#### Low frequency harmonic suppression of incoming current

In order to achieve lower harmonic distortion of grid-connected current, problems such as low-frequency harmonic distortion of grid-connected current must be solved. This article briefly analyzes the causes of low spectrum waves and introduces several current control methods for current suppression of low spectrum waves commonly used in L-filter solar grid tie inverter.

**Read more**: Influence of low frequency harmonics of grid voltage

## 1. Feedforward compensation of grid voltage

The grid voltage is the main factor to generate the fundamental wave error and low frequency spectrum current, so the grid voltage proportional feedforward can achieve a better steady-state response. Its control block diagram is shown in Figure 1, in which G_{inv}(s) is the feedforward compensation function, and G_{f}(s) represents the PWM inverter link considering the delay.

The transfer function from grid voltage to grid current is

Set the above formula equal to 0 to get:

When this formula is satisfied, the low-frequency harmonic voltage in the power grid will not generate low-frequency spectrum waves of the grid current. However, in the actual grid-connected inverter system, G_{inv}(s) contains a delay link, and it is difficult to accurately realize the grid voltage feedforward compensation shown in equation (1.3).

Considering that the phase lag caused by the delay link in the low frequency range can be ignored, in practical applications, the grid voltage feedforward compensation coefficient is usually taken as

Figure 2 shows a schematic diagram of the amplitude-frequency characteristic curve of equation (1.2) with or without grid voltage feedforward compensation. After the grid voltage feedforward is adopted, the amplitude of the transfer function shown in equation (1.2) at low frequencies (below 1kHz) is greatly attenuated. This means that grid voltage harmonics of the same magnitude will produce smaller current harmonics with grid voltage feedforward.

## 2. Harmonic resonance (harmonic resonant, HR) controller

The transfer function of the HR controller is shown in formula (1.5), and the positive integer n represents the harmonic order to be suppressed. In order to suppress the current harmonics in a wide range, multiple harmonic resonance controllers must be added. In practice, HR is usually used in conjunction with PI or PR. Figure 3 shows the Bode plot (k_{r}=1000, ω_{r}=12) of the 1st, 3rd, 5th, and 7th vibration controllers. The regulator has a very high gain at the harmonic frequency, which is beneficial to suppress the current harmonics. It should be pointed out that the phase lag of the regulator is 0° above the 7th harmonic frequency, so in order to avoid the adverse effect of the regulator on the phase margin in practical applications, the value of nω_{0} should be less than the open-loop cut-off frequency.

## 3. Repetitive controllers

The repetitive controller has a high gain for the periodic repetitive disturbance signal, and considering that the main existence of the grid voltage is the periodic harmonic interference, so it is similar to the resonance control, the repetitive controller can better track the fundamental current and suppress the low spectrum current. But the difference is that the structure of the repetitive controller is simpler than that of the HR controller. Equation (1.6) shows a common repetitive controller, where T_{d} is the delay time. When T_{d} is 1/6 of the fundamental wave period, the repetitive controller can be equivalently transformed into a multi-harmonic resonance controller shown in equation (1.7).