#### Capacitor voltage deviation closed-loop control

Based on the above analysis, in the closed-loop control, if the regulator has no response to the DC component or the response to the DC component is small and does not destroy the self-balancing characteristics of 3L-NPC, the self-balancing characteristics of 3L-NPC can be used to achieve capacitor voltage balance control.

According to the influence of closed-loop control on the self-balancing characteristics of 3L-NPC topology, two types of voltage equalization control ideas can be summarized: ① Directly or indirectly perform closed-loop control of the capacitor voltage difference to eliminate the factors that cause the unbalanced capacitor voltage; ② Use an appropriate regulator or control structure to ensure that under the action of closed-loop control, 3L-NPC still has self-balancing characteristics, so as to balance the capacitor voltage of 3L-NPC.

**Capacitor voltage deviation closed-loop control**

There are various schemes for direct or indirect control methods of capacitance dropout.

① Scheme A.1: It can be seen from the formula (1.1) that the capacitor voltage difference V_{d} is proportional to the current I_{o(avg)}. Therefore, the capacitor voltage difference V_{d} is added to the current reference i_{ref}, and its voltage equalization control block diagram is shown in Figure 1, where k_{d} is the proportional coefficient of the capacitor voltage difference feedback. The structure of the half-bridge inverter controlled by the capacitor voltage difference is shown in Figure 2.

Principle: △U_{C}=k_{d}·V_{d}, then control the output current i_{o} to track (i_{ref}+k_{d}·V_{d}), so that the output load current contains the DC component in the same direction as Vd, Thus, a corresponding DC component is generated on the capacitor to eliminate the capacitor voltage difference and realize the capacitor voltage balance.

Features: The capacitor voltage difference link is outside the load current control loop, and has no effect on the open-loop characteristics of the load current control loop, which can realize the decoupling control of the voltage equalization and the load current; due to the use of direct control, the voltage equalization reliability is high; in applications requiring isolation, a sensor for detecting capacitive voltage is added, which increases the system cost.

② Scheme A.2: Under the action of the Pl regulator, it can be known from equations (1.1) and (1.2) that the modulating wave DC component v_{m(avg)} has an inverse relationship with the capacitor voltage difference V_{d}. The v_{m(avg)} is negatively fed back to the current reference i_{ref,} and its control block diagram is shown in Figure 3. Among them, the DC component of the modulating wave v_{m} is obtained through the low-pass filter G_{L}_{f}(s), and the integral link k/s or the Pl regulator (k_{1}+k_{2}/s) is usually selected.

Principle: record v_{m(avg)}=-k_{x}·V_{d}, and k_{x}>0, then the load current i_{o} tracks (i_{ref}-v_{m(avg)}=(i_{ref}+k_{x}·V_{d}), so that the output load current contains a DC component in the same direction as V_{d}. Thus, a corresponding DC component is generated on the capacitor to eliminate the capacitor voltage difference and realize the capacitor voltage balance.

Features: It is necessary to detect the DC component of the modulated wave. If digital control is used, its operation accuracy will have a greater impact on the extraction of the DC component, thereby affecting the voltage equalization effect.

The simulation waveform is shown in Fig. 4. As can be seen from Figure 4, when there is a capacitance deviation and a voltage difference in the DC side capacitor, the capacitor voltage can be quickly balanced. Therefore, adding the voltage equalization control method of the capacitor voltage difference feedforward, the voltage equalization effect is good and the speed is fast.