Control strategy of LCL photovoltaic grid-connected inverter based on quasi-DPC

Aiming at the shortcomings of the non-fixed switching frequency and slow dynamic response of the current closed-loop control in the three-phase LCL photovoltaic grid-connected inverter system, this paper proposes a quasi-DPC method with current control in the inner loop and power control in the outer loop, which takes into account the advantages of both DPC and current control, and has the advantages of fast dynamic response, fixed switching frequency and high current sinusoidality. By building a control system simulation model in Matlab/Simulink, the results show that the control strategy has certain feasibility.

1

Three-phase grid-connected inverter model with LCL filter

Figure 1 shows the topology of a three-phase photovoltaic grid-connected power generation system using an LCL filter. The main circuit of the three-phase grid-connected inverter includes a three-phase full-bridge circuit consisting of an input DC bus filter capacitor C, six insulated slot bipolar high-power transistor (IGBT) switches, and a third-order filter consisting of filter inductors L1, L2 and filter capacitors Cf. In Figure 1, u and i are voltage and current, respectively; id is the current of diode D; VT is the thyristor; r1 and r2 are the internal resistances of filter inductors L1 and L2; ug is the grid voltage; the subscript dc represents direct current; and the subscripts a, b, and c correspond to the A, B, and C phases of the inverter, respectively.

Under the condition of balanced three-phase grid voltage, the three-phase state equation of the inverter is:

In the formula, subscript m=α, β; subscript k=a, b, c; udc is the DC bus voltage of the photovoltaic grid-connected inverter; idc is the DC side input current of the photovoltaic grid-connected inverter; s represents the switching function; subscript o represents that the switch state of the branch is open; subscript n represents the neutral point.

According to Clarke transformation, the state equation of the three-phase grid-connected inverter in the αβ coordinate system is:

Where w is the equivalent control angular frequency of the three-phase grid-connected inverter.

2

Establishment of control strategy model for phase-connected inverter

Figure 2 is a schematic diagram of the control principle of the quasi-DPC three-phase grid-connected inverter. The system is mainly composed of bus voltage control, current control, power control and other links. The outer loop adopts a power loop control strategy based on fuzzy PI to achieve power control of the three-phase grid-connected inverter; the inner loop adopts a repeated PR control strategy to improve the dynamic performance and stability of repeated control and achieve current control of the three-phase grid-connected inverter. Among them, p* is the active power reference value, which is obtained by multiplying the input reference voltage uref and the output of PI control; the reactive power reference value q* is set to zero; the superscript * represents the reference value.

According to the instantaneous power theory, the complex power on the grid side of the inverter can be obtained:

In the formula, ig is the current vector; ugα and ugβ are the voltage components in the αβ coordinate system; igα and igβ are the current components in the αβ coordinate system.

Power Controller Design

The output power of the photovoltaic system is a continuously changing quantity. When the external conditions such as light resources, external temperature, and dust shielding change, the output power also changes continuously, and the traditional PI control method cannot achieve the ideal control effect. The power controller in this paper adopts a control method based on fuzzy PI, and uses the Mamdani fuzzy reasoning mechanism to tune and optimize the PI controller parameters online. Figure 3 is the structure diagram of the fuzzy PI control system. In the figure, Δp/Δq is the input reference active and reactive error instructions; ku is the proportional factor; ke, ke′ are quantization factors; i*αβ is the system grid-connected current reference value under the αβ coordinate; e, e′ are the instantaneous power error and error change rate, respectively, and this controller quantizes them in the [-6, 6] interval.

The fuzzy PI controller will first obtain the fuzzy relationship between kp, ki and e, e′. kp and ki are PI controller parameters, and this controller quantifies them in the interval [-3, 3]. At the same time, e and e′ will be continuously detected during the reasoning process. Finally, the controller will adjust the PID parameters in real time according to the reasoning rules to meet the different requirements of variables e and e′ for control parameters, so that the power controller has good dynamic and static performance.

Current Controller Design

** Repeated PR control system model **

References [11, 12] proposed the proportional resonance control method and repetitive control method of inverter power supply respectively, but PR control has poor ability to suppress high-order harmonics in nonlinear loads, and although repetitive control has good robustness, its disadvantage is poor dynamic performance. To solve the above problems, this paper designs a repetitive control system based on proportional resonance to improve the performance of the controller. Figure 4 is the structure diagram of the repetitive PR control system, zN is the periodic delay signal; Q(z) is the auxiliary compensation value; Kr is the repetitive control gain; S(z) is the compensation value of the controlled object; d(z) is the nonlinear disturbance; P(z) is the equivalent mathematical model of the inverter.

From Figure 4, we can get the control system transfer function E(z) as:

Where G is the inverter transfer function in open loop; the subscript RC represents the resonant controller; and R(z) is the z-transfer matrix resonant controller transfer function.

Let the error transfer function be:

Then we can get the characteristic polynomial y:

It can be seen from formula (13) that when the two characteristic roots of the characteristic polynomial are within the unit circle, the stability of the control system can be maintained.

** Repeat PR controller design **

From the above analysis, it can be seen that the control system will be stable only when the controller parameters are selected within the stable range of the individual PR system. Therefore, the two parameters of the PR controller need to be designed separately. kp is the proportional gain. The value of kp will affect the anti-interference ability and steady-state performance of the control system. Therefore, the value needs to be moderate, neither too large nor too small. If the value is too small, the current harmonic component in the system will increase and reduce the anti-interference ability of the system; and if the value is too large, the amplitude margin of the system will be reduced. The problem was modeled and simulated in the literature [13]. When kp = 0.07, the control system can achieve good control effect.

ki is the integral gain, which affects the control gain. When the ki value is large, the static error of the controller will decay faster, but it will affect the phase margin of the system and make it smaller; when the ki value is small, it will be difficult to eliminate the static error of the system, thus affecting the control accuracy of the system.

This paper simulates and analyzes the control system when ki is 50, 80, 100, and 120 respectively (kp value is fixed). Figure 5 is the PR control Bode diagram of the controlled object.

As shown in Figure 5, when ki is 50 and 120, the phase margin is difficult to meet the requirements of system stability. When ki = 80, the system phase margin is better and a better control effect can be obtained.

The control object of repeated PR control is equivalent to:

Figure 6 is a Bode diagram of the repetitive control equivalent object in the repetitive PR control. As shown in Figure 6, the gain of the equivalent control object in the low frequency band is basically zero, but at the angular frequency w=9260 rad/s, high-frequency resonance occurs, and the resonance peak is 31.2 dB, which is due to the resonance problem of the LCL filter in the inverter. Therefore, if no suppression measures are taken for the controller, the amplitude of the resonance frequency will increase, causing the output voltage waveform to distort. In addition, the system's harmonic attenuation capability is also very limited in the high frequency band, and the ability to suppress harmonics will also deteriorate.

Figure 7 is the Bode diagram of the equivalent object after adjustment by the repeated PR controller. As shown in Figure 7, after adjustment by the repeated PR controller, the high-frequency resonance in Figure 6 is eliminated, and at the same time, the low-frequency gain in the equivalent control object becomes 1. Moreover, the high-frequency band in the equivalent control object is rapidly attenuated, so that the control system has good anti-disturbance ability and the system stability is improved.

3

System simulation analysis

In order to verify the effectiveness of the current inner loop and power outer loop control strategies proposed in this paper, a simulation model of the LCL photovoltaic inverter system was built in the Matlab/ Simulink simulation environment according to the topology of Figure 2, and the above control strategy was used for control. The control system parameters are: the rated power of the grid-connected inverter is 2kW, fk = 12.5 kHz, the switching frequency fs = 20 kHz, Cdc = 2000 μF, L1 = 8 mH, L2 = 2 mH, Cf = 10 μF, and the equivalent
resistance is 0.8 Ω.

Figure 8 shows the simulated waveforms of active power and reactive power of the grid-connected inverter system when the control strategy designed in this paper is adopted. As shown in Figure 8, when the control system power loop adopts the fuzzy PI control system, the system active power can reach the given value in a very short time, and the adjustment process is very fast. When the system reaches stability, the active power fluctuation is very small, and the reactive power is basically kept at zero.