Sage Journals: Discover world-class research

Abstract

The grid-connected inverter is the key to ensure stable, reliable, safe, and efficient operation of the power generation system; the quality of the grid-connected output current waveform directly affects the performance of the entire power generation system. To improve the anti-interference performance and reduce the output current harmonic content of the grid-connected inverter, an improved control strategy that combined repetitive control (RC) and auto disturbance rejection control (ADRC) is designed in this paper. Firstly, decoupled the ADRC to realize the individual adaptation between tracking performance parameters and anti-interference performance parameters of the controller, through which the difficulty of adjusting parameters is reduced. Secondly, the control approach is devised by adding RC to ADRC. To demonstrate the effectiveness of the proposed method in this paper, detailed experimental studies are conducted using proportional integral control, traditional ADRC, and the proposed method under normal power grids, weak power grids, and periodic disturbances. And dynamic performance simulation experiment is done to verify the dynamic performance of the self-disturbance rejection controller before and after the addition of RC links. The results indicated the effectiveness and feasibility of the proposed method. Finally, after simulation, the steady state and dynamic performance are conducted on a hardware testing platform. The impacts of the obtained results indicate the effectiveness and feasibility of the control algorithm proposed, the ability to suppress intermediate frequency disturbances is improved, the bandwidth of the auto disturbance rejection controller is expanded, and the harmonic content of the output current is depressed.

Keywords

Grid-connected inverter resonant peak suppression auto disturbance rejection control repetitive control total harmonic distortion

Introduction

Nowadays, the “dual carbon” green development goal proposed in China 2020 has received attention from various sectors at home and abroad. However, in the context of global energy scarcity, achieving the “dual carbon” goal is a transformative goal for the development of new energy.^1,2 According to the national grid connection standards GB/T14549 and IEEE1547,^3,4 the total harmonic distortion (THD) of electrical energy injected into the power grid must be less than 5%. However, because of the existence of nonlinear factors such as the dead time effect, switching tube conduction voltage drop, and grid voltage fluctuations in grid-connected inverter systems, it is difficult for inverters to maintain good performance; thus, the research on inverters is of great significance.^5,6

At present, the main control strategies for grid-connected inverters include proportional integral (PI) control, proportional resonance (PR) control and repetitive control (RC). The PI controller has the advantages of simple design and easy parameter adjustment. So it is widely used in practical engineering.^7–9 Although the PI controller can provide good performance in DC control applications and be able to achieve zero error tracking. But the tracking and control effects of communication signals are not ideal.^10,11 Zhang et al.¹² adopted a feedback strategy for the grid-side current employing the PI and resonant controller to mitigate the harmonics of the grid-side current and improve the quality of the output power of the grid-connected LCL-filtered inverter, but this strategy can only improve the quality of grid-side current under non-ideal grid conditions. Ahmed et al.¹³ used a simple PI controller-based approach to propose a method for improving the small signal dynamic response of a grid-connected SOFC plant where the controller parameters are adjusted by the DE algorithm. Aouchiche¹⁴ adjusted the gain values of PI regulators in order to enhance the grid-connected system dynamic behavior, but it didn’t compare the performance of the FOPI and PI controllers. Elnady and Alshabi¹⁵ suggested an adaptive PI controller, which has robust performance at different loading conditions, but is complex in its design procedure. Moeti and Asadi¹⁶ proposed an adaptive PI current controller for a two-stage grid-connected photovoltaic inverter, which has the advantage of providing low grid current THD and desirable dynamic response, but it requires an accurate model of the system.

By setting the fundamental frequency point, the PR controller has sufficient gain at the fundamental frequency point while the gains at other points remain unchanged, thus achieving accurate and error-free tracking of the fundamental wave of the AC signal.^17–20 But the control frequency band of the PR controller is narrow and it can only achieve sufficient gain at a fixed frequency.¹¹ Negi et al.²¹ used the PR controller to realize an improved damping strategy that has enough stability margin, but requires an accurate model of the system and high online computational requirements. Yanarates and Zhou²² designed a novel PR controller to resolve the drawbacks of conventional PI controllers in terms of phase management. Xie et al.²³ applied the PR controller to achieve a fixed switching frequency and mitigate steady-state error; however, it is not practical to implement by either analog or digital signal processors. Qiu et al.²⁴ and Sou et al.²⁵ adopted the improved quasi-PR controller, this control method can only achieve zero static error tracking for a single-frequency signal.

Haneyoshi T et al. applied an RC strategy based on the internal model principle to inverters.²⁶ RC has the advantages of strong robustness and high steady-state accuracy. At the same time, it not only achieves zero static error tracking in inverters but also eliminates disturbances. However, the RC control has poor dynamic performance when using a single RC due to the delay link in the internal model.^27–29 Guo et al.³⁰ utilized a current controller which combined repetitive controller with PI controller, the proposed method can eliminate the effects of harmonics and reduce the net current harmonics. Zhang et al.³¹ utilized the control strategy of parallel connecting RC control and PI, in which the RC control was used to suppress harmonics in the system and the PI control was used to realize fast dynamic performance. Mao³² designed a compound control strategy for LCL to improve the compensation effect of harmonic current.

In order to solve the problem of grid-connected current control, a grid-connected current control strategy that combines auto disturbance rejection control (ADRC) and RC control was proposed in this paper. The designed method expands the bandwidth of the self-disruption rejection control and also has better dynamic performance; moreover, the anti-interference ability of grid-connected inverters can be effectively improved, and the output current harmonic content can be reduced. In addition, periodic disturbances can be effectively suppressed.

The remaining structures of the article are arranged as follows: The theoretical basis for the design of grid-connected inverters is analyzed in Section Related Work. The design methods are proposed in Section Methods. Section Experiment methodology and results presented the simulation and experimentation. The experimental conclusions and future research are presented in Section Conclusion.

Related work

Analysis of the structure and working principle of grid-connected inverters

The topology structure of a single-phase LCL grid-connected inverter is shown in Figure 1. U_dc is the DC bus voltage, S₁∼S₄ is the switching, $L_{1}$ , $L_{2}$ and C constitutes an LCL-type filter.

Figure 1.

Topology structure of a single-phase LCL grid-connected inverter.

To facilitate the analysis of the working principle of the LCL grid-connected inverter, the following assumptions need to be made:

The switching devices in the circuit are all ideal devices; the voltage drop and switching time during IGBT conduction are negligible.

The circuit characteristics are ideal; there are no parasitic circuits, distributed inductance, or capacitors.

The DC side voltage is in a stable state.

In the modulation method of the SPWM wave, the unipolar frequency doubling method is selected to control the turn on and off of the switch tube. The modulation principle is shown in Figure 2. Where

u_{r}

and

- u_{r}

are two sine waves with opposite polarity and phase difference of

180^{\circ}

u_{c}

is the carrier triangle wave, set

u_{r}

as the modulation wave of switch tubes

s_{1}

and

s_{2}

on the left bridge arm,

- u_{r}

is the modulation wave of switch tubes

s_{3}

and

s_{4}

on the right bridge arm. When the amplitude of the sine wave is greater than the amplitude of the triangular wave, namely

u_{r} > u_{c}

and

- u_{r} > u_{c}

, switch tubes

s_{1}

s_{3}

turn on and switch tubes

s_{2}

s_{4}

cutoff, on the contrary,

s_{2}

s_{4}

turn on and switch tubes

s_{1}

s_{3}

cutoff. From the pulse sequence

U_{d c}

, it can be seen that during one action of the switch tube conduction, the state of a changed twice, namely,

U_{d c} \to 0 \to U_{d c}

. Therefore, in the unipolar frequency doubling modulation method, the switching frequency of the switch tube is twice the carrier frequency. Under this modulation method, the volume of the AC side filter can be reduced without increasing the switching frequency.

Figure 2.

Unipolar frequency doubling modulation.

Analysis of LCL filter characteristics

The equivalent circuit diagram of the inverter is shown in Figure 3.

Figure 3.

Equivalent circuit diagram of the inverter.

According to Kirchhoff's current law, the equation of the filter can be written as follows:

{\begin{matrix} L_{1} \frac{d i_{L}}{d t} = u_{a b} - u_{c} \\ C \frac{d u_{c}}{d t} = i_{L} - i_{g} \\ L_{2} \frac{d i_{g}}{d t} = u_{c} - u_{g} \end{matrix}

(1)

Where

u_{a b}

is the output side voltage of the inverter;

u_{c}

is the voltage of the filter capacitor;

u_{g}

is the voltage of the grid-side voltage;

i_{L}

is the output current of the inverter;

i_{c}

is the capacity current;

i_{g}

is the grid current.

By applying the Laplace transform to the above equation, it can be obtained that:

{\begin{matrix} I_{L} = \frac{U_{a b} - U_{c}}{s L_{1}} \\ U_{c} = \frac{I_{L} - I_{g}}{s C} \\ I_{g} = \frac{U_{c} - U_{g}}{s L_{2}} \end{matrix}

(2)

According to the above equation, the structural diagram of inverter control can be obtained as shown in Figure 4.

Figure 4.

Control block diagram of an LCL grid-connected inverter.

According to Figure 4, the transfer function from the output side voltage $u_{a b}$ of a grid-connected inverter to grid-connected current $i_{g}$ is defined as follows:

G_{L C L} (s) = \frac{i_{g} (s)}{u_{a b} (s)} = \frac{1}{L_{1} L_{2} C s^{3} + (L_{1} + L_{2}) s} = \frac{1}{L_{1} L_{2} C s} \frac{1}{s^{2} + ω_{r e s}^{2}}

(3)

Where

ω_{r e s}

is the resonance angular frequency, whose expression is as follows:

ω_{r e s} = \sqrt{\frac{L_{1} + L_{2}}{L_{1} L_{2} C}}

(4)

If we only consider damping from the perspective of shunting resistors at both ends of the capacitor, they will have the best damping effect. However, from a circuit perspective, the voltage at both ends of the damping resistor is the grid voltage, which will result in significant power loss on the resistor. Therefore, considering power loss, filtering characteristics, damping characteristics, and control methods comprehensively, this paper adopts the method of connecting resistors in series at both ends of the capacitor. This method has the advantages of low power loss and a simple structure and is widely used in industry.

If the capacitance C is equal to 0, the LCL-type filter will become an L-type filter, and the transfer function is as follows:

G_{L} (s) = \frac{i_{g} (s)}{u_{a b} (s)} = \frac{1}{(L_{1} + L_{2}) s}

(5)

The bode diagrams of the LCL filter and the L filter are shown in Figure 5. Through analysis and comparison, it is found that the frequency characteristics of these two filters are different. The L filter attenuates linearly over the entire frequency range at −20 dB/dec. The LCL filter has the same effect as the L filter in the low-frequency range, but in the high-frequency range it attenuates at −60 dB/dec and has a resonant peak at the resonant frequency

ω_{r e s}

and the phase crossing negative a

180^{\circ}

. According to the principle of automatic control, this will cause a pair of poles to appear in the right half plane of the system, causing instability. Therefore, some measures need to be taken to avoid instability in the system due to the presence of resonance peaks.

Figure 5.

Bode diagram of LCL filter and L filter.

If we only consider damping from the perspective of parallel resistors at both ends of the capacitor, they will have the best damping effect. However, from the circuit perspective, the voltage at both ends of the damping resistor is the grid voltage, which can cause significant power loss on the resistor. So, comprehensive power loss, filtering characteristics, damping characteristics, and control methods. This article adopts the method of connecting resistors in series at both ends of the capacitor, as shown in Figure 6. This method has low power loss, a simple structure and is widely used in industry.

Figure 6.

Capacitor C series resistance.

According to Figure 6, it can be inferred that the transfer function from output voltage $u_{a b}$ to grid-connected current $i_{g}$ is as follows:

G_{c} (s) = \frac{i_{g} (s)}{u_{a b} (s)} = \frac{C R_{3} s + 1}{L_{1} L_{2} C s^{3} + (L_{1} + L_{2}) C R_{3} s^{2} + (L_{1} + L_{2}) s}

(6)

Analysis and design of an active disturbance rejection control strategy

The core idea of active disturbance rejection control technology is to simplify complex systems into integral series systems and treat all parts outside the integral series system as total disturbances; then, through expansion, the observer performs real-time estimation and compensates for the total disturbance. Due to the complexity of nonlinear structures and the difficulty of parameter tuning in practical applications, it is difficult to achieve in engineering. At the beginning of this century, Dr Gao Zhiqiang proposed linear auto disturbance rejection control (LADRC), which is based on the concept of frequency scale and improves and simplifies nonlinear auto disturbance rejection technology, the transition process of tracking differentiators is omitted, feedback error control rate is associated with extended observer and frequency bandwidth, the control structure is simpler, and the control performance is also better. Compared with the PI controller, LADRC has stronger suppression capabilities for high-frequency noise and low-frequency disturbances, and it can avoid overshoot of step signals.^33,34 Therefore, it is widely used in industrial control scenarios such as aircraft control, ship control, and motor control.

Linear expansion observer

The linear expansion observer (LESO) is capable of real-time estimation and compensation of the total disturbance of the system. When the extended observer can accurately estimate disturbances, the system is compensated as a series integral type and achieves control over expected indicators through simple control rates.

For n-order controlled objects:

y^{(n)} = g (t, y, y^{'}, \dots, y^{(n - 1)}, ω) + b u

(7)

Where u and y are the input and output of the controlled objects, respectively; g refers to the consideration of various derivatives, internal uncertainties, and unknown factors of the system;

ω

refers to the external disturbance; b is the gain of the controller (including known and unknown parts). Record the known part as

b_{0}

, classify the unknown part as part of the disturbance. The above equation can be rewritten as follows:

\begin{aligned} y^{(n)} = & g (t, y, y^{'}, \dots y^{(n - 1)}, ω) + (b - b_{0}) u + b_{0} u \\ = & f (t, y, y, \dots y^{(n - 1)}, ω) + b_{0} u \end{aligned}

(8)

Where

f = g + (b - b_{0}) u

is the total disturbance in the system.

With the goal of building an integral series system, f is added to the extended observer to form a new state for estimation and compensation. If $x_{1} = y, x_{2} = y^{(1)}, \dots, x_{n} = y^{(n - 1)}, x_{n + 1} = f,$ then $x = [x_{1}, x_{2}, \dots, x_{n + 1}]^{T}$ . Assuming that the total disturbance f is differentiable, the system can be written as a state space form:

\overset{\cdot}{x} = \underset{A}{\underset{⏟}{[\begin{matrix} 0 & 1 & 0 & \dots & 0 \\ 0 & 0 & 1 & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}]}} x + \underset{B}{\underset{⏟}{[\begin{matrix} 0 \\ 0 \\ ⋮ \\ b_{0} \\ 0 \end{matrix}]}} u + \underset{E}{\underset{⏟}{[\begin{matrix} 0 \\ 0 \\ ⋮ \\ 0 \\ 1 \end{matrix}]}} \overset{\cdot}{f}

(9)

y = \underset{C}{\underset{⏟}{{[\begin{matrix} 1 & 0 & 0 & \begin{matrix} \dots & 0 \end{matrix} \end{matrix}]}^{T}}} x

(10)

The total disturbance f can be estimated by an extended state observer.

{\begin{matrix} \overset{\cdot}{z} = A z + B u + L (y - \overset{\land}{y}) \\ \overset{\land}{y} = C z \end{matrix}

(11)

Where the gain matrix of LESO is

L = [β_{1}, β_{2,} \dots, β_{n,} β_{n}]^{T}

z

is the state vector of LESO,

\overset{\land}{y}

is the estimated value of the system output y by LESO. When the gain matrix is stable, LESO gradually stabilizes,

z_{1} \to y, z_{2} \to y^{2}, \dots, z_{n} \to y^{(n - 1)}, z_{n + 1} \to f

Disturbance compensation

LESO estimates the total disturbance and implements compensation. Finally, the system is calibrated as an integral series system to enhance its stability. The system disturbance compensation is as follows:

u = \frac{u_{0} - z_{n + 1}}{b_{0}}

(12)

Where

u_{0}

is the output of linear error feedback.

Substitute Equation (12) into Equation (8):

y^{(n)} = u_{0} + (f - z_{n + 1}) \approx u_{0}

(13)

From Equation (13), it can be seen that if the disturbance of the system is observable, the system can be approximated as an integral series type. Namely, a structure composed of an integrator and a series of connected dynamic systems, this representation is very useful for designing controllers to resist the influence of disturbances.

Linear error control rate

When the system structure is an integral series type, superior control effects can be achieved with a simple linear error controller. The linear error control rate can be presented as follows:

u_{0} = k_{p} (r - z_{1}) - k_{d 1} z_{2} - k_{d 2} z_{2} \dots - k_{d n - 1} z_{n}

(14)

Where r is the given reference value, and $k_{p}, k_{d 1}, \dots, k_{d n - 1}$ is the proportional coefficient of the controller.

For the n-order control system, the structural block diagram of linear auto disturbance control is shown in Figure 7.

Figure 7.

Block diagram of n-order automatic disturbance rejection control.

Design of an active disturbance rejection controller for grid-connected inverters

According to the analysis in Section 2.3, the transfer function of the grid current to the output voltage of the inverter is as follows:

G_{L C L} (s) = \frac{i_{g} (s)}{u_{a b} (s)} = \frac{C R_{3} s + 1}{L_{1} L_{2} C s^{3} + (L_{1} + L_{2}) C R_{3} s^{2} + (L_{1} + L_{2}) s}

(15)

Obviously, the automatic disturbance rejection designed based on the above transfer function is a third-order controller. However, the design of high-order automatic disturbance rejection controllers in engineering is complex; multiple state variables need to be differentiated, and there are many parameters to be adjusted, which is not conducive to practical applications. Considering that automatic disturbance rejection control does not require an accurate mathematical model, the modeling errors can be considered as part of the disturbance. Therefore, in practice, low-order active disturbance rejection controllers are preferred. Using the Padé approximation method to reduce the order of Equation (15)³⁵:

G_{L} (s) = \frac{i_{g} (s)}{u_{i n} (s)} \approx \frac{1}{(L_{1} + L_{2}) s}

(16)

The Bode diagram of the transfer function of Equations (15) and (16) above is shown in Figure 8. It can be seen that the two transfer functions are basically identical in the low-frequency range. From the perspective of controller design, the controller mainly regulates the low-frequency dynamic characteristics of the system, even if the reduced-order model has errors at high frequencies, it will be regarded as a disturbance by the auto disturbance rejection state observer, then estimated and compensated to eliminate. So, reducing the order design of the auto disturbance rejection controller for the third-order inverter, as long as the extended observer can accurately estimate and compensate for the total disturbance in real-time. The designed first-order auto disturbance rejection controller can achieve the function of a third-order auto disturbance rejection controller, and it is more convenient to apply in practical engineering.

Figure 8.

Bode diagram of the transfer function.

The transfer function from the grid-connected inverter's input current to the inverter side voltage after order reduction processing is as follows Equation (12). According to the above equation, the differential of the incoming and outgoing network currents is derived as follows:

\frac{d i_{g} (t)}{d t} = \frac{1}{L_{1} + L_{2}} u_{i n} (t)

(17)

Due to the presence of nonlinear factors such as inductance, capacitor devices, and dead zones, the mathematical model of the system is not very accurate. Considering external interference

d_{0} (t)

, under the form of auto disturbance rejection, the grid-connected inverter can be expressed as follows:

\overset{\cdot}{x_{1}} (t) = b u (t) + f_{0} x_{1} (t) + d_{0} (t)

(18)

Where

x_{1} (t) = i_{g} (t)

is the controlled current,

u (t)

is the controller input variables.

b = b_{0} + △ b

, in which

b_{0} = 1 / (L_{1} + L_{2})

represents a known part,

△ b u (t) + f_{0} x_{1} (t)

represents unknown parts in inverter modeling, for example, parameter deviation caused by perturbations in filtering parameters and power grid fluctuations. Equation (18) can be written as follows:

\begin{aligned} \overset{\cdot}{x_{1}} (t) = & b_{0} u (t) + △ b u (t) + f_{0} x_{1} (t) + d_{0} (t) \\ = & b_{0} u (t) + f (t) \end{aligned}

(19)

Where

f (t) = △ b u (t) + f_{0} x_{1} (t) + d_{0} (t)

represents the total disturbance in the grid-connected inverter system, including internal and external disturbances.

Let $x_{2} (t) = f (t)$ , matrix $x_{p} (t) = [{x_{1} (t) x_{2} (t)]}^{T}$ , $y (t)$ denote the output of the system, $x_{2} (t)$ is the extended state variables. Using $h (t)$ to represent the first derivative of $f (t)$ , so the state space equation of the grid-connected inverter under the active disturbance rejection control structure can be written as follows:

{\begin{matrix} x_{1} (t) = i_{g} (t) \\ \overset{\cdot}{x_{1}} (t) = \frac{u (t)}{L_{1} + L_{2}} + x_{2} (t) \\ \overset{\cdot}{x_{2}} (t) = \overset{\cdot}{f} (t) = h (t) \end{matrix}

(20)

Make

A = [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]

B = [\begin{matrix} \frac{1}{L_{1} + L_{2}} \\ 0 \end{matrix}]

C = [\begin{matrix} 1 & 0 \end{matrix}]

E = [\begin{matrix} 0 \\ 1 \end{matrix}]

, (16) can be written as follows:

{\begin{aligned} {\dot{x}}_{p} (t) = A x_{p} (t) + B u (t) + E h (t) \\ y (t) = C x_{p} (t) \end{aligned}

(21)

According to the analysis in the previous section, the linear control rate expression of the LCL grid-connected inverter is as follows:

u_{0} (t) = k_{p} (i_{g}^{*} - z_{1} (t))

(22)

Where

u_{0} (t)

and

k_{p}

are the output and gain of the controller, respectively,

i_{g}^{*}

is the given value of grid-connected current. The control rate of the first-order auto disturbance rejection controller is as follows:

u (t) = \frac{u_{0} (t) - z_{2} (t)}{b_{0}}

(23)

In summary, the first-order ADRC control system diagram of the LCL grid-connected inverter is shown in Figure 9. To simplify the parameter tuning process of the auto disturbance rejection controller, the parameter

k_{p}

β_{1}

β_{2}

in the controller is uniformly configured according to the bandwidth method. Assuming

ω_{0}

ω_{c}

are, respectively, the observer bandwidth and controller bandwidth, then the relationship between the control parameters is

β_{1} = 2 ω_{0}

β_{2} = ω_{0}^{2}

k_{p} = ω_{c}

Figure 9.

ADRC control block diagram of the LCL grid-connected inverter. ADRC: auto disturbance rejection control.

In order to make the expanded state observer estimate the total disturbance accurately and compensate for the total disturbance in real time, the observer bandwidth $ω_{0}$ is taken as $(2 \sim 10) ω_{c}$ .

Methods

Improved optimization design of auto disturbance rejection control

Analysis of the coupling problem of the active disturbance rejection controller

When auto disturbance rejection controllers are applied, if the tracking performance of the controller is only related to the control rate, and the anti-interference performance is only related to the extended observer, then the structural design of the auto disturbance rejection controller will be simple, and the parameter adjustment will be easy. But there is a coupling problem between the anti-interference performance and tracking performance parameters of LADRC. The parameter coupling problem of the controller will be explained through the following formula derivation.

For first-order auto disturbance rejection, the relationship between the estimated value of the system state variable u and the control variable and the system output $i_{g}$ can be written as follows:

{\begin{matrix} z_{1} = \frac{b_{0} s}{s^{2} + β_{1} s + β_{2}} u + \frac{β_{1} s + β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g} \\ z_{2} = - \frac{β_{2} b_{0}}{s^{2} + β_{1} s + β_{2}} u + \frac{β_{2} s}{s^{2} + β_{1} s + β_{2}} i_{g} \end{matrix}

(24)

Where s is the Laplacian operator;

β_{1} β_{2}

are gains of the extended observer.

Bring the first equation of the above equation into the LSEF expression Equation (22) of the LCL grid-connected inverter, the expression for the output quantity $u_{0}$ of the controller can be expressed as follows:

u_{0} = k_{p} (i_{g}^{*} - \frac{b_{0} s}{s^{2} + β_{1} s + β_{2}} u - \frac{β_{1} s + β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g})

(25)

Bring the second equation of Equation (24) and Equation (25) into Equation (23), then the control variable u can be written as an expression about the given quantity

i_{g}^{*}

and the system output quantity

i_{g}

u = \frac{1}{b_{0}} \frac{s^{2} + β_{1} s + β_{2}}{s^{2} + β_{1} s + k_{p} s} (k_{p} i_{g}^{*} - \frac{(k_{p} β_{1} + β_{2}) s + k_{p} β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g})

(26)

According to Equation (22), the control block diagram of auto disturbance rejection can be represented as Figure 10:

Figure 10.

Block diagram of ADRC. ADRC: auto disturbance rejection control.

Where:

G_{1} (s) = \frac{s^{2} + β_{1} s + β_{2}}{s^{2} + β_{1} s + k_{p} s}

(27)

H (s) = \frac{(k_{p} β_{1} + β_{2}) s + k_{p} β_{2}}{s^{2} + β_{1} s + β_{2}}

(28)

The closed-loop transfer function of this control block diagram is as follows:

G_{c} (s) = G_{r} (s) + G_{f} (s) = \frac{k_{p}}{s + k_{p}} + \frac{s^{2} + (β_{1} + k_{p}) s}{(s + k_{p}) (s^{2} + β_{1} s + β_{2})}

(29)

From Equation (29), it can be seen that there is a coupling between the extended observer parameter

β_{1} β_{2}

and the control rate parameter

k_{p}

of the auto disturbance rejection controller, as a result, the tracking performance and anti-interference performance of the controller cannot be independently adjusted during the parameter adjustment process which to a certain extent increases the difficulty of parameter adjustment.

Design of decoupling linear auto disturbance rejection controller

To solve the problem of parameter coupling between the tracking performance and disturbance rejection performance of the auto disturbance rejection controller by compensating for the disturbance of the controller and changing the feed-forward channel to achieve decoupling of the extended observer, the decoupling active disturbance rejection control structure diagram is shown in Figure 11. After decoupling, the controller has stronger anti-interference performance against low-frequency and DC disturbances.

Figure 11.

Decoupling ADRC structure diagram. ADRC: auto disturbance rejection control.

The decoupled extended state observer is as follows:

{\begin{matrix} \frac{d}{d t} z_{1} = z_{2} + b_{0} u \\ \frac{d}{d t} z_{2} = β_{1} \frac{d}{d t} (y - z_{1}) + β_{2} (y - z_{1}) \end{matrix}

(30)

Transform the above equation. The relationship between the estimated value of the system state variable and the system output

i_{g}

and the control variable u is as follows:

\begin{aligned} {\begin{matrix} z_{1} = \frac{b_{0} s}{s^{2} + β_{1} s + β_{2}} u + \frac{β_{1} s + β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g} \\ z_{2} = - \frac{b_{0} (β_{1} s + β_{2})}{s^{2} + β_{1} s} u + \frac{s (β_{1} s + β_{2})}{s^{2} + β_{1} s + β_{2}} i_{g} \end{matrix} \end{aligned}

(31)

By bringing the first formula of the above equation into Equation (22), it can be obtained that:

u_{0} = k_{p} (i_{g}^{*} - \frac{b_{0} s}{s^{2} + β_{1} s + β_{2}} u - \frac{β_{1} s + β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g})

(32)

Substitute Equations (31) and (32) into Equation (23), the relationship between the control variable u and system control given quantity

i_{g}^{*}

and the system output quantity

i_{g}

can be expressed as follows:

u = \frac{1}{b_{0}} \frac{s^{2} + β_{1} s + β_{2}}{s^{2} + k_{p} s} (k_{p} i_{g}^{*} - \frac{β_{1} s^{2} + (k_{p} β_{1} + β_{2}) s + k_{p} β_{2}}{s^{2} + β_{1} s + β_{2}} i_{g})

(33)

Then the closed-loop transfer function of the auto disturbance rejection controller can be written as follows:

G_{d} (s) = G_{r} (s) + G_{f} (s) = \frac{k_{p}}{s + k_{p}} + \frac{s}{s^{2} + β_{1} s + β_{2}}

(34)

From the above equation, it can be seen that the tracking performance of the auto disturbance rejection controller is only related to the proportional control rate

k_{p}

at this time, the tracking performance of the controller is only related to the gain

β_{1} β_{2}

of the extended observer. Therefore, by optimizing the controller, the tracking performance and anti-interference performance of the controller can be decoupled, the functions of each part do not affect each other, the parameter adjustment is easier, and the controller structure is simpler.

Analysis of decoupling LADRC immunity performanceAccording to the analysis in the previous section, the disturbance transfer function after decoupling the auto disturbance rejection controller is as follows:

G_{f} (s) = \frac{s}{s^{2} + β_{1} s + β_{2}} = \frac{s}{s^{2} + 2 ω_{o} s + ω_{o}^{2}}

(35)

It can be seen from Equation (35) that the anti-interference performance of ADRC is only related to the bandwidth

ω_{o}

of the extended state observer, the frequency curve of its disturbance transfer function is shown in Figure 12. From the figure, it can be seen that the decoupled ADRC not only suppresses direct current (DC) disturbances, but also has a strong inhibitory effect on disturbances at high and low frequencies. By changing the bandwidth parameter of the extended observer, the low-frequency disturbance gain can be reduced, and the anti-interference ability of the control can be improved. However, in the mid-frequency range, the system's resistance to interference is significantly reduced and cannot achieve complete feed-forward compensation, resulting in ineffective suppression of disturbances in the mid-frequency system, and the control performance of the system will be affected.

Figure 12.

Frequency domain characteristic diagram of the decoupling ADRC disturbance term. ADRC: auto disturbance rejection control.

When the system signal is a step signal, the anti-interference ability of the decoupled ADRC can be obtained from Equation (35); the steady-state error of the system disturbance output is as follows:

e_{s s} = lim_{s \to 0} G_{f} (s) \frac{Δ f}{s} = lim_{s \to 0} s \frac{s}{s^{2} + β_{1} s + β_{2}} \frac{Δ f}{s} = 0

(36)

From Equation (36), it can be concluded that when the input disturbance signal of the system is a step signal, the steady-state disturbance of the output signal is 0, which explains why the decoupled ADRC can completely suppress the disturbance generated by the step signal.

Design of RC structure

For a stable closed-loop system, if a repetitive controller is directly added to the control loop, theoretically, zero static error tracking can be achieved, but this control model will add N poles on the unit circle to the system. According to the Nyquist criterion, the open-loop system will be in a critical stable oscillation state, as long as there is a slight change in the system model parameters, the poles of the closed-loop system will fall outside the unit circle, causing the instability in the system. Therefore, when designing RC algorithms, it is usually necessary to make some changes to the ideal intima, using $Q Z^{- N}$ instead of $Z^{- N}$ , Q is a constant less than 1, usually 0.95, which can also be a low-pass filter.

The improved intima transfer function is as follows:

M_{r c} (z) = \frac{Q Z^{- N}}{1 - Q Z^{- N}}

(37)

The system diagram of RC is shown in Figure 13:

Figure 13.

System diagram of RC. RC: repetitive control.

Where $P (z)$ is the control Object; $r (z)$ is the given reference signal of the system; $C (z)$ is the compensator; y is the output of system; e is the difference between input signal and feedback signal; $d (z)$ is the disturbance signal.

C (z) = k_{r c} z^{k} S (z)

(38)

Where

k_{r c}

is the gain of RC, k is the compensation for delayed beats,

S (z)

is the LPF.

Design of RC-ADRC for grid-connected inverters

To suppress non-periodic and periodic disturbances in grid-connected current, this paper adopted RC-ADRC. This method differs from traditional ADRC in the following two aspects: first, the expansion observer used in ADRC is a decoupled expansion observer, which is capable of decoupling the tracking performance and anti-interference performance of auto disturbance rejection; second, RC parallels the error control rate of self-disturbance rejection, which expands the bandwidth of the ADRC rate and can effectively suppress intermediate frequency disturbances. The extended observer of the decoupled controller can not only suppress constant disturbances but also compensate for the effects of parameter perturbations on the grid-connected inverter. The control structure diagram is shown in Figure 14.

Figure 14.

RC-ADRC control structure diagram. ADRC: auto disturbance rejection control; RC: repetitive control.

Because RC is generally designed in the discrete domain, the duty cycle of PWM interrupt updates in the discrete domain is not updated in real-time, but calculated in the previous cycle, so considering the delay of one sampling period. According to the ADRC model of the inverter in Equation (22), after adding a sampling period delay, the equation of control current of a grid-connected inverter under discretizing conditions can be obtained as follows:

{\begin{matrix} i_{g} (k + 1) = i_{g} (k) + T_{s} (\frac{1}{L_{1} + L_{2}} u (k - 1) + f (k - 1)) \\ f (k) = f (k - 1) + T_{s} h (k - 1) \end{matrix}

(39)

Where

T_{s}

is the sampling period.

According to Equation (39), add a time delay of one cycle to the extended observer, the extended observer for RC-ADRC can be designed as follows:

{\begin{matrix} z_{1 d} (k + 1) = z_{1 d} (k) + T_{s} (z_{2 d} (k - 1) + b_{0 d} u (k - 1)) \\ z_{2 d} (k) = z_{2 d} (k - 1) + T_{s} β_{1} \frac{d}{d t} (i_{g} (k) - z_{1 d} (k)) + T_{s} β_{2} (i_{g} (k) - z_{1 d} (k)) \end{matrix}

(40)

Where

z_{1 d}

is the estimation of grid-connected current by an optimized extended observer,

z_{2 d}

is the estimation of disturbance.

The control rate of RC-ADRC can be designed as follows:

u (k) = \frac{u_{0 d} (k) - z_{2 d} (k)}{b_{0 d}}

(41)

Where

u_{0 d} (k)

is the control input after including RC, whose equation is as follows:

u_{0 d} (k) = (G_{r c} (z) + k_{p}) (i_{g} (k) - z_{1 d} (k))

(42)

Where

M_{r c} (z)

is the RC after adding the compensator.

From the above equation, it can be seen that the dynamic process of RC-ADRC is determined by both the ADRC rate and the repetitive controller, in order to avoid mutual influence between the two, the proportional component should play a dominant role in the dynamic process of the system, while in a stable state, the repetitive controller should play a dominant role; in this way, a better control effect can be achieved.

Stability analysis of RC-ADRC decoupling extended observer

The current loop error transfer function based RC-ADRC can be calculated by Equations (39) and (40).

{\begin{matrix} i_{g} (k + 1) - z_{1 d} (k + 1) = i_{g} (k) - z_{1 d} (k) + T_{s} (f (k - 1) - z_{2 d} (k - 1)) \\ f (k) - z_{2 d} (k) = - T_{s} β_{2} (i_{g} (k) - z_{2 d} (k)) + f (k - 1) - z_{2 d} (k - 1) - T_{s} β_{1} (\frac{d}{d t} (i_{g} (k) \\ - z_{1 d} (k))) + T_{s} h (k - 1) \end{matrix}

(43)

From the first equation above, it can be seen that:

\frac{d}{d t} (i_{g} (k) - z_{1 d} (k)) = \frac{(i_{g} (k + 1) - z_{1 d} (k + 1)) - (i_{g} (k) - z_{1 d} (k))}{T_{s}} = f (k - 1) - z_{2 d}

(44)

The following equation can be obtained by substituting Equation (44) into the second equation of Equation (43):

\begin{aligned} [\begin{matrix} i_{g} (k + 1) - z_{1 d} (k + 1) \\ f (k) - z_{2 d} (k) \end{matrix}] = [\begin{matrix} 1 & T_{s} \\ - T_{s} β_{2} & 1 - T_{s} β_{1} \end{matrix}] [\begin{matrix} i_{g} (k) - z_{1 d} (k) \\ f (k - 1) - z_{2 d} (k - 1) \end{matrix}] \\ + [\begin{matrix} 0 \\ 1 \end{matrix}] T_{s} h (k - 1) \end{aligned}

(45)

According to Equation (45), the characteristic equation of the extended observer can be obtained as follows:

Δ_{0} (z) = det {z I - [\begin{matrix} 1 & T_{s} \\ - T_{s} β_{2} & 1 - T_{s} β_{1} \end{matrix}]} = p_{2} z^{2} + p_{1} z + p_{0} = 0

(46)

Then

p_{0} = 1 - T_{s} β_{1} + T_{s}^{2} β_{2}

p_{1} = T_{s} β_{1} - 2

p_{2} = 1

. The Jury table obtained from the results is shown in Table 1.

Table 1.

Jury table.

	Z⁰	Z¹	Z²
1	P₀	P₁	P₂

The necessary and sufficient conditions for the stability of the extended observer based on the Jury criterion are as follows³⁶:

{\begin{matrix} Δ_{0} (1) = p_{2} + p_{1} + p_{0} > 0 \\ (- 1)^{2} Δ_{0} (- 1) = p_{2} - p_{1} + p_{0} > 0 \\ | p_{0} | < p_{2} \end{matrix}

(47)

Substitute the values of

p_{0}

p_{1}

and

p_{2}

into the above equation to obtain:

{\begin{matrix} T_{s}^{2} β_{2} > 0 \\ 4 - 2 T_{s} β_{1} + T_{s}^{2} β_{2} > 0 \\ | 1 - T_{s} β_{1} + T_{s}^{2} β_{2} < 1 | \end{matrix}

(48)

Therefore, in order to ensure the stability of the decoupled extended state observer, the constraints of Equation (48) above must be met when selecting the parameters of the decoupled extended state observer，usually, the gain parameter

β_{1}

β_{2}

of the decoupled expansion observer is greater than 0, the sampling period

T_{s}

is also greater than 0. So based on the selection conditions of

β_{1}

β_{2}

, and

T_{s}

, Equation (48) can be simplified as follows:

{\begin{matrix} 2 T_{s} β_{1} - T_{s}^{2} β_{2} < 4 \\ - 2 < T_{s}^{2} β_{2} - T_{s} β_{1} < 0 \\ T_{s} β_{1} > 0, T_{s} β_{2} > 0 \end{matrix}

(49)

Solving inequality in Equation (49) can obtain:

0 < T_{s} β_{1} < 2

(50)

The bandwidth method is generally used for parameter selection for extended observers, namely

β_{1} = 2 ω_{o}

β_{2} = ω_{o}^{2}

. So the bandwidth range of the expansion observer can be set as follows:

0 < ω_{o} < \frac{1}{T_{s}}

(51)

Experiment methodology and results

Simulation of grid-connected current control

Simulation of normal grid-connected current control

To verify the application of the designed controller in the LCL grid-connected inverter, the following is a comparative analysis of PI control, ADRC and RC-ADRC for the grid-connected current in the grid-connected power generation system using simulation software. The parameters designed for the grid-connected inverter are as follows: the discrete step size is 1e-6s, and the frequency of PWM is 20 kHz. The PI controller parameters are set as follows: proportional coefficient Ka = 80; integration coefficient K_i = 10. The parameters of the traditional ADRC are set as b₀ = 121.951; K_p = 1200; ω_o = 3600；The parameters of RC-ADRC are set as follows: Q(z) = 0.95; k = 5; $S (z) = \frac{0.03179 z + 0.028}{z^{2} - 1.624 z + 0.6837}$ ; k_r = 10; k_p = 600. The extended observer parameters of ADRC are the same as the traditional ADRC parameter design.

Firstly, simulation comparisons were conducted under the condition that all parameters of the grid-connected inverter were standard parameters. The grid-connected current waveform and THD are shown in Figures 15, 16, and 17.

Figure 15.

Pi control of grid-connected current waveform and THD analysis. THD: total harmonic distortion.

Figure 16.

Traditional ADRC grid-connected current waveform and THD analysis. ADRC: auto disturbance rejection control; THD: total harmonic distortion.

Figure 17.

RC-ADRC grid-connected current waveform and THD analysis. ADRC: auto disturbance rejection control; RC: repetitive control; THD: total harmonic distortion.

From the above figure, it can be seen that the RC-ADRC strategy has a good ability to suppress voltage disturbances in the power grid and can make the incoming current have better waveform quality. When using the PI control strategy, the THD of the incoming current is 2.54%; when using the ADRC strategy, the THD of the incoming current is 1.84%; when using the improved RC-ADRC strategy, the THD of the incoming current is 1.48%. It can be seen that the application of improved ADRC to grid-connected inverters is feasible.

Simulation of weak grid-connected current control

The current waveform of three control strategies in weak current networks is shown in Figures 18, 19, and 20, from the figure, it can be seen that the THD value of the grid connected in the weak current grid state is better than that in the normal grid, this is because, under weak current network conditions, the inductance present in the power grid increases the filtering inductance on the grid side of the grid-connected inverter, thereby improving the filtering effect. But comparing the three different control strategies, the designed RC-ADRC strategy can still maintain a good control effect in weak current networks.

Figure 18.

Analysis of the current waveform and THD using PI control in a weak grid. THD: total harmonic distortion.

Figure 19.

Analysis of the current waveform and THD using ADRC control in a weak grid. ADRC: auto disturbance rejection control; THD: total harmonic distortion.

Figure 20.

Analysis of the current waveform and THD using RC-ADRC control in a weak grid. ADRC: auto disturbance rejection control. RC: repetitive control; THD: total harmonic distortion.

Grid-connected current periodic disturbance experiment

To verify the controller's ability to suppress periodic disturbances, varying degrees of 3rd, 5th, 7th, 9th, and 11th harmonics are simultaneously injected into the grid voltage, then simulating and verifying the auto disturbance rejection controller before and after adding RC. The simulation waveforms of traditional ADRC and RC-ADRC are shown in Figures 21 and 22, from the figure, it can be seen that adding RC to the ADRC has a better suppression effect on periodic disturbances, and its output current waveform THD is lower, indicating that adding RC to the ADRC can suppress periodic disturbances.

Figure 21.

Traditional ADRC current waveform under periodic disturbance. ADRC: auto disturbance rejection control.

Figure 22.

RC-ADRC current waveform under periodic disturbance. ADRC: auto disturbance rejection control; RC: repetitive control.

Dynamic performance simulation

To verify the dynamic performance of the ADRC after adding RC links, an off grid inverter is used. As shown in Figure 23, when a sudden load is applied to an inverter of different control strategies with the same other parameters at 0.3s, the current dynamic response time of RC-ADRC is 3.014 ms, while the current dynamic response time of traditional ADRC is 4.410 ms, which proved that the improved auto disturbance rejection has advantages in dynamic performance.

Figure 23.

Current control dynamic response time. (a) Current dynamic response time of RC-ADRC (b) Current dynamic response time of traditional ADRC. ADRC: auto disturbance rejection control. RC: repetitive control.

Grid-connected current control algorithm experiment

Software design

The simulation in this paper was conducted using Matlab/Simulink software. The overall software model is shown in Figure 24, which is composed of an initialization program module, PWM output, and control system interrupt module. The interrupt module is shown in Figure 25, which mainly consists of signal extraction, SOGI phase-locked loop, control algorithm, and ePWM generation module. The specific execution of the program is as follows: Set the CPU interrupt to³ in the Interrupt module, the PIE interrupt corresponding to¹ is an ePWM interrupt, when an ePWM signal occurs, the program will enter the interrupt program for execution; at this moment, the ADC collects signals, processes the collected voltage and current signals, and sends them into different AD channels. The A/D acquisition unit in the chip extracts the phase angle of the collected voltage signal through the SOGI phase-locked loop module and uses the obtained phase signal as a phase reference for the current signal, furthermore, PI, RC, and active disturbance rejection control are applied to the grid-connected current, and the signal after being standardized by the controller is sent to the ePWM module to control the switch transistor.

Figure 24.

Overall structure diagram of code generation.

Figure 25.

Model of control strategy execution program.

Experimental hardware design

The experimental platform built in this article is shown in Figure 26. The entire experimental platform consists of the collection section, the driving section, the power conversion section, and the controller. The voltage Hall model selected for the sampling circuit is TBV5/25A, with a range of ±700 V and a collection accuracy of 0.5%. The current Hall model selected for the sampling circuit is QBC15LX, with a range of ±10 A and a collection accuracy of 0.7%. The sampling circuit sends the collected voltage and current signals to the controller, which uses TMS320F28335 + AD7606 as the control unit. AD7606 is a 16-bit high-precision acquisition chip, and there are two options for input signal size: ±5 V and ±10 V. The collected signals of this chip can be directly fed into the module, eliminating the need for conditioning circuits. The main parameters of the experiment are shown in Table 2.

Figure 26.

Physical diagram of the experimental platform.

Table 2.

Experimental platform parameters.

Parameter	Value
Input voltage	40 V
Damping circuit	3 Ω
Network side inductance	0.5 mH
Inverter side inductance	2 mH
Grid frequency	50 Hz
Sampling frequency	10 kHz
Filter capacitor	10 μF

Waveform analysis of grid-connected current experiment

During the experiment, due to the fact that the grid voltage is connected to the inverter output side through a voltage regulator, the regulator itself has an inductance; moreover, the waveform of the power supply after passing through the voltage regulator is not so stable. Therefore, this experiment does not conduct waveform analysis under weak current networks, only compares the control strategies. The waveforms are shown in Figures 27 and 28.

Figure 27.

Traditional ADRC current waveform and THD analysis. ADRC: auto disturbance rejection control; THD: total harmonic distortion.

Figure 28.

RC-ADRC current waveform and THD analysis. ADRC: auto disturbance rejection control; RC: repetitive control; THD: total harmonic distortion.

From the figure, it can be seen that when the given peak current is 6 A, the effective value of the output current is 3.91 A, and there is no difference in output accuracy between the two control methods. However, when analyzing the current THD, the harmonic suppression effect of RC-ADRC is better than that of ADRC, which indicates that the application of ADRC in grid-connected inverters has a great advantage.

Due to the fact that the design of RC is incorporated into the tracker of ADRC, therefore, in the experiment, the dynamic performance of adding RC that affects auto disturbance rejection was experimentally verified; the output waveforms are shown in Figures 29 and 30.

Figure 29.

Dynamic response of traditional ADRC. ADRC: auto disturbance rejection control.

Figure 30.

Dynamic response of traditional RC-ADRC. ADRC: auto disturbance rejection control; RC: repetitive control

As shown in the above figure, when the given value of the incoming current suddenly changes from 0A to a peak value of 5A. The adjustment time of traditional ADRC is 0.24 ms; however, the automatic disturbance rejection adjustment time with the addition of RC is 0.16 ms, it can be seen that adding RC has a positive effect on dynamic performance.

Conclusion

This article presents the current control problem of grid-connected inverters and proposes a RC-ADRC strategy to control the grid-connected current. By optimizing the structure of the extended observer, decoupling the tracking and disturbance rejection performance of the active disturbance rejection controller is achieved. Simultaneously incorporating RC into the control rate stage of ADRC. And conduct simulations and experiments on grid-connected control that focus on research and compare the control effects of different control strategies.

The reduction of grid-connected current THD is of great significance for the research of the entire system. In the simulation of normal grid-connected current control, the THD of the grid-connected current is 1.48% when the improved self-disruption rejection combined with RC scheme is adopted, which is better than the THD value when using the PI control strategy and the ADRC strategy. In the simulation of weak current grid-connected current control, the THD obtained by using the strategy designed in this paper is 1.04%. The THD of the current waveform under RC and active disturbance rejection control under periodic disturbances is 3.56%, which is better than the self-disruption rejection without RC in suppressing periodic disturbances. In the dynamic performance simulation experiment, the current dynamic response time of the control strategy designed in this paper is 3.014 ms. The waveform analysis of the grid-connected current experiment shows that the THD using the method in this paper is 2.69%. The experimental results show that the adopted RC-ADRC strategy has better dynamic performance and lower current THD.

This article adopts RC based on the internal model principle as an improvement component of the control rate, but the design of RC is relatively complex. The subsequent research can consider combining control algorithms based on other internal model principles to make controller design simpler.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Xixi Han

Author biographies

Xixi Han holds a master's degree in Electrical Engineering. Her area of research is electrical control and smart power grid.

Bowen Xu is a postgraduate in Electronics. His area of research is electrical machinery and power electronics.

Keqi Kang is a postgraduate in Electrical Engineering. His area of research is modeling and control of power electronic systems.

Songwei Zuo is a postgraduate in Electrotechnics. His area of research is new energy power generation and grid connection.

References

Ranta

Laihanen

Karhunen

. The role of bioenergy in achieving the carbon neutrality target in Finland by 2035: a case study of student surveyed at University in Finland. J Sustainable Bioenergy Syst 2021; 11: 61–81.

Peng

Liu

Geng

. Assessing strategies for reducing the carbon footprint of textile products in China under the shared socioeconomic pathways framework. Clim Change Econ 2022; 13: 2240004.

Sun

Zeng

Jia-Liang

, et al. Research on the evaluation mode of 95% probability value in the national standard GB/T 14549-93. Power Syst Prot Control 2012.

Basso

IEEE 1547 and 2030 standards for distributed energy resources interconnection and interoperability with the electricity grid. 2014.

Wang

Lam

Wong

. Multifunctional hybrid structure of SVC and capacitive grid-connected inverter (SVC//CGCI) for active power injection and nonactive power compensation. IEEE Trans Ind Electron 2019; 66: 1660–1670.

Yang

Meng

, et al. Improved weighted average current control of LCL grid-connected inverter and analysis of its order reduction characteristics. IET Gener Transm Distrib 2022; 16: 2386–2398.

Suresh

Pachauri

Vigneysh

. Decentralized control strategy for fuel cell/PV/BESS based microgrid using modified fractional order PI controller. Int J Hydrogen Energy 2021; 46: 4417–4436.

Liu

. Passivity-based PI control for receiver side of dynamic wireless charging system in electric vehicles. IEEE Trans Ind Electron 2022; 1.

Omar

Ouassaid

Power quality enhancement of grid-connected photovoltaic system using fuzzy-PI control. International symposium on advanced electrical and communication technologies.0[2023-06-13]. DOI:10.1109/ISAECT.2018.8618807.

10.

Dannehl

Wessels

Fuchs F

. Limitations of voltage-oriented PI current control of grid-connected PWM rectifiers with LCL filters. IEEE Trans Ind Electron 2009; 2: 56.

11.

Seifi

Moallem

, et al. An adaptive PR controller for synchronizing grid-connected inverters. IEEE Trans Ind Electron 2018; 66: 2034–2043.

12.

Zhang

Tian

Song

, et al. Mitigating disturbance in harmonic voltage using grid-side current feedback for grid-connected LCL-filtered inverter. J Electr Eng Technol 2020; 15: 1155–1165.

13.

Ahmed

Ullah

Hoque

. Optimal design of proportional–integral controllers for grid-connected solid oxide fuel cell power plant employing differential evolution algorithm. Iran J Sci Technol - Trans Electr Eng 2019; 43: 999–1019.

14.

Aouchiche

. Meta-heuristic optimization algorithms based direct current and DC link voltage controllers for three-phase grid connected photovoltaic inverter. Sol Energy 2020; 207: 683–692.

15.

Elnady

Alshabi

. Operation of parallel inverters in microgrid using new adaptive PI controllers based on least mean fourth technique. Math Probl Eng 2019; 2019: 1–19.

16.

Moeti

Asadi

. Robust model reference adaptive PI controller based sliding mode control for three-phase grid connected photovoltaic inverter. Turk J Electr Eng Comput Sci 2021; 29: 257–275.

17.

Teng

Gao

Czarkowski

, et al. Optimal tracking with disturbance rejection of voltage source inverters. IEEE Trans Ind Electron 2019: 1–1.

18.

Ghive

Jawadekar

. PI And PR controller for grid connected voltage source inverter. 2021.

19.

Danalakshmi

Prathiba

Ettappan

, et al. Reparation of voltage disturbance using PR controller-based DVR in modern power systems. Prod Eng Arch 2021; 27: 16–29.

20.

Zhou

Zhang

Liu

, et al. Implementation of cross-coupling terms in proportional-resonant current control schemes for improving current tracking performance. IEEE Trans Power Electron 2021; 36: 13248–13260.

21.

Negi

Pal

Leena

. Grid-connected photovoltaic system stability enhancement using ant lion optimized model reference adaptive control strategy. Differ EquationsDyn Syst 2020: 1–23.

22.

Yanarates

Zhou

. Fast-converging robust PR-P controller designed by using symmetrical pole placement method for current control of interleaved buck converter-based PV emulator. Energy Sci Eng 2021.

23.

Xie

Zhao

, et al. A new tuning method of multiresonant current controllers for grid-connected voltage source converters. IEEE J Emerging Sel Top Power Electron 2019; 7: 458–466.

24.

Qiu

Hang

Liu

, et al. Novel method for circulating current suppression in MMCs based on multiple quasi-PR controller. J Power Electron 2018; 18: 1659–1669.

25.

Sou

Chao

Gong

, et al. Analysis, design, and implementation of multi-quasi-proportional-resonant controller for thyristor-controlled LC-coupling hybrid active power filter (TCLC-HAPF). IEEE Trans Ind Electron 2022; 69: 29–40.

26.

Haneyoshi

Kawamura

Hoft

. Waveform compensation of PWM inverter with cyclic fluctuating loads. IEEE Trans Ind Appl 1988; 24: 582–589.

27.

Mooren

Witvoet

Oomen

. Gaussian process repetitive control: beyond periodic internal models through kernels. Automatica 2022; 140: 110273.

28.

Jia

. An adaptive smooth second-order sliding mode repetitive control method with application to a fast periodic stamping system. Syst Control Lett 2021; 151: 104912.

29.

Mooren

Witvoet

Oomen

Gaussian process repetitive control for suppressing spatial disturbances. FAC-PapersOnLine 2020; 53: 1487–1492.

30.

Guo

Zhong

Zhao

, et al. First-order and high-order repetitive control for single-phase grid-connected inverter. Complexity 2020.

31.

Zhang

Guo

Liu

, et al. Robust plug-in repetitive control for speed smoothness of cascaded-PI PMSM drive. Mech Syst Signal Process 2022; 163: 108090.

32.

Mao

. A compound control strategy for LCL-based three phase four leg shunt active power filter. IOP Conf Ser: Earth Environ Sci 2021; 692: 022108.

33.

Zheng

Tao

Sun

, et al. Soft Actor-Critic based active disturbance rejection path following control for unmanned surface vessel under wind and wave disturbances. Ocean Eng 2022.

34.

Lin

Fei

, et al. A generalized PID interpretation for high-order LADRC and cascade LADRC for servo systems. IEEE Trans Ind Electron 2021: 1–1.

35.

Cao

Zhao

, et al. ADRC-based current control for grid-tied inverters: design, analysis, and verification. IEEE Trans Ind Electron 2019; 67: 8428–8437.

36.

Zhou

Elsadany

, et al. Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization. Chaos Solitons Fractals 2021; 146: 110936.

Research on the control strategy of LCL grid-connected inverters based on improved auto disturbance rejection

Abstract

Keywords

Introduction

Related work

Analysis of the structure and working principle of grid-connected inverters

Analysis of LCL filter characteristics

Analysis and design of an active disturbance rejection control strategy

Linear expansion observer

Disturbance compensation

Linear error control rate

Design of an active disturbance rejection controller for grid-connected inverters

Methods

Improved optimization design of auto disturbance rejection control

Analysis of the coupling problem of the active disturbance rejection controller

Design of decoupling linear auto disturbance rejection controller

Design of RC structure

Design of RC-ADRC for grid-connected inverters

Stability analysis of RC-ADRC decoupling extended observer

Experiment methodology and results

Simulation of grid-connected current control

Simulation of normal grid-connected current control

Simulation of weak grid-connected current control

Grid-connected current periodic disturbance experiment

Dynamic performance simulation

Grid-connected current control algorithm experiment

Software design

Experimental hardware design

Waveform analysis of grid-connected current experiment

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Author biographies

References