Active disturbance rejection control of photovoltaic microgrids based on disturbance compensation and feed-forward correction strategy

Photovoltaic microgrid (PV) is a promising direction of new energy generation technology. However, due to the performance of low-voltage side interface affected by complex disturbance, PV microgrid has the problem of output voltage fluctuation, which will make the power quality not guaranteed. In order to stabilize the low-voltage side load supply, the active disturbance rejection control strategy with disturbance compensation and feed-forward correction (ADRC-DCFC) is proposed. By expanding the conventional state observer (ESO) dimension, a feed-forward correction link for disturbance tracking compensation is added. In contrast, the internal deviations extracted from the system model are actively added to the disturbance compensation link. In addition, a theoretical analysis of its disturbance observation performance and noise suppression performance is presented. Experimental results on a 300-watt test platform verified the accuracy and effectiveness of the ADRC-DCFC.


Introduction
As an essential part of new energy generation technology, PV microgrids show continuous development and effectively contribute to green and low-carbon energy supply [1].However, the nature of frequent energy interactions between the microgrid and the load side can cause voltage fluctuations.In addition, the volatility and intermittency of distributed power sources with high penetration rates can affect the stability and reliability of microgrids [2].Therefore, it is imperative to handle power quality problems such as voltage fluctuation and voltage flicker in microgrids.The interface converter, as the core part of the DC bus, is the control key to solve the microgrid disturbance-type output voltage fluctuation problem.In the context of wide-band gap devices, it is difficult for conventional PI control to effectively produce a dynamic response to the disturbances of a nonlinear converter [3]- [5].
The Active Disturbance Rejection Control (ADRC) technique is a control strategy with an extended state observer (ESO) as a key component.ADRC could actively tracks and extracts disturbance information before the disturbance significantly affecting the system output and then quickly eliminates the disturbance with a control signal [6].Besides, ADRC shows robustness to nonlinear systems and strong immunity to disturbances; therefore, it has gained wide attention in microgrid interface converter control [7].However, the low-order ESO in conventional ADRC ignores the deviation of the higherorder part and nonlinear part of the controlled object from the first-order output.Moreover, it simply employs an expanded first-order state variable to track and estimate the discrepancies between the standard system form and the actual structure (internal disturbances) and the disturbances encountered by the controlled object (external disturbances).This creates the problem of unsatisfactory control due to low accuracy of disturbance observation and slow dynamic response when applying low-order ADRC for self-anti-disturbance control of interface converters [8][9].It is demonstrated that the dynamic response speed of ESO to the total system disturbance becomes slower as the deviation of the actual order of the controlled object from the estimated model of ESO increases, affecting the compensation of the total disturbance by ADRC.In addition, conventional ADRC ignores the information that can be obtained by the system model and uses this known information as part of the total disturbance, which is tracked and estimated by ESO, reducing the accuracy of the disturbance observation [10].
To address the aforementioned issues, the known model information of the six-phase interleaved parallel converter is incorporated into the coefficient matrix.The actual interface converter model is obtained using the state-space averaging method and Laplace inverse transformation.By comparing the model of a second-order controlled system in traditional disturbance rejection control, the causes of the issues are identified.The scheme adopts a disturbance compensation and feed-forward correction strategy to compensate for disturbances using model features.Meanwhile, it increases the order of the extended state observer, which tracks and estimates disturbances in the bidirectional DC-DC converter.Additionally, feed-forward correction control is performed for the disturbance tracking and estimation process.Finally, the validity of the proposed method was verified by testing on a 300-watt platform.

Mathematical model
The renewable energy sources, loaded within the PV power microgrid, are connected to the DC bus through an interface converter.A common PV power microgrid structure is shown in Figure 1  The analysis in this paper is based on a low-voltage side buck interface converter between the load and the DC bus.The interface converter is modeled as a six-phase interleaved parallel converter structure.Six buck converters with the same structural parameters and similar dynamic processes are connected in parallel.1 1 2 S S is the power MOSFET with a high operating frequency (200 kHz).
1 on R and ESR R denote the parasitic resistance that cannot be eliminated in the actual environment, and the interface converter topology is shown in Figure 2.
One of the single-phase DC-DC converters is taken as an example for analysis.In one cycle of s T ,  1) and (2), respectively.
Duty cycle 0 (1 ) From Equations ( 1)-( 3), the transfer function ( )  G s between the output voltage 0 v and the equivalent duty cycle D is calculated as follows.
The other phases are consistent with the single-phase in Equation ( 4), while each phase conducts to meet the principle of phase shifting control, with each phase conductive signal differing by 60° in turn [11].

Conventional ESO control strategy
The extended state observer (ESO) is the core of ADRC, which expands the external disturbance of the controlled system, tracks the observation of the external disturbance in real-time, and compensates for it.It efficiently solves the core problem of observing the disturbance in active anti-disturbance technology.
The traditional linear extended state observer (LESO) is modeled as follows:

z t z t y t z t z t z t y t b u t z t z t y t
where are adjustable parameters of the state observer, which regulate the dynamic performance of the state observer.Then bandwidth method is used to configure the self-antiturbulence parameters of the extended state observer to achieve a simplification of the parameter regulation process [12].
The second-order system is described in the traditional ADRC strategy as follows: In the performance analysis of LESO, the core issue is to improve the dynamic response and tracking estimation of LESO to the total disturbance.The observed transfer function of LESO to the total disturbance can be expressed as: where 0 25,50,100,150   .The frequency domain performance curve of LESO tracking estimation for disturbance observation is shown in Figure 3.
Figure 3 shows that the bandwidth of the disturbance observation is small, and the tracking estimation is poorly fast.The phase lag and response overshoot are large, and the tracking response speeds up with increasing frequency while the amplitude increases in the higher frequency bands, which shows that the less accurate the observer is in estimating the perturbation.The Laplace inverse transformation of Equation ( 4) yields the actual interface converter model: In conventional ADRC, the second-order controlled system is modeled as: ) By comparing Equations ( 8) and ( 9), it is easy to find that the ESO in conventional ADRC expands the disturbance of the controlled system (interface converter) by completely ignoring the deviation of the higher-order and nonlinear parts of the controlled object model information from the first-order output.This estimation deviation causes the dynamic convergence speed of the expansion dimension of the ESO (the estimated response speed to the total disturbance) to become slower, resulting in a lag in the compensation process for the total disturbance.
In order to solve the above problems, this paper proposes a self-anti-disturbance voltage stabilization control strategy for LESO with disturbance compensation and feed-forward correction based on the idea of compensating the order of conventional ESO, as described below.

Disturbance compensation link based on model features
The accuracy of total disturbance tracking estimation under conventional LESO observation is not high enough and causes delays.To solve the estimation bias problem, the single-phase DC-DC structural model is used to compensate for the total disturbance information, reduce the observer's burden on the estimation of the external disturbance tracking, further reduce the difference between the estimated and actual disturbance, and improve the dynamic response speed of the disturbance observation.Taking , after substituting Equation ( 4) and considering the simplified modeling [13], the controlled system model is reconstructed to compensate for the perturbations to be observed.
    (10) The compensation component 0 ( ) f t together with the estimated ( ) f t tracked by the expansion state observer, constitutes the total disturbance of the system, and the overall reduction is achieved under the action of the inverse signal of the disturbance estimate generated by the controller.

Improved ESO under feed-forward correction
The following modified ESO based on feed-forward correction control is designed.
The modified ESO in Equation ( 11) maintains the third-order state variable to describe the secondorder controlled object model and the disturbance model that is expanded to a new state.It introduces a state variable with a free expansion dimension to provide a real-time by-feed correction to the LESO tracking system disturbance.The improved controller is referred to as ADRC with disturbance compensation and feed-forward correction (ADRC-DCFC), and the ESO-DCFC is its core mechanism, which can improve the accuracy and rapidity of the ESO-DCFC tracking to estimate the total system disturbance by adjusting the parameters of the observation matrix   When the system is converted from passive immunity to active immunity, the system can be reduced to a double integrator series structure.Based on this, the LSEF is reconstructed to replace to eliminate the system oscillations caused by rapid changes in the given signal.
The structure of the ADRC-DCFC is shown in Figure 4.

Disturbance observation performance and noise suppression performance
According to the system of higher order differential equations in the matrix form of ESO-DCFC in Equation (11), the relationship between each state variable in ESO and the input control quantity and the output quantity of the controlled object can be obtained as shown in Equation ( ) The bandwidth method is used to configure the improved state observer and system controller parameters.The damping ratio of the control system is also adjusted to 1 to ensure the dynamic performance of the self-turbulent system.The parameters are designed as follows. ESO-DCFC: LESF: 2 , 2 w effectively reduces the phase lag phenomenon of the tracking signal while having almost no effect on the gain of the high-frequency band.Therefore, the improved ESO has a good noise suppression effect and ensures that the effect of noise on the system observation does not deteriorate with the increase of bandwidth [15].

Experimental validation
In order to verify the effectiveness of ADRC-DCFC and the accuracy of the theoretical analysis, a 300 W buck low-power experimental platform was constructed, as shown in Figure 8.Among the switch tubes used are Infineon model BSC052N08NS5 80V OptiMOS industrial power MOSFET.A programmable load is used to simulate the various characteristics of load changes during photovoltaic power generation.Specific hardware parameters are shown in Table 1.The PI strategy and the ADRC-DCFC strategy proposed in this paper are used as voltage external loop controllers to analyze the immunity performance of the two strategies in actual operation by comparing their voltage variation and adjustment time under increasing and decreasing load conditions.
The experimental results are shown in Figure 9 and Figure 10. Figure 9 shows the control effect of the voltage external loop controller under PI control strategy and ADRC-DCFC strategy in the operating condition of increasing load.The voltage fluctuation is 9.7 V under the PI control strategy and 8.2 V under ADRC-DCFC control, which is 15.5% less than under the PI control strategy and 58.5% less adjustment time.Figure 10 shows that the voltage fluctuation is reduced by 28.2%, and the adjustment time is reduced by 11.8% for the reduced load condition.The comparison shows that the improved ADRC-DCFC strategy can maintain a more stable transient performance with stronger immunity to disturbances when significant fluctuations occur on the load side, thus reliably improving the power quality of the microgrid.

Conclusion
This study introduces the ADRC-DCFC strategy to improve the stability and reliability of PV microgrids while addressing the power quality issues caused by energy interaction and load-side characteristics.By using model characteristics to compensate for perturbations, the burden of tracking the estimation of perturbations by the observer is reduced.The feedforward correction link of the disturbance estimation process is also added by reconfiguring the form of ESO, which further improves the dynamic response speed and tracking performance of the observer.

1 S and 2 S
conduct complementarily.State space equations for time periods  

Figure 3 .
Figure 3. Frequency domain curves of LESO disturbance observation performance

Table 1 .
System parameters