Parallel connection of multiple inverters is an important means to solve the expansion, reserve and protection of distributed power generation, such as photovoltaics. In view of the shortcomings of traditional droop control methods such as weak anti-interference ability, low tracking accuracy of inverter output voltage and serious circulation phenomenon, a finite control set model predictive control (FCS-MPC) strategy of microgrid multi-inverter parallel system based on Mixed Logical Dynamical (MLD) modeling is proposed. Firstly, the MLD modeling method is introduced logical variables, combining discrete events and continuous events to form an overall differential equation, which makes the modeling more accurate. Then a predictive controller is designed based on the model, and constraints are added to the objective function, which can not only solve the real-time changes of the control system by online optimization, but also effectively obtain a higher tracking accuracy of the inverter output voltage and lower total harmonic distortion rate (Total Harmonics Distortion, THD); and suppress the circulating current between the inverters, to obtain a good dynamic response. Finally, the simulation is carried out on MATLAB/Simulink to verify the correctness of the model and the rationality of the proposed strategy. This paper aims to provide guidance for the design and optimal control of multi-inverter parallel systems.

In recent years, with the continuous progress and development of modern society, the demand for energy is constantly increasing, but it has also brought about a large consumption of traditional energy such as coal and oil, resulting in the gradual exhaustion of fossil energy. In addition, the harmful gases produced by traditional fossil fuel combustion will not only seriously pollute our living environment and cause great harm to human health, but also run counter to the sustainable development strategy implemented by my country [

With the development of microgrid, more and more non-linear power electronic devices such as inverters have begun to be integrated into the grid. However, due to the addition of non-linear devices, and the different circuit parameters in the system, the output voltage of the system is distorted. A large circulation is generated between the inverters. In view of these problems in the multi-inverter parallel system, the realization of renewable energy can achieve high-quality grid-connected operation. Therefore, it is necessary to study the control strategy of its photovoltaic inverter parallel system [

The main difficulty in the parallel connection of multiple inverters lies in the hybrid nature of their models. At present, the period average method is generally used for inverter modeling, that is, the system state is averaged within a sampling period [

There are various control methods for parallel inverters. At this stage, droop control is often used to control the parallel operation system of inverters. The droop control method is a key technology of parallel control, and the reasonable design of its droop coefficient directly affects the current sharing effect and dynamic response of the inverter in parallel [

Model Predictive Control (MPC) can fully consider the constraints and nonlinear factors of the control object, and simultaneously achieve multiple control objectives by minimizing the value of the objective function, so it is suitable for the control of multi-inverter parallel systems. Compared with the traditional control using PWM technology, MPC can calculate the optimal switching state through the objective function, and control the inverter. The control principle is simple and easy to implement. So it is a very popular control method at present. However, in practical applications, the mixed integer quadratic programming (MIQP) problem will arise when MPC is applied to power electronic circuits [

The control effect of the above control strategy for multi-objectives is still not ideal. The advantages and limitations of these control strategies are analyzed. In this paper, a multi-inverter parallel FCS-MPC strategy based on MLD modeling is proposed for multi-inverter parallel system in isolated island operation. Firstly, MLD is used to establish the model, FCS-MPC is added to the optimal control process of multi-inverter parallel system, the reference output voltage and the prediction model of micro-grid parallel multi-inverter considering circulating current are established. Secondly, the objective function is established. And then the circulating current is added as a constraint in the objective function value, which can not only solve the real-time change of control system online optimization. But also effectively restrain circulating current, reduce harmonics, improve prediction accuracy, improve output voltage quality and have a good dynamic response. Finally, the simulation on MATLAB/Simulink verifies the correctness of the model and the rationality of the proposed strategy. The purpose of this paper is to provide guidance for the design and optimal control of multi-inverter parallel system.

The multi-inverter parallel system cannot only break through geographical restrictions, and connect different distributed power sources far apart in parallel to improve the power generation capacity, but also form a parallel redundant system to improve the operational reliability of the power generation system. The topology of the multi-inverter parallel system is shown in

The circuit mainly includes four parts: photovoltaic array, DC/DC circuit, DC/AC circuit, and LC filter circuit. In the figure, _{0}~S_{4} are IGBTs (Insulated Gate Bipolar Transistor), VD_{0}~VD_{4} are anti-parallel diodes; _{0}, and a power tube S_{0}; the DC/AC circuit includes S_{1}~S_{4}, and diodes VD_{1}~VD_{4}. The DC side voltage

The MLD model needs to introduce logical variables to represent the logical relationships in the system, express the logical relationships and constraints in the system in the form of inequalities, and add them to the system dynamic difference equation to represent various types of hybrid systems. As shown in

The core of the MLD model is to analyze the system in a single model, and summarize the physical conditions and related algebras in the state space of all regions in the system into the same model for state analysis. By introducing appropriate auxiliary variables, multiple variables of the system can be controlled and system constraints can be optimized.

The main ideas and methods of establishing the hybrid logic dynamic model of the hybrid system are as follows: Firstly, the system circuit topology is analyzed in different operating states of the system, and then appropriate auxiliary logic variables are selected to describe the different operating states in the system. Finally, the logical relationships and system constraints in the system circuit are all integrated together to form an overall function expression. In other words,

The circuit topology of the single-phase photovoltaic inverter system designed in this paper is a non-isolated two-stage topology. After decoupling the front and rear stages, the MPPT control voltage is used to keep the voltage stable. There has been a lot of research on this, and it will not be described here. Therefore, in the inverter control research, to make the research more targeted, the photovoltaic array and DC/DC circuit in the circuit are equivalent to a stable DC voltage source. The simplified model is shown in

According to the control objective of the system, the system state variable is defined as

The state control signal of the 4 switches of the _{m} (

Set the first case: _{1}_{4}_{2}_{3}

The second case: _{2}_{3}_{1}_{4}

Introducing the logic variable _{a}. Setting the positive direction of current _{a} is shown in _{L}> 0, it is represented by

On the contrary, where _{L}< 0, it is represented by

Therefore, according to the circuit topology, the logical relationship between the voltage _{ab} and the inverter switch is obtained:

According to the HYSDEL language, the corresponding MLD model difference equation is obtained by combining the logical relationship and the mixed characteristics:

The dynamic equation under the logic hybrid dynamic modeling is processed, namely, Euler forward method is used for discrete processing, and a new parameter equation is obtained.

FCS-MPC controls the system according to a limited combination of switch states. By comparing the outputs of different switching states, the optimal switching state combination which minimizes the objective function is selected as the best control scheme to control the inverter, so pulse width modulation is not needed and the response speed is faster. In addition, FCS-MPC is also suitable for multi-objective control system and can be used for switching frequency control. Constraints are added to the objective function to control the controlled variables, such as output voltage, output current, suppression of circulating current and reduction of switching frequency. Therefore, it is very feasible to apply FCS-MPC strategy to single-phase photovoltaic inverter system. In addition, FCS-MPC effectively solves the computational problems of MPC according to the discrete characteristics of the system. Because the number of switching states in single-phase photovoltaic inverter system is certain, the control program only carries out online traversal calculation for these states, and then obtains the best control scheme to control the inverter [

^{*} represents the reference value. FCS-MPC first establishes a prediction model

It can be seen from the above control flow that in the FCS-MPC algorithm, the optimization process for the switch function combination is the error comparison process between the predicted value of the controlled variable and the reference value in the objective function. _{1}, _{2} and _{3}), and the reference value is unchanged, where,

In FCS-MPC control, the system prediction model needs to be established according to the controlled quantities in the system, such as voltage, current and so on. In this paper, the MLD method is used for modeling, which can integrate both the linear part and the nonlinear part of the controlled system into a function. At the same time, the objective function is established according to the control objectives and constraints of the system.

The FCS-MPC design generally includes the following three links:

Establish a system prediction model according to the controlled object, and perform discretization processing, to predict the next moment state through the current state. And determine the number of possible switch state combinations in the prediction model.

Establish the objective function according to the controlled quantities and constraints of the system.

Online traversal calculation, namely rolling optimization, obtains the switch function combination that minimizes the objective function value and uses it for the next moment of the inverter.

According to the MPC, the actual output of the system should track the reference output as much as possible. The higher the tracking accuracy is, the better the control effect is. According to the linear Lagrange extrapolation formula, the state of the reference voltage at k+1 is estimated [

The parallel system model studied in this paper is shown in

From the circuit topology shown in

Among them, _{1}, _{2} are the output currents of each inverter unit, _{0} is the load current, and

Discretize the differential equation above, and substitute

After further sorting out and changes, we can get:

At the same time, from

After further sorting out it, we can get:

Substitute _{2} at time

The circulating current expression of the inverter parallel system is defined as:

Therefore, the predicted value of the circulation is solved by the following formula:

From

MPC is to predict the state variable of the next moment through the state variable and switch state of the current moment. By sampling the state variable and switch state at the current moment, after obtaining the estimated value of the state variable at the next moment, the optimization objective function is set, and the selected objective function is:

The FCS-MPC strategy block diagram is shown in

According to the diagram of the strategy block in the

According to the strategy proposed in this chapter, the parallel system of two inverters is designed and simulated by using MATLAB/Simulink software. The simulation parameters are shown in

Parameters | Values | Parameters | Values |
---|---|---|---|

U_{dc}/V |
400 | fs/kHz | 12.8 |

L_{1}/mH |
6.8 | L_{2}/mH |
5.9 |

C_{1}/μF |
24 | C_{2}/μF |
26 |

r_{1}/Ω |
0.56 | r_{2}/Ω |
0.6 |

r_{0}/Ω |
50 | T_{S}/s |
5 × 10^{−6} |

According to the trial-and-error method, the predictive control weight coefficients in the simulation are respectively taken as _{0} = 50 Ω, the follow-up waveforms of the system output voltage is shown in

The

The

When t = 0.02 s, the load is increased from 50 to 100 Ω.

In this paper, for the micro-grid multi-inverter parallel system, the modeling and control strategy design of the photovoltaic micro-grid multi-inverter parallel configuration are carried. Firstly, the multi-inverter parallel system is analyzed, and the dynamic model of MLD is established. Then the circulating current of the inverter parallel system is analyzed and the objective function is established for FCS-MPC. Finally, the simulation results show that the FCS-MPC strategy based on MLD model can obtain higher tracking accuracy of system output voltage, effectively improve the output voltage waveform of inverter, improve the power quality of output voltage, effectively suppress the circulating current between inverters, and have a good dynamic response. The theory is supported by simulation experiments, and it is shown that this method has certain reference value in the research of stable operation control of micro-grid parallel multi-inverter.

Acknowledgement and reference heading should be left justified, bold, with the first letter capitalized but have no numbers. Text below continues as normal.