To reduce current harmonics caused by switching frequency, T-type grid-connected inverter topology with LCL filter is adopted. In view of the disadvantages of the slow response speed of the traditional current control and the failure to eliminate the influence of the LCL filter on the grid-connected current by using current PI control alone, a current double closed loop PI current tracking control is proposed. Through the theoretical analysis of the grid-connected inverter control principle, the grid-connected inverter control model is designed, and the transfer function model of each control link is deduced, and the current loop PI regulator is designed at last. The simulation results show that the control strategy is feasible.

At present, distributed generation technology has become a hot research topic in the electric power industry due to its advantages such as diverse power generation methods and less construction cost. New energy integrating into the power system is a key problem to be solved. The grid-connected type inverter is a new energy power generation device and an interface of energy conversion between power systems, its basic function is to convert direct current produced by renewable clean energy into alternating current that can be incorporated into the power grid, and it plays a vital role in the stable operation of the power system [

At present, the widely used filters are L-type, LC type and LCL type. L-type filter is a first-order filter, and the inductance must be increased to obtain a good filtering effect. LC filter has better effect than L filter in filtering high-frequency harmonics, which is usually used in the case of off-grid; LCL filter is a third-order filter. It has high impedance to high-frequency components. Besides, high frequency harmonic current can play a large attenuation effect.

The control modes of inverters can be divided into two categories: voltage type control and current type control [

When the inverter side current is used for closed-loop control, the phase difference between the grid connected current and the grid voltage will be caused due to the filter capacitor, and the power factor will be reduced [

The main work of this paper is as follows: (1) Configure the parameters of the inner loop and the outer loop respectively to make the controller not only have appropriate damping, but also have good dynamic response performance. (2) Specific design formulas of inner loop and outer loop parameters are given. (3) Draw the open-loop baud diagram before and after the control, and verify the rationality of the parameter design. (4) Verify the steady-state and dynamic response performance of the system under this parameter design.

The grid-connected structure of T-type three-level inverter is shown in

Capacitor circuit and grid-connected current double closed-loop control are selected. The dynamic structure of this control mode is shown in

The whole inverter system should realize the control of DC bus voltage stabilization, phase locking and grid-connected current. The current loop is controlled by current double closed loop, the active damping based on capacitive current feedback is used to increase the system damping in the inner loop, and the unit factor current is used in the outer loop [

LCL filter has third-order characteristics, the frequency response at the resonant frequency will show a low impedance to zero impedance, so that there will be a resonance peak at the resonance. If not restrained, it will produce a large number of harmonics, make the power grid oscillation, resulting in the instability of the system. Therefore, the resonant peak must be suppressed, that is, the damping of the system must be increased. There are two ways to increase damping, one is passive damping, the other is active damping [

The passive damping control effect of capacitor shunt resistance is the best, and its control block diagram is shown in

Among them, the active resistance method based on the capacitive current proportional feedback can achieve the same resistance effect as the passive damping method of capacitor parallel resistance. If the capacitor current is taken as the feedback variable and the feedback function is changed, the feedback function can be obtained as

The inner loop control of the capacitor circuit only increases the damping of the system, and does not consider the response in the frequency domain and time domain, so the stability of the system cannot be guaranteed. Therefore, it is necessary to control the grid-connected current of the system by proportional integration, and design PI parameters according to the root trajectory and frequency response of the system, so that the system can meet the stability requirements.

The diagram of current double closed loop control block after introducing passive damping control based on capacitor circuit feedback is shown in

Derived from the structural block diagram, its open-loop transfer function is

Draw the root locus the system, as shown in

It can be seen from the root locus that when

Lists its Rous Table:

In Rous criterion, if the coefficients in the first row are all positive, then the system is stable, and the following relations must be met:

Without considering the outer loop, analyze the inner loop control based on capacitive current feedback, increase the damping of the system by the inner loop, and then propose its mathematical model, as shown in _{i}(

The transfer function of the inner loop can be obtained as

It is a second-order system, and its damping ratio can be obtained as

According to the damping ratio formula, the larger k is, the larger the system damping is, and the better the inhibition effect of resonant peak is. However, excessive damping will worsen the response performance of the system and lengthen the adjustment time. Damping effect and dynamic performance of the system should be considered at the same time [

The inner loop baud diagram is shown in

After the addition of capacitive current feedback, the damping of the system increases and the resonance peak is effectively controlled, but the amplitude margin is only 2.5 dB and the phase angle margin is only 7.73°, which cannot meet the requirements of frequency domain indicators.

The turning frequency of the outer loop PI controller can be represented by the first-order differential link, thus establishing the relationship between the turning frequency and PI controller parameters, as shown in the

To meet the amplitude and frequency characteristics after correction, the turning frequency of PI controller is set at 160 Hz, then

According to the characteristics of LCL filter, when the frequency is lower than the resonant frequency, the capacitor branch does not work, and the filter can be regarded as a single inductor filter. When the frequency is higher than the turning frequency of PI controller, the integral coefficient _{i} basically has no effect, and PI controller can be equivalent to P controller [

Since the gain of the system at the cutoff frequency is 1,

After finishing, the expression of _{p} can be obtained as

If _{p} is increased, the dynamic response speed of the system will be faster. However, increasing _{p} will lead to the increase of cut-off frequency, which will make the system cut-off frequency close to the resonant frequency, and the stability margin of the system will also become lower. If the cutoff frequency is 800 Hz, _{p} = 0.4608, _{i} = 463.2068 can be obtained.

Double closed loop open loop bod diagram is shown in

The blue line represents the frequency response of the system before compensation, which is attenuated at a rate of –20 dB/dec in the low frequency band and –60 dB/dec in the high frequency band. The cutoff frequency is near resonance, and the amplitude margin and phase angle margin are both very low.

The red line represents the frequency response of the regulator, the turning frequency is 160 Hz, and the descending slope is –20 dB/dec.

The yellow line represents the frequency response of the system after correction, and the falling slope in the low frequency band is –40 dB/dec, which ensures good stability of the system. In the middle frequency band, the descending slope is –20 dB/dec and the middle frequency duration width is 5. The descending slope in the high frequency band is –60 dB/dec, and it has good harmonic suppression ability. At the same time, the cut-off frequency is advanced, which makes the system frequency response have good phase margin and amplitude margin.

It can be seen from the bode diagram that the amplitude margin after compensation is 7.4 dB and the phase angle margin is 34.4°, which meets the frequency domain performance of the inverter system.

For the study of grid-connected control technology at the output end of inverter, voltage outer loop is not designed since there’s no requirement for stablizing the DC bus voltage.

Set the amplitude of current reference signal, which can meet the rated demand when setting _{2q}^{*} to 64.46 A. The simulation parameters are shown in

The simulation parameters | The values |
---|---|

DC power supply | 850 V |

Three-phase grid voltage | 380 V |

The grid frequency | 50 Hz |

Switching frequency | 10 kHz |

Inverter side inductance | 2.1 mH |

Filter capacitor | |

Grid side inductance | 0.7 mH |

Rated power | 30 kW |

When the inner loop is not added to control, the resonant peak of LCL filter can not be controlled, and the system loses stability. Phase A voltage and current are shown in

If the outer loop parameters are _{p} = 0.7285, _{i} = 1098.6. Phase A voltage and current are shown in

It can be seen that the system is stable after adding the inner loop, and its phase A harmonic analysis is shown in the

The inverter is put into half-load from the zero state, and is put into full-load operation at 0.25 s, the grid-connected current waveform is shown in

If the parameters designed in this paper are taken,

The waveform of 5 cycles starting from the grid-connected current 0.25 s is taken for harmonic analysis. Its Phase A harmonic analysis is shown in the

The inverter is put into half-load from zero state, and is put into full-load operation at 0.25 s. The grid-connected current waveform is shown in

Under other working conditions, whether it is the load current fluctuation or voltage fluctuation of the power grid, the system can still reach stable condition quickly by using the control method in this paper. And the system overshoot and adjustment time are to meet the requirements.

The grid voltage drops to 20% of the normal value at 0.1 s and returns to the normal value at 0.2 s. The phase A voltage and current are shown in the

The grid current component in the

The grid voltage increases by 20% of the normal value at 0.1 s and returns to the normal value at 0.2 s. The Phase A voltage and current are shown in the

The grid current component in the

When the load changes from full load to half load, the phase A voltage and current are shown in the

The grid current component in the

As it can be seen from the figure above, under the double closed-loop current control, when the voltage of grid drops, the maximum variation of id is 10.09 A, and when the voltage of the grid rises, the maximum variation of id is 11.63 A. The time to reach the stable value is within 2 ms. When the grid voltage is disturbed to different degrees, it can still reach stability in a very short time.

In this paper, a T-type three-level grid-connected inverter is used as the interface between the distributed power supply and the power grid, and the parameter design of the current double closed-loop control system is given, and the grid-connected control strategy is simulated. In this paper, active damping is used as the inner loop, which can suppress the resonant peak of LCL filter without increasing the loss. The parameter design of controller based on baud diagram can not only have good stability performance, but also have good dynamic response performance. The simulation results show that the T-type three-level inverter has stable grid-connected voltage and current, low harmonic distortion, and good grid-connected effect, which verifies the feasibility and effectiveness of the control method above, and indicates that the control strategy can effectively reduce the grid-connected current harmonics and achieve high power factor grid-connected.

Supported by Science and Technology Projects of State Grid Corporation of China (J2022019).

The authors declare that they have no conflicts of interest to report regarding the present study.