Dual-Loop Control Of A Grid-Connected Inverter Case Study

2. Dual-loop Control of a Grid-Connected Inverter
In this section, the modeling and control of a grid-connected inverter with dual-loop control using the capacitor current feedback is described. Although, this issue has already been addressed in available literatures, the goal is introducing a simplified block diagram which make designing controllers easier.
A grid-connected inverter with the LCL filter is shown in Fig. 1. The LCL filter consists of an inverter-side inductor L1, a filter capacitor C, and a grid-side inductor L2. Parasitic resistances are neglected in order to simplicity.

Fig. 1. Configuration of a grid-connected inverter with LCL filter.

(1)
In Fig. 1, Vdc is the input DC voltage, Vinv is the output voltage of the inverter
2(a), shows the linearized block diagram of the control strategy for a grid-connected inverter in s-domain. In this figure, KP_inner is the proportional controller in the inner loop which is used to enhance cut-off frequency of the inner loop. Considering Fig. 2(a), controller design for such a system is complicate due to interacting loops. To simplify the controllers design, an equivalent model which contains decoupled regulating loops is desirable. The model in Fig. 2(a) can be simplified by adding filter capacitor voltage (vC) to output signal of the transfer function KP_inner, and by replacing feedback signal capacitor current iC with i1-ig. Fig. 2(b), shows the equivalent model of the system. In this way, the design procedure can be done considering decoupled
3.2. Traditional Grid Voltage Feedforward Method
Although, traditional method of grid voltage feedforward has already been addressed in literatures [1] and [9], the goal is to get the reader familiarized with the methodology used along this paper. Hence, this method is introduced, briefly.
Regarding to (9), because of Zg(s) is determined by the power grid conditions, only Zo(s) can be shaped in order to achieve a high value. It should be noted that, increasing the loop gain of control system can enhance the inverter output impedance and reduce the current distortion caused by the grid voltage. However, this approach is compromised by the system stability requirement. Another way which has received special attention recently, is using feedforward of the grid voltage in control system. This method can boost the inverter output impedance very well but, introduces negative phase angle to the control system in weak grids which might cause instability [1]. The main idea which is used, is introducing a virtual impedance such as Zop(s) in parallel with Zo(s) as shown in Fig. 5, in order to boost the equivalent output impedance