# Attenuation of DC-Link Pulsation of a Four-Wire Inverter during Phase Unbalanced Current Operation
## 2 Four-Wire Hybrid Converter with Multi-Resonant Regulators
An error of the converter current is passed to a proportional-resonant regulator (PR) [17]. The regulator is tuned so its resonant frequency matches the main frequency component of the power grid. Adding more proportional-resonant controllers in parallel with the first one, and tuning them for specific harmonics allows additional harmonic compensation, improving the overall \(\text{THD}_{\text{i}}\) of the system [18; 19]. The transfer function of this controller is described by the following equation:  
\[G_{inv\_res\_control}=\left(K_{p}+\sum_{n=1}^{N}\frac{K_{iI\_nH}2\omega_{rcI\_nH} s}{s^{2}+2\omega_{rcI\_nH}s+\omega_{o\_nH}^{2}}\right) \tag{2}\]  
where: \(K_{p}\)--proportional controller gain, \(K_{iI\_nH}\)--resonant controller gain, \(\omega_{rcI\_nH}\)--resonant span parameter \(\omega_{o\_nH}\)--controller resonant pulsation. This system allows independent control over the power flow in each of the phases, enabling asymmetric operation of the inverter. The laboratory setup to evaluate this operation is presented in Figure 4. The consequence of this is pulsation in the DC link occurring when operating with asymmetric currents, as shown in Figures 5-8. Both AC and DC components of the DC link current are affected by asymmetry, causing undesirable states for the energy storage. In an extreme case, the energy storage affected by an AC current pulsation, increases internal energy losses above the permitted limit. This is potentially dangerous situation because energy storage can overheat and combust. Figure 4: Three-phase, four wire converter module used during laboratory tests. Figure 3: Control algorithm for single phase of three-phase four wire converter, where: \(i_{\textit{inf,active,a}}\), \(i_{\textit{inf,active,a}}\)—references for active and reactive current components, \(u_{\textit{g,a}}\), \(u_{\textit{g,b}}\), \(u_{\textit{g,c}}\)—instantaneous phase voltages, \(U_{DC}\)—DC inverter link voltage. Figure 5: Three phase current and DC link current during symmetric operation with 15 A active current inverter mode (experimental results, I_DC measured at \(\text{i}_{\text{stor}}\) point in Figure 1). Figure 6: Three phase current and DC link current during asymmetric operation with 15 A active current on phases: A and B, 4 A reactive current on phase C of inverter (experimental results, I_DC measured at \(\text{i}_{\text{stor}}\) point in Figure 1). The level of Pulsation in the DC link current can be directly linked to the current in neutral wire; in fact, there is a linear relationship (Figure 9). Figure 8: Neutral wire current (**a**) and DC link pulsation current (**b**). Conditions as in Figure 7 (experimental results, I_DC measured at \(\mathrm{i_{stor}}\) point in Figure 1). Figure 7: Three phase current and DC link current during asymmetric operation with 15 A active current on phases: A, B and C—two phases operate as inverter and one phase operates as rectifier (experimental results, I_DC measured at \(\mathrm{i_{stor}}\) point in Figure 1). Figure 2:0 Alternating current pulsation on the DC link as a function of converter neutral wire current, where: \(\mathrm{I_{n+}}\),\(\mathrm{I_{n-}}\)—neutral wire current, \(\mathrm{I_{ACp}}\)—magnitude of current pulsation on DC link. The magnitude of the AC component of the DC link current (\(I_{AC\_DCLink}\)) as a function of the magnitude of the AC component of the neutral wire current (\(I_{n}\)) can be described as:  
Figure 2:1  
where: \(V_{1}\)--phase rms voltage, \(V_{DC}\)--DC link voltage. Instantaneous value of AC component, based on Equations (1) and (3) can be described as:  
Figure 2:2  
where \(\varphi_{n}\)--phase of neutral wire current.