less than 10 ms, and there is no current overshot during transient processes. Because of its high internal resistance, the battery voltage has also undergone a larger change.

(a)

(b)

7.2. Constant Power Load Verification

In Figure 12, it shows experimental waveforms with CPL load. The input voltage is 50 V, and the buck-boost converter works with CPL load of 100 W. At the time t₃, the buck-boost converter starts to change voltage reference from 35 V to 45 V, the voltage tracks the command quickly, and the current decreases from 2.7 A to 2.0 A accordingly. At the time t₄, the reverse voltage reference change process from 45 V to 35 V occurs. The dynamic response time is less than 8 ms, and there is also no current overshot during transient processes.

(a)

(b)

7.3. Constant Resistance Load Verification

In Figure 13, it shows experimental waveforms with CRL load. The input voltage is 50 V, and the buck-boost converter works with CRL load of 20 Ω. At the time t₅, the buck-boost converter starts to change voltage reference from 35 V to 45 V, the voltage tracks the command quickly, and the current increases from 1.7 A to 2.0 A accordingly. At the time t₆, the reverse voltage reference change process from 45 V to 35 V occurs. The dynamic response time is also less than 8 ms, and there is also no current overshot during transient processes.

(a)

(b)

Through the experimental verifications, the PBC control of buck-boost converter has better transient and steady state characteristics whatever in battery load or in CPL load and CRL load.

8. Conclusion

A buck-boost converter is often used in DC microgrid, and it loads battery load, CPL load or CRL load when it connects BESS, PV, and DC loads. In the study, a unified PBC control is applied to buck-boost converter with different loads. Some theoretical analysis, simulation, and experimental verifications have been conducted in the study.

The results show that compared with PI control, the PBC control has smaller current overshot, which has been reduced by 14.29%, and it has smaller current ripples, which has been reduced more than 50% with CPL load. The PBC control has better transient and steady state characteristics over PI control.

Besides, the unified PBC control is applied to different working modes and different loads, and it also has the advantages of simple design and simple implement. It has strong robustness because of its energy control principle, but it does not handle small signal and large signal disturbances separately.

Although some experimental researches have been conducted, more comparison of different control methods and more in-depth research studies still need to be strengthened. In addition, the research of parametric uncertainty verification will be further conducted in the following research.

Data Availability

The data used to support the study are openly available in a public repository.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors give their sincere appreciations to the support of Class B1 Key Scientific Research Projects of State Power Investment Group (Grant no. KYB12022ZH01) and State Natural Science Foundation Program of China (Grant no. 52107176).

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Copyright © 2023 Feng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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