Data-based power management control for battery supercapacitor hybrid energy storage system in solar DC-microgrid | Scientific Reports

Scientific Reports volume 14, Article number: 26164 (2024) Cite this article

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This paper addresses the energy management control problem of solar power generation system by using the data-driven method. The battery-supercapacitor hybrid energy storage system is considered to smooth the power fluctuation. A new model-free control method is utilized in the stand-alone photovoltaic DC-microgrid to provide the power to meet the demand load, while guaranteeing the DC bus voltage is stable. Furthermore, the proposed data-based power management control strategy only needs I/O data. Numerical simulations with real data verify the effectiveness of the proposed method.

The use of solar energy has been very mature and widely used, such as large-scale grid-connected solar power generation systems1, the stand-alone solar power generation systems2. Due to the rapid development of the photovoltaic (PV) industry, the stand-alone PV systems are ushered in vigorous development. In addition to the traditional solar streetlights, solar billboards, etc., many new applications are emerging, such as solar cars3, solar boat4, and solar UAV5. In the application of these stand-alone PV systems, the energy storage system is a key part. Therefore, it is necessary to study advanced energy storage systems.

In many energy storage systems, the output power of the distributed power supply is intermittent, it affects the operation of microgrid and power quality, which is not conducive to the development of power industry. In order to enhance the operation stability and power supply quality of microgrids, the application of energy storage systems is imperative. However, the single energy storage system cannot meet the development needs of the microgrid. Therefore, it is necessary to adopt a hybrid energy storage system (HESS) with more suitable performance6. HESS have attracted widespread attention in the industry and academia due to the advantage of high energy density, fast response, the ability of smoothing complex fluctuations7,8,9,10. The most typical HESS is based on batteries/supercapacitors, which combines the advantages of high energy density of the battery, also high-power density and long cycle life of the supercapacitor11. In recent years, this technology has been applied in many fields, such as electric vehicles12,13, the grid-connected photovoltaic system14, and microgrid15 etc.

Energy management strategy is one of the main factors affecting HESS performance16, which can be divided into two categories: offline design and online optimization. Offline design is generally rule-based control, such as the fuzzy-logic control16, and the neural network controller17, \(H\infty \) controller18. However, traditional controller used in control scheme of HESS has large power fluctuations when dealing with loads that change rapidly11. An effective method to solve the above problem was to use the model predictive control (MPC) algorithm19. However, it was often computationally complex and requires accurate models. Furthermore, an adaptive MPC approach based on the quadratic programming (QP) was proposed to energy management control problem, considered the nonlinearity and uncertainty of system20.

The rule-based method cannot guarantee the optimal performance of the system, so the optimization-based methods were proposed, such as MPC21,22,23, dynamic programming (DP)24,25. In21, an active HESS state space model was established and applied in MPC to minimize battery current fluctuations. In22, in order to reduce the computational burden, the control rate was designed offline and a piecewise linear function was solved. But the two are difficult to apply in nonlinear systems. To solve the multivariate nonlinear problem, researchers replaced the QP process in MPC with DP24. To further reduce the amount of calculations, an MPC method based on convex optimization was introduced into the design of HESS26,27. Following to this idea, using data-driven methods to replace the optimization process in MPC is a promising direction. Until now, there are few studies on the power management control problem of HESS by data-driven technique28.

The design based on models often requires the accurate system model. Due to factors such as the uncertainty and disturbance, the accurate system model is often hard to build. In addition, the effect of strong non-linearity on the modeling makes it more difficult to obtain an accurate model. Besides, in the field of solar energy applications, only a few researches investigated the power management control (PMC) of HESS.

To solve the above problems, this work provides a data-driven control method to deal with the energy management scheduling problem of HESS: A data-based energy management control strategy for HESS is proposed and it is applied to a solar DC-microgrid. The main idea of the model-free adaptive control method29 is to convert the nonlinear system increment to linear increment and use the adaptive algorithm to continuously adjust parameters online to optimize system performance, and it does not need to establish an accurate system model. This approach used in this work has a good nonlinear tracking performance, which can ensure that the voltage across the load remains constant, but when it is used to switch the load, there will often be a large current impact at the moment of switching. Therefore, this design adds a supercapacitor module to reduce the peak power shock caused by solar output power fluctuation and load switching. The main contributions are listed:

We present a data-driven power management control technique that doesn’t require an exact model, just I/O data.

The purpose of a model-free adaptive control-based battery/supercapacitor power distribution controller is to minimize the impact of peak current while guaranteeing a steady power supply to the load.

In contrast to conventional techniques (such as PI controllers), this approach has the ability to adjust controller parameters in real time online in order to accomplish the goal of reducing power fluctuations brought on by variations in load.

The rest of this work are arranged as follows: section "Solar photovoltaic system" introduces the structure of the solar system; section "Power management controller design" gives the presented data-driven power management control scheme. Simulations analysis and the results are shown in section "Results and analysis". Section "Conclusion" presents the discussion of the paper.

The structure of systems.

The structure of the solar-battery-supercapacitor system is shown Fig. 1. It is composed of solar module, battery/supercapacitor HESS module, control and load modules. Electrical part is connected by DC bus. The main purpose of the system is to make full use of the power generated by solar energy and supply it to the load. When the energy is excessive or insufficient, the energy storage system is used to adjust the power supply to ensure the stable operation of the load. The details of each module are discussed next.

After many years of development, solar modules have been relatively mature. Scholars have done a lot of research on models of solar panels. The following form is considered in the work30:

where, \(I_{pv}, I_{ph}, I_0\) are the output current of PV module, the photo current, and diode reverse saturation current, respectively. \(V_{pv}\) is the output voltage of PV module, \(R_s, R_p\) introduce the series and shunt resistance, \(n_s\), m are the number of cells in series and the diode ideality factor.

where, \(V_t\) is the thermal voltage, \(k, T_c\) are the Boltzmann constants and q is electron charge. Moreover, the photo current \(I_{ph}\) is

where, \(G_r\) is the standard solar irradiance, \(T_r\) denotes standard temperature, and \(I_cc\) defines short circuit current. And the diode reverse saturation current \(I_0\) is

where, \(I_{0r}\) is the reverse saturated current. \(V_g\) represents the energy gap. The power output of a PV module may be calculated as:

The PV output power not only depends on the above models, the choice of load, the selection of various module parameters, and the performance of the controller also affect the output power. The DC–DC converter is controlled by the maximum power point tracking (MPPT) controller so that the photovoltaic module can obtain a stable DC voltage while ensuring the maximum power output.

The DC–DC converter is an on-off switch that repeatedly converts a DC voltage or current into a high-frequency square wave voltage or current, and then soothes it to a DC voltage output. The DC–DC converter is generally composed of an inductor, a diode, an IGBT, and a capacitor (see Fig. 2). The DC–DC converter is a voltage converter that effectively outputs a fixed voltage after converting the input voltage. This work uses a PWM boost DC–DC converter, shown as follows.

DC–DC converter.

The left side is connected to the solar voltage output port, and the right side is connected to the DC bus port. The boost size is determined by the duty cycle D.

The circuit diagram of the HESS adopted in this work is shown in Fig. 3, it consists of a battery pack, a SC pack, two bidirectional DC–DC converters and controller.

The structure of HESS.

The main function of the battery module is to store the remaining power after solar power generation meets the load power consumption, and to supply power to the load, when the solar module power supply is insufficient. The charge/discharge power of HESS satisfies the following formula

where, \(P_b, P_{sc}, P_L\) are the power of battery, supercapacitor and load demand, respectively.

The charge and discharge voltage of the battery can be expressed by the following formula31

And the state of charge of the battery can be expressed as

SC is an energy storage element between a capacitor and a battery. It has both the characteristics of fast charging/discharging of a capacitor and the energy storage characteristics of a battery. In addition, SC have the advantages of high-power density and high-power amplifier efficiency. Therefore, it is often selected as the auxiliary energy storage unit. The SC, in general, composes of capacitors, resistors representing the charging or discharging units. The unit cell of the SC is constructed with two RC branches in parallel. The simple model of SC is shown in Fig. 4.

Simple model of supercapacitor.

The voltage of the SC can be obtained through the calculation of a single pack as follows32:

where,\(N_{psc}, N_{ssc}\) are the parallel branches and the serial connection of the SCs, respectively. \(V_{sc}, I_{sc}\) denote the voltage and current of the supercapacitor. And the \({SOC}_{sc}\) is calculated as the ratio between the current SC capacity and the maximum SC capacity.

The HESS composed of battery and SC will be connected to bidirectional DC–DC converter to provide and store energy for the load.

The so-called bidirectional DC–DC converter (see Fig. 5) is the two-quadrant operation of the DC–DC converter. Its input and output voltage polarity are unchanged, but the direction of the input and output current can be changed. The output state of the converter can be changed in one or two quadrants of the V-I plane. The converter’s input and output ports can still complete the voltage conversion function. Power can flow not only from the input terminal to the output terminal but also from the output terminal to the input terminal.

Bidirectional DC–DC converter.

The main purpose of this section is to use the data-driven controller to obtain the reference control quantities of the battery and supercapacitor, and then use the PWM generator to generate control signals to control the charge and discharge of the battery and supercapacitor. Then ensure that its SOC is within a reasonable range to extend battery life.

Figure 6 depicts the power management controller’s construction. Using the power gap and the actual and reference voltages of the DC bus, the data-driven controller (DDC) determines the energy storage system’s reference current. After that, a low-pass filter distributes it to the batteries and ultracapacitors. The PWM module uses the current error that results from comparing the reference current with the actual current flowing through it to create a duty cycle that controls the bi-directional DC–DC converter’s on and off turns, which charges and discharges the battery and supercapacitor.

Power management controller.

The specific SIMULINK-based combined controller design is shown in the following Fig. 7, unlike the existing work in33, the DDC method is introduced to replace the PI controller to obtain the reference current.

Battery and supercapacitor combined controller.

In order to keep the load voltage constant, the difference between the load voltage and the load reference voltage is used as an input, and the reference current of the HESS is obtained through the data-driven controller.

where, \(V_{dcr}(k), V_{dc}(k)\) are the reference voltage and real voltage of DC bus. \(I_r(k)\) is the reference current. \(f(*)\) is a nonlinear function.

Applying the linearization technique, the following equation can be obtained

where, \(\Delta V_{dc}(k+1)=V_{dc}(k+1)-V_{dc}(k)\). \(\hat{\phi }(k)\) is the estimation value of the linearization parameter. \(\Delta I(k)\) is the error increment of current.

The linearization parameters \(\phi (k)\) can be estimated as

where, \(e(k)=V_{dcr}(k)-V_{dc}(k), V_{dcr}(k)\) represents the reference voltage of DC bus. The positive and negative values represent the battery charge/discharge process.

The increase of the reference current can be obtained as:

From (6), the following equation can be obtained

Because the battery and the SC are connected in parallel at the same voltage \(V_{dc}(k)\), the reference current of the SC:

So the reference current at \((k-1)\) is

Then, the actual control current is

The reference battery current \(I_{br}(k)\) is obtained through a low-pass filter.

The difference between the current of the battery and the SC is used to obtain the error, and the control signal is generated by the PWM generator.

In this section, the daily average temperature and irradiation data34 are used in the simulation (see Fig. 8). Two different load cases, which include the constant and time-varying loads are simulated to verify the effectiveness of the proposed method. And the initial value of the DDC parameter \(\hat{\varphi }\left( 0\right) =1, \beta =0.2, \rho =0.7\). This article uses MATLAB/SIMULINK tools for simulation. The parameters of each module are shown in Tables 1, 2 and 3.

Temperature/irradiation profiles over a day.

This article uses Matlab/SIMULINK tools for simulation. The parameters of each module are shown in Tables 1, 2 and 3.

In this subsection, the constant load is selected in the solar system, voltage of the DC bus is shown in Fig. 9a. It can be seen that the proposed method achieves a good voltage regulation effect of 50 V. Moreover, load can also maintain rated power (200 W) operation (see Fig. 9b).

Voltage and power of load.

The simulation results of power can be shown as follows. In Fig. 10, the load required power, solar supplied power and battery/supercapacitor storage power are displayed. At the beginning of the day, when the sun has not yet risen, the load is mainly battery-powered, but starting the load at 0 o’clock requires a large starting current, and a SC is required to complete the power supply to the load. With the gradual increase of the irradiance, the power supply mode is changed from HESS power supply to HESS and PV combined power supply, and then to the PV power supply alone while the remaining power is stored in HESS. Finally, when the sun goes down, the system returns to HESS power supply.

Powers by DDC with SC.

Solar-battery-supercapacitor system supplies power to the load complementary. When the solar module does not generate power, the battery module first supplies power to the load. When the solar module generates power, the power from the solar module is preferentially used, and the remaining power is stored in a hybrid energy storage system composed of a battery and a super capacitor. In addition, the super capacitor also has the function of adjusting the peak power.

For comparing, the PI method, DDC without supercapacitor method and the proposed method are applied, and the DC bus voltage and load power are shown in Fig. 11a,b. The results show that the first two methods of the PI without SC method cannot guarantee the DC bus voltage stability, and the proposed method can effectively stabilize its voltage at 50 V. Furthermore, using the PI method, the load power is significantly greater than the required power, and it also has significant oscillations. The DDC method alone cannot meet the load demand and it will cause the load power to change as the solar power changes.

The voltage and power comparisons.

In this subsection, 200 W industrial DC motor, 100 W DC LED lamp and 600 W DC heater are used to simulate the working state of a DC load under the power supply system. Their working hours are the motor works from 8:00 to 18:00 during the day; the lights work from 18:00 at night to 6:00 the next day; the electric heater works one hour every four hours from zero. The DC bus voltage of 50 V is still maintained, but the time-varying load is considered. Load switching over time simulates power usage of different loads. Figures 12 and 13 show the voltage of DC bus and the load power. From the Figs. 12 and 13, it can be seen that under the condition of switching loads, the proposed method can keep the DC bus voltage stable, and it will not bring large fluctuations in load power when the load is switched.

Voltage of DC bus.

Load power over a day.

It can be seen (from the results of Fig. 14) that the system accomplishes the purpose of solar energy utilization and storage and continuously supplies power to the load.

Power over a day.

In the case of non-periodic switching loads, comparisons between the proposed method and the PI controller with SC are shown in Figs. 15 and 16. Figure 15 shows that frequent switching loads will cause fluctuations in solar DC microgrid power generation. But the proposed method is relatively smooth. Furthermore, from Fig. 16, compared with the traditional PI controller, using the proposed method will reduce the more peak power (i.e. peak current) caused by the increase in load and smooth the power fluctuation.

Comparison of PV power between PI and DDC.

Comparison of load power between DDC and PI.

For a more intuitive presentation, Table 3 is used. By comparing several sets of simulation duration, the average computation time used by the proposed method is 25.78s, which is less than the simulation time of traditional methods (30.28 s). From 9:00 to 10:00, four groups of power data are randomly selected for comparison and shown in Table 3. Whether it’s comparing the maximum error or the total error within a day, the proposed method is smaller than traditional methods. It clearly shows that the error of the proposed method is smaller when dealing with frequent switching loads.

In this research, the PMC problem of HESS was studied, and it was applied to the independent photovoltaic power generation system. A data-based power management control strategy was proposed, and a battery/supercapacitor charge/discharge combined controller was designed to enable the system to provide constant DC voltage power to the load and smooth solar output power and load power. Simulation results also confirm the feasibility of this approach. Future work is to extend the results to the AC grid and consider the issue of coordinated control of several stand-alone PV systems.

All data generated or analyzed during this study are included in this published article.

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This work was supported partly by the Natural Science Foundation of Shandong Province under Grant ZR2022QF080, partly by Postdoctoral Innovation Project of Shandong Province under Grant SDBX2022015, and partly by the Qingdao Postdoctoral Innovation Application Project.

School of Vehicle Engineering, Sichuan Automotive Vocational and Technical College, Mianyang, 621017, China

Qin Hu & Shilong Xie

School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266525, China

Ji Zhang

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Q.H. and S.X. wrote the main manuscript text and J.Z. provided the research ideas and framework of the article, as well as funding support. All authors reviewed the manuscript.

Correspondence to Ji Zhang.

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Hu, Q., Xie, S. & Zhang, J. Data-based power management control for battery supercapacitor hybrid energy storage system in solar DC-microgrid. Sci Rep 14, 26164 (2024). https://doi.org/10.1038/s41598-024-76830-y

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DOI: https://doi.org/10.1038/s41598-024-76830-y

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